Scaled density functional theory correlation functionals

We show that a simple one-parameter scaling of the dynamical correlation energy estimated by the density functional theory (DFT) correlation functionals helps increase the overall accuracy for several local and nonlocal functionals. The approach taken here has been described as the "scaled dynamical correlation" (SDC) method [Ramachandran, J. Phys. Chem. A 2006, 110, 396], and its justification is the same as that of the scaled external correlation (SEC) method of Brown and Truhlar. We examine five local and five nonlocal (hybrid) DFT functionals, the latter group including three functionals developed specifically for kinetics by the Truhlar group. The optimum scale factors are obtained by use of a set of 98 data values consisting of molecules, ions, and transition states. The optimum scale factors, found with a linear regression relationship, are found to differ from unity with a high degree of correlation in nearly every case, indicating that the deviation of calculated results from the experimental values are systematic and proportional to the dynamic correlation energy. As a consequence, the SDC scaling of dynamical correlation decreases the mean errors (signed and unsigned) by significant amounts in an overwhelming majority of cases. These results indicate that there are gains to be realized from further parametrization of several popular exchange-correlation functionals.     

Embedding wave function theory in density functional theory

We present a framework for embedding a highly accurate coupled-cluster calculation within a larger density functional calculation. We use a perturbative buffer to help insulate the coupled-cluster region from the rest of the system. Regions are defined, not in real space, but in Hilbert space, though connection between the two can be made by spatial localization of single-particle orbitals. Relations between our embedding approach and some similar techniques are discussed. We present results for small sample systems for which we can extract essentially exact results, demonstrating that our approach seems to work quite well and is generally more reliable than some of the related approaches due to the introduction of additional interaction terms.     

Scaling dynamical correlation energy from density functional theory correlation functionals

The scaling of dynamical correlation energy in molecules obtained by the correlation functionals of density functional theory (DFT) is examined. The approach taken is very similar to the scaled external correlation method of Brown and Truhlar but is based on the observation that DFT correlation functionals, especially the LYP, appear to represent the dynamical portion of the correlation energy in molecules. We examine whether higher accuracy in atomization energies can be gained by scaling without significant deterioration of the structural and spectroscopic properties of the molecules using four DFT functionals (BLYP, OLYP, B3LYP, and O3LYP) on 19 molecules including the six molecule AE6 database, the latter being representative of a much larger, 109 molecule training set. We show that, with molecule specific scale factors, nearly perfect agreement with experiment can be achieved in atomization energies without increasing the average errors in other molecular properties relative to the DFT calculation. We further show that it is possible to find optimal scale factors which reduce the mean unsigned error per bond to levels comparable to those of some multilevel multicoefficient methods.     

Anharmonic analysis of the vibrational spectrum of ketene by density functional theory using second-order perturbative approach

The paper reports main results of a comprehensive study of the vibrational spectrum of ketene computed using second-order perturbation theory treatment based on quartic, cubic and semidiagonal quartic force constants. Two different models--a homogeneous model using the same density functionals and basis functions for the harmonic calculations and anharmonic corrections, and a hybrid model in which the two parts of the calculation are conducted using different density functionals and basis sets--have been employed in the present calculations. Different DFT and CCSD methods and DZ and TZ extended basis sets involving diffuse and polarization functions have been used to calculate optimized and vibrationally averaged geometrical parameters, the harmonic and anharmonic vibrational frequencies and the spectroscopic constants such as anharmonicity constants, rotational constants, rotation-vibration coupling constants, Nielsen's centrifugal distortion constants and Coriolis coupling constants. Homogeneous model is found to be superior to the hybrid model in several respects. Difficulties in the hybrid model may arise due to one of the following reasons: (a) the basic requirement that the geometry optimization and frequency calculations must be done at the same level of theory to have valid frequencies is not met in the hybrid model; (b) the molecular structure gets reoptimized at the low level for anharmonic corrections; (c) in addition, the perturbation could also diverge for the above reasons, particularly for the very low, very anharmonic terms where the harmonic approximation is not close enough to make the perturbation work.     

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.     

Exchange and correlation energy in density functional theory

Several different versions of density functional theory (DFT) that satisfy Hohenberg–Kohn theorems are characterized by different definitions of a reference or model state determined by an N‐electron ground state. A common formalism is developed in which exact Kohn–Sham equations are derived for standard Kohn–Sham theory, for reference‐state density functional theory, and for unrestricted Hartree–Fock (UHF) theory considered as an exactly soluble model Hohenberg–Kohn theory. A natural definition of exchange and correlation energy functionals is shown to be valid for all such theories. An easily computed necessary condition for the locality of exchange and correlation potentials is derived. While it is shown that in the UHF model of DFT the optimized effective potential (OEP) exchange satisfies this condition by construction, the derivation shows that this condition is not, in general, sufficient to define an exact local exchange potential. It serves as a test to eliminate proposed local potentials that are not exact for ground states. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 77: 521–525, 2000     

Phase-space approach to dynamical density functional theory

The authors consider a system of interacting particles subjected to Langevin inertial dynamics and derive the governing time-dependent equation for the one-body density. They show that, after suitable truncations of the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy, and a multiple time scale analysis, they obtain a self-consistent equation involving only the one-body density. This study extends to arbitrary dimensions previous work on a one-dimensional fluid and highlights the subtleties of kinetic theory in the derivation of dynamical density functional theory.     

Hartree-Fock与密度泛函混合处理中的电子自相关和自旋平行相关问题

电子气近似中的电子相关能与量子化学中的Hartree-Fock相关能在定义上不相互等同。作者从假想的、含N个电子的"有限电子气"出发, 通过比较这类体系与无限电子气在物理模型上的差异, 合理地把电子气相关能定量地分解为单电子自相关、电子自旋平行相关以及Hartree-Fock相关三个部分。并阐明了各组分的构成随N的变化规律。在此基础上建立的Hartree-Fock与密函混合处理方案, 无须借助任何经验参数, 仅通过简捷的计算即可实现原子和分子的相关能校正。平均误差为4.2%, 优于CI-SD和MP4等Hartree-Fock处理的结果。     

密度泛函理论与Hartree-Fock方法混合处理中的稳态相关能校正

本文分析了通常的Hartree-Fock(HF)相关能定义和密度泛函理论(DFT)中的相关能定义的等价性条件。认为在参考电子密度与真实密度相差很大时两种定义是不等价的, 严格的DFT相关能比HF相关能(绝对值)要大。而在DFT与HF混合处理中得到的相关能比HF相关能(绝对值)要小, 两者之差相当于稳态相关能。实际计算表明, 通过合理地选择组态, 采用有限CI可以求得这一差值。本文描绘了双原子分子H2(X^1∑g^+), HF(X^1∑^+), N2(X^1∑g^+)的势能曲线, 结果比完全CISD和MP4的曲线还要好。H2的离解能是0.17a.u., 逼近实验值0.1747a.u..。     

Solvent effect on stabilization energy: An approach based on density functional reactivity theory

In the present article a formalism and the corresponding computational method is developed to take care of the variation of stabilization energy with solvent polarity in the process of adduct formation. For this purpose, a simple but physically insightful definition of “net desolvation energy” is proposed keeping in mind the sequence of events taking place in the process of adduct formation in a solvent. The approach used here is based on density functional reactivity theory (DFRT) and the representative samples chosen are adduct formation between (a) methyltrioxorhenium (MTO) and pyridine and (b) (azidomethyl)benzene and methylpropiolate. The generated data in case (a) is correlated with already known experimental parameter that is, formation constant (K_f). The observed trends claim that with the increase in solvent polarity interaction (or stabilization) energy becomes less negative which means that on increasing the solvent polarity the chances of adduct formation are less. This is further supported by calculating hardness values of adducts in different solvents which goes on decreasing with the increase in solvent polarity. Here, the computed data show that on increasing the polarity (i.e., dielectric constant) of the solvent, the “net desolvation energy” increases. Finally, when “net desolvation energy” is added to the stabilization energy obtained from DFRT the predicted trends are achieved.     

Approximate scaling properties of the density functional theory Tc for atoms

Revealed are scaling properties for T(c)[rho], the kinetic-energy component of the correlation energy density functional for atoms, in terms of the total number of electrons N, the nuclear charge Z, and the total electron density at the nucleus rho(0). T(c) scales well as Nrho(0)/Z(8/3) for both neutral atoms up to Z=18 and the four-electron Be-like cationic species. A model is given that describes these findings, involving a density encoding the cusp information and an effective potential going like r(-4/3).     

Exact exchange-only density functional theory by means of local scaling transformations

The density-constrained variation of the kinetic energy of a non-interacting system carried out within the framework of local-scaling transformations is employed in the present work for the purpose of determining exchange-only Kohri Sham orbitals for the beryllium atom as well as the Kohn-Sham exchange-only correlation potential. The starting basis functions are those of Clementi-Roetti and Raffenetti-types. We have also performed an optimization via a densitydriven method. The resulting exchange-only potentials for the examples studied are almost indistinguishable from the Talman-Shadwick potential for the beryllium atom.     

The chemical Hamiltonian approach in density functional theory

The chemical Hamiltonian approach (CHA) for handling the basis set superposition error problem in intermolecular interactions has been implemented within density functional theory (DFT) using Gaussian atomic basis sets. As test examples, the potential curves of the water dimer were calculated using the Vosko-Wilk-Nusair, Becke-Perdew and Perdew exchange-correlation functionals. Comparisons with the counterpoise correction method show that CHA within DFT performs as well as previously for Hartree-Fock.     

Time-dependent density functional theory based Ehrenfest dynamics

Time-dependent density functional theory based Ehrenfest dynamics with atom-centered basis functions is developed in present work. The equation of motion for electrons is formulated in terms of first-order reduced density matrix and an additional term arises due to the time-dependence of basis functions through their dependence on nuclear coordinates. This time-dependence of basis functions together with the imaginary part of density matrix leads to an additional term for nuclear force. The effects of the two additional terms are examined by studying the dynamics of H(2) and C(2)H(4), and it is concluded that the inclusion of these two terms is essential for correct electronic and nuclear dynamics.     

Exchange and correlation in density functional theory and quantum chemistry

The nature of exchange, dynamic correlation (DC) and left–right correlation (LRC) is considered in density functional theory and wavefunction‐based quantum chemistry. The presence of LRC in approximate exchange density functionals is highlighted and the separation of LRC and DC is considered. For H₂, the Heitler–London approach is shown to include the essential elements of exchange and LRC. The arguments are illustrated by a comparison of Gaussian orbital s‐optimised Heitler–London and OPTX potential energy curves. They agree well near equilibrium, but differ at large distances due to the inability of the OPTX form to describe the dissociation process. LRC and DC values determined using the two approaches are compared. The influence of higher angular momentum functions in the Heitler–London approach is then investigated (commonly called self‐consistent valence bond); the agreement with OPTX degrades, leading to a larger value of LRC and a smaller value of DC at H₂ equilibrium. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Core-valence correlation potentials based on density functional theory. Applications to valence-electron-only calculations on Na and K diatomics

The core-valence correlation potential has been derived for Na and K employing atomic calculations which make use of the density functional formula worked out by Lee, Yang and Parr based on Colle-Salvetti approach. The numerical potential is fitted with a small number of Gaussians leading to a very simple expression for an one-electron corevalence correlation operator? _cv . The core-valence correlation corrections can be computed by applying? _cv on a quite general class of wavefunctions. Applications of the? _cv operator within the framework of valence-electron-only calculations using effective Hamiltonians are presented for Na and K atoms, for Na₂, K₂, NaK and their cations. Almost all the corrections calculated for the physical properties due to the core-valence correlation lead to results which are in good agreement with those obtained from much more sophisticated treatments and experimental data.