Triplet Ground-State-Bridged Photochemical Process: Understanding

Article Cite This: Inorg. Chem. XXXX, XXX, XXX-XXX

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Triplet Ground-State-Bridged Photochemical Process: Understanding the Photoinduced Chiral Inversion at the Metal Center of [Ru(phen)2(L‑ser)]+ and Its Bipy Analogues Lixia Feng,†,‡ Yuekui Wang,*,† and Jie Jia† †

Key Laboratory of Chemical Biology and Molecular Engineering of the Education Ministry, Institute of Molecular Science, Shanxi University, Taiyuan, Shanxi 030006, P. R. China ‡ Department of Chemistry, Taiyuan Normal University, Jinzhong, Shanxi 030619, P. R. China S Supporting Information *

ABSTRACT: One of the main concerns in the photochemistry and photophysics of ruthenium complexes is the de-excitation of the triplet metal centered ligand-field state 3 MC. To understand the mechanism by which the 3MC states in some reversible photochemical reactions could avoid the fate of fast decay and ligand dissociations, the photoinduced chiral inversion at the metal center of the complexes [Ru(diimine)2(L-ser)]+ (diimine = 1,10-phenanthroline or 2,2′-bipyridine, L-ser = L-serine) has been analyzed at the first principle level of theory. The calculated equilibrium constants and ECD curves for the photoinduced equilibrium mixtures are in agreement with the observed ones. The results showed that the reversible photochemical process Δ(δS) ⇌ Λ(δS) on the potential surface of the lowest triplet excited state proceeds in three steps: 3CTΔ ↔ 3MCΔ, 3MCΔ ↔ 3 MCΛ, 3MCΛ ↔ 3CTΛ, where the first and the third steps involve mainly the elongation and compression of the octahedral core of the reactant Δ(δS) and product Λ(δS), respectively. The chiral inversion Δ ↔ Λ takes place in the second step through a much distorted square-pyramid-like transition state, and actually proceeds on the triplet ground state 3MC due to the crossover of the triplet T1 and singlet S0 states. Inspecting the transient structures at the crossing points, we found that they become less distorted and their lowest or imaginary-frequency displacement vectors in triplet state still dominate the reaction path, which makes the reaction reversible without ligand release. Thus, the triplet ground-state-bridged photoinduced mechanism offers a new angle of view to understand the related reversible photochemical reactions.

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3 MC states is crucial for full use of the photochemical and photophysical properties. In this aspect, though much work has been done both experimentally20−22,27 and theoretically,28,29 our knowledge for the photochemical processes involving the 3MC states is still rather limited, because most of the theoretical studies are devoted to the nonreversible photochemical processes, which touch only on a conversion between 3MLCT and 3MC states,30,31 so less attention has been paid to the reversible photochemical reactions. The latter involves a conversion between 3MC states32 of reactant and product, and may form a thermodynamically stable equilibrium in the presence of light, which is also of great interest for chemists. For example, early in 1981, Vagg and Williams found that33,34 the Δ-isomers of cis-[Ru(diimine)2(aa)]+ complexes in aqueous solution can spontaneously invert into the Λ-forms in the presence of light to give a thermodynamically stable equilibrium mixture, where the diimine is either 1,10phenanthroline (phen) or 2,2′-bipyridine (bipy) and aa is an optically active amino acid anion: L-serine (L-ser) or Ltryptophan (L-trp). In view of the lability of the 3MC states,

INTRODUCTION Since the pioneering work of Demas and Crosby1,2 in 1971, ruthenium complexes, particularly Ru(II)-diimine chelates, have been playing a key role in the development of photochemistry and photophysics,3−5 and have contributed highly to various applications in technological6−9 and biomedical10,11 fields. The Ru(II)-diimine chelates in the ground state show remarkable chemical stability,12,13 but they can exhibit many photochemical reactions when exposed to light, such as, photolysis,14,15 photosubstitution,16,17 photoracemization,18,19 and so on. Considerable efforts have been made to understand the photochemical processes with special attention focused on the metal centered (3MC) or ligand-field states,20,21 because these states are thought to have a distorted geometry and are associated with deactivation of the lower-energy metal-to-ligand charge transfer (3MLCT) states,22 as well as responsible for the photoinduced ligand release or substitution.16 This deactivation is typically undesirable for some technological applications8 and artificial photosynthesis,23 as the motivation in these areas is to access the potential energy stored in the 3MLCT states. Nevertheless, the lability of 3MC states is preferable for many photochemical reactions, including photosubstitution,24 photoisomerization,19 selective photodissociation,25 and photoasymmetric synthesis.26 Therefore, understanding the behavior of © XXXX American Chemical Society

Received: August 8, 2017

A

DOI: 10.1021/acs.inorgchem.7b02030 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry

(1) Determines the possible geometries of the ground transition states 1TS between the reactant and product, because this is an one-step reaction, the possible pathways and transition-state geometries for a sixcoordinated metal complex are known, namely, the Bailar36 and Ray−Dutt37 twists, as well as the bondrupture models38 with the latter being depreciable. (2) Determines the key excited transition state 3TS by taking the geometries of 1TS as its initial geometries and changing their multiplicity from 1 to 3. (3) Searches the 3MC states from both sides of 3TS along the displacement vector of the normal mode with imaginary frequency. (4) Locates the transition states 3TSR and 3TSP between 3CT and 3MC. This might be the most stubborn task as it requires a better guess for the initial geometry. To meet this need, we wrote a smooth geometrical interpolation program with the “divide and conquer” algorithm, which works well for mononuclear complexes and will be reported in detail elsewhere. Computational Details. The complexes [Ru(phen)2(Lser)]+ and [Ru(bipy)2(L-ser)]+ are chiral with configurational chirality (Δ/Λ) at the octahedral core {RuN5O} and conformational chirality (δ/λ) due to the twists of the fivemembered chelate ring involving the L-serine ligand (cf. L3 in Figure 2). This ligand has an S-type chiral carbon (C2 in Figure

they thought that this is a unique class of photoinduced inversions at octahedral centers because it involves neither ligand release nor substitution in the coordination sphere, and no redox was observed at the Ru(II) center. So there must be some unknown mechanism which prolongs the lifetime of 3MC states or stabilizes them in the triplet state. In this paper, we report a theoretical analysis on the mechanism of photoinduced chiral inversion at metal center of the complex [Ru(phen)2(L-ser)]+ and its bipy analogues. The main object is to inspect the behavior of 3MC states in the chiral inversion, including their relative energies, structures and bonding, as well as spin-density distribution, etc. Particular attention is paid to elucidating the mechanism that prevents the key 3MC transition-state (3TS) decay to the ground state. We hope that such knowledge may help us get a deep insight into the photochemistry and photophysics properties of the complexes.

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CALCULATION SCHEME AND COMPUTATIONAL DETAILS Calculation Scheme. The photoinduced chiral inversion at the metal center of the [Ru(phen)2(L-ser)]+ cation and its bipy analogues is a reversible photochemical reaction. The reactant is promoted by irradiation to one of the singlet excited states first, say S1, and then it rapidly relaxes to the lowest-energy triplet state T1 with the aid of nonradiative intersystem crossing (ISC). Ignoring this ultrafast photophysical process,35 the photochemical reaction involves at least four metastable excited states and three related transition states, as schematically illustrated in Figure 1. Where 3CTR and 3MCR are the lowest-

Figure 2. Two chiral structures Δ(δS) and Λ(δS) of the [Ru(phen)2(L-ser)]+ complex and atom numbering for part of atoms.

2) whose chirality does not change in the reaction due to a big inversion barrier. It also requires a δ-twisted chelate ring for the L-serine ligand, because the −CH2OH group should locate on the equatorial position of the five-membered chelate ring. Therefore, the absolute configuration of the complexes in aqueous solution is either Δ(δS) or Λ(δS). Nevertheless, for a given configuration, it may have 9 conformers in solution arising from the intramolecular rotation of −CH2OH and −OH, and could be characterized by the two dihedral angles δ(N5−C2−C3−O3) and δ′(C2−C3−O3−H1). In this paper, all geometry optimizations and subsequent frequency verification of the reactants, products, and transition states (TSs) for both singlet ground state (S0) and the lowestenergy triplet excited state (T1) were performed employing the density functional theory (DFT) method with the B3LYP39 functional and the mixed basis set: (8s7p6d2f)/[6s5p3d2f]{311111/22111/411/11} valence basis set40 plus the quasirelativistic Stuttgart ECP28MWB pseudopotential41 for ruthenium and the polarized triple-ζ 6-311G(d) basis set for other atoms. Normal-mode analyses were carried out for all optimized structures to verify the stationary points as local minima (without imaginary frequency) or transition state (with one imaginary frequency). All the transition states 1TS, 3TS, 3 TSR, and 3TSP in both Bailar and Ray−Dutt twists have been

Figure 1. Schematic representation of the excited states and possible transition states involved in the reversible photochemical inversion at metal center of the Ru-diimine complexes along the relaxed groundstate (S0) pathway. Note that the ground states of the reactant and product are labeled with the common symbol S0 for simplicity, which does not mean they are identical due to their different locations on the reaction path.

energy 3MLCT and 3MC metastable excited states of the reactant (R), 3TSR is the transition state between them; similarly, 3CTP, 3MCP, and 3TSP are the corresponding states for the product (P), and 3TS is the key transition state from 3 MCR to 3MCP. To achieve the foregoing goals, we have to determine the energies and geometries of these seven excited states first, including the ground states (S0) of the reactant and product, and then we can discuss the reaction path. Here, the geometry optimization for the two ground states and the lowest-energy 3CT excited ones is a trivial task, but not for the 3 MC and 3TS states. For this reason, following calculation scheme has been adopted: B

DOI: 10.1021/acs.inorgchem.7b02030 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry fully verified either by intrinsic reaction coordinate (IRC)42 calculation (for 1TS) or by geometry optimization along the displacement vector of the normal mode with imaginary frequency. The charge transfer state 3CT and metal centered state 3MC were identified by spin-density analysis43 using natural bond orbitals (NBOs). On the basis of the optimized geometries, the electron circular dichroism (ECD) spectra for both reactant and product, as well as related vertical excitation energies and transition moments, were then calculated using the time-dependent density functional theory (TDDFT) method with the same functional and basis set. All the calculations were carried out with tight convergence criterion and ultrafine integral grid, including the solvent effect (aqueous solution) with the polarizable continuum model (PCM),44 as implemented in the Gaussian09 program package.45

2, and corresponding Cartesian coordinates are collected in Table S1. These two most stable structures will be used to discuss the photoinduced chiral inversion later unless otherwise specified. Besides, the calculated Gibbs free energy of Δ(δS)-0 at room temperature is 0.239 kcal/mol higher than that of Λ(δS)-0, so the reaction Δ(δS) → Λ(δS) is thermodynamically allowed. The corresponding equilibrium constant is 1.50, which is in good agreement with the observed34 value 1.28. For the [Ru(bipy)2(L-ser)]+ complex, the most stable conformers of Δ(δS) and Λ(δS) are structurally very similar to their phen analogues, including their relative stability: Δ(δS)-0 is 0.531 kcal/mol higher than Λ(δS)-0 in total energy. However, the calculated Gibbs free energy of Δ(δS)-0 at room temperature is 0.142 kcal/mol lower than that of Λ(δS)-0. Our analyses showed that the apparently anomalous behavior of the bipy complex compared with that of other related systems34 [Ru(diimine)2(aa)]+ (diimine = phen or bipy, aa = Ltryptophan, L-phenylalanine, L-tyrosine, L-histidine, or L-proline) is mainly due to the influence of vibrational entropy. Therefore, the reverse reaction Δ(δS) ← Λ(δS) is thermodynamically favored in this case. The corresponding equilibrium constant is 0.79, which is also in excellent agreement with the experimental value 0.71, and demonstrates the validity of the functional and basis set used in our calculations. Comparison of the Calculated and Observed ECD Spectra. For the low-energy isomers of the [Ru(phen)2(Lser)]+ and [Ru(bipy) 2 ( L-ser)]+ complexes, the vertical excitation energies to singlet states, oscillators, and rotational strengths were calculated using the TDDFT method. The ECD spectrum for each isomer was generated as a superposition of Gaussian line-shapes, each centered at the calculated transition wavelengths λcal with integral intensity proportional to the rotational strength R of the corresponding transition. The half bandwidths Γ at Δεmax/e were assumed to be46 Γ = k × λcal1.5 with k = 2.887 × 10−3 for λcal < 300 nm, or k = 3.849 × 10−3 for λcal ≥ 300 nm. Finally, the Boltzmann-weighted averaged ECD spectra were calculated for the reactant Δ(δS) and product Λ(δS), as well as their photoinduced equilibrium mixture. In the latter case, the equilibrium constant 1.50 was also taken into consideration. These averaged ECD curves together with the observed34 ones for the [Ru(phen)2(L-ser)]+ complex are depicted in Figure 3.

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RESULTS AND DISCUSSION Geometries of the Ground States. For the Δ(δS) and Λ(δS) chiral configurations of the [Ru(phen) 2 ( L -ser)] + complex, their first four lowest-energy conformers are displayed in Figure S1 (see the Supporting Information). Their relative energies in the ground state S0 are listed in Table 1. It shows Table 1. Labile Dihedral Angles and Relative Energies of the Δ(δS)- and Λ(δS)-Isomers of [Ru(phen)2(L-ser)]+ Complexa Δ(δS)

δNCCO

δ′CCOH

Eel

EZPE

E0

0 1 2 3 Λ(δS)

61.33 −171.51 52.92 −53.00 δNCCO

73.27 −52.18 −170.13 −73.54 δ′CCOH

0.000 0.016 0.794 2.569 Eel

0.000 0.289 −0.169 −0.210 EZPE

0.000 0.304 0.626 2.358 E0

0 1 2 3

64.70 −171.38 53.86 −54.62

71.71 −51.90 −169.84 −74.72

0.000 −0.221 1.083 2.330

0.000 0.336 −0.335 −0.190

0.000 0.115 0.748 2.141

a The numbering of isomers (first column) refers to Figure S1. Dihedral angles are in degrees; the electronic (Eel), zero-point (EZPE), and total (E0) energies relative to isomer-0 are in kcal/mol.

that the most stable conformer is Δ(δS)-0 for Δ(δS) or Λ(δS)0 for Λ(δS). Their optimized geometries are depicted in Figure

Figure 3. Comparison of the calculated (top) and observed (bottom) ECD curves of the [Ru(phen)2(L-ser)]+ complex. The calculated ECDs are Boltzmann-weighted averaged spectra of the lower-energy isomers with given chiral configuration. C

DOI: 10.1021/acs.inorgchem.7b02030 Inorg. Chem. XXXX, XXX, XXX−XXX

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result of the Ray−Dutt twist would be dif ferent f rom that of the Bailar twist in the viewpoint of absolute configuration or chirality. Fortunately, N3 and N4 are symmetry equivalent in our case, so both twists will yield the same result. Besides, according to Rodger’s criterion,49 both twists are possible for the [Ru(phen)2(L-ser)]+-like complexes. Therefore, both transition states should be taken into consideration. To get a reasonable initial guess for the geometry of the transition state 3TS (see Figure 1), the structures of 1TS on the ground state S0 have been determined according to the Bailar and Ray−Dutt twists, respectively. The results are collected in Table S1. Partial bond parameters of the transient structures 1 TSA and 1TSB, together with those of Δ(δS) and Λ(δS), are listed in Table 2 for easier comparison. The ZPE corrected

As far as the signs and relative intensities of the ECD absorption bands are considered, agreement between the calculated and observed ECD patterns is clearly acceptable. Especially for the equilibrium mixture, the calculated band intensities are in good agreement with the observed ones. This agreement also supports the experimental fact that no ligand dissociation or substitution was observed in the photoinduced chiral inversion. A detailed analysis (see Tables S2 and S3) on the Kohn− Sham orbitals (Figure S2) involved in the excitations reveals that all the observed ECD absorption bands in the long wavelength range (λ > 300 nm) are dominated by the metal-toligand charge transfer (MLCT) transitions dz2 → π*phen/π*phen′, except for the shoulder peak at 366 nm which is due to the metal centered (MC) transition dz2 → σ*RuN,RuO (dxz/dyz) with significant Rydberg characteristics. The MLCT characteristic partly accounts for the fact that calculated ECD intensities are generally larger than the observed ones for the reactant Δ(δS) and product Λ(δS), as the intensities of MLCT transitions are solvent-dependent.47 In addition, since the contribution of Rydberg characteristics to the MC transition is seldom observed in solution spectra, therefore, the calculated ECD band around 350 nm splits into a main peak at 335 nm and a shoulder at 366 nm in the observed spectra. However, in the short wavelength range (240 nm < λ < 300 nm), they are dominated by the interligand charge transfer (ILCT) transitions πphen → π*phen′/nOH → π*phen, yielding the two strongest ECD bands with the typical exciton coupling48 pattern. Structures of the Transition State 1TS. In the ground state, there are two non-bond-breaking mechanisms that may yield a lower-energy transition state for the chiral inversion at the metal center of a complex containing three bidentate chelate rings, known as the Bailar36 and Ray−Dutt37 twists, respectively. The Bailar twist proceeds by twisting the chelate about its C3- or pseudo-C3-axis through a triangular prism to the opposite enantiomer, as depicted in Figure 4a, while the

Table 2. Selected Bond Lengths (Å) and Bond and Dihedral Angles (in deg) of the Reactant Δ(δS), Product Λ(δS), and 1 TSA and 1TSB for the [Ru(phen)2(L-ser)]+ Complex Ru−N1 Ru−N2 Ru−N3 Ru−N4 Ru−O1 Ru−N5 mean N1−Ru−N2 N3−Ru−N4 O1−Ru−N5 N1−Ru−O1 N1−Ru−N3 N4−Ru−N5 mean N2N1N4N3 N4N3N5O1

Δ(δS)

Λ(δS)

1

2.077 2.065 2.073 2.103 2.100 2.143 2.093 79.64 79.28 79.61 95.39 96.09 96.74 87.79 94.39 91.59

2.071 2.094 2.065 2.079 2.100 2.148 2.093 79.41 79.71 78.90 92.12 93.18 87.57 85.15 57.04 56.82

2.063 2.073 2.043 2.176 2.189 2.295 2.140 77.28 77.84 71.86 81.15 90.11 85.11 80.56 67.88 69.27

TSA

1

TSB

2.152 2.106 2.158 2.106 2.133 2.153 2.135 76.68 76.40 77.20 80.87 87.73 87.80 81.11 −179.66 −175.24

energies of 1TSA and 1TSB relative to the reactant Δ(δS) are 2.057 and 2.347 eV. Both are too high to thermal activate, as expected. Meanwhile, compared to the mean value of bond lengths of Δ(δS), changes in those of the transition states are less than 0.05 Å. This indicates again the special stability of the reactant and product in ground states. Energies of the 3TS and Related States. Geometry optimizations of the key transition state 3TS were performed starting from those of 1TSA and 1TSB, respectively, and the results 3TSA and 3TSB were verified as transition states by frequency calculations at the same level of theory. We can slightly alter the structures of 3TSA or 3TSB by adding about ±10% of the displacement vector of the normal mode with an imaginary frequency and reoptimize them, yielding two new structures, which were identified as the 3MCR and 3MCP states by the NBO spin-density analysis,43 as shown in Table 3. This imaginary-frequency displacement pilot (IFDP) method works more efficiently than the standard IRC methodology, especially for the correlation of reactant−TS−product in excited states. The 3CTR and 3CTP states were directly obtained by reoptimizing the ground-state geometries of Δ(δS) and Λ(δS) with the restriction of the triplet state. Finally, the 3 TSR and 3TSP transition states were located by optimizing the interpolation geometry between the corresponding 3CT and 3 MC states. They have been verified using the IFDP method, as described above. The results are compiled in Tables S4 and S5.

Figure 4. Schematic illustration of the Bailar (a) and Ray−Dutt (b) twists for the chiral inversion Δ → Λ at the metal center of the [Ru(phen)2(L-ser)]+ complex and its bipy analogues.

Ray−Dutt twist can be seen as analogous to the Bailar twist about another C3- or pseudo C3-axis that would exist only in the parent octahedral core, as illustrated in Figure 4b. The latter involves a transition state TSA with a rhombic geometry of C2or pseudo-C2-symmetry. Thus, they are usually referred to as trigonal twist and rhombic twist, respectively. It is worthwhile to mention that if N3 and N4 were not symmetry equivalent, the D

DOI: 10.1021/acs.inorgchem.7b02030 Inorg. Chem. XXXX, XXX, XXX−XXX

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Table 3. Spin-Density Distribution49 of the Triplet States 3CT, 3MC, and 3TS of [Ru(phen)2(L-ser)]+ in both the Rhombic and Trigonal Prismatic Twists rhom

3

CTR

3

3

TSR

3

MCR

3

TSA

3

MCP

3

TSP

CTP

Ru(II) phen phen′ L-ser trig

0.8794 1.0366 0.0164 0.0675 3 CTR

1.4131 0.4225 0.0248 0.1395 3 TSR

1.8060 0.0875 0.0006 0.1058 3 MCR

1.7356 0.1000 0.0441 0.1203 3 TSB

1.7728 0.0881 0.0077 0.1315 3 MCP

1.3444 0.1367 0.4259 0.0930 3 TSP

0.8820 0.0157 1.0366 0.0657 3 CTP

Ru(II) phen phen′ L-ser

0.8794 1.0366 0.0164 0.0675

1.2974 0.3662 0.1721 0.1642

1.6470 0.0829 0.0830 0.1872

1.6983 0.0404 0.0429 0.2184

1.6424 0.0914 0.0847 0.1816

1.3195 0.1901 0.3255 0.1649

0.8820 0.0157 1.0366 0.0657

Table 4. Relative Energiesa of the Triplet States 3CT, 3MC, and 3TS Involved in the Photoinduced Chiral Inversion of [Ru(phen)2(L-ser)]+ rhombic inversion triplet stateb 3

CTR TSR 3 MCR 3 TSA/B 3 MCP 3 TSP 3 CTP 3

trigonal inversion

Eel

E0

G⧧

ν0

Eel

E0

G⧧

ν0

0.000 7.644 4.210 7.170 4.234 8.043 −0.133

0.000 7.063 4.899 8.038 4.102 7.202 −0.143

0.000 6.131 2.827 8.229 2.117 6.785 0.233

22.4 i316.0 13.4 i20.48 16.1 i383.5 25.6

0.000 7.091 5.134 14.363 4.815 6.462 −0.133

0.000 6.550 5.646 15.227 5.253 5.880 −0.143

0.000 6.418 4.606 15.756 4.032 5.573 0.233

22.4 i196.7 20.7 i36.9 21.6 i183.2 25.6

Eel = electron energy, E0 = total energy with ZPE correction, G⧧ = relative Gibbs free energy at 298.15 K. All energies are in kcal/mol. ν0 = the lowest vibrational frequency (in cm−1) or the imaginary frequency for the transition states. bSubscript: R = reactant, P = product, A = Ray−Dutt or rhombic, B = Bailar or trigonal. a

To facilitate discussion, their relative energies and Gibbs free energies at 298.15 K are tabulated in Table 4. The corresponding optimized geometries are shown in Figure 5. Part of their bond parameters are listed in Table 5. The photochemical reaction Δ(δS) ⇌ Λ(δS) consists of three steps: 3CTR ⇌ 3MCR, 3MCR ⇌ 3MCP, 3MCP ⇌ 3CTP. At first glance over the total energy E0 in Table 4, it is clear that, for the rhombic inversion, the first forward 3CTR → 3MCR and the third backward 3MCP ← 3CTP processes are the ratedetermining steps (RDS), because they have a larger barrier of

about 7.2 kcal/mol while those of the second step are less than 4 kcal/mol. However, recent experimental measurements for the parent chelate50 [Ru(bipy)3]2+ and its derivatives22 showed that these 3CT-to-3MC processes are usually fast steps of a few picoseconds, while the experimentally estimated barrier51 of the bipy chelate is up to 3600 cm−1, that corresponds to a very slow process of microsecond order. This inconsistency may be attributed to the barrier being only a phenomenological or model-dependent parameter. In fact, our recent calculations showed that it is about 3 kcal/mol, and involves some interesting characteristics, which will be reported elsewhere later. To quantitatively estimate their time scales, it is necessary to calculate their rate constants. According to Eyring’s transition-state theory52 (TST), the rate constant of a process is given by53 kTST = κ(kBT/h)exp(−ΔG⧧/RT), where κ is the transmission coefficient, kB is the Boltzmann constant, h is the Planck constant, and ΔG⧧ is the difference between the transition state and the reactant state in Gibbs free energy, respectively. The transmission coefficient κ could be estimated by the Wigner tunnelling correction,54 κ = 1 + (1/24)[hIm(ν⧧)/kBT]2, which involves only the imaginary frequency Im(ν⧧) of the transition state. In this way, the rate constants kq and k−q for the forward and backward reactions of the three steps (q = 1, 2, 3) could be calculated, and their time scales defined by the reciprocal of rate constants τq = 1/kq, τ−q = 1/ k−q, are as follows: τ1 = 4.58 ns, τ−1 = 38.8 ps; τ2 = 1.47 ns, τ−2 = 4.86 ns; τ3 = 0.372 ns, τ−3 = 8.94 ns. Clearly, the 3CT-to-3MC processes are the RDS, though they are only 2 or 3 times slower than the second step. Interestingly, the value of 38.8 ps for the reverse process 3CTR ← 3MCR is comparable with the measured value50 of 50 ps for the [Ru(bipy)3]2+ chelate, though the two complexes are different. Besides, for the trigonal

Figure 5. Optimized geometries of the triplet excited states involved in the chiral inversion paths A (top) and B (bottom) with rhombic and trigonal prismatic transition states, respectively. Their relative energies are in kcal/mol. Clearly, path A is preferred. E

DOI: 10.1021/acs.inorgchem.7b02030 Inorg. Chem. XXXX, XXX, XXX−XXX

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Table 5. Selected Bond Lengths (Å) and Bond and Dihedrala Angles (in deg) for the Triplet States 3CT, 3MC, and 3TS of the [Ru(phen)2(L-ser)]+ Chelate rhombic

a

3

CTR

3

TSR

3

3

MCR

TSA

3

MCP

3

TSP

3

CTP

Ru−N1 Ru−N2 Ru−N3 Ru−N4 Ru−O1 Ru−N5 N1−Ru−N2 N3−Ru−N4 O1−Ru−N5 D(L1L2) D(L1L3) D(L2L3) trigonal

2.084 2.055 2.077 2.118 2.033 2.132 80.64 79.01 79.79 92.73 106.29 81.15 3 CTR

2.088 2.216 2.106 2.103 2.218 2.242 77.84 78.66 74.21 81.43 113.35 77.70 3 TSR

2.128 2.490 2.101 2.101 2.449 2.196 72.48 78.55 73.02 83.61 108.59 71.13 3 MCR

2.440 2.155 2.109 2.112 2.512 2.181 71.24 77.89 69.56 −82.52 −104.30 76.62 3 TSB

2.450 2.125 2.102 2.088 2.111 2.548 73.52 78.79 70.60 −94.87 −100.10 −75.13 3 MCP

2.276 2.106 2.082 2.094 2.155 2.226 76.74 78.88 74.97 −97.83 −100.17 −66.44 3 TSP

2.077 2.115 2.054 2.084 2.037 2.134 79.13 80.67 79.34 −95.15 −98.93 −60.19 3 CTP

Ru−N1 Ru−N2 Ru−N3 Ru−N4 Ru−O1 Ru−N5 N1−Ru−N2 N3−Ru−N4 O1−Ru−N5 D(L1L2) D(L1L3) D(L2L3)

2.084 2.055 2.077 2.118 2.033 2.132 80.64 79.01 79.79 92.73 106.29 81.15

2.082 2.098 2.116 2.101 2.202 2.335 79.39 78.92 72.35 103.99 102.35 78.31

2.085 2.226 2.154 2.088 2.402 2.352 77.36 78.39 69.49 126.53 102.06 77.91

2.143 2.158 2.142 2.160 2.497 2.461 76.30 76.08 66.05 137.89 105.20 116.84

2.150 2.089 2.083 2.232 2.400 2.340 78.51 77.37 69.71 −121.43 −104.02 −79.34

2.121 2.095 2.081 2.105 2.208 2.331 78.90 79.34 72.18 −101.45 −103.13 −76.75

2.077 2.115 2.084 2.054 2.037 2.134 79.13 80.67 79.34 −95.15 −98.93 −60.19

D(L1L2) is the dihedral angle between ligands L1 and L2 (cf., Figure 2), and is measured by the XY planes of their principal axis systems of inertia.

inversion, the calculated time scales τq and τ−q for the three steps are τ1 = 7.85 ns, τ−1 = 3.30 ps; τ2 = 24.0 μs, τ−2 = 63.1 μs; τ3 = 2.10 ps, τ−3 = 1.28 ns. Thus, the second step is the RDS, and it is much slower than that in the rhombic inversion. Therefore, the trigonal inversion is not preferred. Optimized Geometries of the 3TS and Related States. The geometries of transition states are one of the key factors to understand the photochemical and photophysical processes. Table 5 summarizes the main bond lengths, and the bond and dihedral angles for the triplet states 3CT, 3MC, and 3TS involved in the chiral inversion. The dihedral angle between two ligands is defined by the XY planes of their principal axis systems of inertia (cf., Figure S3). Note that these dihedral angles together with the coordinates for the centers of mass of the three ligands can be viewed as the reaction coordinates, as indicated by the geometrical interpolation, though they are not intuitive. From 3CTR to 3CTP, the dihedral angles change their sign at 3TSA/B due to the chirality inversion Δ ↔ Λ of the octahedral core, as expected. To show the structures of 3TSA/B clearly, a pictorial comparison of the transition-state structures between the singlet state S0 and triplet state T1 is depicted in Figure 6. For the rhombic inversion, the influences of the three steps on the geometries of the complex are significantly different from one another. In the first step 3CTR → 3MCR, the octahedral core RuN5O of Δ(δS) is elongated about 20% along the N2−Ru−O1 axis, which makes the lengths of the two shortest bonds Ru−N2 and Ru−O1 increase gradually from 2.055 to 2.490 Å and from 2.033 to 2.449 Å, respectively. At the same time, the bite angles N1−Ru−N2 and O1−Ru−N5 decrease gradually about 10%. The second step 3MCR → 3 MCP is dominated by the twists of ligand 1 (phen) and ligand 3 (L-ser), which keeps their bite angles nearly unchanged, but

Figure 6. Comparison of the transition-state structures between singlet ground state S0 and triplet excited state T1 for the Ray−Dutt (TSA) and Bailar (TSB) twists, respectively.

makes the length of Ru−N2 decrease rapidly to 2.125 Å and that of Ru−N1 increase rapidly to 2.450 Å. Similarly, the bond length of Ru−O1 increases gradually first, and then decreases rapidly to 2.111 Å, while Ru−N5 decreases slightly first, and then increases rapidly to 2.548 Å. This leads to the movement of the Ru atom to the side face composed of four nitrogens, which is also a kind of Jahn−Teller distortion,55 as shown in Figure 6. Just in this step, the long axis of the octahedral core is changed from the N2−Ru−O1 of 3MCR to N1−Ru−N5 of 3 MCP through the 3TSA geometry. The third step is a recover and shrink procedure of the octahedral core, in which the two bond lengths of Ru−N1 and Ru−N5 decrease gradually to the normal lengths. As to ligand 2 (phen′), the bond lengths of F

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Inorganic Chemistry Ru−N3 and Ru−N4, as well as the bite angle of N3−Ru−N4 change slightly in all three steps, as expected. Note that, in the first step 3CTP → 3MCP of the reverse reaction, the octahedral core RuN5O of Λ(δS) is also elongated about 20% along the N1−Ru−N5 axis. In other words, from the 3CT to 3MC state, it always tends to partly break the shortest Ru−N bond of ligand 1 and the counterpart of 3. This is required by the rhombic twist (Figure 4b). In addition, the change in the long axis of the octahedral core in the second step also means that there is a less distorted structure with no much weakened coordination bond between the 3MC and 3TS states. Later we will see that this structure occurs at the triplet−singlet crossing point, which may reduce the possibility of decay for the 3MC state. For the trigonal inversion, however, the two coordination bonds of ligand 3 are significantly elongated in the process of 3 CTR → 3TSB, which may lead to the dissociation of ligand 3 (cf., Figure 6) under the proper conditions but may not in aqueous solution. Therefore, the trigonal inversion mechanism may not be safely ruled out. In addition, Figure 6 shows that, in the ground state S0, the geometries of 1TSA and 1TSB are regular rhombic and trigonal prismatic forms, respectively, and both are body centered. However, in the triplet excited state T1, the corresponding forms are not body centered due to the central atom shifting to the side face composed of four nitrogens, leaving two much weakened bonds in the prism. Here, the metal atom and the four nitrogens form a flattened square pyramid (FSP) geometry with a height of about 0.3 Å. Strictly speaking, therefore, the two chiral inversion forms of the complex in the triplet state are neither rhombic nor trigonal prismatic, but mixed with the bond-rupture forms, at least partly. To understand the chiral inversion mechanisms more precisely, a video has been prepared and is presented in the Supporting Information. What Prolongs the Lifetime of the 3TS State. The 3MC state is believed to be the main channel of the 3CT state decay to the ground state22 due to its much displaced geometry. Compared to the 3MC, the geometry of the 3TSA/B state is even more distorted, so it is reasonable to expect that the 3TSA/B state might be short-lived, and easy to deactive to the ground state by radiationless decay or by ligand dissociation. However, these phenomena were not observed. One might ask what prolongs the lifetime of 3TSA/B or prohibits the decay to the ground. To clarify this issue, the relaxed energy curve of the triplet state T1 along the key inversion path 3MCR ⇌ 3MCP, together with that of the singlet state S0 calculated at the triplet optimized geometries, is shown in Figure 7. Here, the geometries of 3MCR, 3TSA, 3TSB, and 3MCP are fully optimized; the pathways of 3MCR → 3TSA/B and 3TSA/B → 3MCP are characterized by the geometry interpolation ratio p and 1 + p′ (0 ≤ p, p′ ≤ 1), respectively. The interpolation geometries are optimized with the restrictions of the relative orientations of the three ligands being fixed. The green and yellow dots represent the calculated energies of T1 and S0, respectively. The red and blue lines are the fitting curves of the discrete energy points to locate the crossing points between S0 and T1. Now it is clear that, in the key step 3MCR ⇌ 3MCP, T1 becomes the ground state over one-half of the pathway at both sides of the 3TSA/B state. It is this mechanism that prolongs the lifetime of the transition state 3TSA/B. Inspecting the displacement vector of the imaginary frequency, we found that it is orthogonal to that of the ligand dissociation, because the former is a rocking normal mode, but the latter is dominated by a stretching mode. This orthogonality precludes or at least does

Figure 7. Potential energy curves of the relaxed T1 and vertical S0 states along the rhombic (top) and trigonal (bottom) inversion pathways of 3MCR ⇌ 3MCP, respectively.

not benefit the ligand dissociation. Since the chiral inversion proceeds on the ground state T1, which strongly resembles that on the S0 state, we could say that the role of photons is promoting the reactant from its singlet ground state S0 to triplet ground state T1 of higher energy, on which the chiral inversion could take place. After that, the product returns to its normal ground state S0 with light emitting. In this sense, the reversible photochemical reaction Δ(δS) ⇌ Λ(δS) is nothing but a photoinduced chemical process performed on the triplet ground state. The importance of this angle of view is that it establishes a relationship between the normal chemical reactions and photochemical ones. Concerning the decay of 3MC states to the ground, the only way is by nonradiative relaxation as the radiation transitions are both spin- and parity-forbidden. Heully et al.56 thought that an efficient decay occurs via a deactivation funnel which is the crossing point between the 3MC and the ground-state S0 potential energy surfaces. Figure 7 shows that two crossing points appear at one-fourth and three-fourths of the rhombic inversion path, or one-fifth and four-fifths of the trigonal inversion path, respectively. Their energies are 0.094 and 0.128 eV above the bottom of the corresponding 3MC state. Inspecting the transient structures at the crossing points, we found that they become less distorted due to the change of the elongated axis, as indicated in the previous section. In addition, their lowest or imaginary-frequency displacement vectors are parallel to the reaction path in the triplet state, and deviate from the path only in the singlet state. The latter is a stretch mode and hence may lead to ligand dissociation. Since such ligand dissociation was not detected experimentally, we could say that the lowest or imaginary-frequency normal mode of the 3MC state at the crossing points still dominates the reaction path. In other words, the percentage of the singlet component mixed in the triplet state is small. This conclusion is consistent with the result calculated by Heully et al. for the [Ru(bipy)3]2+ chelate, who found that56 the spin−orbital coupling is indeed small for the lowest 3MC state. Moreover, between the two points, the 3 MC states become the ground state, in which de-excitation is impossible. Since the second step in the rhombic inversion is not the RDS, we therefore believe that decay of the 3MC states at the crossing points is not a main issue in this case. G

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of the π*-component. At the electron level, it is the mixture of d and π*phen orbitals that dominates the change of the T1 state and spin density in the chiral inversion.

Potential Intrusion of Other States upon the T1. To inspect whether some excited state besides the S0 intrudes the T1 in the chiral inversion, all the low-energy states were also calculated at the triplet optimized geometries using the TDDFT method, and the results are displayed in Figure S4. Here, the triplet and singlet states are, respectively, indicated by red and blue lines. Obviously, the T1 state is always isolated from the others by a big gap, so no other state intrudes on the T1 in the reaction except for S0. Moreover, from Figure S4 we see that, for each pair of structures (3CTR, 3CTP), (3TSR, 3TSP), and (3MCR, 3MCP), their energy state sequences are similar to one another, but for different groups of structures, they are significantly different. Especially for the key transition state 3 TSA/B, the distribution is unique due to its triplet ground state in nature. To comprehensively understand the chiral inversion Δ(δS) ⇌ Λ(δS), the DFT energy levels of the optimized structures involved in the reaction are collected in Figure 8. The green

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CONCLUSIONS A detailed theoretical analysis on the photoinduced chiral inversion at the metal center of complex [Ru(phen)2(L-ser)]+ and its bipy analogues has been performed at the first principle level of theory. The results show that the reversible photochemical reaction Δ(δS) ⇌ Λ(δS) takes place on the potential surface of the lowest triplet excited state T1, and proceeds in three steps: 3CTR ↔ 3TSR ↔ 3MCR, 3MCR ↔ 3 TSA/B ↔ 3MCP, and 3MCP ↔ 3TSP ↔ 3CTP. In the first step, the octahedral core of the reactant Δ(δS) is significantly elongated along the shortest axis N2−Ru−O1 due to the contraction of spin density from ligand 1 to the central metal atom. In the second step, the long axis of the elongated octahedral core is changed from N2−Ru−O1 to N1−Ru−N5 through a much distorted square-pyramid-like geometry of 3 TSA/B, accompanying the chiral inversion Δ → Λ at the metal center. The change of the long axis means that it is neither a typical Ray−Dutt twist nor Bailar twist, but partly mixed with the bond departure form. More importantly, the triplet−singlet state crossing also occurs in this step at both sides of the key transition state 3TSA/B. Thus, the 3MC states become the ground state in between the two crossing points, and the chiral inversion actually proceeds on the triplet ground state about one-half of the path! The third step is a shrink procedure of the octahedral core along the new long axis with a redistribution of the spin density. For the transient structures at the triplet−singlet crossing points, we found that the lowest or imaginary-frequency displacement vectors in the triplet state still dominate the reaction path. Also, between the two points, the de-excitation is impossible. It is this mechanism that makes the 3MC states including 3TSA/B avoid the fate of fast decay and ligand dissociations. To our knowledge, this mechanism has never been reported in the literature. In addition, for the phen and bipy complexes, the calculated equilibrium constants and ECD curves of the equilibrium mixtures both are in excellent agreement with the observation that neither ligand dissociation nor redox products were detected. Since the chiral inversion on the triplet ground state strongly resembles that on the S0 state, we could say that the reversible photochemical reaction Δ(δS) ⇌ Λ(δS) is nothing but a triplet ground-state-dominated photoinduced chemical reaction. In view of the complexity of the potential surface, this angle of view is helpful to understand the related reversible photochemical reactions, and the related structure changes also provide some clues to improve the complexes for technological applications.

Figure 8. DFT energy levels of the singlet and triplet states involved in the photoinduced chiral inversion Δ(δS) ⇌ Λ(δS) of [Ru(phen)2(Lser)]+ with the rhombic (top) and trigonal (bottom) prismatic transition states. The green and white dots mean α and β electrons, respectively.

and white dots represent α and β electrons, respectively; d0 is the dz2 orbital, d±1 is a mixed orbital of dxz and dyz. This figure clearly depicts the change in energies of the Kohn−Sham orbitals (KSO) during the chiral inversion, especially for the highest singly occupied KSO and the lowest unoccupied KSO: Upon excitation of the reactant Δ(δS), a β-electron is promoted from the dz2 orbital to the π*phen-dominated orbital. Its energy decreases with the reaction proceeding from 3CTR to 3 TSA/B due to the invading of dxz and dyz orbitals, then increases from 3TSA/B to 3CTP with the departure of the d-components. Meanwhile, the energy of the unoccupied dz2 orbital increases from 3CTR to 3TSA/B due to the mixture of the π*phen orbital, and then decreases from 3TSA/B to 3CTP with the disappearance

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.7b02030. Complete ref 45; the low-energy isomers, DFT energy levels, Kohn−Sham orbitals, excitation energies, and transition moments of the reactant Δ(δS) and product Λ(δS); the optimized Cartesian coordinates for all the metastable and transition-state structures involved in the H

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photoinduced chiral inversion of the complex [Ru(phen)2(L-ser)]+ (with data for bipy analogues available from the authors upon request) (PDF) Video showing the rhombic and trigonal inversions (AVI)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Yuekui Wang: 0000-0001-8435-1980 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We gratefully acknowledge the financial support from the National Natural Science Foundation of China (Grant 21273139).

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