Using &amp;lt;i&amp;gt;ScalIT&amp;lt;/i&amp;gt; for Performing Accurate Rovibrational Spectroscopy Calculations for Triatomic Molecules: A Practical Guide

Corey Petty,Bill Poirier

doi:10.4236/am.2014.517263

Abstract

This paper presents a practical guide for use of the ScalIT software package to perform highly accurate bound rovibrational spectroscopy calculations for triatomic molecules. At its core, ScalIT serves as a massively scalable iterative sparse matrix solver, while assisting modules serve to create rovibrational Hamiltonian matrices, and analyze computed energy levels (eigenvalues) and wavefunctions (eigenvectors). Some of the methods incorporated into the package include: phase space optimized discrete variable representation, preconditioned inexact spectral transform, and optimal separable basis preconditioning. ScalIT has previously been implemented successfully for a wide range of chemical applications, allowing even the most state-of-the-art calculations to be computed with relative ease, across a large number of computational cores, in a short amount of time.

Highlights

ScalIT, in principle, can be applied across a broad range of scientific disciplines; recent development and application has been geared toward molecular chemical dynamics, performing exact time-independent quantum dynamics calculations
In this paper we focus on the operation of ScalIT from the non-expert user’s perspective, after a brief description of the underlying numerical methods
High level modules have been created for performing calculations on systems up to four atoms; for simplicity, we restrict ourselves to discuss only triatomic molecules, the procedure described is nearly identical for more difficult systems

Summary

Introduction

ScalIT, in principle, can be applied across a broad range of scientific disciplines; recent development and application has been geared toward molecular chemical dynamics, performing exact time-independent quantum dynamics calculations. V is a diagonal matrix, and each Ti is diagonal with respect to all dofs excluding that of its own subscript(s) This discretized grid-based representation of the molecular Hamiltonian yields a resultant matrix with a highly structured block-form, characterized by diagonal blocks of precisely the same size, and off-diagonal blocks which are themselves diagonal. Sparse iterative approaches have shown to be a viable means for solving linear algebra problems with such large matrices [11] [12] [18] [21]-[25], for matrix-vector products scale with the number of nonzero elements, reducing computational effort with increasing sparsity. Computational burden is increased due to the calculation of these off-diagonal elements, yet studies have shown that this is greatly overcome by the reduction in L, especially in high-density-of-state regimes

Using ScalIT

Applications

Conclusion