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     

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.     

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     

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 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.     

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.     

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.     

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.     

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.     

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.     

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.     

Theoretical study of intermolecular potential energy surface for HCl dimer: Example of nonspherical atom–atom exchange repulsion interaction

The intermolecular part of the potential energy surface for the HCl dimer has been studied with ab initio quantum chemical methods. An intermolecular potential, based on quantum chemical calculations has been constructed. The interaction energy consists of electrostatic, induction, and dispersion terms calculated from the monomer properties of the interacting molecules and an exchange repulsion term. The latter term was parameterized from the results of the quantum chemical calculations and estimates of the electrostatic and induction energies. It was found necessary to use nonspherical atom–atom exchange repulsion interaction parameters, and the parameters describing the deviation from spherical behavior could be obtained from the expectation values of r² for the electrons assigned to an atom. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1816–1825, 1998     

New exact relations for improving the exchange and correlation potentials

For the purpose of improving present approximations to the exchange and correlation potentials, newly derived properties of the exact exchange and correlation potentials are summarized. Present approximations are not expected to generally satisfy these properties. The summarized properties include relations at the Fermi level, low-density requirements, and a new density functional formula for computing ionization energies. © 1995 John Wiley & Sons, Inc.     

Influence of the exchange screening parameter on the performance of screened hybrid functionals

This work reexamines the effect of the exchange screening parameter omega on the performance of the Heyd-Scuseria-Ernzerhof (HSE) screened hybrid functional. We show that variation of the screening parameter influences solid band gaps the most. Other properties such as molecular thermochemistry or lattice constants of solids change little with omega. We recommend a new version of HSE with the screening parameter omega=0.11 bohr(-1) for further use. Compared to the original implementation, the new parametrization yields better thermochemical results and preserves the good accuracy for band gaps and lattice constants in solids.     

Imidazole-substituted oxoverdazyl radical as a mediator of intramolecular and intermolecular exchange interaction

The 3-(2'-imidazolyl)-1,5-dimethyl-6-oxoverdazyl radical (imvd(*)) and the corresponding tetrazane H3imvd were prepared and structurally characterized, the former as two different hydrates. Reaction of imvd(*) with [M(hfac)2] led to the formation of monometallic complexes [M(hfac)2(imvd(*))] (M = Ni and Mn). They were characterized by single-crystal X-ray diffraction. In the solid state, all four radical-containing compounds exhibit imidazole-oxoverdazyl pi stacking. Following the structural analysis, imvd(*) behaves as an antiferromagnetic (AF) coupled chain with J = -100 cm(-1) (H = -J summation operator SiS(i+1)). The magnetic behavior of [M(hfac)2(imvd(*))] complexes is interpreted with a four-coupled spin model with a metal ion radical intramolecular interaction (JMn = -62.5 cm(-1) and JNi = 193 cm(-1); H = -JSMSimvd) and an AF intermolecular interaction (JMn' = -12.6 cm(-1) and JNi' = -4.3 cm(-1)) related to imidazole-oxoverdazyl pi stacking.