Multimode wavelet basis calculations via the molecular self-consistent-field plus configuration-interaction method

Abstract

Wavelets provide potentially useful quantum bases for coupled anharmonic vibrational modes in polyatomic molecules as well as many other problems. A single compact support wavelet family provides a flexible basis with properties of orthogonality, localization, customizable resolution, and systematic improvability for general types of one-dimensional and separable systems. While direct product wavelet bases can be used in coupled multidimensional problems, exponential scaling of basis size with dimensionality ultimately provides limits on the number of coupled modes that can be treated simultaneously in exact quantum calculations. The molecular self-consistent-field plus configuration-interaction method is used here in multimode wavelet calculations to reduce the basis size without sacrificing flexibility or the ability to systematically control errors. Both two-dimensional Cartesian coordinate and three-dimensional curvilinear coordinate systems are examined with wavelets serving as universal bases in each case. The first example uses standard Daubechies [Ten Lectures on Wavelets (SIAM, Philadelphia (1992)] wavelets for each mode and the second adapts symmlet wavelets to intervals for each of the curvilinear coordinates.

Ab initio effective rotational and rovibrational Hamiltonians for non-rigid systems via curvilinear second order vibrational Møller–Plesset perturbation theory

“…VMP2 is analogous to the electronic MP2 method [18]: after performing a mean-field VSCF calculation, vibrational correlation effects are taken into account via Rayleigh-Schrödinger second order perturbation theory. While originally developed for the normal mode Watson Hamiltonian, VSCF and VSCF-based methods have been successfully extended to curvilinear reaction path Hamiltonians [19,20], as well as more general curvilinear vibrational Hamiltonians [21][22][23][24][25][26][27][28].…”

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.…”

Higher-order wavelet reconstruction/differentiation filters and Gibbs phenomena

“…For a finite interval, such modifications at each edge lead to "wavelets on the interval." Such intervalized wavelets have been used in our group for quantum problems with both boundary [22][23][24] and initial [25,26] value conditions. However, they do not allow one to beat the approximation order at the edges in reconstruction or, in a related context discussed by Jameson, application of the differentiation matrix [27].…”