Dependence of Absorption and Emission Spectra on Polymorphs of

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C: Surfaces, Interfaces, Porous Materials, and Catalysis

Dependence of Absorption and Emission Spectra on Polymorphs of Gold(I) Isocyanide Complexes: Theoretical Study with QM/MM Approach Shinji Aono, Tomohiro Seki, Hajime Ito, and Shigeyoshi Sakaki J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b10602 • Publication Date (Web): 01 Feb 2019 Downloaded from http://pubs.acs.org on February 3, 2019

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The Journal of Physical Chemistry

Dependence of Absorption and Emission Spectra on Polymorphs of Gold(I) Isocyanide Complexes: Theoretical Study with QM/MM Approach Shinji Aono,† Tomohiro Seki,‡ Hajime Ito,‡ and Shigeyoshi Sakaki∗,† Fukui Institute for Fundamental Chemistry, Kyoto University, Nishihiraki-cho, Takano, Sakyo-ku, Kyoto 606-8103, Japan, and Division of Applied Chemistry, Graduate School of Engineering, Hokkaido University, Sapporo, Hokkaido 060-8628, Japan E-mail: [email protected]

∗ To

whom correspondence should be addressed Institute for Fundamental Chemistry, Kyoto University, Nishihiraki-cho, Takano, Sakyo-ku, Kyoto 6068103, Japan ‡ Division of Applied Chemistry, Graduate School of Engineering, Hokkaido University, Sapporo, Hokkaido 0608628, Japan † Fukui

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Abstract We theoretically investigated phenyl(phenyl isocyanide) gold(I) (PhNC)Au(Ph) 1 and phenyl(dimethylphenyl isocyanide) gold(I) (dimPhNC)Au(Ph) 2 in crystal using our periodic quantum mechanics/molecular mechanics (QM/MM) method based on the self-consistent point charges to elucidate interesting mechano-chemical changes of absorption and emission spectra of 1 and 2 in crystal. To characterize 1 and 2 in crystal, their absorption and emission spectra in crystal were compared with those in gas phase and CHCl3 solvent, where 3D reference interaction site model self-consistent field (RISM-SCF) was employed to incorporate solvation effect. To investigate phosphorescence emission spectrum in crystal, we optimized geometry of molecule at triplet state in crystal which had ground state geometry, because the population of excited state is very small generally. The QM/MM calculations displayed that 1 formed two polymorphs 1b and 1y, 2 formed two polymorphs 2b and 2g, and 1y was more stable than 1b, which agree with the experimental findings. In 1b and 2b, ligand-to-ligand charge transfer (LLCT) state is the lowest energy excited state in the absorption and π -π ∗ locally excited state on the PhNC moiety is the lowest energy triplet state in the emission. In 1y and 2g, on the other hand, metal-metal-to-ligand charge transfer (MMLCT) state is the lowest energy excited state in both of absorption and emission. These characteristic differences between two crystal structures arise from the geometrical features that the Au-Au distance is much shorter in 1y and 2g than in 1b and 1y and the intermolecular torsion angle η between two Au-PhNC moieties is much smaller in 1y and 2g than in 1b and 2b, respectively; the short Au-Au distance raises the energy level of antibonding orbital consisting of two Au dσ orbitals and the small

η angle lowers the energy level of bonding orbital consisting of two PhNC π ∗ orbitals, leading to the presence of lower energy MMLCT state. The QM/MM calculations also disclosed intramolecular torsion angle τ between the Ph and PhNC planes and CH-π interaction of the Ph plane significantly influence absorption spectrum. Based on those computational results, discussion is presented on the differences in absorption and emission spectra among gas, solution, and crystal, the assignments of experimentally observed excitation and emission spectra in crystal, and their energy shifts induced by single-crystal to single-crystal phase transition.

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Introduction Polymorphic crystal has attracted much attention from both of physical chemistry and material science because in general physical and chemical properties such as melting point, solubility, and photochemical properties depend on phase transition. Formation of single-crystal phase is largely influenced by crystallization conditions such as temperature, pressure, and crystallization procedure, and so on, 1–6 indicating that single-crystal phase is not rigid but sensitive to various conditions. Actually, single-crystal to single-crystal (SCSC) phase transition is induced by external perturbation such as heat, 7–9 light, 10–12 pressure, 13,14 and exposure to small molecules. 15–19 Control of the SCSC phase transition is important and challenging issue to develop and design molecular materials and devices such as photo-devices, sensors, probes, and memory devices because the property of molecular crystal largely depend on their structures. It is of considerable interest to understand relative stabilities of polymorphic crystal phases and dependency of molecular properties on crystal phase based on electronic structure. Recently, a series of mechano-responsive materials consisting of gold(I) isocyanide complexes have been reported by Ito and coworkers, in which the SCSC phase transition was triggered by small mechanical stimulation or contact with a crystal seed of different polymorph. 20–24 These materials exhibit interesting absorption and emission spectra depending on single-crystal phase, as summarized below: Phenyl(phenyl isocyanide) gold(I) (PhNC)Au(Ph) 1 is one of the simplest gold(I) isocyanide complexes which forms two different polymorphic crystals 1b and 1y, where PhNC and Ph are used to represent phenyl isocyanide and phenyl group directly bound to Au hereafter, respectively; see Scheme 1a for their structures. Interestingly, 1b and 1y exhibit blue and yellow photo-luminescence, respectively. In 1b, all the monomers of 1 take twisted structure, in which the phenyl plane of PhNC is twisted with the phenyl plane of the Ph group by about 70 degree. The minimum unit cell consists of two molecules of 1 with long Au-Au distance (4.73 Å), in which one gold(I) isocyanide complex forms two CH-π interactions with other neighboring gold(I) isocyanide complex; both sides of the Ph plane interact with H atoms of PhNCs of two neighboring complexes and both sides of phenyl plane of PhNC interact with H atoms of Phs of two neighbor3



ing complexes. In 1y, on the other hand, all the monomers of 1 take parallel structure, in which the phenyl plane of PhNC is almost parallel to the Ph plane. The minimum unit cell consists of four molecular layers (sixteen molecules), in which each molecular layer contains four molecules with short Au-Au distances (3.18 and 3.79 Å) and dihedral angle between two layers is 90 degree. Both sides of the Ph plane interact with H atoms of PhNCs of two neighboring complexes like in 1b, while one side of the phenyl plane of PhNC forms CH-π interaction with H atom of Ph of neighboring complex and the other side interacts with the phenyl plane of PhNC of the different neighboring complex through π -π stacking unlike in 1b. Phase 1b is produced through fast crystallization of 1 and phase 1y is through slow crystallization. 20 Phase 1b changes to 1y by the mechanical stimulation without heat and light; in other words, the SCSC phase transformation irreversibly occurs from 1b to 1y, indicating that 1y is more thermally stable than 1b. The Au-Au distance is long (4.73 and 5.73 Å) in 1b but becomes short (3.18 and 3.79 Å) in 1y. Excitation and emission spectra depend on polymorphs 1y and 1b; the large excitation spectrum is observed at 4.0 eV in 1b and 2.9 eV in 1y and the large emission spectrum is observed at 2.5 and 2.7 eV in 1b and 2.2 eV in 1y (Scheme 2a). Also, phenyl(3,5-dimethylphenyl isocyanide) gold(I) (dimPhNC)Au(Ph) 2, in which two methyl groups are introduced into PhNC, forms two different polymorphic crystals 2b and 2g, where 2b and 2g exhibit blue and green photo-luminescence, respectively; 21 see Scheme 1b for their structures. In 2b crystal, all the molecules showed rational disorder on the Ph plane and dimethylphenyl ring of dimPhNC, 21 suggesting that the parallel and twisted structure are involved in the crystal. Its minimum unit cell consists of four molecules with long Au-Au distance of 4.78 and 9.06 Å, in which one dimPhNC forms two CH-π interactions with two Ph planes of neighboring complexes using the H atom of the methyl group. In 2g, the minimum unit cell consists of four symmetrically minimal subunits (twenty-four molecules), in which each symmetrically minimal subunit contains six molecules with shorter Au-Au distance of 3.11 - 3.27 Å; in the symmetrically minimal subunit, two monomers, mono1 and mono6, take the parallel structure and the remaining four monomers, mono2 - mono5, take the twisted structure, as shown in Scheme 1b. One dim-

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PhNC moiety forms two CH-π interactions with two Ph planes of two neighboring complexes like in 2b but some of dimPhNC moieties form this interaction using the H atom of phenyl moiety of dimPhNC unlike in 2b (note that the H atom of phenyl moiety of dimPhNC does not participates in this interaction in 2b). Other difference between 2b and 2g is that mono1 and mono6 in symmetrically minimal subunit form one π -π stacking interaction with the phenyl plane of dimPhNC of the neighboring minimal subunit in 2g, while no π -π stacking interaction is formed in 2b (Scheme 1b). In 2, the SCSC phase transformation from 2g to 2b (in which the Au-Au distance becomes longer) is induced by mechanical stimulation without heat and light in contrast to that from 1b to 1y (in which the Au-Au distance becomes shorter). These results indicate that two methyl substituents on the dimPhNC induce the significant difference in stability of polymorphic crystals. The experimentally observed excitation and emission spectra also depend on 2g and 2b; 2b exhibits the large excitation spectrum at 4.0 eV but 2g exhibits broad peak in the energy range of 3.3 to 4.0 eV, while 2g exhibits the large emission spectrum at 2.3 eV but 2b exhibits weak and broad peak at 2.2 eV, as shown in Scheme 2b. 25 These characteristic features, summarized in Scheme 2c, are interesting in the viewpoint of molecular science and physical chemistry. However, no theoretical study has been carried out on these polymorphic crystals. Actually, it is challenging for electronic structure theory to reproduce relative stabilities of these phases, evaluate correctly these weak CH-π and π -π stacking interactions in crystal, and elucidate the reasons. Also, it is not easy to optimize the excited state geometry, evaluate the emission spectrum, and make assignment of absorption and emission spectra in crystal. In the present study, we theoretically investigated the geometries of these molecular crystals, CH-π and π -π interactions, and absorption and emission spectra of 1 and 2 in crystal to present assignments of those spectra under consideration of crystal effects and to elucidate the reason why those spectra differ significantly between two different polymorphic crystals. 26 To incorporate the crystalline effects, we employed the quantum mechanics/molecular mechanics (QM/MM) method

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based on the periodic MM crystal model with the self-consistent point charges. 27,28 In our method, QM molecule is embedded in infinitely periodic MM crystal, the point charges and geometries of which are determined as mirror image of the QM molecule in the self-consistent filed (SCF) manner by applying the translational and symmetrizing operations to the minimum unit cell. One of the strong points of our method is to construct the periodic MM crystal model in the closed-shell singlet ground state assuming that all the symmetrically minimal subunits have the same structures and charge distributions. Because of this feature, the periodic MM crystal can be constructed without determining the potential energy functions with respect to bond lengths, bond angles, and torsion angles of MM molecule. The other strong point is that we can optimize excited state geometry of target QM molecule(s) in the presence of ground state geometry and electron distribution of remaining MM moiety; 32 remember that the population of excited state is much less than that of molecule at the ground state. This feature is indispensable for theoretical study of excited molecule in crystal.

Theoretical Method Since the basic concept of the QM/MM method was introduced in 1976 by Warshel and Levitt, 27 the QM/MM approach has been established as a powerful tool for modeling large biomolecular systems, chemical reactions, and molecular properties of large inorganic and organometallic compounds in explicit solvent system. The most important advantage of the QM/MM approach is its efficiency to evaluate effects of protein and solution, because MM simulation can be performed without heavy computational cost (scale of O(N) to O(N 2 )) in the presence of QM region determined accurately. In the present study, we applied the QM/MM method to the absorption and emission spectra in crystal. The strong point of the present periodic QM/MM method is to incorporate long-range electrostatic effects by crystal and short-range steric effects by neighboring molecules on the target QM molecule(s), which is a bit different from the usual QM/MM method applied to biomolecular and solution systems because the present method uses periodic boundary

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condition for representing MM region in an SCF manner with the QM region.

Model for ground state structure and absorption spectrum To incorporate influence of molecular crystal on absorption spectrum of target molecule, we constructed MM crystal model in closed-shell singlet ground state by using the periodic QM/MM calculation with the self-consistent point charge representation. 28 We optimized the geometry by the periodic QM/MM method, minimizing the averaged crystal avg

energy Ecrystal per one monomer which is defined by Eq. (1), avg

I Ecrystal ≡ Ecrystal /nI .

(1)

I where the potential energy Ecrystal of QM subunit I is defined by the sum of QM self energy and

a half of two-body QM-MM interaction energy of I. 28 The nI is the number of molecules in the symmetrically minimal subunit I. Note that the factor of 1/nI in Eq. (1) is reasonable because all the molecules in the single-crystal are the same molecular species. In the same manner, the avg

avg

averaged QM internal energy EQM and averaged QM-MM interaction energy EInt(QM-MM) per one monomer are defined by Eqs. (2) and (3); avg

I EQM ≡ EQM /nI , avg

EInt(QM-MM) ≡ (

∑

IJ EInt(QM-MM) )/nI ,

(2) (3)

J(̸=I) I IJ where EQM is the self energy of QM subunit I and EInt(QM-MM) is the QM-MM interaction energy

between the QM subunit I and the MM subunit J. Our periodic QM/MM method can be applied to either unit cell or symmetrical subunit cell. In 1b and 2b, one unit cell consists of two and four gold(I) complexes, respectively (Figure 1). In these crystals, we took four gold(I) complexes as target QM molecular system at the ground state, where the Au-Au distance is long. In 1y, one symmetrical subunit cell consists of two

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dimers, 29 where dimer is separated from each other by moderately long Au-Au distance. In 2g, one symmetrical subunit cell consists of six gold(I) complexes named“ hexamer ”experimentally, 21,22 where Au-Au distance is short in the hexamer but Au-Au distance is long between two hexamers. The geometry optimization was carried out using either these unit cell (1b and 2b) or symmetrical subunit cell (1y and 2g). One of the important tasks of this work is to explore the geometries at excited state and the emission spectra of these gold(I) complexes; for such purpose, it is particularly important to elucidate whether Au-Au bond is formed at the excited state or not, because the formation of Au-Au bond at the excited state significantly changes emission spectrum. Therefore, we need to optimize the geometry of target QM molecule(s) at the excited state in the presence of surrounding gold(I) complexes which have ground state geometry, the reason of which will be explained below. Therefore, the crystal structure at the ground state must be optimized correctly; if not, the geometry at the excited state cannot be optimized well. Considering that the intermolecular potential energy surface (PES) is very flat and flexible and the PES is determined by delicate balance among steric repulsion, dispersion interaction, and long-range electrostatic interaction, we were afraid that the optimized intermolecular distance involved some errors because it is not easy to evaluate the above-mentioned delicate balance in QM/MM calculation of molecular crystal. In this work, we optimized the geometry of molecular crystal at the ground state by fixing the position of Au atom and the lattice vector to be the same as those of experimental structure to avoid the error(s) in the optimized geometry at the ground state. 30 Though this optimization procedure is not perfect, we can explore the ligand geometry including orientation and conformation which is determined by electrostatic, CH-π , and π -π stacking interactions. Those information is necessary in the optimization at the excited state; in other words, this partial optimization is not perfect, but this is one reasonable choice for theoretical study of the excited state. 31 In the calculation of absorption spectrum, the target QM molecular system was taken to be the same as that employed in the geometry optimization. In 1b and 2b, the target two QM monomers are surrounded by two QM molecules and infinite number of MM molecules; because

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QM molecules are placed at the adjacent to the target QM molecules, the absorption spectrum is calculated considering the nearest intermolecular interaction at the QM level. In 1y, the target two QM molecules, in which Au-Au distance is short, touch QM molecules at one side but touch MM molecules at the other side. This modeling is not very unreasonable because the Au-Au distance is not short but rather long between two dimers. In 2g, the target hexamer is not sandwiched by QM molecule but this is also not very unreasonable because the Au-Au distance is long between two hexamers.

Model for emission spectrum To investigate the emission spectrum, we optimized the geometry of target QM molecules at the triplet state in the presence of the ground state MM crystal, which was frozen to be the same as that optimized by the periodic QM/MM calculation at the ground state. This is reasonable because the population of excited state is very small in general. In this calculation, we optimized the geometry of target QM molecule(s) under consideration of the infinitely periodic MM crystal in the same manner as that in Ref. [32]. To describe better the Au-Au bond formation and the relaxation of surrounding molecules at the triplet state, we constructed models for excited state, as follows: In 1b and 2b, we focused on two gold(I) complexes with the Au-Au distance of 4.73 Å and that of 9.06 Å (Figure 1) as the target QM molecules, respectively, because all the Au complexes are well separated from each other by the long Au-Au distance. To describe the interaction between the target two QM molecules and the nearest neighboring molecules, we added two nearest neighboring QM monomers to sandwich the target two QM molecules; one is above the target and the other is below the target, as shown in Scheme 3a. Therefore, the model consisting of four QM molecules was employed in the geometry optimization at the triplet state in 1b and 2b; note that the locally π -π ∗ triplet state is the lowest energy triplet state in 1b and 2b, as will be discussed below, the geometry and the emission energy of which are influenced little by the surrounding molecules, indicating that these four QM molecules are enough for discussion of emission spectra of 1b and 2b. In 1y and 2g, on the other 9



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hand, four QM molecules are not sufficient to describe the surrounding effects at the excited state because the Au-Au distances are short in the ground state, as shown in Schemes 3b and 3c. In 1y, we focused on the dimer with the shortest Au-Au distance of 3.18 Å (Figure 1) as the target QM molecules. 29 To consider the interaction between the target dimer and the nearest neighboring molecules at the QM level, we added two nearest neighboring QM dimers so as to sandwich the target QM dimer, because the adjacent gold(I) complex also forms the dimer with other molecule (Scheme 3b) unlike in 1b and 2b. In 2g, we focused on the hexamer (i.e. symmetrically minimal subunit of 2g) with the short Au-Au distances of 3.20, 3.27, 3.24, 3.20, 3.11 Å (Figure 1) as the target QM molecules, 29 to take into consideration all the possibilities of the MMLCT excitations. In this case, we did not add the nearest neighboring molecules because the Au-Au distance is not short but rather long between the target QM hexamer and the adjacent hexamer, as shown in Scheme 3c. Therefore, six QM molecules were taken in the geometry optimization at the triplet state in 1y and 2g. In summary, four gold(I) complexes were taken as the target QM molecular system in 1b and 2b but six gold(I) complexes were taken as that in 1y and 2g; see the section of “Emission Spectra of Polymorphic Crystals, 1b, 1y, 2b, and 2g” for details.

Model for relative stability of polymorphic crystal at the ground state To investigate the relative stabilities of polymorphs, we need to evaluate the π -π stacking and CH-

π interaction energies with the reliable computational quality such as the post Hartree-Fock (HF) avg

level. Also, we must remember that the computational results of EQM (Eq. (2)) depend on how to select the QM molecules (number and position) because the numbers of QM-QM interactions and QM-MM interactions are influenced by the selection of the QM region. This means that the comparison of one phase with different phase must be performed carefully when they have different number of QM molecules. To make such comparison between two crystal phases, we firstly evaluated the averaged potenavg2

tial energy Ecrystal per one monomer by Eq. (4) and their components by Eqs. (5) to (7), in which 10


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the target QM molecular system is divided into small fragments, according to the key idea of the fragment molecular orbital (FMO) method proposed by Kitaura et. al. 33 avg2

avg2

avg2

avg2

Ecrystal [B3LYP-D3] ≡ (ESelf(QM) + EInt(QM-QM) + EInt(QM-MM) )B3LYP-D3 , { } nI

∑ ESelf(QM)

avg2

ESelf(QM) =

mi

i=1 j(̸=i)

{ =

nI

∑∑

avg2

avg2 EInt(QM-MM)

/nI ,

(5)

i=1

{ EInt(QM-QM) =

(i)

nI

∑

nI

EInt(QM-QM) /2 + ∑

∑

2-body(i, j)

i=1 k(̸=i)∈MM

(4)

mi

mi

∑ ∑

i=1 j(̸=i) j′ (̸=i, j)

} 3-body(i, j, j′ )

EInt(QM-QM) /3 /nI , (6)

}

(i,k) EInt(QM-MM) /2

/nI ,

(7)

where mi represents the number of the nearest neighboring QM molecules j and j′ around the (i)

QM molecule i. The first term of Eq. (4) is the average of self-energy ESelf(QM) of target QM monomer i in crystal, the second term is the average of the sum of two-body and three-body QMQM interaction energies (per one molecule) between target QM molecule i and surrounding QM molecules j and j′ , and the third term is the average of two-body QM-MM interaction energy (per one molecule) between target QM molecule i and surrounding MM molecules k; see page S4 in ESI for detail. Because all these terms are defined as averaged value per one molecules, comparison of two crystal phases can be made even if the number of QM molecules is different. For discussing correctly the relative stabilities of several polymorphs, we need to evaluate the self-energy of the target QM molecule i at the CCSD(T) level 34 and the two-body QM-QM interaction energy at the MP2 level. 35 For such calculation, we further divided the crystal energy

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into three terms, as shown in Eq. (8). [ avg2

Ecrystal [CCSD(T)/MP2/B3LYP-D3] =

{(

nI

∑

i=1

(i)

ESelf(QM) +

1 2

mi

∑

j(̸=i)∈QM

)

1 (i,k) EInt(QM-MM) ∑ 2 k(̸=i, j)∈MM 1 2 1 3

mi

∑

+ CCSD(T)

) ( 2body(i, j) (i, j) EInt(QM-QM) − EInt(QM-MM)

j(̸=i) mi

(i, j)

EInt(QM-MM) +

mi

∑ ∑

j(̸=i) j′ (̸=i, j)

(

3-body(i, j, j′ )

EInt(QM-QM)

MP2

+

}]

) B3LYP-D3

/nI

(8)

The first three terms were evaluated at the CCSD(T) level under the condition that only the target monomer i was taken as the QM region and the remaining molecules were taken as the MM molecules. This term corresponds to the CCSD(T) correction; the concept of this correction is the same as that employed in the ONIOM method. 36,37 The second term was evaluated at the MP2 level under the condition that the target monomer i and the surrounding molecule j were taken as QM molecule and the remaining molecules k were taken as the MM molecules. This term corresponds to the post HF correction of the two-body QM-MM interaction energy, which is similar to the pair-wise correction of dispersion interaction; actually the corrections at the MP2, MP4(SDQ), and CCSD(T) levels successfully improved the description of van der Waals interactions in solid systems and metal-organic frameworks, as reported recently; 38–45 considering many successful results, this type of correction is believed to be useful for correct evaluation of weak non-covalent interaction energy. The last term was evaluated at the DFT level with the B3LYP functional and D3 version of Grimme ’s dispersion correction (called “B3LYP-D3”) 46–50 under the condition that the target monomer i and the surrounding molecules j and j′ were taken as QM molecule and the remaining molecules k were taken as the MM molecules. This term corresponds to the three-body QM-QM interaction energy. 51 In this calculation, the nearest neighboring eight monomers surrounding the target monomer i were employed as the QM molecules j and j′ in all the polymorphic crystals, 1b, 1y, 2b, and

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2y, because these eight QM molecules are close to the π orbitals of Ph and PhNC moieties and d orbitals of Au atom of target monomer i but other molecules are not found close to those orbitals; see also Scheme S1 for details.

Computational Details We implemented our own in-house codes of the periodic QM/MM method 28 and 3D-RISM-SCF method 52–54 into GAMESS-US (version 1-MAY-2013) program code. 55 In both of optimization of geometry and calculation of absorption and emission spectra, we used (2111111/411/2111/1) basis set for valence electrons of Au with effective core potentials (ECPs) of the Stuttgart group for core electrons of Au, 56 where one f polarization function was added. For other atoms, we used the 6-31++G** basis sets. To discuss the relative stability of two different polymorphic crystals, we used the cc-pVDZ basis sets for N, C, and H atoms. Two f polarization functions 58 were added to Au and the diffuse functions were added to N and C atoms. In the QM/MM calculation, the Lennard-Jones (LJ) parameters of molecule were taken from the AMBER except for Au atom, (σAu , εAu ) = (3.2 Å, 0.240 kcal mol−1 ), 57 the LJ parameters of which were determined using the profile of interaction energy between two gold(I) isocyanide complexes and between one gold isocyanide and CH3 Cl at the MP2 with the basis set superposition error (BSSE) correction. 59 As the first step (step (i)), we modeled the ground state structure and charge distribution of crystal using the R-DFT calculation with the B3LYP-D3, 46–50 where the crystalline effect was incorporated by the periodic QM/MM method with the self-consistent charge representation. 28 The geometry was optimized under the conditions that the lattice vectors and the positions of Au atoms were fixed to be the same as those in the experimental observation to save the CPU time. 30,31 The optimization threshold of energy gradient was taken to be 0.0008 au bohr−1 . In the second step (ii), we evaluated excitation energy Eex and oscillator strength f using the TD-DFT method with the B3LYP functional, 60–62 because the TD-DFT calculation with the B3LYP functional provided

13



better agreement with experimental results than those with other functionals including LC-BLYP and 5-state-averaged (5SA) GMC-QDPT calculation; 63,64 see pages S8-S9, Tables S1-S2, and Scheme S2 in electronic Supporting Information (ESI). To take into consideration the crystalline effect on the absorption spectrum, the target QM molecule(s) was embedded in the MM crystal of the ground state, where the geometry and charge distribution of the MM crystal were fixed to be the same as those determined by the step (i) like the conventional QM/MM method. In the next step (iii), we investigated the phosphorescent spectrum, where we optimized the geometry of target QM molecule(s) in the triplet state, using the U-DFT calculation with the B3LYP-D3 under the condition that the target QM molecule(s) is embedded in the ground state MM crystal obtained at the step (i). For making comparison of absorption and emission spectra between crystal and solution phases, we performed the three-regions 3D-RISM-SCF-DFT calculation with the B3LYP-D3 functional to determine the geometry of solute and solvation structure of CHCl3 , 52,53 because the absorption spectrum was experimentally observed in CHCl3 . 20 The optimization threshold of energy gradient was taken to be the same as that (0.0008 au bohr−1 ) in the QM/MM calculation for the crystal phase. In this calculation, we employed the Kovalenko-Hirata (KH) closure in the 3D-RISM integral equation. 65–84 As the initial step of the 3D-RISM-SCF-DFT calculation, the 1D-RISM calculation was carried out to set up the solvent-solvent total correlation functions with the density

ρW = 1.48 g cm−3 and temperature T = 298.15 K. The point charges and the LJ parameters of CHCl3 molecule were taken from five-sites model. 85 The 1D-RISM calculation was performed on a grid of 8096 points, corresponding to the 1D space radius of 56.2 Å. In the 3D-RISM calculation, the LJ parameters were taken to be the same as those employed in the above-mentioned QM/MM calculation of molecular crystal. As a box size of solvent, a cubic grid of 128 points/axis was set with the spacing of 0.5 Å for geometry optimization. To divide the solvent grid space into three regions, the boundary distances of rin and rout were taken to be 15.0 and 18.0 Å, respectively; the electrostatic potential (ESP) acting on the solvent site is evaluated directly by one-electron integral in the range of r < rin , evaluated by the point charge approximation in the range of r < rout , and

14


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these ESPs are smoothly connected by using the switching function in the range of rin ≤ r ≤ rout ; see Ref. [52] for the details. In the RISM-SCF calculation, the electrostatic asymptotics of the 3D site correlation functions and electrostatic potentials was evaluated in analytical manner using the nonperiodic asymptotics under the identically zero concentration of ionic species. Under (as)

such condition, the long-range asymptotics of the 3D site total correlation function hs (r) can be (as)

determined by evaluating hs (k = 0) with the polynomial extrapolation on a radial k-grid. 86–88

Results and Discussion Charge Distribution and Absorption Spectra of 1 and 2 in Gas Phase and Weakly Polar CHCl3 Solvent Prior to the discussion of absorption spectra of 1 and 2 in polymorphic crystal, we investigated the charge distributions of 1 and 2 in gas phase and weakly polar CHCl3 solvent, using the RDFT method with the B3LYP-D3 functional, because those are fundamental information about the reason why these complexes are significantly influenced by surrounding molecules such as solvent and crystal, as shown in Table S3 in ESI. Based on the NBO analysis, 89 both of 1 and 2 exhibit the similar charge distribution to each other and their polarization moderately increases in polar solvent (Table S3 in ESI); for instance, when going from gas phase to weakly polar CHCl3 solvent, the negative charge on the Ph moiety increases from -0.49 e to -0.51 e and the positive charges on the phenyl part of PhNC moiety and the dimethylphenyl part of dimPhNC increase from 0.27 e to 0.30 e (Table S3 in ESI). The large polarization of 1 and 2 plays important roles in the electrostatic (ES) interaction with the surrounding molecules in both of solution and solid phases. In weakly polar CHCl3 , the positively charged H atom of CHCl3 solvent molecule approaches the negatively charged Ph moiety and the negatively charged Cl atom of CHCl3 approaches the positively charged PhNC moiety. As a result, the CHCl3 solvent lowers the π (Ph) and π ∗ (Ph) orbital energies but raises the π (PhNC) and π ∗ (PhNC) orbital energies, as shown by the orbital energy in parenthesis in Scheme 4. This 15



Scheme also shows the abbreviation of important MOs; for instance, the π orbitals on the Ph and PhNC moieties are named π (Ph) and π (PhNC), respectively. Because of the above-mentioned orbital energy changes, the absorption spectra of 1 and 2 are largely influenced by CHCl3 solvation effect, as shown in Figure 2; see also pages S5-S11, Figures S1-S4, Scheme S2, and Tables S1-S2, and S4 in ESI. The largest absorption peak of ∗ (PhNC) local excitation, which is influenced 4.9 - 5.0 eV is assigned as the πout (PhNC)→ πout

little by both of the solvation effect and the change in torsion angle τ between the Ph and PhNC planes; see Scheme 4 for the definition of π orbitals and Scheme 5 for definition of τ which represents intramolecular rotation of the Ph and PhNC. It should be noted that the torsion angle τ changes with nearly no energy barrier; 0.4 kcal mol−1 in 1 and 0.6 kcal mol−1 in 2 at the CCSD(T) level, as shown in Figures S1 and S2 in ESI. On the other hand, the second largest absorption peak is largely influenced by both of the solvation effect and the τ angle; in the parallel structure ∗ (PhNC) charge transfer (CT) excitation at 3.3 (τ = 0 degree), it is assigned as the πout (Ph)→ πout

- 3.4 eV in gas phase and 3.8 - 3.9 eV in CHCl3 solvent (red line in Figure 2). In the twisted ∗ (PhNC) CT excitation at 4.2 - 4.3 structure (τ = 90 degree), it is assigned as the πout (Ph)→ πin

eV in gas phase and 4.6 eV in CHCl3 solvent (purple line in Figure 2). Thus-calculated excitation energy Eex of the intramolecular ligand-to-ligand CT (LLCT) transition largely increases in CHCl3 solvent, indicating that the effects of surrounding molecules must be taken into consideration even in weakly polar CHCl3 solvent. In the twisted structure with τ = 90 degree, the TD-DFT-calculated absorption spectrum of 1 well agrees with the experimental observation in weakly polar CHCl3 solvent because the absorption at 3.8 eV is very small at τ = 90 degree and the lowest energy observable absorption is calculated at 4.2 eV in gas phase and 4.6 eV in CHCl3 solvent. In the parallel structure with τ = 0 degree, however, the oscillator strength of the excitation at 3.8 eV is calculated to be very large, which differs from the experimental observation; see Figure 2. Because the oscillator strength significantly depends on the τ angle, we investigated the CCSD(T)-calculated potential energy curve against τ , as shown in Figures S1a and S2a in ESI. The twisted structure is moderately more stable

16


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than the parallel one by 0.4 and 0.6 kcal mol−1 in 1 and 2, respectively, but the energy difference is too small to neglect the contribution of the parallel structure (τ = 0 degree) to the absorption spectrum in CHCl3 solution (Figure 2). For better understanding, we investigated the probabil(i)

ity density function (PDF) Pvib of vibrational state i against τ , considering two different solvation pictures; (a) one is the equilibrium limit in which the solvation structure is always optimized by following the solute rotational motion of τ and (b) the other is the non-equilibrium limit in which the solvation structure is not changed from that for the most stable structure (τ = 90 degree); see pages S12-S13 in ESI for detail and Figure S5 in ESI for PDFs of (a) and (b). The case (b) is more reasonable than the case (a), because the rotations of Ph and PhNC easily occur with very small energy barrier and the solvation structure cannot follow such rapid rotation. The statistically averaged PDF value, Pvib (τ ), becomes negligibly small at τ = 0 degree in the case (b) and avg

the calculated absorption spectrum in the non-equilibrium solvation picture agrees with the experimentally observed absorption spectrum despite of the tiny rotational energy barrier (0.4 kcal mol−1 in 1 and 0.6 kcal mol−1 in 2) in the equilibrium solvation picture. In summary, both of 1 and 2 have the negatively charged Ph and positively charged PhNC moieties and their largely polarized electronic structures induce large solvation effect on the π and

π ∗ orbital energies even in weakly polar CHCl3 solvent, leading to the considerably large difference in Eex of π (Ph)→ π ∗ (PhNC) transition between gas and solution phases. This means that the influence of the surrounding molecules must be considered in theoretical study of absorption and emission spectra in condensed phase such as solution and crystal.

Relative Stabilities of Polymorphic Crystals; 1b vs. 1y and 2b vs. 2g We calculated MM crystal model in the ground state by employing four gold(I) complexes as the QM molecular system, as shown in Figure 1, except for 2g in which six gold(I) complexes were employed because the symmetrically minimal subunit consists of six gold(I) complexes in 2g, as mentioned in the section of “Model for ground state structure and absorption spectrum”. In the 2b crystal, the intramolecular torsion angle τ has not been experimentally determined due 17



Page 18 of 67

to the rotational disorder on the Ph plane and the dimethylphenyl ring of dimPhNC. 21 Thus, we examined almost all possible combinations of two limited structures participating in the disorder and found that three crystal structures were important; see page S14 and Figure S6 in ESI for details. Then, we investigated the three important crystal structures using the periodic QM/MM method; the minimum unit cell consists of four parallel monomers in the first one (2bP ), four twisted monomers in the second (2bT ), and two parallel monomers and two twisted ones in the third (2bPT ); see Figure S7 in ESI for detailed difference. The optimized intramolecular torsion angle τ and intermolecular torsion angle η between two neighboring PhNC moieties were summarized in Table S5 in ESI; see Scheme 5 for the definition. These calculated torsion angles agree well with the experimental values within error of 2 - 3 degree. The potential energy curve along τ is very shallow (see the section of “Charge Distribution and Absorption Spectra of 1 and 2 in Gas Phase and Weakly Polar CHCl3 Solvent”), suggesting that the intermolecular interaction between the Ph and PhNC moieties plays important roles in determining avg

the position and the orientation of 1 and 2. We evaluated the averaged crystal energy Ecrystal per one molecule, using the periodic QM/MM method, as shown in Table 1A; in bracket of 2g is the energy relative to that of 2bP calculated by employing six gold(I) complexes as the QM molecular system avg

for comparison at the same level. Ecrystal values indicate that the 1y crystal is more stable than the 1b by 1.9 kcal mol−1 . This result agrees with the experimental differential scanning calorimetry (DSC) analysis that the enthalpic change (∆H) of 1b→1y SCSC transition is approximately -7 kJ mol−1 , indicating that 1y is more stable in enthalpy than 1b. 20,21 In 2, 2bP , 2bPT , and 2bT crystals are more stable than 2g by 2.2, 1.9, and 1.1 kcal mol−1 , respectively. This result means that the 2g→2b SCSC transition is exothermic, which does not agree with the DSC analysis that the ∆H value of 2g→2b SCSC transition is approximately +5 kJ mol−1 ; 22 this results will be discussed below in more detail. To discuss the relative stabilities of 1b and 1y and those of 2PT /2P and 2g at higher level, avg2

avg2

we further evaluated the averaged crystal energy Ecrystal , the averaged self energy ESelf(QM) , the avg2

averaged interaction energy EInt(QM-QM) with the nearest neighboring eight molecules, and the 18


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avg2

averaged interaction energy EInt(QM-MM) with remaining MM molecules, incorporating CCSD(T) and MP2 corrections defined by Eqs. (4) - (8); see the section of “Model for relative stabilavg2

ity of polymorphic crystal at the ground state”. In 1, both of Ecrystal [CCSD(T)/MP2/B3LYP-D3] and Ecrystal [B3LYP-D3] indicate that 1y is more stable than 1b by 1.3 - 1.4 kcal mol−1 like the avg2

avg

Ecrystal [B3LYP-D3] (Table 1A), as shown in Table 1B, which agrees with the experimental observation that the SCSC phase transformation occurs irreversibly from 1b to 1y by the mechanical avg2

stimulation without heat and light. 20 In Ecrystal [CCSD(T)/MP2/B3LYP-D3], the averaged interacavg2

avg2

tion energy EInt(QM-QM) + EInt(QM-MM) of 1y is more negative (more attractive) than that of 1b by 1.7 kcal mol−1 , while the averaged self energy ESelf(QM) of 1y is less negative (more unstable) avg2

than that of 1b by 0.4 kcal mol−1 . These results indicate that not the self energy ESelf(QM) but the avg2

avg2

avg2

interaction energy EInt(QM-QM) + EInt(QM-MM) is responsible for the larger stability of 1y than that avg2

avg2

of 1b. The EInt(QM-MM) value is very small but the EInt(QM-QM) value is significantly large in 1b. In avg2

1y, on the other hand, the EInt(QM-QM) value is less negative (less attractive) than in 1b by 6.3 kcal mol−1 but the EInt(QM-MM) value is more negative (more attractive) than in 1b by 8.0 kcal mol−1 , avg2

avg2

indicating that the EInt(QM-MM) plays important role in stabilizing 1y more than 1b. 90 avg2

In 2, the Ecrystal [CCSD(T)/MP2/B3LYP-D3] value indicates that 2bP is more stable than 2g by 0.4 kcal mol−1 but 2bPT and 2bT are less stable than 2g by 0.7 and 2.0 kcal mol−1 , respecavg

avg2

tively, as shown in Table 1B, unlike the Ecrystal [B3LYP-D3] (Table 1A) and Ecrystal [B3LYP-D3], suggesting that the CCSD(T) and MP2 corrections in Eq. (8) are crucial. The averaged self energy avg2

ESelf(QM) is slightly less negative (less stable) in 2bP , 2bPT , and 2bT than in 2g only by 0.1 kcal mol−1 (Table 1B), indicating that the ESelf(QM) is almost the same between 2bP /2bPT /2bT and 2g avg2

avg2

avg2

and the averaged interaction energy EInt(QM-QM) + EInt(QM-MM) is responsible for the difference avg2

in energy between 2b and 2g. However, the EInt(QM-MM) value of 2bP is less negative (less stable) than that of 2g by 1.3 kcal mol−1 and almost the same as those of 2bPT and 2bT . On the avg2

other hand, the EInt(QM-QM) value is more negative (more attractive) in 2bP and 2bPT than in 2g by 1.8 and 0.6 kcal mol−1 , respectively, but less negative (less attractive) in 2bT than in 2g by 0.2 kcal mol−1 . These results indicate that the larger stability of 2bP than those of 2bPT , 2bT , and

19



avg2

avg2

2g arises from the EInt(QM-QM) rather than the EInt(QM-MM) ; actually, the difference between the avg2

avg2

Ecrystal [CCSD(T)/MP2/B3LYP-D3] and Ecrystal [B3LYP-D3] arises from the MP2 correction of the two-body QM-QM interaction energy rather than the CCSD(T) correction of the QM self energy. avg2

This means that the intermolecular interaction EInt(QM-QM) between the target molecule and the nearest neighboring eight molecules is important for determining the relative stabilities of these crystals; see also pages S15-S16, Tables S6-S8, and Figure S8 in ESI for the discussion on the avg2

relative stabilities of 2bP , 2bPT , and 2bT . In 2b, the Ecrystal [CCSD(T)/MP2/B3LYP-D3] is calculated to increase in the order 2bP < 2g < 2bPT < 2bT , indicating that 2bP is the most plausible polymorph of 2b from the viewpoint of potential energy. However, the entropy of 2bPT is larger than that of 2bP , 91,92 suggesting that the Gibbs free energy difference between 2bPT and 2bP is very small and it is not easy to determine computationally which of 2bP and 2bPT is the most stable. The 2g→2bP SCSC transition is calculated to be slightly exothermic but the 2g→2bPT SCSC transition is endothermic by 0.7 kcal mol−1 ; the latter exothermicity does not differ very much from the experimentally observed enthalpy change (+5 kJ mol−1 ) in the 2g→2b transition. In summary, the present QM/MM calculation successfully reproduced well the experimentally observed tendency that 1y is more stable than 1b, which is consistent with the experimentally observed 1b→1y SCSC transition. The 2bP crystal phase is more stable than 2bPT in potential energy, but the energy difference is very small. It is not easy to computationally determine which of 2bP and 2bPT is the crystal phase in 2b, because both of 2bP and 2bPT satisfy the experimentally observed disordered structure and the energy difference is marginal.

Absorption Spectra of Polymorphic Crystals, 1b, 1y, 2b, and 2g Using the ground state structure of crystal optimized by the periodic QM/MM method, we performed TD-DFT calculation with the B3LYP functional under consideration of the surrounding molecular effect. Here we investigated both of the molecule in crystal and that on surface of the crystal, as shown in Scheme 6, because molecule near the surface is much more irradiated by light than inside molecule in the crystal. Molecules near the surface were modeled by the usual slab 20


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approximation in which vacuum layer of 50 Å was placed. In such slab calculation, we employed the same geometry of target molecule as that optimized in the crystal without the re-optimization of molecule on the surface for elucidating the surface effects. For this investigation, we calculated the target molecule on ab- and ac-surfaces in 1b, ab-surface in 1y, bc-surface in 2b, and bc-surface in 2g; note that the number of CH-π interaction on the π (Ph) or π (PhNC) plane of the target molecule is smaller on the surface than in the crystal by one, as will be discussed below; see Scheme 4 for the definition of π orbitals. Other surfaces were not modeled here because it was difficult to smoothly cut them from the entire crystal. In 1b, all the excitations in the crystal occur at moderately higher energy (4.1 and 4.5 eV), as shown in Figure 3a; see also Figure S9a in ESI for the MO character. In the crystal, both sides of the PhNC plane form the CH-π interaction with two neighboring Ph moieties, which largely raises the π ∗ (PhNC) orbital energy to enlarge the Eex value. In the molecules on the ac-surface, only one side of the PhNC plane forms the CH-π interaction with one neighboring Ph moiety and therefore, the small peak is calculated at lower energy (3.7 eV). These three excitations (at 4.5, 4.1, and 3.7 eV) correspond to the experimentally observed large peak at 3.9 eV, shoulder around 3.5 eV, and small peak at 3.3 eV, respectively. 93 The peaks calculated at 4.1 and 4.5 eV in the crystal ∗ (PhNC) and that from the are assigned as the LLCT excitation from the πout (Ph) orbital to the πout

πout (Ph) orbital to the πin∗ (PhNC). These Eex values are larger than those in gas phase by about 0.8 eV because the approach of the negatively charged Ph moiety to the PhNC moiety raises the

π ∗ orbital energy of the CH-π bonding partner PhNC moiety and the approach of the positively charged PhNC moiety to the Ph moiety lowers the π orbital energy of the CH-π bonding partner Ph moiety. The excitation calculated at 3.7 eV on the ac-surface is assigned as the intramolecular ∗ (PhNC) one. 94 LLCT excitation from the πout (Ph) orbital to the πout

In 1y, the lowest energy excitation exhibits the large oscillator strength both in the crystal and on the ab-surface, as shown in Figure 3b; see also Figure S9b in ESI for the MO character. The Eex value was calculated to be 3.1 eV for the molecules on the ab-surface and 3.2 eV for the molecules in the crystal. These excitations are assigned as the MMLCT excitation from the anti-

21



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1y 1y bonding combination φ(d a of four dσ (Au) orbitals to the bonding combination φPhNC(π ∗ σ -dσ )

∗ b out -πout )

∗ (PhNC) orbitals, 95 where superscripts “a” and “b” mean “antibonding” and “bonding” of four πout

combinations, respectively. It is noted that the largest peak of 1y is calculated at the lower energy than that (4.5 eV) of 1b by about 1.3 eV, which agrees with the experimentally observed difference (1.1 eV) in excitation spectrum between 1b and 1y (Scheme 2c). Also, the LLCT excitation from ∗ (PhNC), which is the origin of the large peak in 1b, is not observed in 1y the πout (Ph) to the πin

because the oscillator strength becomes very small in the parallel structure (τ = 1 degree) of 1y unlike in the twisted structure (τ = 70 - 72 degree) of 1b. 96 In the energy range of 4.0 - 4.3 eV, on 1y ∗ the other hand, the MMLCT excitation from the φ(d a to the πin (PhNC) and the intramolecular σ -dσ ) ∗ (PhNC) exhibit large oscillator strengths, as shown LLCT excitation from the πout (Ph) to the πout

in Figure 3b. These two excitations correspond to the experimentally observed shoulder around 3.5 eV. 97 In 2bP , 2bPT , and 2bT , the important excitations are calculated to be almost the same as those calculated in 1b, as shown in Figures 4a, 4b, and 4c; see also Figures S10a and S10b in ESI for the MO characters of 2bP and 2bT , respectively. The molecule in the crystal, in which both sides of the dimPhNC plane forms the CH-π interaction with two neighboring Ph moieties, exhibit the large peaks at 4.0 - 4.1 eV and 4.7 - 4.9 eV. The molecules on the bc-surface, in which only one side of dimPhNC plane forms the CH-π interaction with one neighboring Ph moiety, exhibit the small peak at 3.8 - 3.9 eV. These three excitations correspond to the experimentally observed large peak at 3.9 eV, shoulder around 3.5 eV, and small peak at 3.2 eV, respectively. The excitations calculated at 4.0 - 4.1 and 4.7 - 4.9 eV in the crystal are assigned as the LLCT excitation from the ∗ (dimPhNC) and that from the π (Ph) to the π ∗ (dimPhNC). Because πout (Ph) orbital to the πout out in ∗ (dimPhNC) the molecule in 2P (τ = 20 degree) has larger overlap between the πout (Ph) and the πout ∗ (dimPhNC) than that in 2 (τ = 54 orbitals but smaller overlap between the πout (Ph) and the πin T

degree), the LLCT excitation at 4.1 eV exhibits larger oscillator strength than that at 4.9 eV in 2bP but smaller oscillator strength than that at 4.8 eV in 2bT . The trend of excitation energies and oscillator strengths in 2bPT and 2bT , which are similar to those in 1b, agree with the experimental

22


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observation of 2b, indicating that the real system of 2b contains both the monomer with the twisted structure and that with the parallel structure. 91,92 In 2g, the lowest energy excitation exhibits the large oscillator strength both in the crystal and on the bc-surface, as shown in Figure 4d; see also Figure S10c in ESI for the MO character. The Eex value is calculated to be 2.9 eV for the molecules on the surface and the molecules in the crystal, which exists at lower energy than those (3.1 and 3.2 eV, respectively) of 1y by 0.2 and 0.3 eV. The 2g excitation is assigned as the MMLCT transition from the anti-bonding combination φ(d a of six σ -dσ ) 2g dσ (Au) orbitals to the bonding combination φdimPhNC( π∗

∗ b out -πout )

∗ (dimPhNC) orbitals. It is of six πout

noted that the first peak (2.9 eV) of 2g was calculated at significantly lower energy than the largest peak (4.7 eV) of 2bT by about 1.8 eV. This lowest excitation energy of 2g is similar to that of 1y but no peak was experimentally observed around this energy region in 2g unlike in 1y, as shown in Figure 4d. It is likely that this excitation of 2g may be involved in the experimentally observed shoulder in this energy region, while the reason why this MMLCT excitation is not experimentally observed in 2g is still open question. One plausible reason is that the experimental data was not absorption spectrum but excitation spectrum. The other characteristic difference between 2g and ∗ (dimPhNC); it is calculated at 1y is found in the MMLCT excitation from the φ(dσ -dσ )a to the πin

3.7 eV in 2g (Figure S10c in ESI), which is lower than that (4.0 eV) in 1y by 0.3 eV. This peak at 3.7 eV can be assigned to the experimental peak at 3.4 eV.

Emission Spectra of 1 and 2 in Gas Phase and Weakly Polar CHCl3 Solvent Prior to the discussion of phosphorescence emission spectra of 1 and 2 in polymorphic crystal, we investigated here the emission spectra of the monomer and dimer in gas phase and weakly polar CHCl3 solvent, using the U-DFT and 3D-RISM-SCF-U-DFT methods with the B3LYP-D3 functional, respectively, to elucidate how much the dimerization of gold(I) complexes and the solvation effect of CHCl3 influence the emission spectrum in comparison to that of monomer in gas phase. This investigation is important to disclose the difference in emission spectrum between crystal and other atmosphere. 23



Firstly, we optimized the monomer geometry at triplet state in gas phase and CHCl3 solvent to evaluate the emission energy Eem of the monomer, as shown in Figure S11 in ESI. Both of 1 and 2 have the parallel structure (τ = 0 degree) at the triplet state in gas phase and CHCl3 solvent. The Eem values of 1 and 2 were calculated to be 2.73 and 2.61 eV, respectively, in gas phase and 2.71 and 2.58 eV in CHCl3 solvent, as shown in Table 2. The SOMOs of 1 and 2 mainly consist of ∗ (PhNC), indicating that the emission of monomer is induced by the local the πout (PhNC) and πout ∗ (PhNC) to the π (PhNC), as shown in Figure S11 in ESI. Therefore, the transition from the πout out

Eem value of monomer is not largely influenced by the surrounding CHCl3 molecules because both ∗ (PhNC) orbital energies similarly change by CHCl solvation, as shown of πout (PhNC) and πout 3 ∗ (PhNC) in Scheme 4, and hence the difference in orbital energy between πout (PhNC) and πout

changes little by the surrounding CHCl3 molecules. Then, we investigated three kinds of dimer at triplet state in gas phase and CHCl3 solvent, where geometry was determined at the DFT/B3LYP-D3 level. The first one (named 3 (π -π )P ) is formed by Au-Au bonding and π -π stacking interactions, the second (named 3 (CH-π )P ) is formed by Au-Au bonding and CH-π interactions, and the third (named 3 (CH-π )NB P ) is formed by only CH-

π interaction without Au-Au bonding interaction, as shown in Figure S11 in ESI, where subscript "P" means that the dimer consists of two parallel monomers. The 3D-RISM-SCF-DFT/B3LYPD3-calculated Gibbs free energy change ∆G0 relative to two monomers (Table 2) indicates that the 3 (π -π ) P

3 is the most stable, the 3 (CH-π )NB P is the most unstable, and the (CH-π )P is the medium

in both of gas phase and CHCl3 solvent. 98 The ∆G0 at the MP4(SDQ) level 99 with the BSSE correction indicates that the dimer at triplet state is not formed in gas phase but formed in CHCl3 solvent, while the dimer at the ground state is not formed in both of gas phase and CHCl3 solvent (see ∆G0 values in parentheses in Tables 2 and S4 in ESI). 100,101 In gas phase, therefore, the monomers of 1 and 2 participate in emission spectrum because the dimer is not formed at both of the ground state and triplet excited state. In CHCl3 solvent, on the other hand, the emission process is a bit complicated, depending on whether or not the emission process occurs faster in monomer than dimer formation. In both of

24


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the 3 (π -π ) and 3 (CH-π ), the Au-Au distance is much shorter than in the 3 (CH-π )NB . Though the

τ angle is similar among three structures (16 - 20 degree in gas phase and 18 - 28 degree in CHCl3 solvent), the intermolecular torsion angle η largely differs between the 3 (π -π )P and 3 (CH-π )P dimers; in both of 1 and 2, the η is smaller in the 3 (π -π )P than in the 3 (CH-π )NB P by more than 100 degree (Figure S11 in ESI), while the η is similar in the 3 (CH-π )P and 3 (CH-π )NB P . In both of 1 and 2, the effective bond order between two Au atoms of the 3 (π -π )P dimer is calculated to be 0.26 in gas phase and 0.30 in CHCl3 solvent and that in the 3 (CH-π )P is calculated to be 0.35 in gas phase and 0.36 in CHCl3 solvent, where the effective bond order is evaluated from the Wiberg bond index in the NAO basis. 102 This means that the weak Au-Au bond is formed in the 3 (π -π )P and 3 (CH-π )P dimers unlike in the 3 (CH-π )NB P whose effective bond order is 0.00. The Eem value of the 3 (CH-π )NB is similar to that of monomer but those of the 3 (π -π )P and 3 (CH-π ) P

become much smaller than that of monomer following the order, monomer ∼ 3 (CH-

3 3 π )NB P > (CH-π )P > (π -π )P , as shown in Table 2. The Au-Au distance is not the reason for the

difference in Eem value between the 3 (π -π )P and 3 (CH-π )P dimers because the Au-Au distance of the 3 (π -π )P is rather longer than that of the 3 (CH-π )P ; the calculated Au-Au distances of 1 and 2 in the 3 (π -π )P dimer are 2.89 and 2.88 Å, respectively, in gas phase and 2.83 and 2.82 Å in CHCl3 solvent, while those in the 3 (CH-π )P dimer are 2.80 and 2.80 Å in gas phase and 2.78 and 2.78 Å in CHCl3 solvent. In the 3 (π -π )P dimer, the Eem values of 1 and 2 are calculated to be 1.86 and 1.90 eV, respectively, in gas phase and 1.97 and 2.04 eV in CHCl3 solvent, indicating that the surrounding molecules moderately influence the Eem value in the 3 (π -π )P dimer. In the 3 (CH-π ) P

dimer, on the other hand, the Eem values of 1 and 2 are calculated to be 2.45 and 2.48 eV,

respectively, in gas phase and 2.43 and 2.51 eV in CHCl3 solvent, indicating that the surrounding molecules influence a little the Eem value in the 3 (CH-π )P dimer. These results suggest that the large red-shift of Eem value must be experimentally observed in CHCl3 solvent if the 3 (π -π )P dimer is formed at the triplet excited state. However, it was experimentally reported that 1 and 2 exhibited the large emission spectrum at 2.92 eV and 2.85 eV, respectively, in CH2 Cl2 solvent. These Eem values are close to those calculated for monomer but

25



considerably differ from those for dimer, indicating that the emission process occurs without dimer formation at the triplet excited state; see Figure S12 in ESI and ESI of Ref. [21] for experimental emission spectra of 1 and 2. As discussed above, the ∆G0 at the MP4(SDQ) level with the BSSE correction (Table S4 in ESI) indicates that the dimer at the ground state is not formed in CHCl3 solvent but can be formed at the triplet state. These features of 1 and 2 largely differ from those of [Au(CN)2 ]− in aqueous phase, 103,104 in which the oligomer [Au(CN)2 ]n− n is formed at both of the ground state and the excited state. Important difference between [Au(CN)2 ]− and the present gold(I) complexes (1 and 2) would arise from the size of ligand; CN ligand in [Au(CN)2 ]− is small but Ph and PhNC/dimPhNC ligands in 1 and 2 are large. On the basis of these results, it is likely concluded that emission from the triplet state occurs in monomer more rapidly than the formation of the 3 (π -π )P dimer because 1 and 2 do not form the dimer at the ground state; see also page S17 and Figure S11 in ESI for the character of SOMOs in dimer structures. In summary, the TD-DFT calculations disclosed that the Eem value of dimer largely depends on the Au-Au distance and the intermolecular torsion angle η in both of the gas phase and CHCl3 solvent, because the shorter Au-Au distance more raises the φ(dσ -dσ )a orbital energy and more lowers the φPhNC(πout ∗ -π ∗ )b and φdimPhNC(π ∗ -π ∗ )b orbital energies. In CHCl3 solvent, however, the out out out red-shift of the Eem value is not experimentally observed, indicating that the dimer is not formed at the excited state and the emission occurs without the dimer formation. The ∆G0 calculated for the 3 (π -π )P and 3 (CH-π )P dimers are considerably negative but the ∆G0 calculated for the dimer is positive at the ground state, indicating that the dimer is not formed at the ground state. These results suggest that even though the dimer formation is possible at the triplet state from the viewpoint of the ∆G0 , the dimer is not formed at the triplet excited state when the dimer can not be formed at the ground state because of the short lifetime of the triplet excited state.

Emission Spectra of Polymorphic Crystals, 1b, 1y, 2b, and 2g In crystal, monomer is close to each other in the ground state unlike in CHCl3 solvent, suggesting that the emission spectrum can be largely influenced by the polymorphic crystal structure and also 26


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by the formation of dimer or aggregate in the similar manner to that of [Au(CN)2 ]− in aqueous phase. 103,104 To theoretically investigate the emission energy Eem in polymorphic crystal, we optimized the geometry of target molecules at the triplet state by the U-DFT with the B3LYP-D3 functional under the conditions that the structure and charge distribution of MM molecules were taken to be the same as those of the crystal optimized at the ground state by the periodic QM/MM calculation see the section of “Relative Stabilities of Polymorphic Crystals; 1b vs. 1y and 2b vs. 2g”); remember that the population of the excited state is very small at room temperature. To take into consideration the effects of surrounding molecules on the dimer at the triplet excited state, four QM molecules were employed in 1b and 2b and six QM molecules were employed in 1y and 2g, as mentioned in the section of “Model for emission spectrum”. The use of four QM molecules in 1b and 2b is reasonable because the nearest neighboring monomer is well separated from the target molecules; see the long Au-Au distance between two adjacent Au complexes in 1b and 2b (Scheme 3a). In 1y and 2g, on the other hand, we placed two dimers above and below the target QM dimer because the Au-Au distance in the dimer is short and it is not good to separate the dimer into two monomers (Schemes 3b and 3c). 105 For comparison, the molecules on surface were modeled by the usual slab approximation like in the calculation of absorption spectrum (the section of “Absorption Spectra of Polymorphic Crystals, 1b, 1y, 2b, and 2g”). In such slab calculation, we employed the same geometry of target molecule as that optimized in the crystal without the re-optimization of molecule on the surface for showing clearly the surface effects. In 1b, two geometries of the 3 (π -π ∗ ) locally excited states 3 LE1 and 3 LE2 were optimized by the QM/MM method, as shown in Figure 5a, but the 3 MMLCT geometry could not be determined as the lowest energy triplet state. In both of 3 LE1 and 3 LE2, the QM molecules in the triplet state consists of one triplet monomer and three singlet monomers. In 3 LE1, one triplet monomer has the ∗ (PhNC). In local excitation character in which the excitation occurs from the πout (PhNC) to the πout 3 LE2,

one triplet monomer has the local excitation character in which the excitation occurs from

∗ (Ph). We also searched the 3 LLCT state in which the excitation occurs the πout (Ph) to the πout ∗ (PhNC), but we could not find it as the lowest energy triplet state. from the πout (Ph) to the πout

27



As shown in Table 3A, 3 LE1 is much more stable than 3 LE2 by 8.4 kcal mol−1 and the emission energy is calculated to be 2.71 eV for 3 LE1 and 3.10 eV for 3 LE2 in the crystal but 2.73 eV for 3 LE1

and 3.08 eV for 3 LE2 at the surface. Hence, one of the experimentally observed emission

peaks of 1b at 2.53 and 2.72 eV can be assigned to 3 LE1. However, the other peak is difficult to be assigned to 3 LE2 because 3 LE2 is much more unstable than 3 LE1 by 7 - 8 kcal mol−1 . One of the plausible reasons for the experimentally observed two peaks is the electron-phonon coupling with vibrational state of the C≡N stretching mode. This C≡N stretching frequency of Au complex 1 was calculated to be about 2250 cm−1 at the ground state in gas phase, 106 which corresponds to the difference in vibrational energy of 0.29 eV; this is close to the difference (0.19 eV) between two experimentally observed peaks. In 1y, two geometries of the 3 (d-π ∗ ) CT excited states 3 MMLCT1 and 3 MMLCT2 were optimized as the lowest energy excited state by the QM/MM method, as shown in Figure 5b. 3 MMLCT1

is moderately more stable than 3 MMLCT2 by about 1 kcal mol−1 and both of

3 MMLCT1

and 3 MMLCT2 are more stable than the 3 (π -π ∗ ) locally excited states, 3 LE1 and

3 LE2,

as shown in Table 3B. In both of 3 MMLCT1 and 3 MMLCT2, the excitation occurs from

1y the anti-bonding combination φ(d a of dσ (Au) orbitals to the bonding combination σ -dσ ) 1y φPhNC( π∗

∗ b out -πout )

∗ (PhNC); both of them are delocalized over four molecules. One imporof πout

tant difference between 3 MMLCT1 and 3 MMLCT2 is found in the spin population, which is largely delocalized on the CH-π interacting dimer consisting of mono3 and mono4 in 3 MMLCT1 but delocalized on the π -π stacking dimer consisting of mono2 and mono3 in 3 MMLCT2; see Figure 5b for mono1 to mono6. In 3 MMLCT1, the Au-Au distance of the CH-π interacting dimer (mono3-4) is 2.85 Å which is close to that (2.80 Å) of the dimer in CHCl3 solvent (see Figure S11 in ESI) but in 3 MMLCT2 the Au-Au distance (3.15 Å) of the π -π stacking dimer (mono2-3) is much longer than in CHCl3 solvent probably due to the crystalline effects. Using the Wiberg bond index in the NAO basis, the effective bond order between these two Au atoms is calculated to be 0.31 for 3 MMLCT1 and 0.25 for 3 MMLCT2, which are similar to that (0.30) in the CH-π interacting dimer in CHCl3 solvent. The calculated Eem value (2.37 eV) of 3 MMLCT1 is moderately

28


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larger than the experimental value (2.19 eV) and the calculated red-shift (0.35 eV) of the emission spectrum by the 1b→1y SCSC phase transformation agrees well with the experimental value (0.34 1y eV). Because the short Au-Au distance raises the φ(d a orbital energy and the π -π stacking σ -dσ ) 1y interaction between PhNC moieties lowers the φPhNC( π∗

∗ b out -πout )

3 MMLCT2

orbital energy, the 3 MMLCT1 and

are the lowest energy triplet state to participate in the emission spectrum in 1y unlike

in 1b. The intermolecular torsion angle η (45 degree) between mono2 and mono3 in 3 MMLCT2 is larger than those (9 and 21 degree, respectively) in gas phase and CHCl3 solvent and hence the 1y φPhNC( π∗

∗ b out -πout )

orbital energy does not become very low in 1y in comparison to that of 3 (π -π )P

dimer in gas phase and CHCl3 solvent. This is the reason why the Eem value in crystal is smaller than that of monomer in gas phase and CHCl3 solvent but larger than that of dimer in gas phase and CHCl3 solvent. In 2b, two stable geometries of 3 LE1 and 3 LE2 were optimized by the QM/MM method. They are more stable than 3 MMLCT and their geometries hardly differ among 2bP , 2bPT , and 2bT except for the torsion angle η ; see Figure 6a for 2bP and Figure S13 in ESI for 2bPT and 2bT . In both of 3 LE1 and 3 LE2, the QM molecules in the triplet state consists of one triplet monomer and three singlet monomers like in 1b. In 3 LE1, one triplet monomer has the local excitation character ∗ (dimPhNC). In 3 LE2, one triplet monomer in which excitation occurs from πout (dimPhNC) to πout ∗ (Ph). As shown has the local excitation character in which excitation occurs from πout (Ph) to πout

in Table 3C, 3 LE1 is more stable than 3 LE2 by about 11 kcal mol−1 in the crystal and the Eem value in the crystal is calculated to be 2.61 - 2.63 eV in 3 LE1 and 3.11 - 3.12 eV in 3 LE2. We also searched the intra- and intermolecular CT triplet geometries but could not find it as the lowest energy triplet state like in 1b. The Eem value calculated on the bc-surface was 2.63 - 2.65 eV in 3 LE1

and 3.06 - 3.10 eV in 3 LE2 like that in the crystal, indicating that the Eem values of 3 LE1

and 3 LE2 differ little between the crystal and the bc-surface and between the parallel and twisted structures.

3 LE1

can be assigned to one of the experimentally observed emission peaks of 2b.

However, it is difficult to explain the reason why the experimentally observed peaks are so broad in 2b (Scheme 2b), because it is likely that the Eem value of the 3 (π -π ∗ ) locally excited state is not

29



influenced so much by the surrounding molecular effects unlike that of the CT excited state. In 2g, three geometries of 3 MMLCT1, 3 MMLCT2, and 3 MMLCT3 were optimized, as shown in Figure 6b. They are more stable than the 3 (π -π ∗ ) locally excited states, 3 LE1 and 3 LE2. 3 MMLCT3 3 MMLCT2,

is the lowest energy among them, as shown in Table 3D. In all 3 MMLCT1,

2g and 3 MMLCT3, the excitation occurs from φ(d a to φdimPhNC(π ∗ -π ∗ )b which are out out σ -dσ )

delocalized over four molecules. One significant difference among 3 MMLCT1, 3 MMLCT2, and 3 MMLCT3 is found in the spin population, which is largely delocalized on the dimer consisting of

mono2 and mono3 in 3 MMLCT1, on the dimer consisting of mono3 and mono4 in 3 MMLCT2, and on the dimer consisting of mono4 and mono5 in 3 MMLCT3; see Figure 6b for mono1 to mono6. The calculated Eem value (2.46 eV) of 3 MMLCT3 agrees with the experimental value (2.32 eV). This Eem value of 2g is larger than that of 1y, which agrees with the experimental tendency that the emission spectrum is observed at the higher energy in 2g than in 1y by about 0.1 2g eV (Scheme 2c). Because the shorter Au-Au distance raises more the φ(d a orbital energy, the σ -dσ )

shorter Au-Au distance of 3 MMLCT1, 3 MMLCT2, and 3 MMLCT3 is responsible for the lower energy emission spectrum in 2g than in 2b. Actually, the Au-Au distance of 2g was calculated to be 2.88 Å between mono2 and mono3 in 3 MMLCT1, 3.00 Å between mono3 and mono4 in 3 MMLCT2,

and 2.89 Å between mono4 and mono5 in 3 MMLCT3. 107 All these distances are

much shorter than those (4.78 - 4.79 Å) of 2b in LE1. This is essentially the same as the emission spectra of 1y and 1b in which the shorter Au-Au distance of 1y in MMLCT1 than that of 1b in LE1 is responsible for the lower energy emission spectrum in 1y than in 1b. However, the decreasing order of the Au-Au distance in 2g, 3 MMLCT2 > 3 MMLCT3 ∼ 3 MMLCT1, is not exactly the same as the decreasing order of the Eem value, 3 MMLCT1 > 3 MMLCT3 ∼ 3 MMLCT2 (Table 3D). This result suggests that not only the orbital overlap of Au dσ orbitals between the central 2g two monomers, which considerably influences the φ(d a energy, but also the orbital overlap beσ -dσ )

tween the central monomer and the other neighboring monomer is important for determining the Eem value. Actually, 3 MMLCT2 has two considerably short Au-Au distances (2.97 and 3.01 Å, respectively) between mono2 and mono3 and between mono4 and mono5 but 3 MMLCT3 has

30


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one considerably short Au-Au distance (2.97 Å) between mono5 and mono6. Based on the results discussed above, it should be concluded that the emission occurs from the ∗ (PhNC) locally excited state in 1b and 2b and from the φ πout (PhNC)→πout (dσ -dσ )a →

φPhNC(πout ∗ -π ∗ )b MMLCT excited state in 1y and 2g. The Eem values of 1y and 2g are much smaller out than those of 1b and 2b, because the short Au-Au distance largely raises the φ(dσ -dσ )a orbital energy and

the

large

overlap

between

∗ (PhNC) πout

two

orbitals

largely

lowers

the

φPhNC(πout ∗ -π ∗ )b orbital energy in 1y and 2g unlike in 1b and 2b. The emission spectrum in 1y out and 2g is characteristic feature of crystal because the 3 MMLCT cannot be formed in gas and solution phases.

Conclusions One of the important features of 1 and 2 is the polarized electronic structure; Ph has largely negative charge (about -0.5 e) but PhNC has somewhat large positive charge (about 0.3 e), indicating that the positively charged atom of surrounding molecule approaches Ph but the negatively charged one approaches PhNC. Hence, surrounding molecules lower the orbital energy of out-of-plane π of Ph and raise that of PhNC. Actually, in CHCl3 solvent, the Eex value of the LLCT excitation ∗ (PhNC) considerably increases by about 0.4 eV due to solvation effect. from the πout (Ph) to the πout

The oscillator strength of this LLCT excitation is largely influenced by the intramolecular torsion angle τ between Ph and PhNC planes. The experimentally observed absorption spectrum was reproduced by considering the twisted structure, which is more stable than the parallel structure at the CCSD(T) level. The emission spectrum depends on whether or not the emission process occurs faster in the triplet monomer than the exciplex formation of dimer. Judging from the experimental observation and computational results, it is likely concluded that the emission occurs without the dimer formation in gas phase and CHCl3 solvent. To investigate the relative stability of polymorphic crystals in the ground state and the reason for the difference in excitation and emission spectra among polymorphic crystals, we performed the

31



periodic QM/MM calculation with the self-consistent point-charge approximation. In the ground state, the QM/MM calculation provided the reasonable crystal structure and relative stability that 1y is more stable than 1b, which agrees with the experimental observation. In 2b, the relative energy is calculated to increase in the order 2bP < 2g < 2bPT < 2bT , but the entropy of 2bPT is larger than that of 2bP , 91,92 suggesting that the Gibbs free energy difference between 2bPT and 2bP is very small. The 2g→2bP SCSC transition is slightly exothermic but the 2g→2bPT SCSC transition is endothermic; the latter exothermicity agrees with the experimental observation; however, it is not easy to determine computationally which of 2bP and 2bPT is the crystal phase of 2b because of the very small energy difference and the contribution of entropy term. In the absorption spectra of 1b and 2b, the molecule in the crystal exhibits two peaks which are assigned to ∗ (PhNC) and π (Ph)→ π ∗ (PhNC) LLCT excitations in the low energy region. the πout (Ph)→ πout out in ∗ (PhNC) excitation at lower The molecule at the surface of the crystal exhibits the πout (Ph)→ πout

energy than that of the molecule in the crystal by 0.4 eV, because the CH-π interaction on the

π (Ph) enlarges the Eex value of intramolecular LLCT transition from Ph to PhNC and the CH-π interaction is stronger in the inside molecule of crystal than that at the surface. In 1y and 2g, on the other hand, the short Au-Au distance raises the φ(dσ -dσ )a orbital energy and increases the over∗ (PhNC) orbitals to lower the bonding φ lap between the πout ∗ -π ∗ )b orbital energy, leading PhNC(πout out

to the low energy MMLCT excitation from the φ(dσ -dσ )a to the φPhNC(πout ∗ -π ∗ )b . This excitation is out observed at lower energy than the largest absorption peak of 1b and 2b by more than 1.0 eV. In the Eem values of 1b and 2b, the locally excited states 3 LE1 and 3 LE2 are calculated as the ∗ (PhNC) in the 3 LE1 and lowest energy triplet state; the excitation occurs from πout (PhNC) to πout ∗ (Ph) in the 3 LE2. The E 3 from πout (Ph) to πout em value of LE1 is calculated to be 2.6 eV in 1b

and 2.7 eV in 2b, respectively, which are assigned to the largest emission peak in the low energy region. In 1y and 2g, the MMLCT excited states 3 MMLCTs are calculated to be more stable than the locally excited states 3 LEs. In these complexes, the excitation occurs from the φ(dσ -dσ )a to the

φPhNC(πout ∗ -π ∗ )b . The Eem value (2.37 eV) of 1y is calculated to be smaller than that (2.46 eV) of 2g out by 0.09 eV and the red-shift of the Eem value by the 1b→1y SCSC phase transition is calculated to

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be 0.35 eV, which agrees well with the experimental observation (0.13 and 0.34 eV, respectively). Because the φ(dσ -dσ )a and φPhNC(πout ∗ -π ∗ )b orbital energies are considerably influenced by the SCSC out phase transition through the change in the Au-Au distance and intermolecular torsion angle η . These are reasons why both of absorption and emission spectra largely differ between polymorphic crystals 1b and 1y and between 2b and 2g. In the present study, our QM/MM method was successfully applied to the absorption and emission spectra in crystal. The consideration of surrounding molecular effect is indispensable to determine the structure of dimer or aggregate in crystal which significantly differs from those in gas and solution phases. In particular, our method clearly shows the characteristic features of polymorphs; for instance, the MMLCT excited state is possible in some of polymorphs in which the Au-Au distance is short.

Acknowledgement This work was financially supported in part by JSPS Grant-in-Aid for Young Scientists (No. JP17K14437) and by the Japanese Ministry of Education, Culture, Sports, Science and Technology (MEXT) via the “Grant-in-Aid for Scientific Research on Innovative Areas; SoftCrystal” (No. JP18H04513). This paper is based on some results obtained from a project commissioned by the New Energy and Industrial Technology Development Organization (NEDO) supported by the Ministry of Economy, Trade and Industry, Japan. We are grateful to IMS computer center and ACCMS, Kyoto University for the supply of CPU time.

Supporting Information Available Details of RISM-SCF method, evaluation of QM-QM interaction energy, absorption spectra calculated in gas phase and weakly polar CHCl3 solvent, 5SA-GMC-QDPT-calculated profiles of the ground state, the energy and MO character of dimer structures in CHCl3 solvent, analysis of probability density function of vibrational state against the τ angle in CHCl3 solvent, NBO charges

33



on Au, Ph, and PhNC moieties, dependence of TD-DFT-calculated excitation energies on functionals, the QM/MM calculated geometrical parameters, the QM/MM calculated MO character of absorption and emission, difference in QM-QM interaction among 2bP , 2bPT , and 2bT , and experimentally observed absorption, excitation, and emission spectra of 1 in CH2 Cl2 solvent. This material is available free of charge via the Internet at http://pubs.acs.org/.

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(19) Lim, S. H.; Olmstead, M. M.; Balch, A. L. Inorganic topochemistry. Vapor-induced solid state transformations of luminescent, three-coordinate gold(I) complexes. Chem. Sci. 2013, 4, 311-318. (20) Ito, H.; Muromoto, M.; Kurenuma, S.; Ishizaka, S.; Kitamura, N.; Sato, H.; Seki, T. Mechanical stimulation and solid seeding trigger single-crystal-to-single-crystal molecular domino transformations. Nat. Commun. 2013, 4, 2009. (21) Seki, T.; Sakurada, K.; Ito, H. Controlling mechano- and seeding-triggered single-crystal-tosingle-crystal phase transition: Molecular domino with a disconnection of aurophilic bonds. Angew. Chem. Int. Ed. 2013, 2, 12828-12832. (22) Seki, T.; Sakurada, K.; Muromoto, M.; Seki, S.; Ito, H. Detailed investigation of the structural, thermal, and electronic properties of gold isocyanide complexes with mechanotriggered single-crystal-to-single-crystal phase transitions. Chem. Eur. J. 2016, 22, 19681978. (23) Ito, H.; Saito, T.; Oshima, N.; Kitamura, N.; Ishizaka, S.; Hinatsu, Y.; Wakeshima, M.; Kato, M.; Tsuge, K.; Sawamura, M. Reversible mechanochromic luminescence of[(C6 F5 Au)2 (µ 1,4-diisocyanobenzene)]. J. Am. Chem. Soc. 2008, 130, 10044-10045. (24) Seki, T.; Kurenuma, S.; Ito, H. Luminescence color-tuning through polymorph doping: preparation of a white‐emitting solid from a single gold(I)-isocyanide complex by simple precipitation. Chem. Eur. J. 2013, 19, 16214-16220. (25) In particular, it was suggested that the broad peak of 2b arises from the remaining traces of the more unstable 2g domain because of the weak intensity of emission spectra of 2b but the emission in the energy range of 2.7 to 3.1 eV appears only in 2b. (26) Strictly speaking, it is believed that the experimentally observed excitation and absorption spectra do not largely differ in characteristic feature of low energy region; for example, see

37



Figure S12 in ESI. However, the excitation spectrum largely depends on not only the absorption band of molecule but also the deexcitation process exhibiting the emission band within the detection range. Therefore, it is usually difficult to compare the calculated absorption spectrum with the experimentally observed excitation spectrum in the high energy region. (27) Warshel, A.; Levitt, M. Theoretical studies of enzymic reactions: Dielectric, electrostatic and steric stabilization of the carbonium ion in the reaction of lysozyme. J. Mol. Biol. 1976, 103, 227-249. (28) Aono, S.; Sakaki, S. Proposal of new QM/MM approach for geometry optimization of periodic molecular crystal: Self-consistent point charge representation for crystalline effect on target QM molecule. Chem. Phys. Lett. 2012, 544, 77-82. (29) The Au-Au bond is not formed at the ground state in both of 1y and 2g despite the short Au-Au distance (∼ 3.2 Å), because both of the bonding and antibonding combinations of Au d orbitals are doubly occupied; actually, the Au-Au effective bond order is calculated to be zero in the ground state. Hence, strictly speaking, “dimer” in 1y and “hexamer” in 2g may not be appropriate in a formal sense. However, we used the terms of “dimer” and “hexamer” to represent molecular system when intermolculear Au-Au distance is around 3.2 Å at the ground state, according to the experimental works [20] and [21]. However, we did not use the term of “dimer” when the Au-Au distance is longer than 4.0 Å in crystal phase. In such case, we used the name “molecule” or “monomer”. In the excited state, we used the name of “dimer” when the Au-Au bond was formed between two Au complexes. If not, we used the name “molecule” or “monomer”. In gas phase and CHCl3 solvent, we used the name of “dimer” when two monomers form the π -π stacking structure or the CH-π interacting structure. (30) The lattice vector can be optimized by the periodic QM/MM method. However, it is timeconsuming. Also, the purpose of this work is to investigate the absorption and emission spec-

38


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tra in molecular crystal, which is challenging. As the first step of such theoretical study, we employed the experimental lattice vector. (31) One of the main tasks of this work is to study theoretically emission spectrum in molecular crystal. In the triplet state, we must consider the possibility that the Au-Au distance becomes very short because of the formation of Au-Au bond in some of crystal structures. In the geometry optimization of the triplet excited state, therefore, the position of Au of target QM molecular system must be optimized, considering surrounding QM and MM molecules whose positions and structures are taken to be the same as those in the ground state. In this regard, the ground state geometry is used for optimizing the excited state. To obtain good geometry of the excited state, we need the correct geometry at the ground sate. For such purpose, we optimized the ground state geometry using the Au position taken to be the same as that in the experimental work. Of course, the best is to optimize the ground state geometry correctly. However, we need very long computational time and huge efforts to optimize the ground state geometry including everything such as Au position, lattice vector, intermolecular distance, and so on, because the intermolecular distance is very flexible and its potential energy curve is very flat. Some error(s) at the ground state would induce significant error at the excited state. The inconsistency seemingly exists in geometry optimization between the ground state and the excited state, but this is not very unreasonable because the purpose of geometry optimization is different between the ground state and the excited state. (32) Aono, S.; Sakaki, S. QM/MM approach to isomerization of ruthenium(II) sulfur dioxide complex in crystal; comparison with solution and gas phases. J. Phys. Chem. C 2018, 122, 20701-20716. (33) Kitaura, K.; Ikeo E.; Asada, T.; Nakano, T.; Uebayasi, M. Fragment molecular orbital method: an approximate computational method for large molecules Chem. Phys. Lett. 1999, 313, 701-706.

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(34) Raghavachari, K.; Trucks, G. W.; Pople, J. A.; Head-Gordon, M. A fifth-order perturbation comparison of electron correlation theories. Chem. Phys. Lett. 1989, 157, 479-483. (35) Head-Gordon, M.; Pople, J. A.; Frisch, M. J. MP2 energy evaluation by direct methods. Chem. Phys. Lett. 1988, 153, 503-506. (36) Svensson, M.; Humbel, S.; Froese, R. D. J.; Matsubara, T.; Sieber, S.; Morokuma, K. ONIOM: A multilayered integrated MO + MM method for geometry optimizations and single point energy predictions. A test for Diels-Alder reactions and Pt(P(t-Bu)3 )2 + H2 oxidative addition. J. Phys. Chem. 1996, 100, 19357-19363. (37) Dapprich, S.; Komaromi, I.; Byun, K. S.; Morokuma, K.; Frisch, M. J. A new ONIOM implementation in Gaussian 98. 1. The calculation of energies, gradients and vibrational frequencies and electric Field derivatives. J. Mol. Struct. THEOCHEM, 1999, 462, 1-21. (38) Tuma, C.; Sauer, J. Treating dispersion effects in extended systems by hybrid MP2:DFT calculations-protonation of isobutene in zeolite ferrierite. Phys. Chem. Chem. Phys. 2006, 8, 3955-3965. (39) Svelle, S.; Tuma, C.; Rozanska, X.; Kerber, T.; Sauer, J. Quantum chemical modeling of zeolite-catalyzed methylation reactions: Toward chemical accuracy for barriers. J. Am. Chem. Soc. 2008, 130, 816-825. (40) Tuma, C.; Kerber, T.; Sauer, J. The tert-butyl cation in H-zeolites: Deprotonation to isobutene and conversion into surface alkoxides. Angew. Chem., Int. Ed. 2010, 49, 4678-4680. (41) Ab initio prediction of adsorption isotherms for small molecules in metal-organic frameworks: The effect of lateral interactions for methane/CPO-27-Mg J. Am. Chem. Soc. 2012, 134, 18354-18365. (42) Kundu, A.; Piccini, G.; Sillar, K. ; Sauer J. Ab initio prediction of adsorption isotherms for small molecules in metal-organic frameworks. J. Am. Chem. Soc. 2016, 138, 14047-14056. 40


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(43) Deshmukh, M.; Sakaki, S. Two-step evaluation of binding energy and potential energy surface of van der Waals complexes. J. Compt. Chem. 2012, 33, 617-628. (44) Zheng, J. -J.; Kusaka, S.; Matsuda, R.; Kitagawa, S.; Sakaki, S. Characteristic features of CO2 and CO adsorptions to paddle-wheel-type porous coordination polymer. J. Phys. Chem. C 2017, 121, 19129-19139. (45) Zheng, J. -J.; Kusaka, S.; Matsuda, R.; Kitagawa, S.; Sakaki, S. Theoretical Insight into Gate-Opening Adsorption Mechanism and Sigmoidal Adsorption Isotherm into Porous Coordination Polymer J. Am. Chem. Soc., 2018, 140, 13958-13969. (46) Becke, A. D. Density-functional thermochemistry. III. The role of exact exchange. J. Chem. Phys., 1993, 98, 5648-5652. (47) Vosko, S. H.; Wilk, L.; Nusair, M. Accurate spin-dependent electron liquid correlation energies for local spin density calculations: A critical analysis. Can. J. Phys., 1980, 58, 12001211. (48) Lee, C.; Yang, W; Parr, R. G. Development of the Colic-Salvetti correlation-energy formula into a functional of the electron density. Phys. Rev. B, 1988, 37, 785-789. (49) Miehlich, B.; Savin, A.; Stoll, H.; Preuss, H. Results obtained with the correlation energy density functionals of Becke and Lee, Yang and Parr. Chem. Phys. Lett., 1989, 157, 200-206. (50) Grimme, S.; Antony, J.; Ehrlich, S.; Krieg, H. A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu. J. Chem. Phys. 2010, 132, 154104. (51) The three-body interaction energy was evaluated at B3LYP-D3 level because the MP2 calculation of trimer is too time-consuming in the present system. (52) Aono, S.; Sakaki, S. Evaluation procedure of electrostatic potential in 3D-RISM-SCF method

41



and its application to hydrolyses of cis- and transplatin complexes. J. Phys. Chem. B 2012, 116, 13045-13062. (53) Aono, S.; Hosoya, T.; Sakaki, S. A 3D-RISM-SCF method with dual solvent boxes for a highly polarized system: application to 1,6-anhydrosugar formation reaction of phenyl α and β -D-glucosides under basic conditions. Phys. Chem. Chem. Phys. 2013, 17, 6368-6381. (54) Aono, S.; Mori, T.; Sakaki, S. 3D-RISM-MP2 approach to hydration structure of Pt(II) and Pd(II) complexes: unusual H-ahead mode vs usual O-ahead one. J. Chem. Theory Comput. 2016, 12, 1189-1206. (55) Schmidt, M. W.; Baldridge, K. K.; Boatz, J. A.; Elbert, S. T.; Gordon, M. S.; Jensen, J. H.; Koseki, S.; Matsunaga, N.; Nguyen, K. A.; Su, S.; Windus, T. L.; Dupuis, M.: Montgomery, J. A. General atomic and molecular electronic structure system. J. Comput. Chem. 1993, 14, 1347-1363. (56) Andrae, D.; Haeussermann, U.; Dolg, M.; Stoll, H.; Preuss, H. Energy-adjusted ab initio pseudopotentials for the second and third row transition elements. Theor. Chem. Acc. 1990, 77, 123-141. (57) Cornell, W. D.; Cieplak, P.; Bayly, C. I.; Gould, I. R.; Merz, K. M., Jr.; Ferguson, D. M.; Spellmeyer, D. C.; Fox, T.; Caldwell, J. W.; Kollman, P. A. A second generation force field for the simulation of proteins, nucleic acids, and organic molecules. J. Am. Chem. Soc. 1995, 117, 5179-5197. (58) Mendizabal, F.; Zapata-Torres, G.; Olea-Azar C. Theoretical study of the d10 -d8 interaction between Au(I) and Au(III) on the cis/trans-[PH3 Au(I)C(L)=C(L)Au(III)(R)2 PH3 ] (R=-H, CH3 ; L=-H, -CH3 ) systems. Chem. Phys. Lett. 2003, 382, 92-99. (59) LJ parameter of Au atom was determined by fitting the potential energy calculated for the system consisting of two gold(I)-isocyanide complexes 1 and that consisting of one gold(I)isocyanide complex and CH3 Cl in gas phase at the MP2 level with the BSSE correction. 42


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For the former calculation, we changed the Au-Au distance between two gold(I) complexes, where the dihedral angle was fixed to 90 degree. For the latter calculation, we changed the Au· · · Cl distance between one gold(I) complex and CH3 Cl, where the angle of C-Cl· · · Au was fixed to 180 degree. The same LJ parameters were employed for both of 1 and 2 in crystal phase and CHCl3 solvent. (60) Casida, M. E. Time-dependent density functional response theory for molecules, In Recent Advances in Density Functional Methods; Chong, D. P. Ed.; World Scientific: Singapore, 1995; Vol. 1, pp. 155-192. (61) Casida, M. E. Time-dependent density functional response theory of molecular systems: theory, computational methods, and functionals, In Recent Developments and Applications of Modern Density Functional Theory; Seminario, J. M. Ed.; Elsevier: Amsterdam, 1996; Vol. 4, pp. 391-440. (62) Bauernschmitt, R.; Ahlrichs, R. Treatment of electronic excitations within the adiabatic approximation of time dependent density functional theory. Chem. Phys. Lett. 1996, 256, 454464. (63) Ebisuzaki, R.; Watanabe, Y.; Nakano, H. Efficient implementation of relativistic and nonrelativistic quasidegenerate perturbation theory with general multiconfigurational reference functions. Chem. Phys. Lett. 2007, 442, 164-169. (64) Nakano, H.; Uchiyama, R.; Hirao, K. Quasi-degenerate perturbation theory with general multiconfiguration self-consistent field reference functions. J. Comput. Chem. 2002, 23, 11661175. (65) In the RISM-SCF method, 66,67 electronic structure of solute is calculated in the presence of equilibrium solvent distribution about the solute based on the statistical mechanics of liquid. 68,69 Analytical gradient of the RISM-SCF free energy was evaluated under the variational principle. 70 Based on the density functional theory of non-uniform polyatomic liq43



uid, 71,72 the 3D-RISM integral equation was developed by many researchers; 73–75 see Supporting Information (SI) pages S2-S3 for detail. Kovalenko and Hirata derived the 3D generalization of the RISM method from the six-dimensional (6D) molecular Ornstein-Zernike integral equation and combined it with the electronic structure calculations. 76–82 Analytical gradient of the 3D-RISM-SCF free energy was also derived at both the DFT and HF levels. 83,84 (66) Ten-no, S.; Hirata, F.; Kato, S. A hybrid approach for the solvent effect on the electronic structure of a solute based on the RISM and Hartree-Fock equations. Chem. Phys. Lett. 1993, 214, 391-396. (67) Ten-no, S.; Hirata, F.; Kato, S. Reference interaction site model self-consistent field study for solvation effect on carbonyl compounds in aqueous solution. J. Chem. Phys. 1994, 100, 7443-7453. (68) Chandler, D.; Anderson, H. C. Optimized cluster expansions for classical fluids. II. Theory of molecular liquids. J. Chem. Phys. 1972, 57, 1930-1931. (69) Hirata, F.; Rossky, P. J. An extended RISM equation for molecular polar fluids. Chem. Phys. Lett. 1981, 83, 329-334. (70) Sato, H.; Hirata, F.; Kato, S. Analytical energy gradient for the reference interaction site model multiconfigurational selfconsistent-field model. J. Chem. Phys. 1996, 105, 1546-1551. (71) Chandler, D.; McCoy, J.; Singer, S. Density functional theory of nonuniform polyatomic systems. I. General formulation. J. Chem. Phys. 1986, 85, 5971-5976. (72) Chandler, D.; McCoy, J.; Singer, S. Density functional theory of nonuniform polyatomic systems. II. Rational closures for integral equations. J. Chem. Phys. 1986, 85, 5977-5982. (73) Beglov, D.; Roux, B. Numerical solution of the hypernetted chain equation for a solute of arbitrary geometry in three dimensions. J. Chem. Phys. 1995, 103, 360-364. 44


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(74) Beglov, D.; Roux, B. An integral equation to describe the solvation of polar molecules in liquid water. J. Phys. Chem. B 1997, 101, 7821-7826. (75) Du, Q.; Beglov, D.; Roux, B. Solvation free energy of polar and nonpolar molecules in water: An extended interaction site integral equation theory in three dimensions. J. Phys. Chem. B 2000, 104, 796-805. (76) Kovalenko, A.; Hirata, F. Self-consistent description of a metal-water interface by the KohnSham density functional theory and the three-dimensional reference interaction site model. J. Chem. Phys. 1999, 110, 10095-10112. (77) Kovalenko, A.; Hirata, F. Potential of mean force between two molecular ions in a polar molecular solvent: A study by the three-dimensional reference interaction site model. J. Phys. Chem. B 1999, 103, 7942-7957. (78) Kovalenko, A. Three-dimensional RISM theory for molecular liquids and solid-liquid interfaces, In Molecular Theory of Solvation; Hirata, F., Ed.; Understanding Chemical Reactivity (series); Mezey, Paul G., Series Ed.; Kluwer Acadamic Publishers: Dordrecht, The Netherlands, 2003; Vol. 24, pp 169-275. (79) Kovalenko, A.; Hirata, F. Three-dimensional density profiles of water in contact with a solute of arbitrary shape: A RISM approach. Chem. Phys. Lett. 1998, 290, 237-244. (80) Kovalenko, A.; Hirata, F. Potentials of mean force of simple ions in ambient aqueous solution. I. Three-dimensional reference interaction site model approach. J. Chem. Phys. 2000, 112, 10391-10402. (81) Kovalenko, A.; Hirata, F. Potentials of mean force of simple ions in ambient aqueous solution. II. Solvation structure from the three-dimensional reference interaction site model approach, and comparison with simulations. J. Chem. Phys. 2000, 112, 10403-10417.

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(82) Sato, H.; Kovalenko, A.; Hirata, F. Self-consistent field, ab initio molecular orbital and threedimensional reference interaction site model study for solvation effect on carbon monoxide in aqueous solution. J. Chem. Phys. 2000, 112, 9463-9468. (83) Gusarov, S.; Ziegler, T.; Kovalenko, A. Self-consistent combination of the three-dimensional RISM theory of molecular solvation with analytical gradients and the Amsterdam density functional package. J. Phys. Chem. A 2006, 110, 6083-6090. (84) Yoshida, N.; Hirata, F. A new method to determine electrostatic potential around a macromolecule in solution from molecular wave functions. J. Comput. Chem. 2006, 27, 453-462. (85) Kamath, G.; Georgiev, G.; Potoff, J. J. Molecular modeling of phase behavior and microstructure of acetone-chloroform-methanol binary mixtures. J. Phys. Chem. B, 2005, 109, 1946319473. (86) Kaminski, J. W.; Gusarov, S.; Wesolowski, T. A.; Kovalenko, A. Modeling solvatochromic shifts using the orbital-free embedding potential at statistically mechanically averaged solvent density. J. Phys. Chem. A 2010, 114, 6082-6096. (87) Gusarov, S.; Pujari, B. S.; Kovalenko, A. Efficient treatment of solvation shells in 3D molecular theory of solvation. J. Comput. Chem. 2012, 33, 1478-1494. (88) Perkyns, J. S.; Lynch, G. C.; Howard, J. J.; Pettitt, B. M. Protein solvation from theory and simulation: Exact treatment of Coulomb interactions in three-dimensional theories. J. Chem. Phys. 2010, 132, 064106. (89) Glendening, E. D.; Badenhoop, J. K.; Reed, A. E.; Carpenter, J. E.; Bohmann, J. A.; Morales, C. M.; Weinhold, F. NBO 5.0. Theoretical Chemistry Institute, University of Wisconsin, Madison, 2001. (90) In our approach, three-body interaction is not taken explicitly into consideration in the QMavg

MM interaction but involved in the QM-QM interaction. In the calculation of Ecrystal (method 46


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1), four gold(I) complexes were employed as the QM molecular system except for 2g in which six gold(I) complexes were employed as the QM molecular system. In this case, two-, three-, and four-body QM-QM interactions were evaluated in four QM molecules in 1b, 1y, and 2b and two-, three-, four-, five-, and six-body QM-QM interactions were evaluated in six avg2

QM molecules in 2g. In the calculation of Ecrystal (method 2), QM calculation was carried out for all possible dimer and trimer pairs consisting of one of the target QM molecules and one or two QM molecule(s) selected from the nearest neighboring eight QM molecules; in other avg2

words, the larger number of three-body QM-QM interaction was counted in the Ecrystal than avg

in the Ecrystal . Though the number of three-body QM-QM interactions is different between the Ecrystal and Ecrystal , the relative energy between 1b and 1y is 1.9 kcal mol−1 in the Ecrystal avg

avg2

avg

(method 1) and 1.4 kcal mol−1 in the Ecrystal (method 2). Because the energy difference avg2

avg

avg2

avg

is similar between the Ecrystal and Ecrystal , the Ecrystal value is not bad, suggesting that the avg

geometry optimization based on the Ecrystal is not bad. (91) There are 8 stable unit cell structures in 2bPT but 4 structures in 2bP (Figure S6 in ESI). Therefore, the entropy S of 2bPT is R·ln(8)/4 and that of 2bP is R·ln(4)/4 (one unit cell has four molecules), with which 2bPT can receive 0.1 kcal mol−1 stabilization energy from the entropy term at room temperature. This value does not overcome the enthalpy difference between 2bPT and 2bP . However, the error in potential energy of about 1 kcal mol−1 is not bad, considering that the size of molecule is not small and the large molecular crystal system is calculated here. (92) The vibrational entropy is one of the important factors to determine thermodynamical stability. However, the intermolecular frequency in crystal is very small and contains in many cases unharmonicity which induces significant error in evaluating intermolecular vibrational entropy. Also, it is difficult to calculate the intermolecular frequency in the QM/MM method, because there are huge numbers of vibrations including QM-QM vibrations, QM-MM vibrations, and MM-MM vibrations. This issue is open question which should be considered in

47



future. (93) In crystal, the QM/MM-calculated excitation energies are larger than the experimental values by about 0.4 eV, while the 3D-RISM-SCF-calculated excitation energies in CHCl3 solution agree with the experimental ones (purple lines in Figures S1-S2 in ESI). We could not find clear reason of these results. However, the good agreement of the computational results with experimental ones in CHCl3 solution indicates that the electronic structure of one gold(I) complex can be calculated successfully in CHCl3 solution, incorporating solvation effects with 3D-RISM-SCF model. This result suggests that the crystal effect is not incorporated perfectly in the QM/MM calculation to induce somewhat error of absorption spectrum in the solid crystal. In our QM/MM calculations, the crystal effect is incorporated using LJ potential and charge-distribution, which is similar to that by 3D-RISM-SCF model. However, several important differences exist; in solution, the charge-distribution of CHCl3 is considered in the calculation, where the distribution of solvent molecules is determined according to statistic mechanics. Also, the charge-distribution becomes completely random at infinitely separated position from the target QM system because solvent molecules are completely random at the infinite separation, which means that the solvent molecules at sufficiently separated position do not provide large electrostatic influence to the target molecule. In crystal, the orientation of MM molecules is taken to be the same as the QM target molecules, which means that the infinitely separated molecules in crystal provide significant electrostatic influence to the target molecule because molecules at infinitely separated position are regularly oriented. Moreover, the gold(I) complex is much more polarized than CHCl3 , indicating that the MM molecules provide larger electrostatic influence to the target QM molecule than CHCl3 . As a result, the error of electrostatic interaction becomes larger in the molecular crystal than in the solution. The other reason is the error of experimentally measured absorption spectrum. In crystal, it is not clear whether molecules at the surface mainly contribute to the absorption spectrum or molecules at inside of crystal mainly contribute to the absorption spectrum. Maybe, both contribute to the experimental absorption spectra but it is not clear how much each molecule 48


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contributes to the absorption spectrum. This means that the experimental spectrum is not clear very much relative to that in solution. ∗ (PhNC) (94) In the TD-DFT calculation of four QM molecules in gas phase, the πout (Ph)→ πout

excitation energy was calculated to be 3.2 eV, using the optimized geometry reported in the previous work. 20 This value well agrees with the experimentally observed small peak at 3.3 eV. However, the modeling employed in the previous calculation does not seem very good, as follows: the excitation calculated at 3.2 eV occurs on the two outside monomers, which have no CH-π interaction between the π (Ph) orbital of one monomer and the H atom of the ∗ (PhNC) excitation energy of two PhNC of remaining monomers, while the πout (Ph)→ πout

central monomers, which have one CH-π interaction between the π (Ph) of one monomer and the H atom of the PhNC of other monomer, was calculated to be 3.6 - 3.7 eV. If there is no defect in crystal, molecule with no CH-π interaction does not exist in crystal and on the surface of 1b. The Eex value (3.7 eV) calculated by the present QM/MM method is similar to the Eex value calculated for two central monomers of four QM molecules in gas phase (the previously employed model). This means that the Eex value (3.2 eV) calculated for the two outside monomers of four QM molecules is not reasonable. These results suggest that the Eex value (3.6 - 3.7 eV) calculated for the molecule at the surface of the crystal is not very bad, though it is about 0.4 eV larger than the experimental one. (95) The dσ (Au) consists of Au 5dσ orbital and Au 6s orbital. (96) The small oscillator strength of this LLCT excitation in 1y was confirmed by the TD-DFT QM/MM calculation of dimer model for 1y, considering enough number of excited states, because such TD-DFT calculation of four QM molecules including enough number of excited states was difficult for 1y due to heavy CPU cost. (97) The large oscillator strengths calculated here are not seemingly consistent with the experimentally observed spectrum at shoulder. However, this is not unreasonable, as follows: All the molecules inside in crystal cannot participate well in absorption spectrum and the 49



molecules on the surface more contribute to absorption spectrum than the molecules in crystal; in other words, the oscillator strength experimentally observed should be smaller for the inside molecules than for molecules on the surface. Other plausible reason is that the experimentally observed spectrum is not the absorption but the excitation spectrum. (98) In solution phase, the translation entropy was calculated with the modified free volume; see Mammen, M. Shakhnovich, E. I.; Deutch, J. M.; Whitesides, G. M. Estimating the entropic cost of self-assembly of multiparticle hydrogen-bonded aggregates based on the cyanuric acid-melamine lattice. J. Org. Chem. 1998, 63, 3821-3830. (99) Trucks, G. W.; Salter, E. A.; Sosa, C.; Bartlett, R. J. Theory and implementation of the MBPT density matrix: An application to one-electron properties. Chem. Phys. Lett., 1988, 147, 359-366. (100) The RISM free energy ∆A is the sum of the solute energy Esolu and the solvation free energy ∆µ . In other words, the ∆A does not contain the zero-point energy and entropy term of the solute motions. The Gibbs free energy ∆G is corrected by adding the zero-point energy and entropy term to the RISM free energy ∆A. (101) On the basis of the MP4(SDQ) with the BSSE correction, we discussed the possibility of dimer formation. However, the DFT/B3LYP-D3-calculated energy profile differs from that calculated at the MP4(SDQ) level with the BSSE correction; for instance, the most stable dimer of 1 is formed with the Gibbs free energy change ∆G0 of -8.6 kcal mol−1 and that of 2 is formed with the ∆G0 of -7.0 kcal mol−1 in CHCl3 solvent (see Table S4 in ESI), indicating that the dimer is formed at the ground state. At the triplet excited state, 3 (π -π ) is more favorably formed than at the ground state because the ∆G0 of 3 (π -π ) is calculated to be -13.8 kcal mol−1 for 1 and -10.8 kcal mol−1 for 2. Based on the experimental and computational results of absorption and emission spectra, however, it is likely that the DFT/B3LYP-D3-calculated ∆G0 seems to overestimate the stabilization energy of dimer and the dimer is not formed at the ground state and excited states, as discussed in “Results and Discussion” section. 50


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(102) Wiberg, K. Application of the pople-santry-segal CNDO method to the cyclopropylcarbinyl and cyclobutyl cation and to bicyclobutane. Tetrahedron 1968, 24, 1083-1096. (103) Iwamura, M.; Nozaki, K.; Takeuchi, S.: Tahara, T. Real-time observation of tight AuAu bond formation and relevant coherent motion upon photoexcitation of [Au(CN)2 − ] oligomers. J. Am. Chem. Soc. 2013, 135, 538-541. (104) Kim, K. H.; Kim, J. G.; Nozawa, S.; Sato, T.; Oang, K. Y.; Kim, T. W.; Ki, H.; Jo, J.; Park, S.; Song, C. et. al. Direct observation of bond formation in solution with femtosecond X-ray scattering. Nature 2015, 518, 385-389. (105) Actually, in 1b and 2b, the π -π ∗ locally excited state is the lowest energy triplet state, which exhibited the localized SOMOs on one of the target QM molecules. This means that the model consisting of four QM molecules is enough for 1b and 2b. In 1y and 2g, the MMLCT excited state is the lowest energy triplet state. This MMLCT state exhibited the delocalized SOMOs in which the adjacent two QM molecules sandwiching the target QM dimer have moderately large MO coefficients but the next nearest neighboring two QM molecules have tiny MO coefficients, suggesting that four QM molecules are not enough but six QM molecules are enough for investigating the excited state of 1y and 2g. (106) The frequency of Au complex 1 at the ground state was calculated for the monomer in gas phase, using the DFT method with the B3LYP-D3 functional. (107) Using the Wiberg bond index in the NAO basis, the effective bond order between two Au atoms is calculated to be 0.30 for 3 MMLCT1, 0.26 for 3 MMLCT2, and 0.36 for 3 MMLCT3,

which are similar to those (0.30 and 0.36) in the 3 (π -π )P and 3 (CH-π )P dimers,

respectively, in CHCl3 solvent.

51



Page 52 of 67

Table 1: Relative stability (in kcal mol−1 ) of polymorphic crystals.a 1y 1b (A) Method 1b 1.9 0.0

avg

Ecrystal [B3LYP-D3]

(B) Method 2d 1.4 (0.3)e avg2 Ecrystal [CCSD(T)/MP2/B3LYP-D3] 1.3 (0.2)e avg2 Component of Ecrystal [CCSD(T)/MP2/B3LYP-D3] avg2 -0.4 ESelf(QM)

avg2 Ecrystal [B3LYP-D3]

avg2 avg2 EInt(QM-QM) + EInt(QM-MM) avg2

EInt(QM-QM) avg2

EInt(QM-MM)

2bP

2bPT

2bT

2g

0.0

0.3

1.1

0.5 [2.2]c

0.0 (0.0) 0.0 (0.0)

0.0 (0.0) 0.0 (0.0)

0.9 (1.0) 1.1 (1.2)

1.9 (2.1) 2.4 (2.6)

1.8 (2.5) 0.4 (1.1)

0.0

0.0

0.0

0.0

-0.1

-33.0 (-40.4)e -30.2 (-37.6)e -2.8

-34.7 (-41.0) -23.9 (-30.2) -10.8

1.7 -4.5

-3.2 -7.6

-34.2 -33.1 -31.8 (-41.7) (-40.5) (-39.1) -26.7 -25.5 -24.7 (-34.2) (-32.9) (-32.0) -7.5 -7.6 -7.1

-33.7 (-40.5) -24.9 (-31.7) -8.8

avg2

Component of EInt(QM-MM) ES part LJ part a E avg , crystal

avg2

avg

avg2

1.2 -8.7

1.0 -8.6

1.2 -8.3

Ecrystal , and ESelf(QM) of 1y and 2bP are taken to be zero. b Ecrystal is calculated by Eq. (1). c In bracket is the energy relative to that of 2bP calculated by employing six gold(I) complexes as the QM avg2 molecular system. d Ecrystal is calculated by Eqs. (4) and (8). e In parentheses are calculated without three-body QM-QM interactions.

52


-0.7 -8.1

Page 53 of 67 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 2: Relative stability and emission energy Eem of monomer and dimers of (A) 1 and (B) 2 in gas phase and weakly polar CHCl3 solvent.a,b monomer dimerc 3 (CH-π )NB Expt. dissociated 3 (π -π )P 3 (CH-π )P P (A) 1 Potential energy ∆E and RISM free energy ∆A (in kcal mol−1 ) ∆E in gas phase 0.0 -28.1 -24.9 -22.0 (-15.1)d ∆A in CHCl3 0.0 -23.2 -22.1 -18.3 (-9.8)d Gibbs free energy ∆G0 (in kcal mol−1 ) ∆G in gas phase 0.0 -10.1 -7.6 -3.9 (3.0) ∆G in CHCl3 0.0 -13.8 -12.9 -9.4 (-0.9) Eem (in eV) in gas phase 2.73 (2.96) 1.86 2.45 2.73 (3.10) e in CHCl3 2.92 2.71 (2.91) 1.97 2.43 2.72 (3.05) (B) 2 Potential energy ∆E and RISM free energy ∆A (in kcal mol−1 ) ∆E in gas phase 0.0 -27.9 -22.9 -24.2 (-15.5)d ∆A in CHCl3 0.0 -22.3 -20.7 -20.0 (-10.3)d Gibbs free energy ∆G0 (in kcal mol−1 ) ∆G in gas phase 0.0 -8.7 -5.0 -4.6 (4.1) ∆G in CHCl3 0.0 -10.8 -9.9 -10.0 (-0.3) Eem (in eV) in gas phase 2.61 (3.02) 1.90 2.48 2.60 (2.97) in CHCl3 2.85 f 2.58 (2.99) 2.04 2.51 2.59 (2.95) a Evaluated

by the U-DFT and 3D-RISM-SCF-U-DFT with the B3LYP-D3 functional, where the BSSE correction was made. b The sum of energies of isolated monomers at the singlet or triplet state taken to be zero. c “CH-π ” and “π -π ” represent the CH-π interacting structure and π -π stacking one, respectively; see Figure S11 in ESI. d In parentheses are calculated at the MP4(SDQ) level with the BSSE correction, which is approximately calculated by adding the difference between PCM-MP2 and PCM-MP4(SDQ) free energies to the RISM-MP2 free energy. However, we could not obtain reasonable binding energy for 3 (π -π ) and 3 (CH-π ) dimers at the MP2 to MP4(SDQ) levels, these dimers have Au-Au bonding P P interaction at the triplet excited state, as represented by non-zero Au-Au effective bond order, and such electronic structure cannot be calculated well by Moller-Plesset perturbation theory due to small HOMO-LUMO energy gap. e Experimentally observed in CH2 Cl2 solvent; see Figure S12 in ESI. f Experimentally observed in CH2 Cl2 solvent; see ESI of Ref. [21].

53



Page 54 of 67

Table 3: Relative energy (∆E) and emission energy Eem of polymorphic crystals 2b and 2g.a,b (A) 1b L1c

L2

on surfaced in crystal

0.0 0.0

7.0 8.4

on surfaced in crystal

2.73 3.08 2.71 3.10 2.53, 2.72

Expt.

∆E (kcal mol−1 )

ML1

ML2

(B) 1y L1

L2

0.0 0.0

2.0 1.1

4.4 3.2

9.6 9.2

2.30 2.37

2.33 2.35

Expt.

Eem (eV)

(C) 2b

on surface f in crystal on surface f in crystal

2.19

2bPT e

2bP

2bT L1 L2 Expt. ∆E (kcal mol−1 ) 0.0 8.5 0.0, 1.4 11.0, 12.9 0.0 9.6 0.0 10.3 0.0, 0.1 10.5, 11.2 0.0 11.0 Eem (eV) 2.65 3.06 2.67, 2.66 3.07, 3.10 2.66 3.08 2.61 3.11 2.63, 2.62 3.12, 3.12 2.63 3.12 2.7 - 3.0 L1c

2.73 2.79 2.72 2.77 (D) 2g

L2

L1

L2

a Evaluated

ML1 ML2 ML3

L1

L2

0.8 1.8

0.3 0.5

0.0 0.0

1.4 2.4

5.4 6.0

2.48 2.52

2.45 2.46

2.45 2.46

2.69 2.68

2.92 2.92

Expt.

2.32

by the QM/MM calculation with U-DFT/B3LYP-D3. b The energies at “LE1”s of 2bP , 2bPT , and 2bT and that at “MMLCT3” of 2g are taken to be zero. c “L1”, “L2”, “ML1”, “ML2”, and “ML3” represent 3 LE1, 3 LE2, 3 MMLCT1, 3 MMLCT2, and 3 MMLCT3, respectively. d Molecule on ac-surface was calculated for 1b, while that on ab-surface was calculated for 1y. e In 2bPT , the first and second values correspond to the energies of parallel and twisted monomers, respectively. f Molecule on bc-surface was calculated for 2b and 2g.

54


Page 55 of 67 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(a) Au complex 1. 1 Au C N Ph

CH∙∙∙π

1b

π∙∙∙π

1y Au

Au

lattice

4.73 Å

PhNC

PhNC Ph

Au PhNC

Au

73 Å 5.73

3.17 Å

PhNC

Au Ph

3.79 Å

PhNC

Au

3.79 Å

4.73 Å

PhNC PhNC

Au

Au

twisted

parallel All PhNC moieties have one π-π stacking interaction.

All PhNC moieties have no π-π stacking interaction.

(b) Au complex 2. 2 Me

lattice

Me dimPhNC

π∙∙∙π

2g

Ph

PhNC

Au C N Ph

CH∙∙∙π

2b

PhNC Au

Ph

Ph

PhNC

Au6

PhNC

3.11 Å mono6

4.78 8Å PhNC

Ph

Au

Au5

Ph

3.20 Å

Ph

Au4 PhNC Au3 3.27 Å

PhNC

3.24 Å

PhNC

Au2

mono1

parallel + twisted

3.20 Å PhNC

PhNC

Au1

All PhNC moieties have no π-π stacking interaction.

4 parallel + 2 twisted Two PhNC moieities of mono1 and mono6 have one π-π stacking interaction but other four PhNC moieties have no π-π stacking one.

Scheme 1: Experimentally observed structures of (a) 1 and (b) 2 in crystal.

55



(b) Complex 2 normalized intensity based on excitation spectrum

(a) Complex 1

normalized intensity

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 56 of 67

wavelength [nm]

wavelength [nm]

(c) Characteristic features

1b Au-Au excitation E [eV] emission E [eV]

SCSC

long 4.0 2.5 - 2.7

1y

short 2.9 2.2

2g

SCSC

2b

long short 3.3 - 4.0 4.0 2.3 2.2 (2.7 - 3.1)

Scheme 2: Experimentally observed excitation (solid line) and emission spectra (dotted line) of polymorphic crystals (a) 1b and 1y, (b) 2b and 2g, and (c) their characteristic features.

56


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(b) 1y

(a) 1b and 2b

(c) 2g

long short neighboring monomer

target two monomers

long long

middle

neighboring dimer

short middle

target dimer

long

neighboring monomer

long

neighboring dimer

long surrounding molecules

long

short target hexamer

short short

short

short

middle

short

short

short

middle surrounding molecules

long

short

long surrounding molecules

short

Scheme 3: Difference in Au-Au distance among polymorphs (a) 1b and 2b, (b) 1y, and (c) 2g and models for investigating the emission spectrum.

57



parallel (τ = 0) π*in(PhNC) Unocc.

twisted (τ = 90)

-1.12 eV (-1.22 eV)

N C Au

-2.22 eV (-2.17 eV)

π*out (PhNC)

N C Au

π out (Ph)

-5.89 eV (-6.39 eV)

N C Au

N C Au

-1.39 eV π*out2 (PhNC) (-1.20 eV)

N C Au

π out2 (Ph)

-2.22 eV (-2.16 eV)

π*out (PhNC)

N C Au

-6.12 eV (-6.65 eV)

N C Au

π out (Ph)

dσ (Au)

-1.40 eV π*out2 (PhNC) (-1.20 eV)

N C Au

-5.89 eV (-6.40 eV)

N C Au

-6.36 eV (-6.76 eV)

dσ (Au)

-1.16 eV (-1.33 eV)

π*in(PhNC)

π out2 (Ph)

-6.05 eV (-6.64 eV)

N C Au

-6.36 eV (-6.76 eV)

Occ.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 58 of 67

N C Au

π out (PhNC)

-7.72 eV (-7.64 eV)

N C Au

N C Au

-8.06 eV

π out2 (PhNC) (-7.87 eV) N C Au

-7.64 eV

-8.07 eV

π out (PhNC) (-7.58 eV) π out2 (PhNC)(-7.88 eV) N C Au

N C Au

Scheme 4: Important MOsa,b participating in low energy excitations of 1 at the R-DFT/B3LYPD3 level; a πout (Ph) and πout2 (Ph) are the highest and the next highest energy occupied out-of∗ (PhNC) is unoccupied in-plane π ∗ MO of the PhNC, plane π MOs of the Ph, respectively, πin ∗ (PhNC) and π ∗ (PhNC) are the lowest and the next lowest energy unoccupied out-ofand πout out2

plane π ∗ MOs of the PhNC, respectively. b In parentheses are orbital energies calculated at the 3D-RISM-SCF-R-DFT/B3LYP-D3 level in weakly polar CHCl3 solvent.

58


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intra-molecular torsion 2i

1i

1i

2i

τ i ≡ τ(CPh -CPh -CPhNC -CPhNC )

1i

1i

j

1j

i

1i

Au CPhNC

CPhNC

CPhNC

Au C N j

1j

Au CPhNC

Au C N Ph

i

η i,j ≡ η(CPhNC -Au -Au -CPhNC )

2i

2i

CPh 1i CPh

inter-molecular torsion

PhNC

Ph

Au C N

Scheme 5: Definitions of intra- and intermolecular torsion angles τ and η .

59


PhNC

π(PhNC) has no CH-π interaction unlike inside in crystal (one CH-π).


60 π(Ph) has one CH-π interaction unlike inside in crystal (two CH-π).

Au3

Au1 Au2

π(Ph) of mono1 and 6 has one CH-π interaction unlike inside in crystal (two CH-π).

Au4 Au5

Au6

symmetrycally minimal subunit

π(Ph) has one CH-π interaction unlike inside in crystal (two CH-π).

ab-surface of 1y

π(PhNC) has one CH-π and π-π interactions like inside.

bc-surface of 2g

π(Ph) has one CH-π interaction unlike inside in crystal (two CH-π).

π(PhNC) of mono2 and 5 has no CH-π interaction unlike inside in crystal (one CH-π).

π(PhNC) has one CH-π interaction like inside in crystal.

ac-surface of 1b

Scheme 6: Difference between inter-molecular interaction between molecules at the surface and that in the crystal.

π(PhNC) has no CH-π interaction like inside in crystal.

bc-surface of 2b

π(Ph) has two CH-π interactions like inside in crystal.

ab-surface of 1b

π∙∙∙π

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 CH∙∙∙π

The Journal of Physical Chemistry Page 60 of 67

Page 61 of 67 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(a) Polymorphic crystal of 1

1b

two minimum units Au

(b) Polymorphic crystal of 2

5.73 Au 4.73

Au2

9.06

Au

Au

9.06 Au4

2g

Au 3.18

4.78 Au3 mono3

3.18

Au Au

mono1 9.06 Au1 Au2 mono2 diff. 4.78 9.06 Au3 mono3 mono4 Au4 diff.

diff. mono1 and 3; parallel struct. mono2 and 4; twisted struct. The minimum unit cell consists of 4 molecules.

All; twisted struct. Au 3.20 3.24 Au

mono4 mono5

symmetrically minimal subunit

Au

mono3 3.27

Au

one minimum unit

mono1 mono2

3.79

mono2

4.78

Au3 diff. mono4 All; parallel struct. mono1 Au1 2bT 9.06 Au2

All; twisted struct. The minimum unit cell consists of 2 molecules. symmetrically minimal subunit

2bPT

Au1

Au4

5.73

1y

9.06

2bP

Au Au Au

Au

3.20 Au 3.11 Au

Au Au Au

mono6

All; parallel struct. The minimum unit cell consists of 4 subunits.

mono1 and 6; twisted struct. mono2, 3, 4 and 5; parallel struct.

The minimum unit cell consists of 4 subunits.

Figure 1: Selection of QM molecules to construct the crystal model of (a) 1b and 1y and (b) 2b and 2g at the ground state by the periodic QM/MM calculation with self-consistent point-charge representation.

61



(B) CHCl3 solution

(A) gas phase 5.0 eV

0.5 0.4

τ=0 30 60 90

0.6

4.2 eV 3.3 eV

0.3

τ=0

5.0 eV

30 60 90

Expt.

0.5 4.6 eV

0.4

0.2

0.1

0.1

2.0 1.5

3.8 eV

0.3

0.2

2.5 x 104

1.0 0.5 0.0

0

0 250

300 350 400 450 wavelength [nm]

250

500

[(L*mol*cm) -1 ]

oscillator str.

0.6

0.7 oscillator str.

0.7

molar absorption coefficient

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 62 of 67

300 350 400 450 wavelength [nm]

500

Figure 2: Absorption spectrum of 1 calculated in (A) gas phase and (B) CHCl3 solvent.a,b a Calculated

by the TD-DFT and 3D-RISM-TD-DFT with B3LYP functional. b Solid line in (B)

represents experimental absorption spectrum. See Ref. [20] for detail of experimentally observed excitation spectrum (solid line).

62


Page 63 of 67

(a) 1b

(b) 1y

in crystal

in crystal

ac-surface

ab-surface

4.3 eV

3.9 eV

oscillator str.

0.15

ab-surface

0.3

0.2

0.25

Expt.

state45 4.5 eV

2.9 eV

4.0 eV

3.5 eV

0.2

state1 3.2 eV

state7 0.1

Expt.

0.15

4.1 eV

state1 state1 0.05

3.7 eV V

3.1 eV

0.1

3.3 eV

0.05 0 275 300 325 350 375 400 425 450 475 500


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0 275 300 325 350 375 400 425 450 475 500

wavelength [nm]

wavelength [nm]

Figure 3: Excitation energy and oscillator strength of (a) 1b and (b) 1y.a,b a Evaluated by the QM/MM calculation in the presence of the ground state MM crystal.

b The

R-TD-DFT/B3LYP

method was used for QM calculation; see Scheme 6 for surfaces and Figure S9 in ESI for MO character of important excited states. Dotted line is the experimentally observed excitation spectrum (not absorption spectrum). See reference [20] for detail of experimentally observed excitation spectrum (dotted line).

63



oscillator str.

(a) 2b P

(b) 2b T

in crystal in crystal bc-surface bc-surface 0.5 0.5 3.9 eV 0.45 0.45 3.9 eV 0.4 0.4 0.35 0.35 3.5 eV 3.5 eV state67 0.3 0.3 state55 state72 state58 0.25 4.9 eV 0.25 4.7 eV Expr. s state4 0.2 0.2 state7 Expr. 4.1 eV 4.1 . eV 0.15 0.15 0.1 0.1 3.2 eV 3.2 eV te state6 state4 0.05 0.05 3.9 eV 3.8 eV 0 0 250 275 300 325 350 375 400 425 450 475 500 250 275 300 325 350 375 400 425 450 475 500


wavelength [nm]

wavelength [nm]

oscillator str.

(c) 2bPT

(d) 2g

in crystal in crystal bc-surface bc-surface 0.5 0.5 3.9 eV 0.45 0.45 3.4 eV 0.4 0.4 Expr. state61 0.35 0.35 state1 state62 3.5 eV st state11 0.3 0.3 state1 4.8 eV state10 2.9 eV 0.25 0.25 3.7 eV state2 Expr. 0.2 0.2 4.0 eV 0.15 0.15 0.1 0.1 3.2 eV st t e5 state5 0.05 0.05 3.8 eV 0 0 250 275 300 325 350 375 400 425 450 475 500 300 325 350 375 400 425 450 475 500


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 64 of 67

wavelength [nm]

wavelength [nm]

Figure 4: Excitation energy and oscillator strength of (a) 2bP , (b) 2bPT , (c) 2bT , and (d) 2g.a,b a Evaluated

by the QM/MM calculation in the presence of the ground state MM crystal. b The R-

TD-DFT/B3LYP method was used for QM calculation; see Scheme 6 for surfaces and Figure S10 in ESI for MO character of important excited states. Dotted line is the experimentally observed excitation spectrum (not absorption spectrum). See reference [21] for detail of experimentally observed excitation spectrum (dotted line).

64


Page 65 of 67 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(a) 1b

3

3

SOMO1 ε = -8.12 eV

LE1

mono1

Ph2

Au1

Au1

5.87 Au2

mono2 (3et)

SOMO1 ε = -7.68 eV

LE2

mono1

4.69

mono2 (3et)

PhCN2

Au3

mono3 5.87 mono4

SOMO2 ε = -4.52 eV

5.87 Au2 4.69

Au3

mono3 5.86 mono4

Au4

SOMO2 ε = -3.45 eV Ph2

Au4

PhCN2

(b) 1y

Au1-2: 3.31 Å Au2-3: 3.36 Å Au3-4: 2.85 Å Au4-5: 3.41 Å Au5-6: 3.29 Å

3

MMLCT1 mono1 Au1 Au2 Au3 Au4

mono2 mono3

Au1-2: 3.11 Å Au2-3: 3.15 Å

SOMO2 Au3-4: mono4 ε = -3.29 eV 2.92 Å

Au5 Au6

3

SOMO1 ε = -6.26 eV

mono5

Au4-5: 3.69 Å

mono6

Au5-6: 3.33 Å

MMLCT2

3

SOMO1 ε = -6.29 eV Au1-2: 3.26 Å

Au1 Au2

Au2-3: 3.68 Å

Au3 SOMO2 ε = -3.30 eV

Au4 Au5

Au3-4: 3.26 Å Au4-5: 3.68 Å

Au6

Au5-6: 3.26 Å

LE1

SOMO1 ε = -8.19 eV

Au1 Au2 Au3 Au4

SOMO2 ε = -4.42 eV

Au5 Au6

Figure 5: Triplet state geometries of (a) 1b and (b) 1y.a.b a Optimized by the QM/MM calculation in the presence of the ground state MM crystal. b The U-DFT/B3LYP-D3 method was used for QM calculation.

65



(a) 2bP

3

LE1

mono1 mono2 (3et) 9.03 Au3

Au1

3

SOMO1 ε = -8.00 eV PhCN2

4.77 mono3 Au4

LE2

SOMO1 ε = -7.83 eV Au1

mono1 mono2 (3et) Au3

4.77 Au2

Page 66 of 67

SOMO2 ε = -4.32 eV PhCN2

9.03

4.77

Ph2

Au2

SOMO2 ε = -3.49 eV

4.77 mono3

Au4

mono4

mono4

Ph2

(b) 2g 3

MMLCT1

mono1 Au1-2: 3.18 Å

mono2

MMLCT2

Au1-2: 3.27 Å

Au1 Au2

Au2-3: mono3 2.88 Å Au3 Au3-4: 3.15 Å Au4 mono4 Au4-5: Au5 Au6 3.12 Å mono5 Au5-6: 3.25 Å

3

SOMO1 ε = -5.95 eV

Au2-3: 2.97 Å Au3-4: SOMO2 ε = -2.88 eV 3.00 Å Au4-5: 3.01 Å

Au2

MMLCT3

Au1-2: 3.31 Å

Au1

Au2

SOMO1 ε = -5.96 eV

Au1

Au2-3: 3.18 Å

Au3

SOMO2 ε = -2.87 eV

Au4 Au5

3

SOMO1 ε = -5.89 eV

Au6

Au3-4: 3.23 Å Au4-5: 2.89 Å

Au3

SOMO2 ε = -2.94 eV

Au4 Au5

Au6

Au5-6: 2.97 Å

Au5-6: 3.20 Å

mono6

Figure 6: Triplet state geometries of (a) 2bP and (b) 2g optimized by the QM/MM calculation in the presence of the ground state MM crystal at the U-DFT/B3LYP-D3 level; see also Figure S13 in ESI for 2bPT and 2bT

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Graphical TOC Entry Me

Complex 1 Emission spectrum in crystal

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


AuI C N

AuI C N

Complex 2

SCSC Au1 Au2

Phase 1b

Phase 1y

Au3 Au4 3

LE

SCSC

Phase 2b

Au1 Au2 Au3 Au4 Au5

Au2 Au3

Au1 Au3

3

400

500

600

3

MMLCT

700 [nm]

LE 3

300

67

Au1

Au4 Au5 Au6

Au2

Au4 Au6

300

Me

Phase 2g

400

500


600

MMLCT

700 [nm]

Dependence of Absorption and Emission Spectra on Polymorphs of

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