Theoretical studies on the photoisomerization mechanism of osmium(II) sulfoxide complexes

Abstract

Photochromic compounds, employing photonic energy for excited-state bond rupture and bond construction processes, are excellent candidates for application as optical molecular information storage devices. In this work, a dispersion corrected density functional theory (DFT-D) study was carried out on the photoisomerization mechanism of the osmium sulfoxide complex, [Os(bpy)₂(DMSO)₂]²⁺ (bpy = 2,2′-bipyridine; DMSO = dimethyl sulfoxide), which features a pronounced photochromic character based on an ultrafast photo-triggered linkage isomerization located at the SO-ligand. Calculated results demonstrate that the Os–S → Os–O isomerization proceeds adiabatically on the potential energy surface (PES) of the lowest metal-to-ligand charge transfer excited states ³MLCT_S → ³MLCT_O, and the metal centered ligand field (³LF_S) excited state is not involved. However, attributed to the weakened Os–DMSO bond-strength upon Os–S to Os–O isomerization, the population of the ³LF_O excited state is thermally accessible. Therefore, photodissociation of DMSO from the Os center occurs via homolytic cleavage of the Os–O bond after an avoided curve crossing between the lowest ³MLCT_O state and the ³LF_O repulsive state along the stretching coordinate of the Os–O bond.

---

1. Introduction

Due to their excited-state bond rupture and bond construction characters, photochromic complexes based on d⁶ transition metal complexes are promising and versatile candidates for applications in light energy storage and light-activated switches.^1–6 Among them, polypyridine ruthenium(II)^7–10 and osmium(II)^11,12 sulfoxide complexes, in which the intramolecular isomerization of the coordinated sulfoxide group from the Mⁿ⁺–S to Mⁿ⁺–O linkage mode can be triggered by external light signal, are highly appealing and have attracted a great deal of attention.

Intramolecular isomerization of the sulfoxide group in polypyridine ruthenium(II) complexes was firstly observed for [Ru(bpy)₂(DMSO)₂]²⁺ (bpy = 2,2′-bipyridine; DMSO = dimethyl sulfoxide) by the group of F. R. Keene.¹³ In their studies, a color change from yellow to red was observed due to the photo-induced one DMSO ligand isomerization upon exposure to sunlight or UV irradiation. Soon afterwards, photochromic character of osmium sulfoxide complexes was reported by the group of J. J. Rack.¹⁴ In their studies, photo-induced one DMSO ligand isomerization was observed in [Os(bpy)₂(DMSO)₂]²⁺, as displayed in Fig. 1. Correspondingly, their absorption maximum was shifted from 355 nm to a new peak 403 nm by such molecular rearrangement. In the last few years, many investigations have been devoted to the synthesis and characterization studies for such polypyridine ruthenium or osmium complexes with photoisomerizable sulfoxide group.^15–22 Except for experimental achievements, theoretical studies have also been carried out for exploring the electronic and photophysical properties of such transition-metal based chromophores.^23–27 It is found that the HOMO–LUMO energy gap is decreased by Mⁿ⁺–S → Mⁿ⁺–O linkage isomerization due to the decreased electron transfer amount from surrounding ligands to central Mⁿ⁺, which makes the absorption of such photochromic ruthenium(II) or osmium(II) sulfoxide complexes red shifted.²⁶

Fig. 1 Chemical structures of the S-bonded (left) and O-bonded (right) isomers of [Os(bpy)₂(DMSO)₂]²⁺ complexes with the labeling scheme used throughout this work.

It has been realized that quite different excited-state characters can be formed after one-electron excitation from the ground state (¹GS) attributed to the different orbital parentage.²⁸ The potential energies of the ground state and two triplet states are displayed in the model diagram, Fig. 2. The two triplet states are the metal-to-ligand charge transfer (³MLCT) and the metal centered excited ligand field (³LF) excited state. Among them, ³MLCT indicates the lowest excited triplet state of transition-metal complexes formed by promotion of an electron from a π_M metal orbital to the π_L* ligand orbitals, which exhibits long lifetime and intense luminescence emission. ³LF indicates a higher triplet energy involving the bonding and antibonding orbitals of a Mⁿ⁺–L bond between surrounding ligand and Mⁿ⁺ center, which often leads to fast radiationless decay to the ground state/or ligand dissociation reactions. According to previous report, ³MLCT excited state will be raised inevitably to a region very close to or even higher than the upper lying ³LF excited state by the dissociation along the Mⁿ⁺–L bond.²⁸ Then, these two states mix and intersect, which is called avoided crossing. If the energy barrier (E_a) from left to right can be overcome, ³LF becomes the lowest triplet state in the stretched Mⁿ⁺–L bond region instead of ³MLCT in the equilibrium geometry region on the left of avoided crossing. As a result, the transition-metal complexes will undergo fast homolytic dissociation following the repulsive ³LF curve. It has been demonstrated that ³LF excited states play a central role in the photoisomerization mechanism of photochromic polypyridine ruthenium sulfoxide complexes.²⁷ Thereby, nonadiabatic pathways for such photoisomerization process in photochromic [Ru(bpy)₂(OSO)]⁺ can be explained due to their fast radiationless decay to the ground state from the ³LF states.⁸

Fig. 2 Model potential–energy curves of the ground state and two relevant excited triplet states of transition metal (Mⁿ⁺) complexes along the stretching of one Mⁿ⁺–L bond between surrounding ligand and Mⁿ⁺ center (see text for a detailed description).

However, it is still unclear that whether the ³LF excited state is involved in the photoisomerization mechanism of osmium sulfoxide complexes or not. For better understanding the extra-light triggered intramolecular isomerization mechanism of osmium sulfoxide complexes, intrinsic reaction paths (IRPs) for the Os–S₁ → Os–O₁ and Os–O₁ → Os–S₁ processes in ground and excited states of [Os(bpy)₂(DMSO)₂]²⁺ complex were examined theoretically.

2. Computational details

Considering Os–S and Os–O bonds are weak interactions and the bond lengths are overestimated by current density functional theory, the empirical dispersion correction²⁹ was added to the density functional theory (DFT) with Becke's and Johnson's rational damping function³⁰ in optimization calculations, and dubbed this variant DFT-D3(BJ). Based on the results from a number of benchmark calculations, collected in Table S1,† the appropriate PBE0-D3(BJ)³¹ exchange correlation functional was employed for the fully gradient optimization of the osmium complexes. Two basis set (BS1 and BS2) was considered. BS1 is made of SDD³² for osmium, a correlation-consistent polarized double-ζ basis set (cc-pVDZ)³³ for H atoms, and a correlation-consistent polarized triple-ζ basis set (cc-pVTZ)³³ for C, N, O and S atoms. BS2 is made of pseudopotential-based augmented correlation-consistent basis set (aug-cc-pVDZ-pp)³⁴ for osmium and aug-cc-pVDZ for non-metal atoms. In addition, conductor-like polarizable continuum model (CPCM)³⁵ using solvent acetonitrile (ε = 35.688) was also considered for optimization calculations of the involved geometries. Harmonic vibrational frequencies were calculated analytically at the same level to ascertain the nature of the optimized structures. The QST3 algorithm was employed for the location of the transition structures (TS) which were confirmed by having only one imaginary frequency with the corresponding eigenvector pointing toward the reactants and products. In addition, intrinsic reaction coordinate (IRC)^36,37 calculations were also performed to make sure that the optimized transition states were connected with two relevant minima.

To shed light on the nature of the excited states of the S- and O-linked osmium complexes, vertical transition energies were calculated on the basis of the optimized S0 and T1 structures via time-dependent DFT (TD-DFT)³⁸ at the same level (BS1) which promises a way forward to study excited states of large metallic complexes. Natural transition orbital (NTO)³⁹ analyses were performed to examine the nature of the excited states.

Charge distribution was evaluated with the natural population analysis (NPA)⁴⁰ for the aim to examine the degree of charge transfer between surrounding ligands and central osmium.

All calculations were performed by using the Gaussian 09 package.⁴¹

3. Results and discussion

Photo-induced one DMSO ligand isomerization upon exposure to sunlight or UV irradiation has been observed experimentally in polypyridine osmium(II) complex, [Os(bpy)₂(DMSO)₂]²⁺.¹⁴ Chemical structures of these two different isomers with S₁- and O₁-linkage mode are displayed in Fig. 1. Optimized geometrical parameters are collected in Table 1, available experimental results¹⁴ are also included for comparison. A good agreement between them can be obtained. NPA charge distribution results for these isomers in the ground and excited states are listed in Table 2. Calculated reaction energies as well as energy barriers for the intramolecular bond rupture and bond construction processes in [Os(bpy)₂(DMSO)₂]²⁺ are given in Table 3. It is found that the influences of the electron density redistribution induced by one-electron excitation on the intrinsic reaction paths (IRPs) of intramolecular isomerization of [Os(bpy)₂(DMSO)₂]²⁺ are significantly.

Table 1 Calculated bond lengths (angstroms) and bond angles (degrees) for Os(II) complexes, as determined at the PBE0-D3(BJ)/BS2 level of theory. Optimizations are conducted in acetonitrile by using the CPCM model

Bond	S-bonded				O-bonded
	^1GSS	Exptl.^a	^3MLCTS	^3LFS	^1GSO	^3MLCTO	^3LFO
a Ref. 14.
Os–S1	2.286	2.276	2.381	2.832	—	—	—
Os–O1	—	—	—	—	2.147	2.058	2.830
S1–O1	1.494	1.471	1.481	1.512	1.551	1.574	1.521
Os–S2	2.286	2.268	2.342	2.304	2.271	2.345	2.292
S2–O2	1.494	1.477	1.483	1.494	1.491	1.482	1.492
Os–Nb1	2.009	2.100	2.118	2.131	2.067	2.083	2.145
Os–N′b1	2.101	2.091	2.101	2.246	2.038	2.052	2.268
Os–Nb2	2.101	2.097	2.076	2.091	2.088	2.078	2.089
Os–N′b2	2.009	2.094	2.024	2.071	2.094	2.086	2.059
α-(O1–S1–Os)/α-(S1–O1–Os)	116.0	115.8	113.5	77.0	120.6	123.6	116.8
α-(S1–Os–Nb1)/(O1–Os–Nb1)	98.0	97.8	99.6	95.6	91.4	91.1	83.8
α-(O2–S2–Os)	116.3	116.0	115.2	118.1	117.9	118.4	117.9

---

Table 2 Natural population charges distributed on the Os complexes (Q)^a

	S-bonded			O-bonded
	^1GSS	^3MLCTS	^3LFS	^1GSO	^3MLCTO	^3LFO
a Q (ligand) indicates the charge on all the atoms in ligand.
S1	1.594	1.568	1.204	1.228	1.218	1.218
O1	−0.952	−0.931	−1.007	−0.856	−0.818	−0.991
Os	−0.443	−0.049	0.353	−0.062	0.351	0.355
DMSO1	0.569	0.634	0.064	0.330	0.407	0.121
DMSO2	0.569	0.577	0.479	0.519	0.592	0.467
BPY1	0.652	0.696	0.523	0.619	0.018	0.497
BPY2	0.652	0.142	0.581	0.594	0.631	0.560

---

Table 3 Energy parameters associated with the intramolecular isomerization in [Os(bpy)₂(DMSO)₂]²⁺ obtained at the PBE0-D3(BJ)/BS1 and PBE0-D3(BJ)/BS2 level of theory. (energies are in eV)

	BS1		BS2
	Ea	Er	Ea	Er
^1GSS → ^1GSO	1.29	0.27	1.28	0.20
^3MLCTS → ^3MLCTO	0.45	−0.27	0.36	−0.19
^1GSO → ^1GSS	1.01	−0.27	1.08	−0.20
^3MLCTO → ^3LFO	0.56	0.42	0.41	0.28

---

3.1. Os–sulfoxide bond-strength changes upon one-electron excitation

As listed in Table 1, optimized Os–S₁ bond in the ground state (¹GS_S) of S₁-[Os(bpy)₂(DMSO)₂]²⁺ is 2.286 Å, which is shorter than that in the metal-to-ligand charge transfer excited state (³MLCT_S) by about 0.095 Å. On the contrary, the Os–O₁ bond in the ¹GS_O state is longer than that in the ³MLCT_O state for about 0.089 Å. It means the Os–S₁ bond is weakened, while Os–O₁ bond is strengthened upon one-electron excitation.

Frontier molecular orbitals (MOs) play an important role in photoresponsive materials because location of the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) is quite reasonable for the description of the first excited singlet transition. As shown in Fig. 3, for these [Os(bpy)₂(DMSO)₂]²⁺ isomers, the HOMO is mainly distributed on central osmium, while the LUMO is mainly distributed on the bpy ligands. Thereby, the ³MLCT_O and ³MLCT_O excited states were formed with one-electron promotion from a π_Os metal orbital to the π_bpy* bpy ligand orbitals. Electron configuration and singly occupied molecular orbitals of the excited states are shown in Fig. 4. NPA charge calculation results demonstrate that the charge distributed on central osmium is decreased by 0.394 and 0.413 e, respectively, upon one-electron excitation from S₁- and O₁-linked isomers.

Fig. 3 Chemical structures of the S-bonded (left) and O-bonded (right) isomers of [Os(bpy)₂(DMSO)₂]²⁺ complexes with the labeling scheme used throughout this work.

Fig. 4 Electron configuration for the singly occupied molecular orbitals of the excited states of [Os(bpy)₂(DMSO)₂]²⁺.

As known, S-bonding is favored in the case of ‘soft’ metal atoms where the sulfoxides act as moderate π-acceptor ligands,⁴² so that the metal to sulfur bond is strengthened when electron distribution on central metal is increased. Thereby, weakened Os–S₁ bond upon one-electron excitation from a π_Os orbital to the π_bpy* orbitals can be explained. Differently, it has been proved that O-bonding is favored in the case of ‘hard’ metal atoms where the sulfoxides act as moderate σ-donor ligands, so that the metal–oxygen bond is strengthened when electron distribution on central metal is decreased. Thereby, the Os–O₁ bond is strengthened by one-electron excitation from a π_Os orbital to the π_bpy* orbitals.

The variation trends of the S–O bond distances are also rationalized considering the metal–sulfoxide bonding changes upon one-electron excitation. As listed in Table 2, the weakened Os–S₁ bond-strength reduces the positive charge of sulfur atom from 1.594 to 1.568 e, and thus the electronegativity of S₁ atom is decreased. Therefore, there is additional electron transfer from O₁ to S₁ (the charge on O₁ is decreased from −0.952 to −0.931 e) for compensation, which leads to the increased double bond character of the S₁–O₁. As a result, the S₁–O₁ bond in the ground state of S₁-[Os(bpy)₂(DMSO)₂]²⁺ (¹GS_S) is decreased from 1.494 to 1.481 Å upon one-electron excitation. For the O₁-linked isomer, the charge on O₁ atom is changed from −0.856 to −0.818 e by one-electron excitation, which makes the electronegativity of O₁ atom increased. Due to the equalization of atom electronegativities,⁴³ this is compensated by electron transfer from the sulfur atom and the methyl groups which makes the positive charge on the S₁ atom decreased from 1.228 to 1.218 e. Furthermore, attributed to the increased O₁ electronegativity, the π-electron transfer from O₁ to S₁ is decreased. As a result, the S–O bond-strength is weakened and its bond-length is increased from 1.551 to 1.574 Å.

3.2. Intrinsic reaction paths

As shown in Fig. 5, S₁-[Os(bpy)₂(DMSO)₂]²⁺ is stable than its O₁-linked isomer, O₁-[Os(bpy)₂(DMSO)₂]²⁺, for about 0.20 eV because Os–S linkage mode of DMSO is preferred in the ground state of Os(II) complex. Energy barrier for the isomerization from S- to O-linkage is about 1.08 eV. Computational results demonstrated that the energy barrier between S₁- and O₁-linked isomers in the lowest excited states is lower than that in the ground states by about 0.92 eV. It means such intramolecular isomerization process should be much easier to proceed in the lowest excited state. Thereby, stimulated by external light, one DMSO ligand isomerization from Os–S₁ to Os–O₁ linkage mode in [Os(bpy)₂(DMSO)₂]²⁺ was observed in experimental studies. As mentioned above, the Os–S₁ bond is weakened and the Os–O₁ bond is strengthened by electron density redistribution upon one-electron excitation, which makes the energy of S₁-[Os(bpy)₂(DMSO)₂]²⁺ higher than O₁-[Os(bpy)₂(DMSO)₂]²⁺ by about 0.36 eV in the lowest ³MLCT excited states. As a result, the Os–S₁ to Os–O₁ isomerization process is changed from endothermic to exothermic reaction upon one-electron excitation. However, calculated results show that the S₁-[Os(bpy)₂(DMSO)₂]²⁺ in the lowest ³MLCT excited state is stable than that in the ³LF_S state for about 0.16 eV. This means ³MLCT_S → ³MLCT_O isomerization is more thermodynamically favored in the excited state compared with the ³MLCT_S → ³LF_S pathways.

Fig. 5 Calculated Reaction pathways for the Os–S₁ to Os–O₁ isomerization of [Os(bpy)₂(DMSO)₂]²⁺. Energies are in eV.

It is obvious that the photoisomerization mechanism of ruthenium sulfoxide complex, [Ru(bpy)₂(OSO)]⁺, is different with that of [Os(bpy)₂(DMSO)₂]²⁺. As reported by A. J. Göttle and his coworkers, ³LF state plays a central role in the Ru–S → Ru–O nonadiabatic photoisomerization mechanism of [Ru(bpy)₂(OSO)]⁺ complexes.²⁷ Thereby, no O-bonded excited state, ³MLCT_O, of [Ru(bpy)₂(OSO)]⁺ complex can be observed experimentally.⁸ It is proposed that the ³LF_S excited state is more stable than the ³MLCT_O state. Thereby, the ³LF_S excited state in [Ru(bpy)₂(OSO)]⁺ should be thermally accessible from the initial radiative ³MLCT_S electron state and no ³MLCT_O excited state of [Ru(bpy)₂(OSO)]⁺ complex was observed.

Differently, along with the Os–O bond rupture in the lowest ³MLCT_O excited state of O₁-[Os(bpy)₂(DMSO)₂]²⁺, instead of Os–S bond construction, a new O₁-linked osmium complex in the ³LF_O state is formed. Optimized geometrical parameters of the O₁-[Os(bpy)₂(DMSO)₂]²⁺ in the ³LF_O state are listed in Table 1. It means, for the excited-state Os–O bond breaking process, nonradiative ³LF_O excited state should be accessible from the initial radiative ³MLCT_O electron state. As shown in Fig. 6, it is because the energy barrier for the ³MLCT_O → ³LF_O process (0.41 eV) is smaller than that for the ³MLCT_O → ³MLCT_S pathway (0.56 eV). Considering promotion to the ³LF state often leads to fast radiationless decay to the ground state or ligand dissociation reactions,⁴⁴ it can be predicted that photodissociation of DMSO from Os center may occur via homolytic cleavage of Os–O bond after an avoided curve crossing between the lowest ³MLCT_O state and a ³LF repulsive state along the stretching mode of the Os–O bond.

Fig. 6 Calculated Reaction pathways for the Os–O₁ bond breaking process in [Os(bpy)₂(DMSO)₂]²⁺. Energies are in eV.

This can be confirmed with TD-DFT calculation results. As shown in the Fig. 7 and Table S2,† NTO results demonstrated that the first transition (S₁) of S-[Os(bpy)₂(DMSO)₂]²⁺ is from the ground state (¹GS_S) to ¹MLCT (formed with π_L* ligand orbitals and d_xy, d_yz or d_xz metal orbitals) and the third transition (S₃) is from ¹GS_S to ¹LF_S (formed with π_L*ligand orbitals and d_x²−y² or d_z² metal orbitals). For O-[Os(bpy)₂(DMSO)₂]²⁺, the S₁ is from ¹GS_O to ¹MLCT_O and the S₂ is from ¹GS_O to ¹LF_O. The energy gap between ¹MLCT_S and ¹LF_S is lower than that between ¹MLCT_O and ¹LF_O (0.28 eV). This is in good agreement with DFT calculation results. More importantly, from TD-DFT results, it is observed that the ¹MLCT_O excited state is more stable that the ¹MLCT_S excited state. Moreover, the energy of the ¹LF_O excited state is lower than that of the ¹MLCT_S excited state. This can be used for better understanding that why the Os–S₁ → Os–O₁ isomerization proceeds adiabatically on the PES of MLCT_S → MLCT_O and the LF_S excited state is not involved. Differently, for the excited-state Os–O bond breaking process, nonradiative LF_O excited state should be accessible from the initial radiative MLCT_O excited state.

Fig. 7 Photophysical properties of [Os(bpy)₂(DMSO)₂]²⁺ isomers obtained from TD-DFT calculations. The nature of the orbitals involved in the relevant excited states is also included.

4. Conclusion

A DFT-D study was carried out on the photo-triggered intramolecular linkage isomerization of osmium sulfoxide complex, [Os(bpy)₂(DMSO)₂]²⁺, for better understanding the photoisomerization mechanism of osmium complexes as well as the role of the ³LF excited state in the bond rupture (Mⁿ⁺–X) and bond construction (Mⁿ⁺–Y) processes.

The metal-to-ligand charge transfer excited states (³MLCT_S and ³MLCT_O) were formed by one-electron promotion from a π_Os metal orbital to the π_bpy* bpy ligand orbitals which makes the electron distribution on central osmium decreased. As a consequence, the Os–S₁ bond is weakened because S-bonding is favored in the case of ‘soft’ metal atoms, while the Os–O₁ bond is strengthened because O-bonding is favored in the case of ‘hard’ metal atoms. As a result, the Os–S₁ to Os–O₁ isomerization process is changed from endothermic to exothermic reaction upon one-electron excitation. It means such intramolecular isomerization process should be much easier to proceed in the lowest excited state.

Moreover, it is found that the Os–S₁ → Os–O₁ isomerization proceeds adiabatically on the PES of ³MLCT_S → ³MLCT_O, and the ³LF_S state is not involved. Differently, along with the Os–O bond rupture in the lowest ³MLCT_O excited state of O₁-[Os(bpy)₂(DMSO)₂]²⁺, no Os–S bond construction is observed and a new O₁-linked osmium complex in the ³LF_O state is formed. It means, for the excited-state Os–O bond breaking process, nonradiative ³LF_O excited state should be accessible from the initial radiative ³MLCT_O electron state. As a result, photodecomposition of the DMSO ligand from the ³LF_O excited state complex may occur along with the Os–O bond stretching mode because promotion to the ³LF state often leads to fast radiationless decay to the ground state or ligand dissociation reactions.

Acknowledgements

This work is supported by the National Natural Science Foundation of China (21403037, 51478123, 21463003), the Natural Science Foundation of Jiangxi Province (20142BAB213014), Jiangxi Provincial “Ganpo Talents 555 Projects” and the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry, PR China.

References

1. N. V. Mockus, D. Rabinovich, J. L. Petersen and J. J. Rack, Angew. Chem., Int. Ed., 2008, 47, 1458–1461.
2. M. N. Roberts, C.-J. Carling, J. K. Nagle, N. R. Branda and M. O. Wolf, J. Am. Chem. Soc., 2009, 131, 16644–16645.
3. T. Ishizuka, T. Sawaki, S. Miyazaki, M. Kawano, Y. Shiota, K. Yoshizawa, S. Fukuzumi and T. Kojima, Chem.–Eur. J., 2011, 17, 6652–6662.
4. S. Bonnet and J.-P. Collin, Chem. Soc. Rev., 2008, 37, 1207–1217.
5. V. Marin, E. Holder, R. Hoogenboom and U. S. Schubert, Chem. Soc. Rev., 2007, 36, 618–635.
6. K. Garg, A. W. King and J. J. Rack, J. Am. Chem. Soc., 2014, 136, 1856–1863.
7. B. A. McClure, N. V. Mockus, D. P. Butcher, Jr, D. A. Lutterman, C. Turro, J. L. Petersen and J. J. Rack, Inorg. Chem., 2009, 48, 8084–8091.
8. B. A. McClure, E. R. Abrams and J. J. Rack, J. Am. Chem. Soc., 2010, 132, 5428–5436.
9. A. A. Rachford and J. J. Rack, J. Am. Chem. Soc., 2006, 128, 14318–14324.
10. B. A. McClure and J. J. Rack, Inorg. Chem., 2011, 50, 7586–7590.
11. J. J. Rack, Coord. Chem. Rev., 2009, 253, 78–85.
12. K. Garg, S. I. M. Paris and J. J. Rack, Eur. J. Inorg. Chem., 2013, 1142–1148.
13. M. K. Smith, J. A. Gibson, C. G. Young, J. A. Broomhead, P. C. Junk and F. R. Keene, Eur. J. Inorg. Chem., 2000, 1365–1370.
14. (a) N. V. Mockus, J. L. Petersen and J. J. Rack, Inorg. Chem., 2006, 45, 8–10; (b) B. A. McClure and J. J. Rack, Eur. J. Inorg. Chem., 2010, 3895–3904.
15. N. V. Mockus, S. Marquard and J. J. Rack, J. Photochem. Photobiol., A, 2008, 200, 39–43.
16. A. W. King, Y. Jin, J. T. Engle, C. J. Ziegler and J. J. Rack, Inorg. Chem., 2013, 52, 2086–2093.
17. A. A. Rachford, J. L. Petersen and J. J. Rack, Dalton Trans., 2007, 3245–3251.
18. A. E. Phillips, J. M. Cole, T. d'Almeida and K. S. Low, Inorg. Chem., 2012, 51, 1204–1206.
19. B. A. McClure and J. J. Rack, Angew. Chem., Int. Ed., 2009, 48, 8556–8558.
20. B. L. Portera, B. A. McClurea, E. R. Abramsa, J. T. Engleb, C. J. Zieglerb and J. J. Rack, J. Photochem. Photobiol., A, 2011, 217, 341–346.
21. A. A. Rachford, J. L. Petersen and J. J. Rack, Inorg. Chem., 2006, 45, 5953–5960.
22. D. P. Butcher, A. A. Rachford, J. L. Petersen and J. J. Rack, Inorg. Chem., 2006, 45, 9178–9180.
23. I. Ciofini, C. A. Daul and C. Adamo, J. Phys. Chem. A, 2003, 107, 11182–11190.
24. D. A. Lutterman, A. A. Rachford, J. J. Rack and C. Turro, J. Phys. Chem. A, 2009, 113, 11002–11006.
25. (a) H. F. Li, L. S. Zhang, H. Lin and X. L. Fan, RSC Adv., 2014, 4, 45635–45640; (b) H. F. Li, L. S. Zhang, H. Lin and X. L. Fan, Chem. Phys. Lett., 2014, 604, 10–14.
26. H. F. Li, L. S. Zhang, X. L. Fan and Y. Zhao, J. Phys. Chem. A, 2015, 119, 4244–4251.
27. A. J. Göttle, I. M. Dixon, F. Alary, J.-L. Heully and M. Boggio-Pasqua, J. Am. Chem. Soc., 2011, 133, 9172–9174.
28. (a) S. Bonnet and J. P. Collin, Chem. Soc. Rev., 2008, 37, 1207–1217; (b) Q. Sun, S. Mosquera-Vazquez, L. M. L. Daku, L. Guénée, H. A. Goodwin, E. Vauthey and A. Hauser, J. Am. Chem. Soc., 2013, 135, 13660–13663; (c) J. T. Hewitt, J. J. Concepcion and N. H. Damrauer, J. Am. Chem. Soc., 2013, 135, 12500–12503.
29. (a) S. Grimme, J. Antony, S. Ehrlich and H. Krieg, J. Chem. Phys., 2010, 132, 154104; (b) L. Goerigk and S. Grimme, Phys. Chem. Chem. Phys., 2011, 13, 6670–6688.
30. (a) A. D. Becke and E. R. Johnson, J. Chem. Phys., 2005, 123, 154101; (b) E. R. Johnson and A. D. Becke, J. Chem. Phys., 2005, 123, 024101; (c) E. R. Johnson and A. D. Becke, J. Chem. Phys., 2006, 124, 174104.
31. C. Adamo and V. Barone, J. Chem. Phys., 1999, 110, 6158–6170.
32. D. Andrae, U. Häussermann, M. Dolg, H. Stoll and H. Preuss, Theor. Chim. Acta, 1990, 77, 123–141.
33. T. H. Dunning, J. Chem. Phys., 1989, 90, 1007–1023.
34. K. A. Peterson and C. Puzzarini, Theor. Chem. Acc., 2005, 114, 283–296.
35. V. Barone and M. Cossi, J. Phys. Chem. A, 1998, 102, 1995–2001.
36. K. Fukui, Acc. Chem. Res., 1981, 14, 363–368.
37. H. P. Hratchian and H. B. Schlegel, J. Chem. Phys., 2004, 120, 9918–9924.
38. S. Fantacci, F. D. Angelis and A. Selloni, J. Am. Chem. Soc., 2003, 125, 4381–4387.
39. R. L. Martin and V. Affiliations, J. Chem. Phys., 2003, 118, 4775–4777.
40. A. E. Reed, L. A. Curtiss and F. Weinhold, Chem. Rev., 1988, 88, 899–926.
41. M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, G. Scalmani, V. Barone, B. Mennucci, G. A. Petersson, H. Nakatsuji, M. Caricato, X. Li, H. P. Hratchian, A. F. Izmaylov, J. Bloino, G. Zheng, J. L. Sonnenberg, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, T. Vreven, J. A. Montgomery, Jr, J. E. Peralta, F. Ogliaro, M. Bearpark, J. J. Heyd, E. Brothers, K. N. Kudin, V. N. Staroverov, T. Keith, R. Kobayashi, J. Normand, K. Raghavachari, A. Rendell, J. C. Burant, S. S. Iyengar, J. Tomasi, M. Cossi, N. Rega, J. M. Millam, M. Klene, J. E. Knox, J. B. Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R. E. Stratmann, O. Yazyev, A. J. Austin, R. Cammi, C. Pomelli, J. W. Ochterski, R. L. Martin, K. Morokuma, V. G. Zakrzewski, G. A. Voth, P. Salvador, J. J. Dannenberg, S. Dapprich, A. D. Daniels, O. Farkas, J. B. Foresman, J. V. Ortiz, J. Cioslowski and D. J. Fox, Gaussian 09, Revision D.01, Gaussian, Inc., Wallingford CT, 2013.
42. M. Calligaris, Coord. Chem. Rev., 2004, 248, 351–375.
43. (a) W. J. Mortier, Struct. Bonding, 1987, 66, 125; (b) R. T. Sanderson, J. Chem. Educ., 1954, 31, 2.
44. (a) P. S. Wagenknecht and P. C. Ford, Coord. Chem. Rev., 2011, 255, 591–616; (b) Q. Sun, S. Mosquera-Vazquez, L. M. L. Daku, L. Guénée, H. A. Goodwin, E. Vauthey and A. Hauser, J. Am. Chem. Soc., 2013, 135, 13660–13663; (c) J. T. Hewitt, J. J. Concepcion and N. H. Damrauer, J. Am. Chem. Soc., 2013, 135, 12500–12503.

---

Footnote

† Electronic supplementary information (ESI) available: Benchmark calculations. TD-DFT results. Optimized Cartesian coordinates, electronic structures, energies of all stationary points and partial optimization results. See DOI: 10.1039/c5ra06723e

---