Computational Studies of a Paramagnetic Planar Dibenzotetraaza [14

Dec 22, 2014 - *E-mail: [email protected]., *E-mail: [email protected]. This article is part of the Jacopo Tomasi Festschrift special issue...
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Computational Studies of a Paramagnetic Planar Dibenzotetraaza[14]annulene Ni(II) Complex Hassan Rabaâ,*,† Hamid Khaledi,‡ Marilyn M. Olmstead,§ and Dage Sundholm*,∥ †

Department Department § Department ∥ Department ‡

of of of of

Chemistry, Chemistry, Chemistry, Chemistry,

University Ibn Tofail, P.O. Box 133, 14000 Kenitra, Morocco University of Malaya, Kuala Lumpur 50603, Malaysia University of California, Davis, California 95616, United States P.O. Box 55 (A. I. Virtanens plats 1), FI-00014 University of Helsinki, Helsinki, Finland

S Supporting Information *

ABSTRACT: A square-planar Ni(II) dibenzotetraaza[14]annulene complex substituted with two 3,3-dimethylindolenine groups in the meso positions has recently been synthesized and characterized experimentally. In the solid-state, the Ni(II) complex forms linear π-interacting stacks with Ni···Ni separations of 3.448(2) Å. Measurements of the temperature dependence of the magnetic susceptibility revealed a drastic change in the magnetic properties at a temperature of 13 K, indicating a transition from low-to-high spin states. The molecular structures of the free-base ligand, the lowest singlet, and triplet states of the monomer and the dimer of the Ni complex have been studied computationally using density functional theory (DFT) and ab initio correlation levels of theory. In calculations at the second-order Møller− Plesset (MP2) perturbation theory level, a large energy of 260 kcal mol−1 was obtained for the singlet−triplet splitting, suggesting that an alternative explanation of the observed magnetic properties is needed. The large energy splitting between the singlet and triplet states suggests that the observed change in the magnetism at very low temperatures is due to spin−orbit coupling effects originating from weak interactions between the fine-structure states of the Ni cations in the complex. The lowest electronic excitation energies of the dibenzotetraaza[14]annulene Ni(II) complex calculated at the time-dependent density functional theory (TDDFT) levels are in good agreement with values deduced from the experimental UV−vis spectrum. Calculations at the second-order algebraic-diagrammatic construction (ADC(2)) level on the dimer of the meso-substituted 3,3-dimethylindolenine dibenzotetraaza[14] annulene Ni(II) complex yielded Stokes shifts of 85−100 nm for the lowest excited singlet states. Calculations of the strength of the magnetically induced ring current for the free-base 3,3-dimethylindolenine-substituted dibenzotetraaza[14]annulene show that the annulene ring is very weakly antiaromatic, sustaining a paratropic ring-current strength of only −1.7 nA/T.

1. INTRODUCTION Nickel(II) complexes show various magnetic behavior, depending on the coordination environment and the nature of the ligands. In general, octahedral complexes are paramagnetic and the tetrahedral complexes show magnetic moments which vary significantly with the temperature. Square-planar complexes have all the d electrons paired, implying that they are expected to be diamagnetic. However, there are few examples, like certain Ni[P(tBu)2(O)NR2] complexes with planar coordination,1 which disobey this rule and show temperature-dependent paramagnetism. Dibenzotetraaza[14]annulenes are a class of synthetic macrocyclic ligands that have a planar coordination environment for a wide range of metal cations.2−10 The annulene ring is 14-membered with 16 conjugated π-electrons constituting a formally Hückel antiaromatic system. We recently synthesized the meso-substituted dibenzotetraaza[14]annulene ([LH2]) and its complexes with a number of transition metals, including Ni(II).11The molecular structure of the free-base is shown in Figure 1.12 The nickel complex showed diamagnetic character © XXXX American Chemical Society

Figure 1. Molecular structure of free-base 3,3-dimethylindolenine dibenzotetraaza[14]annulene ([LH2]). The figure has been made with ChemDraw.12

in solution as expected for a square planar Ni(II) complex. However, in the solid state, the effective magnetic moment was Special Issue: Jacopo Tomasi Festschrift Received: September 29, 2014 Revised: December 19, 2014

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Figure 2. Packing view of crystal structure of [Ni(L)] in the solid state. The dashed vertical line shows the linear chain of Ni(II) atoms. Note the alternating direction of the methyl groups and the slightly staggered orientation of the [Ni(L)] units.11

strongly temperature-dependent, ranging from 0.56 μB at 20 K to 1.65 μB at 300 K, suggesting that multiplet states are thermally accessible in the solid state. It has previously been proposed that doubly charged benzenoid polycyclic molecules have a small energy gap between low-lying singlet and triplet states, leading to an equilibrium between diamagnetic and paramagnetic antiaromatic molecules at ambient temperatures,13 which could explain the magnetic properties of the Ni complex in the solid state. The X-ray crystallography analysis11 showed that the planar molecules in the solid state are stacked along an axis perpendicular to the molecular plane forming a linear chain arrangement of the Ni atoms with metal−metal separation of 3.448(2) Å as shown in Figure 2.14 The adjacent molecules along the stack are staggered by 22° and connected through C−H···N interaction between the methyl hydrogens and the indolenine nitrogens. Such an arrangement was assumed to be responsible for the small gap between the ground state and a spin-multiplet excited state.11 In order to shed some light on the nature of the observed peculiar magnetism behavior, we have calculated the energy splitting between the lowest singlet and triplet states at density functional theory (DFT) and correlated ab initio levels of theory. We have estimated the aromatic character of the metalfree dibenzotetraaza[14]annulene ([LH2]) by performing calculations of the strength of the magnetically induced ring current at the density-functional theory (DFT) level using the gauge-including magnetically induced current (GIMIC) method.15−17 The electronic excitation spectra of the [LH2], [Ni(L)], and the dimeric [Ni(L)]2 were studied at the time-dependent density functional theory (TDDFT) level of theory.18,19 The excitation energies of the singlet and triplet states of [Ni(L)]2 were also calculated at the second-order algebraic diagrammatic construction (ADC(2)) level.20,21 This article is organized as follows. In Section 2, we present the employed computational methodologies. The computed structures of [LH2], [Ni(L)], and the dimeric [Ni(L)]2 are described in Section 3. The aromaticity and the magnetic susceptibility of the studied molecules are discussed in Sections

4 and 5, respectively. In Section 6, the calculated excitation energies for [LH2] and [Ni(L)] are compared to values deduced from the experimental UV−vis spectra. Stokes shifts of the [Ni(L)] solid-state material are also estimated by performing calculations on the lowest excited states of the [Ni(L)]2 dimer. The main conclusions are summarized in Section 7.

2. COMPUTATIONAL METHODS The molecular structures of the lowest singlet and triplet states of the studied molecules were optimized with Gaussian09 at the DFT level using the B3P86 functional. The LANL2DZ effective core potential (ECP) and basis sets were used for Ni, whereas the 6-311G++(d,p) basis sets were employed for the rest of the atoms.22−27 Restricted Kohn−Sham calculations were carried out for the singlet spin states, and for the triplet states we used unrestricted Kohn−Sham-based DFT. The obtained structures were found to be minima on the potential energy surface. The molecular structures of the lowest singlet and triplet states of the studies molecules were reoptimized with Turbomole at the DFT level using the B3LYP functional in combination with Grimme’s semiempirical van der Waals correction (D3) and the def2-TZVP basis sets.24,28−32 The relative energies between the different spin states of [Ni(L)]2 were obtained in single-point calculations at the second-order Møller−Plesset perturbation (MP2),33,34 spincomponent scaled MP2 (SCS-MP2),35 and scaled-opposite spin MP2 (SOS-MP2)36,37 levels of theory using the def2TZVP basis sets. The relative energies of [Ni(L)]2 were also calculated at the Hartree−Fock (HF) and B3LYP levels using the def2-TZVP basis sets. The molecular structure optimized for the lowest singlet state at the B3LYP level was employed in the single-point calculations at the ab initio correlation levels. The lowest singlet and triplet excitation energies of [Ni(L)]2 were calculated at the ADC(2) level20,21,39 using the resolutionof-the-identity (RI) approximation40−42 and the Laplacetransformed (LT) scaled-opposite-spin (SOS) approach in combination with the reduced virtual space (RVS) approximation with an energy cutoff threshold of 60 eV.36,37,43−46 The lowest singlet and triplet excitation energies of [Ni(L)] and B

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The Journal of Physical Chemistry A [LH2] were calculated at the TDDFT level18,19 using the B3LYP and BHLYP functionals in combination with the def2TZVP basis sets.24,47−52 The electronic structure of diatomic Ni···Ni species were studied at the singles and doubles coupled-cluster level with a perturbative correction for connected triples (CCSD(T)) using the def2-TZVP basis sets.38

The ring-current strengths calculated for the 14-membered annulene ring of the free-base [LH2] and the unsubstituted dibenzotetraaza[14]annulene are only −1.7 and −2.5 nA/T, respectively. The small current strengths as compared with the ring-current strength of 11.8 nA/T calculated at the same level of theory for benzene53 suggest that the dibenzotetraaza[14]annulene ring is very weakly antiaromatic or almost nonaromatic. Therefore, a near-degeneracy between the singlet and triplet states due to antiaromaticity is unlikely.

3. MOLECULAR STRUCTURES The molecular structure optimization of the metal-free dibenzotetraaza[14]annulene ([LH2]) at the DFT level yielded a saddled structure, whereas [LH2] is planar in the crystalline structure.11 The calculations on the corresponding annulene without the dimethylindolenine substituents yielded an essentially planar structure. The computed structures exhibit substantial bond-length alternation within the propanediiminate fragments, which is also observed in the crystal structure of [LH2], suggesting that the π delocalization is incomplete in the propanediiminate moiety. The optimized structure of the nickel complex ([Ni(L)]) is practically planar with similar geometric parameters, as observed in the crystal structure. The molecular structure optimization of the first singlet and triplet states of the [Ni(L)]2 dimer yielded structures with coplanar [Ni(L)] units that are staggered by ∼22°, which is consistent with experimental observations. In the singlet state structure, the two Ni atoms are separated by 3.32 Å, which is somewhat shorter than the distance of 3.45 Å found in the crystal structure. Calculations on the dimer of the dibenzotetraaza[14]annulene Ni(II) complex without the dimethylindolenine substituents resulted in an eclipsed structure with a Ni−Ni distance of 3.58 Å, indicating that the interactions between the methyl groups and the nitrogens of the indolenines are responsible for the staggered conformation of [Ni(L)]2. The stronger van der Waals interaction of the full annulene complex pulls the [Ni(L)] molecules closer to each other, which leads to a shorter Ni−Ni distance than for the dimer of the unsubstituted dibenzotetraaza[14]annulene Ni(II) complex. The interactions between the methyl and indolenine groups also allow for a closer contact between the individual [Ni(L)] units. The first excited triplet state of the [Ni(L)]2 dimer shows an interplanar distance of 3.23 Å. The Ni atoms are slightly pulled out of the annulene planes, leading to a Ni−Ni distance of 3.00 Å. The structure of the triplet state is somewhat nonplanar with the largest dihedral angle of the annulene ring of 5.5°. The crystal structure agrees better with the optimized structure of the singlet state than with that of the triplet state, suggesting that the [Ni(L)] units of the solid-state material couple to a singlet. The Cartesian coordinates of the molecular structures are given as Supporting Information.

5. MAGNETIC SUSCEPTIBILITY Measurements of the magnetic susceptibility at low temperatures showed that the solid-state material is paramagnetic above 13 K, whereas closer to 0 K it is diamagnetic.11 Thus, the experimental study suggested that the lowest diamagnetic and the lowest paramagnetic states are almost degenerate. Singlepoint MP2 calculations on [Ni(L)]2 showed that the singlet state is 260 kcal mol−1 lower in energy than the first triplet state, which implies that the magnetic behavior at low temperatures must have another origin than a temperatureinduced transition between these states. At the Hartree−Fock (HF) level, the triplet state is below the singlet, whereas in the B3LYP calculations, the singlet is 29 kcal mol−1 below the triplet. The MP2 and B3LYP calculations show that electron correlation effects shifts the order of the singlet and triplet states. Calculations at the SCS-MP2 and SOS-MP2 levels yielded practically the same singlet−triplet splitting as obtained in the MP2 calculations, indicating that higher-order correlation effects do most likely not change the order of the states and they do not significantly affect the singlet−triplet splitting, either. The relative energy splitting between the lowest singlet and triplet states of [Ni(L)]2 calculated at different levels of theory are summarized in Table 1. Table 1. Relative Energies (in kilocalories per mol) of [Ni(L)]2 Calculated at Different Levels of Theorya computational level

singlet

triplet

HF MP2 SCS-MP2 SOS-MP2 B3LYP

54 0.0 0.0 0.0 0.0

0.0 260 244 236 29

a

At the MP2 level, the D1 diagnostics are 0.069 and 0.068 for the singlet and triplet states, respectively.

The unexpected magnetic behavior of the [Ni(L)] solid at low temperatures might originate from the electronic structure of the weakly interacting Ni atoms. The electronic structure of diatomic Ni···Ni was therefore studied at the CCSD(T) level. The CCSD(T) calculations were performed on diatomic Ni4+ 2 and Ni2+ 2 species, which simulate the weakly interacting Ni···Ni moiety of the [Ni(L)] solid. For Ni4+ 2 , the calculations yielded a large energy separation of 208 kcal mol−1 between the singlet ground state and the first triplet state. Higher multiplets are also energetically far above the singlet. The lowest pentuple −1 state of Ni4+ above the singlet ground state. 2 is 135 kcal mol The CCSD(T) calculations on Ni2+ 2 show that the triplet and pentuple states are 222 and 149 kcal mol−1 above the singlet, respectively. The CCSD diagnostics for the singlet and triplet 4+ states of Ni2+ 2 and Ni2 are 0.013, 0.018, 0.034, and 0.042, suggesting that the calculated energies are reliable. Because the energy separation between the lowest spin states of the

4. AROMATICITY OF THE DIBENZOTETRAAZA[14]ANNULENES Antiaromatic molecules might have a very small gap between the frontier orbitals rendering the lowest-unoccupied molecular orbital of the ground state thermally accessible.13 To assess whether such a mechanism is relevant for the studied molecules, the aromatic character of [LH 2 ] and the corresponding annulene without the dimethylindolenine substituents was estimated from the magnetically induced current-density susceptibilities calculated by using the gaugeincluding magnetically induced current (GIMIC) method.15−17 C

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6. ELECTRONIC EXCITATION ENERGIES 6.1. Free-Base 3,3-Dimethylindolenine Dibenzotetraaza[14]annulene. The molecular structure of [LH2] is assumed to belong to the C2 point group having states of the A and B irreducible representations. The lowest singlet and triplet excitation energies calculated at the B3LYP level are given in Table 2. The oscillator strengths of the two lowest A

diatomic Ni···Ni species calculated at the CCSD(T) level are of the same size as obtained at the MP2 level for [Ni(L)]2, there must be another reason for the near-degenerate diamagnetic and paramagnetic states. The long Ni−Ni separation in [Ni(L)]2 implies that the magnetic properties of the [Ni(L)] solid may be traced back to the atomic energy levels of Ni cations. The ground state of Ni2+ has the electron configuration 1s22s22p63s23p63d8 coupling to 3 54 FJ. However, population analysis suggests that the electronic configuration of the Ni atom in the complex is s0.3d8.7. The open d shell of the Ni cations is due to spin−orbit interaction split into fine-structure states. The relative energies of the three fine-structure 3FJ states of Ni2+ are 0.0 (J = 4), 1360.7 cm−1 (J = 3), and 2269.6 cm−1 (J = 2), and the spin−orbit splitting of the d9 2DJ [J = (3/2) and (5/2)] states of Ni1+ is 1506.94 cm−1.54 For example, the energy separation of 1360.7 cm−1 between the J = 4 and J = 3 states corresponds to 3.9 kcal mol−1, which is almost 2 orders of magnitude smaller than the singlet−triplet splitting of the [Ni(L)]2 complex calculated at the MP2 level. However, an energy splitting of 4 kcal mol−1 corresponds to a temperature of 2000 K, which is 2 orders of magnitude too large to explain the observed magnetic behavior. Calculations on [Ni(L)]2 and on the diatomic Ni2 species as well as the experimental energy levels of atomic Ni2+ suggest that the change in the magnetic properties of solid [Ni(L)] at low temperatures must be due to thermal occupation of states originating from the fine-structure splittings of the Ni cation. In the ligand field of the annulene ligand, the J levels of the Ni cations split into nondegenerate MJ levels. For example, the energy levels of the 2D(5/2) states with MJ values of ± (5/2), ± (3/2), and ± (1/2) have different energies due to the ligand field. Assuming that the hole in the d shell has an MJ value of ± (1/2), there are two states, namely, |J, MJ⟩ =|(5/2), (1/2)⟩ |(5/ 2), −(1/2)⟩ that are degenerate. However, in the solid state, the |J, ± (1/2)⟩ states couple to the corresponding states of the adjacent Ni atoms. The coupling can either be ferromagnetic or antferromagnetic, which have slightly different energies. The same reasoning also holds if the hole occupies any of the other | J,MJ⟩ states. The energy gap between the spin-coupled pairs of | J,MJ⟩ states is expected to be significantly smaller than the energy difference between the J levels. The expected energy splitting due to the magnetic exchange coupling is in the observed energy range. The change in the magnetic susceptibility at low temperatures is then due to the temperature-dependence of the Boltzmann occupation of these states. Since the computational results cannot unequivocally verify the origin of the observed magnetism of the linear molecular chains in solid Ni(L), an experimental inquiry is in progress to ascertain the reason for the obtained magnetic results. One avenue of investigation concerns the possibility of partial occupancy of the Ni sites in the solid-state structure. The potential for partial occupancy is high since the free ligand ([LH2]) is isostructural with that of Ni(L).11 In fact, several different preparations have yielded crystallographically determined occupancies, ranging from 0.75 to 1.00 for the Ni cations in the solid-state structure, which has also lead to changes in the magnetic behavior. An alternative interpretation is that the lower occupancies are due to the presence of mixed valent nickel species, which is also expected to lead to the observed magnetic behavior.

Table 2. Singlet and Triplet Excitation Energies (E in Electronvolts) and the Corresponding Wave Lengths (λ in nm) for [LH2] Calculated at the B3LYP Level Using the Molecular Structure of the Singlet State in the C2 Symmetrya singlet state 2A 3A 4A 5A 6A 1B 2B 3B 4B 5B

E 2.38 3.26 3.41 3.75 3.85 2.84 3.17 3.38 3.77 3.84

λ 521 380 364 331 322 436 391 367 329 323

triplet f −2

0.2 × 10 0.2 × 10−6 0.060 0.005 0.087 0.050 0.365 1.267 0.451 0.070

E

λ

1.88 2.63 3.02 3.27 3.41 2.10 2.60 2.83 3.03 3.49

659 471 411 380 364 590 477 439 409 355

a

Oscillator strengths ( f) for the singlet transitions are also reported. The absorption wave length of the strong transition of the experimental UV-Vis spectrum is 377 nm (3.29 eV). A shoulder in the experimental spectrum appears at 294 nm (4.22 eV).

states are small, implying that they might be difficult to observe, whereas the excitation energies of the 4A to 6A states appear at 3.41−3.85 eV (364−322 nm), which is in the high-energy region of the recorded spectrum. The 4A-6A transitions may be part of the broad peak in the experimental spectrum measured for [LH2] in CHCl3. The 1B state at 2.84 eV (436 nm) has an oscillator strength of 0.05, whereas the band strength of the 2B state at 3.17 eV (391 nm) is seven times larger. The transition to the 3B state at 3.38 eV (367 nm) is the strongest transition with an oscillator strength of 1.27. The 4B state at 3.77 eV (329 nm) has also a strong ground-state transition. The experimental spectrum has a peak maximum at 377 nm (3.29 eV) with a shoulder at 294 nm (4.22 eV). The broad peak has also some structure on the low-energy side of the peak maximum that might correspond to the electronic transitions with small band strengths. In DFT calculations, using the BHLYP functional, the excitation energies are blue-shifted in comparison to the excitation energies calculated at the B3LYP level and to the experimental spectrum. At the BHLYP level, the five A states appear in the energy range of 2.95−4.73 eV. They have also somewhat larger oscillator strengths than obtained in the B3LYP calculations. The excitation energies of the five lowest B states calculated at the BHLYP level are in the energy range of 3.64−4.93 eV. At the BHLYP level, the three lowest states are the bright states, suggesting that the weak 1B state at the B3LYP level is an artificial low-lying charge-transfer state. Comparison of the B3LYP excitation energies with the energy of the peak maximum of the experimental UV−vis spectrum shows that the agreement is good. The energy of the peak maximum at 377 nm (3.29 eV) can be compared with the excitation energy of the 3B state at 367 nm (3.38 eV). The strong 2B state at 391 nm (3.17 eV) might lead to the broadening of the main peak on the low-energy side of the peak D

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The Journal of Physical Chemistry A maximum. The experimental spectrum shown in Figure 3 is recorded in chloroform (CHCl3), whereas we have not considered any solvent effects in our calculations.

Table 3. Singlet and Triplet Excitation Energies (E in Electronvolts) and the Corresponding Wave Lengths (λ in Nanometers) for [Ni(L)] Calculated at the B3LYP Level Using the Molecular Structure of the Singlet State in the C2 Symmetrya singlet state

E

λ

2A 3A 4A 5A 6A 1B 2B 3B 4B 5B

2.28 2.51 2.92 3.01 3.27 2.35 2.65 2.86 2.99 3.40

544 494 425 412 379 528 468 434 415 364

triplet E

λ

1.01 1.89 2.38 2.57 2.74 1.10 1.55 2.12 2.56 2.60

1227 656 521 483 452 1125 802 585 484 477

f 0.5 × 0.5 × 0.6 × 0.1 × 0.2 × 0.7 × 0.7 × 0.7 × 0.428 1.209

10−8 10−7 10−6 10−5 10−5 10−3 10−2 10−4

a

Oscillator strengths ( f) for the singlet transitions are also reported. The absorption wavelengths of the two strong transitions of the experimental UV-Vis spectra are 429 nm (2.89 eV) and 382 nm (3.25 eV). A shoulder in the experimental spectrum appears at 294 nm (4.22 eV).

Figure 3. Experimental UV spectra (in Nanometers) of [Ni(L)] measured in CHCl3 (red) and in acetic acid (purple) as well as the UV spectrum of [LH2] measured in CHCl3 (blue).

The B3LYP excitation energy of the two lowest triplet states are 1.88 and 2.10 eV. The eight higher triplet states have energies between 2.60 and 3.49 eV, which is in the same energy range as for the excited singlet states. At the BHLYP level, the energies of the two lowest excited triplet states are 1.77 and 2.00 eV. 6.2. 3,3-Dimethylindolenine Dibenzotetraaza[14]annulene Ni(II). The molecular structure of [Ni(L)] belongs to the C2h point group, whereas optimized structure has C2 symmetry because in the calculation, the orientation of the methyl groups slightly breaks the symmetry. The B3LYP calculations of the lowest A and B states shows that the transitions to the five lowest A states are practically forbidden. The three lowest B states also have small oscillator strengths, whereas the transitions to the 4B and 5B states are the strong bands that are easily detected experimentally. The excitation energies of the 4B and 5B states are 2.99 eV (415 nm) and 3.40 eV (364 nm), which agree well with the maxima at 429 and 382 nm of the two main peaks in the experimental spectrum shown in Figure 3. The lowest singlet and triplet excitation energies for [Ni(L)] calculated at the B3LYP level are given in Table 3. The experimental spectra are recorded in solutions of chloroform (CHCl3) and acetic acid (AcOH), whereas in the calculations, we have not considered any solvent effects. Calculations at the BHLYP level yield qualitatively the same results. The excitation energies of the strong transitions are blue-shifted to 355 nm (3.49 eV) and 315 nm (3.94 eV). The triplet states have significantly smaller excitation energies. At the B3LYP level, the excitation energies of the two lowest triplet states are 1.01 and 1.10 eV. The rest of the calculated triplet states have excitation energies in the visible range of the energy spectrum. The energies of the triplet states could not be calculated at the BHLYP level that has 50% Hartree−Fock exchange because the reference is triplet instable at the BHLYP level. 6.3. 3,3-Dimethylindolenine Dibenzotetraaza[14]annulene Ni(II) Dimer. The lowest singlet and triplet excited states were calculated at the LT-SOS-ADC(2) level for the singlet and triplet structures of [Ni(L)]2 using the RVS approach.20,21,39,46,55 The obtained excitation energies are

summarized in Table 4. The magnitude of the Stokes shift can be estimated from the difference in the excitation energies Table 4. Lowest Singlet and Triplet Excitation Energies of [Ni(L)]2 (in Electronvolts) Calculated at the ADC(2) Level Using the Optimized Molecular Structures of the Lowest Singlet and Triplet Statesa spin→

singlet

triplet

structure→

singlet

triplet

singlet

triplet

state

energy

energy

energy

energy

1 2 3 4 5

2.54 2.62 2.90 2.91 3.28

2.16 2.17 2.35 2.42 2.58

1.01 1.01 1.03 1.03 1.25

0.25 0.36 0.51 1.07 1.12

a

The molecular structures were optimized at the B3LYP/def2-TZVP level. The oscillator strengths of the five lowest singlet states are smaller than 10−3.

calculated using the molecular structures of the singlet and triplet states, respectively. Thus, it is assumed that the molecular structures of the lowest triplet state and the first excited singlet state are similar. This is a reasonable assumption because for both states, an electron is formally excited from the highest occupied molecular orbital (HOMO) to the lowest unoccupied molecular orbital (LUMO). The computationally demanding optimization of the molecular structure of the first excited singlet state is thereby avoided and replaced by the cheaper structural optimization of the lowest triplet state. The Stokes shifts of higher excited states are difficult to compute because of level crossings. The excitation energy of the first singlet excited state of 2.54 eV corresponds to an absorption at 488 nm. For the molecular structure of the first triplet state, the corresponding excitation energy of 2.16 eV corresponds to an emission wavelength of 574 nm. The calculated Stokes shifts for the lowest singlet states of [Ni(L)]2 are 85−100 nm (0.38−0.55 eV), which is probably also close to the Stokes shift of the [Ni(L)] solid-state E

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The Journal of Physical Chemistry A material. The ADC(2) calculations of the excitation energies of the lowest triplet states yield values of about 1 eV, which are in close agreement with the lowest excitation energies of the triplet states of the [Ni(L)] monomer as obtained in calculations at the B3LYP level. The excitation energies of the three lowest triplet states calculated at the ADC(2) level using the molecular structure of the lowest triplet state are 0.255, 0.235, and 0.511 eV, suggesting that the phosphorescence of the [Ni(L)] solid can be expected to occur in the infrared region. The UV−vis spectrum of solid [Ni(L)] has strong peaks at 495 nm (2.51 eV) and 388 nm (3.20 eV), which are in close agreement with the ADC(2) excitation energies for [Ni(L)]2 of 2.54, 2.62, and 3.28 eV, respectively. The first strong peak in the experimental spectrum has a shoulder on the high-energy side of the first strong peak, which might be related to the transitions at 2.90−2.91 eV in the calculated spectrum for [Ni(L)]2. The assignment must be used with some caution because interpreting the UV−vis spectrum of a solid based on calculations of the excitation energies of the dimer involves some risks. The experimental UV−vis absorption spectrum of [Ni(L)] in the solid-state is given in the Supporting Information.

The electronic excitation energies calculated at the timedependent density functional theory (TDDFT) level for the free-base 3,3-dimethylindolenine dibenzotetraaza[14]annulene [LH2] and for [Ni(L)] are in very good agreement with values deduced from experimental UV−vis spectra. Calculations at the second-order algebraic-diagrammatic construction (ADC(2)) level were performed on the singlet and triplet structures of the [Ni(L)]2 for estimating the size of the Stokes shift of [Ni(L)] in the solid state. At the ADC(2) level, the Stokes shifts of the lowest singlet states of [Ni(L)]2 are 0.38−0.55 eV (85−100 nm). The calculated aromatic character of the annulene ring, the calculated excitation spectra, and the calculated energy separations between the lowest singlet and triplet states all suggest that there are no low-lying multiplet states that are almost degenerate with the singlet ground state.

■

ASSOCIATED CONTENT

S Supporting Information *

Cartesian coordinates of the studied molecules and the experimental UV−vis absorption spectrum of [Ni(L)] in the solid state. This material is available free of charge via the Internet at http://pubs.acs.org.

■

7. CONCLUSIONS The recently synthesized dibenzotetraaza[14]annulene Ni(II) complex with two 3,3-dimethylindolenine groups in the meso positions. [Ni(L)] has been studied computationally at ab initio and density functional theory levels. Low-temperature measurements of the magnetic susceptibility of [Ni(L)] show that the magnetic properties drastically change at 13 K, indicating a transition from a singlet spin state to a high-spin state. However, calculations on the [Ni(L)]2 dimer yield a large singlet−triplet splitting, indicating that the observed magnetic behavior must have another origin. Since the population analysis shows that there is a hole in the 3d shell, we here proposed that the fine-structure levels of the individual cations with an open d shell are split by the ligand field of the surrounding annulene. The hole in the d shell can then couple in a parallel or an antiparallel fashion with the neighboring Ni atoms, leading to two nearly degenerate spin-coupled bands of the solid-state material. The Boltzmann occupation of the bands of the near-degenerate states gives rise to the observed change in the magnetic susceptibility at very low temperatures. Since the computational studies were not able to unambiguously explain the observed magnetism of [Ni(L)] in the solid state, the experimental study will be extended to crystallographic measurements as well as magnetic and spectroscopic studies of single-crystal and microcrystalline samples in order to cast more light on this mysterious result. Computational studies will be used for elucidating the possibility of mixed valency, symmetry breaking, and noninnocent ligand behavior. Such studies will require computationally demanding inclusions of larger chains and open-shell molecular structures. Calculations of the strength of the magnetically induced ring current for the free-base dibenzotetraaza[14]annulene show that the annulene ring is very weakly antiaromatic, sustaining a paratropic ring-current strength of only −1.7 nA/T. The annulene ring is almost nonaromatic and not antiaromatic as one would expect when counting the number of π electrons and applying Hückel’s rule for aromaticity.

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected].fi. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research has been supported by the Academy of Finland through projects (137460 and 266227) and its Computational Science Research Programme (LASTU/258258). We thank the Magnus Ehrnrooth foundation for financial support. H.K. acknowledges support from the University of Malaya (HIR Grant UM.C/625/1/HIR/151). H.R. acknowledges the financial support from the University of Helsinki, the University of California Davis, and the University of Ibn Tofail. For computational resources, we thank the CASCaM at UNT, Texas, XSEDE (NSF Grants CHE140026), and CSC, the Finnish IT Center for Science.

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REFERENCES

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