  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.
