Calculation of reaction rate constants using approximate evolution of quantum trajectories in imaginary and real time

Reaction rate constants can be directly obtained from evolution of the flux operator eigenvectors under the Boltzmann and Hamiltonian operators. This is achieved by evolving the quantum trajectory ensemble, representing a wavefunction, in imaginary time seamlessly switching to the real-time dynamics. Quantum–mechanical effects are incorporated through the quantum potential dependent on the trajectory momenta or on the derivatives of the wavefunction amplitude. For practicality the quantum potential and wavefunction nodes are described using linear basis, which is exact for Gaussian wavefunctions. For the Eckart barrier approximate rate constants show significant improvement over the parabolic barrier rate constants.