# Time-dependent linear-response variational Monte Carlo

## TL;DR

This paper extends variational Monte Carlo to compute electronic excitation energies and oscillator strengths using a time-dependent linear-response approach, showing promising results over traditional methods.

## Contribution

It introduces a novel linear-response VMC method that incorporates wave-function derivatives, enabling accurate excited-state calculations.

## Key findings

- LR-VMC outperforms CIS in excitation energy accuracy
- Method successfully applied to beryllium atom excitations
- LR-VMC shows promise for excited-state properties of molecules

## Abstract

We present the extension of variational Monte Carlo (VMC) to the calculation of electronic excitation energies and oscillator strengths using time-dependent linear-response theory. By exploiting the analogy existing between the linear method for wave-function optimisation and the generalised eigenvalue equation of linear-response theory, we formulate the equations of linear-response VMC (LR-VMC). This LR-VMC approach involves the first-and second-order derivatives of the wave function with respect to the parameters. We perform first tests of the LR-VMC method within the Tamm-Dancoff approximation using single-determinant Jastrow-Slater wave functions with different Slater basis sets on some singlet and triplet excitations of the beryllium atom. Comparison with reference experimental data and with configuration-interaction-singles (CIS) results shows that LR-VMC generally outperforms CIS for excitation energies and is thus a promising approach for calculating electronic excited-state properties of atoms and molecules.