A Parallel Iterative Method for Computing Molecular Absorption Spectra

TL;DR

This paper introduces a fast parallel iterative method for calculating molecular absorption spectra using TDDFT, significantly improving computational speed and efficiency through Krylov subspace techniques and hybrid parallelization.

Contribution

The paper presents a novel parallel iterative approach with a local basis and Krylov subspace methods, achieving an order of magnitude speedup over previous techniques.

Findings

Code is about ten times faster than previous full-matrix methods.

Parallel implementation with hybrid MPI and OpenMP enhances scalability.

Validated on large molecules across various parallel computing architectures.

Abstract

We describe a fast parallel iterative method for computing molecular absorption spectra within TDDFT linear response and using the LCAO method. We use a local basis of "dominant products" to parametrize the space of orbital products that occur in the LCAO approach. In this basis, the dynamical polarizability is computed iteratively within an appropriate Krylov subspace. The iterative procedure uses a a matrix-free GMRES method to determine the (interacting) density response. The resulting code is about one order of magnitude faster than our previous full-matrix method. This acceleration makes the speed of our TDDFT code comparable with codes based on Casida's equation. The implementation of our method uses hybrid MPI and OpenMP parallelization in which load balancing and memory access are optimized. To validate our approach and to establish benchmarks, we compute spectra of large molecules on various types of parallel machines. The methods developed here are fairly general and we believe they will find useful applications in molecular physics/chemistry, even for problems that are beyond TDDFT, such as organic semiconductors, particularly in photovoltaics.