Calculation of the Zero-point Energy from Imaginary-time Quantum Trajectory Dynamics in Cartesian Coordinates

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The imaginary-time quantum dynamics is implemented in Cartesian coordinates using the momentum-dependent quantum potential approach. A nodeless wavefunction, represented in terms of quantum trajectories, is evolved in imaginary time according to the quantum-mechanical Boltzmann operator in the Eulerian frame-of-reference. The quantum potential and its gradient are determined approximately, from the global low-order (quadratic) polynomial fit to the trajectory momenta, which makes the approach practical in high dimensions. Implementation in the Cartesian coordinates allows one to work with the Hamiltonian of the simplest form, to setup calculations in the molecular dynamics-compatible framework and to naturally mix quantum and classical description of particles. Localization of wavefunctions in the center-of-mass degrees of freedom and in the overall rotation, which makes the quadratic polynomial fitting in Cartesian coordinates accurate, is accomplished by the addition of a quadratic constraining potential, and its contribution to the zero-point energy is analytically subtracted. For illustration, the zero-point energies are computed for model clusters consisting of up to 11 atoms (33 dimensions).