Quantum dynamics of multiple modes for reactions in complex systems

Two different approaches for investigating the quantum dynamics of multiple modes for reactions in complex systems are presented. The first is time-dependent self-consistent-field dynamics based on a reaction path Hamiltonian (TDSCF-RPH), which allows the calculation of the real-time quantum dynamics of gas-phase chemical reactions involving polyatomic molecules. The TDSCF-RPH equations of motion are derived for straightline diabatic reaction path Hamiltonians, including the case in which the minimum-energy path has negligible curvature and the case in which the minimum-energy path has large curvature but the system follows a straightline path instead of the minimum-energy path. The advantage of the diabatic representation is that the TDSCF dynamics reduces to a one-dimensional numerical time propagation, even for the case of large coupling between the vibrational modes. The second approach is the multiconfigurational molecular dynamics with quantum transitions (MC-MDQT) method, which combines a multiconfigurational self-consistent-field (MC-SCF) formulation for the vibrational wavefunction with the MDQT non-adiabatic mixed quantum-classical molecular dynamics method. The MC-MDQT method allows the quantum dynamical treatment of multiple modes within a mixed quantum-classical framework for reactions in condensed-phase systems. The advantages of the MC-MDQT method are that it incorporates the significant correlation between the quantum modes, is valid in the adiabatic and non-adiabatic limits and the intermediate regime, and provides real-time dynamical information. The application of MC-MDQT to simulate the real-time non-equilibrium quantum dynamics of proton transport along protonated chains of water molecules is presented.