Chemical accuracy with σ-functionals for the Kohn–Sham correlation energy optimized for different input orbitals and eigenvalues (original) (raw)
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Journal of Chemical Physics, 2021
Recently, a new type of orbital-dependent functional for the Kohn-Sham (KS) correlation energy, σ-functionals, was introduced. Technically, σ-functionals are closely related to the well-known direct random phase approximation (dRPA). Within the dRPA, a function of the eigenvalues σ of the frequency-dependent KS response function is integrated over purely imaginary frequencies. In σfunctionals, this function is replaced by one that is optimized with respect to reference sets of atomization, reaction, transition state, and non-covalent interaction energies. The previously introduced σ-functional uses input orbitals and eigenvalues from KS calculations with the generalized gradient approximation (GGA) exchange-correlation functional of Perdew, Burke, and Ernzerhof (PBE). Here, σ-functionals using input orbitals and eigenvalues from the meta-GGA TPSS and the hybrid-functionals PBE0 and B3LYP are presented and tested. The number of reference sets taken into account in the optimization of the σ-functionals is larger than in the first PBE based σ-functional and includes sets with 3d-transition metal compounds. Therefore, also a reparameterized PBE based σ-functional is introduced. The σ-functionals based on PBE0 and B3LYP orbitals and eigenvalues reach chemical accuracy for main group chemistry. For the 10 966 reactions from the highly accurate W4-11RE reference set, the B3LYP based σ-functional exhibits a mean average deviation of 1.03 kcal/mol compared to 1.08 kcal/mol for the coupled cluster singles doubles perturbative triples method if the same valence quadruple zeta basis set is used. For 3d-transition metal chemistry, accuracies of about 2 kcal/mol are reached. The computational effort for the post-self-consistent evaluation of the σ-functional is lower than that of a preceding PBE0 or B3LYP calculation for typical systems.
Journal of Chemical Theory and Computation, 2007
The reliable prediction of molecular properties is a vital task of computational chemistry. In recent years, density functional theory (DFT) has become a popular method for calculating molecular properties for a vast array of systems varying in size from small organic molecules to large biological compounds such as proteins. In this work we assess the ability of many DFT methods to accurately determine atomic and molecular properties for small molecules containing elements commonly found in proteins, DNA, and RNA. These properties include bond lengths, bond angles, ground state vibrational frequencies, electron affinities, ionization potentials, heats of formation, hydrogen bond interaction energies, conformational energies, and reaction barrier heights. Calculations are carried out with the 3-21G*, 6-31G*, 3-21+G*, 6-31+G*, 6-31++G*, cc-pVxZ, and aug-cc-pVxZ (x=D,T) basis sets, while bond distance and bond angle calculations are also done using the cc-pVQZ and aug-cc-pVQZ basis sets. Members of the popular functional classes, namely, LSDA, GGA, meta-GGA, hybrid-GGA, and hybrid-meta-GGA, are considered in this work. For the purpose of comparison, Hartree-Fock (HF) and second order many-body perturbation (MP2) methods are also assessed in terms of their ability to determine these physical properties. Ultimately, it is observed that the split valence bases of the 6-31G variety provide accuracies similar to those of the more computationally expensive Dunning type basis sets. Another conclusion from this survey is that the hybrid-meta-GGA functionals are typically among the most accurate functionals for all of the properties examined in this work.
Journal of Chemical Theory and Computation, 2014
We present the WCCR10 data set of ten ligand dissociation energies of large cationic transition metal complexes for the assessment of approximate exchangecorrelation functionals. We analyze nine popular functionals, namely BP86, BP86-D3, B3LYP, B3LYP-D3, B97-D-D2, PBE, TPSS, PBE0, and TPSSh by mutual comparison and by comparison to experimental gas-phase data measured with wellknown precision. The comparison of all calculated data reveals a large, systemdependent scattering of results with nonnegligible consequences for computational chemistry studies on transition metal compounds. Considering further the comparison with experiment, the non-empirical functionals PBE and TPSS turn out to be among the best functionals for our reference data set. The deviation can be lowered further by including Hartree-Fock exchange. Accordingly, PBE0 and TPSSh are the two most accurate functionals for our test set, but also these functionals exhibit deviations from experiment by up to 50 kJ mol −1 for individual reactions. As an important result we found no functional to be reliable for all reactions. Furthermore, for some of the ligand dissociation energies studied in this work, dispersion corrections yield results which increase the deviation from experiment. This deviation increases further if structure optimization including dispersion corrections is performed. Finally, we compare our results to other benchmark studies and highlight that the performance assessed for different density functionals depends significantly on the reference molecule set chosen.
The Journal of Chemical Physics, 2007
Density functional theory optimized basis sets for gradient corrected functionals for 3d transition metal atoms are presented. Double zeta valence polarization and triple zeta valence polarization basis sets are optimized with the PW86 functional. The performance of the newly optimized basis sets is tested in atomic and molecular calculations. Excitation energies of 3d transition metal atoms, as well as electronic configurations, structural parameters, dissociation energies, and harmonic vibrational frequencies of a large number of molecules containing 3d transition metal elements, are presented. The obtained results are compared with available experimental data as well as with other theoretical data from the literature.
The Journal of Chemical Physics, 1999
The Kohn-Sham ͑KS͒ solution is constructed from an accurate CI density and the KS exchange and correlation energies E x and E c , as well as the corresponding exchange and exchange-correlation energy densities ⑀ x (r) and ⑀ xc (r), which are obtained for the hydrogen abstraction reaction HϩH 2 and the symmetrical four-center exchange reaction H 2 ϩH 2. The KS quantities are compared with those of the standard GGAs. Comparison shows that the GGA exchange functional represents both exchange and molecular nondynamical left-right correlation, while the GGA correlation functional represents only the dynamical part of the correlation. This role of the GGA exchange functional is especially important for the transition states ͑TS͒ of the reactions where the left-right correlation is enhanced. Standard GGAs tend to underestimate the barrier height for the reaction HϩH 2 and to overestimate it for the reaction H 2 ϩH 2. For H 2 ϩH 2 the Kohn-Sham orbital degeneracy in the square TS is represented with an equi-ensemble KS solution for both accurate KS/CI and GGA, while near the TS ensemble solutions with unequal occupations of the degenerate highest occupied orbitals are obtained. For the GGA ensemble solution a special ensemble formula for the GGA exchange functional is proposed. Application of this formula to the H 2 ϩH 2 reaction reduces appreciably the reaction barriers calculated with GGAs and leads to much better agreement with the accurate value. The too low GGA barriers for the HϩH 2 reaction are attributed to overestimation of the dynamical correlation in the TS by the GGA correlation functionals. In order to correct this error, it is recommended to modify the dependence of the approximate correlation functionals on the local polarization with the purpose of reducing the approximate correlation energy for intermediate values, which are expected to characterize the TS's of radical abstraction reactions.
Journal of Computational Chemistry, 2005
The performance of a number of different implementations of density functional theory (DFT) for predicting the s/d interconfigurational energies of the 3d transition metal cations is investigated. Systematic comparisons of computed results with experimental data indicate that gradient corrected correlation functionals, like the LYP GGA, efficiently correct the flaws of the LDA, but reveal shortcomings in the treatment of exchange by currently available GGAs. The admixture of exact exchange in hybrid functionals eventually leads to largely reduced errors. Several basis sets available for the 3d elements are tested in combination with the B3LYP functional. Finally, the influence of variations of the admixture of exact exchange is systematically tested. The results reveal that computed s/d excitation energies obtained for the individual ions depend in markedly different ways on the amount of exact exchange admixture and that there is no single optimal and transferable exchange parameter to create a hybrid functional that yields improved results for all ions alike. Several of the recently devised functionals perform as good as or slightly better than the B3LYP functional in the present study. But given the fact that the B3LYP functional has been identified as the most successful DFT method in an overwhelming number of systematic investigations in very many areas of chemical research, there is no persuasive motivation to recommend its replacement by one of the other functionals, as much less is known about their robustness.
The Journal of Chemical Physics, 2010
Thirty four density functional approximations are tested against two diverse databases, one with 18 bond energies and one with 24 barriers. These two databases are chosen to include bond energies and barrier heights which are relevant to catalysis, and in particular the bond energy database includes metal-metal bonds, metal-ligand bonds, alkyl bond dissociation energies, and atomization energies of small main group molecules. Two revised versions of the Perdew-Burke-Ernzerhof ͑PBE͒ functional, namely the RPBE and revPBE functionals, widely used for catalysis, do improve the performance of PBE against the two diverse databases, but give worse results than B3LYP ͑which denotes the combination of Becke's 3-parameter hybrid treatment with Lee-Yang-Parr correlation functional͒. Our results show that the Minnesota functionals, M05, M06, and M06-L give the best performance for the two diverse databases, which suggests that they deserve more attention for applications to catalysis. We also obtain notably good performance with the-HCTHhyb, B97X-D, and MOHLYP functional ͑where MOHLYP denotes the combination of the OptX exchange functional as modified by Schultz, Zhao, and Truhlar with half of the LYP correlation functional͒.
A Density Functional That Accounts for Medium-Range Correlation Energies in Organic Chemistry
Organic Letters - ORG LETT, 2006
It has recently been pointed out that current density functionals are inaccurate for computing stereoelectronic effects and energy differences of isomerization reactions and isodesmic reactions involving alkanes; this has been interpreted as an incorrect prediction of medium-range correlation energies. This letter shows that the recently published M05-2X functional has good accuracy for all three of the recently highlighted problems, and it should be useful for a wide variety of problems in organic chemistry.
Journal of Computational Chemistry, 2001
We explore the use of density functionals in calculating the equilibrium distances, dissociation energies, and harmonic vibrational frequencies of the homonuclear diatomics of the second-row transition metals, platinum, and gold. The outermost s-d interconfigurational energies (ICEs) and the outermost s and d ionization potentials (IPs) were also calculated for the second-and third-row transition metal atoms. Compared with the first-row transition metal dimer calculations (J Chem Phys 2000, 112, 545-553), the binding energies calculated using the combination of the Becke 1988 exchange and the one-parameter progressive correlation (BOP) functional and Becke's three-parameter hybrid (B3LYP) functional are in better agreement with the experiment. However, the pure BOP functional still gives the deep and narrow dissociation potential wells for the electron configurations containing high-angular-momentum open-shell orbitals. Analysis of the s-d ICEs and the s and d IPs suggests that the overestimation may be due to the insufficient long-range interaction between the outermost s and d orbitals in the exchange functional. The hybrid B3LYP functional seems to partly solve this problem for many systems by the incorporation of the Hartree-Fock exchange integral. However, this still leads to an erroneous energy gap between the configurations of fairly different spin multiplicity, probably because of the unbalance of exchange and correlation contributions.
Journal of Chemical Theory and Computation, 2014
The 3d-series transition metals (also called the fourth-period transition metals), Sc to Zn, are very important in industry and biology, but they provide unique challenges to computing the electronic structure of their compounds. In order to successfully describe the compounds by theory, one must be able to describe their components, in particular the constituent atoms and cations. In order to understand the ingredients required for successful computations with density functional theory, it is useful to examine the performance of various exchange−correlation functionals; we do this here for 4s N 3d N ′ transition-metal atoms and their cations. We analyze the results using three ways to compute the energy of the open-shell states: the direct variational method, the weighted-averaged broken symmetry (WABS) method, and a new broken-symmetry method called the reinterpreted broken symmetry (RBS) method. We find the RBS method to be comparable in accuracy with the WABS method. By examining the overall accuracy in treating 18 multiplicity-changing excitations and 10 ionization potentials with the RBS method, 10 functionals are found to have a mean-unsigned error of <5 kcal/mol, with ωB97X-D topping the list. For local density functionals, which are more practical for extended systems, the M06-L functional is the most accurate. And by combining the results with our previous studies of p-block and 4d-series elements as well as databases for alkyl bond dissociation, main-group atomization energies, and π−π noncovalent interactions, we find five functionals, namely, PW6B95, MPW1B95, M08-SO, SOGGA11-X, and MPWB1K, to be highly recommended. We also studied the performance of PW86 and C09 exchange functionals, which have drawn wide interest in recent studies due to their claimed ability to reproduce Hartree−Fock exchange at long distance. By combining them with four correlation functionals, we find the performance of the resulting functionals disappointing both for 3d transition-metal chemistry and in broader tests, and thus we do not recommend PW86 and C09 as components of generalized gradient approximations for general application. a GS − electronic state of neutral ground state; ES − electronic state of neutral excited state; ΔE − excitation energy of neutral atom, kcal/mol; GS + − electronic state of cation ground state; ES + − electronic state of cation excited state; ΔE + − excitation energy of cation, kcal/mol; IP − ionization potential, kcal/mol Journal of Chemical Theory and Computation Article dx.doi.org/10.1021/ct400712k | J. Chem. Theory Comput. 2014, 10, 102−121 Journal of Chemical Theory and Computation Article dx.doi.org/10.1021/ct400712k | J. Chem. Theory Comput. 2014, 10, 102−121 a MUE is in kcal/mol. The functionals are arranged in order of increasing MUE for the RBS method. When the MUE for RBS is the same (rounded to the nearest tenth of a kcal/mol), the order is the sum of the MUs for the variational, WABS, and RBS methods.