Efficient parabolic evaluation of coupling terms in hybrid quantum/classical simulations

A parabolic interpolation function of time is proposed to evaluate the non-adiabatic coupling matrix elements and the adiabatic energies at intermediate times within the classical time integration interval in hybrid quantum/classical simulations. The accuracy and the computational efficiency of this parabolic approximation are illustrated by carrying out a numerical application to the well-studied vibrational relaxation of I2 in liquid xenon.