Static polarizability and hyperpolarizability in atoms and molecules through a Cartesian-grid DFT

Recent Advances in Cartesian-Grid DFT in Atoms and Molecules

In the past several decades, density functional theory (DFT) has evolved as a leading player across a dazzling variety of fields, from organic chemistry to condensed matter physics. The simple conceptual framework and computational elegance are the underlying driver for this. This article reviews some of the recent developments that have taken place in our laboratory in the past 5 years. Efforts are made to validate a viable alternative for DFT calculations for small to medium systems through a Cartesian coordinate grid- (CCG-) based pseudopotential Kohn-Sham (KS) DFT framework using LCAO-MO ansatz. In order to legitimize its suitability and efficacy, at first, electric response properties, such as dipole moment ( μ ), static dipole polarizability ( α ), and first hyperpolarizability ( β ), are calculated. Next, we present a purely numerical approach in CCG for proficient computation of exact exchange density contribution in certain types of orbital-dependent density functionals. A Fourier convolution theorem combined with a range-separated Coulomb interaction kernel is invoked. This takes motivation from a semi-numerical algorithm, where the rate-deciding factor is the evaluation of electrostatic potential. Its success further leads to a systematic self-consistent approach from first principles, which is desirable in the development of optimally tuned range-separated hybrid and hyper functionals. Next, we discuss a simple, alternative time-independent DFT procedure, for computation of single-particle excitation energies, by means of "adiabatic connection theorem" and virial theorem. Optical gaps in organic chromophores, dyes, linear/non-linear PAHs, and charge transfer complexes are faithfully reproduced. In short, CCG-DFT is shown to be a successful route for various practical applications in electronic systems.

Charge-Transfer Excitation within a Hybrid-(G)KS Framework through Cartesian Grid DFT

Organic molecules that exhibit charge-transfer (CT) excited states are known to play an important role in processes linked to electron transfer properties and molecular conductance. In this article, we present a simple technique based on "Becke's excitation theorem" that offers an accurate picture of these electronic states. It expresses the correlated energy splitting between triplet and its corresponding singlet states by a two-electron integral, which is numerically evaluated by our recently developed strategy on Cartesian grid. We first examine the consistency of our adopted numerical strategy to evaluate the integral with the original prescribed technique. Then we assess the method on weakly bound CT complexes with three different functionals (BLYP, B3LYP, and LC-BLYP). The accuracy on asymptotic limit of CT excitation is also explored. Finally in order to illustrate the strength and feasibility, it is further extended to a few "challenging" molecules. The method, when employed with hybrid B3LYP functional, turns out to be quite accurate to describe CT excitation energy.