Reduction of CO₂ in the presence of light via excited-state hydride transfer reaction in a NADPH-inspired derivative

Abstract

The photo-catalytic reduction of CO₂ into chemical feedstocks using solar energy has attracted vast interest in environmental science because of global warming. Based on our previous study on the CO₂ complex with one of the benzimidazoline (BI) derivatives, we explore the photochemical reduction of CO₂ in one of the benzimidazoline derivatives (1,3-dimethyl-5,6-diol-2,3-dihydro-1H-benzimidazole) by quantum-chemical methods. Our results reveal that carbon dioxide can be reduced to formate (HCOO⁻) by a hydride transfer reaction in the excited state of this complex of benzimidazoline derivative and CO₂. While the ground-state hydride transfer reaction in this complex exhibits a substantial barrier, a charge-transfer can occur in the first singlet excited state of the complex in the UV-A region (326 nm), and after overcoming a moderate barrier (∼0.4 eV) the system can have access to the products. The interaction with a polar solvent decreases further the barrier such that the reaction in dimethyl sulfoxide can proceed with a negligibly small barrier (∼0.1 eV) or in a nearly barrierless manner. Our results show that this benzimidazoline derivative may act as a catalyst in the photoreduction of CO₂.

---

Introduction

Atmospheric carbon dioxide (CO₂) as one of the most important green-house gases continues to attract attention of scientists and researchers because of its potential role in global warming and climate change. Technologies and materials for selectively removing atmospheric CO₂ from gases, its capture and conversion into value-added materials pose one of the most pressing scientific challenges and goals.^1,2 An especially interesting topic is the solar-driven reduction of CO₂ and its conversion into useful chemicals or energy-bearing products.

The conversion of CO₂ into formic acid is favoured amongst all the other routes because formic acid is an energy-storage medium for hydrogen, it is also a useful fuel and has far more promising commercial potential compared to its competitors like methanol, CO or long-chain hydrocarbons.³ The transfer of the hydride ion (H⁻) from the hydride donor to the C atom of CO₂ to yield formate is one of the most interesting routes as it requires the bending of an extremely stiff CO₂ molecule and the formation of a new C–H bond.

The drawbacks of metal-based catalysts including gas poisoning susceptibility, limited selectivity, restricted availability, high cost etc. opened the way to the new non-toxic reagents for the reduction of CO₂ under metal-free conditions.^4–15 Metal-free hydrides based on benzimidazoline represent promising hydride sources to reduce CO₂ efficiently to the formate anion, HCOO⁻.¹⁶ Benzimidazoline-based catalysts belong to the group of biomimetic analogs of nicotinamide adenine dinucleotide phosphate (NADP). As is well known, NADP is used in the biosysthetic reactions in the Calvin cycle and helps the transformation of CO₂ into glycose.

Lim et al. showed that for the benzimidazole-based catalyst a reduction of CO₂ is achieved via a hydride transfer reaction (Scheme 1), and the hydride donor was quantitatively oxidized to its aromatic benzimidazolium cation, establishing its recyclability.¹⁶ They also obtained the electrochemical reduction of the benzimidazolium cation to its organo-hydride form in quantitative yield. The reaction proceeds in the absence of biological enzymes, a sacrificial Lewis acid, or a base to activate the substrate or reductant. The reaction took place in a polar medium with dimethyl sulfoxide (DMSO) as solvent. DMSO serves as a polar solvent that helps the charged species benzimidazolium cation and formate to be stabilized, and both CO₂ and benzimidazole are sufficiently soluble in DMSO. The results of the study by Lim et al. showed that one of the methyl derivatives of benzimidazole (1,3-dimethyl-2,3-dihydro-1H-benzimidazole) has an experimentally proven reduction ability with formate with yields as high as 66% under certain reaction conditions.¹⁶ However, successful application of benzimidazole-based compounds for CO₂ reduction to formate is restricted by the fact that the hydride transfer (HT) to CO₂ exhibits sluggish kinetics. Weerasooriya et al. proposed that the conventional HT mechanism may be replaced by an orthogonal HT mechanism that involves a separate transfer of electrons and a proton to CO₂ and that may lead to lower kinetic barriers for the CO₂ reduction to HCOO⁻.¹⁷

Scheme 1 Catalytic cycle for the reduction of CO₂ to formate anion by 1,3-dimethyl-5,6-diol-2,3-dihydro-1H-benzimidazole.

Xie et al. have reported very recently that catalysts for CO₂ reduction based on benzimidazole can be regenerated using a carbazole photosensitizer and visible light.¹⁸ They have also shown that the system is capable of producing formate with a turnover number exceeding 8000 without generating other products such as CO and H₂. Moreover, BI derivatives have various biological activities such as anticancer, antiviral, antioxidant, or hormone antagonist to name but a few.¹⁹

The model compound employed in this study is 1,3-dimethyl-5,6-diol-2,3-dihydro-1H-benzimidazole (it is denoted by 1d). It is derived by substitution from dihydrobenzimidazoline as the basic structure in which there are two –OH substitutions on the benzene ring of the benzimiadzoline unit and two methyl groups substituted on the imidazole ring of the benzimidazoline unit (Scheme 1). It was also denoted as 1d in our previous study.²⁰ According to the results presented in our previous paper, 1d is capable of reducing CO₂ to HCOO⁻ in DMSO. To provide insight into the hydride donor ability of 1d, we have investigated the thermodynamic hydricity (ΔG_H⁻) of this species, which is the free energy required to cleave its C–H bond and generate a hydride ion (H⁻). Furthermore, since hydricities are expected to change significantly as a result of solvent interactions with the charged species, solvent effects have to be taken into account. The calculated hydricity for 1d was presented in our previous paper.²⁰ It was calculated at the PW6B95/-D3(BJ)^21,22/6-311++G(d,p) level of theory with solvent effects modelled via the Integral Equation Formalism Polarizable Continuum Model (IEFPCM)^23–42 with the SMD⁴³ option for DMSO as a solvent. Like the 1a species (1,3-dimethyl-2,3-dihydro-1H-benzimidazole), which hydricity is calculated to be 42.0 kcal mol⁻¹,²⁰1d also possesses good hydride donation strength which is 39.9 kcal mol⁻¹.²⁰ The hydricity of 1d is lower than the hydricity of formate which makes it a useful species for the CO₂ reduction.⁴⁴ Its activation free energy for the hydride transfer reaction, , is 18.6 kcal mol⁻¹, while the reaction free energy, ΔG_rxn, is 8.8 kcal mol⁻¹.

We turn now to the electrochemical regeneration of 1d which is another important characteristic in using it as a catalyst. In our previous paper²⁰ we presented the pathways for the electrochemical reduction involving initial electron transfer (ET) followed by a protonation (PT) and finally by another electron transfer (ET). The regeneration pathway for obtained cation 1d (1d → 2d˙ → 1d˙⁺ → 2d) begins with the electron transfer, after which the neutral species 2d˙ is formed. The energy required for the first electron transfer is 50 kcal mol⁻¹. The second step, protonation, is exergonic with ΔG_PT = −14 kcal mol⁻¹. The second electron transfer is slightly endergonic with 0.5 kcal mol⁻¹ for the 1d˙⁺ species. The comparison of energy diagram profiles for the regeneration pathway ET → PT → ET for the electrochemical conversion from benzimidazoline cation-based species to the corresponding organo-hydride is possible both for the 1a and 1d species.

The aim of the present study is to investigate possible routes for the photochemical reduction of CO₂⁴⁵ employing this benzimidazole-based hydride by theoretical methods and to guide future experiments. We are specifically interested in the question whether this benzimidazoline derivative can react with CO₂ in excited electronic states after absorbing visible or UV light similar to the derivative 1,3-dimethyl-2,3-dihydro-1H-benzimidazole. To date, we are aware of only our recent study on accessible chromophores of benzimidazole derivatives that can absorb photons in the visible/UV range and react with CO₂ in the excited electronic state to generate formate.²⁰

This study is structured as follows: we first give a general introduction and outline of the theoretical methods applied. The following section presents the results of equilibrium and transition-state structures, excitation energies and important molecular orbitals. We then critically discuss the photochemical reduction of CO₂. We close with a conclusion and outlook.

Computational details

The ground-state equilibrium geometries of the 1d⋯CO₂ and 2d⋯HCOO⁻ complexes were carried out using the ωB97-XD⁴⁶ functional with a 6-311+G(d,p) basis set and an ultrafine numerical grid. The normal modes and vibrational frequencies at equilibrium geometries of the state in question were then obtained. Excited-state equilibrium geometries and transition state geometry optimization in the first excited state with a subsequent frequency analysis were performed at the same level of theory from time dependent DFT (TD-DFT). The intrinsic reaction coordinate (IRC) pathways for the reaction 1d + CO₂ → 2d + HCOO⁻ related to both the ground and excited state of the 1d⋯CO₂ complex were obtained with the (TD)-DFT method employing the ωB97-XD functional with a smaller 6-31+G(d,p) basis set. The IRC path was integrated from the corresponding transition state in the backward direction (reactants: 1d and CO₂) and forward direction (products: 2d and HCOO⁻) of both the ground and first singlet excited state potential energy surfaces (PES) at the DFT and TD-DFT level, respectively. All DFT/TD(DFT) calculations were performed applying an ultrafine DFT integration grid as implemented in the Gaussian program package.⁴⁷

Vertical excitation energies and energy profiles along the pathways relevant for the hydride transfer were obtained with the complete-active-space self-consistent-field (CASSCF) method^48,49 complemented by second-order perturbation theory (CASPT2) i.e. with the internally contracted multi-reference second-order perturbation theory code (RS2C)⁵⁰ as implemented in the program code Molpro.⁵¹ The chosen active CAS space consists of three doubly occupied π orbitals and eleven lowest unoccupied orbitals. All doubly occupied orbitals from the active space are located on the 1d species. Among the unoccupied orbitals, two orbitals are located on the CO₂ molecule, two π* orbitals on the 1d species and four σ* orbitals on the 1d species, while the remaining three unoccupied orbitals are diffuse and possess also charge distributions located between the H atom of the 1d species and the carbon of CO₂ (see Fig. S1 in the ESI†). The active space consists of a total of 14 orbitals and 6 electrons. A relatively large active space with many unoccupied orbitals and smaller number of electrons was chosen to describe properly the lower-lying electronic states of both 1d⋯CO₂ and the 2d⋯HCOO⁻ complexes. Additional details about test calculations for the active space are given in the ESI.†

State-averaged CASSCF calculations were performed including the first five singlet states and the first three triplet states employing equal weights for all states. To avoid problems with intruder states, the RS2C calculations were performed with a standard level shift of 0.3 a.u. The oscillator strengths were obtained from the energy differences calculated at the CASPT2 level and transition dipole moments determined for the CASSCF wave functions. The dipole moments for the ground and excited singlet and triplet states were obtained from the CASSCF wave functions. The CASSCF/CASPT2 calculations have been performed employing the Molpro program.⁵¹ The basis sets employed were segmented contracted def2-type basis sets.⁵² They consist of a def2-TZVP basis set on carbon and def2-SVP basis sets on oxygen, nitrogen and hydrogen.

At the CASSCF level we have obtained the geometry of the S₀/S₁ conical intersection of the 1d⋯CO₂ complex employing the 6 orbital active space and using the procedure implemented in Molpro.⁵¹ The details are given in the ESI.† We have also located the geometry at the CASPT2 level which is most likely related to the nearby S₀/S₁ conical intersection of the multidimensional potential energy surfaces. Since at the CASPT2 level its energy is lower than the energy of the corresponding CASSCF conical intersection, we have adopted the CASPT2 geometry (Fig. 8) for further analysis. More accurate characterization of the minimum energy conical intersection would require an optimization at the CASPT2 level which is beyond the scope of the present study. After the geometry of the conical intersection relevant for the hydride transfer reaction and formation of the formate ion was identified, we constructed a linearly interpolated internal-coordinate (LIIC) reaction path that connects that conical intersection with the minimum of the first singlet excited state of the 1d⋯CO₂ complex. The LIIC was constructed in such a way that internal coordinates of the geometry corresponding to the minimum of the first singlet excited state were scaled such that the geometry of the conical intersection is obtained when the scaling factor is equal to one. Single-point energy calculations have been performed along the LIIC path using the CASPT2 method to obtain the reaction-path potential energy profile. Since the test calculations on the IRC reaction path from 1d + CO₂ to 2d + HCOO⁻ showed that only the ground and the first excited state are relevant for the reaction path, three singlet roots with equal weights were included in the CASSCF/CASPT2 calculations along the LIIC reaction path.

In order to predict the strength of the singlet–triplet interaction between the relevant states, we have performed ab initio calculations for the spin–orbit coupling matrix elements. At the selected geometry, the matrix elements 〈Ψ_a|H_SO|Ψ_b〉 have been calculated employing the CASSCF method with the second-order Douglas–Kroll–Hess (DKH) Hamiltonian as incorporated in the MOLPRO program package. The Douglas–Kroll valence triple zeta plus polarization basis set (cc-pVTZ-DK) has been employed for the calculations.

To account for solvation effects of dimethyl sulfoxide on the excited state, we applied the TD-DFT method and the corrected linear response solvation (cLR-PCM) continuum model in its non-equilibrium limit as implemented in Gaussian.⁵³ It has been shown that this model is essential for the proper description of excited states with charge transfer (CT) character.^54–58 The calculated atomic charges were obtained by a natural population analysis (NPA) using the natural bond orbital (NBO) method of Weinhold^59,60 at the MP2/aug-cc-pVDZ level of theory.

Results and discussion

Equilibrium and transition state structures

The equilibrium structure of the 1d⋯CO₂ complex in its ground state is characterized by CO₂ placed above the plane of the benzene ring of the benzimidazoline unit and the O–C–O angle which is close to linear (178.6°) (Fig. 1(a)). The equilibrium geometry of the 2d⋯HCOO⁻ complex in its ground state is shown in Fig. 1(c). The O–C–O angle in the ground state of the 2d⋯HCOO⁻ complex is bent (127.5°) and HCOO⁻ is shifted toward the plane of the imidazoline unit. The C–H distance in HCOO⁻ species is 1.115 Å. We have also optimized the first singlet excited state of the 1d⋯CO₂ complex. It is also characterized by almost linear O–C–O angle (178.9°) and CO₂ is shifted more toward the benzene ring of the benzimidazoline unit (Fig. 2(a)). The optimization of the first singlet excited state of the 2d⋯HCOO⁻ complex led to the minimum-energy structure with the O–C–O angle of 144.0° and HCOO⁻ placed above the imidazoline unit of the complex. This structure is shown in Fig. 2(b).

Fig. 1 Equilibrium structure of the ground state of the 1d⋯CO₂ complex (a), the ground state transition state structure for the reaction 1d⋯CO₂ → 2d⋯HCOO⁻ (b), and the ground state of the 2d⋯HCOO⁻ complex obtained at the DFT employing the ωB97-XD functional with a 6-311+G(d,p) basis set. (c). Upper panel refers to the side view and lower panel to the top view. The equilibrium CO₂ bending angle is also shown.

Fig. 2 Equilibrium structure of the first excited state of the 1d⋯CO₂ complex (a) and the first excited state of the 2d⋯HCOO⁻ complex (b) obtained at the TD-DFT level employing the ωB97-XD functional with a 6-311+G(d,p) basis set. The equilibrium CO₂ bending angle is also shown.

The hydride-detachment coordinate involves changing the distance between the carbon of CO₂ and the hydrogen of the organo-hydride coupled with the out-of-plane distortion of the five-membered ring system of the BI unit. The imaginary frequency of the transition state in both the ground and excited electronic states of the 1d⋯CO₂ complex correspond to the collective and concerted C–H stretching mode in which bond breaking and bond making between the C atom and the hydride at 1d, respectively, and the formation of the formic acid anion, occurs in a single step. The transition state structures are displayed in Fig. 3. The O–C–O angle in the TS ground state is 141° while it is 138° in the TS of the first singlet excited state. The C–H distance between carbon of formic acid and migrating hydrogen (C_f–H) in the ground TS state is 1.267 Å while the distance between the carbon of hydride donor and hydrogen (C_1d–H) is 1.539 Å. In the TS excited state the C_f–H distance is 1.298 Å while the C_1d–H distance is 1.593 Å which indicate that in both electronic states the TS structure corresponds more to the product-like arrangement. In the ground TS the C–H–C angle is 147°. In the first excited TS the C–H–C angle shows also bent structure at 144°. It is well known that the C⋯H⋯C angle in the hydride transfer transition state is often (but not always) bent.⁶¹

Fig. 3 (a) Ground and (b) first singlet excited TS structures for the 1d⋯CO₂ complex obtained at the DFT and TD-DFT level, respectively, employing the ωB97-XD functional with a 6-311+G(d,p) basis set. Important bond lengths (in Å) are denoted.

Excitation energies and molecular orbitals

Table 1 gives the vertical excitation energies, oscillator strengths and dipole moments of low-lying singlet and triplet electronic states of the 1d⋯CO₂ complex at the ground state equilibrium geometry. The first excited singlet state lies at 3.80 eV above the ground state. It possesses large oscillator strength of 0.073, the largest value of all four calculated excited states. It can be excited directly by light in the UV-A wavelength region. The second and the third singlet excited states (S₂ and S₃) are at 5.33 eV and 5.61 eV, respectively, while the energy of the fourth excited state is calculated to be 6.33 eV. The first three electronic states (1¹A, 2¹A, and 3¹A) of the 1d⋯CO₂ complex state are of low polarity with the dipole moment μ = 3.58, 3.38, and 3.35, respectively. The third excited state has much larger dipole moment (μ = 6.76) while the fourth excited state is highly polar (μ = 12.71). The frontier molecular orbitals at the equilibrium geometry of the ground electronic state of the 1d⋯CO₂ complex are displayed in Fig. 4. Since the five-membered ring of the benzimidazole unit does not remain planar along the reaction path, the separation between the σ–π molecular orbitals is not conserved along the reaction pathways in the ground and the excited states of the complex. Therefore, the σ and π character of the orbitals denoted in dominant electronic configuration in Tables 1 and 2 is related to their character at the equilibrium geometries where benzimidazoline unit is planar. The highest molecular orbital (HOMO) is of π character (63a orbital). The lowest unoccupied molecular orbital (64a orbital) is of π* character. The first excited state of the 1d⋯CO₂ complex corresponds to the excitation 63a→ 64a and partly from 62a to 65a. It can be seen that the S₀ → S₁ vertical excitation at the S₀ equilibrium geometry is not accompanied by a shift of electron density from benzimidazoline unit to CO₂. The third excited state corresponds to the excitation into orbital 66a which is characterized by the charge distribution located on the CO₂ molecule. This excited state is of charge-transfer (CT) character.^62–64 The S₃ state is characterized by much smaller oscillator strength. It is optically dark state and it is rather high in energy (5.61 eV) at the ground-state equilibrium geometry of the 1d⋯CO₂ complex. The fourth excited state corresponds to the excitation into 67a orbital which is also characterized by a charge distribution located on the CO₂ molecule. In the triplet manifold, two lowest triplet states are below the first singlet excited state. The T₁ state lies at 3.34 eV, T₂ is located at 3.51 eV while T₃ is found to lie at 4.29 eV above the minimum of the ground state of the 1d⋯CO₂ complex.

Table 1 CASPT2 vertical excitation energies (ΔE), CASSCF/CASPT2 oscillator strengths (f), CASSCF dipole moments (μ) and main electronic configuration of the lowest excited states of the 1d⋯CO₂ complex and the 2d⋯HCOO⁻ complex calculated at the respective equilibrium geometry indicated in the parentheses. The excitation energies with respect to the minimum of the ground state of the 1d⋯CO₂ complex are given. The numeration of the molecular orbitals of the respective active space of the CASSCF calculations are given in Fig. S1 and S3 in the ESI

State	ΔE (eV)	f	μ (D)	Electronic excitation
1d⋯CO2 (S0)
S0	0.00	—	3.58
S1 (^1ππ*)	3.80	0.073	3.38	(63a → 64a) + (62a → 65a)
S2 (^1ππ*)	5.33	0.019	3.35	(63a → 65a) + (62a → 64a)
S3 (^1πσ*)	5.61	0.0008	6.76	(63a → 66a)
S4 (^1πσ*)	6.33	0.022	12.71	(62a → 67a)
T1 (^3ππ*)	3.34	—	3.75	(63a → 64a)
T2 (^3ππ*)	3.51	—	3.70	(63a →65a)
T3 (^3ππ*)	4.29	—	3.36	(62a → 64a)
1d⋯CO2 (S1)
S0	0.65	—	3.58
S1 (^1ππ*)	3.74	0.074	3.67
S2 (^1ππ*)	5.76	0.018	4.02
S3 (^1πσ*)	5.98	0.024	7.44
S4 (^1ππ*)	6.34	0.010	3.65
2d⋯HCOO^− (S0)
S0	0.87	—	7.85
S1 (^1σπ*)	4.91	0.082	7.93	(63a → 64a) + (62a → 66a)
S2 (^1ππ*)	6.13	0.180	7.58	(61a → 64a)
S3 (^1σπ*)	6.29	0.033	8.71	(62a → 64a) + (63a → 66a)
S4 (^1σπ*)	6.32	0.016	12.38	(63a → 65a)

---

Fig. 4 The frontier molecular orbitals involved in the electronic excitations of the lower-lying excited states of the 1d⋯CO₂ complex obtained by the CASSCF calculations and determined at the equilibrium geometry of the ground state of the 1d⋯CO₂ complex.

Table 2 CASPT2 vertical excitation energies (ΔE), CASSCF/CASPT2 oscillator strengths (f), CASSCF dipole moments (μ) and main electronic configuration of the lowest excited states of 1d calculated at the equilibrium geometry of the ground state. The excitation energies with respect to the minimum of the ground state of 1d are given

State	ΔE (eV)	f	μ (D)	Electronic excitation
1d (S0)
S0	0.00	—	3.27
S1 (^1ππ*)	3.76	0.059	3.14	(52a → 53a)
S2 (^1ππ*)	5.09	0.018	2.76	(52a → 54a)
S3 (^1πσ*)	6.03	0.004	10.05	(52a → 56a)
S4 (^1πσ*)	6.19	0.0001	9.75	(52a → 55a)
T1 (^3ππ*)	3.27	—	3.32	(52a → 53a)
T2 (^3ππ*)	3.48	—	3.28	(52a → 54a) + (51a → 53a)
T3 (^3ππ*)	4.24	—	3.04	(51a → 53a) + (52a → 54a)

---

The vertical excitation energies, oscillator strengths and dipole moments of the 1d⋯CO₂ complex at the equilibrium geometry of the first singlet excited state are collected in Table 1. At the equilibrium geometry of the first singlet excited state of the 1d⋯CO₂ complex, the ground state lies approximately 3.09 eV below S₁. The second, third and fourth excited states are well separated from these two states, they are at 5.11 eV, 5.33 eV and 5.69, respectively, above the S₀ state at the equilibrium geometry of the S₁ state. The energy of the S₁ state is stabilized only slightly (∼0.06 eV) upon geometry optimization. The oscillator strength of the S₁ state at this equilibrium geometry shows that the complex absorbs moderately strongly (∼0.07). The vertical excitation energies, oscillator strengths and dipole moments of the 2d⋯HCOO⁻ complex at the ground state equilibrium geometry of this complex are given in Table 1. The first excited state calculated at the equilibrium geometry of the ground state of the 2d⋯HCOO⁻ complex has dominant configurations that correspond to 63a → 64a and 62a → 66a excitations (Fig. S3 ESI†). Both 62a and 63a molecular orbitals are characterized by charge distributions both on the benzimidazoline unit and on HCOO⁻.

For comparison, we also present the vertical spectrum involving lower-lying singlet and triplet electronic states of 1d. Upon inspection of the results in Table 2 one can notice that the energies are slightly different. As for the first singlet excited state, it is at 3.80 eV in the 1d⋯CO₂ complex while the excitation energy of the first singlet state in 1d is 3.76 eV. The energies of the triplet states are also very similar, 3.34, 3.51, and 4.29 eV for 1d⋯CO₂ and 3.27, 3.48, and 4.24 eV for 1d.

Photoreduction of CO₂ in the 1d⋯CO₂ complex

We first investigated the potential energy surfaces at the geometries around the minimum of the ground state of the 1d⋯CO₂ complex. We chose one of the normal modes around the equilibrium structure of the ground state as the driving coordinate for the hydride transfer reaction. It is the vibrational mode which corresponds mostly to the bending of the O–C–O angle and subsequent approach of CO₂ to the hydrogen of the imidazole unit. The O–C–O angles and CH⋯H distances of the selected vibrational mode are presented on the abscissa in Fig. 5(a). The right inset in Fig. 5(a) shows the atomic displacement coordinates of this mode. The energy of the S₀ state as a function of the driving coordinate rises gradually. The vertical excitation from this state by a photon leads to the S₁ state. The S₁ state exhibits a local minimum in the vicinity of the equilibrium geometry of the ground electronic state. The potential energy function of the second singlet excited state is crossed by the ¹CT state. The S₂–¹CT conical intersection can be reached in almost barrierless manner. The ¹CT state is further stabilized with further increase of the selected driving coordinate. Second conical intersection takes place between S₁ and ¹CT and induces a barrier on the S₁ state. The crossing between these two states is about 0.9 eV above the minimum of the potential energy curve for the S₁ state. On the basis of the computations an upper limit for the barrier of 0.9 eV is predicted for the S₁–¹CT crossing. Taking this into account, from the Franck–Condon region of the S₁ state, this conical intersection becomes accessible beyond certain excitation energy. Further stabilization of the ¹CT state leads to the conical intersection of this state with the ground state. This intersection takes place at the lower energy than the minimum of the first singlet excited state. Along the rigid scan presented in Fig. 5(a), the energy of the ¹CT state is lowered considerably, whereas the energy of the S₁ state rises. The ¹CT state is stabilized by about 1.9 eV along this rigid scan. At highly bent geometries, the ¹CT state becomes even the lowest state.

Fig. 5 (a) CASPT2 potential-energy profiles of the lower-lying singlet and triplet states of the 1d⋯CO₂ complex along the vibrational mode corresponding to the simultaneous O–C–O bending and CH⋯H stretching and starting from the equilibrium geometry of the ground state. The diabatic correlation of the states is shown. The snapshots of the important molecular orbitals along the driving coordinate are shown. Top-right inset represents atomic displacements of the selected vibrational mode in the ground electronic state. The change of the character of the S₁ state is indicated along the pathway. (b) Dipole moments of the ground (blue) and the first excited singlet state (red) along the abovementioned vibrational mode obtained at the CASSCF level. The change of the character of the S₁ state is indicated along the pathway. The change of the transition dipole moment between S₀ and S₁ states along the driving coordinate is presented by dashed line. The absolute value of the largest component is shown.

We now turn to the triplet manifold presented in Fig. 5(a). The potential energy curves of the first two triplet states are beyond the potential energy curve or the 2¹A state and almost parallel to it in the range of the O–C–O angles between 180° and 157°. Upon further bending of CO₂ there is a crossing between ¹CT state and T₁ as well as with T₂. In order to estimate if this curve crossings can give rise to intersystem crossings, we have estimated the singlet–triplet coupling between S₁ and T₁ at their crossing by calculating the spin–orbit coupling matrix element (SOCME) at the CASSCF level employing the active space with 14 orbitals and cc-pVTZ-DK basis set. The results show that SOCME for these two states is very small (〈S₁|H_SO|T₁〉 = 0.17 cm⁻¹). Further investigation of possible mixing of singlet and triplet states by spin–orbit coupling at other relevant geometries to investigate if triplet states can give rise to hydride transfer may be the topic for future theoretical studies.

In Fig. 6(a) are displayed potential energy curves calculated at the geometries around the minimum of the first singlet excited state. The potential energy curves of the 2¹A, 3¹A, and 5¹A states are again parallel to the ground state in the range of the O–C–O angles between 180° and 160°. The minimum of the potential energy curve of the ground state is shifted to higher energy. From the computational results presented it can be anticipated that the system prepared in the 2¹A state by optical excitation with sufficient excess energy will bypass the conical intersection via the barrier of about 0.9 eV and evolve on the surface of the ¹CT state. The energy profile of the 2¹A state follows the profile of the 1¹A state in a wide range of driving coordinate. Due to a shallow minimum in the 2¹A excited state a broad range of reaction coordinates can be activated in the zero-point vibrational motion. It should be kept in mind that the presented rigid scans of the potential energy functions are not intended to give quantitative energy information since the potential energy curves in Fig. 5(a) and 6(a) are not related to the minimum-energy path.

Fig. 6 (a) The CASPT2 energy profiles of the low-lying singlet states of the 1d⋯CO₂ complex computed at the CASPT2 level. The profiles were obtained by a rigid scan from the equilibrium geometry of the first excited state of the 1d⋯CO₂ complex along the vibrational mode most relevant for the reaction (simultaneous C–H⋯C stretching and O–C–O bending). The diabatic correlation of the states is shown. Top-right inset represents atomic displacements of the selected vibrational mode in the first singlet excited state. (b) Dipole moments of the ground (blue) and the first excited singlet state (red) along the abovementioned vibrational mode. The change of the character of the S₁ state is indicated along the pathway. The change of the transition dipole moment between S₀ and S₁ states along the driving coordinate is presented by dashed line. The absolute value of the largest transition dipole moment component is shown. The dipole moments and transition dipole moments are obtained at the state-averaged CASSCF level.

Additional insight into the charge redistribution process that occurs during the hydride transfer reaction can be obtained from the inspection of the orbitals in the dominant configuration of the states involved. In the first singlet excited state the dominant configuration involves excitation from the 63a orbital to the 64a orbital and partly from 62a to 65a. The shape of the 64a orbital at the minimum of the S₀ state and its transformation further along the driving coordinate are shown in Fig. 5(a). It can be seen that at the equilibrium geometry of the ground state the HOMO and the 64a orbital are located on the benzimidazole unit. With increasing driving coordinate (∠O–C–O ∼ 155°), a flow of the electronic charge in the region between the benzimidazole and CO₂ in the 64a orbital can be seen. With further increase of the driving coordinate (∠O–C–O ∼ 140°), the charge in the 64a orbital is completely localized on the CO₂ molecule.

As we have already mentioned, the results of the rigid scan presented in Fig. 5(a) and 6(a) are not intended to give quantitative information on the hydride transfer reaction. Therefore, we searched for the minimum energy S₁/S₀ conical intersection that could lead to a hydride transfer and the formation of a formate ion. In Fig. 7 we present potential energy profiles of the first three excited states along the IRC reaction path optimized for the first singlet excited state of the 1d⋯CO₂ complex. For the hydride transfer from the benzimidazoline unit to the CO₂ molecule, the reaction coordinate which represents the reduction reaction cannot be described by a simple intermolecular coordinate. Instead, it is a combination of the O–C–O bending, the C–H⋯C coordinate which involves changing the distance between the carbon of CO₂ and the hydrogen of the organo–hydride, and an out-of-plane distortion of the five-membered ring system of the benzimidazoline unit. The critical C⋯H distances and O–C–O angles for the specified steps along the IRC pathway for the hydride transfer reaction in the 1d⋯CO₂ complex calculated for the first singlet excited state are given in Table S2 of the ESI.† From Fig. 7 we see that the activation energy for the reduction process CO₂ + 1d → HCOO⁻ + 2d in the first excited state is far higher compared to the ground state. It strongly indicates that the reduction of CO₂ in the first excited state is not a thermodynamically favoured process. Therefore, the shape of the excited state potential energy surface does not favour the formation of HCOO⁻ and 2d species compared to the ground state surface. Hence, in order to have an excited state involved for the efficient production of the formate ion, we require a potential energy crossing with the ground state surface around a convenient crossing point.⁶⁵ We have located the S₁/S₀ minimum energy conical intersection (2.7 eV) that is well below the vertical excitation from the ground state to the first excited state of the 1d⋯CO₂ complex, and also well below the minimum of the first excited state of this complex.

Fig. 7 Hydride transfer profiles of the S₀ state (cubes, green) and the S₁ state (circles, red) connecting the conical intersection (CI) of these two states with the transition state (TS) and product along the IRC pathway calculated at the geometries optimized at the first excited state of the 1d⋯CO₂ complex. The S₂ state (diamonds, blue) is also shown. The energy profile obtained at the CASPT2 level is presented. The minus sign for the reaction coordinate denotes reverse direction while plus sign denotes forward direction. The structures shown as insets represent conical intersection (left) and product at the corresponding geometry (right). See Table S2 in the ESI† for the critical internal coordinates related to the displayed reaction coordinates. Dashed lines indicate the diabatic correlation of the states.

The geometry of the S₁/S₀ minimum energy conical intersection is presented in Fig. 8. The O–C–O angle of 137° differs significantly from that of the ground-state structure. The CO₂ molecule is displaced from the central position above the benzimidazoline plane in the ground state so that it is shifted toward the position above one of the carbons of the imidazoline unit. The dihedral angles characterizing this displacement are: α(O1–C2–H1–C1) = 67.7° and α(O2–C2–H1–C1) = −155.3°. At the geometry of the S₁/S₀ conical intersection (CI), the HOMO is again localized at the benzimidazole unit while the charge distribution of the lowest unoccupied molecular orbital (LUMO) is located completely at the CO₂ molecule (Fig. 9). The charge-transfer character of the S₁ state around the CI provides a driving force for the hydride transfer.

Fig. 8 Structure of the lowest-energy S₁/S₀ conical intersection of the 1d⋯CO₂ complex located at the CASPT2 level. The numbers denote bond lengths in Å.

Fig. 9 Molecular orbitals involved in the excitation at the S₀ → S₁ conical intersection geometry of the 1d⋯CO₂ complex. The highest occupied molecular orbital (a) and the lowest unoccupied molecular orbital (b) in the ground state of the 1d⋯CO₂ complex. The center of the charge distribution in LUMO is located on the carbon of the CO₂ molecule.

In the following we restrict ourselves on the dipole moment and transition dipole moment functions of the ground and first singlet state. In Fig. 5(b) and 6(b) the dipole moment functions of the S₀ and S₁ states are presented. We observe in the region related to the O–C–O bending angle between 150° and 160° a steep increase of the dipole moment of the S₁ state while it is not the case for the dipole moment function of the S₀ state. The steep increase of the S₁ dipole moment function reflects its change of character after crossing with the charge-transfer state in which a significant amount of electronic charge is transfer from the benzimidazoline unit to the CO₂ molecule. The largest component of the transition-dipole moment function (TDM) between S₀ and S₁ states also shows a steep increase. We present in Fig. 10 the dipole moment curves along the minimum-energy path of the first excited state of the 1d⋯CO₂ complex and toward the excited transition state. While the dipole moment function of the ground state along this IRC pathway is weakly dependent on the reaction coordinate, the dipole moment function of the first singlet excited state shows a very different behaviour along the hydride transfer coordinate (Fig. 10). The complex behaviour of the dipole-moment function of the excited state is reflected by rapid changes of the wavefunction and consequently the dipole moment values along this path. The dipole moment of the ¹CT state first decreases steeply with increasing C_d–H bond length until the intersection of the energy functions at the value of the reaction coordinate −7.26 (C_d–H = 1.096 Å and C_a–H = 2.535 Å), where there is an avoided crossing due to the same symmetry. Actually, at this point the dipole moment value of the first excited state collapses abruptly to 5.3 D and at this geometry the dipole moments of both states have similar values. The changing the C_a–H distance by only 0.03 Å causes sudden rise of the dipole moment value of the excited state to 12 D. Upon further elongation of the C_d–H distance, the dipole moment function decreases until it reaches the value of 6.7 D at the geometry of the exited transition state. The dipole moment of the ground state gradually increases until it reaches a value of 7.9 D at the TS geometry of the excited state. The explanation for the large dipole moment of the CT state can be obtained from the analysis of the molecular orbitals involved in the dominant configuration of this excited state (Fig. 9): the 63 → 64 excitation involves a shift of the electronic charge from the rings to the C atom of the CO₂ molecule. The charge separation results in a very large dipole moment of this state. Therefore, the vertical excitation from the ground state of the 1d⋯CO₂ complex into the first excited state increases the dipole moment of the system substantially. The change of the components of the transition dipole moment functions between S₀ and S₁ states with the nuclear geometry is also presented in Fig. 10. In the vicinity of the reaction coordinate −7.26 (C_d–H = 1.096 Å and C_a–H = 2.535 Å) at which we have located the S₀/S₁ conical intersection, one can see that the components of the S₀ → S₁ TDMs are rapidly varying functions with the nuclear geometry.

Fig. 10 Dipole moments of the ground (blue) and the first excited state (red) and the transition dipole moment components between S₀ and S₁ states (absolute values are presented by dashed lines) along the IRC path for first excited state of the 1d + CO₂ → 2d + HCOO⁻ reaction presented from the conical intersection region of the 1d⋯CO₂ complex to TS of the first excited state. The dipole moments and transition dipole moments are obtained by the state-averaged CASSCF calculations. See Table S2 in the ESI† for the critical internal coordinates related to the displayed reaction coordinates.

We have identified three nuclear coordinates as possibly important for the relaxation from the Franck Condon region of the S₁ potential energy surface towards S₁/S₀ minimum energy conical intersection with the ground state and further toward the transition state of the ground state. These are: the O–C–O bending, hydride transfer, and the pyramidization at the carbon atom of CO₂. The pyramidalization angle is defined as the angle between the bond H–O1 and the normal vector of the plane spanned by atoms O1, O2 and C. The angle has been referred to as the φ(H–O–O–C) pyramidalization angle. The potential energy profiles along the LIIC reaction path reveal that the energy of the S₁ state decreases by almost 1 eV along the LIIC path, while the ground state energy increases sharply by more than 2 eV (Fig. 11(a)). Therefore, the S₁/S₀ minimum energy conical intersection becomes accessible by the O–C–O bending as well as the hydride transfer and pyramidization at the carbon atom of CO₂. The changes of the S₀ and S₁ dipole moment functions and the components of the S₀ → S₁ transition dipole moment functions along the LIIC reaction path for the hydride transfer reaction 1d + CO₂ → 2d + HCOO⁻ are displayed in Fig. 11b. It can be noticed that there is an increase of all three S₀ → S₁ TDM components as the S₀ and S₁ energies approach each other along the reaction path.

Fig. 11 (a) Energy profiles of the first three singlet states of the 1d⋯CO₂ complex along the LIIC reaction path for the hydride transfer reaction 1d + CO₂ → 2d + HCOO⁻ computed at the CASPT2 level obtained by linear interpolation between the equilibrium geometry of the first excited state of the 1d⋯CO₂ complex and the optimized S₁/S₀ minimum energy conical intersection. The inset at left represents the equilibrium geometry of the first excited state of the 1d⋯CO₂ complex, while the inset at the right is the geometry of the S₁/S₀ minimum energy conical intersection for the hydride transfer. Units of the reaction path on the abscissa axis are arbitrary. (b) Dipole moments of the ground (blue) and the first excited state (red) along the reaction path. The change of the character of the S₁ state is indicated along the pathway. Transition dipole moment components between S₀ and S₁ states are displayed by dashed lines. The dipole moments and transition dipole moments are obtained by the state-averaged CASSCF calculations.

We would like to shed some additional light on the molecular mechanism of this photoinduced CO₂ reduction reaction, specifically if formate anion (HCOO⁻) or formate radical (HCOO˙) is formed in the investigated reaction. The geometry of the CO₂ moiety changes as the 1d⋯CO₂ complex approaches the transition state of the complex. The bending of the CO₂ moiety occurs, and it induces changes in the energy of the molecular orbitals predominantly located on the CO₂ moiety. As it was discussed and illustrated in the paper by Álvares et al.⁶⁶ for the isolated CO₂ molecule, the lowering of the energy of the in-plane 2π_u molecular orbital upon bending makes the carbon atom of the CO₂ molecule more reactive. The O–C–O angle of the equilibrium geometry of the CO₂ radical anion is 135.1° and its singly occupied molecular orbital (SOMO) is energetically close to the LUMO of the neutral CO₂ at the O–C–O angle of 135°. The equilibrium C–O bond length and the O–C–O angle as well as the orbital characters of the formate anion are very similar to those of the CO₂ radical anion. Instead, the formate radical (HCOO˙) is characterized by a different equilibrium geometry – the equilibrium O–C–O angle is 112.5° as calculated at the (U)CCSD/cc-pVTZ level of theory.⁶⁶ It can be seen from the results presented in this paper that the equilibrium geometry of the 2d⋯HCO₂⁻ complex in its ground state (Fig. 1(c)) is characterized by the O–C–O angle of 127° similar to the geometry of the formate anion but not of the formate radical. In order to confirm the formation of formate anion upon reaction of 1,3-dimethyl-2,3-dihydro-1H-benzimidazole derivatives with CO₂, Lim et al.⁴ performed ¹H NMR spectroscopy and electrospray ionization mass spectrometry (ESI-MS) measurements. These two analytical methods confirmed the presence of formate as a product of the reaction of benzimidazoline derivatives and CO₂. To further validate their proposed mechanism of reduction, they have conducted experiments with isotopically enriched ¹³CO₂ gas (99 atom % ¹³C) which further corroborated the presence of isotopically enriched H¹³COO⁻. For additional details see ESI† in ref. 4. In order to additionally validate the molecular mechanism of the CO₂ reduction with the derivative 1d, we have undertaken calculations of the NPA partial charges on HCO₂ and CO₂ species along the IRC pathway of the ground state of the 1d⋯CO₂ complex. Fig. 12 provides further support of the formation of the formate ion. It can be noticed that the partial charges change considerably between the transition state and product species along the reaction path 1d⋯CO₂ →2d⋯HCO₂⁻. The partial charge on the HCO₂ species (red line in Fig. 12) changes from −0.571 in the TS structure of the ground state of the complex to −0.916 in the product 2d⋯HCO₂⁻ as expected from receiving a hydride.

Fig. 12 The variation of the NPA partial charges condensed on HCO₂ and CO₂ along the IRC path for the ground state of the 1d⋯CO₂ complex. The NPA partial charges are calculated at the MP2/aug-cc-pVDZ level of theory.

Finally, the results of the calculations of the excited states in dimethyl sulfoxide as polar solvent along the IRC pathway for the hydride transfer reaction in the ground and first singlet excited state show that inclusion of a polar solvent significantly influences the possibility for such a reaction. The comparison between potential energy curves along the IRC pathway obtained in the ground state for the CO₂ + 1d → HCOO⁻ + 2d reaction in the gas phase (Fig. 13(a)) and in DMSO (Fig. 13(c)) shows that the ground state is remarkably stabilized upon going from the transition state to the products. The stabilization is even more pronounced along the IRC path obtained in the first singlet excited state for the CO₂ + 1d → HCOO⁻ + 2d reaction in the gas phase (Fig. 13(b)) and in DMSO (Fig. 13(d)). One can see that the barrier of about 0.4 eV which the system has to surmount in the gas phase to access the products, HCOO⁻ and 2d (Fig. 13(b)), reduces to about 0.1 eV in polar environment (Fig. 13(d)).

Fig. 13 Hydride transfer profile for the CO₂ reduction to the formate anion for 1d⋯CO₂ obtained from single-point calculations along the IRC path of the ground state (a) and first excited state (b) in the gas phase and along the IRC path of the ground state (c) and first excited state (d) in polar solvent (DMSO). Ground and first three excited states are obtained at the (TD)-wB97XD/6-311+G(d,p) level of theory and the cLR-model for DMSO as a solvent. The minus sign for the reaction coordinate denotes reverse direction while plus sign denotes forward direction. Dashed lines in (a) indicate the diabatic correlation of the states. See Table S2 in the ESI† for the critical internal coordinates related to the displayed reaction coordinates.

Summarizing this section, the following mechanism for the deactivation of the excited state of the 1d⋯CO₂ complex after optical excitation emerges from the results of our calculations: the optically prepared wave packet on the 2¹A potential energy surface will spread over the 2¹A surface and will transfer to the ¹CT state. One part of the wave packet can be deactivated to the ground electronic state (Fig. 14). On the other hand, according to the results of our calculations, a part of the wave packet can reach a reactive part of the potential energy surface that can lead the system to the transition state of the ground state and further to the products: HCOO⁻ and 2d (Fig. 7). For the reaction proceeding on the potential-energy surface of the ground state after an S₁/S₀ minimum energy conical intersection, the system has to overcome a moderate barrier of about 0.4 eV in order to reach the ground transition state. In a polar medium such as dimethyl sulfoxide, there is a significant lowering of the transition state with charge-transfer character and the barrier is reduced to only 0.1 eV so that the products can be formed almost barrierless. Therefore, after the conical intersection between the S₀ and S₁ states, even a small barrier that has to be surmounted on the way to the transition state for the hydride transfer reaction can be completely eliminated in polar solvents.^67,68

Fig. 14 Schematic view of the mechanism of the light-driven hydride transfer reaction in the 1d⋯CO₂ complex. Vertical red solid arrow represents vertical excitation energy of a given state computed at the respective ground-state minimum. Dashed blue arrows denote relevant processes on a given PES. Dashed black lines indicate the diabatic correlation of the states. S₀ – ground state; S₁ – first singlet excited state; CI – conical intersection; TS – transition state. The approximate change of the character of the S₁ state is indicated along the pathway.

Conclusions

The results of our calculations reveal that the excited electronic states of the complex of the derivative of benzimidazoline 1,3-dimethyl-5,6-diol-2,3-dihydro-1H-benzimidazole (1d) with CO₂ play an important role in the hydride detachment reaction and formation of formic acid anion. The key features of these states are:

(1) The charge-transfer state is strongly stabilized by the bending of the O–C–O angle. The charge-separated character of this state implies that its energetic location relative to other less polar states is strongly dependent on the environment.

(2) This charge-transfer state is stabilized by about 2 eV along the driving coordinate that includes simultaneous change of the O–C–O angle and CH⋯H distances.

(3) Along the LIIC reaction pathway on the PES of the first excited state of the 1d⋯CO₂ complex connecting the minimum of the first excited state and the located conical intersection of this state with the ground state, a charge-transfer state is stabilized while the ground state is destabilized.

In the present work we postulate that the following mechanism can be used for releasing the hydride ion by cleavage of the C–H bond in the complex of CO₂ and the benzimidazoline derivative 1d and the subsequent formation of the formate ion HCOO⁻. The system is first promoted by absorption of a UV quantum to the S₁ state. On this potential energy surface the system evolves toward the seam of intersection between S₁ and the ¹CT state. On this seam of intersection, the system can reach a conical intersection with the ground state, and after surmounting a moderate barrier (∼0.4 eV) on the pathway to the ground transition state for the hydride detachment reaction, the 1d⋯CO₂ complex can be transformed into 2d⋯HCOO⁻. The interaction of this molecular system with polar environment such as dimethyl sulfoxide leads to further reduction of the barrier so that the hydride transfer reaction and reduction of CO₂ can proceed with a negligible small barrier (∼0.1 eV) or in a nearly barrierless fashion.

The located S₁/S₀ minimum energy conical intersection (2.7 eV) is well below the vertical excitation energy from the ground state to the first excited state of the 1d⋯CO₂ complex and also well below the minimum of the first excited state of this complex. It should be mentioned that the presented mechanism does not exclude the existence of the competing decay pathways such as internal conversion to the ground state of the 1d⋯CO₂ complex and intersystem conversion to the triplet manifold. The study of these potentially competing pathways is deferred to future work in our group.

Benzimidazoles can be selected as promising candidates for the photochemical reduction of CO₂ because they use renewable energy, they are built from available elements and represent biomimetic analogues of NADP. As the analysis of the electronic-structure calculations shows, the 1d⋯CO₂ complex absorbs at 326 nm which falls into the UV-A radiation wavelength region (315–400 nm), i.e. the ultraviolet radiation that makes it through the atmosphere onto the Earth's surface. Therefore, this benzimidazoline derivative is a promising homogeneous catalyst for the light-driven reduction of CO₂ into formate. Quantum chemical calculations of excited electronic states of CO₂ complexation with other benzimidazoline derivatives are currently in progress as well.

Author contributions

The manuscript was written through contributions of all authors.

Conflicts of interest

There are no conflicts of interest to declare.

Acknowledgements

B. O. and D. Đ. are thankful for the financial support received from the Ministry of Science, Technological Development and Innovation of the Republic of Serbia (contract no: 451-03-47/2023-01/200026). We are indebted to two anonymous reviewers for their valuable suggestions and helpful comments.

References

1. E. Sanz-Pérez, C. Murdock, S. Didas and C. Jones, Chem. Rev., 2016, 116, 11840–11876; W. Gao, S. Liang, R. Wang, Q. Jiang, Y. Zhang, Q. Zheng, B. Xie, C. Toe, X. Zhu, J. Wang, L. Huang, Y. Gao, Z. Wang, C. Jo, Q. Wang, L. Wang, Y. Liu, B. Louis, J. Scott, A. Roger, R. Amal, H. He and S. Park, Chem. Soc. Rev., 2020, 49, 8584–8686.
2. S. Park, D. Bézier and M. Brookhart, J. Am. Chem. Soc., 2012, 134, 11404–11407.
3. X. Lu, D. Y. C. Leung, H. Wang, M. K. H. Leung and J. Xuan, ChemElectroChem, 2014, 1, 836–849.
4. C. Lim, S. Ilic, A. Alherz, B. Worrell, S. Bacon, J. Hynes, K. Glusac and C. Musgrave, J. Am. Chem. Soc., 2018, 141, 272–280.
5. Z. Lu, H. Hausmann, S. Becker and H. A. Wegner, J. Am. Chem. Soc., 2015, 137, 5332–5335.
6. G. Ménard and D. Stephan, J. Am. Chem. Soc., 2010, 132, 1796–1797.
7. D. Mukherjee, H. Osseili, T. Spaniol and J. Okuda, J. Am. Chem. Soc., 2016, 138, 10790–10793.
8. J. Chen, L. Falivene, L. Caporaso, L. Cavallo and E. Chen, J. Am. Chem. Soc., 2016, 138, 5321–5333.
9. T. Matsuo and H. Kawaguchi, J. Am. Chem. Soc., 2006, 128, 12362–12363.
10. M. Courtemanche, M. Légaré, L. Maron and F. Fontaine, J. Am. Chem. Soc., 2013, 135, 9326–9329.
11. M. Courtemanche, M. Légaré, L. Maron and F. Fontaine, J. Am. Chem. Soc., 2014, 136, 10708–10717.
12. A. Berkefeld, W. Piers and M. Parvez, J. Am. Chem. Soc., 2010, 132, 10660–10661.
13. S. Chakraborty, J. Zhang, J. Krause and H. Guan, J. Am. Chem. Soc., 2010, 132, 8872–8873.
14. S. Bontemps, L. Vendier and S. Sabo-Etienne, J. Am. Chem. Soc., 2014, 136, 4419–4425.
15. P. Zimmerman, Z. Zhang and C. Musgrave, Inorg. Chem., 2010, 49, 8724–8728.
16. C. Lim, S. Ilic, A. Alherz, B. Worrell, S. Bacon, J. Hynes, K. Glusac and C. Musgrave, J. Am. Chem. Soc., 2018, 141, 272–280.
17. R. Weerasooriya, J. Gesiorski, A. Alherz, S. Ilic, G. Hargenrader, C. Musgrave and K. Glusac, J. Phys. Chem. Lett., 2021, 12, 2306–2311.
18. W. Xie, J. Xu, U. Md Idros, J. Katsuhira, M. Fuki, M. Hayashi, M. Yamanaka, Y. Kobori and R. Matsubara, Nat. Chem., 2023, 15, 794–802.
19. B. Narasimhan, D. Sharma and P. Kumar, Med. Chem. Res., 2010, 21, 269–283.
20. B. Ostojić, B. Stanković, D. Đorđević and P. Schwerdtfeger, Phys. Chem. Chem. Phys., 2022, 24, 20357–20370.
21. Y. Zhao and D. G. Truhlar, J. Phys. Chem. A, 2005, 109, 5656–5667.
22. S. Grimme, J. Comput. Chem., 2006, 27, 1787–1799.
23. S. Miertuš, E. Scrocco and J. Tomasi, Chem. Phys., 1981, 55, 117–129.
24. S. Miertuš and J. Tomasi, Chem. Phys., 1982, 65, 239–245.
25. J. L. Pascual-Ahuir, E. Silla and I. Tuñón, J. Comput. Chem., 1994, 15, 1127–1138.
26. M. Cossi, V. Barone, R. Cammi and J. Tomasi, Chem. Phys. Lett., 1996, 255, 327–335.
27. V. Barone, M. Cossi and J. Tomasi, J. Chem. Phys., 1997, 107, 3210–3221.
28. E. Cancès, B. Mennucci and J. Tomasi, J. Chem. Phys., 1997, 107, 3032–3041.
29. B. Mennucci and J. Tomasi, J. Chem. Phys., 1997, 106, 5151–5158.
30. B. Mennucci, E. Cancès and J. Tomasi, J. Phys. Chem. B, 1997, 101, 10506–10517.
31. V. Barone and M. Cossi, J. Phys. Chem. A, 1998, 102, 1995–2001.
32. M. Cossi, V. Barone, B. Mennucci and J. Tomasi, Chem. Phys. Lett., 1998, 286, 253–260.
33. V. Barone, M. Cossi and J. Tomasi, J. Comput. Chem., 1998, 19, 404–417.
34. M. Cossi, V. Barone and M. A. Robb, J. Chem. Phys., 1999, 111, 5295–5302.
35. J. Tomasi, B. Mennucci and E. Cancès, J. Mol. Struct., 1999, 464, 211–226.
36. R. Cammi, B. Mennucci and J. Tomasi, J. Phys. Chem. A, 2000, 104, 5631–5637.
37. M. Cossi and V. Barone, J. Chem. Phys., 2000, 112, 2427–2435.
38. M. Cossi and V. Barone, J. Chem. Phys., 2001, 115, 4708–4717.
39. M. Cossi, N. Rega, G. Scalmani and V. Barone, J. Chem. Phys., 2001, 114, 5691–5701.
40. M. Cossi, G. Scalmani, N. Rega and V. Barone, J. Chem. Phys., 2002, 117, 43–54.
41. M. Cossi, N. Rega, G. Scalmani and V. Barone, J. Comput. Chem., 2003, 24, 669–681.
42. F. Lipparini, G. Scalmani, B. Mennucci, E. Cances, M. Caricato and M. J. Frisch, J. Chem. Phys., 2010, 133, 014106.
43. A. V. Marenich, C. J. Cramer and D. G. Truhlar, J. Phys. Chem. B, 2009, 113, 6378–6396.
44. S. Ilic, J. L. Gesiorski, R. B. Weerasooriya and K. D. Glusac, Acc. Chem. Res., 2022, 55, 844–856.
45. Z. Lu, H. Hausmann, S. Becker and H. Wegner, J. Am. Chem. Soc., 2015, 137, 5332–5335.
46. J.-D. Chai and M. Head-Gordon, Phys. Chem. Chem. Phys., 2008, 10, 6615–6620.
47. M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, G. Scalmani, V. Barone, G. A. Petersson, H. Nakatsuji, X. Li, M. Caricato, A. V. Marenich, J. Bloino, B. G. Janesko, R. Gomperts, B. Mennucci, H. P. Hratchian, J. V. Ortiz, A. F. Izmaylov, J. L. Sonnenberg, D. Williams-Young, F. Ding, F. Lipparini, F. Egidi, J. Goings, B. Peng, A. Petrone, T. Henderson, D. Ranasinghe, V. G. Zakrzewski, J. Gao, N. Rega, G. Zheng, W. Liang, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, T. Vreven, K. Throssell, J. A. Montgomery, Jr., J. E. Peralta, F. Ogliaro, M. J. Bearpark, J. J. Heyd, E. N. Brothers, K. N. Kudin, V. N. Staroverov, T. A. Keith, R. Kobayashi, J. Normand, K. Raghavachari, A. P. Rendell, J. C. Burant, S. S. Iyengar, J. Tomasi, M. Cossi, J. M. Millam, M. Klene, C. Adamo, R. Cammi, J. W. Ochterski, R. L. Martin, K. Morokuma, O. Farkas, J. B. Foresman and D. J. Fox, Gaussian 16, Revision C.01, Gaussian, Inc., Wallingford CT, 2016.
48. H.-J. Werner and P. J. Knowles, J. Chem. Phys., 1985, 82, 5053–5063.
49. P. J. Knowles and H.-J. Werner, Chem. Phys. Lett., 1985, 115, 259–267.
50. P. Celani and H.-J. Werner, J. Chem. Phys., 2000, 112, 5546–5557.
51. H.-J. Werner, P. J. Knowles, G. Knizia, F. R. Manby, M. Schütz and others, MOLPRO, version 2015.1, A package of ab initio programs, see https://www.molpro.net.
52. F. Weigend and R. Ahlrichs, Phys. Chem. Chem. Phys., 2005, 7, 3297.
53. M. Caricato, B. Mennucci, J. Tomasi, F. Ingrosso, R. Cammi, S. Corni and G. Scalmani, J. Chem. Phys., 2006, 124, 124520.
54. C. Guido, D. Jacquemin, C. Adamo and B. Mennucci, J. Chem. Theory Comput., 2015, 11, 5782–5790.
55. R. Improta, Phys. Chem. Chem. Phys., 2008, 10, 2656–2664.
56. D. Jacquemin, B. Mennucci and C. Adamo, Phys. Chem. Chem. Phys., 2011, 13, 16987–16998.
57. B. Mennucci, C. Cappelli, C. A. Guido, R. Cammi and J. Tomasi, J. Phys. Chem. A, 2009, 113, 3009–3020.
58. A. Pedone, J. Chem. Theory Comput., 2013, 9, 4087–4096.
59. A. E. Reed, L. A. Curtiss and F. Weinhold, Chem. Rev., 1988, 88, 899–926.
60. NBO version 3.1 is incorporated within this version of the Gaussian suite: D. E. Glendening, A. E. Reed, J. E. Carpenter and F. Weinhold, NBO, Version 3.1.
61. S. Gronert and J. R. Keeffe, J. Am. Chem. Soc., 2005, 127, 2324–2333.
62. A. L. Sobolewski and W. Domcke, J. Phys. Chem. A, 2001, 105, 9275–9283.
63. A. L. Sobolewski, W. Domcke, C. Dedonder-Lardeux and C. Jouvet, Phys. Chem. Chem. Phys., 2002, 4, 1093–1100.
64. W. Domcke and A. l Sobolewski, Science, 2003, 302, 1693–1694.
65. Conical Intersections: Electronic Structure, Dynamics and Spectroscopy, ed. W. Domcke, D. R. Yarkony and H. Köppel, World Scientific, Singapore, 2004.
66. A. Álvarez, M. Borges, J. J. Corral-Pérez, J. G. Olcina, L. Hu, D. Cornu, R. Huang, D. Stoian and A. Urakawa, ChemPhysChem, 2017, 18, 3135–3141.
67. W. Sudholt, A. Staib, A. L. Sobolewski and W. Domcke, Phys. Chem. Chem. Phys., 2000, 2, 4341–4353.
68. O. W. Morawski, Ł. Kielesiński, D. T. Gryko and A. L. Sobolewski, Chem. – Eur. J., 2020, 26, 7281–7291.

---

Footnote

† Electronic supplementary information (ESI) available: Computational details of additional calculations of the 1d⋯CO₂ complex, molecular orbitals and IRC reaction coordinates. See DOI: https://doi.org/10.1039/d3cp05635j

---