Density Functional Theory with Fractional Orbital Occupations (original) (raw)
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Density Functional Model for Nondynamic and Strong Correlation
A single-term density functional model for the left−right nondynamic/ strong electron correlation is presented based on single-determinant Kohn−Sham density functional theory. It is derived from modeling the adiabatic connection for kinetic correlation energy based on physical arguments, with the correlation potential energy based on the Becke'13 model (Becke, A.D. J. Chem. Phys. 2013, 138, 074109). This functional satisfies some known scaling relationships for correlation functionals. The fractional spin error is further reduced substantially with a new density-functional correction. Preliminary tests with self-consistent-field implementation show that the model, with only three empirical parameters, recovers the majority of left−right nondynamic/strong correlation upon bond dissociation and performs reasonably well for atomization energies and singlet−triplet energy splittings. This study also demonstrates the feasibility of developing DFT functionals for nondynamic and strong correlation within the single-determinant KS scheme.
Some Fundamental Issues in Ground-State Density Functional Theory: A Guide for the Perplexed
Journal of Chemical Theory and Computation, 2009
Some fundamental issues in ground-state density functional theory are discussed without equations: (1) The standard Hohenberg-Kohn and Kohn-Sham theorems were proven for a Hamiltonian that is not quite exact for real atoms, molecules, and solids. (2) The density functional for the exchange-correlation energy, which must be approximated, arises from the tendency of electrons to avoid one another as they move through the electron density. (3) In the absence of a magnetic field, either spin densities or total electron density can be used, although the former choice is better for approximations. (4) "Spin contamination" of the determinant of Kohn-Sham orbitals for an open-shell system is not wrong but right. (5) Only to the extent that symmetries of the interacting wave function are reflected in the spin densities should those symmetries be respected by the Kohn-Sham noninteracting or determinantal wave function. Functionals below the highest level of approximations should however sometimes break even those symmetries, for good physical reasons. (6) Simple and commonly used semilocal (lower-level) approximations for the exchange-correlation energy as a functional of the density can be accurate for closed systems near equilibrium and yet fail for open systems of fluctuating electron number. The exact Kohn-Sham noninteracting state need not be a single determinant, but common approximations can fail when it is not. (8) Over an open system of fluctuating electron number, connected to another such system by stretched bonds, semilocal approximations make the exchange-correlation energy and hole-density sum rule too negative. (9) The gap in the exact Kohn-Sham band structure of a crystal underestimates the real fundamental gap but may approximate the first exciton energy in the large-gap limit. (10) Density functional theory is not really a mean-field theory, although it looks like one. The exact functional includes strong correlation, and semilocal approximations often overestimate the strength of static correlation through their semilocal exchange contributions. (11) Only under rare conditions can excited states arise directly from a ground-state theory.
The combination of density functional theory with multi-configuration methods – CAS-DFT
Chemical Physics Letters, 2000
CAS-DFT is presented as a method that allows an economical simultaneous treatment of static and dynamic correlation effects in molecules with multi-reference character. Central problems of CAS-DFT concern the double counting of dynamic correlation effects and the choice of the proper input quantities for the DFT functional. Also, the question of treating both active and inactive orbitals in a consistent way is discussed. Test calculations with CAS-DFT for the ring opening of dioxirane and the excitation energies of methylene prove that the method works reasonably. q 2000 Elsevier Science B.V. All rights reserved. 0009-2614r00r$ -see front matter q 2000 Elsevier Science B.V. All rights reserved.
A density difference based analysis of orbital-dependent exchange-correlation functionals
Molecular Physics, 2014
We present a density difference based analysis for a range of orbital-dependent Kohn-Sham functionals. Results for atoms, some members of the neon isoelectronic series and small molecules are reported and compared with ab initio wave-function calculations. Particular attention is paid to the quality of approximations to the exchange-only optimized effective potential (OEP) approach: we consider both the Localized Hartree Fock as well as the Krieger-Li-Iafrate methods. Analysis of density differences at the exchange-only level reveals the impact the approximations have on the resulting electronic densities. These differences are further quantified in terms of the ground state energies, frontier orbital energy differences and highest occupied orbital energies obtained. At the correlated level an OEP approach based on a perturbative second-order correlation energy expression is shown to deliver results comparable with those from traditional wave function approaches, making it suitable for use as a benchmark against which to compare standard density-functional approximations.
New Orbital-Free Approach for Density Functional Modeling of Large Molecules and
2016
Development of the orbital-free (OF) approach of the density functional theory (DFT) may result in a power instrument for modeling of complicated nanosystems with a huge number of atoms. A key problem on this way is calculation of the kinetic energy. We demonstrate how it is possible to create the OF kinetic energy functionals using results of Kohn-Sham calculations for single atoms. Calculations provided with these functionals for dimers of sp-elements of the C, Si, and Ge periodic table rows show a good accordance with the Kohn-Sham DFT results.
Annals of the New York Academy of Sciences, 2003
A BSTRACT : As molecular electronics advances, efficient and reliable computation procedures are required for the simulation of the atomic structures of actual devices, as well as for the prediction of their electronic properties. Density-functional theory (DFT) has had widespread success throughout chemistry and solid-state physics, and it offers the possibility of fulfilling these roles. In its modern form it is an empirically parameterized approach that cannot be extended toward exact solutions in a prescribed way, ab initio . Thus, it is essential that the weaknesses of the method be identified and likely shortcomings anticipated in advance. We consider four known systematic failures of modern DFT: dispersion, charge transfer, extended conjugation, and bond cleavage. Their ramifications for molecular electronics applications are outlined and we suggest that great care is required when using modern DFT to partition charge flow across electrode-molecule junctions, screen applied electric fields, position molecular orbitals with respect to electrode Fermi energies, and in evaluating the distance dependence of through-molecule conductivity. The causes of these difficulties are traced to errors inherent in the types of density functionals in common use, associated with their inability to treat very long-range electron correlation effects. Heuristic enhancements of modern DFT designed to eliminate individual problems are outlined, as are three new schemes that each represent significant departures from modern DFT implementations designed to provide a priori improvements in at least one and possible all problem areas. Finally, fully semiempirical schemes based on both Hartree-Fock and Kohn-Sham theory are described that, in the short term, offer the means to avoid the inherent problems of modern DFT and, in the long term, offer competitive accuracy at dramatically reduced computational costs.
Journal of Chemical Theory and Computation, 2009
A multistate density functional theory in the framework of the valence bond model is described. The method is based on a block-localized density functional theory (BLDFT) for the construction of valence-bond-like diabatic electronic states and is suitable for the study of electron transfer reactions and for the representation of reactive potential energy surfaces. The method is equivalent to a valence bond theory with the treatment of the localized configurations by using density functional theory (VBDFT). In VBDFT, the electron densities and energies of the valence bond states are determined by BLDFT. A functional estimate of the off-diagonal matrix elements of the VB Hamiltonian is proposed, making use of the overlap integral between Kohn-Sham determinants and the exchangecorrelation functional for the ground state substituted with the transition (exchange) density. In addition, we describe an approximate approach, in which the off-diagonal matrix element is computed by wave function theory using block-localized Kohn-Sham orbitals. The key feature is that the electron density of the adiabatic ground state is not directly computed nor used to obtain the ground-state energy; the energy is determined by diagonalization of the multistate valence bond Hamiltonian. This represents a departure from the standard single-determinant Kohn-Sham density functional theory. The multistate VBDFT method is illustrated by the bond dissociation of and a set of three nucleophilic substitution reactions in the DBH24 database. In the dissociation of , the VBDFT method yields the correct asymptotic behavior as the two protons stretch to infinity, whereas approximate functionals fail badly. For the S N 2 nucleophilic substitution reactions, the hybrid functional B3LYP severely underestimates the barrier heights, while the approximate two-state VBDFT method overcomes the self-interaction error, and overestimates the barrier heights. Inclusion of the ionic state in a three-state model, VBDFT(3), significantly improves the computed barrier heights, which are found to be in accord with accurate results. The BLDFT method is a versatile theory that can be used to analyze conventional DFT results to gain insight into chemical bonding properties, and it is illustrated by examining the intricate energy contributions to the ion-dipole complex stabilization.
A quantum chemical view of density functional theory
The Journal of Physical Chemistry …, 1997
A comparison is made between traditional quantum chemical approaches to the electron correlation problem and the one taken in density functional theory (DFT). Well-known concepts of DFT, such as the exchangecorrelation energy E xc ) ∫F(r) xc (r) dr and the exchange-correlation potential V xc (r) are related to electron correlation as described in terms of density matrices and the conditional amplitude (Fermi and Coulomb holes). The Kohn-Sham one-electron or orbital model of DFT is contrasted with Hartree-Fock, and the definitions of exchange and correlation in DFT are compared with the traditional ones. The exchangecorrelation energy density xc (r) is decomposed into kinetic and electron-electron potential energy components, and a practical way of calculating these from accurate wave functions is discussed, which offers a route to systematic improvement. V xc (r) is likewise decomposed, and special features (bond midpoint peak, various types of step behavior) are identified and related to electronic correlation. X Figure 4. Correlation energy density in He compared to a number of model correlation energy densities: PW, Perdew-Wang; 11 WL, Wilson-Levy; 127 LYP, Lee-Yang-Parr; 8 LW, local Wigner. 126 (a) -F(r) c(r) from r ) 0.0-0.5 bohr. (b) -4π r 2 F(r) c(r) from r ) 0.0-2.0 bohr. Feature Article
The Journal of Chemical Physics, 2008
A recently proposed series of corrections to the earliest JK-only functionals has considerably improved the prospects of density matrix functional theory ͑DMFT͒. Still, the most advanced of these functionals ͑correction C3͒ requires a preselection of the terms in the pair density ⌫͑r 1 , r 2 ͒ involving the bonding and antibonding natural orbitals ͑NOs͒ belonging to an electron pair bond. Ideally, a DMFT functional should only depend on the NOs and their occupation numbers, and we propose a functional with an occupation number driven weighing of terms in the pair density. These are formulated as "damping" for certain ranges of occupation numbers of the two-electron cumulant that arises in the expansion of the two-particle density matrix of the paradigmatic two-electron system. This automatic version of C3, which we denote AC3, provides the correct dissociation limit for electron pair bonds and it excellently reproduces the potential energy curves of the multireference configuration interaction ͑MRCI͒ method for the dissociation of the electron pair bond in the series of the ten-electron hydrides CH 4 , NH 3 , H 2 O, and HF. AC3 reproduces closely the experimental equilibrium distances and at R e it yields correlation energies of the ten-electron systems with an average error in the absolute values of only 3.3% compared to the MRCI values. We stress the importance of treatment of strong correlation cases ͑NO occupation numbers differing significantly from 2.0 and 0.0͒ by appropriate terms in the cumulant.