A multiscale approach to coupled nuclear and electronic dynamics. I. Quantum-stochastic Liouville equation in natural...

Multiscale methods are powerful tools to describe large and complex systems. They are based on a hierarchical partitioning of the degrees of freedom (d.o.f.) of the system, allowing one to treat each set of d.o.f. in the most computationally efficient way. In the context of coupled nuclear and electronic dynamics, a multiscale approach would offer the opportunity to overcome the computational limits that, at present, do not allow one to treat a complex system (such as a biological macromolecule in explicit solvent) fully at the quantum mechanical level. Based on the pioneering work of Kapral and Ciccotti [R. Kapral and G. Ciccotti, J. Chem. Phys.110, 8919 (1999)], this work is intended to present a nonadiabatic theory that describes the evolution of electronic populations coupled with the dynamics of the nuclei of a molecule in a dissipative environment (condensed phases). The two elements of novelty that are here introduced are (i) the casting of the theory in the natural, internal coordinates, that are bond lengths, bond angles, and dihedral angles; (ii) the projection of those nuclear d.o.f. that can be considered at the level of a thermal bath, therefore leading to a quantum-stochastic Liouville equation. Using natural coordinates allows the description of structure and dynamics in the way chemists are used to describe molecular geometry and its changes. The projection of bath coordinates provides an important reduction of complexity and allows us to formulate the approach that can be used directly in the statistical thermodynamics description of chemical systems.