Hybrid exchange correlation functionals and potentials: Concept elaboration

This paper deals with hybrid functionals that contain exact exchange energy and are the most popular and effective functionals in modern density functional theory. Emphasis is laid on generalization of the notion of a “hybrid functional,” which arises from the introduction of the spatial dependence of the exact exchange admixture (local hybrid functionals). Problems inherent in hybrid functionals are considered along with problems inherent in a wider class of so-called orbital-dependent functionals. In particular, the technique for constructing the local and multiplicative potentials, including the optimized effective potential method, is considered in detail. The theoretical approaches under study are illustrated by calculations of atomization molecular energies and magnetic resonance parameters.     

Short-range exchange and correlation energy density functionals: beyond the local-density approximation

We propose approximations which go beyond the local-density approximation for the short-range exchange and correlation density functionals appearing in a multideterminantal extension of the Kohn-Sham scheme. A first approximation consists of defining locally the range of the interaction in the correlation functional. Another approximation, more conventional, is based on a gradient expansion of the short-range exchange-correlation functional. Finally, we also test a short-range generalized-gradient approximation by extending the Perdew-Burke-Ernzerhof exchange-correlation functional to short-range interactions.     

The inclusion of electron correlation in intermolecular potentials: applications to the formamide dimer and liquid formamide

A test of the quality of the electrostatic properties and polarizabilities used in the nonempirical molecular orbital (NEMO) potential is carried out for formamide by calculating the molecular dipole moment and polarizability at the second-order M?ller–Plesset (MP2) level of theory. The molecular dipole moment is 11% lower at the MP2 level than at the Hartree–Fock (HF) level, whereas the isotropic part of the polarizability is increased by 36% by adding electron correlation and using a considerably larger basis set. The atomic charges, dipole moments and polarizabilities obtained at the HF level are rescaled to get the correct molecular properties at the MP2 level. The potential minimum for the cyclic dimer of formamide is −17.50 kcal/mol with the MP2-scaled properties and is significantly lower than other potentials give. Two intermolecular potentials are constructed and used in subsequent molecular dynamics simulations: one with the regular NEMO potential and the other with the rescaled MP2 properties. A damping of the electrostatic field at short intermolecular distances is included in the present NEMO model. The average energies for liquid formamide are lower for the MP2-scaled model and are in good agreement with experimental results. The lowering of the simulation energy for the MP2-scaled potential indicates the strong dispersive interactions in liquid formamide. Received: 20 March 2000 / Accepted: 18 April 2000 / Published online: 18 August 2000     

Molecular dynamics simulations of fluid methane properties using ab initio intermolecular interaction potentials

Intermolecular interaction energy data for the methane dimer have been calculated at a spectroscopic accuracy and employed to construct an ab initio potential energy surface (PES) for molecular dynamics (MD) simulations of fluid methane properties. The full potential curves of the methane dimer at 12 symmetric conformations were calculated by the supermolecule counterpoise‐corrected second‐order Møller‐Plesset (MP2) perturbation theory. Single‐point coupled cluster with single and double and perturbative triple excitations [CCSD(T)] calculations were also carried out to calibrate the MP2 potentials. We employed Pople's medium size basis sets [up to 6‐311++G(3df, 3pd)] and Dunning's correlation consistent basis sets (cc‐pVXZ and aug‐cc‐pVXZ, X = D, T, Q). For each conformer, the intermolecular carbon–carbon separation was sampled in a step 0.1 Å for a range of 3–9 Å, resulting in a total of 732 configuration points calculated. The MP2 binding curves display significant anisotropy with respect to the relative orientations of the dimer. The potential curves at the complete basis set (CBS) limit were estimated using well‐established analytical extrapolation schemes. A 4‐site potential model with sites located at the hydrogen atoms was used to fit the ab initio potential data. This model stems from a hydrogen–hydrogen repulsion mechanism to explain the stability of the dimer structure. MD simulations using the ab initio PES show quantitative agreements on both the atom‐wise radial distribution functions and the self‐diffusion coefficients over a wide range of experimental conditions. © 2008 Wiley Periodicals, Inc. J Comput Chem 2009     

Theoretical study on intermolecular interaction of epoxyethane dimer

Ab initio calculations at Hartree–Fock and fourth‐order Mø ller–Plesset (MP4) correlation correction levels with 6‐31G* basis set have been performed on the epoxyethane dimer. Dimer binding energies have been corrected for the basis set superposition error (BSSE) and the zero‐point energy. The greatest corrected dimer binding energy is −8.36 kJ/mol at the MP4/6‐31G*//HF/6‐31G* level. The natural bond orbital analysis has been performed to trace the origin of the weak interactions that stabilize dimer. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 78: 94–98, 2000     

General performance of density functionals

The density functional theory (DFT) foundations date from the 1920s with the work of Thomas and Fermi, but it was after the work of Hohenberg, Kohn, and Sham in the 1960s, and particularly with the appearance of the B3LYP functional in the early 1990s, that the widespread application of DFT has become a reality. DFT is less computationally demanding than other computational methods with a similar accuracy, being able to include electron correlation in the calculations at a fraction of time of post-Hartree-Fock methodologies. In this review we provide a brief outline of the density functional theory and of the historic development of the field, focusing later on the several types of density functionals currently available, and finishing with a detailed analysis of the performance of DFT across a wide range of chemical properties and system types, reviewed from the most recent benchmarking studies, which encompass several well-established density functionals together with the most recent efforts in the field. Globally, an overall picture of the level of performance of the plethora of currently available density functionals for each chemical property is drawn, with particular attention being dedicated to the relative performance of the popular B3LYP density functional.     

Comparison of the performance of various gradient-corrected exchange and correlation functionals in density functional theory: Case studies of CO and N2O molecules

An investigation of the influence of various gradient-corrected exchange and correlation functionals on the bond lengths and dipole moments of CO and N₂O has been carried out using density functional theory. It is shown that whereas some functionals are found to be more sensitive to the basis set quality than are others, the more commonly used gradient-corrected functionals lead to properties in very good agreement with experiment provided that a sufficiently large basis set is employed. © 1995 John Wiley & Sons, Inc.     

A theoretical study on the intermolecular interaction of energetic system-Nitromethane dimer

Three optimized geometries of nitromethane dimer have been obtained at the HF/6-31G level.Dimer binding energies have been corrected for the basis set superposition error (BSSE) and the zero point energy.Computed results indicate that the cyclic structure of (CH3NO2)2 is the most stable of three optimized geometries,whose corrected binding energyis 17.29 kJ mol-1 at the MP4SDTQ/6-31G//HF/6-31G level.In the optimized structures of nitromethane dimer,the inter-molecular hydrogen bond has not been found; and the charge-transfer interaction between CH3NO2 subsystems is weak; and the correlation interaction energy makes a little contribution to the intermolecular interaction energy of the dimer.     

A note on the AB initio calculation of intermolecular potentials: the HF dimer

Large scale SCF and CEPA PNO calculations have been performed for the HF dimer. The geometry has been optimized at the SCF level. Stabilization energies and harmonic force constants have been computed and compared with previous results.     

Calculation of intermolecular interactions in the benzene dimer using coupled-cluster and local electron correlation methods

Potential energy curves for the parallel-displaced, T-shaped and sandwich structures of the benzene dimer are computed with density fitted local second-order M?ller-Plesset perturbation theory (DF-LMP2) as well as with the spin-component scaled (SCS) variant of DF-LMP2. While DF-LMP2 strongly overestimates the dispersion interaction, in common with canonical MP2, the DF-SCS-LMP2 interaction energies are in excellent agreement with the best available literature values along the entire potential energy curves. The DF-SCS-LMP2 dissociation energies for the three structures are also compared with new complete basis set estimates of the interaction energies obtained from accurate coupled cluster (CCSD(T)) and DF-SCS-MP2 calculations. Since LMP2 is essentially free of basis set superposition errors, counterpoise corrections are not required. As a result, DF-SCS-LMP2 is computationally inexpensive and represents an attractive method for the study of larger pi-stacked systems such as truncated sections of DNA.     

Investigation of the intermolecular interaction in the ethylene dimer by a modified CNDO method

The interaction energy of the ethylene dimer has been calculated for two orientations of the molecules in a modified CNDO method with consideration of the superposition error of the basis set. A comparison with the results of perturbationtheory calculations and nonempirical calculations has been made. The satisfactory agreement between these results and a significant improvement over the CNDO/2 method has been noted.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 21, No. 5, pp. 529–535, September–October, 1985.     

Nonlocal functionals for exchange and correlation in density functional theory: Application to atoms and to small atomic clusters

The local density approximation (LDA ) to exchange and correlation effects has well-known limitations. The nonlocal weighted density approximation (WDA ) corrects some of those defects. This is illustrated here by applications to free atoms and small atomic clusters. The WDA also induces a nonlocal kinetic energy functional that is tested for atoms. © 1995 John Wiley & Sons, Inc.     

Photodissociation spectrum of cyanobenzene dimer cation. Absence of intermolecular resonance interaction

Electronic spectra of a homo-molecular dimer cation, (C₆H₅CN)₂ ⁺, are measured by photodissociation spectroscopy in the gas phase. Broad features appeared in the 450–650 nm region are characteristic of π₃ → π_CN transitions of the C₆H₅CN⁺ chromophore. No intense band is observed in the 650–1300 nm region, where other aromatic dimer cations usually show charge resonance bands. Two component molecules of (C₆H₅CN)₂ ⁺ cannot take a parallel sandwich configuration suitable for the resonance interaction, because of geometrical constraints due to other stronger interactions.     

Avoiding singularity problems associated with meta-GGA (generalized gradient approximation) exchange and correlation functionals containing the kinetic energy density

Convergence problems of meta-GGA (generalized gradient approximation) XC (exchange and correlation) functionals containing a self-interaction correction term are traced back to a singularity of the latter that occurs at critical points of the electron density. This is demonstrated for the bond critical point of equilibrium and stretched H2. A simple remedy is suggested that cures meta-XC functionals such as VSXC, TPSS, M05, M06, and their derivatives without extra cost.     

The importance of middle-range Hartree-Fock-type exchange for hybrid density functionals

Hybrid functionals are responsible for much of the utility of modern Kohn-Sham density functional theory. When rigorously applied to solid-state metallic and small band gap systems, however, the slow decay of their nonlocal Hartree-Fock-type exchange makes hybrids computationally challenging and introduces unphysical effects. This can be remedied by using a range-separated hybrid which only keeps short-range nonlocal exchange, as in the functional of Heyd et al. [J. Chem. Phys. 118, 8207 (2003)]. On the other hand, many molecular properties require full long-range nonlocal exchange, which can also be included by means of a range-separated hybrid such as the recently introduced LC-omegaPBE functional [O. A. Vydrov and G. E. Scuseria, J. Chem. Phys. 125, 234109 (2006)]. In this paper, we show that a three-range hybrid which mainly includes middle-range Hartree-Fock-type exchange and neglects long- and short-range Hartree-Fock-type exchange yields excellent accuracy for thermochemistry, barrier heights, and band gaps, emphasizing that the middle-range part of the 1/r potential seems crucial to accurately model these properties.     

Comparative analysis of the performance of commonly available density functionals in the determination of geometrical parameters for zinc complexes

A set of 44 Zinc‐ligand bond‐lengths and of 60 ligand‐metal‐ligand bond angles from 10 diverse transition‐metal complexes, representative of the coordination spheres of typical biological Zn systems, were used to evaluate the performance of a total of 18 commonly available density functionals in geometry determination. Five different basis sets were considered for each density functional, namely two all‐electron basis sets (a double‐zeta and triple‐zeta formulation) and three basis sets including popular types of effective‐core potentials: Los Alamos, Steven‐Basch‐Krauss, and Stuttgart‐Dresden. The results show that there are presently several better alternatives to the popular B3LYP density functional for the determination of Zn‐ligand bond‐lengths and angles. BB1K, MPWB1K, MPW1K, B97‐2 and TPSS are suggested as the strongest alternatives for this effect presently available in most computational chemistry software packages. In addition, the results show that the use of effective‐core potentials (in particular Stuttgart‐Dresden) has a very limited impact, in terms of accuracy, in the determination of metal‐ligand bond‐lengths and angles in Zinc‐complexes, and is a good and safe alternative to the use of an all‐electron basis set such as 6‐31G(d) or 6‐311G(d,p). © 2009 Wiley Periodicals, Inc. J Comput Chem 2009     

An application of correlation energy density functionals to atoms and molecules

Four density functionals — including that recently introduced by Perdew ((1986) Phys Rev B33: 8822)—are tested for first-row atoms, hydrides and dimers. Calculated contributions of the correlation energy to the ionization potentials and electron affinities of atoms and to the dissociation energies of molecules are compared with empirical values which were reevaluated for this purpose. An improvement over Hartree-Fock is found in all cases if the self-interaction or the gradient correction are included in the density functional, although there is a rather large variation in the accuracy of the predictions.