Density-functional expansion methods: grand challenges

Abstract

We discuss the source of errors in semiempirical density functional expansion (VE) methods. In particular, we show that VE methods are capable of well-reproducing their standard Kohn-Sham density functional method counterparts, but suffer from large errors upon using one or more of these approximations: the limited size of the atomic orbital basis, the Slater monopole auxiliary basis description of the response density, and the one- and two-body treatment of the core-Hamiltonian matrix elements. In the process of discussing these approximations and highlighting their symptoms, we introduce a new model that supplements the second-order density-functional tight-binding model with a self-consistent charge-dependent chemical potential equalization correction; we review our recently reported method for generalizing the auxiliary basis description of the atomic orbital response density; and we decompose the first-order potential into a summation of additive atomic components and many-body corrections, and from this examination, we provide new insights and preliminary results that motivate and inspire new approximate treatments of the core-Hamiltonian.

Quantum mechanical study of solvent effects in a prototype SN2 reaction in solution: Cl− attack on CH3Cl

“…These changes should be reflected in the repulsive exchange and correlation dispersion potentials, requiring the van der Waals radii to adjust. 65,66 The static Lennard-Jones parameters used in this study were developed to obtain solvation free energy of a chloride ion in non-polarizable water, as is the case for the QM/MM system, and do not consider the solvation free energy of methyl chloride. It is therefore likely to be in error.…”

ACKS2: Atom-condensed Kohn-Sham DFT approximated to second order

“…By substituting this expansion in the DFT energy functional, one develops a model for the first-and second-order derivatives of the electronic energy towards the expansion coefficients. 40,[79][80][81][82] Although the density basis expansion is also useful in this paper, the starting point of our derivation is constrained DFT. 83,84 By imposing constraints on the electron density, people have already successfully studied charge transfer during bond dissociation, 58 long-range charge transfer, 85 and intermolecular charge-transfer and induction effects.…”

“…SQE+Q 0 , that use integer reference populations corresponding to the oxidation states of the atoms. 33,70 In line with the derivation of the CPE and related models, 40,[79][80][81][82] the density is expanded to first order:…”

Extended Polarization in Third-Order SCC-DFTB from Chemical-Potential Equalization

“…14–16 Another approach which has been shown to be promising is the chemical potential equilization (CPE) method, founded by Sanderson 26 as an electronegativity equalization approach, which was later modified and improved. 27,28 In the framework of CPE extended MNDO 39 and 2nd order SCC-DFT 34 (DFTB2), Giese and York were able to accurately reproduce polarizabilities compared to DFT with a large ao-basis. Concerning SCC-DFTB the accuracy is limited not only by the minimal ao-basis approach but also by the monopole basis representation of charge density fluctuations in second order.…”

“…Concerning Raman intensities, we will have to have a closer look on the polarizability tensor as a whole, while most of the previous studies 17,18,34,37,39 focused just on the mean polarizability, i.e. the average of the tensors diagonal elements.…”