The method of dispersion correction as an add-on to standard Kohn-Sham density functional theory (DFT-D) has been refined regarding higher accuracy, broader range of applicability, and less empiricism. The main new ingredients are atom-pairwise specific dispersion coefficients and cutoff radii that are both computed from first principles. The coefficients for new eighth-order dispersion terms are computed using established recursion relations. System (geometry) dependent information is used for the first time in a DFT-D type approach by employing the new concept of fractional coordination numbers (CN). They are used to interpolate between dispersion coefficients of atoms in different chemical environments. The method only requires adjustment of two global parameters for each density functional, is asymptotically exact for a gas of weakly interacting neutral atoms, and easily allows the computation of atomic forces. Three-body nonadditivity terms are considered. The method has been assessed on standard benchmark sets for inter- and intramolecular noncovalent interactions with a particular emphasis on a consistent description of light and heavy element systems. The mean absolute deviations for the S22 benchmark set of noncovalent interactions for 11 standard density functionals decrease by 15%-40% compared to the previous (already accurate) DFT-D version. Spectacular improvements are found for a tripeptide-folding model and all tested metallic systems. The rectification of the long-range behavior and the use of more accurate C(6) coefficients also lead to a much better description of large (infinite) systems as shown for graphene sheets and the adsorption of benzene on an Ag(111) surface. For graphene it is found that the inclusion of three-body terms substantially (by about 10%) weakens the interlayer binding. We propose the revised DFT-D method as a general tool for the computation of the dispersion energy in molecules and solids of any kind with DFT and related (low-cost) electronic structure methods for large systems.

http://dns2.asia.edu.tw/~ysho/YSHO-English/1000%20WC/PDF/J%20Che%20Phy132,%20154104.pdf

A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu

Multiwfn is a multifunctional program for wavefunction analysis. Its main functions are: (1) Calculating and visualizing real space function, such as electrostatic potential and electron localization function at point, in a line, in a plane or in a spatial scope. (2) Population analysis. (3) Bond order analysis. (4) Orbital composition analysis. (5) Plot density-of-states and spectrum. (6) Topology analysis for electron density. Some other useful utilities involved in quantum chemistry studies are also provided. The built-in graph module enables the results of wavefunction analysis to be plotted directly or exported to high-quality graphic file. The program interface is very user-friendly and suitable for both research and teaching purpose. The code of Multiwfn is substantially optimized and parallelized. Its efficiency is demonstrated to be significantly higher than related programs with the same functions. Five practical examples involving a wide variety of systems and analysis methods are given to illustrate the usefulness of Multiwfn. The program is free of charge and open-source. Its precompiled file and source codes are available from http://multiwfn.codeplex.com.

Multiwfn: a multifunctional wavefunction analyzer.

Dispersion corrections to standard Kohn–Sham density functional theory (DFT) are reviewed. The focus is on computationally efficient methods for large systems that do not depend on virtual orbitals or rely on separated fragments. The recommended approaches (van der Waals density functional and DFT-D) are asymptotically correct and can be used in combination with standard or slightly modified (short-range) exchange–correlation functionals. The importance of the dispersion energy in intramolecular cases (conformational problems and thermochemistry) is highlighted. © 2011 John Wiley & Sons, Ltd. WIREs Comput Mol Sci 2011 1 211-228 DOI: 10.1002/wcms.30

Density functional theory with London dispersion corrections

Density functional theory (DFT) is an incredible success story. The low computational cost, combined with useful (but not yet chemical) accuracy, has made DFT a standard technique in most branches of chemistry and materials science. Electronic structure problems in a dazzling variety of fields are currently being tackled. However, DFT has many limitations in its present form: too many approximations, failures for strongly correlated systems, too slow for liquids, etc. This perspective reviews some recent progress and ongoing challenges.

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Perspective on density functional theory

Density functional theory has been spectacularly successful in physics, chemistry, and related fields, and it keeps finding new applications. This paper gives an overview of the history of the method and its many applications since it gained wide acceptance, as well as a discussion of its likely future.

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Density functional theory: Its origins, rise to prominence, and future

An improved density matrix functional [correction to Buijse and Baerends functional (BBC)] is proposed, in which a hierarchy of physically motivated repulsive corrections is employed to the strongly overbinding functional of Buijse and Baerends (BB) The first correction C1 restores the repulsive exchange-correlation (xc) interaction between electrons in weakly occupied natural orbitals (NOs) as it appears in the exact electron pair density rho(2) for the limiting two-electron case The second correction C2 reduces the xc interaction of the BB functional between electrons in strongly occupied NOs to an exchange-type interaction The third correction C3 employs a similar reduction for the interaction of the antibonding orbital of a dissociating molecular bond In addition, C3 applies a selective cancellation of diagonal terms in the Coulomb and xc energies (not for the frontier orbitals) With these corrections, BBC still retains a correct description of strong nondynamical correlation for the dissociating electron pair bond BBC greatly improves the quality of the BB potential energy curves for the prototype few-electron molecules and in several cases BBC reproduces very well the benchmark ab initio potential curves The average error of the self-consistent correlation energies obtained with BBC3 for prototype atomic systems and molecular systems at the equilibrium geometry is only ca 6%

/pdf/an-improved-density-matrix-functional-by-physically-497wwjd6e6.pdf

An improved density matrix functional by physically motivated repulsive corrections.

A new density functional (DF) method is proposed for calculations of intermolecular interaction energies. The exchange-correlation functional was optimized in such a way that the method recovers the interaction energies with the dispersion (including exchange-dispersion) component subtracted and therefore our approach is named the dispersionless DF (dlDF) method. The dlDF method is shown to predict very well the dispersionless part of the interaction energy for all types of intermolecular interactions. Thus, if combined with a dispersion component, computed ab initio or from a simple function fitted to ab initio values, it provides accurate and physically justified interaction energies in the whole range of intermolecular separations. Our dispersion function is significantly more accurate than the published ones.

Dispersionless density functional theory.

The electron localizability indicator (ELI) is based on a functional of the same-spin pair density. It reflects the correlation of the motion of same-spin electrons. In the Hartree–Fock approximation the ELI can be related to the electron localization function (ELF). For correlated wavefunctions the ELI formula differs from the one for the ELF.

Electron localizability indicator for correlated wavefunctions. I. Parallel-spin pairs

A detailed analysis that benefits from a slate of new approximate numerical and exact asymptotic results produces highly accurate properties of the ground state of the harmonium atom as functions of the confinement strength ω and quantifies the domains of the weakly and strongly correlated regimes in this system. The former regime, which encompasses the values of ω greater than ωcrit≈4.011 624×10−2, is characterized by the one-electron density ρ(ω;r1) with a global maximum at r1=0. In contrast, the harmonium atom within the latter regime, which corresponds to ω<ωcrit, differs fundamentally from both its weakly correlated counterpart and Coulombic systems. Resembling a Wigner crystal of a homogeneous electron gas, it possesses a radially localized pair of angularly correlated electrons that gives rise to ρ(ω;r1) with a “fat attractor” composed of a cage critical point and a (1, −1) critical sphere. Allowing for a continuous variation in ω, the new compact representation of the ground-state wave function an...

The ground state of harmonium

Recent advances in reduced density matrix functional theory (RDMFT) and linear response time-dependent reduced density matrix functional theory (TD-RDMFT) are reviewed. In particular, we present various approaches to develop approximate density matrix functionals which have been employed in RDMFT. We discuss the properties and performance of most available density matrix functionals. Progress in the development of functionals has been paralleled by formulation of novel RDMFT-based methods for predicting properties of molecular systems and solids. We give an overview of these methods. The time-dependent extension, TD-RDMFT, is a relatively new theory still awaiting practical and generally useful functionals which would work within the adiabatic approximation. In this chapter we concentrate on the formulation of TD-RDMFT response equations and various adiabatic approximations. None of the adiabatic approximations is fully satisfactory, so we also discuss a phase-dependent extension to TD-RDMFT employing the concept of phase-including-natural-spinorbitals (PINOs). We focus on applications of the linear response formulations to two-electron systems, for which the (almost) exact functional is known.

Katarzyna Pernal

Papers

An improved density matrix functional by physically motivated repulsive corrections.

Dispersionless density functional theory.

Electron localizability indicator for correlated wavefunctions. I. Parallel-spin pairs

The ground state of harmonium

Reduced Density Matrix Functional Theory (RDMFT) and Linear Response Time-Dependent RDMFT (TD-RDMFT).