Path Integral Monte Carlo Simulation on Molecular Systems with Multiple Electronic Degrees of Freedom

We present an imaginary time path-integral formalism for molecular systems including nuclear and electronic degrees of freedom based on the previous work of [Schmidt, J. R.; Tully, J. C. <i>J. Chem. Phys.</i> 2007, 127, 094103]. To sample the resulting path integral expression efficiently, a path integral Monte Carlo scheme is proposed, allowing the computation of finite temperature equilibrium properties of molecular systems including multiple low-lying electronic states directly from ab initio potential energy surfaces. Finally, we show how this generalized approach in combination with the Monte Carlo scheme can reproduce exact results for a simple model system including nonadiabatic couplings as well as thermodynamic equilibrium properties of H₂ and C₂. Our implementation of the algorithm is available as an open-source code.