Search

Static electric response properties of atoms and molecules are reported within the real-space Cartesian grid implementation of pseudopotential Kohn-Sham (KS) density functional theory (DFT). A detailed systematic investigation is made for a representative set of atoms and molecules, through a number of properties like total ground-state electronic energies, permanent dipole moment ($\bm{\mu}$), static average dipole polarizability ($\overline{\alpha}$). This is further extended to first-hyperpolarizability ($\bm{\beta}$) in molecules. It employs a recently developed non-uniform grid-optimization technique, with a suitably chosen fixed initial applied field. A simple variant of the finite-field method, using a rational function fit to the dipole moment with respect to electric field, is adopted. We make use of Labello-Ferreira-Kurtz (LFK) basis set, which has performed quite well in these scenarios. To assess the efficacy and feasibility, four XC functionals such as LDA, BLYP, PBE and LBVWN are chosen. Present results are compared with available literature (both theoretical and experimental) values, whenever possible. In all instances, they show excellent agreement with the respective atom-centered-grid results, very widely used in many quantum chemistry programs. This demonstrates a viable alternative towards accurate prediction of response properties of many-electron systems in Cartesian coordinate grid., Comment: 18 pages, 4 tables

Within the finite-field Kohn-Sham framework, static electric response properties of diatomic molecules are presented. The electronic energy, dipole moment ({\boldmath$\mu$}), static dipole polarizability ({\boldmath$\alpha$}) and first-hyperpolarizability ({\boldmath$\beta$}) are calculated through a pseudopotential-DFT implementation in Cartesian coordinate grid, developed in our laboratory earlier. We engage the Labello-Ferreira-Kurtz (LFK) basis set; while four local and non-local exchange-correlation (LDA, BLYP, PBE and LBVWN) functionals have been adopted. A detailed analysis of \emph{grid convergence} and its impact on obtained results, is presented. In each case the \emph{electric field optimization} was carefully monitored through a recently prescribed technique. For all three molecules (HCl, HBr, HI) considered, the agreement of all these quantities with widely successful and popular atom-centered-grid procedure, is excellent. To assess the efficacy and feasibility, companion calculations are performed for these on a representative molecule (HCl) at distorted geometries, far from equilibrium. Wherever possible, relevant comparison is made with available \emph{all-electron} data and experimental results. This demonstrates that Cartesian grid provides accurate, reliable results for such properties of many-electron systems within pseudopotential representation., Comment: 25 pages, 4 tables, 2 figures

We present a purely numerical approach in Cartesian grid, for efficient computation of Hartree-Fock (HF) exchange contribution in the HF and density functional theory models. This takes inspiration from a recently developed algorithm [Liu \emph{et al.}, J.~Chem.~Theor.~Comput.~ \textbf{13}, 2571 (2017)]. A key component is the accurate evaluation of electrostatic potential integral, which is the rate-determining step. This introduces the Fourier convolution theorem in conjunction with a range-separated Coulomb interaction kernel. The latter is efficiently mapped into real grid through a simple optimization procedure, giving rise to a constraint in the range-separated parameter. The overall process offers logarithmic scaling with respect to molecular size. It is then extended towards global hybrid functionals such as B3LYP, PBE0 and BHLYP within pseudopotential Kohn-Sham theory, through an LCAO-MO ansatz in Cartesian grid, developed earlier in our laboratory. For sake of comparison, a parallel semi-numerical approach has also been worked out that exploits the familiar Obara-Saika recursion algorithm. An excellent agreement between these two routes is demonstrated through total energy and orbital energy in a series of atoms and molecules (including 10 $\pi$-electron molecules), employing an LANL2DZ-type basis function. A critical analysis of these two algorithms reveals that the proposed numerical scheme could lead to very attractive and competitive scaling. The success of our approach also enables us for further development of optimally tuned range-separated hybrid and hyper functionals., Comment: 26 pages, 6 tables, 66 references

For 1 Dimensional loop space, a nonlinear nonlocal transformation of fields is given to make the action of the self-interacting quantum field to the free one. A specific type of Classically broken symmetry is restored in Quantum theory. 1-D Sine Gordon system and Sech interactions are treated as the explicit example., Comment: 5 pages, 0 figures, Comments are welcome