Co–C Bond Dissociation Energies in Cobalamin Derivatives and Dispersion Effects: Anomaly or Just Challenging?

Cryogenic Ion Vibrational Predissociation (CIVP) Spectroscopy of Aryl Cobinamides in the Gas Phase: How Good Are the Calculations for Vitamin B12 Derivatives?

Aryl corrins represent a novel class of designed B12 derivatives with biological properties of "antivitamins B12". In our previous study, we experimentally determined bond strength in a series of aryl-corrins by the threshold collision-induced dissociation experiments (T-CID) and compared the measured bond dissociation energies (BDEs) with those calculated with density functional theory (DFT). We found that the BDEs are modulated by the side chains around the periphery of the corrin unit. Given that aryl cobinamides have many side chains that increase their conformational space and that the question of a specific structure, measured in the gas phase, was important for further evaluation of our T-CID experiment, we proceeded to analyze structural properties of aryl cobinamides using cryogenic ion vibrational predissociation (CIVP) spectroscopy, static DFT, and Born-Oppenheimer molecular dynamic (BOMD) simulations. We found that none of the examined DFT models could reproduce the CIVP spectra convincingly; both "static" DFT calculations and "dynamic" BOMD simulations provide a surprisingly poor representation of the vibrational spectra, specifically of the number, position, and intensity of bands assigned to hydrogen-bonded versus non-hydrogen-bonded NH and OH moieties. We conclude that, for a flexible molecule with ca. 150 atoms, more accurate approaches are needed before definitive conclusions about computed properties, specifically the structure of the ground-state conformer, may be made.

Insight into the Mechanism Underlying Dehalococcoides mccartyi Strain CBDB1-Mediated B12-Dependent Aromatic Reductive Dehalogenation

Anaerobic bacteria transform aromatic halides through reductive dehalogenation. This dehalorespiration is catalyzed by the supernucleophilic coenzyme vitamin B₁₂, cob(I)alamin, in reductive dehalogenases. So far, the underlying inner-sphere electron transfer (ET) mechanism has been discussed controversially. In the present study, all 36 chloro-, bromo-, and fluorobenzenes and full-size cobalamin are analyzed at the quantum chemical density functional theory level with respect to a wide range of theoretically possible inner-sphere ET mechanisms. The calculated reaction free energies within the framework of Co^I···X (X = F, Cl, and Br) attack rule out most of the inner-sphere pathways. The only route with feasible energetics is a proton-coupled two-ET mechanism that involves a B₁₂ side-chain tyrosine (modeled by phenol) as a proton donor. For 12 chlorobenzenes and 9 bromobenzenes with experimental data from Dehalococcoides mccartyi strain CBDB1, the newly proposed PC-TET mechanism successfully discriminates 16 of 17 active from 4 inactive substrates and correctly predicts the observed regiospecificity to 100%. Moreover, fluorobenzenes are predicted to be recalcitrant in agreement with experimental findings. Conceptually, based on the Bell-Evans-Polanyi principle, the computational approach provides novel mechanistic insights and may serve as a tool for predicting the energetic feasibility of reductive aromatic dehalogenation.

A local pair-natural orbital-based complete-active space perturbation theory using orthogonal localized virtual molecular orbitals

The multireference second-order perturbation theory (CASPT2) is known to deliver a quantitative description of various complex electronic states. Despite its near-size-consistent nature, the applicability of the CASPT2 method to large, real-life systems is mostly hindered by large computational and storage costs for the two-external tensors, such as two-electron integrals, amplitudes, and residuum. To this end, Menezes and co-workers developed a reduced-scaling CASPT2 scheme by incorporating the local pair-natural orbital (PNO) representation of the many-body wave functions using non-orthonormal projected atomic orbitals (PAOs) into the CASPT theory [F. Menezes et al., J. Chem. Phys. 145, 124115 (2016)]. Alternatively, in this paper, we develop a new PNO-based CASPT2 scheme using the orthonormal localized virtual molecular orbitals (LVMOs) and assess its performance and accuracy in comparison with the conventional PAO-based counterpart. Albeit the compactness, the LVMOs were considered to perform somewhat poorly compared to PAOs in the local correlation framework because they caused enormously large orbital domains. In this work, we show that the size of LVMO domains can be rendered comparable to or even smaller than that of PAOs by the use of the differential overlap integrals for domain construction. Optimality of the MOs from the CASSCF treatment is a key to reducing the LVMO domain size for the multireference case. Due to the augmented Hessian-based localization algorithm, an additional computational cost for obtaining the LVMOs is relatively minor. We demonstrate that the LVMO-based PNO-CASPT2 method is routinely applicable to large, real-life molecules such as Menshutkin SN2 reaction in a single-walled carbon nanotube reaction field.

BSE49, a diverse, high-quality benchmark dataset of separation energies of chemical bonds

We present an extensive and diverse dataset of bond separation energies associated with the homolytic cleavage of covalently bonded molecules (A-B) into their corresponding radical fragments (A. and B.). Our dataset contains two different classifications of model structures referred to as "Existing" (molecules with associated experimental data) and "Hypothetical" (molecules with no associated experimental data). In total, the dataset consists of 4502 datapoints (1969 datapoints from the Existing and 2533 datapoints from the Hypothetical classes). The dataset covers 49 unique X-Y type single bonds (except H-H, H-F, and H-Cl), where X and Y are H, B, C, N, O, F, Si, P, S, and Cl atoms. All the reference data was calculated at the (RO)CBS-QB3 level of theory. The reference bond separation energies are non-relativistic ground-state energy differences and contain no zero-point energy corrections. This new dataset of bond separation energies (BSE49) is presented as a high-quality reference dataset for assessing and developing computational chemistry methods.

Surprising Homolytic Gas Phase Co-C Bond Dissociation Energies of Organometallic Aryl-Cobinamides Reveal Notable Non-Bonded Intramolecular Interactions

Aryl-cobalamins are a new class of organometallic structural mimics of vitamin B12 designed as potential 'antivitamins B12 '. Here, the first cationic aryl-cobinamides are described, which were synthesized using the newly developed diaryl-iodonium method. The aryl-cobinamides were obtained as pairs of organometallic coordination isomers, the stereo-structure of which was unambiguously assigned based on homo- and heteronuclear NMR spectra. The availability of isomers with axial attachment of the aryl group, either at the 'beta' or at the 'alpha' face of the cobalt-center allowed for an unprecedented comparison of the organometallic reactivity of such pairs. The homolytic gas-phase bond dissociation energies (BDEs) of the coordination-isomeric phenyl- and 4-ethylphenyl-cobinamides were determined by ESI-MS threshold CID experiments, furnishing (Co-Csp 2 )-BDEs of 38.4 and 40.6 kcal mol-1 , respectively, for the two β-isomers, and the larger BDEs of 46.6 and 43.8 kcal mol-1 for the corresponding α-isomers. Surprisingly, the observed (Co-Csp 2 )-BDEs of the Coβ -aryl-cobinamides were smaller than the (Co-Csp 3 )-BDE of Coβ -methyl-cobinamide. DFT studies and the magnitudes of the experimental (Co-Csp 2 )-BDEs revealed relevant contributions of non-bonded interactions in aryl-cobinamides, notably steric strain between the aryl and the cobalt-corrin moieties and non-bonded interactions with and among the peripheral sidechains.

Theoretical study on conformational energies of transition metal complexes

Conformational energies are an important chemical property for which a performance assessment of theoretical methods is mandatory. Existing benchmark sets are often limited to biochemical or main group element containing molecules, while organometallic systems are generally less studied. A key problem herein is to routinely generate conformers for these molecules due to their complexity and manifold of possible coordination patterns. In this study we used our recently published CREST protocol [Pracht et al., Phys. Chem. Chem. Phys., 2020, 22, 7169-7192] to generate conformer ensembles for a variety of 40 challenging transition metal containing molecules, which were then used to form a comprehensive conformational energy benchmark set termed TMCONF40. Several low-cost semiempirical, density functional theory (DFT) and force-field methods were compared to high level DLPNO-CCSD(T1) and double-hybrid DFT reference values. Close attention was paid to the energetic ordering of the conformers in the statistical evaluation. With respect to the double-hybrid references, both tested low-cost composite DFT methods produce high Pearson correlation coefficients of rp,mean,B97-3c//B97-3c = 0.922 and rp,mean,PBEh-3c//B97-3c = 0.890, with mean absolute deviations close to or below 1 kcal mol-1. This good performance also holds for a comparison to DLPNO-CCSD(T1) reference energies for a smaller subset termed TMCONF5. Based on DFT geometries, the GFNn-xTB methods yield reasonable Pearson correlation coefficients of rp,mean,GFN1-xTB//B97-3c = 0.617 (MADmean = 2.15 kcal mol-1) and rp,mean,GFN2-xTB//B97-3c = 0.567 (MADmean = 2.68 kcal mol-1), outperforming the widely used PMx methods on the TMCONF40 test set. Employing the low-cost composite DFT method B97-3c on GFN2-xTB geometries yields an slightly improved correlation of rp,mean,B97-3c//GFN2-xTB = 0.632. Furthermore, for 68% of the investigated complexes at least one low-energy conformer was found that is more stable than the respective crystal structure conformation, which signals the importance of conformational studies. General recommendations for the application of the CREST protocol and DFT methods for transition metal conformational energies are given.

Dehalococcoides-Mediated B12-Dependent Reductive Dehalogenation of Aromatics Does Not Proceed through Outer-Sphere Electron Transfer

Several anaerobic bacteria can couple the reduction of aromatic halides to energy conservation. This organohalide respiration is catalyzed by enzymes containing cob(I)alamin, an activated supernucleophilic form of the coenzyme vitamin B₁₂. However, the mechanism underlying the electron transfer (inner-sphere vs outer-sphere ET) still remains elusive. To clarify this issue, we selected 36 fluoro-, chloro-, and bromobenzenes as representative substrates and calculated their free-energy barriers at the quantum chemical density functional theory level, considering a wide range of theoretically possible outer-sphere ET mechanisms. Across all 336 reaction routes addressed, 334 routes involve free-energy barriers larger than 20 kcal/mol. For two reaction routes with highly brominated benzenes, free-energy barriers below 20 kcal/mol imply abiotic reduction as observed in experiments. Thus, microbial B₁₂-dependent aromatic reductive dehalogenation does not proceed through an outer-sphere ET mechanism. Instead, the present study strongly suggests that microbe-catalyzed reductive dehalogenation of aromatic halides is governed by inner-sphere ET.

Evaluation of the Lewis acidity of metal complexes using ESI mass spectrometry

Metal complexes have extensive applications in catalysis, however, the efficient evaluation of Lewis acidity of metal complexes is still a challenge. Herein, we report a method by using electrospray ionization mass spectrometry (ESI-MS) to evaluate the Lewis acidity of metal complexes in the presence of a reference Lewis base, in which the value of the Lewis acidity can be quantized by the bond dissociation energy (BDE) of the resultant Lewis acid-base pairs. Using this method, the Lewis acidity of tetradentate Schiff-base metal complexes (designated as salenMX), a class of common metal complexes in the homogeneous catalysis, was studied in detail. For the salenM(III)X complexes (M = Al, Cr, Fe, Co), the Lewis acidity tendency is Al > Cr > Fe > Co due to a strong affinity between the Al complex and the reference Lewis base while a weak affinity concerning on the Co complex. Additionally, the effect of ligand steric and electronic nature on the Lewis acidity was studied by using Co complex. Furthermore, density functional theory (DFT) was employed to calculate the BDE, which consists with the results obtained from ESI-MS. The ESI-MS method provides a convenient and efficient method for evaluating the Lewis acidity of metal complexes.

Exploration of Chemical Compound, Conformer, and Reaction Space with Meta-Dynamics Simulations Based on Tight-Binding Quantum Chemical Calculations

The semiempirical tight-binding based quantum chemistry method GFN2-xTB is used in the framework of meta-dynamics (MTD) to globally explore chemical compound, conformer, and reaction space. The biasing potential given as a sum of Gaussian functions is expressed with the root-mean-square-deviation (RMSD) in Cartesian space as a metric for the collective variables. This choice makes the approach robust and generally applicable to three common problems (i.e., conformer search, chemical reaction space exploration in a virtual nanoreactor, and for guessing reaction paths). Because of the inherent locality of the atomic RMSD, functional group or fragment selective treatments are possible facilitating the investigation of catalytic processes where, for example, only the substrate is thermally activated. Due to the approximate character of the GFN2-xTB method, the resulting structure ensembles require further refinement with more sophisticated, for example, density functional or wave function theory methods. However, the approach is extremely efficient running routinely on common laptop computers in minutes to hours of computation time even for realistically sized molecules with a few hundred atoms. Furthermore, the underlying potential energy surface for molecules containing almost all elements ( Z = 1-86) is globally consistent including the covalent dissociation process and electronically complicated situations in, for example, transition metal systems. As examples, thermal decomposition, ethyne oligomerization, the oxidation of hydrocarbons (by oxygen and a P450 enzyme model), a Miller-Urey model system, a thermally forbidden dimerization, and a multistep intramolecular cyclization reaction are shown. For typical conformational search problems of organic drug molecules, the new MTD(RMSD) algorithm yields lower energy structures and more complete conformer ensembles at reduced computational effort compared with its already well performing predecessor.

Theoretical investigation of the mechanism for the reductive dehalogenation of methyl halides mediated by the CoI-based compounds cobalamin and cobaloxime

Theoretical calculations focusing on the cleavage of the C-X bond in methyl halides (CH₃X; X = Cl, Br, I) as mediated by Co^I-based systems have been carried out using the hybrid functional ωB97-XD together with the basis set 6-311++G(2d,2p). A total of seven Co^I-based compounds were evaluated: cob[I]alamin (Co^ICbl) in its base-on form and cobaloxime (Co^ICbx) with either no ligand or different ligands (either pyridine (PYR), tributylphosphine (TBP), dimethyl sulfide (DMS), cyclohexylisocyanide (CI), or 5,6-dimethylbenzimidazole (DMB)) at the lower axial position. For the large Co^ICbl system, an ONIOM scheme was employed, where the high layer was described at the DFT level and the low layer was computed using the semi-empirical method PM6. A full DFT model was employed for the Co^ICbx cases. An S_N2-like mechanism was evaluated in all cases. The intrinsic reaction coordinate profiles suggested early transition states with activation energies of ≈ 12 kcal/mol, ≈ 10 kcal/mol, and ≈ 5 kcal/mol for C-Cl, C-Br, and C-I cleavage, respectively, which is consistent with the leaving group abilities of these halides. The evolutions of the atomic charges in and the bond orders of Co-C and C-X were computed, and the results confirmed the existence of early transition states (δB_av≈ 40%), where the polarization C^δ+-X^δ- (%E_v ≈ 43%) is the determining factor in the reaction process. Finally, a comparison of all the determined parameters showed that the reaction in the DMB-Co^ICbx system resembles the process that occurs in the larger Co^ICbl, suggesting that the former system could be a reliable model for the study of reductive dehalogenation mediated by vitamin B₁₂, which is key to the anaerobic microbiological treatment of halocarbon contaminants.

Spin States and Other Ligand-Field States of Aqua Complexes Revisited with Multireference ab Initio Calculations Including Solvation Effects

High-level multireference (CASPT2, NEVPT2) calculations are reported for transition metal aqua complexes with electronic configurations from (3d)¹ to (3d)⁸. We focus on the experimentally evidenced excitation energies to their various ligand-field states, including different spin states. By employing models accounting for both explicit and implicit solvation, we find that solvation effect may contribute up to 0.5 eV to the excitation energies depending on the charge of ion and character of the electronic transition. We further demonstrate that with an adequate choice of the active space and the energetics extrapolated to the complete basis set limit, the presently computed excitation energies are in a good agreement with the experimental data. This allows us to conclusively resolve significant discrepancies reported in earlier theory works [e.g., J. Phys. Chem. C 2014 , 118 , 29196 - 29208 ]. For the benchmark set of 19 spin-forbidden and 24 spin-allowed transitions (for which experimental data are unambiguous), we find the mean absolute error of 0.15 or 0.13 eV and the maximum error of 0.56 or 0.42 eV for CASPT2 or NEVPT2 calculations, respectively. For the particularly challenging sextet-quartet gap for [Fe(H₂O)₆]³⁺, we support our interpretation by additional calculations with multireference configuration interaction (MRCI) and coupled cluster theory up to the CCSDT(Q) level. By underlining a rather subtle interplay between the solvation and correlation effects, the findings of this Article are relevant not only for modeling and interpretation of optical spectra of transition metal complexes but also in further benchmarking of theoretical methods for the challenging problem of spin-state energetics.

A new near-linear scaling, efficient and accurate, open-shell domain-based local pair natural orbital coupled cluster singles and doubles theory

The Coupled-Cluster expansion, truncated after single and double excitations (CCSD), provides accurate and reliable molecular electronic wave functions and energies for many molecular systems around their equilibrium geometries. However, the high computational cost, which is well-known to scale as O(N⁶) with system size N, has limited its practical application to small systems consisting of not more than approximately 20-30 atoms. To overcome these limitations, low-order scaling approximations to CCSD have been intensively investigated over the past few years. In our previous work, we have shown that by combining the pair natural orbital (PNO) approach and the concept of orbital domains it is possible to achieve fully linear scaling CC implementations (DLPNO-CCSD and DLPNO-CCSD(T)) that recover around 99.9% of the total correlation energy [C. Riplinger et al., J. Chem. Phys. 144, 024109 (2016)]. The production level implementations of the DLPNO-CCSD and DLPNO-CCSD(T) methods were shown to be applicable to realistic systems composed of a few hundred atoms in a routine, black-box fashion on relatively modest hardware. In 2011, a reduced-scaling CCSD approach for high-spin open-shell unrestricted Hartree-Fock reference wave functions was proposed (UHF-LPNO-CCSD) [A. Hansen et al., J. Chem. Phys. 135, 214102 (2011)]. After a few years of experience with this method, a few shortcomings of UHF-LPNO-CCSD were noticed that required a redesign of the method, which is the subject of this paper. To this end, we employ the high-spin open-shell variant of the N-electron valence perturbation theory formalism to define the initial guess wave function, and consequently also the open-shell PNOs. The new PNO ansatz properly converges to the closed-shell limit since all truncations and approximations have been made in strict analogy to the closed-shell case. Furthermore, given the fact that the formalism uses a single set of orbitals, only a single PNO integral transformation is necessary, which offers large computational savings. We show that, with the default PNO truncation parameters, approximately 99.9% of the total CCSD correlation energy is recovered for open-shell species, which is comparable to the performance of the method for closed-shells. UHF-DLPNO-CCSD shows a linear scaling behavior for closed-shell systems, while linear to quadratic scaling is obtained for open-shell systems. The largest systems we have considered contain more than 500 atoms and feature more than 10 000 basis functions with a triple-ζ quality basis set.

Calculation of Ligand Dissociation Energies in Large Transition-Metal Complexes

The accurate calculation of ligand dissociation (or equivalently, ligand binding) energies is crucial for computational coordination chemistry. Despite its importance, obtaining accurate ab initio reference data is difficult, and density-functional methods of uncertain reliability are chosen for feasibility reasons. Here, we consider advanced coupled-cluster and multiconfigurational approaches to reinvestigate our WCCR10 set of 10 gas-phase ligand dissociation energies [ J. Chem. Theory Comput. 2014, 10, 3092]. We assess the potential multiconfigurational character of all molecules involved in these reactions with a multireference diagnostic [ Mol. Phys. 2017, 115, 2110] in order to determine where single-reference coupled-cluster approaches can be applied. For some reactions of the WCCR10 set, large deviations of density-functional results including semiclassical dispersion corrections from experimental reference data had been observed. This puzzling observation deserves special attention here, and we tackle the issue (i) by comparing to ab initio data that comprise dispersion effects on a rigorous first-principles footing and (ii) by a comparison of density-functional approaches that model dispersion interactions in various ways. For two reactions, species exhibiting nonnegligible static electron correlation were identified. These two reactions represent hard problems for electronic structure methods and also for multireference perturbation theories. However, most of the ligand dissociation reactions in WCCR10 do not exhibit static electron correlation effects, and hence, we may choose standard single-reference coupled-cluster approaches to compare with density-functional methods. For WCCR10, the Minnesota M06-L functional yielded the smallest mean absolute deviation of 13.2 kJ mol^-1 out of all density functionals considered (PBE, BP86, BLYP, TPSS, M06-L, PBE0, B3LYP, TPSSh, and M06-2X) without additional dispersion corrections in comparison to the coupled-cluster results, and the PBE0-D3 functional produced the overall smallest mean absolute deviation of 4.3 kJ mol^-1. The agreement of density-functional results with coupled-cluster data increases significantly upon inclusion of any type of dispersion correction. It is important to emphasize that different density-functional schemes available for this purpose perform equally well. The coupled-cluster dissociation energies, however, deviate from experimental results on average by 30.3 kJ mol^-1. Possible reasons for these deviations are discussed.

Modeling the Reactions Catalyzed by Coenzyme B12 Dependent Enzymes: Accuracy and Cost-Quality Balance

The reactions catalyzed by coenzyme B₁₂ dependent enzymes are formally initiated by the homolytic cleavage of a carbon-cobalt bond and a subsequent or concerted H-atom-transfer reaction. A reasonable model chemistry for describing those reactions should, therefore, account for an accurate description of both reactions. The inherent limitation due to the necessary system size renders the coenzyme B₁₂ system a suitable candidate for DFT or hybrid QM/MM methods; however, the accurate description of both homolytic Co-C cleavage and H-atom-transfer reactions within this framework is challenging and can lead to controversial results with varying accuracy. We present an assessment study of 16 common density functionals applied to prototypical model systems for both reactions. H-abstraction reactions were modeled on the basis of four reference reactions designed to resemble a broad range of coenzyme B₁₂ reactions. The Co-C cleavage reaction is treated by an ONIOM(QM/MM) setup that is in excellent agreement with solution-phase experimental data and is as accurate as full DFT calculations on the complete model system. We find that the meta-GGAs TPSS-D3 and M06L-D3 and the meta-hybrid M06-D3 give the best overall performance with MUEs for both types of reactions below 10 kJ mol^-1. Our recommended model chemistry allows for a fast and accurate description of coenzyme B₁₂ chemistry that is readily applicable to study the reactions in an enzymatic framework.

Theoretical analysis of C-F bond cleavage mediated by cob[I]alamin-based structures

In the present work, C-F bond cleavage mediated by the super-reduced form of cobalamin (i.e., Co^ICbl) was theoretically studied at the ONIOM(BP86/6-311++G(d,p):PM6) + SMD level of theory. Dispersion effects were introduced by employing Grimme's empirical dispersion at the ONIOM(BP86-D/6-311++G(d,p):PM6) + SMD level. In the first stage of the study, cobalamin was characterized in terms of the coordination number of the central cobalt atom. The ONIOM(BP86/6-311++G(d,p):PM6) results showed that the base-off form of the system is slightly more stable than its base-on counterpart (ΔE = E _base-off - E _base-on ~ -2 kcal/mol). The inclusion of dispersive forces in the description of the system stabilizes the base-on form, which becomes as stable as its base-off counterpart. Moreover, in the latter case, the energy barrier separating both structures was found to be negligible, with a computed value of 1.02 kcal/mol. In the second stage of the work, the reaction Co^ICbl + CH₃F → MeCbl + F^- was studied considering the base-off and the base-on forms of Co^ICbl. The reaction that occurs in the presence of the base-on form of Co^ICbl was found to be kinetically more favorable (ΔE ^≠ = 13.7 kcal/mol) than that occurring in the presence of the base-off form (ΔE ^≠ = 41.2 kcal/mol). Further reaction-force analyses of the processes showed that the energy barrier to C-F bond cleavage arises largely due to structural rearrangements when the reaction occurs on the base-on form of the Co^ICbl complex, but is mainly due to electronic rearrangements when the reaction takes place on the base-off form of the complex. The latter behavior emerges from differences in the synchronicity of the bond strengthening/weakening processes along the reaction path; the base-on mode of Co^ICbl is able to decrease the synchronicity of the chemical events. This work gives new molecular-level insights into the role of Cbl-based systems in the cleavage of C-F bonds. These insights have potential implications for research into processes for degrading fluorine-containing pollutants.

Comprehensive theoretical study of all 1812 C60 isomers

All 1812 C₆₀ isomers are investigated with high-level quantum chemical methods to benchmark semiempirical approaches and find appropriate stability criteria.

Calibrating Reaction Enthalpies: Use of Density Functional Theory and the Correlation Consistent Composite Approach in the Design of Photochromic Materials

Acquisition of highly accurate energetic data for chromium-containing molecules and various chromium carbonyl complexes is a major step toward calibrating bond energies and thermal isomerization energies from mechanisms for Cr-centered photochromic materials being developed in our laboratories. The performance of six density functionals in conjunction with seven basis sets, utilizing Gaussian-type orbitals, has been evaluated for the calculation of gas-phase enthalpies of formation and enthalpies of reaction at 298.15 K on various chromium-containing systems. Nineteen molecules were examined: Cr(CO)₆, Cr(CO)₅, Cr(CO)₅(C₂H₄), Cr(CO)₅(C₂ClH₃), Cr(CO)₅(cis-(C₂Cl₂H₂)), Cr(CO)₅(gem-(C₂Cl₂H₂)), Cr(CO)₅(trans-(C₂Cl₂H₂)), Cr(CO)₅(C₂Cl₃H), Cr(CO)₅(C₂Cl₄), CrO₂, CrF₂, CrCl₂, CrCl₄, CrBr₂, CrBr₄, CrOCl₂, CrO₂Cl₂, CrOF₂, and CrO₂F₂. The performance of 69 density functionals in conjunction with a single basis set utilizing Slater-type orbitals (STO) and a zeroth-order relativistic approximation was also evaluated for the same test set. Values derived from density functional theory were compared to experimental values where available, or values derived from the correlation consistent composite approach (ccCA). When all reactions were considered, the functionals that exhibited the smallest mean absolute deviations (MADs, in kcal mol^-1) from ccCA-derived values were B97-1 (6.9), VS98 (9.0), and KCIS (9.4) in conjunction with quadruple-ζ STO basis sets and B97-1 (9.3) in conjunction with cc-pVTZ basis sets. When considering only the set of gas-phase reaction enthalpies (Δ_rH°_gas), the functional that exhibited the smallest MADs from ccCA-derived values were B97-1 in conjunction with cc-pVTZ basis sets (9.1) and PBEPBE in conjunction with polarized valence triple-ζ basis set/effective core potential combination for Cr and augmented and multiple polarized triple-ζ Pople style basis sets (9.5). Also of interest, certainly because of known cancellation of errors, PBEPBE with the least-computationally expensive basis set combination considered in the present study (valence double-ζ basis set/effective core potential combination for Cr and singly-polarized double-ζ Pople style basis sets) also provided reasonable accuracy (11.1). An increase in basis set size was found to have an improvement in accuracy for the best performing functional (B97-1).

Comprehensive Benchmark of Association (Free) Energies of Realistic Host-Guest Complexes

The S12L test set for supramolecular Gibbs free energies of association ΔGa (Grimme, S. Chem. Eur. J. 2012, 18, 9955-9964) is extended to 30 complexes (S30L), featuring more diverse interaction motifs, anions, and higher charges (-1 up to +4) as well as larger systems with up to 200 atoms. Various typical noncovalent interactions like hydrogen and halogen bonding, π-π stacking, nonpolar dispersion, and CH-π and cation-dipolar interactions are represented by "real" complexes. The experimental Gibbs free energies of association (ΔGa exp) cover a wide range from -0.7 to -24.7 kcal mol-1. In order to obtain a theoretical best estimate for ΔGa, we test various dispersion corrected density functionals in combination with quadruple-ζ basis sets for calculating the association energies in the gas phase. Further, modern semiempirical methods are employed to obtain the thermostatistical corrections from energy to Gibbs free energy, and the COSMO-RS model with several parametrizations as well as the SMD model are used to include solvation contributions. We investigate the effect of including counterions for the charged systems (S30L-CI), which is found to overall improve the results. Our best method combination consists of PW6B95-D3 (for neutral and charged systems) or ωB97X-D3 (for systems with counterions) energies, HF-3c thermostatistical corrections, and Gibbs free energies of solvation obtained with the COSMO-RS 2012 parameters for nonpolar solvents and 2013-fine for water. This combination gives a mean absolute deviation for ΔGa of only 2.4 kcal mol-1 (S30L) and 2.1 kcal mol-1 (S30L-CI), with a mean deviation of almost zero compared to experiment. Regarding the relative Gibbs free energies of association for the 13 pairs of complexes which share the same host, the correct trend in binding affinities could be reproduced except for two cases. The MAD compared to experiment amounts to 1.2 kcal mol-1, and the MD is almost zero. The best-estimate theoretical corrections are used to back-correct the experimental ΔGa values in order to get an empirical estimate for the "experimental", zero-point vibrational energy exclusive, gas phase binding energies. These are then utilized to benchmark the performance of various "lowcost" quantum chemical methods for noncovalent interactions in large systems. The performance of other common DFT methods as well as the use of semiempirical methods for structure optimizations is discussed.

Toward Quantitatively Accurate Calculation of the Redox-Associated Acid-Base and Ligand Binding Equilibria of Aquacobalamin

Redox processes in complex transition metal-containing species are often intimately associated with changes in ligand protonation states and metal coordination number. A major challenge is therefore to develop consistent computational approaches for computing pH-dependent redox and ligand dissociation properties of organometallic species. Reduction of the Co center in the vitamin B12 derivative aquacobalamin can be accompanied by ligand dissociation, protonation, or both, making these properties difficult to compute accurately. We examine this challenge here by using density functional theory and continuum solvation to compute Co-ligand binding equilibrium constants (Kon/off), pKas, and reduction potentials for models of aquacobalamin in aqueous solution. We consider two models for cobalamin ligand coordination: the first follows the hexa, penta, tetra coordination scheme for Co(III), Co(II), and Co(I) species, respectively, and the second model features saturation of each vacant axial coordination site on Co(II) and Co(I) species with a single, explicit water molecule to maintain six directly interacting ligands or water molecules in each oxidation state. Comparing these two coordination schemes in combination with five dispersion-corrected density functionals, we find that the accuracy of the computed properties is largely independent of the scheme used, but including only a continuum representation of the solvent yields marginally better results than saturating the first solvation shell around Co throughout. PBE performs best, displaying balanced accuracy and superior performance overall, with RMS errors of 80 mV for seven reduction potentials, 2.0 log units for five pKas and 2.3 log units for two log Kon/off values for the aquacobalamin system. Furthermore, we find that the BP86 functional commonly used in corrinoid studies suffers from erratic behavior and inaccurate descriptions of Co-axial ligand binding, leading to substantial errors in predicted pKas and Kon/off values. These findings demonstrate the effectiveness of the present approach for computing electrochemical and thermodynamic properties of a complex transition metal-containing cofactor.

Photolytic properties of cobalamins: a theoretical perspective

This Perspective Article highlights recent theoretical developments, and summarizes the current understanding of the photolytic properties of cobalamins from a computational point of view. The primary focus is on two alkyl cobalamins, methylcobalamin (MeCbl) and adenosylcobalamin (AdoCbl), as well as two non-alkyl cobalamins, cyanocobalamin (CNCbl) and hydroxocobalamin (HOCbl). Photolysis of alkyl cobalamins involves low-lying singlet excited states where photodissociation of the Co-C bond leads to formation of singlet-born alkyl/cob(ii)alamin radical pairs (RPs). Potential energy surfaces (PESs) associated with cobalamin low-lying excited states as functions of both axial bonds, provide the most reliable tool for initial analysis of their photochemical and photophysical properties. Due to the complexity, and size limitations associated with the cobalamins, the primary method for calculating ground state properties is density functional theory (DFT), while time-dependent DFT (TD-DFT) is used for electronically excited states. For alkyl cobalamins, energy pathways on the lowest singlet surface, connecting metal-to-ligand charge transfer (MLCT) and ligand field (LF) minima, can be associated with photo-homolysis of the Co-C bond observed experimentally. Additionally, energy pathways between minima and seams associated with crossing of S1/S0 surfaces, are the most efficient for internal conversion (IC) to the ground state. Depending on the specific cobalamin, such IC may involve simultaneous elongation of both axial bonds (CNCbl), or detachment of axial base followed by corrin ring distortion (MeCbl). The possibility of intersystem crossing, and the formation of triplet RPs is also discussed based on Landau-Zener theory.

Fluorophore Assisted Photolysis of Thiolato-Cob(III)alamins

Cobalamins are known to react with thiols to yield stable β-axial Co(III)-S bonded thiolato-cobalamin complexes. However, in stark contrast to the Co-C bond in alkylcobalamins, the photolability of the Co-S bond in thiolato-cobalamins remains undetermined. We have investigated the photolysis of N-acetylcysteinyl cob(III)alamin at several wavelengths within the ultraviolet and visible spectrum. To aid in photolysis, we show that attaching fluorophore "antennae" to the cobalamin scaffold can improve photolytic efficiency by up to an order of magnitude. Additionally, electron paramagnetic resonance confirms previous conjectures that the photolysis of thiolato-cobalamins at wavelengths as long as 546 nm produces thiyl radicals.