Which DFT functional performs well in the calculation of methylcobalamin? Comparison of the B3LYP and BP86 functionals and evaluation of the impact of empirical dispersion correction

Controversy remains regarding the suitable density functionals for the calculation of vitamin B(12) systems that contain cobalt. To identify the optimum functionals, geometry optimization calculations were performed on a full-size model of methylcobalamin (MeCbl) using the B3LYP, B3LYP-D, BP86, and BP86-D methods in conjunction with the 6-31G* basis set. Single-point energy evaluations were also performed with the 6-311+G(2d,p) basis set. Consistent with previous studies, the BP86-optimized geometry showed fairly good agreement with the experimental geometry. Various factors that may influence the homolytic bond dissociation energy (BDE) of the Co-C bond of MeCbl were systematically evaluated with these methods. Our analysis demonstrated that dispersion was the largest correction term that influenced the magnitude of BDE. Previous studies have shown that B3LYP significantly underestimates BDE, whereas BP86 gives BDE values that are fairly close to the experimental values (36-37 kcal/mol). The same trend in the relative magnitudes of the BDEs was observed in the present calculations. However, BP86 underestimated the BDE for a full model of MeCbl. When the amount of Hartree-Fock exchange in the B3LYP functional was reduced to 15% and the dispersion correction was made (i.e., B3LYP*-D), the calculated BDE was in good accord with experimental values. B3P86-D also performed well. A detailed analysis was undertaken to determine which atoms in cobalamin have large dispersion interactions with a methyl fragment of MeCbl.     

Electronic structures of 4d transition metal monoxides by density functional theory

Bond distances, dissociation energies, ionization potentials and electron affinities of 4d transition metal monoxides from YO to CdO and their positive and negative ions were studied by use of density functional methods B3LYP, BLYP, B3PW91, BPW91, B3P86, BP86, SVWN, MPW1PW91 and PBE1PBE. It was found that calculated properties are highly dependent on the functionals employed, especially for dissociation energy. For most neutral species, pure density functionals BLYP, BPW91 and BP86 have good performance in predicting dissociation energy than hybrid density functionals B3LYP, B3PW91 and B3P86. In addition, BLYP gives the largest bond distance compared with other density functional methods, while SVWN gives shortest bond distance, largest dissociation energy and electron affinity. For the ground state, the spin multiplicity of the charged species can be obtained by ± 1 of their corresponding neutral species.     

Numerical examination of performance of some exchange-correlation functionals for molecules containing heavy elements

The performance of 17 exchange-correlation functionals for molecules containing heavy elements are numerically examined through four-component relativistic density DFT calculations. The examined functionals show the similar accuracy as they do for the molecules containing light elements only except for bond lengths. LDA and OP86 produce good results for bond lengths and frequencies but bad bond energies. Different functionals do not show much different performance for bond energies except LDA. BP86 and GP86 produce results with average accuracy while LYP does not perform well. Although encouraging results are obtained with functional B97GGA-1, other heavily parameterized and meta-GGA functionals do not produce impressive results.     

Remarkable aspects of unsaturation in trinuclear metal carbonyl clusters: the triiron species Fe3(CO)n (n = 12, 11, 10, 9)

The trinuclear iron carbonyls Fe(3)(CO)(n) (n = 12, 11, 10, 9) have been studied by density functional theory using the B3LYP and BP86 functionals. The experimentally known C(2)(v) isomer of Fe(3)(CO)(12), namely Fe(3)(CO)(10)(mu-CO)(2), is found to be the global minimum below the unbridged D(3)(h) isomer analogous to the known structures for Ru(3)(CO)(12) and Os(3)(CO)(12). The lowest-energy isomer found for Fe(3)(CO)(11) is Fe(3)(CO)(9)(mu(3)-CO)(2) with iron-iron distances in the Fe(3) triangle, suggesting the one double bond (2.460 A by B3LYP and 2.450 A by BP86) and two single bonds (2.623 A by B3LYP and 2.604 A by BP86) required to give each Fe atom the favored 18-electron configuration. Two different higher-energy dibridged structures Fe(3)(CO)(9)(mu(2)-CO)(2) are also found for Fe(3)(CO)(11). The lowest-energy isomer found for Fe(3)(CO)(10) is Fe(3)(CO)(9)(mu(3)-CO) with equivalent iron-iron distances in the Fe(3) ring (2.47 A by B3LYP or BP86). The lowest-energy isomer found for Fe(3)(CO)(9) is Fe(3)(CO)(6)(mu-CO)(3) with distances in the Fe(3) triangle possibly suggesting one single bond (2.618 A by B3LYP and 2.601 A by BP86), one weak double bond (2.491 A by B3LYP and 2.473 A by BP86), and one weak triple bond (2.368 A by B3LYP and 2.343 A by BP86). A higher-lying isomer of Fe(3)(CO)(9), i.e., Fe(3)(CO)(8)(mu-CO), at approximately 21 kcal/mol above the global minimum, has iron-iron distances strongly suggesting two single bonds (2.6 to 2.7 A) and one quadruple bond (2.068 A by B3LYP and 2.103 A by BP86). Wiberg Bond Indices are also helpful in evaluating the iron-iron bond orders.     

Binding of CO, NO, and O2 to heme by density functional and multireference ab initio calculations

Using the CASSCF/CASPT2 approach, along with several DFT methods (PBE0, B3LYP, BP86, OLYP), we have investigated the bonding of CO, NO, and O2 molecules to two model heme systems: an iron(II) porphyrin with and without an axial imidazole ligand. The experimentally available binding energies are best reproduced by the CASPT2 method and with the OLYP functional. The other functionals considered perform much worse, either severely overbinding (BP86) or underbinding (B3LYP, PBE0). Significant discrepancies between the different density functionals are observed, not only for the energetics but sometimes also for structure predictions. This confirms our viewpoint that a balanced treatment of the electronic exchange and correlation is vital to describe the weak metal-ligand bond between heme and CO, NO, or O2. The binding energies DeltaEb were split into two contributions: the so-called spin-pairing energy DeltaE sp and the "inherent" binding energy DeltaEb0, and both contributions were analyzed in terms of method and basis set effects. We have also investigated the spin density distributions resulting from the bonding of the NO molecule (a noninnocent ligand) to heme. Our analysis at the DFT and CASSCF level shows that, while various density functionals predict qualitatively very different spin distributions, the CASSCF spin populations most closely correspond to the results obtained with the pure BP86 or OLYP rather than with the hybrid functionals.     

Density functional study of AuXq (X = O, S, Se, Te, q = +1, 0, -1) molecules

Bond distances, vibrational frequencies, electron affinity, ionization potential, and dissociation energies of the title molecules were studied by use of density functional methods B3LYP, B3P86, B3PW91, BHLYP, BLYP, BP86, mPW1PW91, and PBE1PBE. It was found that the ground electronic state is doublet for neutral species, singlet for the anion, and triplet for the cation, in agreement with experiments and previous theoretical studies. The calculated properties are highly dependent on the functionals employed, in particular for the dissociation energy. The predicted bond distances and vibrational frequencies are in agreement with experiments and previous theoretical results. BP86 and BLYP have relatively good performance in reproducing the experimental results, while BHLYP is the worst functional method compared with the other density functional methods used for the title molecules.     

Performance of density functionals for first row transition metal systems

This article investigates the performance of five commonly used density functionals, B3LYP, BP86, PBE0, PBE, and BLYP, for studying diatomic molecules consisting of a first row transition metal bonded to H, F, Cl, Br, N, C, O, or S. Results have been compared with experiment wherever possible. Open-shell configurations are found more often in the order PBE0>B3LYP>PBE approximately BP86>BLYP. However, on average, 58 of 63 spins are correctly predicted by any functional, with only small differences. BP86 and PBE are slightly better for obtaining geometries, with errors of only 0.020 A. Hybrid functionals tend to overestimate bond lengths by a few picometers and underestimate bond strengths by favoring open shells. Nonhybrid functionals usually overestimate bond energies. All functionals exhibit similar errors in bond energies, between 42 and 53 kJmol. Late transition metals are found to be better modeled by hybrid functionals, whereas nonhybrid functionals tend to have less of a preference. There are systematic errors in predicting certain properties that could be remedied. BLYP performs the best for ionization potentials studied here, PBE0 the worst. In other cases, errors are similar. Finally, there is a clear tendency for hybrid functionals to give larger dipole moments than nonhybrid functionals. These observations may be helpful in choosing and improving existing functionals for tasks involving transition metals, and for designing new, improved functionals.     

Interaction of Dihydrogen with Transition Metal (Pd,Ni, Ag,Cu) Clusters

Quantum calculations of interaction of the molecular hydrogen with transition-metal clusters have been performed. The aim of the project is to compare the results for different metals and different methods of calculations. The calculations have been mostly based on the gradient-corrected methods of the density functional theory. The list of the exchange-correlation functionals includes: the gradient corrected functional BP86, the hybrid functionals B3P86, B3LYP, B3PW9, and the local SVWN functional. The calculations of the potential energy surface (PES) for the hydrogen molecule positioned over the planar Pd₅ clusters have been performed. It was found that the H–H bond activation is without barrier for most of the functionals used. However, the results obtained for the B3LYP functional suggest very small potential barrier, of the order of 0.003 eV. The calculations of the PES for dihydrogen in contact with metal clusters have been performed for Ni₅, Ag₅, Cu₅ clusters and for mixed clusters Ag₄Pd, AgPd₄, NiCu₄, and NiPd₄. The dissociation paths for all the cases with the exception of Ag₅ and Cu₅ have been found and the dissociation energies and activation barriers have been estimated.     

Bioinorganic chemistry modeled with the TPSSh density functional

In this work, the TPSSh density functional has been benchmarked against a test set of experimental structures and bond energies for 80 transition-metal-containing diatomics. It is found that the TPSSh functional gives structures of the same quality as other commonly used hybrid and nonhybrid functionals such as B3LYP and BP86. TPSSh gives a slope of 0.99 upon linear fitting to experimental bond energies, whereas B3LYP and BP86, representing 20% and 0% exact exchange, respectively, give linear fits with slopes of 0.91 and 1.07. Thus, TPSSh eliminates the large systematic component of the error in other functionals, reducing rms errors from 46-57 to 34 kJ/mol. The nonhybrid version of the functional, TPSS, gives a slope of 1.08, similar to BP86, implying that using 10% exact exchange is the main reason for the success of TPSSh. Typical bioinorganic reactions were then investigated, including spin inversion and electron affinity in iron-sulfur clusters, and breaking or formation of bonds in iron proteins and cobalamins. The results show that differences in reaction energies due to exact exchange can be much larger than the usually cited approximately 20 kJ/mol, sometimes exceeding 100 kJ/mol. The TPSSh functional provides energies approximately halfway between nonhybrids BP86 and TPSS, and 20% exact exchange hybrid B3LYP: Thus, a linear correlation between the amount of exact exchange and the numeric value of the reaction energy is observed in all these cases. For these reasons, TPSSh stands out as a most promising density functional for use and further development within the field of bioinorganic chemistry.     

Adenine versus guanine quartets in aqueous solution: dispersion-corrected DFT study on the differences in π-stacking and hydrogen-bonding behavior

We have investigated the performance of the dispersion-corrected density functionals (BLYP-D, BP86-D and PBE-D) and the widely used B3LYP functional for describing the hydrogen bonds and the stacking interactions in DNA base dimers. For the gas-phase situation, the bonding energies have been compared to the best ab initio results available in the literature. All dispersion-corrected functionals reproduce well the ab initio results, whereas B3LYP fails completely for the stacked systems. The use of the proper functional leads us to find minima for the adenine quartets, which are energetically and structurally very different from the C_4h structures, and might explain why adenine has to be sandwiched between guanine quartets to form planar adenine quartets.     

Vibrational frequencies of the homoleptic cobalt carbonyls: Co4(CO)12 and Co6(CO)16

The homoleptic cobalt carbonyls Co4(CO)12 and Co6(CO)16 are characterized by their equilibrium geometries, thermochemistry, and vibrational frequencies using density functional theory (DFT) methods with the B3LYP, BLYP, and BP86 functionals. The B3LYP predicted CoCo distances are 2.51 and 2.47 A for the C3v and Td structures, respectively, of Co4(CO)12. The global minimum for Co4(CO)12 has C3v symmetry with three bridging and nine terminal carbonyls. The 2.51 and 2.52 A CoCo distances suggest the single bond required for an 18-electron configuration for the metal atoms. This structure is close to an experimentally realized structure. A more symmetrical Co4(CO)12 structure with Td symmetry, analogous to that observed in the valence isoelectronic Ir4(CO)12 molecule, lies approximately 28 kcal/mol higher in energy and exhibits a small imaginary vibrational frequency ( approximately 40i). It has a slightly shorter CoCo distance of 2.47 A. Both Co4(CO)12 structures satisfy the 18-electron rule. The Co6(CO)16 structure has Td symmetry and satisfies the Wade-Mingos rules for an octahedral cluster. The nu(CO) carbonyl frequencies for both Co4(CO)12 and Co6(CO)16 computed with the BP86 functional are closer to the experimental values than those computed with the B3LYP and BLYP functionals. The structure of Co6(CO)16 is not known experimentally, but the BP86 functional predicts 2.56 A (CoCo), 1.77 and 2.02 A (CoC), and 1.66 and 1.20 A (CO) for the bond distances.     

Agreement between experiment and hybrid DFT calculations for O--H bond dissociation enthalpies in manganese complexes

Information on the accuracy of DFT functionals for redox reactions in transition metal systems is rather limited. To analyze the performance of some popular functionals for redox reactions in manganese systems, calculated O--H bond dissociation enthalpies for Mn-ligands in six different complexes are compared to experimental results. In this benchmark, B3LYP performs well with a mean absolute error of 3.0 kcal/mol. B98 gives similar results to B3LYP (error of 3.8 kcal/mol). B3LYP* gives lower O--H bond strengths than B3LYP and has a mean error of 5.0 kcal/mol. Compared to B98 and B3LYP, B3LYP* has an error trend for the manganese ligands that is more similar to the error for a free water molecule. The nonhybrid functional BLYP consistently and significantly underestimates the O--H bond strengths by approximately 20 kcal/mol. HCTH407 has a rather large mean error of 9.4 kcal/mol and shows no consistent trend. The results support the use of hybrid functionals and the present computational method for large model systems containing manganese. An example is the oxygen evolving complex in photosystem II where hybrid functionals predict the appearance of a Mn(IV)-oxyl radical before the O--O bond formation step.     

On the applicability of density functional theory to manganese‐based complexes with catalytic activity toward water oxidation

The present contribution assesses the performance of several popular and accurate density functionals, namely B3LYP, BP86, M06, MN12L, mPWPW91, PBE0, and TPSSh toward manganese‐based coordination complexes. These compounds show promising properties toward application to catalytic water oxidation. Although manganese with N‐ and O‐biding ligands tends to give rise to high spin complexes, the results show that BP86, mPWPW91, and specially MN12L, tend to yield low‐spin complexes. The usage of these functionals for such compounds is, thus, discouraged. All the functionals considered deliver accurate geometries. The present results show, however, that B3LYP delivers geometries deviating from experimental values when compared to the other functionals of the set. M06, PBE0, and TPSSh deliver geometries of similar accuracy, PBE0 outstanding slightly with respect to the other two. © 2017 Wiley Periodicals, Inc.     

The infrared spectra of polycyclic aromatic hydrocarbons containing a five-membered ring: symmetry breaking and the B3LYP functional

The infrared spectra of six molecules, each of which contains a five-membered ring, and their cations are determined using density functional theory; both the B3LYP and BP86 functionals are used. The computed results are compared with the experimental spectra. For the neutral molecules, both methods are in good agreement with experiment. Even the Hartree–Fock (HF) approach is qualitatively correct for the neutral species. For the cations, the HF approach fails, as found for other organic ring systems. The B3LYP and BP86 approaches are in good mutual agreement for five of the six cation spectra, and are in good agreement with experiment for four of the five cations where the experimental spectra are available. It is only for the fluoranthene cation where the BP86 and B3LYP functionals yield different results; the BP86 approach yields the expected C _{2 v} symmetry, while the B3LYP approach breaks symmetry. The experimental spectra support the BP86 spectra over the B3LYP spectra, but the quality of the experimental spectra does not allow a critical evaluation of the accuracy of the BP86 approach for this difficult system. Received: 9 February 1999 / Accepted: 31 March 1999 / Published online: 14 July 1999     

Electronic spectroscopy and computational studies of glutathionylco(III)balamin

We have studied glutathionylcobalamin (GS-Cbl) by optical spectroscopy and with density functional theory (DFT) and time-dependent DFT (TD-DFT) electronic structure methods of truncated geometric models. We examined the geometric structure of the models by comparison of DFT calculations with recent high-resolution experimental X-ray structure data ( Hannibal, L. et al. Inorg. Chem. 2010, 49, 9921) for GS-Cbl, and we examined the TD-DFT excitation simulations by comparison of the models with measured optical spectra. The calculations employed the B3LYP hybrid functional and the nonhybrid BP86 functional in both vacuum and water (conductor polarized continuum model (cpcm)) with the 6-311G(d,p) basis set. The optimized geometric structure calculations for six truncated models were made by varying the chemical structure, solvent model, and the two DFT functionals. All showed similar geometry. Charge decomposition analysis (CDA) and extended charge decomposition analysis (ECDA), especially with BP86 shows the similar charge transfer nature of the Co-S bond in GS-Cbl and the Co-C bond in CH(3)Cbl. Mayer and Wiberg bond orders illustrate the similar covalent nature of the two bonds. Finally, absolute optical spectral simulation calculations were compared with the experimental UV-visible extinction spectrum and the electronic circular dichroism (ECD) differential extinction spectrum. The BP86 method shows more spectral features, and the best fit was found for a GS-Cbl model with 5,6-dimethylbenzimidazole at the BP86/6-311G(d,p) level with a water cpcm solvent model. The excited state transitions were investigated with Martin's natural transition orbitals (NTOs). The BP86 calculations also showed π bonding interactions between Co and the axial S of the GS- ligand in the molecular orbitals (MOs) and NTOs.