DFT Studies of Trans and Cis Influences in the Homolysis of the CoâC

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DFT Studies of Trans and Cis Influences in the Homolysis of the Co–C Bond in Models of the Alkylcobalamins Penny Govender, Isabelle Navizet, Christopher B Perry, and Helder M Marques J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/jp311788t • Publication Date (Web): 19 Mar 2013 Downloaded from http://pubs.acs.org on March 26, 2013

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The Journal of Physical Chemistry

jp-2012-11788t Revised manuscript

DFT Studies of Trans and Cis Influences in the Homolysis of the Co–C Bond in Models of the Alkylcobalamins Penny P. Govendera,b, Isabelle Navizeta, Christopher B. Perrya and Helder M. Marques*a a

Molecular Sciences Institute, School of Chemistry, University of Witwatersrand, PO Wits, Johannesburg, 2050 South Africa; bDepartment of Applied Chemistry,

University of Johannesburg, PO Box 17011, Doornfontein, Johannesburg, 2028 South Africa Abstract

Density Functional Theory (DFT) calculations (BP86/6-31+G(d,p)) and an analysis of the electron density using Bader's quantum theory of atoms in molecules (QTAIM), are used to explore factors that influence the bond dissociation energy (BDE) of the Co–C bond in models for the cofactor in the coenzyme B12-dependent enzymes. An increase in the basicity of L in [L–Co(III)(corrin)–CH3]n+, L = NH3, NH2– and NH2–, causes an elongation of the trans Co–C bond but this does not necessarily cause the BDE to decrease. The bond between the metal and the N-donor of L, Co–Nα, usually becomes shorter after Co–C homolysis as the resulting five-coordinate product permits the metal ion to move towards L. This contraction increases with the basicity of L and stabilizes the five-coordinate product. The BDE is found to correlate well with two variables, the basicity of L and the difference in the Co–Nα bond length between the five coordinate product and the six coordinate ground state. When L is a naturally-occurring amino acid or a model for its metal-coordinating side chain, the BDE is found to be moderately dependent on L and decrease with an increase in the softness of the donor atom of L. Sulfides produce a BDE < 30 kcal mol–1 whereas neutral alcohol donors produce a stronger Co–C bond with a BDE of 34–35 kcal mol-1. All other ligands are associated with a trans Co–C bond that is almost invariant in strength and with a BDE of 31– 33

kcal

mol-1.

Models

of

the

type

[H3N–Co(III)(N4)–CH3]n+

where

N4

=

bis(dimethylglyoxime), porphyrin, corrin and corrole show that the nature of the tetraaza

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equatorial ligand can change BDE values by over 8 kcal mol-1; the BDE when N4 = bis(dimethylglyoxime) is significantly larger than for the other three systems, amongst which differences in BDE are quite small (2.4 kcal mol-1). The differential stabilization of the 5coordinate product by the shrinking of Co–Nα bond (in corrin and in corrole) or its elongation (in porphyrin and in bis(dimethylglyoxime)) is an important factor in determining the BDE of these systems. Corrin has the longest and weakest Co–C bond; this, together with a significant contraction of the Co–Nα after homolysis, is likely to be the origin of its relatively low BDE.


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1.

Introduction Vitamin B12 and its derivatives are utilized in the adenosylcobalamin

(AdoCbl)-dependent mutases, eliminases and aminomutases; the methylcobalamin (CH3Cbl)-dependent methyltransferases; and the dehalogenases. AdoCbl and CH3Cbl feature a Co–C bond (to 5'-deoxyadenosyl and methyl, respectively). In the first enzyme family, the initial step in the enzyme-catalyzed reaction is homolysis of the Co–C bond, which we shall refer to as Co–Cβ, to the upper, or β ligand, while in the methyltransferases the bond ruptures heterolytically.1 The AdoCbl-dependent enzymes fall into three classes.2 The Class I enzymes (the mutases) catalyze carbon skeleton rearrangements in which the migrating group is a carbon fragment. The Class II enzymes include the eliminases which catalyze the migration and subsequent elimination of an hydroxyl or amino group, and ribonucleoside triphosphate reductase which catalyzes the reduction of ribonucleoside triphosphates. The Class III enzymes, the aminomutases, catalyze the migration of an amino group to an adjacent carbon. The Class I and Class III enzymes bind AdoCbl in a base-off form with the bottom, or α ligand position occupied by the imidazole of a His residue and the nucleotide loop buried in a hydrophobic pocket. This is the same mode of co-factor binding observed in the methyltransferase, methionine synthase.3

In the Class II enzymes AdoCbl is bound with the axial 5,6-

dimethylbenzimidazole (dmbzm) ligand coordinated to the metal. A notable feature of the biological chemistry of the AdoCbl-dependent enzymes is the tremendous rate enhancement of the homolysis of Co–Cβ imparted by the protein, which has been reported4-8 to be >1012. How this rate enhancement is effected is still the subject of considerable interest. We have recently reported the results of two investigations into the cis influence of the equatorial macrocycle in B12 chemistry. In the first,9 we used DFT and TD-DFT methods to probe how the electronic spectrum of complexes of the type [CN–Co(III)(corrin)–CN] are affected as the C10H of the corrin is replaced by a variety of electron-donating and electron-withdrawing substituents. In the second,10 DFT calculations on [NH3–Co(III)(corrin)–CH3]+, where the C10H of corrin was again replaced by electron-donating or electron-withdrawing groups, explored the dependence of the strength of the Co–Nα and the Co–Cβ bond on the electronic structure of the macrocycle.


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Reports of DFT as a tool to delineate the behavior of Co–Cβ in cobalamins first appeared at the beginning of the millennium, and have been reviewed by Jensen and Ryde in 2009.11 Early calculations generally involved the use of a simplified model system comprising a full corrin core with all side chains and methyl groups replaced by hydrogen atoms.

These calculations made use of the B3LYP12-15

functional which had previously been used to successfully model related systems.16-20 Andruniów et al.21,22 were able to reproduce the experimentally observed inverse trans influence for a series of α alkyl ligands (the concurrent elongation of the bond lengths to two mutually trans – axial, in this case – ligands in a metal complex). They were also able to reproduce the inverse relationship that exists between the length of Co–Cβ and the extent of folding of the corrin ring (the angle between the mean planes through N21, C4, C5, C6, N22, C9, C10 and through C10, C11, N23, C14, C15, C16, N24).23 Similar observations were reported by Jensen and co-workers,24 who also showed that the HOMO–LUMO gap in a model of methylcobalamin is significantly larger than in a model of AdoCbl, which offers a possible explanation why the former undergoes Co–C bond heterolysis whereas homolysis dominates in the case of the latter. The regular and inverse trans influence was further studied by Randaccio et al.25 who showed that cobalamins containing a β sulfur ligand exhibit a regular trans influence as opposed to the inverse trans influence observed when the β ligand is CF3, Me, and CMe3. A study by Dölker et al.26 demonstrated that the lower-axial dmbzm ligand has a very minor influence on the homolytic cleavage Co–Cβ, arguing against a mechanochemical triggering mechanism27-29 as a means of Co–Cβ bond activation. A subsequent study30 confirmed this result and showed the Co–Nα bond to be highly flexible as it is around 5 times weaker than the Co–Cβ bond. The implication of this is that the Co–Cβ bond has a strong trans influence on Co–Nα, whereas the α → β trans influence is much weaker. Jensen and Ryde30 studied the effect of the stronger imidazolate base on the properties of Co–Cβ and found that in contrast to imidazole and dmbzm, the Co–Cβ bond dissociation energy (BDE) decreases if Co–Nα is constrained by either elongation or compression. In either case, the reduction to the Co–Cβ BDE was shown to be small, amounting to about 4 kcal mol-1 at most. In a comprehensive study, Kozlowski and Zgierski31 studied the effect of the trans axial base and the


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nature of the β ligand on the Co–Cβ BDE. They showed that for a given base, a linear correlation exists between the length of Co–Cβ and its BDE. It was also shown that for a given α ligand the Co–Cβ BDE is very weakly dependent on the nature of the trans axial base, although a correlation was found between the Co–Cβ BDE and the basicity of the base in the case of isosteric para-substituted pyridines. Initial attempts at calculating the absolute Co–Cβ BDE values in model alkyl cobalamin complexes underestimated experimental values by between 9 and 14 kcal mol-1 for methylcobalamin, and by between 6 and 13 kcal mol-1 for adenosylcobalamin.26,32 A detailed investigation into this discrepancy33 revealed that the problem was not unique to methyl- and adenosylcobalamin, but was a general one for metal–carbon BDE’s calculated using the B3LYP functional in tetrapyrroles and related systems. The problem with the B3LYP functional was shown to be caused by a large bias of the exact Hartree-Fock exchange, and to a lesser extent the LYP correlation functional, towards the homolysis fragments, resulting in underestimated BDE’s.33,34

The BP86 functional35,36 was found to reproduce the experimentally

observed Co–Cβ BDE’s more accurately than B3LYP33,37 and almost all subsequent computational studies in the field have used this functional.9,10,37-53 It has recently been suggested54,55 that the main source of error when calculating Co–Cβ BDE’s is not the inclusion of Hartree-Fock exchange in hybrid functionals, but rather the inadequate treatment of dispersion effects by the majority of DFT functionals. More accurate results, for example, have been obtained with a modified version of B3LYP incorporating 15% Hartree-Fock exchange and an empirical dispersion correction to the BDE.55,56

Benchmark studies based on DFT and Completely Renormalized

Coupled-Cluster (CC-CR) calculations, however, reconfirm the original suggestion that the poor performance of hybrid functionals is due to incorporation of exact Hartree-Fock exchange.57

The authors show that underestimated Co–Cβ BDE’s,

obtained from calculations employing hybrid functionals are due to the overstabilization of the increasing diradical structures that emerge as Co–Cβ is elongated and subsequently broken, rather than the neglect of dispersion forces. If a hybrid functional is used, inclusion of dispersion was shown to be necessary for obtaining BDE’s in the experimental range if large basis sets are used, and Basis Set Superposition Error (BSSE) effects are considered. We report here the results of our investigation into some factors that might influence the stability of the Co–Cβ bond. We examine (i) the electronic and steric


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effects of the α ligand, L, on models of the form [L–Co(III)(N4)–CH3]n+ where L is a simple amine and N4 represents a model for the equatorial ligand corrin; (ii) the effect of changing L, including models of the side chains of a variety of amino acids; and (iii) the effect of changing the equatorial ligand N4 to bis(dimethylglyoxime), commonly called cobaloxime, porphyrin, corrin or corrole.

2.

Computational Methods DFT calculations were carried out using the BP8635,36 functional with a 6-

31+G(d,p) basis set applied to all atoms as implemented in the Gaussian 0958 suite of programs. Geometry optimizations were carried out in all relevant spin states (S = 0 and 2 for Co(III) and S = 1/2 and 3/2 for Co(II)) and characterized as true minima by calculating their normal vibrations within the harmonic approximation. In all the calculations of Co(III) complexes and of the post-homolysis Co(II) complexes we found that the low spin d6 and d7 structures, respectively, gave the lowest energy. We therefore only report results for the low spin structures here, but have carried out the calculations on all relevant spin states. All energies reported included a correction to the zero-point energy. On the recommendation of a referee, we also carried calculations on selected compounds taking dispersion effects into account.

As

dispersion is currently not integrally implemented in a Gaussian 09 calculation, we used the ORCA electronic structure package59 for this purpose.

DFT geometry

optimizations were performed with the BP86 functional,60,61 the TZVP basis set62 and corresponding auxiliary basis set, and the empirical van der Waals correction of Grimme et al.,63 and employed the RI-J approximation.64-70 Most of the frequency calculations in ORCA proved to be problematic and in only one case, for [NH2– Co(III)(corrin)–CH3], did the calculation converge. The value obtained for the zeropoint energy with ORCA (0.4238 kcal mol–1) was virtually identical to the value obtained with Gaussian 09 (0.4227 kcal mol–1); we therefore used the values for the ZPVE from calculations using the latter package. As pointed out by Kozlowski,57 the values of the ZPVE correction are relatively insensitive to the level of theory used in their calculation. Partial atomic charges were assessed from a Natural Population Analysis 71,72

(NPA)

while the topological properties of the electron density (ρ) was obtained

using Bader's quantum theory of atoms in molecules (QTAIM) approach as implemented in AIMALL.73


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Our interest was focused on factors that influence the bond dissociation energy (BDE) and the enthalpy (∆H) for the homolysis of the Co–Cβ bond (eqns. 1 – 3, where E refers to the electronic energy). n+

n+

 L – Co(III) ( N 4 ) − CH 3  →  L – Co(II) ( N 4 )  + CH 3• BDE = ( E ) − E n+ + E n+ CH •  L–Co(II)( N 4 )

∆H = ( H

L–Co(II)( N 4 ) 

n+

3

+ H CH• ) − H 3

 L–Co(III)( N 4 ) –CH3 

 L–Co(III)( N 4 ) –CH 3 

n+

(1) (2) (3)

For this, six-coordinate models of alkylcobalamins, [L–Co(III)(N4)–CH3]n+, were examined; N4 represents a corrin with all substituents replaced by H; CH3 was the "upper" or β axial ligand; and the "lower" or α ligand, L, was an amine, chosen to have a range of different electronic (as assessed from its gas phase basicity) and steric properties (as assessed from the Tolman cone angle). The gas phase basicity (GB) of a neutral molecule or anion is ∆G of the reactions in vacuo represented by eqns. 4 and 5, respectively.74,75 Y + H+ → HY+ –

(4)

+

X + H → HX

(5)

All GB values were calculated using BP86/6-31+G(d,p). The Tolman cone angle is the average of the sum of the semivertex angles76 for which we used an arbitrary Co–N bond length of 2.22 Å. The van der Waals radii used were from the Cambridge Crystallographic Data Centre (CCDC). The absolute hardness77,78 of the α ligand, η = [Ionization Potential – Electron Affinity]/2, was calculated using BP86/631+G(d,p). Models were also examined in which L was an amino acid or a model of the side chains of one of the naturally-occurring amino acids capable of coordinating metal ions.

Finally, models of the type [H3N–Co(III)(N4)–CH3]n+, where the

equatorial ligand, N4 = bis(dimethylglyoxime), or cobaloxime, porphyrin, corrin and corrole, were examined to assess the cis influence of the equatorial ligand.


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3.

Results and Discussion

3.1

The trans influence of amines: electronic effects

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Table 1 gives the dependence of the axial bond lengths, the BDE of Co–Cβ, the GB values, and ∆H for the homolysis of this bond in [L–Co(III)(corrin)–CH3]n+ as a function of the α ligand, while in Table 2 are listed the topological properties of the electron density, ρ, at the bond critical points (bcp's) of the axial bonds. The ligands NH3 and NH2–, and NH2F and NHF–, enable the effect of increasing basicity to be assessed whilst they remain sterically undemanding. We also did calculations with L = NH2– and NF2–. In these cases, the overall charge on the molecule is -1 and, as pointed out by a reviewer, this may be problematic because of self-interaction errors (SIEs) in the approximate DFT method used.79 This could be the reason why, for example, we were unable to obtain an energy-minimized structure with L = N3–. Since the results we are interested in (see below) are essentially derived from a comparison of the Co(II) homolysis product and the Co(III) reactant, and the charge on the two species is the same, it seems likely that this error cancels. We therefore continue our analysis including these ligands, but evaluate our conclusions if the ligands were to be omitted from our data set. As anticipated, the bond between the metal and the N donor of the α ligand, Co(III)–Nα, becomes shorter (Table 1) and stronger (ρ, a measure of the strength of a chemical bond,80-87 increases, Table 2) as the basicity of the L increases. The bond becomes more covalent since the ratio of the potential and kinetic energy densities, |V(r)|/G(r), which typically has a value of 2 for a covalent bond,88 increases; this is confirmed by the decrease in the difference in the NBO charge on the metal and the Nα donor, from 1.24 e when α = NH3 to 0.99 e when α = NH2–, and from 0.53 to 0.26 e when α = NH2F and NF2-, respectively (Table 1). The decrease in the Co–Nα bond length persists in the Co(II) homolysis produce (Table 1). A similar effect of the α ligand basicity on the Co–Nα bond length was noted by Kozlowski and Zgierski;31 in their study, a linear dependence of the bond length between the metal and the N-donor of 4-substituted pyridines and the pKa of the pyridine, both in model Co(III) and Co(II) corrin complexes, was found. In response to the change in the bond between the metal and L, the Co–Cβ bond becomes longer (Table 1), weaker (ρ decreases, Table 2), and less covalent (|V(r)|/G(r) decreases, Table 2; the difference in NBO charge between the metal and


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the Cβ carbon increases from 0.90 e when α = NH3 to 1.033 e when α = NH2–, and from 0.86 e to 1.02 e when α = NH2F and NF2–, respectively. We conclude that increasing the basicity of the L in the cobalt corrins results in a normal ground state trans influence with an elongation of the Co–Cβ bond. However, and importantly, this does not translate into a smaller BDE or a lower ∆H (Table 1). There is very little difference in the BDE when L = NH3 and NH2–, or between L = NH2F and NHF–; there is a very significant decrease in both parameters when very basic NH2– or NF2- is the α ligand, but, as pointed out by a reviewer, this could be a limitation of approximate DFT. The data reported by Kozlowski and Zgierski31 on complexes of the type [4-Xpy–Co(III)(corrin)–Rib]+ (Rib = ribosyl) show a similar trend. (The BDE values reported in that study are significantly smaller than those reported here because of the use of the B3LYP functional, as discussed in the Introduction, but it is the trend rather than the values themselves that are germane to this discussion.)

Although the

correlation is weak, the Co–Cβ BDE actually increases with an increase in the basicity of the α pyridine ligand (the effect is very small; the BDE changes by only 0.6 kcal mol–1 between when X = CN and X = NMe2) whilst there is no correlation between the Co–Cβ bond length to Rib and the Co–Nα bond length. We return to the observations in this and the previous study31 below.

3.2

The trans influence of amines: steric effects Substitution of H by CH3 in the α ligand (L = NH3, NH2CH3, NH(CH3)2,

N(CH3)3) causes an increase in the basicity of the ligand, but so does its steric demand (quantifiable by the Tolman cone angle, Table 1); the net effect is that the Co–Nα bond becomes longer (Table 1) and weaker (ρ decreases, Table 2). The charge on Co becomes more positive, but that on Nα becomes less negative (Table 1) so overall there is little change in the ionicity of the bond as assessed by |V(r)|/G(r), Table 2. There is very little change in the Co–Cβ bond length (Table 1) or in the strength of that bond (the ρ values do not change appreciably, Table 2). Yet there is a small, but monotonic decrease in the BDE and in ∆Hfor the homolysis reaction (Table 1). Kozlowski and Zgierski31 also noted a small but monotonic decrease in the BDE of the Co–Cβ bond (to Rib) as the bond length to the trans base increases (Figure 8 in Ref. 31). They comment specifically that this does not have to do with a change


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in the Co–Cβ bond length, but appear not to offer an explanation for the origin of this effect. Our results show that the Co–Nα bond tends to shrink after homolysis of the Co–Cβ bond (values of ∆5c-6c, the difference in Co–Nα bond length between the 5coordinate product and 6-coordinate reactant, are usually negative, Table 1). The absence of the β ligand allows the metal ion to move out of the equatorial plane towards the α ligand (the distance between the metal and the mean plane of the equatorial N donors, Co···Nplane, increases, and the extent of the increase correlates with the basicity of L, Table 1).

The Co–Nα bond becomes stronger (ρ values

increase, Table 2) and the bond become less ionic. There is therefore a differential stabilization of the Co–Nα ligand between the five-coordinate homolysis product and the six-coordinate ground state; the extent of the stabilization increases with the basicity of L. Since BDE and ∆H are a function of the relative stabilities of the five- and six-coordinate complexes (eq. 2 and 3), this suggests a correlation between these quantities and ∆5c-6c. In order to explore that correlation we obtained further data by examining the structure where L is deprotonated methylamine, viz., NHCH3–. (We were unable to obtain an energyminimized structure with L = NCH32–, possibly because of the SIEs referred to above.) The results are listed in Tables 1 and 2 as well. If dispersion effects are taken into account (Table S1 and Figure S1 of the Supplementary Information), the trends remain the same, although the numerical values are different. Thus, the BDE values increase by 8.6 ± 0.1 kcal–1, the Co–Cβ bond length increases by 0.012 ± 0.009 Å, while the Co–Nα bond lengths to Co(III) and Co(II) decreases by 0.03 ± 0.02 and 0.03 ± 0.03 Å, respectively. Therefore the conclusions we reach below are not affected by the exclusion of the dispersion energy since the conclusions rely upon trends rather than absolute numerical values. We noted in 3.1 above that ligand basicity influences BDE and ∆H. We therefore performed a multiple linear regression analysis of the dependence of the BDE on two variables, the GB value of the ligand, and the ∆5c-6c values for, firstly, all ten structures in Table 1, and then omitted the ligands NH2- and NF2- in case the suspected SIEs in these cases. We used the calculated GB values for this purpose because of the absence of experimental data for many of the ligands; we note, however, that the calculated values are in good agreement with the available experimental values. We found a reasonable correlation (r2 = 0.964, n = 10) of the


10

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form BDE = 39.1(9) – 0.026(2)GB + 23(3)∆5c-6c (see Figure S2 and Table S2 of the Supplementary Information) such that the BDE can be predicted (p < 0.05) from a linear combination of the two variables GB (p = 1.6 × 10-5) and ∆5c-6c (p = 1.7 × 10-4). If we omit the data for NH2- and NF2- the correlation is poorer (r2 = 0.804, n = 8), BDE = 34.7(9) – 0.010(3)GB + 8(3)∆5c-6c, p(GB) = 0.029, p(∆5c-6c) = 0.049) but the conclusion still holds. If we limit our data set to neutral ligands only, the correlation persists (see Supplementary Information, Table S4). Applying a similar regression analysis to the data of Kozlowski and Zgierski31 for the BDE in complexes of the type [L–Co(III)(corrin)–Rib]+ (L = an imidazole or a pyridine derivative, Table 3 of Ref. 31) also gave a good correlation (r2 = 0.974, n = 7) of the form BDE = 26.3(3) – 1.49(4)pKa + 19(2)∆5c-6c (Figure S2 of the Supplementary Information; Table S5); the BDE can be predicted (p < 0.05) from a linear combination of the variables pKa (p = 0.013) and ∆5c-6c (p = 5.6 × 10-4). As for the results reported here, the BDE decreases as the basicity of the α ligand increases and as ∆5c-6c becomes more negative. What has been demonstrated, both for our data and that of Kozlowski and Zgierski,31 is that the stability of the post-homolysis product is an important factor in determining the BDE of the Co–Cβ bond. Whether this is relevant for the coenzyme B12-dependent enzymes is unclear.

Based on MCD observations and DFT

calculations on cob(II)alamin in the active site of methylmalonyl-CoA mutase (MMCM), especially in the presence of the substrate or a substrate analog, Brunold and co-workers89 showed that there is stabilization of the Co 3d orbitals relative to the corrin π/π*-based molecular orbitals.

By contrast,90 there is no enzymatic

perturbation of the electronic structure of cob(III)alamin when AdoCbl is bound to the MMCM active site. They therefore argue that a major contributor to Co–Cβ bond activation in MMCM occurs by stabilization of the post-homolysis product. On the other hand, Morokuma’s ONIOM(DFT/MM) calculations91 on MMCM suggest that a significant source of the decrease in the BDE of AdoCbl in the enzyme compared to the gas phase is related to distortions of the 5′-deoxyadenosyl ligand induced by the protein matrix. Car-Parrinello molecular dynamics simulations reported recently92 suggest it is the favorable interaction of the Ado• radical with protein residues which guide its diffusion to the substrate, that is at the heart of catalysis by MMCM. But these workers observed that as Ado• diffuses away from the metal, Co(II) moves


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towards His-610 to optimize its interaction with the proximal ligand, i.e., as we find in this work, the Co–Nα bond length decreases in going from the 6-coordinate ground state to the 5-coordinate product state. They suggest that this may serve an important function by depressing the recrossing rate. It would have been interesting to see the effect of freezing the Co–Nα bond length in these calculations.

3.3

The trans influence: models of amino acid side chains As mentioned in the Introduction, all the AdoCbl-dependent enzymes, as far as

is known, either have the imidazole side-chain of a His residue or the dmbzm base of B12 coordinated to the metal ion. It is interesting to speculate why nature should have chosen these as the axial ligands for Co(III). Several other amino acids have sidechains that could provide the α ligand of the metal,93 including Lys (for example, to Co(II) in the glycine amidoribonucleotide transformylase from A. Aeolicus94), Asp (to Co(II)

in

human

methionine

aminopeptidase95),

Glu

(to

Co(II)

in

metallocarboxypeptidase-1 from T. cruzi96), Tyr (to Co(II) in human methionine aminopeptidase97), Ser (to Co(II) in the GTPase Rab598), Cys (to Co(III) in Cocontaining nitrile hydratase99) and Met (to Co(II) of the iron-dependent regulator from M. tuberculosis100). We therefore performed calculations on the structures of the type [L– Co(III)(corrin)–CH3]n+, as well as the post-homolysis product [L–Co(II)(corrin)]n+, where L was a complete amino acid or a realistic model for the side chain of an amino acid. Amino acids in proteins, of course, are part of a protein chain whereas in this work, where complete amino acids are used, we modeled them as zwitter ions with deprotonated carboxylate and a protonated amino group. We used L = His and imidazole (as a model for His in a protein); Gly and CH3NH2 (for Gly and Lys); Ser, CH3OH and (CH3)2CHOH (for Ser and Thr); (CH3)2S (for Met); Cys (with a deprotonated thiol), CH3SH and CH3S– (for Cys); the phenolate anion and Tyr itself (for Tyr); and CH3CO2– (for Glu and Asp). Table 3 gives the dependence of the axial bond lengths, the Co–Cβ BDE and ∆H for the homolysis of this bond; the topological properties of the electron density at the bcp's of the axial bonds are listed in Table 4. The BDE and ∆H values closely parallel each other (r2 = 0.998); for convenience we therefore focus on the BDE values. The values we obtained vary by a modest 5.6 kcal mol-1 across the series of ligands studied and appear to decrease as the softness of the donor atom of the α


12

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ligand, Lα, increases. To place this on a more quantitative footing, the absolute hardness77,78 η was calculated for the small models of the amino acid side-chains (CH3COO–, CH3NH2, imidazole, CH3SH, CH3S–, CH3SCH3, (CH3)2CHOH, CH3OH, Table 5). There is a reasonable correlation between the η value of L and the Co–Cβ BDE (Figure 1A). As shown in Figure 1B, there is a weak correlation between the electron density at the Co–Cβ bcp and the BDE, with the ligands falling into three groups: anionic sulfides weaken the Co–Cβ which results in a BDE < 30 kcal mol–1; neutral alcohols produce a much stronger Co–Cβ bond and the BDE is 34–35 kcal mol-1; all other ligands, (aliphatic and aromatic N donors, ligands with phenolate or carboxylate, neutral thiols and thioethers) are associated with a trans Co–Cβ bond that is almost invariant in strength (0.112 < ρ < 0.116) and BDE (between 31 and 33 kcal mol-1). An increase in the electron density at the bcp of the bond between Co(III) and the donor atom of the base in the α coordination site, Lα, causes a decrease in the electron density at the bcp of the trans Co–Cβ bond, i.e., a normal trans influence occurs (Figure 1C). The correlation is not straightforward as the ligands fall into two distinct classes: those with neutral O (CH3OH; (CH3)2CHOH; Ser), neutral S (CH3SH; CH3SCH3), and anionic S (CH3S–; Cys) donors, and then those with aliphatic N (Gly, CH3N), aromatic N (His, imidazole) or anionic O donors (Tyr; PhO–, acetate). In conclusion, we observe that the BDE of Co–Cβ is only moderately dependent on the identity of the trans ligand and decreases as the softness of its donor atom increases. It is therefore interesting to speculate that nature has chosen an α ligand (His or Im in dmbzm) in the AdoCbl-dependent isomerases which is of intermediate hardness. Use of an amino acid such as Ser or Thr would lead to a more stable Co–Cβ bond, whereas a soft amino acid (Cys) would lead to a Co–Cβ bond which might be too unstable to survive; but a wide range of other amino acids (Asp, Glu, Met, Lys, Tyr) might have been chosen (insofar as their donor properties in this system are concerned) without unduly influencing the stability of the Co–Cβ bond.


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Figure 1. (A) Dependence of the Co–Cβ bond dissociation energy on the absolute hardness of the trans ligand L in [L–Co(III)(corrin)–CH3]n+. (B) Correlation between the electron density at the Co–Cβ bond critical point and the BDE for homolysis of this bond. (C) The value of ρCo–C correlates inversely with the electron density at the bcp of the Co–Lα bond. The ligands appear to fall into two classes: those with a neutral O, neutral S or anionic S donors (), and those with aliphatic N, imidazole N or anionic O donors ().


14

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3.4

The cis influence of the equatorial ligand To explore what effect the equatorial ligand has on the BDE and ∆H for the

homolysis reaction (eqn. 1–3), we examined models of the type [H3N–Co(III)(N4)– CH3]n+ where N4 = bis(dimethylglyoxime), porphyrin, corrin and corrole (Figure 2). The Co(III) complexes of bis(dimethylglyoxime) have been widely used as models for the corrins.101 Porphyrins have a larger macrocyclic cavity than corrins and the porphyrin macrocycle, in its complex with a metal, is a dianion. Metallated corroles have the same topology as corrins, but are fully aromatic and are trianions. Table 6 gives the dependence of the axial bond lengths, the Co–Cβ BDE and ∆H for the homolysis of this bond and the topological properties of the electron density at the bcp's of the axial bonds are listed in Table 7. We emphasize again that in all cases calculations were carried out on all relevant spin states and that low spin Co(III) and low spin Co(II) always gave the lowest energy

Figure 2. Equatorial ligands examined in this work. A: bis(dimethylglyoxime), or cobaloxime; B: porphyrin; C: corrin; D: corrole.

The Co–Cβ bond is longest (by more than 0.02 Å) and weakest when the equatorial ligand is bis(dimethylglyoxime) (ρ at its bcp has the smallest value of the four systems studied), yet the values of ∆H and BDE for its homolysis are the highest. The corrin system gave the lowest value for the BDE. We see again that the length and strength of the Co–Cβ bond in the ground state of these complexes is not in itself a measure of the BDE. The Co–Nα bond shrinks after homolysis of the Co–Cβ bond in the corrin and corrole systems (∆5c-6c is negative) but increases in the other two cases (∆5c-6c is positive), with the greatest increase occurring in cobaloxime. This suggests, as we saw in 3.1 and 3.2 above, that the stabilization of the 5-coordinate product is an


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Page 16 of 31

important factor in determining the BDE of these systems. The very significant increase in the Co–Nα bond length (from 2.076 to 2.091 Å) on homolysis of Co–Cβ in the cobaloxime system may be the principal reason why its BDE is significantly higher than in the others. Of the corrin, porphyrin and corrole systems, corrin has a Co–Cβ bond that is longest (1.982 Å, but 1.973 Å in porphyrin and 1.970 Å in corrole) and weakest (ρ = 0.1162 au, cf. 0.1181 and 0.1178 au).

This, together with a

contraction of the Co–Nα after homolysis of the Co–Cβ bond, may be the origin of its low BDE.

4.

Conclusions In complexes of the type [L–Co(III)(corrin)–CH3]n+, L = NH3, NH2– and NH2–,

increasing the basicity of L results in a normal ground state trans influence and an elongation of the Co–Cβ bond. However, this does not necessarily cause the BDE or ∆H for homolysis of the Co–Cβ bond to decrease. The Co–Nα bond tends to shrink after homolysis of the Co–Cβ bond since the absence of the β ligand allows the metal ion to move out of the mean plane of the four corrin N donors towards the α ligand, L. The Co–Nα bond becomes stronger and more covalent. The contraction of the Co–Nα bond, which increases with the basicity of L, stabilizes the five-coordinate homolysis product relative to the six-coordinate ground state. The BDE is found to correlate well with two variables, the basicity of L and ∆5c-6c, the difference in the Co–Nα bond length between the Co(II) five coordinate homolysis product and the Co(III) six coordinate ground state, whereas neither variable on its own provides a good correlation with the BDE. Calculations where L is a naturally-occurring amino acid or a model for the metal-coordinating side chain of such an amino acid, indicate that the BDE of Co–Cβ is moderately dependent on the identity of the trans ligand. The BDE values decrease as the softness of the donor atom of the α ligand, Lα, increases and a reasonable correlation between the absolute hardness, η, of L and BDE is observed. In particular, sulfides weaken the trans Co–Cβ bond and produce a BDE < 30 kcal mol–1 but neutral alcohol donors produce a significantly stronger Co–Cβ bond with a BDE of 34–35 kcal mol-1. All other ligands, (with aliphatic and aromatic N donors, with phenolate or carboxylate, or with neutral thiol or a thioether) are associated with a


16

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trans Co–Cβ bond that is almost invariant in strength and a BDE of between 31 and 33 kcal mol-1. Models

of

the

type

[H3N–Co(III)(N4)–CH3]n+

where

N4

=

bis(dimethylglyoxime), porphyrin, corrin and corrole show that the nature of the tetraaza equatorial ligand can change BDE values by over 8 kcal mol-1; specifically, BDE when N4 = bis(dimethylglyoxime) is significantly larger than for the other three systems, amongst which differences in BDE are small (2.4 kcal mol-1).

The

differential stabilization of the 5-coordinate product by the shrinking of Co–Nα bond (in corrin – significantly – and in corrole – marginally) or its elongation (marginally in porphyrin, significantly in bis(dimethylglyoxime)) is an important factor in determining the BDE of these systems. Of the corrin, porphyrin and corrole systems, corrin has the longest and weakest Co–Cβ bond; this, together with a significant contraction of the Co–Nα after homolysis, is likely to be the origin of its relatively low BDE.

Acknowledgements The financial assistance of the Department of Science and Technology, the National Research Foundation, Pretoria, through the South African Research Chairs Initiative (HMM, IN), the University of the Witwatersrand, Johannesburg (CBP, HMM, IN), and a Thuthuka grant from the National Research Foundation, Pretoria (PPG), is gratefully acknowledged. The Centre of High Performance Computing, Cape Town, is thanked for access to their clusters.

Supporting Information Supporting information with the results of the calculations including dispersion effect and comparison of these with calculation that exclude them, a graphical representation of the dependence of the BDE with GB and ∆5c-6c for different data sets is available. This information is available free of charge via the Internet at http://pubs.acs.org.


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Table 1. Dependence of Axial Bond Lengths, BDE and ∆H for Homolysis of the Co–Cβ bond in [L–Co(III)(corrin)–CH3]n+ and [L– Co(II)(corrin)]n+ Corrins on the α Ligand α ligand, L

Cone Anglea /deg

Expt GB / kcal mol-1

Calc GB / kcal mol-1

∆5c-6cf /Å

Bond Lengths/Å

NH3 NH2– NH2–

33.1 15.3 8.2

204

197 394 554

Co(III)– Cβ 1.982 2.044 2.066

NH2CH3 NH(CH3)2 N(CH3)3 NH2F NHF–

41.8 51.8 57.8 33.2 26.0

214 220 225

207 214 217 173 372

1.986 1.987 1.983 1.982 2.042

2.227 2.302 2.549 2.162 2.047

2.203 2.247 2.362 2.098 2.127

NF2– NHCH3–

12.7 30.1

540 391

2.058 2.046

1.969 2.076

1.783 2.174

Co(III)– N αd 2.220 2.062 2.002

Co(II)– Nαe 2.196 2.144 1.828

Co(III) ···Nplane /pm g

Co(II) Energies / ···Nplane kcal mol-1 /pm g BDE ∆H

-0.024 0.082 -0.174 -0.024 -0.055 -0.187 -0.064 0.080 -0.186 0.098

1 2 6 0 0 0 1 2 9 1

14 11 25 14 15 17 15 11 29 11

NBO Charge /e [L–Co(III)(corrin)– CH3]n+ Co Cβ Nα

32.85 34.10 0.189 -0.711 -1.048 32.29 33.54 0.140 -0.834 -1.113 20.47 21.63 0.131 -0.902 -0.860 32.48 33.75 0.215 -0.720 -0.821 31.88 33.14 0.258 -0.721 -0.631 31.15 32.26 0.326 -0.709 -0.483 32.61 33.86 0.154 -0.705 -0.377 31.59 32.93 0.118 -0.829 -0.414 20.59 21.86 0.109 -0.898 -0.152 31.10 32.43 0.177 -0.839 -0.838

[L– Co(II)(corrin)]n+ Co Nα 0.452 0.347 0.365 0.461 0.485 0.532 0.410 0.310 0.300 0.353

-1.062 -1.103 -0.672 -0.827 -0.626 -0.465 -0.402 -0.399 -0.037 -0.800

a

The average of the sum of the semivertex angles at an arbitrary Co–N bond length of 2.22 Å;76 van der Waals radii from the Cambridge Crystallographic Data Centre (CCDC), http://www.ccdc.cam.ac.uk/products/csd/radii/table.php4. bFrom Ref. 75. cSee Computational Methods in text. dThe axial bond length between Co(III) and Nα, the N donor of the α ligand, in the 6-coordinate complex. eThe axial bond length between Co(II) and Nα in the 5 coordinate complex. fThe difference in Co–Nα bond length between the 5-coordinate and 6-coordinate complex. gDistance of the metal ion from the mean plane through the four equatorial N donor atoms.

18 ACS Paragon Plus Environment

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Table 2. Topological Properties of the Electron Density at the BCP of Co(III)– CH3 and Co(III)–Nα Bonds in [L–Co(III)(corrin)–CH3]n+ and Co(III)–Nα Bonds in [L–Co(II)(corrin)]n+ Corrins as a Function of the α Liganda α ligand L

ρ

∇2 ρ

NH3 NH2– NH2– NH2CH3 NH(CH3)2 N(CH3)3 NH2F NHF– NF2– NHCH3–

0.1162 0.1025 0.0964 0.1153 0.1150 0.1153 0.1163 0.1030 0.0979 0.1021

0.0483 0.0948 0.1239 0.0493 0.0461 0.0390 0.0446 0.0895 0.1239 0.0913


0.0534 0.0857 0.0985 0.0541 0.0473 0.0297 0.0593 0.0889 0.1050 0.0833

0.1980 0.2365 0.2703 0.1881 0.1437 0.0751 0.2518 0.2732 0.3351 0.2267


0.0582 0.0736 0.1449 0.0590 0.0551 0.0445 0.0710 0.0763 0.1608 0.0696

0.2013 0.1609 0.4036 0.1904 0.1600 0.1123 0.2907 0.1855 0.5341 0.1454

V(r) G(r) Co(III)–Cβ -0.1296 0.0708 -0.1174 0.0705 -0.1137 0.0723 -0.1286 0.0705 -0.1281 0.0698 -0.1282 0.0690 -0.1293 0.0702 -0.1174 0.0699 -0.1156 0.0733 -0.1165 0.0697 Co(III)–Nα -0.0716 0.0606 -0.1069 0.0830 -0.1269 0.0973 -0.0709 0.0590 -0.0579 0.0469 -0.0294 0.0241 -0.0854 0.0742 -0.1162 0.0922 -0.1459 0.1148 -0.1033 0.0800 Co(II)–Nα -0.0775 0.0639 -0.0867 0.0634 -0.2121 0.1565 -0.0768 0.0622 -0.0682 0.0541 -0.0497 0.0389 -0.1040 0.0883 -0.0938 0.0701 -0.2602 0.1968 -0.0801 0.0582

H(r)

|V(r)|/G(r)

-0.0588 -0.0468 -0.0414 -0.0582 -0.0583 -0.0592 -0.0591 -0.0475 -0.0423 -0.0468

1.8295 1.6639 1.5718 1.8252 1.8348 1.8587 1.8412 1.6797 1.5775 1.6724

-0.0111 -0.0239 -0.0297 -0.0119 -0.0110 -0.0053 -0.0112 -0.0239 -0.0310 -0.0233

1.1827 1.2878 1.3051 1.2025 1.2345 1.2204 1.1513 1.2596 1.2704 1.2915

-0.0136 -0.0232 -0.0556 -0.0146 -0.0141 -0.0108 -0.0156 -0.0237 -0.0633 -0.0219

1.2127 1.3660 1.3553 1.2347 1.2609 1.2778 1.1771 1.3384 1.3217 1.3757

a

The values of charge density (ρ) and its Laplacian (∇2ρ) at the bcps are in au (1 au of ρ = 6.7483 eÅ-3, and 1 au of ∇2ρ = 24.099 eÅ-5). The values of the total potential energy density V(r), the kinetic energy density G(r) and the total energy density H(r) at the bcps are in au (1 au = 627.5095 kcal mol-1).


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Table 3. Dependence of Axial Bond Lengths, BDE and ∆H for Homolysis of the Co–Cβ bond in [L–Co(III)(corrin)–CH3]n+ and [L– Co(II)(corrin)]n+ on Various Trans Ligands used as Models for Side Chains of Amino Acids α ligand, L

Donor atom of L, Lα

Cone Anglea /deg

∆5c-6cb / Å

Bond Lengths/Å

Co(III)–Cβ

Co(III)– Lαc

Co(II)– Lαd

Co(III) ···Nplane /pm h

Co(II) ···Nplane /pm h

Energies / kcal mol-1 BDE

∆H

NBO Charge /e [L–Co(III)(corrin)–CH3]n+ Co

Cβ

[L–Co(II)(corrin)]n+

Lα

Co

Lα

(CH3)2CHOH

neutral O

32.9

1.97

2.408

2.297

-0.111

5

11

34.96

36.13

0.304

-0.690

-0.714

0.564

-0.713

Serine

neutral O

47.9

1.968

2.497

2.309

-0.188

6

10

34.91

35.97

0.307

-0.685

-0.712

0.56

-0.711

CH3OH

neutral O

29.9

1.969

2.369

2.268

-0.101

5

10

34.66

35.76

0.292

-0.690

-0.703

0.553

-0.703

Acetate

O, carbonate

15.2

1.991

2.097

2.107

0.010

1

12

32.95

34.00

0.233

-0.750

-0.632

0.471

-0.632

Tyrosine

O, phenolate

22.9

1.994

2.094

2.119

0.025

2

12

32.54

33.74

0.251

-0.756

-0.641

0.475

-0.637 -0.827

Methylamine

aliphatic N

41.8

1.986

2.227

2.203

-0.024

0

14

32.48

33.75

0.215

-0.720

-0.821

0.461

Imidazole

aromatic N

35.8

1.984

2.176

2.140

-0.036

0

15

32.45

33.73

0.193

-0.714

-0.426

0.448

SHCH3

S, thiol

33.6

1.979

2.721

2.511

-0.210

2

15

32.27

33.38

0.155

-0.691

0.116

0.335

0.174

Phenolate

O, phenolate

36.2

1.997

2.091

2.122

0.031

2

11

32.14

33.37

0.252

-0.762

-0.651

0.470

-0.646

-0.438

Glycine

aliphatic N

43.2

1.995

2.176

2.180

0.004

0

15

32.03

33.24

0.215

-0.754

-0.828

0.438

-0.835

Histidine

aromatic N

35.9

1.982

2.196

2.140

-0.056

0

15

31.89

33.13

0.201

-0.711

-0.422

0.449

-0.431

Dimethylsulfide

S, thioether

39.3

1.983

2.676

2.512

-0.164

1

15

31.52

32.65

0.144

-0.698

0.376

0.339

0.412

Cysteine

S, thiolate

35.9

2.010

2.509

2.509

0.000

0

13

30.02

31.21

0.072

-0.766

-0.253

0.29

-0.251

CH3S–

S, thiolate

19.8

2.025

2.457

2.496

0.039

1

12

29.39

30.66

0.035

-0.798

-0.172

0.247

-0.190

a

The average of the sum of the semivertex angles at an arbitrary Co–Nα bond length of 2.22 Å.76 bThe difference in Co–Nα bond length between the 5-coordinate and 6coordinate complex. cThe axial bond length between Co(III) and the donor atom Lα of the base acting as α ligand, in the 6-coordinate complex. dThe axial bond length between Co(II) and Lα in the 5 coordinate complex.


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Table 4. Topological Properties of the Electron Density at the BCP of Co(III)–CH3 and Co(III)–Lα bonds in [L–Co(III)(corrin)–CH3]n+ and Co(III)–Lα bonds in [L– Co(II)(corrin)]n+ Corrins as a Function of α Ligand Models for Side Chains of Amino Acids α ligand, L

ρ

∇2ρ

Acetate CH3OH Serine (CH3)2CHOH Tyrosine Phenolate Glycine Methylamine Imidazole Histidine Dimethylsulfide SHCH3 Cysteine CH3S–

0.1140 0.1183 0.1182 0.1181 0.1134 0.1125 0.1131 0.1153 0.1160 0.1163 0.1151 0.1159 0.1094 0.1061

0.0719 0.0371 0.0350 0.0358 0.0728 0.0751 0.0702 0.0493 0.0483 0.0474 0.0412 0.0387 0.0747 0.0843

Acetate CH3OH Serine (CH3)2CHOH Tyrosine Phenolate Glycine Methylamine Imidazole Histidine Dimethylsulfide SHCH3 Cysteine CH3S–

0.0613 0.0321 0.0255 0.0305 0.0615 0.0621 0.0620 0.0541 0.0575 0.0547 0.0353 0.0318 0.0510 0.0589

0.2677 0.1183 0.0848 0.1045 0.2660 0.2641 0.2115 0.1881 0.2267 0.2105 0.0783 0.0744 0.0784 0.0759

Acetate CH3OH Serine (CH3)2CHOH Tyrosine Phenolate Glycine Methylamine Imidazole Histidine Dimethylsulfide SHCH3

0.0630 0.0413 0.0387 0.0393 0.0614 0.0614 0.0640 0.0590 0.0644 0.0642 0.0506 0.0500

0.2415 0.1559 0.1356 0.1400 0.2223 0.2151 0.1906 0.1904 0.2395 0.2401 0.0957 0.0985

V(r) Co(III)–Cβ -0.1290 -0.1321 -0.1319 -0.1316 -0.1288 -0.1280 -0.1278 -0.1286 -0.1292 -0.1297 -0.1280 -0.1288 -0.1238 -0.1207 Co(III)–Lα -0.0849 -0.0414 -0.0296 -0.0377 -0.0851 -0.0852 -0.0808 -0.0709 -0.0794 -0.0746 -0.0369 -0.0324 -0.0539 -0.0619 Co(II)–Lα -0.0842 -0.0554 -0.0500 -0.0510 -0.0805 -0.0794 -0.0812 -0.0768 -0.0890 -0.0890 -0.0573 -0.0573

G(r)

H(r)

|V(r)|/G(r)

0.0737 0.0707 0.0703 0.0703 0.0735 0.0734 0.0727 0.0705 0.0707 0.0708 0.0691 0.0693 0.0712 0.0709

-0.0557 -0.0614 -0.0616 -0.0613 -0.0553 -0.0546 -0.0552 -0.0582 -0.0586 -0.0589 -0.0588 -0.0596 -0.0525 -0.0498

1.7559 1.8687 1.8756 1.8727 1.7523 1.7442 1.7587 1.8252 1.8292 1.8326 1.8510 1.8604 1.7379 1.7028

0.0759 0.0355 0.0254 0.0319 0.0758 0.0756 0.0669 0.0590 0.0680 0.0636 0.0283 0.0255 0.0367 0.0405

-0.0090 -0.0059 -0.0042 -0.0058 -0.0093 -0.0096 -0.0140 -0.0119 -0.0114 -0.0110 -0.0087 -0.0069 -0.0171 -0.0215

1.1185 1.1660 1.1656 1.1810 1.1226 1.1267 1.2092 1.2025 1.1670 1.1730 1.3072 1.2709 1.4662 1.5307

0.0723 0.0472 0.0420 0.0430 0.0680 0.0666 0.0644 0.0622 0.0745 0.0745 0.0406 0.0410

-0.0119 -0.0082 -0.0081 -0.0080 -0.0125 -0.0128 -0.0168 -0.0146 -0.0146 -0.0145 -0.0167 -0.0163

1.1648 1.1739 1.1923 1.1864 1.1831 1.1927 1.2601 1.2347 1.1957 1.1945 1.4109 1.3990


21


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Cysteine CH3S–

0.0527 0.0558

0.0710 0.0655

-0.0529 -0.0548

0.0353 0.0356

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-0.0176 -0.0192

1.4976 1.5395

Table 5. The Absolute Chemical Hardness of the Donor Atom Lα of Alpha Ligand, L α ligand, Lα

NH2CH3 CH3SCH3 Imidazole CH3COO– CH3SH CH3S– CH3OH Phenolate (CH3)2CHOH

Calculated Adiabatic IP values /eV a 8.83 8.57 8.77 10.39 9.34 1.91 10.47 0.68 9.59

IP/eV Experimental values 8.80102 8.69(2)102 8.78103

10.85(1)102 10.17(2)102

η calculated /eV b 5.01 4.77 4.80 5.58 4.91 3.38 5.86 4.48 5.29

a

Both the neutral and ionized ligand were geometry optimized and then the thermal corrected energy was used to calculate the IP value. bChemical hardness calculated as ((IP–EA)/2).104,105


22

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Table 6. Dependence of Axial Bond Lengths, BDE and ∆H for Homolysis of the Co–Cβ bond in [H3N–Co(III)(N4)–CH3]n+ and [NH3–Co(II)(N4)]n+ on the equatorial N4 ligand

∆5c-6cc / Å

N4 Bond Lengths/Å Co(III)– Co(III)– Co(II)– Cβ Nαa Nαb bis(dimethylglyoxime) porphyrin corrin corrole

2.002 1.973 1.982 1.970

2.076 2.167 2.220 2.197

2.091 2.173 2.196 2.192

0.015 0.006 -0.024 -0.005

Energies / kcal mol-1

NBO Charge /e [NH3–Co(III)(corrin)– [NH3– CH3]n+ Co(II)(corrin)]n+

BDE

∆H

Co

Cβ

Nα

Co

Nα

41.06 33.28 32.85 35.24

42.50 34.39 34.10 36.48

0.032 0.263 0.189 0.189

-0.744 -0.727 -0.711 -0.730

-1.010 -1.048 -1.048 -1.039

0.322 0.534 0.452 0.441

-1.045 -1.072 -1.062 -1.066

a

The axial bond length between Co(III) and Nα, the N donor of the α ligand, in the 6-coordinate complex. bThe axial bond length between Co(II) and Nα in the 5 coordinate complex.



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Table 7. Topological Properties of the Electron Density at the BCP of Co(III)–CH3 and Co(III)–Nα bonds in in [H3N–Co(III)(L4)–CH3]n+ and [L–Co(II)(L4)]n+ Complexes L4

ρ

∇2ρ

bis(dimethylglyoxime) porphyrin corrin corrole

0.1099 0.1181 0.1162 0.1178

0.0695 0.0586 0.0483 0.0831


0.0731 0.0592 0.0534 0.0544

0.3242 0.2396 0.1980 0.2227


0.0720 0.0604 0.0582 0.0571

0.2977 0.2218 0.2013 0.2116

V(r) G(r) Co(III)–Cβ -0.1236 0.0705 -0.1331 0.0739 -0.1296 0.0708 -0.1352 0.0780 Co(III)–Nα -0.1084 0.0947 -0.0830 0.0714 -0.0716 0.0606 -0.0761 0.0659 Co(II)–Nα -0.1046 0.0895 -0.0828 0.0691 -0.0775 0.0639 -0.0786 0.0657


H(r)

|V(r)|/G(r)

-0.0531 -0.0592 -0.0588 -0.0572

1.7535 1.8016 1.8305 1.7335

-0.0137 -0.0115 -0.0110 -0.0102

1.1443 1.1614 1.1815 1.1552

-0.0151 -0.0137 −0.0136 -0.0128

1.1686 1.1975 1.2127 1.1952

24

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Graphic for Abstract/Table of Contents 148x132mm (96 x 96 DPI)



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Figure 1. (A) Dependence of the Co–Cβ bond dissociation energy on the absolute hardness of the trans ligand L in [L–Co(III)(corrin)–CH3]n+. (B) Correlation between the electron density at the Co–Cβ bond critical point and the BDE for homolysis of this bond. (C) The value of ρCo–C correlates inversely with the electron density at the bcp of the Co–Lα bond. The ligands appear to fall into two classes: those with a neutral O, neutral S or anionic S donors (ν), and those with aliphatic N, imidazole N or anionic O donors (λ). 154x272mm (300 x 300 DPI)


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Figure 2. Equatorial ligands examined in this work. A: bis(dimethylglyoxime), or cobaloxime; B: porphyrin; C: corrin; D: corrole. 67x17mm (300 x 300 DPI)


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