Additions to the class of symmetric-antisymmetric multiwavelets: Derivation and use as quantum basis functions

Abstract

Multiwavelet bases have been shown recently to apply to a variety of quantum problems. There are, however, only a few multiwavelet families that have been defined to date. Chui-Lian-type symmetric and antisymmetric multiwavelets are derived here that equal and exceed the polynomial interpolating power of previously available examples. Adaptations to domain edges are made with a view to use in curvilinear coordinate molecular calculations. The new highest-order multiwavelet family is shown to provide uniformly better performance for (i) basis representation of terms such as 1r(2) in near approach to the singularity at r=0 and (ii) eigenvalue calculation of a bending Hamiltonian taken from a curvilinear model of the ground-state vibrations of nitrosyl chloride.

Chemical Compound Design Using Nuclear Charge Distributions

“…In absence of the exact functional, we have derived an approximate functional for the optimization of an electronic property under the constraint of physical viability. Ongoing efforts to develop general purpose electronic basis sets, e.g., wavelets (22)(23)(24) or finite element methods (25)(26)(27) open up the potential to use these same bases for efficient, systematic explorations of chemical space via nuclear charge distributions.…”

Optimization of numerical orbitals using the Helmholtz kernel

“…7,8,[18][19][20][21][22][23][24][25][26][27][28] Tensorial based wavelet methods have been developed for calculating electrostatic potentials and solving electronic structure equations using the same approach. 1,2,5,7,11,23,[29][30][31][32][33][34][35][36][37][38][39] 0021-9606/2017/146(8)/084102/6/$30.00…”