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Evaluation of the quantum time-correlation functions employing the Hamilton–Jacobi dynamics framework
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Evaluation of the quantum time-correlation functions employing the Hamilton–Jacobi dynamics framework
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Journal Article
Evaluation of the quantum time-correlation functions employing the Hamilton–Jacobi dynamics framework
2019
Overview
The quantum Hamilton–Jacobi equation (QHJE) is formally equivalent to the time-dependent Schrödinger equation, and the solutions to the QHJE can be easily interpreted in terms of trajectories providing a link between classical and quantum mechanics. The trajectory-based approaches to quantum molecular dynamics are, generally, appealing because they circumvent exponential scaling associated with exact quantum methods with the system size, and because, unlike classical molecular dynamics, such methods incorporate dominant quantum effects due to delocalization of wavefunctions describing the nuclei. We explore the utility of the QHJE framework for calculations of the time-correlation functions (TCFs) involving quantum evolution defined by the Boltzmann density operator and by the Hamiltonian time-evolution operator. The implementation is based on solutions to the imaginary-time counterpart to the QHJE, which yield approximations to the ground state wavefunction. The resulting nodeless wavefunction is used to generate a basis in coordinate space, which is efficient for evaluation of the low-lying excited states and of the quantum TCFs, including the Kubo-transformed TCFs, at low temperature. The QHJE/basis approach is illustrated on several model systems in and out of thermal equilibrium, i.e., the H2 dimer and bound anharmonic potentials. If a system exhibits large amplitude motion, e.g., in case of the nonequilibrium dynamics, then the real-time trajectory propagation provides an alternative to the basis representation, as demonstrated on a model describing the inversion mode of the ammonia molecule and ion.
Publisher
Springer Nature B.V
