A Simple Coupling Scheme between Hartree−Fock and Local Spin-Density Functional Theories

Abstract

A simple coupling scheme between nonlocal Hartree−Fock exchange, gradient corrected local spin-density exchange, and the Pade approximated Vosko, Wilk, and Nusair correlation functional is reported. The combination of these functionals with the electrons kinetic and Coulomb repulsion terms yields a method that scales as ∼N 3, where N is the number of basis functions, compared to ∼N 7 for Gaussian-2 (G2) ab initio theory and ∼N 4 and ∼N 5 for Becke's B3LYP and Bx88/Bc95 density functional approaches. The reported method is denoted by HFS−BVWN, which stands for Hartree−Fock−Slater−Becke−Vosko−Wilk−Nusair. The results of HFS−BVWN/6-311+g(3df, p) computations on atoms of the first two rows of the periodic table, hydrogen−argon, and selected small molecules showed that the method underestimates atomic and molecular exchange-correlation (XC) energies by ∼ 0.13% and 0.14%, respectively. We demonstrated that the application of Dewar's atom equivalent scheme to atomic energies partially compensated for the errors in XC energies. Atom equivalents for hydrogen through chlorine, excluding the noble gases, were derived. In a data set comprised of 150 atomic and molecular species, the reported method achieved average absolute errors of 1.8 kcal/mol and 0.12 and 0.13 eV for room temperature heats of formation, ionization potentials, and electron affinities, respectively. The overall average absolute error of HFS−BVWN method, 2.5 kcal/mol, is thus within 0.5 kcal/mol from the corresponding accuracies of G2 and Bx88/Bc95 theories, 2 kcal/mol, and superior to the B3LYP (3.5 kcal/mol) and BLYP (3.9 kcal/mol) methods. The HFS−BVWN/6-311+g(3df, p) level of theory is much less computer intensive than the G2, B3LYP, and Bx88/Bc95 theories and, thus, may be applicable to larger molecular systems than those attainable by the latter approaches.

DFT Study of the NMR Properties of Xenon in Covalent Compounds and van der Waals Complexes—Implications for the Use of 129Xe as a Molecular Probe

“…[16,17] Among these, we note that GIAO-HF calculations of xenon shifts in Xe@C 60 , as well as an MP2 calculation for the Xe ¥¥¥ benzene complex at a selected distance, have been reported. [18] Recently, the HF-level calculation of xenon shifts in xenon dimers and other simple van der Waals complexes have also been reported, [19] with the aim of modelling the NMR properties of xenon in nanochannels.…”

“…[13] e) Exploiting isotope shifts of xenon caged in a deuterated cryptophane. [14] f) Study of Xe@C 60 , for which an experimental 129 Xe NMR spectrum has been obtained. [15] [a] Prof. A. Bagno Dipartimento di Chimica Organica Universita ¡ di Padova Via Marzolo, 1, 35131 Padova (Italy) Fax: ( 39) 0498275239 E-mail: alessandro.bagno@unipd.it…”

Computation of the Electronic and Spectroscopic Properties of Carbohydrates Using Novel Density Functional and Vibrational Self-Consistent Field Methods

“…35 ' 36 In the K2-BVWN scheme, the total exchange-correlation energy functional, Exc, was approximated by a sum of two terms. Namely, an exchange component, Ex, and a correlation term, Ec.…”

“…The Ex term consisted of a hybrid mixture of 37.5% exact exchange and the appropriate local spin density exchange using the adiabatic connection formula. 35 On the other hand, the Ec component was a linear combination of the Vosko, Wilk and Nusair (VWN) correlation energy functional of the free electron gas, Ec(VWN), 34 and a generalized gradient approximation (GGA) term containing one adjustable parameter, as described in detail elsewhere. 35 -36 The K2BVWN method has previously been applied to the calculation of room temperature heats of formation, ionization potentials, electron and proton-affinities of 350 Downloaded by [Australian National University] at 14:31 01 June 2016 molecular systems, including the G2 database of Curtiss et al 41 The overall performance of the K2-BVWN methodology was comparable to the accurate G2 ab initio theory, 41 with a total average error in computed electronic and thermodynamic properties of 1.4 kcal/mol.…”

“…35 -36 The K2BVWN method has previously been applied to the calculation of room temperature heats of formation, ionization potentials, electron and proton-affinities of 350 Downloaded by [Australian National University] at 14:31 01 June 2016 molecular systems, including the G2 database of Curtiss et al 41 The overall performance of the K2-BVWN methodology was comparable to the accurate G2 ab initio theory, 41 with a total average error in computed electronic and thermodynamic properties of 1.4 kcal/mol. 35 ' 36 The main advantage of the K2-BVWN methodology over G2-theory is in its A* 3 scaling, where N is the number of basis functions, compared to JV 7 for G2-theory.…”