Local diabatic representation of conical intersection quantum dynamics

Conical intersections are ubiquitous in polyatomic molecules and responsible for a wide range of phenomena in chemistry and physics. We introduce and implement a local diabatic representation for the correlated electron-nuclear dynamics around conical intersections. It employs the adiabatic electronic states but avoids the singularity of nonadiabatic couplings, and is robust to different gauge choices of the electronic wavefunction phases. Illustrated by a two-dimensional conical intersection model, this representation captures nonadiabatic transitions, electronic coherence, and geometric phase

Estimation Of The Quantum Effects Of Nuclei in Large Molecular Systems

Chemical dynamics, in principle, should be understood by solving the time-dependent Schrödinger equation for a molecular system, describing motion of the nuclei and electrons. However, the computational efforts to solve this partial second-order differential equation scales exponentially with the system size, which prevents us from getting exact numerical solutions for systems larger than 4-5 atoms. Thus, approximations simplifying the picture are necessary. The so-called Born-Oppenheimer approximation, separating motion of the electrons and nuclei is the central one: solution to the electronic Schrödinger equation defines the potential energy surface on which the nuclear motion unfolds, and there are standard quantum chemistry software packages for solving the electronic Schrödinger equation. For the nuclear Schrödinger equation, however, there are no widely applicable quantum-mechanical approaches, and most simulations are performed using classical Newtonian mechanics which is often adequate due to large nuclear masses. However, the nuclear quantum effects are significant for chemical processes involving light nuclei at low energies, and including these effects into simulation, even approximately, is highly desirable. In this dissertation, an approximate methodology of including quantum-mechanical effects within the quantum trajectory or the de Broglie-Bohm formulation of the Schrödinger equations is developed. Use of the trajectory framework makes the approach scalable to hundreds of degrees of freedom. The methodology is applied to study high-dimensional systems (solid He4 and others) relevant to chemistry

Diagrammatic representation and nonperturbative approximation of exact time-convolutionless master equation

The time-convolutionless master equation provides a general framework to model non-Markovian dynamics of an open quantum system with a time-local generator. A diagrammatic representation is developed and proven for the perturbative expansion of the exact time-local generator for an open quantum system interacting with arbitrary environments. A truncation of the perturbation expansion leads to the perturbative time-convolutionless quantum master equations. We further introduce a nonperturbative approach that approximates the time-convolutionless generator as a nested time-ordered exponential function