Highly Efficient Algorithms for CIS Type Excited State Wave Function Overlaps

Abstract

Two algorithms for calculating overlaps between CIS (or TDDFT) type excited state wave functions are presented, one based on expansion of overlap determinants into level 2 minors (OL2M) and the other based on an expansion of the wave functions into natural transition orbitals (ONTO). Both are significantly faster than previously available algorithms, with the ONTO algorithm reducing the cost of a single overlap element calculation by a factor of the square of the number of occupied orbitals in the system, resulting in orders of magnitude faster calculations for large systems and significantly increasing the size of systems for which TDDFT based nonadiabatic dynamics simulations can be performed. The OL2M algorithm is significantly slower for a single overlap matrix element, but becomes preferred when overlaps between large numbers of states are required. Additionally, we test the accuracy of approximate overlaps calculated using truncated wave functions and show that truncation can lead to very large errors in the overlaps. Lastly, we provide examples of applications for wave function overlaps outside the context of nonadiabatic dynamics.

Structure-Aware Calculation of Many-Electron Wave Function Overlaps on Multicore Processors

“…The work presented in [10] improved the idea in [7] by computing the determinants of the minors obtained from the second-level recursive Laplace expansion.…”

“…In this work, we improve the algorithm presented in [10] for computing the overlaps between excited states using CIS-type wave functions. In particular, we optimize the algorithm denoted there as OL2M an approach based on the level-2 minors obtained from Laplace's recursive formula, or in other words, the minors obtained by removing two rows and two columns from the input referent matrix.…”

Following the evolution of excited states along photochemical reaction pathways

“…Computing the overlap between full electronic wave functions is a common practice to compare ESs at the same or different molecular geometries . On the other hand, the nature of the ESs can also be described by inspecting only the nature of the “hole” and the “particle” entities.…”

“…Computing the overlap between full electronic wave functions is a common practice to compare ESs at the same or different molecular geometries. [38][39][40]45] On the other hand, the nature of the ESs can also be described by inspecting only the nature of the "hole" and the "particle" entities. Indeed, computing the mono-electronic wave function overlap between NTOs has proven to be a robust procedure to compare ESs.…”

“…Following our same line of thought, Sapunar and co-workers have very recently proven the superior computational efficiency of NTO-over CI-based algorithms for the computation of ESs wave function overlaps. [40] Furthermore, in our seminal work presenting for the first time a NTO's overlap-based state-tracking formalism, [36] we showed that ES optimizations can be unambiguously accomplished using NTOs even in the most difficult cases where standard ES following algorithms fail, namely,…”