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.

/pdf/perspective-on-density-functional-theory-1bq1migq5h.pdf

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.

/pdf/density-functional-theory-its-origins-rise-to-prominence-and-3my4nkvzsc.pdf

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

We propose a multiconfiguration density functional combining a short-range density functional approximation with a novel long-range correction for dynamic correlation effects. The correction is derived from the adiabatic connection formalism so that the resulting functional requires access only to one- and two-electron reduced density matrices of the system. In practice, the functional is formulated for wavefunctions of the complete active space (CAS) type and the short-range density functional part is made dependent on the on-top pair density via auxiliary spin densities. The latter allows for reducing the self-interaction and the static correlation errors without breaking the spin symmetry. We study the properties and the performance of the non-self-consistent variant of the method, termed lrAC0-postCAS. Numerical demonstration on a set of dissociation energy curves and excitation energies shows that lrAC0-postCAS provides accuracy comparable with more computationally expensive ab initio rivals.

Long-range-corrected multiconfiguration density functional with the on-top pair density.

We present an electron-pairs-based method employing a generalized valence bond perfect-pairing (GVB-PP) ansatz that provides a uniformly accurate description of systems where various types of elect...

Generalized Valence Bond Perfect-Pairing Made Versatile Through Electron-Pairs Embedding.

We present a formulation of the multiconfigurational (MC) wave function symmetry-adapted perturbation theory (SAPT). The method is applicable to noncovalent interactions between monomers which require a multiconfigurational description, in particular when the interacting system is strongly correlated or in an electronically excited state. SAPT(MC) is based on one- and two-particle reduced density matrices of the monomers and assumes the single-exchange approximation for the exchange energy contributions. Second-order terms are expressed through response properties from extended random phase approximation (ERPA). The dispersion components of SAPT(MC) have been introduced in our previous works [Hapka, M. J. Chem. Theory Comput. 2019, 15, 1016-1027; Hapka, M. J. Chem. Theory Comput. 2019, 15, 6712-6723]. SAPT(MC) is applied either with generalized valence bond perfect pairing (GVB) or with complete active space self-consistent field (CASSCF) treatment of the monomers. We discuss two model multireference systems: the H2 ··· H2 dimer in out-of-equilibrium geometries and interaction between the argon atom and excited state of ethylene. Using the C2H4* ··· Ar complex as an example, we examine second-order terms arising from negative transitions in the linear response function of an excited monomer. We demonstrate that the negative-transition terms must be accounted for to ensure qualitative prediction of induction and dispersion energies and develop a procedure allowing for their computation. Factors limiting the accuracy of SAPT(MC) are discussed in comparison with other second-order SAPT schemes on a data set of small single-reference dimers.

Symmetry-Adapted Perturbation Theory Based on Multiconfigurational Wave Function Description of Monomers.

An embedding method for a one-electron reduced density matrix (1-RDM) is proposed. It is based on partitioning of 1-RDM into domains and describing each domain in the effective potential of the other ones. To assure N-representability of the total 1-RDM N-representability and strong-orthogonality conditions are imposed on the domains. The total energy is given as a sum of single-domain energies and domain–domain electron interaction contributions. Higher than two-body inter-domain interaction terms are neglected. The two-body correlation terms are approximated by deriving inter-domain correlation from couplings of density fluctuations of two domains at a time. Unlike in most density embedding methods kinetic energy is treated exactly and it is not required that densities pertaining to the domains are only weakly overlapping. We propose to treat each domain by a corrected perfect-pairing functional. On a few examples it is shown that the embedding reduced density matrix functional method (ERDMF) yields excellent results for molecules that are well described by a single Lewis structure even if strong static intra-domain or dynamic inter-domain correlation effects must be accounted for.

Reduced density matrix embedding. General formalism and inter-domain correlation functional

Common features are identified in the properties of the pure (PF) and ensemble (EF) energy functionals defined within the density matrix functional theory (DMFT) as well as their free-form (FFF) approximations These features rationalize abandoning, in the common DMFT practice, prohibitively complicated generalized Pauli constraints (GPCs) Specifically, it is shown that the exact PF and EF coincide on the set of the v-representable first-order reduced density matrices (1RDMs), while FFFs approximate the common PF and EF for such 1RDMs It is revealed that for some types of FFFs, for example for the geminal-based approximations, the GPCs are essentially trivialized to the pairwise natural occupation numbers (NONs) degeneracy conditions, routinely imposed for closed-shell systems

Katarzyna Pernal

Papers

Long-range-corrected multiconfiguration density functional with the on-top pair density.

Generalized Valence Bond Perfect-Pairing Made Versatile Through Electron-Pairs Embedding.

Symmetry-Adapted Perturbation Theory Based on Multiconfigurational Wave Function Description of Monomers.

Reduced density matrix embedding. General formalism and inter-domain correlation functional

Approximating one-matrix functionals without generalized Pauli constraints