The Need, Benefits, and Demonstration of a Minimization Principle for Excited States

TL;DR

This paper introduces a new minimization principle for excited states that improves wave function accuracy in truncated spaces, especially near avoided crossings, by using a functional F$_n$.

Contribution

It presents a novel functional F$_n$ that ensures better excited state wave functions in truncated spaces, addressing limitations of standard methods.

Findings

The functional F$_n$ minimizes deviations from exact excited states.

Near avoided crossings, the wave function with the lowest F$_n$ corresponds to the true excited state.

The method improves the accuracy of excited state calculations in multiconfigurational self-consistent field methods.

Abstract

It is shown that the standard methods of computing excited states in truncated spaces must yield wave functions that, beyond truncation, are in principle veered away from the exact, and a remedy is demonstrated via a presented functional, F$_n$, obeying a minimization principle for excited states. It is further demonstrated that near avoided crossings, between two MCSCF 'flipped roots' the wave function that leads to the excited state has the lowest F$_n$.