Beyond the Coulson-Fischer point: Characterizing single excitation CI and TDDFT for excited states in single bond dissociations

TL;DR

This paper investigates the limitations of TDDFT and CIS methods in describing excited states during single bond dissociation, revealing unphysical behaviors and the importance of double excitations through analytical and numerical studies.

Contribution

It provides a detailed analysis of excited state potential energy surfaces beyond the Coulson-Fisher point, highlighting issues with spin states and the role of double excitations in TDDFT and CIS.

Findings

Sharp kinks at the Coulson-Fisher point in excited state surfaces.

Unphysical dissociation behavior of certain triplet states.

Analytical insights from minimal model systems like H₂.

Abstract

Linear response time dependent density functional theory (TDDFT), which builds upon configuration interaction singles (CIS) and TD-Hartree-Fock (TDHF), is the most widely used class of excited state quantum chemistry methods and is often employed to study photochemical processes. This paper studies the behavior of the resulting excited state potential energy surfaces beyond the Coulson-Fisher (CF) point in single bond dissociations, when the optimal reference determinant is spin-polarized. Many excited states exhibit sharp kinks at the CF point, and connect to different dissociation limits via a zone of unphysical concave curvature. In particular, the unrestricted M$_S=0$ lowest triplet T$_1$ state changes character, and does not dissociate into ground state fragments. The unrestricted $M_S=\pm 1$ T$_1$ CIS states better approximate the physical dissociation limit, but their degeneracy is broken beyond the CF point for most single bond dissociations. On the other hand, the $M_S=\pm 1$ T$_1$ TDHF states reach the asymptote too soon, by merging with the ground state from the CF point onwards. Use of local exchange-correlation functionals causes $M_S=\pm 1$ T$_1$ TDDFT states to resemble their unphysical $M_S= 0$ counterpart. The 2 orbital, 2-electron model system of minimal basis H$_2$ is analytically treated to understand the origin of these issues, revealing that the lack of double excitations is at the root of these remarkable observations. The behavior of excited state surfaces is also numerically examined for species like H$_2$, NH$_3$, C$_2$H$_6$ and LiH in extended basis sets.