Time-Dependent Density Functional Theory Study of the

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Time-Dependent Density Functional Theory Study of the Luminescence Properties of Gold Phosphine Thiolate Complexes Emilie Brigitte Guidez, and Christine M. Aikens J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/jp5104033 • Publication Date (Web): 20 Mar 2015 Downloaded from http://pubs.acs.org on March 21, 2015

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The Journal of Physical Chemistry

Time-Dependent Density Functional Theory Study of the Luminescence Properties of Gold Phosphine Thiolate Complexes Emilie B. Guidez§ and Christine M. Aikens* Department of Chemistry, Kansas State University, Manhattan, KS 66506 § Current address: Department of Chemistry, Iowa State University, Ames, IA 50011 *[email protected], 785-532-0954 Abstract The origin of the emission of the gold phosphine thiolate complex (TPA)AuSCH(CH3)2 (TPA=1,3,5-triaza-7-phosphaadamantanetriylphosphine) is investigated using time-dependent density functional theory (TDDFT). This system absorbs light at 3.6 eV, which corresponds mostly to a ligand-to-metal transition with some inter-ligand character. The P-Au-S angle decreases upon relaxation in the S1 and T1 states. Our calculations show that these two states are strongly spin-orbit coupled at the ground state geometry. Ligand effects on the optical properties of this complex are also discussed by looking at the simple AuP(CH3)3SCH3 complex. The excitation energies differ by several tenths of an eV. Excited state optimizations show that the excited singlet and triplet of the (TPA)AuSCH(CH3)2 complex are bent. On the other hand, the Au-S bond breaks in the excited state for the simple complex and TDDFT is no longer an adequate method. The excited state energy landscape of gold phosphine thiolate systems is very complex, with several state crossings. This study also shows that the formation of the [(TPA)AuSCH(CH3)2]2 dimer is favorable in the ground state. The inclusion of dispersion interactions in the calculations affects the optimized geometries of both ground and excited states. Upon excitation, the formation of a Au-Au bond occurs, which results in an increase in energy of the low energy excited states in comparison to the 1 ACS Paragon Plus Environment


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monomer. The experimentally observed emission of the (TPA)AuSCH(CH3)2 complex at 1.86 eV cannot be unambiguously assigned and may originate from several excited states.

Keywords: Emission, fluorescence, phosphorescence, excited state optimizations, spinorbit coupling, gold (I) dimers

Introduction Gold (I) complexes have attracted much research attention1 due to their unique luminescence properties2-7 as well as their potential applications in sensing8,9 and in the medical field.10 In addition, gold (I) thiolate complexes are well known as the protecting units, or semi-rings, of a wide variety of gold nanoclusters. Such nanoclusters were synthesized in a wide variety of sizes.11-14 Typical examples include Au25(SR)18-,15 Au144(SR)60,16 Au102(SR)4417,18 and Au38(SR)24.19 The emission of these complexes can arise from ligand to metal charge transfer (LMCT), metal to ligand charge transfer (MLCT) or metal centered emission (MC).20,21 The emission properties highly depend on the bulkiness and electronwithdrawing/donating nature of the ligand.5,21 In 1995, Forward and co-workers synthesized a large variety of gold phosphine thiolate complexes and studied their emission.5,22 They concluded that the emission was a phosphorescence process and that it originated from ligand to metal charge transfer. The aim of this work is to determine the origin of the emission of the phosphine gold complex (TPA)AuSCH(CH3)2 (TPA=1,3,5-triaza-7phosphaadamantanetriylphosphine) synthesized by Forward5 using time-dependent

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density functional theory (TDDFT) calculations. Two isomers are considered, as shown in Figure 1A and 1B. We also investigate how different ligands may affect this emission by looking at the simpler complex (CH3)3PAuSCH3 (Figure 1C).

Figure 1. Optimized A) (TPA)AuSCH(CH3)2 complex (1). B) (TPA)AuSCH(CH3)2 complex (1’). C) (CH3)3PAuSCH3 complex (2). Yellow: gold. Orange: Sulfur. Blue: Nitrogen. Purple: Phosphorus. Black: Carbon. White: Hydrogen.

Computational methods All geometry optimizations are performed using Density Functional Theory (DFT) as implemented in the ADF 2010.01 program.23 The BP86 exchange-correlation functional24,25 is used with a triple zeta polarized basis set (TZP) for all calculations. Dispersion interaction is included using the semi-empirical correction by Grimme.26 Calculations including the Grimme dispersion correction are performed with version 3 ACS Paragon Plus Environment


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2013.01 of ADF. All structures are optimized in the gas phase. Since relativistic effects are important for heavy elements such as gold, scalar relativistic effects are treated with the zeroth order regular approximation (ZORA).27,28 Excited state calculations are computed using time-dependent density functional theory (TDDFT) as implemented in the ADF package.29 Excitation calculations including spin-orbit coupling are also performed.30 In ZORA, the non-relativistic kinetic energy operator (one-electron operator) is replaced by a quasi-relativistic two-component Hamiltonian, which is an approximation to the Dirac kinetic energy operator. This operator can be split into a scalar relativistic part and a spin-orbit coupling part. The scalar relativistic part depends on the momentum of the electrons and is considered for all DFT and TDDFT calculations discussed in this work whereas the full ZORA operator, which also depends on the Pauli spin matrix vector, is considered for calculations that include spin-orbit coupling. In ADF, a noncollinear scheme for the exchange-correlation potential is used to calculate the off-diagonal elements of the TDDFT equations in addition to the adiabatic approximation.30 Electric dipole radiative lifetimes are computed using the relation:31

1

τ

=

4 3 α 0 ( ∆E )3 ∑ M α 3t0 α ∈( x ,y ,z )

2

where τ is the radiative lifetime, α0 is the fine structure constant, ∆E is the excitation energy and Mα is the transition dipole moment in the α = x, y or z direction. t0 =

4πε 0 h3 , me e 4

where ε 0 is the vacuum dielectric constant, me is the mass of the electron, e is the electronic charge and h is the Planck constant divided by 2π.


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Results and discussion 1) Geometry and electronic structure in the ground state. The (TPA)AuSCH(CH3)2 complex is optimized with two different configurations of the thiolate group, shown in Figure 1A and 1B. The complex with the isopropyl group pointing toward the gold is labeled (1). The complex with the isopropyl group pointing away from the gold is labeled (1’). Both structures have similar energies and are considered in this work. In order to determine the effect of the ligand size, we also investigated the (CH3)3PAuSCH3 complex labeled (2), displayed in Figure 1C. Table 1 shows the bond lengths and bond angles of all three complexes in the gas phase. The PAu-S angle has a value of 176.2 degrees for (1) and 178.3 degrees for (1’). Therefore, the arrangement of the isopropyl group in (1’) favors a more linear P-Au-S angle. In comparison, Forward et al. obtained a S-Au-P angle of 173.58 degrees for the related (TPA)AuSPh complex.5 (Geometrical parameters for (TPA)AuSCH(CH3)2 are not available in Ref. 5.) The S-Au-P angle is 176.4 degrees for (2), which is similar to (1). The P-Au bond length is 2.29 Å for (1), 2.28 Å for (1’) and 2.30 Å for (2). The (TPA)AuSPh complex has a P-Au bond length of 2.25 Å, which is slightly smaller.5 The S-Au bond length is 2.32 Å for (1) and (2), and 2.31 Å for (1’). For the (TPA)AuSPh complex, this bond measures 2.31 Å. The average P-C bond length is 1.88 Å for (1) and (1’) whereas it is 1.84 Å for (2). All three P-C bond lengths within each complex are identical. Overall, the different ligands investigated here do not greatly affect the geometry of the complex in the ground state.



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Table 1. Geometrical parameters of the (TPA)AuSCH(CH3)2 and (CH3)3PAuSCH3 complexes in the ground state at the BP86/TZP level of theory. (TPA)AuSCH(CH3)2 (TPA)PAuSCH(CH3)2 (CH3)3PAuSCH3 (1) (1’) (2) P-Au-S angle (°)

176.2

178.3

176.4

P-Au length (Å)

2.29

2.28

2.30

S-Au length (Å)

2.32

2.31

2.32

Average P-C length (Å)

1.88

1.88

1.84

S-C length (Å)

1.86

1.87

1.85

2) TDDFT calculations Excitation calculations have been performed for the two isomers of the (TPA)AuSCH(CH3)2 complex (1) and (1’) as well as for the (CH3)3PAuSCH3 complex (2) in the gas phase. The first three singlet and triplet excited state energies and oscillator strengths are reported in Table 2. The excitation energies for the two isomers (1) and (1’) are very similar. The S1 state is at 2.97 eV for both isomers and corresponds to a HOMOLUMO excitation. The Kohn-Sham orbitals of (1) in the ground state are shown in Figure 2. Because the corresponding orbitals in (1’) and (2) look the same as in (1), they are not displayed here. The HOMO is primarily composed of a p orbital located on the sulfur atom with a small contribution from a gold d orbital. The LUMO is a pi bonding orbital between gold and phosphorus atoms. It is interesting to see that the oscillator strength for the S1 state is two orders of magnitude larger for (1’) than for (1) but still weak in both cases (7.1 x 10-5 and 1.6 x 10-7 a.u., respectively). The S2 state lies at 3.59 eV for (1) and 3.57 eV for (1’) and has a high oscillator strength value (f~0.1 a.u.). The S2 excitation is found in this work to arise from a HOMO to LUMO+1 transition. The LUMO+1 orbital 6 ACS Paragon Plus Environment

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is a bonding pi orbital between the gold and phosphorus atom, similar to the LUMO orbital, with some contribution from the TPA and methyl ligands for (1) and (2) respectively. The S1 and S2 excitations can be characterized as LMCT transitions but also show some inter-ligand charge transfer character. The S1 state likely has a much lower oscillator strength than S2 because the HOMO and LUMO orbitals lie in different planes. On the other hand, the HOMO and LUMO+1 orbitals lie in the same plane. The (TPA)AuSCH(CH3)2 complex has an experimental absorption maximum at 348 nm (= 3.57 eV),5 which is similar to the calculated high-intensity S2 excitation energy. The S3 state lies at 3.88 eV for (1) and 3.85 eV for (1’) and has a moderate oscillator strength (f~0.005 a.u.). The S3 state corresponds to a HOMO-LUMO+2 excitation. The LUMO+2 orbital is mostly located on the TPA ligand.

Figure 2. HOMO, LUMO, LUMO+1, and LUMO+2 orbitals of (1). Contour value=0.03.



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Table 2. Excited state energies and oscillator strengths for the (TPA)AuSCH(CH3)2 and (CH3)3PAuSCH3 complexes. (TPA)AuSCH(CH3)2 (1)

(TPA)AuSCH(CH3)2 (1’)

Energy (eV)

Oscillator strength (a.u.)

Energy (eV)


Energy (eV)


T1

2.91

0

2.91

0

3.07

0

S1

2.97

1.6*10-7

2.97

7.1*10-5

3.14

0.00011

T2

3.18

0

3.16

0

3.33

0

S2

3.59

0.098

3.57

0.1060

3.73

0.079

T3

3.81

0

3.78

0

3.72

0

S3

3.88

0.0047

3.85

0.0049

3.78

0.0067

State

(CH3)3PAuSCH3 (2)

For (2), the energy of the S1 state is 3.14 eV. The oscillator strength of this state is three orders of magnitude larger than the oscillator strength of the S1 state of (1), although it still remains weak. The S2 state occurs at 3.73 eV with a high oscillator strength (f = 0.079 a.u.). The S3 state lies at 3.78 eV and has moderate oscillator strength (f = 0.0067 a.u.). Compared to (1), the first two singlet excited states are blue-shifted in (2) whereas the third singlet excited state is red-shifted. Overall, the intensities follow the same trends regardless of the ligand, with S1 being very weak and S2 being the strongest. Excitations to the triplet states are spin-forbidden and therefore have zero oscillator strength. Spin-orbit coupling (SOC) can be important for gold and transitions to these states may then be allowed. In fact, SOC may affect excited state energies and oscillator strengths. It might also induce additional excited state crossings. The spin-orbit coupled excitations in Table 3 show that the first four excited states have very similar energies for all three complexes. These four states can be matched to the components of 8 ACS Paragon Plus Environment

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the T1 and S1 states in the non-SOC calculations. State number 3 has an oscillator strength of 0.0028, 0.0033 and 0.0025 for (1), (1’) and (2) respectively. These values are orders of magnitude larger than the corresponding ones obtained for S1 without spin-orbit coupling. Due to spin-orbit coupling, states 1-4 cannot be assigned as singlet or triplet states, although state 3 possibly has a larger contribution from the S1 state due to its larger oscillator strength. States 5, 6 and 7 appear to correspond to the components of the T2 state since they are nearly degenerate with very small oscillator strength, and state 8 closely emulates the S2 state. The nonzero oscillator strengths of states 1-4 and the moderate oscillator strength of state 6 show that SOC is significant at the nearly linear ground state geometry. Thus, intersystem crossing to triplet states is possible. Table 3. Spin-orbit coupled excited state energies and oscillator strengths for the (TPA)AuSCH(CH3)2 and (CH3)3PAuSCH3 complexes. (TPA)AuSCH(CH3)2 (1)

(TPA)AuSCH(CH3)2 (1’)

Energy (eV)


Energy (eV)


Energy (eV)


1

2.84

2.5*10-5

2.84

2.1*10-5

3.00

2.3*10-5

2

2.84

9.2*10-5

2.84

1.0*10-4

3.00

0.00013

3

2.87

0.0028

2.88

0.0033

3.03

0.0025

4

2.89

1.1*10-6

2.89

9.6*10-6

3.05

0.00010

5

3.23

3.2*10-5

3.20

3.0*10-5

3.38

3.0*10-5

6

3.23

0.00014

3.21

0.00013

3.38

0.00018

7

3.24

4.2*10-6

3.22

3.1*10-5

3.39

4.8*10-5

8

3.59

0.088

3.57

0.096

3.69

0.034

State


(CH3)3PAuSCH3 (2)


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Excited state gradients are calculated for all three complexes in order to determine the origin of the emission. According to Kasha's rule, emission typically occurs only from the lowest excited state of a given multiplicity of a complex, so the S1 and T1 states (corresponding to HOMO-LUMO transitions) are considered here. The optimized S1 and T1 states for (1) are shown in Figure 3A and 3B respectively. The data for (1’) is similar to (1) and is presented in the supporting information. From here on, only (1) is discussed. We note that TDDFT gradients with spin-orbit coupling are not supported in ADF, so only scalar relativistic effects are taken into account here. Bond angles and distances as well as excited state energies and oscillator strengths are given in Table 4 for the S1 and T1 states. The optimized S1 state of (1) has a P-Au-S angle of 160 degrees and a S1-S0 energy of 1.52 eV. The T1 state displays a P-Au-S angle of 157 degrees and its energy lies 1.30 eV above S0 at the optimized T1 geometry. These energies are much lower than the experimental emission of 1.86 eV. A large increase of 0.16 Å and 0.18 Å of the Au-S bond length occurs for S1 and T1 respectively in comparison to the equilibrium geometry of the ground state. An increase in the Au-S bond length was also observed during the first 200 fs of the S1 excited state dynamics of the Au2(SCH3)(PH3)2+ complex using a combination of TDDFT and Ehrenfest dynamics.32 In addition, one of the P-C bonds is elongated by 0.19 Å for S1 and 0.14 Å for T1 in comparison to the ground state geometry, where all P-C bond lengths are similar. We note that the optimized S1 and T1 excited state structures obtained here may not be identical to the minima obtained when spin-orbit coupling is considered. Nonetheless, both the singlet and triplet states undergo similar geometrical rearrangements and the degree of spin-orbit coupling lessens as the complex bends, which suggests that the results obtained at the bent geometries obtained without


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SOC may be similar to those obtained with full spin-orbit coupled geometrical relaxations. The effect of spin-orbit coupling on the excitation spectrum is discussed in more detail further.

Figure 3. A) Optimized S1 and B) T1 states of (1). Table 4. Excited state optimized geometries, oscillator strength and energies of (1). Excited State

S1

T1

Energy (eV)

1.52

1.30


0.0006123

0

P-Au-S angle (°)

159.69

156.94

P-Au length (Å)

2.33

2.36

S-Au length (Å)

2.48

2.50

S-C length (Å)

1.85

1.85

Average P-C length (Å)

1.94

1.93

The ground state LUMO orbital at the S1 state geometry is shown in Figure 4. This orbital is mostly located on the gold atom, with some antibonding character with the ligands, consistent with the observed bond elongations. Notably, this orbital strongly differs from the ground-state geometry LUMO orbital shown in Figure 2. The oscillator strength of the S1 state is quite low which would correlate to a long lifetime for radiative 11 ACS Paragon Plus Environment


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emission. However, it should be noted that the long excited state lifetime of 17 µs observed experimentally has been suggested to correspond to a phosphorescence-type emission.5

Figure 4. LUMO orbital of (1) at the optimized S1 excited state geometry. Contour value=0.03. Single-point TDDFT excitation calculations were performed with spin-orbit coupling at the optimized S1 and T1 geometries (Table 5). Since the two structures are similar, energies and oscillator strengths are quite close. The fourth excited state is well separated from the first three in comparison to the ground state geometry, which suggests that the S1 state is not highly spin-orbit coupled with the T1 state at the bent geometry. In the next section, we will discuss the correlation between the bending of the P-Au-S angle and excited state energies. State numbers 3, 4 and 7 have small but non-negligible oscillator strengths with excited state lifetimes between 15 and 55 µs, similar to the experimental value of 17 µs. Notably, the fourth state (which is essentially the singlet S1 state) and third state (a T1 component) have similar radiative lifetimes, so the lifetime itself cannot be used to distinguish fluorescence and phosphorescence in this case. The excited state energies of states 3 and 4 are lower than the experimental emission energy of 1.86 eV but are within the error margin of the calculations. The observed emission could potentially originate from either of these states. The geometrical difference


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between the ground and excited states as well as the fact that the S1 state is essentially dark at the ground state geometry may be responsible for the long lifetimes observed experimentally. Table 5. Spin-orbit coupled excited state energies, oscillator strengths, and radiative lifetimes at the S1 and T1 geometries of (1). S1 geometry State

T1 geometry

Energy (eV)


Electric dipole radiative lifetime (ms)

Energy (eV)



1

1.36

3.3*10-7

37.2

1.29

1.3*10-6

10.86

2

1.36

2.3*10-6

5.4

1.29

2.7*10-6

5.1

3

1.37

0.00047

0.026

1.30

0.00043

0.032

4

1.50

0.00059

0.017

1.45

0.00071

0.015

5

2.10

1.8*10-6

2.8

2.01

1.7*10-6

3.3

6

2.11

6.2*10-6

0.84

2.02

3.2*10-5

0.18

7

2.11

0.00016

0.032

2.02

0.00010

0.055

8

2.53

0.020

0.00017

2.50

0.027

0.00014

Optimization of the S1 and T1 states of (2) leads to breaking of the Au-S bond, thus TDDFT is no longer an adequate method. However, an optimization of the lowest triplet state yields a bent structure with a P-Au-S angle of 87.5 degrees (cf Table S2 of the Supporting information) and an energy of 2.7 eV. Triplet state distortions were previously observed for the [Au(PH3)3]+ complex where the ground state has a trigonal planar shape whereas the lowest triplet state distorts toward a T-shape.33 We note that the relaxed structure of the T1 state for (1) is not as bent as the triplet state of (2) and has a 13 ACS Paragon Plus Environment


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higher T1-S0 energy. The complex with the TPA and isopropyl ligands cannot bend as much as the simple complex due to steric hindrance, which will thus affect the optical properties. Silver (I) complexes with diphosphine ligands show similar properties, where bulkier ligands prevent the structural relaxation of the triplet state, and therefore lead not only to a higher phosphorescence energy but also a higher quantum yield.34 The excitation energies from the S0 state to the S1, S2, T1 and T2 states are calculated at different S-Au-P angles for (2) and (1) without spin-orbit coupling, as shown in Figure 5A and 5B, respectively. For (2), the T2 state crosses the S1 state at an angle of 113 degrees. At 105 degrees, the T2 state is only 0.08 eV higher in energy than the T1 state. The S1 and T1 states are very close in energy at the linear geometry and separate as the complex bends. At a P-Au-S angle of 120 degrees, the T2 and S1 state of (1) have similar energies. This angle is 7 degrees larger than the P-Au-S angle where S1 and T2 cross for the simple (2) complex. This data suggests that the size of the ligands plays an important role in the structure and energy of the excited states and therefore the luminescence properties. As in (2), the T1 and S1 states for (1) have similar energies at the linear geometry and separate as the molecule bends. Similar calculations including spinorbit coupling were also performed on these two complexes, as shown in Figure 6A and 6B. In both cases, numerous crossings between the states exist. The first four states have the same energy at the initial linear geometry. As the complex bends, the fourth state becomes higher in energy than the first three. Therefore, we can conclude that the first triplet state is spin-orbit coupled with the first singlet state at a P-Au-S angle of 180 degrees. Additionally, the fifth, sixth and seventh excited states cross the eighth state at angle of 145 degrees for (2) and 152 degrees for (1). We note that the first four states of


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(1) have an energy between 1.5 and 2 eV for S-Au-P angles smaller than 132 degrees, which is close to the emission energy observed by Forward et al.5

Figure 5. S1, S2, T1 and T2 excitation energies of A) (CH3)3PAuSCH3 (2) and B) (TPA)AuSCH(CH3)2 (1) at various P-Au-S angles.



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Figure 6. Spin-orbit coupled excited states of A) (CH3)3PAuSCH3 (2) and B) (TPA)AuSCH(CH3)2 (1) at various P-Au-S angles. 3) [(TPA)AuSCH(CH3)2] 2 dimer Emission in Au (I) complexes has long been attributed to aggregation.35-38 The (TPA)AuSCHCH3 complex emission was experimentally studied in the solid state at 77 16 ACS Paragon Plus Environment

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K,5 so consideration of the emissive properties of a dimer of this complex is critical. Aggregation of Au (I) complexes is aided by the aurophilic interaction (interactions between the d electrons of gold (I) atoms in gold complexes). In order to investigate this effect, a [(TPA)AuSCH(CH3)2]2 dimer is modeled without and with dispersion interactions, as shown in Figure 7A and 7B respectively. The dimer optimized without dispersion will be referred to as (3) and the dimer optimized with dispersion will be referred to as (3'). Geometrical parameters for both structures are given in Table 6. The gold-gold distance in (3) is 3.72 Å, which is longer than the typically observed Au-Au distances of 3.00 to 3.50 Å for other complexes.6,21,39,40 With dispersion, the Au-Au bond is 3.22 Å in (3'), which is within this range. In addition, the two monomers are arranged in a nearly antiparallel fashion when dispersion is not considered whereas there is a SAu-Au-S dihedral angle of -126.8 degrees when dispersion is considered. The geometry of each molecule in the dimers is nearly identical to the one obtained for a separately optimized monomer. Therefore, dispersion does not significantly affect intramolecular geometries. This is also shown by the geometry of monomer (1) optimized with dispersion (Table S3, supporting information).

Figure 7. Optimized ground state of the [(TPA)AuSCH(CH3)2]2 dimer in the gas phase A) without dispersion (3) and B) with dispersion (3').



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Table 6. Geometrical parameters of the [(TPA)AuSCH(CH3)2]2 optimized dimer with dispersion (3') and without dispersion (3). (3)

(3')

3.72

3.22

-179.7

-126.8

P-Au-S angle (°)

177.1

176.7

P-Au length (Å)

2.29

2.28

S-Au length (Å)

2.33

2.34

Au-Au length (Å) S-Au-Au-S angle (°)

The binding energy between the two monomers is -0.35 eV without dispersion and -1.42 eV with dispersion at the BP86/TZP level of theory, indicating that this dimerization is favorable. The isomerization of structure (3) to (3') has an energy of -0.34 eV when dispersion is included. This indicates that the (3') structure is thermodynamically more stable than the (3) geometry at this level of theory. In the next section, the TDDFT absorption spectra of (3) and (3’) are described. Subsequently, the optimized excited states of these two systems are discussed. 3.1) TDDFT absorption of the dimers (3) and (3’) The excitation energies of (3) and (3') are calculated and the results are reported in Tables 7 and 8 for the singlet and triplet states, respectively.


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Table 7. Excited state energies and oscillator strengths of the singlet states for the dimer [(TPA)AuSCH(CH3)2]2 optimized without (3) and with (3’) dispersion. (3) (3') Energy Oscillator Energy Oscillator State (eV) strength (a.u.) (eV) strength (a.u.) S1 3.16 3.54*10-6 3.10 0.0025 S2 3.17 0.022 3.17 0.004 -6 S3 3.57 3.35*10 3.23 0.019 S4 3.59 0.027 3.30 0.030 S5 3.66 0.043 3.65 0.0046 S6 3.69 1.03*10-5 3.66 0.0035 S7 3.69 0.021 3.68 0.0013 -6 S8 3.73 1.16*10 3.70 0.0089 S9 3.85 4.58*10-6 3.73 0.026 S10 3.87 0.033 3.74 0.0075 -6 S11 3.92 2.72*10 3.75 0.014 S12 3.97 0.13 3.77 0.0012 S13 4.02 1.03*10-5 3.82 0.041 Table 8. Excited triplet state energies for the dimer [(TPA)AuSCH(CH3)2]2 optimized without (3) and with (3’) dispersion. State

Structure (3)

Structure (3')

T1

3.05

2.99

T2

3.06

3.05

T3

3.41

3.10

T4

3.43

3.14

T5

3.58

3.59

T6

3.64

3.62

T7

3.66

3.64

T8

3.67

3.65



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Figure 8. HOMO-2, HOMO-1, HOMO, LUMO, LUMO+1 and LUMO+2 orbitals of the [(TPA)AuSCH(CH3)2]2 complex (3) at the ground state geometry. Contour value=0.03 The (3) complex is discussed first. Orbitals for this system are shown in Figure 8. The S1 state at 3.16 eV and the S2 state at 3.17 eV of (3) correspond to a HOMO-1 → LUMO and a HOMO → LUMO transition respectively. The quasi-degenerate HOMO and HOMO-1 orbitals are localized mostly on the sulfur p orbital with some contribution from a gold d orbital, and result from the interaction of the two monomer HOMOs. The interaction between the orbitals is slightly bonding for the HOMO-1 and slightly antibonding for the HOMO. The S1 state of the monomer therefore yields the S1 and S2 states of the dimer, where S2 has a larger oscillator strength than S1. The splitting of these states is small since the HOMO and HOMO-1 are very close in energy (0.01 eV gap). Although the energy of the S2 state is lower than that for the absorption peak observed experimentally at 3.6 eV, it is within a typical error range for a pure GGA functional. The strong oscillator strength for this transition (0.022 a.u.) is surprising, since the orbitals 20 ACS Paragon Plus Environment

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primarily involved are closely related to the HOMO and LUMO orbitals of the monomer, and the HOMO→LUMO transition is very weak for the monomer case; we hypothesize that this may be due to changes in relative orientation of the orbitals involved when the complex undergoes dimerization. The strong excitation to the S4 state at 3.59 eV corresponds to a HOMO1→LUMO+1 transition. This state has an energy similar to the peak experimentally observed and corresponds to a LMCT transition within the monomers with some interligand character, as described previously. States S3 at 3.57 eV (HOMO → LUMO+1 transition) and S4 at 3.59 eV (HOMO-1 → LUMO+1 transition) originate from the splitting of the S2 state of the monomer. S3 is very weak (f = 3*10-6 a.u.) whereas S4 is strong (f = 0.027 a.u.). We note that a similar type of inter-ligand charge transfer has been observed during a dynamic study of the S1 excited state of the Au2(SCH3)(PH3)2+ complex during the first 50 fs.32 The S5 state at 3.66 eV also has a large oscillator strength and corresponds to a HOMO-2 to LUMO transition. The HOMO-2 is mainly localized on the nitrogen and phosphorus atoms of the TPA ligands. The S7 state at 3.69 eV has an oscillator strength comparable to that of the S4 state and corresponds to a HOMO-4 (also localized on the TPA ligand, not shown) to LUMO transition. We note that these two absorption peaks may also contribute to the experimentally observed absorption. However, they may not be easily resolved experimentally. SOC excitation calculations are also performed on the (3) and (3') complexes and the results are reported in Table 9. In (3), states 8 and 19 at 3.10 eV and 3.53 eV closely emulate states S2 and S4. The first six states at about 3 eV appear to be related to the first two triplet states in the non-SOC formalism. Notably, state 3 at 2.99 eV has a moderate oscillator strength (f=



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0.00135 a.u.), which suggests that intersystem crossing is possible in the dimer. In a similar way, states 14, 16, and 17 at 3.38, 3.52, and 3.52 eV, respectively, also have a moderate oscillator strength. States 19, 23, and 26 at 3.53, 3.58, and 3.61 eV all have a large oscillator strength. These states seem to emulate the S4, S5, and S7 states and may be responsible for the 3.59 eV experimental absorption. Since they are very close in energy, they may not be resolved in the absorption spectrum. Table 9. Spin-orbit coupled excited state energies and oscillator strengths for the dimer [(TPA)AuSCH(CH3)2]2 optimized without and with dispersion. Structure (3) State 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

Energy (eV) 2.98 2.99 2.99 3.00 3.00 3.00 3.09 3.10 3.36 3.36 3.36 3.37 3.38 3.38 3.50 3.52 3.52 3.52 3.53 3.57 3.57 3.58 3.58 3.60 3.60 3.61 3.62

Oscillator strength (a.u.) 5.34*10-5 3.92*10-4 0.00135 2.98*10-8 2.39*10-9 7.29*10-8 9.19*10-6 0.0206 1.59*10-8 1.61*10-8 5.28*10-8 3.45*10-5 7.46*10-4 0.00159 4.14*10-6 0.00103 0.00105 1.56*10-4 0.0244 4.82*10-7 9.26*10-7 3.71*10-6 0.0304 1.11*10-5 3.17*10-4 0.0202 2.28*10-4

Structure (3') Energy (eV) 2.89 2.89 2.90 2.98 3.00 3.01 3.01 3.05 3.05 3.07 3.10 3.14 3.15 3.17 3.22 3.26 3.49 3.49 3.50 3.51 3.52 3.53 3.54 3.55 3.55 3.56 3.57

Oscillator strength (a.u.) 3.22*10-6 3.06*10-4 2.09*10-4 0.00418 2.91*10-5 9.91*10-4 6.55*10-4 1.75*10-4 4.47*10-5 6.62*10-4 0.00294 0.00437 1.71*10-4 0.00467 0.0152 0.0223 1.70*10-5 4.71*10-5 3.92*10-4 7.78*10-4 7.06*10-5 0.00122 0.00379 0.00506 5.52*10-5 0.00712 0.00272


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28

3.62

4.51*10-7

3.58

0.00183

The (3’) dimer optimized with dispersion is now discussed. The excited singlet states of the (3') structure displayed in Table 7 all have moderate to strong oscillator strength. Ground state optimized orbitals are shown in Figure S2 of the supporting information. Orbitals below the HOMO-2 are localized on the TPA ligand. HOMO and HOMO-1 are p orbitals on the sulfur atoms, similar to (3). The LUMO orbital is a sigma bonding orbital between the gold atoms, also like (3). The LUMO+1 orbital is a pi bonding orbital between the gold atoms. In contrast, the LUMO+1 orbital of (3) is a pi orbital localized between the gold and phosphorous atoms of each monomer. The S3, S4, S9, S11 and S13 states of the (3') complex at 3.23, 3.30, 3.73, 3.75 and 3.82 eV have the largest oscillator strength. Multiple transitions contribute to the excited states, as shown in Table S4 of the supporting material. Excited states lower than 3.65 eV (S1 to S5) are mostly LMCT (also with some inter-ligand character). They correspond to transitions from the HOMO and HOMO-1 orbitals (mostly localized on the sulfur ligand) to LUMO and LUMO+1 orbitals (delocalized between the gold atoms of the dimer). Contrary to (3), these excitations all have moderate to high oscillator strength, possibly due to a more favorable arrangement of the orbitals in this lower-symmetry complex. The transitions involved in higher energy states are from orbitals localized on the TPA ligands to the LUMO and LUMO+1 orbitals. Spin-orbit coupled calculations performed on (3') in Table 9 indicate that two states at 3.22 and 3.26 eV have a large oscillator strength similar to S3 and S4 in the non-SOC formalism. Excited states between 3.53 and 3.58 eV have moderate oscillator strengths.



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3.2 Excited state optimizations of the dimers (3) and (3’) Excited state optimizations have also been performed without spin-orbit coupling for complexes (3) and (3’). (3) is discussed first. The optimized T2 and S2 geometries of (3) are shown in Figure 9A and 9B, respectively. These are the only two states that could be optimized with TDDFT. Other states may require multireference methods. The S2 and T2 states correspond to a transition from the HOMO-1 (which is mostly located on the sulfur of each monomer) to the bonding LUMO (Figure 10). Excited state energies, oscillator strengths, relevant bond lengths and bond angles are displayed in Table 10. In both states, the complex is bent. We note that the gold-gold distances are much smaller in these excited states than in the ground state case (2.83 Å and 2.84 Å for the T2 and S2 states, respectively), indicating a stronger binding interaction between the gold atoms. Such a decrease in Au-Au bond length upon excitation was observed previously.32 The PAu-S angles are bent with an angle of 152.3 degrees for each monomer at the S2 geometry. At the T2 geometry, the P-Au-S angles are 155.2 degrees. These angles are reminiscent of the corresponding monomer excited state geometries. The two molecules are arranged in a nearly trans configuration with a P-Au-Au-S dihedral angle of -57.1 degrees for the T2 state and -35.8 degrees for the S2 state.

Figure 9. A) Optimized T2 and B) S2 states of (3). 24 ACS Paragon Plus Environment

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Table 10. Excited state optimized geometries, oscillator strengths, and energies of the dimer [(TPA)AuSCH(CH3)2]2 (3). Excited State

S2

T2

Energy (eV)

1.76

1.57


0.000027

0

Average P-Au-S angle (°)

152.3

155.2

P-Au-Au-S Dihedral angle (°)

-35.8

-57.1

Au-Au length (Å)

2.84

2.83

P-Au length (Å)

2.31

2.31

S-Au length (Å)

2.42

2.41

Figure 10. HOMO-1, HOMO, LUMO and LUMO+1 orbitals of the (TPA)AuSCH(CH3)2 dimer complex (3) at the S2 state geometry. Contour value=0.03. 25 ACS Paragon Plus Environment


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The frontier orbitals at the S2 geometry are displayed in Figure 10. Since the T2 and S2 geometries are similar, the Kohn-Sham orbitals are also similar and only the S2 orbitals are shown here. The energy of the optimized T2 state is 1.57 eV, which is 0.27 eV larger than the T1 state in the monomer case. The optimized S2 state energy is 1.76 eV. These excited state energies are now closer to those obtained experimentally and either of these states could be responsible for the observed emission at 1.86 eV, especially given the typical underestimation of excitation energies by pure GGA functionals. In addition, the S1 and T1 states lie close in energy to the S2 and T2 states (at 1.66 and 1.56 eV respectively for the S2 optimized geometry and at 1.59 eV and 1.49 eV for the T2 optimized geometry). Therefore relaxation to these states may occur. At the S2 and T2 geometries, the S1 state has a moderate oscillator strength (~0.003 a.u.) Also, we previously showed that low energy excited states within the monomer may occur while the complex bends (S1 and T2 states, Figures 5B and 6B), which also suggests that relaxation to the lower energy states may occur. Spin-orbit coupled TDDFT calculations have been performed on the dimer (3) at the S2 and T2 geometries. Excitation energies, oscillator strengths, and radiative lifetimes are reported in Table 11. At the S2 geometry, state 4 has an energy of 1.61 eV, a moderate oscillator strength of 0.003 and a radiative lifetime of about 3 µs. States 9 and 10 have energies of 2.07 eV and radiative lifetimes of 27 and 31 µs, respectively. However, their oscillator strengths are an order of magnitude lower than state 4. The radiative lifetimes of all three states are close to the experimentally observed value of 17 µs and the energies are in the right range. At the T2 geometry, state number 4 at 1.53 eV and state number 7 at 1.57 eV have a moderate


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oscillator strength and a radiative lifetimes of 4 and 6.5 µs respectively. State 11 at 2.14 eV has a radiative lifetime of 20 µs. The oscillator strength is one order of magnitude smaller than that of state 7. Overall, states 1 to 3 seem to emulate the T1 state due to their low oscillator strength and degeneracy. State number 4 seems to emulate the S1 state due to its higher energy than states 1-3 and its larger oscillator strength. The moderate oscillator strength of this state along with the radiative lifetime of 3-4 µs suggest it is possibly at the origin of the observed emission but this cannot be confirmed since this state could not be optimized. At the T2 geometry, state number 7 at 1.57 eV also has a moderate oscillator strength and a lifetime similar to the experimental one. This state seems to emulate the T2 state as shown by the near-degeneracy of states 5-7 but it might also contain contributions from singlet components. Table 11. Spin-orbit coupled excited state energies, oscillator strengths, and radiative lifetimes at the optimized S2 and T2 geometries of (3). S2 geometry State

T2 geometry

Energy (eV)



Energy (eV)



1

1.52

1.22*10-6

8.19

1.46

1.42*10-6

7.67

2

1.52

6.10*10-5

0.163

1.46

8.08*10-5

0.135

3

1.53

3.06*10-5

0.323

1.46

6.91*10-5

0.156

4

1.61

0.00318

0.00280

1.53

0.00244

0.00404

5

1.64

9.76*10-5

0.0882

1.54

6.82*10-5

0.142

6

1.64

2.63*10-5

0.327

1.54

7.18*10-5

0.135

7

1.65

4.55*10-5

0.187

1.57

0.00144

0.00649

8

1.72

8.35*10-6

0.928

1.62

3.11*10-6

2.81



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9

2.07

1.98*10-4

0.0273

2.14

1.27*10-5

0.399

10

2.07

1.73*10-4

0.0312

2.14

7.87*10-6

0.641

11

2.07

5.78*10-6

0.933

2.14

2.52*10-4

0.0200

12

2.13

2.71*10-6

1.87

2.14

9.37*10-6

0.537

13

2.13

1.90*10-6

2.67

2.14

3.79*10-7

13.2

14

2.14

4.95*10-4

0.0102

2.15

5.28*10-4

0.00949

Table 12. S2 excited state optimized geometry, oscillator strength, and energy of the dimer (3'). Excited State

S2

Energy (eV)

1.84


4.33*10-5

Average P-Au-S angle (°)

165.7

P-Au-Au-S Dihedral angle (°)

-77.5

Au-Au length (Å)

2.85

P-Au length (Å)

2.29

S-Au length (Å)

2.38

The S2 state of (3') was also optimized. Data is shown in Table 12. This state lies at 1.84 eV, which is very close to the observed experimental emission but it has a very weak oscillator strength. We note that the S-Au-Au-S dihedral angle is about twice as large (-77.6 degrees) as the S2 state obtained for (3) without dispersion. Other excited states could not be optimized with TDDFT for this system. However, we note that the S1 state at this geometry has an energy of 1.82 eV, very close to the S2 energy. The oscillator 28 ACS Paragon Plus Environment

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strength of this state is much larger (~0.002 a.u.) and emission from this state may occur following relaxation. The T1 state lies at 1.74 eV at the S2 optimized geometry and may also be responsible for emission if intersystem crossing occurs. Excited state energies and oscillator strengths with spin-orbit coupling at the S2 geometry of (3') are shown in Table 13. Table 13. Spin-orbit coupled excited state energies, oscillator strengths, and radiative lifetimes at the optimized S2 geometry of (3'). State Energy (eV) Oscillator strength(a.u.) lifetime (ms) 1 1.71 1.16*10-5 0.685 -4 2 1.71 1.12*10 0.0707 3 1.71 5.16*10-5 0.152 4 1.74 0.0011 0.00689 -5 5 1.75 8.69*10 0.0866 6 1.75 1.51*10-4 0.0496 7 1.80 0.00145 0.00493 8 1.81 1.20*10-5 0.0582 -6 9 2.45 1.67*10 2.30 10 2.45 4.68*10-7 8.19 -4 11 2.45 2.97*10 0.0129 State 4 at 1.74 eV has a moderate oscillator strength of 0.0011 a.u. The radiative lifetime is 7 µs. State 7 at 1.80 eV also has a moderate oscillator strength of 0.0015 a.u. and a radiative lifetime of 5 µs. Both of these states are within the range of the observed experimental emission at 1.86 eV and both excited state lifetimes are close to the experimentally observed 17 µs. As in (3), state 4 seems to emulate the S1 state and state 7 seems to emulate the T2 state. The energy, oscillator strength and radiative lifetimes suggest they may also be responsible for the emission. It seems that the relative orientation of the monomers in (3’) can explain the observed emission. However since the orientation of the monomers in the solid state in unknown, we cannot draw any definite conclusion. 29 ACS Paragon Plus Environment


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Overall, several states found in this work could be at the origin of the experimental emission in these gold (I) systems. Although a single state cannot be unambiguously determined as the origin of the emission, it is evident that several states are likely possibilities especially when spin-orbit coupling is considered in these complexes.

Conclusions In this study, the optical properties of the complex (TPA)AuSCHCH3 are investigated using TDDFT. This complex is linear in the ground state and absorbs at 3.59 eV. This excitation involves a charge transfer from the thiolate ligand to the gold atom. The first excited singlet state and the first excited triplet state are spin-orbit coupled at this linear geometry. Excited state optimizations show that the S-Au-P angle bends in the excited state and the triplet state becomes lower in energy than the singlet state. Both the S1 state at 1.52 eV and the T1 state at 1.30 eV have radiative lifetimes in the range of those observed experimentally when spin-orbit coupling is considered, although the state energies are over 0.3 eV lower than the experimental emission peak. To improve the prediction of the emission energy, aggregates of (TPA)AuSCHCH3 have also been investigated in this work. There is a favorable aurophilic interaction between two complexes in the ground state. The dimer was optimized with and without dispersion. When dispersion is included, the two molecules are not arranged in an antiparallel fashion. The inclusion of dispersion therefore affects the ground state geometry. In the excited state, a stronger bonding interaction between the gold centers occurs. The dimer optimized without dispersion is predicted to have


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strong absorption at 3.17 eV, 3.59 and 3.66 eV. Optimized S2 and T2 states lead to systems with a bent geometry and energies of 1.76 and 1.57 eV, respectively. Other excited states could not be optimized with TDDFT and may require the use of multireference methods. When dispersion is included, the dimer is predicted to have strong absorption at 3.23, 3.30, 3.73, 3.75 and 3.82 eV. Only the S2 state could be optimized for this structure. This state lies at 1.84 eV, very close to the experimentally observed emission. Overall, a large geometrical change is required during the emission process. Calculations that consider spin-orbit coupling demonstrate that several states (both singlet-like and triplet-like, although spin is no longer a good quantum number) have reasonable energies and radiative lifetimes in comparison with experiment. Either phosphorescence or fluorescence could be at the origin of the experimentally observed emission. Acknowledgements This material is based on work supported by the National Science Foundation under grants no. EPS-0903806 and CHE-1213771. The authors also thank Kansas State University for funding this work. C.M.A. is grateful to the Alfred P. Sloan Foundation for a Sloan Research Fellowship (2011-2013) and the Camille and Henry Dreyfus Foundation for a Camille Dreyfus Teacher-Scholar Award (2011-2016). Supporting Information Excited state geometries of monomer complexes. Geometry of the monomer with dispersion interactions included. Kohn-Sham orbitals of the dimer optimized with dispersion interactions. Transitions involved in the excited states of the dimer optimized with dispersion interactions. Excited state potential energy surfaces of the dimer with



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varying Au-Au distance. This material is available free of charge via the Internet at http://pubs.acs.org.

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Time-Dependent Density Functional Theory Study of the

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