THE QUANTUM CLASSICAL THEORY

By SOPHIA GONZALEZ

CONTENTS INTRODUCTION RIGOROUS THEORIES PATH-INTEGRAL APPROACH THE SHORT TIME PROPAGATOR THE CLASSICAL LIMIT THE VAN VLECK PROPAGATOR GAUSSIANS AT WORK CELLULAR DYNAMICS A SEMI-CLASSICAL IVR PROPAGATOR AN ORTHORGONAL BASIS SET BOHMIAN MECHANICS MIXING OF GAUSS-HERMITE AND ORDINARY BASIS SETS THE CLASSICAL PATH APPROXIMATION THE EXACT EQUATIONS OF MOTION IN THE TDGH BASIS BOUND STATES AND GAUSS-HERMITE FUNCTIONS THE MORSE-OSCILLATOR IN A GAUSS-HERMITE BASIS TREATMENT OF 2D SYSTEMS IN THE G-H BASIS THE QUANTUM-CLASSICAL CORRELATION SPHERICAL HARMONICS IN A GAUSS-HERMITE BASIS SET SECOND QUANTIZATION AND GAUSS-HERMITE FUNCTIONS QUANTUM DRESSED CLASSICAL MECHANICS THE DVR SCHEME ARBITRARILY SIZED SYSTEMS THE MCTDH APPROACH 2 10 SUMMARY APPROXIMATE THEORIES TIME-DEPENDENT SCF THE CLASSICAL PATH THEORY RELATION TO OTHER THEORIES ENERGY TRANSFER THE VQRQTC METHOD THE VQRCTC METHOD THE VQRCTC METHOD FOR DIATOM-DIATOM COLLISIONS REACTIVE SCATTERING SUMMARY NON-ADIABATIC TRANSITIONS PECHUKAS THEORY TULLY’S APPROACH SPAWNING METHOD THE MULTI-TRAJECTORY AND TDGH-DVR METHODS SECOND QUANTIZATION DIATOM-DIATOM COLLISIONS GENERAL HAMILTONIANS MORE COMPLEX SYSTEMS POTENTIAL ENERGY SURFACES THE BORN-OPPENHEIMER SEPARATION APPROXIMATE INTERACTION POTENTIALS POLYATOMIC MOLECULES SECOND QUANTIZATION SOLUTION FOR U THE CLASSICAL DEGREES OF FREEDOM RATE-CONSTANTS SOME CASE STUDIES CHEMICAL PROCESSES AT SURFACES REACTION PATH METHODS SURFACE CHARACTERISTICS THE REACTION PATH METHOD REACTION PATH CONSTRAINTS ABSOLUTE RATE-CONSTANTS SECOND QUANTIZATION APPROACH INITIALIZATION OF THE REACTION PATH DYNAMICS CROSS SECTIONS AND RATE-CONSTANTS THE REACTION VOLUME APPROACH A SIMPLI?ED HAMILTONIAN CHEMICAL PROCESSES IN CLUSTERS AND SOLUTION CENTROID MOLECULAR DYNAMICS CONCLUSION