  Determining the properties of molecules and materials is one of the premier
applications of quantum computing. A major question in the field is how to use
imperfect near-term quantum computers to solve problems of practical value.
Inspired by the recently developed variants of the quantum counterpart of the
equation-of-motion (qEOM) approach and the orbital-optimized variational
quantum eigensolver (oo-VQE), we present a quantum algorithm (oo-VQE-qEOM) for
the calculation of molecular properties by computing expectation values on a
quantum computer. We perform noise-free quantum simulations of BeH$_2$ in the
series of STO-3G/6-31G/6-31G* basis sets and of H$_4$ and H$_2$O in 6-31G using
an active space of four electrons and four spatial orbitals (8 qubits) to
evaluate excitation energies, electronic absorption, and, for twisted H$_4$,
circular dichroism spectra. We demonstrate that the proposed algorithm can
reproduce the results of conventional classical CASSCF calculations for these
molecular systems.
