Accurate prediction of vertical electronic transitions of Ni(II) coordination compounds via time dependent density functional theory

Time dependent density functional theory calculations are completed for five Ni(II) complexes formed by polydentate peptides to predict the electronic absorption spectrum. The ligands examined were glycyl‐glycyl‐glycine (GGG), glycyl‐glycyl‐glycyl‐glycine (GGGG), glycyl‐glycyl‐histidine (GGH), glycyl‐glycyl‐cysteine (GGC), and triethylenetetramine (trien). Fifteen functionals and two basis sets were tested. On the basis of the mean absolute percent deviation (MAPD), the ranking among the functionals is: HSE06 ∼ MPW1PW91 ∼ PBE0 > ω‐B97x‐D ∼ B3P86 ∼ B3LYP ∼ CAM‐B3LYP > PBE ∼ BLYP ∼ BP86 > TPSS > TPSSh > BHandHLYP > M06 ≫ M06‐2X. Concerning the basis sets, the triple‐ζ def2‐TZVP performs better than the double‐ζ LANL2DZ. With the functional HSE06 and basis set def2‐TZVP the MAPD with respect to the experimental λ_max is 1.65% with a standard deviation of 1.26%. The absorption electronic spectra were interpreted in terms of vertical excitations between occupied and virtual MOs based on Ni‐d atomic orbitals. The electronic structure of the Ni(II) species is also discussed.     

Is the spin‐orbit coupling important in the prediction of the 51V hyperfine coupling constants of VIVO2+ species? ORCA versus Gaussian performance and biological applications

Density functional theory calculations of the (51)V hyperfine coupling (HFC) tensor A, have been completed for eighteen V(IV)O(2+) complexes with different donor set, electric charge and coordination geometry. A tensor was calculated with ORCA software with several functionals and basis sets taking into account the spin-orbit coupling contribution. The results were compared with those obtained with Gaussian 03 software using the half-and-half functional BHandHLYP and 6-311g(d,p) basis set. The order of accuracy of the functionals in the prediction of A(iso), A(z) and dipolar term A(z,anis) is BHandHLYP > PBE0 > B3PW > TPSSh > B3LYP > BP86 > VWN5 (for A(iso)), BHandHLYP > PBE0 > B3PW > TPSSh > B3LYP > BP86 > VWN5 (for A(z)), B3LYP > PBE0 ～ B3PW ～ BHandHLYP > TPSSh > BP86 ～ VWN5 (for A(z,anis)). The good agreement in the prediction of A(z) with BHandHLYP is due to a compensation between the overestimation of A(iso) and underestimation of A(z,anis) (A(z) = A(iso) + A(z,anis)), whereas among the hybrid functionals PBE0 performs better than the other ones. BHandHLYP functional and Gaussian software are recommended when the V(IV)O(2+) species contains only V-O and/or V-N bonds, whereas PBE0 functional and ORCA software for V(IV)O(2+) complexes with one or more V-S bonds. Finally, the application of these methods to the coordination environment of V(IV)O(2+) ion in V-proteins, like vanadyl-substituted insulin, carbonic anhydrase, collagen and S-adenosylmethionine synthetase, was discussed.     

The confirmation of accurate combination of functional and basis set for transition‐metal dimers: Fe2, Co2, Ni2, Ru2, Rh2, Pd2, Os2, Ir2, and Pt2

Eight kinds of density functionals named B3LYP, PBE1PBE, B1B95, BLYP, BP86, G96PW91, mPWPW91, and SVWN along with two different valence basis sets (LANL2DZ and CEP‐121g) are employed to study the transition‐metal dimers for the elements of group VIII. By comparing the equilibrium bond distances, vibrational frequencies, and dissociation energies of the ground state of these dimers with the available experimental values and theoretical data, we show that the “pure” DFT methods (G96PW91, BLYP, and BP86) with great‐gradient approximation always give better results relative to the hybrid HF/DFT schemes (B3LYP, PBE1PBE, and B1B95). The striking case found by us is that the G96PW91 functional, which is not tested in previous systemic studies, always predicts the dissociation energy to be well. The Ru₂ and Os₂ dimers are sensitive to not only the functionals employed but also the valence basis sets adopted. The natural bond orbital population is analyzed, and the molecular orbitals of the unpaired electrons are determined. Furthermore, our results indicate that the s and d orbitals of these dimers always hybridize with each other except for Rh₂ and Pt₂ molecules. And by analyzing the electron configuration of the bonding atom, the dissociation limit of the ground state is obtained. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

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.     

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.     

How accurate are TD-DFT excited-state geometries compared to DFT ground-state geometries?

In this work, we take a different angle to the benchmarking of time-dependent density functional theory (TD-DFT) for the calculation of excited-state geometries by extensively assessing how accurate such geometries are compared to ground-state geometries calculated with ordinary DFT. To this end, we consider 20 medium-sized aromatic organic compounds whose lowest singlet excited states are ideally suited for TD-DFT modeling and are very well described by the approximate coupled-cluster singles and doubles (CC2) method, and then use this method and six different density functionals (BP86, B3LYP, PBE0, M06-2X, CAM-B3LYP, and ωB97XD) to optimize the corresponding ground- and excited-state geometries. The results show that although each hybrid functional reproduces the CC2 excited-state bond lengths very satisfactorily, achieving an overall root mean square error of 0.011 Å for all 336 bonds in the 20 molecules, these errors are distinctly larger than those of only 0.004–0.006 Å with which the hybrid functionals reproduce the CC2 ground-state bond lengths. Furthermore, for each functional employed, the variation in the error relative to CC2 between different molecules is found to be much larger (by at least a factor of 3) for the excited-state geometries than for the ground-state geometries, despite the fact that the molecules/states under investigation have rather uniform chemical and spectroscopic character. Overall, the study finds that even in favorable circumstances, TD-DFT excited-state geometries appear intrinsically and comparatively less accurate than DFT ground-state ones.     

The accuracy of DFT-optimized geometries of functional transition metal compounds: a validation study of catalysts for olefin metathesis and other reactions in the homogeneous phase

We have investigated the performance of eight popular density functionals, four of which are "standard" functionals not including dispersion (B3LYP, BP86, PBE, and TPSS) and four of which have been constructed to account for dispersion (B97D, wB97XD, M06, and M06L), in reproducing 18 molecular structures derived from single-crystal X-ray diffraction experiments on ruthenium-based olefin metathesis catalyst precursors. Our analysis of all the internuclear distances reveals that standard DFT predicts systematically expanded structures. In contrast, all the methods accounting for dispersion give rise to more compact structures, removing the systematic overestimation of internuclear distances. The contracting effect of dispersion is general and also affects chemical bonds, thus reducing the general overestimation of bond lengths. The best overall performance is observed for wB97XD, which offers relatively small statistical errors when considering the overall structure as well as selected distances. Only for the coordination center geometry is the accuracy of wB97XD matched by standard functionals such as PBE and TPSS, whereas M06 and M06L are associated with larger errors. At the other end of the scale, B3LYP is seen to give the largest statistical errors in general, both when considering the complete structures and the geometries of the coordination centers alone. For the organic ligands, however, B3LYP performs clearly better than the other standard functionals although not as well as the functionals accounting for dispersion. Extending the basis sets is seen to improve the structures in particular of the coordination center, thus underlining the importance of using sufficiently flexible basis sets if highly accurate geometries are to be obtained. Similar conclusions to those obtained for the ruthenium catalysts can be drawn from comparisons of the X-ray crystal structures of 10 other organometallic complexes of relevance to homogeneous catalysis, covering first (Ti, Fe, Co, Ni), second (Zr, Mo, Rh, Pd) and third (W, Ir) row transition metals, with those of DFT. The latter analyses thus offer a first indication that the picture obtained for the ruthenium alkylidene complexes may be extended to other classes of relatively large transition metal complexes.     

Calibration of DFT Functionals for the Prediction of Fe Mössbauer Spectral Parameters in Iron-Nitrosyl and Iron-Sulfur Complexes: Accurate Geometries Prove Essential

Six popular density functionals in conjunction with the conductor-like screening (COSMO) solvation model have been used to obtain linear M?ssbauer isomer shift (IS) and quadrupole splitting (QS) parameters for a test set of 20 complexes (with 24 sites) comprised of nonheme nitrosyls (Fe-NO) and non-nitrosyl (Fe-S) complexes. For the first time in an IS analysis, the Fe electron density was calculated both directly at the nucleus, ρ(0)(N), which is the typical procedure, and on a small sphere surrounding the nucleus, ρ(0)(S), which is the new standard algorithm implemented in the ADF software package. We find that both methods yield (near) identical slopes from each linear regression analysis but are shifted with respect to ρ(0) along the x-axis. Therefore, the calculation of the Fe electron density with either method gives calibration fits with equal predictive value. Calibration parameters obtained from the complete test set for OLYP, OPBE, PW91, and BP86 yield correlation coefficients (r(2)) of approximately 0.90, indicating that the calibration fit is of good quality. However, fits obtained from B3LYP and B3LYP* with both Slater-type and Gaussian-type orbitals are generally found to be of poorer quality. For several of the complexes examined in this study, we find that B3LYP and B3LYP* give geometries that possess significantly larger deviations from the experimental structures than OLYP, OPBE, PW91 or BP86. This phenomenon is particularly true for the di- and tetranuclear Fe complexes examined in this study. Previous M?ssbauer calibration fit studies using these functionals have usually included mononuclear Fe complexes alone, where these discrepancies are less pronounced. An examination of spin expectation values reveals B3LYP and B3LYP* approach the weak-coupling limit more closely than the GGA exchange-correlation functionals. The high degree of variability in our calculated S(2) values for the Fe-NO complexes highlights their challenging electronic structure. Significant improvements to the isomer shift calibrations are obtained for B3LYP and B3LYP* when geometries obtained with the OLYP functional are used. In addition, greatly improved performance of these functionals is found if the complete test set is grouped separately into Fe-NO and Fe-S complexes. Calibration fits including only Fe-NO complexes are found to be excellent, while those containing the non-nitrosyl Fe-S complexes alone are found to demonstrate less accurate correlations. Similar trends are also found with OLYP, OPBE, PW91, and BP86. Correlations between experimental and calculated QSs were also investigated. Generally, universal and separate Fe-NO and Fe-S fit parameters obtained to determine QSs are found to be of good to excellent quality for every density functional examined, especially if [Fe(4)(NO)(4)(μ(3)-S)(4)](-) is removed from the test set.     

The prediction of Fe Mössbauer parameters by the density functional theory: a benchmark study

We report the performance of eight density functionals (B3LYP, BPW91, OLYP, O3LYP, M06, M06-2X, PBE, and SVWN5) in two Gaussian basis sets (Wachters and Partridge-1 on iron atoms; cc-pVDZ on the rest of atoms) for the prediction of the isomer shift (IS) and the quadrupole splitting (QS) parameters of M?ssbauer spectroscopy. Two sources of geometry (density functional theory-optimized and X-ray) are used. Our data set consists of 31 iron-containing compounds (35 signals), the M?ssbauer spectra of which were determined at liquid helium temperature and where the X-ray geometries are known. Our results indicate that the larger and uncontracted Partridge-1 basis set produces slightly more accurate linear correlations of electronic density used for the prediction of IS and noticeably more accurate results for the QS parameter. We confirm and discuss the earlier observation of Noodleman and co-workers that different oxidation states of iron produce different IS calibration lines. The B3LYP and O3LYP functionals have the lowest errors for either IS or QS. BPW91, OLYP, PBE, and M06 have a mixed success whereas SVWN5 and M06-2X demonstrate the worst performance. Finally, our calibrations and conclusions regarding the best functional to compute the M?ssbauer characteristics are applied to candidate structures for the peroxo and Q intermediates of the enzyme methane monooxygenase hydroxylase (MMOH), and compared to experimental data in the literature.     

Performance of Density Functional Theory for Transition Metal Oxygen Bonds

The accuracy of density functional theory (DFT) limits predictions in theoretical catalysis, and strong chemical bonds between transition metals and oxygen pose a particular challenge. We benchmarked 30 diverse density functionals against the bond dissociation enthalpies (BDE) of the 30 MO and 30 MO⁺ diatomic systems of all the 3d, 4d, and 5d metals, to test universality across the d-block as required in comparative studies. Seven functionals, B98, B97-1, B3P86, B2PLYP, TPSSh, B3LYP, and B97-2, display mean absolute errors (MAE) <30 kJ/mol. In contrast, many commonly used functionals such as PBE and RPBE overestimate M−O bonding by +30 kJ/mol and display MAEs from 48–76 kJ/mol. RPBE and OPBE reduce the over-binding of PBE but remain very inaccurate. We identify a linear relationship (p-value 7.6 ⋅ 10⁻⁵) between the precision and accuracy of DFT, i. e. inaccurate functionals tend to produce larger, unpredictable random errors. Some functionals commonly deviate from this relationship: Thus, M06-2X is very precise but not very accurate, whereas B3LYP* and MN15-L are more accurate but less precise than M06-2X. The best-performing hybrids have 10–30 % HF exchange, but this can be relieved by double hybrids (B2PLYP). Most functionals describe trends well, but errors comparing 5d to 4d/3d are ∼10 kJ/mol larger than group-wise errors, due to uncertainties in the spin-orbit coupling corrections for effective core potentials, affecting e. g. Pt/Pd or Au/Ag comparisons.     

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.     

Vibrational frequency scale factors for density functional theory and the polarization consistent basis sets

Calculated harmonic vibrational frequencies systematically deviate from experimental vibrational frequencies. The observed deviation can be corrected by applying a scale factor. Scale factors for: (i) harmonic vibrational frequencies [categorized into low (<1000 cm^?1) and high (>1000 cm^?1)], (ii) vibrational contributions to enthalpy and entropy, and (iii) zero‐point vibrational energies (ZPVEs) have been determined for widely used density functionals in combination with polarization consistent basis sets (pc‐n, n = 0,1,2,3,4). The density functionals include pure functionals (BP86, BPW91, BLYP, HCTH93, PBEPBE), hybrid functionals with Hartree‐Fock exchange (B3LYP, B3P86, B3PW91, PBE1PBE, mPW1K, BH&HLYP), hybrid meta functionals with the kinetic energy density gradient (M05, M06, M05‐2X, M06‐2X), a double hybrid functional with Møller‐Plesset correlation (B2GP‐PLYP), and a dispersion corrected functional (B97‐D). The experimental frequencies for calibration were from 41 organic molecules and the ZPVEs for comparison were from 24 small molecules (diatomics, triatomics). For this family of basis sets, the scale factors for each property are more dependent on the functional selection than on basis set level, and thus allow for a suggested scale factor for each density functional when employing polarization consistent basis sets (pc‐n, n = 1,2,3,4). A separate scale factor is recommended when the un‐polarized basis set, pc‐0, is used in combination with the density functionals. © 2012 Wiley Periodicals, Inc.     

Assessing the performance of density functional theory for the dynamic polarizabilities of amino acids: Treatment of correlation and role of exact exchange

The theoretical determination of electric response properties of the biological systems is a field where the application of density functional theory (DFT) appears to be quite promising. In this work, the performance of 41 density functional methods is evaluated in predicting dynamic polarizabilities of an experimental benchmark set of 20 proteinogenic amino acids. The behavior of a large number of density functionals, including various types of the local spin density approximation (LSDA), generalized gradient approximation (GGA), meta‐GGA (m‐GGA), hybrid‐GGA (h‐GGA), hybrid meta‐GGA (hm‐GGA), and range‐separated hybrid‐GGA (rsh‐GGA), has been assessed for the purpose. Analyzing the results of our DFT benchmarking, we found that these computationally economical methods show very diverse predictive capability and a careful selection of DFT functionals is very important in the polarizability calculations. Considering the role of exchange, correlation, dispersion and long‐range corrections, it turned out that in the LSDA class, SVWN3 gives better results than SPL and SVWN5 toward the reference values. Of the GGA methods, OPBE outperforms all other functionals. The M06‐L is the best method of m‐GGA class. The B3LYP and TPSSh are the best functionals of h‐GGA and hm‐GGA lineages, respectively. Finally, CAM‐B3LYP is the best method of rsh‐GGA functionals that predicts the most accurate polarizability for amino acids by a large margin with respect to others. Overall, the best performing functionals turn out to be hm‐GGAs TPSSh, TPSS1KCIS, M05, tau‐HCTHhyb, and h‐GGA B3LYP. Hopefully, the results of this investigation might provide the useful guidance to propose a new exchange‐correlation functional for calculating the optical properties of biomolecular materials. © 2013 Wiley Periodicals, Inc.     

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.     

Which density functional is close to CCSD accuracy to describe geometry and interaction energy of small noncovalent dimers? A benchmark study using Gaussian09

A benchmark study on all possible density functional theory (DFT) methods in Gaussian09 is done to locate functionals that agree well with CCSD/aug‐cc‐pVTZ geometry and Ave‐CCSD(T)/(Q‐T) interaction energy (E_int) for small non‐covalently interacting molecular dimers in “dispersion‐dominated” (class 1), “dipole‐induced dipole” (class 2), and “dipole‐dipole” (class 3) classes. A DFT method is recommended acceptable if the geometry showed close agreement to CCSD result (RMSD < 0.045) and E_int was within 80–120% accuracy. Among 382 tested functionals, 1–46% gave good geometry, 13–44% gave good E_int, while 1–33% satisfied geometry and energy criteria. Further screening to locate the best performing functionals for all the three classes was made by counting the acceptable values of energy and geometry given by each functionals. The meta‐generalized gradient approximation (GGA) functional M06L was the best performer with total 14 hits; seven acceptable energies and seven acceptable geometries. This was the only functional “recommended” for at least two dimers in each class. The functionals M05, B2PLYPD, B971, mPW2PLYPD, PBEB95, and CAM‐B3LYP gave 11 hits while PBEhB95, PW91B95, Wb97x, BRxVP86, BRxP86, HSE2PBE, HSEh1PBE, PBE1PBE, PBEh1PBE, and PW91TPSS gave 10 hits. Among these, M05, B971, mPW2PLYPD, Wb97x, and PW91TPSS were among the “recommended” list of at least one dimer from each class. Long‐range correction (LC) of Hirao and coworkers to exchange‐correlation functionals showed massive improvement in geometry and E_int. The best performing LC‐functionals were LC‐G96KCIS and LC‐PKZBPKZB. Our results predict that M06L is the most trustworthy DFT method in Gaussian09 to study small non‐covalently interacting systems. © 2013 Wiley Periodicals, Inc.     

Broken symmetry density functional study of a mixed‐valence unsymmetrical dinuclear iron complex

Density functional theory (DFT) calculations with different exchange‐correlation functionals were performed for a mixed valence Fe(II)/Fe(III) binuclear complex with μ‐methoxo and two μ‐carboxylate bridging ligands, (1) with geometry optimizations being performed for all possible spin multiplicities (M_S = 2, 4, 6, 8, and 10). Within the exchange‐correlation functionals studied, only the hybrid GGA functionals B3P and B3LYP and also the pure GGA functional RPBE, predicts the geometry with high spin (S = 9/2) to be more stable than the geometry with low spin state (S = 1/2) by 20 kcal/mol, in agreement with the experimental findings. These functionals also predict the same stability order for the different spin states, being M_S = 10>8>6>2>4. The meta‐GGA functionals TPSS and TPSSh and also the pure GGA functionals BLYP and BP86 predict different stability orders. The computed average EPR g‐tensor, g_av, of 2.03, at the B3LYP level, is in good agreement with the experimental findings. Heisenberg exchange coupling constants, J, were calculated within the broken‐symmetry formalism, at the B3LYP level, showing that the two iron centers are antiferromagnetic coupling, with a very weak coupling constant of about ?7 cm^?1, in good agreement with the experimental value. Additionally, the effect of using different multiplicities of the reference geometries on the computed J value is discussed. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Nickel-catalyzed alkyl coupling reactions: evaluation of computational methods

The B3LYP, M06, M06L, M062X, MPW1K, and PBE1PBE DFT methods were evaluated for modeling nickel-catalyzed coupling reactions. The reaction consists of a nucleophilic attack by a carbanion equivalent on the nickel complex, S(N)2 attack by the anionic nickel complex on an alkyl halide, and reductive elimination of the coupled alkane product, regenerating the nickel catalyst. On the basis of CCSD(T)//DFT single-point energies, the B3LYP, M06, and PBE1PBE functionals were judged to generate the best ground state geometries. M06 energies are generally comparable or superior to B3LYP and PBE1PBE energies for transition state calculations. The MP2 and CCSD methods were also evaluated for single-point energies at the M06 geometries. The rate-determining step of this reaction was found to be nucleophilic attack of a L(2)NiR anion on the alkyl halide.