Comparison of DFT methods for molecular orbital eigenvalue calculations

We report how closely the Kohn-Sham highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) eigenvalues of 11 density functional theory (DFT) functionals, respectively, correspond to the negative ionization potentials (-IPs) and electron affinities (EAs) of a test set of molecules. We also report how accurately the HOMO-LUMO gaps of these methods predict the lowest excitation energies using both time-independent and time-dependent DFT (TD-DFT). The 11 DFT functionals include the local spin density approximation (LSDA), five generalized gradient approximation (GGA) functionals, three hybrid GGA functionals, one hybrid functional, and one hybrid meta GGA functional. We find that the HOMO eigenvalues predicted by KMLYP, BH&HLYP, B3LYP, PW91, PBE, and BLYP predict the -IPs with average absolute errors of 0.73, 1.48, 3.10, 4.27, 4.33, and 4.41 eV, respectively. The LUMOs of all functionals fail to accurately predict the EAs. Although the GGA functionals inaccurately predict both the HOMO and LUMO eigenvalues, they predict the HOMO-LUMO gap relatively accurately (approximately 0.73 eV). On the other hand, the LUMO eigenvalues of the hybrid functionals fail to predict the EA to the extent that they include HF exchange, although increasing HF exchange improves the correspondence between the HOMO eigenvalue and -IP so that the HOMO-LUMO gaps are inaccurately predicted by hybrid DFT functionals. We find that TD-DFT with all functionals accurately predicts the HOMO-LUMO gaps. A linear correlation between the calculated HOMO eigenvalue and the experimental -IP and calculated HOMO-LUMO gap and experimental lowest excitation energy enables us to derive a simple correction formula.     

Energy landscapes of nucleophilic substitution reactions: a comparison of density functional theory and coupled cluster methods

We have carried out a detailed evaluation of the performance of all classes of density functional theory (DFT) for describing the potential energy surface (PES) of a wide range of nucleophilic substitution (SN2) reactions involving, amongst others, nucleophilic attack at carbon, nitrogen, silicon, and sulfur. In particular, we investigate the ability of the local density approximation (LDA), generalized gradient approximation (GGA), meta-GGA as well as hybrid DFT to reproduce high-level coupled cluster (CCSD(T)) benchmarks that are close to the basis set limit. The most accurate GGA, meta-GGA, and hybrid functionals yield mean absolute deviations of about 2 kcal/mol relative to the coupled cluster data, for reactant complexation, central barriers, overall barriers as well as reaction energies. For the three nonlocal DFT classes, the best functionals are found to be OPBE (GGA), OLAP3 (meta-GGA), and mPBE0KCIS (hybrid DFT). The popular B3LYP functional is not bad but performs significantly worse than the best GGA functionals. Furthermore, we have compared the geometries from several density functionals with the reference CCSD(T) data. The same GGA functionals that perform best for the energies (OPBE, OLYP), also perform best for the geometries with average absolute deviations in bond lengths of 0.06 A and 0.6 degrees, even better than the best meta-GGA and hybrid functionals. In view of the reduced computational effort of GGAs with respect to meta-GGAs and hybrid functionals, let alone coupled cluster, we recommend the use of accurate GGAs such as OPBE or OLYP for the study of SN2 reactions.     

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.     

Oxidative addition of the fluoromethane C-F bond to Pd. An ab initio benchmark and DFT validation study

We have computed a state-of-the-art benchmark potential energy surface (PES) for two reaction pathways (oxidative insertion, OxIn, and S(N)2) for oxidative addition of the fluoromethane C-F bond to the palladium atom and have used this to evaluate the performance of 26 popular density functionals, covering LDA, GGA, meta-GGA, and hybrid density functionals, for describing these reactions. The ab initio benchmark is obtained by exploring the PES using a hierarchical series of ab initio methods (HF, MP2, CCSD, CCSD(T)) in combination with a hierarchical series of seven Gaussian-type basis sets, up to g polarization. Relativistic effects are taken into account through a full four-component all-electron approach. Our best estimate of kinetic and thermodynamic parameters is -5.3 (-6.1) kcal/mol for the formation of the reactant complex, 27.8 (25.4) kcal/mol for the activation energy for oxidative insertion (OxIn) relative to the separate reactants, 37.5 (31.8) kcal/mol for the activation energy for the alternative S(N)2 pathway, and -6.4 (-7.8) kcal/mol for the reaction energy (zero-point vibrational energy-corrected values in parentheses). Our work highlights the importance of sufficient higher angular momentum polarization functions for correctly describing metal-d-electron correlation. Best overall agreement with our ab initio benchmark is obtained by functionals from all three categories, GGA, meta-GGA, and hybrid DFT, with mean absolute errors of 1.4-2.7 kcal/mol and errors in activation energies ranging from 0.3 to 2.8 kcal/mol. The B3LYP functional compares very well with a slight underestimation of the overall barrier for OxIn by -0.9 kcal/mol. For comparison, the well-known BLYP functional underestimates the overall barrier by -10.1 kcal/mol. The relative performance of these two functionals is inverted with respect to previous findings for the insertion of Pd into the C-H and C-C bonds. However, all major functionals yield correct trends and qualitative features of the PES, in particular, a clear preference for the OxIn over the alternative S(N)2 pathway.     

Density functionals for inorganometallic and organometallic chemistry

We present a database of 21 bond dissociation energies for breaking metal-ligand bonds. The molecules in the metal-ligand bond energy database are AgH, CoH, CoO+, CoOH+, CrCH3+, CuOH2+, FeH, Fe(CO)5, FeO, FeS, LiCl, LiO, MgO, MnCH3NiCH2+, Ni(CO)4, RhC, VCO+, VO, and VS. We have also created databases of metal-ligand bond lengths and atomic ionization potentials. The molecules used for bond lengths are AgH, BeO, CoH, CoO+, FeH, FeO, FeS, LiCl, LiO, MgO, RhC, VO, and VS and the ionization potentials are for the following atoms: C, Co, Cr, Cu, Ni, O, and V. The data were chosen based on their diversity and expected reliability, and they are used along with three previously developed databases (transition metal dimer bond energies and bond lengths and main-group molecular atomization energies) for assessing the accuracy of several kinds of density functionals. In particular, we report tests for 42 previously defined functionals: 2 local spin density approximation (LSDA) functionals, 14 generalized gradient approximation (GGA) methods, 13 hybrid GGA methods, 7 meta GGA methods, and 8 hybrid meta GGA methods. In addition to these functionals, we also examine the effectiveness of scaling the correlation energy by testing 13 functionals with scaled or no gradient-corrected correlation energy, and we find that functionals of this kind are more accurate for metal-metal and metal-ligand bonds than any of the functionals already in the literature. We also present a readjusted GGA and a hybrid GGA with parameters adjusted for metals. When we consider these 57 functionals for metal-ligand and metal-metal bond energies simultaneously with main-group atomization energies, atomic ionization potentials, and bond lengths we find that the most accurate functional is G96LYP, followed closely by MPWLYP1M (new in this article), XLYP, BLYP, and MOHLYP (also new in this article). Four of these five functionals have no Hartree-Fock exchange, and the other has only 5%. As a byproduct of this work we introduce a convenient diagnostic, called the B1 diagnostic, for ascertaining the multireference character in a bond.     

Oxidative addition of the ethane C-C bond to Pd. An ab initio benchmark and DFT validation study

We have computed a state-of-the-art benchmark potential energy surface (PES) for the archetypal oxidative addition of the ethane C-C bond to the palladium atom and have used this to evaluate the performance of 24 popular density functionals, covering LDA, GGA, meta-GGA, and hybrid density functionals, for describing this reaction. The ab initio benchmark is obtained by exploring the PES using a hierarchical series of ab initio methods [HF, MP2, CCSD, CCSD(T)] in combination with a hierarchical series of five Gaussian-type basis sets, up to g polarization. Relativistic effects are taken into account either through a relativistic effective core potential for palladium or through a full four-component all-electron approach. Our best estimate of kinetic and thermodynamic parameters is -10.8 (-11.3) kcal/mol for the formation of the reactant complex, 19.4 (17.1) kcal/mol for the activation energy relative to the separate reactants, and -4.5 (-6.8) kcal/mol for the reaction energy (zero-point vibrational energy-corrected values in parentheses). Our work highlights the importance of sufficient higher angular momentum polarization functions for correctly describing metal-d-electron correlation. Best overall agreement with our ab initio benchmark is obtained by functionals from all three categories, GGA, meta-GGA, and hybrid DFT, with mean absolute errors of 1.5 to 2.5 kcal/mol and errors in activation energies ranging from -0.2 to -3.2 kcal/mol. Interestingly, the well-known BLYP functional compares very reasonably with a slight underestimation of the overall barrier by -0.9 kcal/mol. For comparison, with B3LYP we arrive at an overestimation of the overall barrier by 5.8 kcal/mol. On the other hand, B3LYP performs excellently for the central barrier (i.e., relative to the reactant complex) which it underestimates by only -0.1 kcal/mol.     

Small clusters of aluminum and tin: highly correlated calculations and validation of density functional procedures

We present results of molecular electronic structure treatments of multireference configuration interaction (MRCI) type for clusters Al(n) and Sn(n) in the range up to n = 4, and of coupled cluster singles and doubles with perturbative triples corrections (CCSD(T)) type in the range up to n = 10. Basis sets of quadruple zeta size are employed, computed energy differences, such as cohesive energies, E(coh), or dissociation energies for the removal of a single atom, D(e), differ from the complete basis set limit by only a few 0.01 eV. MRCI and CCSD(T) results are then compared to those obtained from density functional theory (DFT) treatments, which show that all computational procedures agree with the general features of D(e) and E(coh). The best agreement of DFT with CCSD(T) is found for the meta-GGA (generalized gradient approximation) TPSS (Tao, Perdew, Staroverov, Scuseria) for which D(e) differs from CCSD(T) by at most 0.15 eV for Al(n) and 0.21 eV for Sn(n). The GGA PBE (Perdew, Burke, Ernzerhof) is slightly poorer with maximum deviations of 0.23 and 0.24 eV, whereas hybrid functionals are not competitive with GGA and meta-GGA functionals. A general conclusion is that errors of D(e) and/or energy differences of isomers computed with DFT procedures may easily reach 0.2 eV and errors for cohesive energies E(coh) 0.1 eV.     

On the accuracy of density-functional theory exchange-correlation functionals for H bonds in small water clusters: benchmarks approaching the complete basis set limit

The ability of several density-functional theory (DFT) exchange-correlation functionals to describe hydrogen bonds in small water clusters (dimer to pentamer) in their global minimum energy structures is evaluated with reference to second order Moller-Plesset perturbation theory (MP2). Errors from basis set incompleteness have been minimized in both the MP2 reference data and the DFT calculations, thus enabling a consistent systematic evaluation of the true performance of the tested functionals. Among all the functionals considered, the hybrid X3LYP and PBE0 functionals offer the best performance and among the nonhybrid generalized gradient approximation functionals, mPWLYP and PBE1W perform best. The popular BLYP and B3LYP functionals consistently underbind and PBE and PW91 display rather variable performance with cluster size.     

Low-lying electronic states of M(3)O(9)(-) and M(3)O(9)(2-) (M = Mo, W)

Multiple low-lying electronic states of M(3)O(9)(-) and M(3)O(9)(2-) (M = Mo, W) arise from the occupation of the near-degenerate low-lying virtual orbitals in the neutral clusters. We used density functional theory (DFT) and coupled cluster theory (CCSD(T)) with correlation consistent basis sets to study the structures and energetics of the electronic states of these anions. The adiabatic and vertical electron detachment energies (ADEs and VDEs) of the anionic clusters were calculated with 27 exchange-correlation functionals including one local spin density approximation functional, 13 generalized gradient approximation (GGA) functionals, and 13 hybrid GGA functionals, as well as the CCSD(T) method. For M(3)O(9)(-), CCSD(T) and nearly all of the DFT exchange-correlation functionals studied predict the (2)A(1) state arising from the Jahn-Teller distortion due to singly occupying the degenerate e' orbital to be lower in energy than the (2)A(1)' state arising from singly occupying the nondegenerate a(1)' orbital. For W(3)O(9)(-), the (2)A(1) state was predicted to have essentially the same energy as the (2)A(1)' state at the CCSD(T) level with core-valence correlation corrections included and to be higher in energy or essentially isoenergetic with most DFT methods. The calculated VDEs from the CCSD(T) method are in reasonable agreement with the experimental values for both electronic states if estimates for the corrections due to basis set incompleteness are included. For M(3)O(9)(2-), the singlet state arising from doubly occupying the nondegenerate a(1)' orbital was predicted to be the most stable state for both M = Mo and W. However, whereas M(3)O(9)(2-) was predicted to be less stable than M(3)O(9)(-), W(3)O(9)(2-) was predicted to be more stable than W(3)O(9)(-).     

A comparative relativistic DFT and ab initio study on the structure and thermodynamics of the oxofluorides of uranium(IV), (V) and (VI)

All the possible uranium(VI, V, IV) oxides, fluorides and oxofluorides were studied theoretically by using density functional theory (DFT) in the generalised gradient approximation (GGA), and three different relativistic methods (all-electron scalar four component Dyall RESC method (AE), relativistic small-core ECPs, and zeroth order regular approximation ZORA). In order to test different correlation methods, for the two former relativistic methods hybrid DFT, and, for the AE method, MP2 molecular orbital calculations were performed as well. Single-point AE-CCSD(T) energies were calculated on MP2 geometries as well. Energies of the uranium(VI) and (V) oxofluorides dissociation, uranium(VI) fluoride hydrolysis and oxofluoride disproportionation were calculated and compared against the available experimental thermochemical data. AE-CCSD(T) energies were the closest to the experiment. For GGA DFT methods, all the relativistic methods used yield similar results. For thermochemistry, the best quantitative agreement with the experimental and CCSD(T) values for both U=O and U-F bond strengths was obtained with hybrid DFT methods, provided that a reliable basis set was used. Both the GGA DFT and MP2 MO methods show overbinding of these bonds; moreover, this overbinding was found to be not uniform but strongly dependent on the coordination environment of the uranium atom in each case. U=O vibrational frequencies given by hybrid DFT, however, are systematically overestimated, and are better reproduced by GGA DFT; MP2 values usually fall in-between. Reaction enthalpies, U=O frequencies and complex geometries given by the PBE, MPBE, BPBE, BLYP and OLYP GGA functionals are quite similar, with OLYP performing slightly better than the others but still not as good as hybrid DFT. The geometries of the molecules are found to be influenced by the following factors: the inverse transinfluence (ITI) of the oxygen ligand and, for U(V), and U(IV), the Jahn-Teller distortion.     

Assessment of recently developed exchange-correlation functionals for the description of torsion potentials in pi-conjugated molecules

Newly developed exchange-correlation functionals in density functional theory (DFT) have been applied to describe conjugation effects in organic molecules. The performance of the various approaches is assessed through the calculation of torsion energy profiles and their critical comparison with available experimental data. Our results indicate that the OPTX-B95 exchange-correlation functional as well as its corresponding hybrid versions perform better than the well-established BLYP or B3LYP schemes when dealing with pi-conjugated molecules. In contrast, the recently introduced VSXC functional is not as reliable as other DFT methods for the systems examined here.     

Density functional study of double ionization energies

In this paper, double ionization energies (DIEs) of gas-phase atoms and molecules are calculated by energy difference method with density functional theory. To determine the best functional for double ionization energies, we first study 24 main group atoms in the second, third, and fourth periods. An approximation is used in which the electron density is first obtained from a density functional computation with the exchange-correlation potential V xc known as statistical average of orbital potentials, after which the energy is computed from that density with 59 different exchange-correlation energy functionals E xc. For the 24 atoms, the two best E xc functional providing DIEs with average absolute deviation (AAD) of only 0.25 eV are the Perdew-Burke-Ernzerhof functional modified by Hammer et al. [Phys. Rev. B 59, 6413 (1999)] and one known as the Krieger-Chen-Iafrate-Savin functional modified by Krieger et al. (unpublished). Surprisingly, none of the 20 available hybrid functionals is among the top 15 functionals for the DIEs of the 24 atoms. A similar procedure is then applied to molecules, with opposite results: Only hybrid functionals are among the top 15 functionals for a selection of 29 molecules. The best E xc functional for the 29 molecules is found to be the Becke 1997 functional modified by Wilson et al. [J. Chem. Phys. 115, 9233 (2001)]. With that functional, the AAD from experiment for DIEs of 29 molecules is just under 0.5 eV. If the two suspected values for C2H2 and Fe(CO)5 are excluded, the AAD improves to 0.3(2) eV. Many other hybrid functionals perform almost as well.     

Binding energy curves from nonempirical density functionals. I. Covalent bonds in closed-shell and radical molecules

Binding or potential energy curves have been calculated for the ground-state diatomics H(2)(+), He(2)(+), LiH(+), H(2), N(2), and C(2), for the transition state H(3), and for the triplet first excited state of H(2) using the nonempirical density functionals from the first three rungs of a ladder of approximations: the local spin density (LSD) approximation, the Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation (GGA), and the Tao-Perdew-Staroverov-Scuseria (TPSS) meta GGA. Good binding energy curves in agreement with coupled cluster or configuration interaction calculations are found from the PBE GGA and especially from the TPSS meta GGA. Expected exceptions are the symmetric radicals H(2)(+) and He(2)(+), where the functionals suffer from self-interaction error, and the exotically bonded C(2). Although the energy barrier for the reaction H(2) + H --> H + H(2) is better in PBE than in TPSS, the transition state H(3) is a more properly positioned and curved saddle point of the energy surface in TPSS. The triplet first excited state of H(2) obeys the Aufbau principle and thus is one of the exceptional excited states that are computable in principle from the ground-state functional. The PBE GGA and TPSS meta GGA are useful not only for chemical applications but also for the construction of higher-rung nonempirical functionals that can further improve the binding energy curves.     

Six-dimensional potential energy surface for H2 at Ru(0001)

The six-dimensional (6D) potential energy surface (PES) for the H(2) molecule interacting with a clean Ru(0001) surface has been computed accurately for the first time. Density functional theory (DFT) and a pseudopotential based periodic plane-wave approach have been used to calculate the electronic interactions between the molecule and the surface. Two different generalized gradient approximation (GGA) exchange-correlation functionals, PW91 and RPBE, have been adopted. Based on the DFT/GGA calculated potential energies, an analytical 6D PES has been constructed using the corrugation reducing procedure. A very accurate representation of the DFT/GGA data has been achieved, with an average error in the interpolation of about 3 meV and a maximum error not larger than about 30 meV. The top site is found to be the most reactive site for both functionals used, but PW91 predicts a higher reactivity than RPBE, with lower-energy and earlier-located dissociation barriers. The energetic corrugation displayed by the RPBE PES is larger than the PW91 PES while the geometric corrugation is smaller. The differences between the two PESs increase as the distance of the molecular center of mass to the surface decreases. A direct comparison with experimental investigations on H(2)/Ru(0001) could shed light on the suitability of these XC potentials often used in DFT calculations.     

Orbital-dependent correlation energy in density-functional theory based on a second-order perturbation approach: success and failure

We have developed a second-order perturbation theory (PT) energy functional within density-functional theory (DFT). Based on PT with the Kohn-Sham (KS) determinant as a reference, this new ab initio exchange-correlation functional includes an exact exchange (EXX) energy in the first order and a correlation energy including all single and double excitations from the KS reference in the second order. The explicit dependence of the exchange and correlation energy on the KS orbitals in the functional fits well into our direct minimization approach for the optimized effective potential, which is a very efficient method to perform fully self-consistent calculations for any orbital-dependent functionals. To investigate the quality of the correlation functional, we have applied the method to selected atoms and molecules. For two-electron atoms and small molecules described with small basis sets, this new method provides excellent results, improving both second-order Moller-Plesset expression and any conventional DFT results significantly. For larger systems, however, it performs poorly, converging to very low unphysical total energies. The failure of PT based energy functionals is analyzed, and its origin is traced back to near degeneracy problems due to the orbital- and eigenvalue-dependent algebraic structure of the correlation functional. The failure emerges in the self-consistent approach but not in perturbative post-EXX calculations, emphasizing the crucial importance of self-consistency in testing new orbital-dependent energy functionals.     

Performance of density functionals for modeling vapor liquid equilibria of CO2 and SO2

Vapor liquid equilibria (VLE) and condensed phase properties of carbon dioxide and sulfur dioxide are calculated using first principles Monte Carlo (FPMC) simulations to assess the performance of several density functionals, notably PBE‐D3, BLYP‐D3, PBE0‐D3, M062X‐D3, and rVV10. GGA functionals were used to compute complete vapor liquid coexistence curves (VLCCs) to estimate critical properties, while the hybrid and nonlocal van der Waals functionals were used only for computing density at a single state point due to the high computational cost. Our results show that the BLYP‐D3 functional performs well in predicting VLE properties for both molecules when compared with other functionals. In the liquid phase, pair correlation functions reveal that there is not a significant difference in the location of the peak for the first solvation shell while the peak heights are different for different functionals. Overall, the BLYP‐D3 functional is a good choice for modeling VLE of acidic gases with significant environmental implications such as CO₂ and SO₂. © 2017 Wiley Periodicals, Inc.     

Comparison of density functionals for energy and structural differences between the high- [5T2g:(t2g)4(eg)2] and low- [1A1g:(t2g)6(eg)0] spin states of iron(II) coordination compounds. II. More functionals and the hexaminoferrous cation, [Fe(NH3)6]2+

The ability of different density functionals to describe the structural and energy differences between the high- [(5)T(2g):(t(2g))(4)(e(g))(2)] and low- [(1)A(1g):(t(2g))(6)(e(g))(0)] spin states of small octahedral ferrous compounds is studied. This work is an extension of our previous study of the hexaquoferrous cation, [Fe(H(2)O)(6)](2+), [J. Chem. Phys. 120, 9473 (2004)] to include a second compound-namely, the hexaminoferrous cation, [Fe(NH(3))(6)](2+)-and several additional functionals. In particular, the present study includes the highly parametrized generalized gradient approximations (GGAs) known as HCTH and the meta-GGA VSXC [which together we refer to as highly parametrized density functionals (HPDFs)], now readily available in the GAUSSIAN03 program, as well as the hybrid functional PBE0. Since there are very few experimental results for these molecules with which to compare, comparison is made with best estimates obtained from second-order perturbation theory-corrected complete active space self-consistent field (CASPT2) calculations, with spectroscopy oriented configuration interaction (SORCI) calculations, and with ligand field theory (LFT) estimations. While CASPT2 and SORCI are among the most reliable ab initio methods available for this type of problem, LFT embodies many decades of empirical experience. These three methods are found to give coherent results and provide best estimates of the adiabatic low-spin-high-spin energy difference, DeltaE(LH) (adia), of 12 000-13 000 cm(-1) for [Fe(H(2)O)(6)](2+) and 9 000-11 000 cm(-1) for [Fe(NH(3))(6)](2+). All functionals beyond the purely local approximation produce reasonably good geometries, so long as adequate basis sets are used. In contrast, the energy splitting, DeltaE(LH) (adia), is much more sensitive to the choice of functional. The local density approximation severely over stabilizes the low-spin state with respect to the high-spin state. This "density functional theory (DFT) spin pairing-energy problem" persists, but is reduced, for traditional GGAs. In contrast the hybrid functional B3LYP underestimates DeltaE(LH) (adia) by a few thousands of wave numbers. The RPBE GGA of Hammer, Hansen, and Norskov gives good results for DeltaE(LH) (adia) as do the HPDFs, especially the VSXC functional. Surprisingly the HCTH functionals actually over correct the DFT spin pairing-energy problem, destabilizing the low-spin state relative to the high-spin state. Best agreement is found for the hybrid functional PBE0.     

一些密度泛函方法预测电子亲和势

选取了杂化泛函B3LYP, B3PW91, O3LYP, PBE0, 以及与之相对应的GGA泛函BLYP, BPW91, OLYP和PBE, 还选取了能更好地兼顾强相互作用和弱相互作用的X3LYP泛函和在预测NMR的化学位移有较好表现的OPBE泛函, 以及两种meta-GGA泛函VSXC和TPSS, 共12种泛函, 详细地考察了这些泛函在预测EA方面的准确性.