Quantum chemistry of the excited state: recent trends in methods developments and applications

Abstract

Advances (2016)(2017) in Quantum Chemistry of the Excited State (QCEX) are presented in this book chapter focusing firstly on developments of methodology and excited-state reaction-path computational strategies and secondly on the applications of QCEX to study light-matter interaction in distinct fields of biology, (nano)-technology, medicine and the environment. We highlight in this contribution developments of static and dynamic electron-correlation methods and methodological approaches to determine dynamical properties, recent examples of the roles of conical intersections, novel DNA spectroscopy and photochemistry findings, photo-sensitisation mechanisms in biological structures and the current knowledge on chemiexcitation mechanisms that give rise to light emission (in the chemiluminescence and bioluminescence phenomena).

Full Configuration Interaction Excited-State Energies in Large Active Spaces from Subspace Iteration with Repeated Random Sparsification

“…In analogy to eq (E10), the values of single-excitation elements in Q (5) are 1. Double-excitation elements in Q (5) are Q (5) (2,i, j,a,b),(2,i, j,a) = | jb|b j | 1/2 X −1…”

“…Each of the matrices Q (1) , Q (2) , ..., Q (5) is constructed to have less than O(M) nonzero elements per column. Because the vector resulting after each compression operation has at most m nonzero elements, the cost of the multiplication operations involving these matrices is limited to O(Mm).…”

“…Although it is possible to choose the matrices B (τ,k) and Q (1) , Q (2) , ..., Q (5) in eq (D1) such that X (τ+1) equals (1 − εH)X (τ) in expectation, it is often advantageous to relax this requirement and construct B (τ, j) differently, according to an approach known as the initiator approximation, originally developed for FCIQMC. 25,49 This approximation introduces a bias in the resulting eigenvalue estimates.…”

“…The initiator approximation involves constructing B (τ,k) such that, in the course of the matrix multiplications in eq (D1), only elements in X (τ) :k with magnitudes greater than an initiator threshold are allowed to contribute to elements of X (τ+1) :k that are zero in X (τ) :k . Specific formulas for the elements of B (τ,k) , as well as those of Q (1) , Q (2) , ..., Q (5) , are provided in Section E.…”

“…Excited electronic states of molecules and solid-state systems play a crucial role in determining their chemical properties, including their response to irradition by light [1][2][3][4][5][6][7][8] and their behavior at finite temperature. 9,10 But calculating excited-state properties from first principles often proves challenging, particularly for systems of strongly correlated electrons.…”