Theoretical Modeling of Low Energy Electronic Absorption Bands in Reduced Cobaloximes

Abstract

The reduced Co(I) states of cobaloximes are powerful nucleophiles that play an important role in the hydrogen-evolving catalytic activity of these species. In this work we have analyzed the low energy electronic absorption bands of two cobaloxime systems experimentally and using a variety of density functional theory and molecular orbital ab initio quantum chemical approaches. Overall we find a reasonable qualitative understanding of the electronic excitation spectra of these compounds but show that obtaining quantitative results remains a challenging task.

2 Introduction

Cobaloximes are pseudo-macrocyclic bis(dialkylglyoximato) cobalt complexes, first developed in the seventies as vitamin B₁₂ mimics. This family of complexes has become of renewed interest in the past few years, following reports in 2005 [1, 2] and 2007 [3, 4, 5] of their promising hydrogen-evolving catalytic capability. Today, cobaloximes, and the related diimine-dioxime cobalt complexes [6, 7, 8, 9], are recognized as some of the most efficient molecular catalysts for electro- and photo-catalytic hydrogen evolution [10, 11, 12]. These compounds are known to be powerful nucleophiles in their reduced Co(I) state. It is accepted that the catalytic cycle for hydrogen evolution proceeds via protonation of the Co(I) species, yielding a Co(III)–H hydridocobaloxime intermediate that, after further reduction to the Co(II)–H state, can evolve dihydrogen through either protonation of the hydride moiety or bimolecular reductive elimination [1, 2, 3, 4, 5, 10, 11, 6, 13, 14, 15, 16, 17, 18].

Recent reports from the groups of Muckerman [19], Hammes-Schiffer [20] and Jiang [21] have addressed aspects of the catalytic activity of these compounds using quantum chemical approaches and confirm the role of the Co(I) species. Experimentally, the spectroscopic signatures of Co(I) intermediates have been observed during the course of electro- and photo-catalytic experiments [4, 5, 22], and the Co(I) species [14, 23, 24, 9], and its protonated Co(III)-H form [25, 26, 27], have been isolated and characterized in a few, rare cases. In this context, we recently examined the sole hydridocobaloxime isolated to date, [HCo(dmgH)₂(PnBu₃)] [26], using a mixture of experiment and theory [25]. The current article follows up this latter study by focusing on a deeper understanding of the electronic state of the reduced Co(I) form of the cobaloxime catalysts. For this purpose we have chosen two previously characterized Co(I)-oxime complexes — [Na][Co(dmgH)₂(PnBu₃)] [25] and [Na][Co(dmgBF₂)₂(CH₃CN)] [14] — which we denote compounds 1 and 2, respectively (see Figure 1). We have employed both time-dependent density functional theory (TDDFT) and correlated molecular orbital methods to characterize the electronic excitation spectra of these compounds and show that a reasonable qualitative description of them can be obtained.

Figure 1.

Compounds 1 and 2 together with their truncated models. The du isomers of compound 2 are shown, with the left-hand BF₂ groups in their u positions and the right-hand groups in their d positions (note that d and u refer to orientations away from or toward the axial ligand, respectively).

3 Methods

3.1 Calculations

The ORCA [28] program (version 2.9) was employed for all DFT and TDDFT calculations. Geometry optimizations were performed at the DFT level using the BP86 [29, 30] and B3LYP [31, 32] functionals. Test calculations were also carried out with the addition of empirical van der Waals corrections [33] on compound 2 but the effects were found to be small and so will not be considered further here. To be precise, the relative ordering of the energies of the different isomers remained unchanged and the RMS heavy atom coordinate differences between equivalent optimized structures was, at most, 0.05 Å.

All geometry optimizations were done with the Ahlrichs TZVP basis sets (ORCA option ACC-OPT), which are of triple-ζ quality [34]. These were followed with single point energy and TDDFT calculations after optimization with a basis set of TZVP quality but augmented with extra polarization and diffuse functions (ORCA option DFT-ENERGY+). The combination of the BP86 functional, in particular, and a triple-ζ basis set has been shown to perform well for systems similar to the ones that we are studying, including the ground and excited states of cobalt corrinoids [35, 36].

In addition to DFT calculations, we also carried out single-point energy and spectra computations using higher-level ab initio multireference molecular orbital methods. All methods we tried were based on CASSCF wavefunctions, which in themselves are inadequate for describing dynamic correlation. However, these can be supplemented by the application of perturbative corrections or of multireference configuration interaction (MRCI). We did both by employing the CASPT2 [37] and NEVPT2 [38] perturbative methods, and the spectroscopy-oriented CI (SORCI) method developed by Neese et al. [39]. The CASSCF/NEVPT2 and SORCI calculations were performed using ORCA, whereas the CASSCF/CASPT2 computations were carried out with the MOLCAS [40, 41] program (version 7.4). All the calculations at this level were effected using the DFT optimized geometries obtained previously. For the results that we report in this paper, the basis sets that were employed were as follows: CASPT2 — both the ANO-L-VDZP and ANO-L-VTZP bases [42]; NEVPT2 — a composite basis consisting of an Ahlrich’s TZVP basis for the metal, the four equatorial coordinating nitrogens and, where applicable, the phosphorus, but with an Ahlrichs split valence with polarization (SVP) basis for all other atoms; SORCI — an SVP basis for all atoms. We would have preferred to use full TZVP bases for the NEVPT2 and SORCI calculations but were unable to obtain a complete set of converged results with this larger basis (see section 4.3 for a fuller discussion).

All calculations, both DFT and ab initio, were done in an implicit solvent model of acetonitrile, using the COSMO [43] and PCM [44, 45] methods implemented in ORCA and in MOLCAS, respectively.

3.2 Experiments

[Co(dmgBF₂)₂(CH₃CN)₂] was prepared according to the method of Bakac and Espenson [46]. [Na][Co(dmgBF₂)₂(CH₃CN)] was prepared by reaction of [Co(dmgBF₂)₂(CH₃CN)₂] with excess sodium mercury amalgam (0.5% Na) under vacuum in anhydrous acetonitrile, analogous to a literature preparation for the diphenyl-glyoximato analogue [47]. The solution of the partially reduced species was transferred over a frit to a fused 2-mm quartz cuvette; the reduction process was monitored via UV-vis absorption spectroscopy (Hewlett-Packard 8452 spectrophotometer) until the reduction was complete.

4 Results

4.1 Geometries

Summaries of pertinent bond distances and angles in the optimized DFT structures of compounds 1 and 2 are given in Table 1. Preliminary calculations (data not shown) indicated that both functionals strongly favored penta-coordination for the cobalt, leaving one axial position unoccupied, and that the singlet state of the compounds was the one that was energetically preferred. The B3LYP functional favored smaller, although still significant, energy gaps to the higher spin states (~ 50 kJ mol⁻¹) than BP86 (~ 125 kJ mol⁻¹).

Table 1.

A comparison of important bond lengths (Å) and bond angles (°) between the BP86 and B3LYP optimized geometries for compounds 1 and 2 in acetonitrile (MeCN).

Bond Length or Angle	BP86			B3LYP
Compound 1
Co–P	2.233			2.312
Co–N	1.871			1.886
	1.874			1.888
	1.879			1.896
	1.882			1.897
Compound 2	dd	du	uu	dd	du	uu
Co–N (MeCN)	1.924	1.928	1.931	2.082	2.003	2.005
N–C (MeCN)	1.164	1.163	1.162	1.148	1.149	1.148
Co–N	1.861	1.863	1.869	1.868	1.873	1.883
	1.862	1.864	1.869	1.872	1.874	1.884
	1.862	1.865	1.869	1.880	1.881	1.885
	1.862	1.866	1.869	1.883	1.883	1.889
Co–N–C (MeCN)	179.8	179.6	179.8	168.9	174.7	170.8

A feature of the coordination around cobalt in compound 2 is that each of its BF₂ groups can adopt two orientations relative to the plane containing the cobalt and its four coordinating equatorial nitrogens. We denote these possibilities as d or u if a BF₂ points away from or towards the coordinating axial acetonitrile, respectively. This gives three different isomers which are labelled as dd, du and uu in Table 1. We note that previous theoretical work on these compounds seem to have considered only the du isomer [19, 20]. With each functional, we find that the dd isomer is the most stable, followed by du and then uu. However, the energy differences are very small being only 1 kJ mol⁻¹ between the dd and uu isomers with B3LYP and 4 kJ mol⁻¹ with BP86.

Structurally the two functionals give similar complexes with the most significant differences occurring between the cobalt and the atoms to which it is bound. Overall it can be seen that BP86 favors shorter bond distances to cobalt than B3LYP, and that it favors a more nearly four-fold symmetrical coordination environment in compound 2 as the equatorial Co–N bond distances are almost equal and the Co–N–C (MeCN) bond angles are almost straight. We note that the compound 2 geometries are, to a very good approximation, of C_s symmetry, whereas those of compound 1 belong to the C₁ point group.

4.2 Experimental and DFT spectra

The experimental and calculated TDDFT UV spectra, both obtained in acetonitrile, are shown for compounds 1 and 2 in the top panels of Figure 2 and the values of the absorption bands in Table 2.

Figure 2.

Experimental and calculated spectra for compound 1 (left panels) and compound 2 (right panels). Calculations in the middle and bottom panels were done on the truncated models at their B3LYP optimized geometries. All simulated spectra were fitted using Gaussian line shapes with FWHM of 3000 cm⁻¹. The spectra of compound 2 were determined as a Boltzmann weighted average at 300 K of the spectra of its three isomers.

Table 2.

Experimental and calculated UV-VIS absorption bands for compounds 1 and 2 in acetonitrile. The oscillator strengths of calculated bands are given in brackets after the wavelengths. All BP86 calculations were done at the BP86-optimized geometries and all other calculations at the B3LYP-optimized geometries. Only the dominant bands with wavelengths between 400 and 750 nm and with oscillator strengths larger than 10⁻² are shown.

Method	Isomer	Band Wavelengths (nm) and Oscillator Strengths
Compound 1
Experiment		606
BP86		509 (0.09)
B3LYP		535 (0.08)	463 (0.05)	393 (0.15)
CAS(12,14)/CASPT2		511 (0.17)	383 (0.14)	338 (0.10)
CAS(14,11)/NEVPT2		595 (0.20)
CAS(8,7)/SORCI		567 (0.16)	470 (0.05)	432 (0.09)
Compound 2
Experiment		628	553
BP86	dd	547 (0.07)	448 (0.02)
	du	550 (0.05)	456 (0.01)
	uu	535 (0.03)	466 (0.02)
B3LYP	dd	638 (0.04)	492 (0.16)	414 (0.17)
	du	606 (0.03)	502 (0.07)	412 (0.17)
	uu	585 (0.01)	504 (0.09)	424 (0.27)
CAS(12,14)/CASPT2	dd	581 (0.35)	526 (0.18)
	du		524 (0.26)	433 (0.20)
	uu	533 (0.13)	531 (0.14)	451 (0.26)
CAS(14,11)/NEVPT2	dd	596 (0.11)	517 (0.16)	448 (0.22)
	du	551 (0.15)	440 (0.25)	424 (0.10)
CAS(10,7)/SORCI	du	610 (0.02)	558 (0.07)	504 (0.04)

Experimentally compound 1 has a single dominant absorption maximum at 606 nm within the 400–750 nm wavelength window. The absorption at shorter wavelengths is significant with a shoulder at ~520 nm and an increase in absorption towards 400 nm. By contrast, compound 2 has two dominant maxima, at 553 and 628 nm, with the former being slightly more intense, and the absorption decreases markedly at shorter wavelengths [14].

The calculated BP86 and B3LYP TDDFT spectra for compound 1 both show single dominant bands within the 400–750 nm wavelength range but they occur at wavelengths that are too short (by 97 and 71 nm, respectively) with respect to the experimental band. At shorter wavelengths, the B3LYP spectrum has significant absorption but that of the BP86 spectrum decays rapidly to zero, unlike experiment.

The calculated TDDFT spectra for compound 2 show more structure. The BP86 spectra for each isomer show two dominant bands, like experiment, but they are again shifted to shorter wavelengths (~ 80–100 nm), and the longer wavelength band is more intense. By contrast, the B3LYP spectra have three bands, at approximately 100 nm intervals, that increase in oscillator strength on going to shorter wavelengths. The two longest wavelength bands are also shifted to shorter wavelengths compared to experiment but less markedly so, by ~ 20–40 nm, than those of BP86. We note that the B3LYP spectrum of compound 2 is very similar to that obtained by Muckerman and Fujita for the du isomer [19].

4.3 Ab initio spectra

In principle, ab initio methods provide a systematically improvable route to the calculation of electronic properties. For transition metal compounds, a reasonable starting point for the calculation of electronic spectra is the use of a correlated CASSCF method [48]. The problem here is that the computational and memory requirements of these calculations for molecules as large as compounds 1 and 2 (~ 70 atoms), with reasonably sized active spaces, are extremely challenging, even with the most powerful desktop workstations. To overcome this in the present case, we employed truncated models for these compounds (see Figure 1), in which the methyl groups of the rings in both compounds have been replaced by hydrogens, and the n-butyl groups in compound 2 have been replaced by methyls.

Caution must be taken during the structural optimization of these truncated models, as we have found that full optimization can bring about considerable change in the metal coordination environment. This is especially so for compound 1 as truncation of the large n-butyl groups attached to the phosphine ligand has an important influence on the geometry about the cobalt atom. Therefore, as an alternative strategy, we took the geometry-optimized structures of the full compounds and only optimized the hydrogen atom positions. As an aside we note that we enforced C_s symmetry on the truncated compound 2 structures. For the BP86 and B3LYP uu optimized structures, this required adjustments of the heavy atom coordinates of less than 0.01 Å as the structures were already very nearly symmetric. For the dd and du B3LYP optimized structures, the adjustments were somewhat greater as the CCH₃ portion of the axial acetonitrile ligands did not lie in the symmetry plane and so needed to be rotated (by ~ 15 and 5°, respectively). Nevertheless, we note that the final optimized energy differences between the symmetrized and unsymmetrized pairs of structures were always within 1 kJ mol⁻¹, and that the symmetric forms were often the more stable.

TDDFT calculations of the spectra of these partially-optimized truncated models show that the effect on the excitation energies is quite small (see the top panels of Figure 2). In all cases, the bands in the truncated models are shifted to slightly shorter wavelengths with the maximum shifts being 6, 10, 11 and 15 nm for the compound 1 B3LYP and BP86, and compound 2 B3LYP and BP86 spectra, respectively. These differences are minor given the error inherent in the quantum chemical description, and the fact that it permits the application of higher level of theories. These observations are in agreement with the results of other workers who have employed similar strategies [35].

For our multireference calculations we employed the ORCA and MOLCAS programs, the former for its CASSCF/NEVPT2 and SORCI methods, and the latter for its CASSCF/CASPT2 approach. We found MOLCAS to be much more robust for CASSCF computations than ORCA. In particular, the CASSCF procedure always progressed smoothly with MOLCAS, whereas convergence was troublesome, and often impossible, with ORCA, especially with the larger active spaces. Calculations with both programs were computationally very demanding at these levels of theory, even for the truncated models, and so we have certainly not been able to achieve converged results, either in terms of basis set or the size of the active space. Nevertheless, the results we obtained are consistent with those of the TDDFT calculations and give qualitative insights into the nature of the low-energy electronic absorption bands for these compounds. Exploratory calculations with ORCA showed that the B3LYP optimized geometries consistently had the lowest energies with the ab initio methods (by ~ 50 kJ mol⁻¹) and so we consider only these in what follows.

The choice of active space is crucial when performing CASSCF calculations and involves both chemical intuition and much trial and error. Systematic routes to active space selection, such as identifying orbitals with partial occupancies from DFT and MP2 calculations, tend to give spaces that are too large for feasible calculation [48]. Overall, the calculations we consider most reliable were obtained using the CASSCF/CASPT2 method in MOLCAS with an active space consisting of 12 electrons in 14 active orbitals, which we denote CAS(12,14). This was designed to include the five cobalt 3d occupied orbitals and an extra d-shell to account for the 3d double-shell effect. The highest occupied and a correlating lowest unoccupied ligand molecular orbital per irreducible representation were also included, giving a total of 4 (as compound 2 has C_s symmetry and so two irreducible representations), to allow for possible LMCT and MLCT excitations. The 3d double-shell correlation effect occurs in firstrow transition metals with more than half filled 3d shells because these atoms have a relatively dense 3d shell due to a large number of electrons located in a contracted spatial distribution [49].

The CASSCF and CASPT2 calculations [37] were performed in vacuum and PCM implicit solvent with ANO-L-VDZP and ANO-L-VTZP basis sets [42]. The results were actually very similar for all four combinations of environment and basis set with differences of a maximum of 6 nm in the wavelengths of the dominant bands for the two calculations in solvent and a slightly larger 10 nm between those in solvent and in vacuum. The values that we show in Figure 2 and Tables 2 and 3 are those obtained with the ANO-L-VDZP basis in an acetonitrile implicit solvent. Compound 1 had C₁ symmetry and its lowest 15 roots were state-averaged with equal weights. Compound 2 had C_s symmetry and its basis was symmetry-adapted. State-averaged CASSCF calculations were performed including the lowest 5 and 10 roots with equal weights for the A′ and A″ irreducible representations. In the CASPT2 calculations, the external part of the zero order Hamiltonian was shifted by 0.3 atomic units to eliminate contributions from intruder states. All valence electrons were correlated, excluding the cobalt 3s electrons. For calculations performed in PCM solvent, reaction field effects were added in the one-electron Hamiltonian in the CASPT2 calculation. Non-equilibrium solvation effects were also included in the excited state CASSCF calculations. Finally, oscillator strengths were obtained by performing state interaction calculations from the CASSCF wavefunctions.

Table 3.

Analysis of the main absorption bands from the CASPT2 calculations. The first line of each band gives the natural orbital occupancies, whereas the subsequent lines detail the dominant configurations and their weights. d — spin down; f_o — oscillator strength; GS — ground state; L — ligand π orbital; λ — wavelength; u — spin up. The prime subscripts indicate the symmetries of the ligand orbitals for compound 2.

λ/nm	f o	Active Space Orbitals									Weight	Character
Compound 1
		L	L	3yz	3z2	3xz	3x2-y2	L	L	3xy
GS		2	2	2	2	2	2	0	0	0
511	0.17	2	2	2	1.5	1.5	2	0.5	0.5	0		MLCT
		2	2	2	2	u	2	d	0	0	0.10	3xz → L
		2	2	2	u	2	2	d	0	0	0.14	3z2 → L
		2	2	2	2	2	u	2	0	d	0.11	3xz → L
383	0.15	2	1.5	2	1	1.5	2	0.5	0.5	1		MIVT
		2	2	2	u	2	2	0	0	d	0.18	3z2 → 3xy
338	0.10	2	1	2	2	1.5	2	0	0.5	1
		2	u	2	2	d	2	u	d	0	0.13	Double excitation
		2	u	2	2	d	2	0	u	d	0.14	Double excitation
Compound 2
		L′	3z2	3x2-y2	3xy	L′	L″	3xz	L″	3yz
GS		2	2	2	2	0	2	2	0	0
du isomer
524	0.26	2	2	1	2	0	2	2	1	0		MLCT
		2	2	2	u	0	2	2	d	0	0.27	3xy → L″
		2	2	u	2	0	2	2	d	0	0.41	3x2-y2 → L″
433	0.20	2	1.5	2	2	0.5	2	1.5	0	0.5		MIVT/MLCT
		2	2	2	2	u	2	d	0	0	0.28	3xz → L′
		2	u	2	2	0	2	2	0	d	0.31	3z2 → 3yz
uu isomer
533	0.13	2	2	1.5	1.5	0	2	2	0.5	0.5		MIVT/MLCT
		2	2	2	u	0	2	2	0	d	0.34	3xy → 3yz
		2	2	u	2	0	2	2	d	0	0.21	3x2-y2 → L″
		2	u	2	2	0	2	2	d	0	0.11	3z2 → L″
531	0.14	2	2	1	2	0	2	2	1	0		MLCT
		2	2	2	2	u	2	d	0	0	0.15	3xz → L′
		2	2	2	u	0	2	2	0	d	0.12	3xy → 3yz
		2	2	u	2	0	2	2	d	0	0.54	3x2-y2 → L″
451	0.26	2	2	2	2	1	2	1	0	0		MLCT
		2	2	2	2	u	2	d	0	0	0.56	3xz → L′
		2	2	2	u	0	2	2	0	d	0.11	3xy → 3yz

The CASPT2 spectra are shown for compounds 1 and 2 in the middle panels of Figure 2 and the values of the absorption bands in Table 2. From the figures it appears that the CASPT2 spectra have the same qualitative features as the experimental data but that the peaks are shifted in a systematic manner. A linear-least squares fit between the experimental and calculated data, in energy space, gives a common adjustment parameter of −3350 cm⁻¹, which when applied to the raw CASPT2 spectra gives the shifted curves that are also shown in Figure 2 and are in much better quantitative agreement with experiment. This shift of the CASPT2 spectra in comparison to experiment is in line with the normal error bar for CASPT2 excitation energies (≈ 0.3 eV) [50].

The order of stability of the isomers of compound 2 at this level of theory, in contrast to the DFT results, is du < uu << dd. An analysis of the correlation energies shows that these are much more favorable for du and uu than dd. The exact values depend on the basis and the environment, but with the ANO-L-VTZP basis and in implicit solvent, the relative energies of the CASSCF ground states are 0, 6 and 13 kJ mol⁻¹ for the dd, du and uu isomers, respectively, but these change to 131, 0 and 2 kJ mol⁻¹ when the CASPT2 corrections are included. This implies that the dd isomer is unpopulated and so does not contribute to the spectra shown in Figure 2.

As mentioned above, we found the MOLCAS program to be more robust when performing the higher level calculations. Nevertheless, we were able to obtain some data using ORCA, two examples of which we show in the bottom panels of Figure 2 and in Table 2. The perturbative approach that ORCA implements is a strongly contracted version of NEVPT2, which has the advantage over CASPT2 of being free from intruder states [38]. We show results for NEVPT2 applied to the largest state-averaged CASSCF wavefunction that we were able to obtain with ORCA, namely 14 electrons in 11 active orbitals, consisting of 5 Co d orbitals and 6 predominantly ligand orbitals. In each case 10 roots were calculated with, for compound 2, 5 roots each of the A′ and A″ irreducible representations.

The CAS(14,11)/NEVPT2 spectrum for compound 1 is actually in very good quantitative agreement with experiment at longer wavelengths although in common with the B3LYP spectrum for the truncated model it lacks the absorptions at shorter wavelengths. By contrast, the CAS(14,11)/NEVPT2 spectrum for compound 2 resembles closely the CAS(12,14)/CASPT2 spectrum, with an equivalent shift with respect to experiment, but with an inversion in the oscillator strengths of the two strongest bands. For comparison, we note that a CAS(12,9) space gave spectra for the compound 2 isomers with the same dominant bands but at wavelengths shorter by between 7 and 13 nm. By contrast, the CAS(12,9)/NEVPT2 spectrum of compound 1 also had a single dominant band, like its CAS(14,11) counterpart, but shifted to a higher wavelength by 43 nm.

The second set of ab initio results that we obtained with ORCA are for SORCI calculations based upon CASSCF wavefunctions with CAS(8,7) and CAS(10,7) spaces for compounds 1 and 2, respectively. We present these for illustrative purposes only as we think that this is a very promising technique but do not feel that we were able to employ large enough active spaces, nor compute sufficient CI roots (due to the expense of the computations), to draw definitive conclusions.

4.4 Analysis of the absorption bands

Examination of the low-energy absorption bands of the calculated spectra show that they are dominated by MLCT but with some contributions from metal intravalence orbital transitions (MIVT). The presence of low-energy transitions involving ligand orbitals implies that the ligands are potentially redox active as we have observed in previous work [25]. In the remainder of this section, we treat the CAS(12,14)/CASPT2 spectra as reference and then contrast them with the spectra determined using the other approaches. An analysis of the configurations that contribute to the CASPT2 absorption bands is given in Table 3. Note that the 4d active space orbitals that were included to account for the double shell effect are omitted as they have zero occupancy for all the configurations that we discuss in this section. For illustration, we also show in Figure 3 the active space orbitals for the truncated model compounds that make the largest contributions to the low-energy transitions.

Figure 3.

Active space orbitals for the truncated models of compounds 1 (left column) and 2 (right column). Only those orbitals that make the largest contribution to the dominant absorption bands in the spectra are shown. The HOMO (bottom three) and LUMO (top two) notation refers to the occupancies of the orbitals in the nominal doubly-occupied ground state configuration. The orbitals were obtained from NEVPT2 calculations but they are typical of what are found with the other methods.

Analysis of the compound 1 calculations indicates that the ground state is essentially a single configuration with the active space orbital configurations shown in Table 3. The most intense absorption, at 511 nm, is of MLCT-type with major and minor contributions from (3xz) → L and (3z²) → L single excitations, respectively. The second most intense band, at 383 nm, is dominated by an internal single excitation between the cobalt’s (3z²) and (3xy) orbitals. Finally, the third band, at 338 nm, is primarily a mixture of double excitations between ligand and cobalt 3d orbitals.

The nature of the three main bands in the B3LYP spectrum for the full model of compound 1 (see Table 2) resembles very closely the CASPT2 results — namely two MLCT transitions with an intervening transition primarily of MIVT type. By contrast, in the remaining compound 1 spectra — BP86, NEVPT2 and SORCI — MIVT is much less significant and all bands are dominanted by transitions of type MLCT.

The CASPT2 wavefunction of compound 2 has a more complicated structure than that of compound 1. The active space in these calculations consists of 8 and 6 orbitals of symmetry character a′ and a″, respectively, of which only 5 a′ and 4 a″ orbitals are shown in Table 3 as the 4d orbitals have zero occupancy and are omitted. The ground states of the three isomers in both vacuum and implicit solvent, and for both basis sets, display a pronounced multiconfigurational character. They all have a main configuration with a weight of ~ 65% that is shown in Table 3, but there are also several di-radical contributions with weights of ≤ 15% in the total wavefunction.

In the CASPT2 spectra for all three isomers of compound 2, the two highest oscillator strength excitations were of type MLCT 3x²-y² (long wavelength) and MLCT 3xz (short wavelength) with minor contributions from MIVT 3z²/3xy → 3yz. This contrasts to the spectrum of compound 1 for which excitations of the latter two types were significant but MLCT 3x²-y² transitions were not observed.

Unlike compound 1, the absorption bands in the compound 2 spectra obtained with the other methods all share the same MLCT and MIVT features between equivalent orbitals, with the exception of the SORCI spectrum for which MLCT bands dominate. In the B3LYP compound 2 spectra, there are three principal peaks, which correspond to MLCT, MIVT and MLCT transitions, respectively. By contrast, in the BP86 spectra, there are two peaks with the longer wavelength corresponding to the MLCT 3x²-y² transition and the shorter wavelength peak being a mixture of MLCT 3xz and MIVT 3xy→ 3yz character. Likewise, in the NEVPT2 spectra, the shorter wavelength bands involve combinations of MLCT and MIVT transitions.

5 Conclusions

In this work we have investigated the low energy electronic absorptions of two cobaloxime systems that show promise as molecular bio-inspired catalysts for hydrogen evolution. Being able to reliably predict the electronic structure and transitions of these compounds, via calculation, is essential for elucidating their mechanisms of hydrogen evolution and for designing improved catalysts. We have studied the performance of both TDDFT and ab initio methods, using full structural models for the TDDFT calculations and truncated models for the more computationally intensive ab initio techniques. Overall, we find reasonable qualitative agreement between experiment and the spectra obtained using the different theoretical approaches, with the dominant contributions to the absorption bands coming from MLCT between the cobalt d-orbitals and the equatorial ligands, with transitions within the metal’s valence orbitals playing a less important role. A quantitative reproduction of the experimental spectra, however, remains a task for future work.