Semiquantal time-dependent Hartree approach to condensed phase chemical dynamics: application to the system-bath model

A corpuscular picture of electrons in chemical bond

We introduce a theory of chemical bond with a corpuscular picture of electrons. It employs a minimal set of localized electron wave packets with "floating and breathing" degrees of freedom and the spin-coupling of non-orthogonal valence-bond theory. Its accuracy for describing potential energy curves of chemical bonds in ground and excited states of spin singlet and triplet is examined.

Canonical averaging in the second order quantized Hamilton dynamics by extension of the coherent state thermodynamics of the harmonic oscillator

A conceptually simple approximation to quantum mechanics, quantized Hamilton dynamics (QHD) includes zero-point energy, tunneling, dephasing, and other important quantum effects in a classical-like description. The hierarchy of coupled differential equations describing the time evolution of observables in QHD can be mapped in the second order onto a classical system with double the dimensionality of the original system. While QHD excels at dynamics with a single initial condition, the correct method for generating thermal initial conditions in QHD remains an open question. Using the coherent state representation of thermodynamics of the harmonic oscillator (HO) [Schnack, Europhys. Lett. 45, 647 (1999)], we develop canonical averaging for the second order QHD [Prezhdo, J. Chem. Phys. 117, 2995 (2002)]. The methodology is exact for the free particle and HO, and shows good agreement with quantum results for a variety of quartic potentials.

Semiquantal analysis of hydrogen bond

The semiquantal time-dependent Hartree (SQTDH) theory is applied to the coupled Morse and modified Lippincott-Schroeder (LS) model potentials of hydrogen bond. The structural correlation between the heavy atoms distance and the proton position, the geometric isotope effect, the energy of hydrogen bond formation, and the proton vibrational frequency shift are examined in a broad range of structural parameters. In particular, the geometric isotope effect is found to depend notably on the choice of the potential model, for which the LS potential gives the isotope shift of the heavy atoms distance in the range of 0.02-0.04 A, in quantitative agreement with the experimental findings from assortment of hydrogen bonding crystals. The fourth-order expansion approximation to the semiquantal extended potential was confirmed to be highly accurate in reproducing the full SQTDH results. The approximation is computationally efficient and flexible enough to be applied to general models of hydrogen bond.

Second-order quantized Hamilton dynamics coupled to classical heat bath

Starting with a quantum Langevin equation describing in the Heisenberg representation a quantum system coupled to a quantum bath, the Markov approximation and, further, the closure approximation are applied to derive a semiclassical Langevin equation for the second-order quantized Hamilton dynamics (QHD) coupled to a classical bath. The expectation values of the system operators are decomposed into products of the first and second moments of the position and momentum operators that incorporate zero-point energy and moderate tunneling effects. The random force and friction as well as the system-bath coupling are decomposed to the lowest classical level. The resulting Langevin equation describing QHD-2 coupled to classical bath is analyzed and applied to free particle, harmonic oscillator, and the Morse potential representing the OH stretch of the SPC-flexible water model.

A canonical averaging in the second-order quantized Hamilton dynamics

Quantized Hamilton dynamics (QHD) is a simple and elegant extension of classical Hamilton dynamics that accurately includes zero-point energy, tunneling, dephasing, and other quantum effects. Formulated as a hierarchy of approximations to exact quantum dynamics in the Heisenberg formulation, QHD has been used to study evolution of observables subject to a single initial condition. In present, we develop a practical solution for generating canonical ensembles in the second-order QHD for position and momentum operators, which can be mapped onto classical phase space in doubled dimensionality and which in certain limits is equivalent to thawed Gaussian. We define a thermal distribution in the space of the QHD-2 variables and show that the standard beta=1/kT relationship becomes beta'=2/kT in the high temperature limit due to an overcounting of states in the extended phase space, and a more complicated function at low temperatures. The QHD thermal distribution is used to compute total energy, kinetic energy, heat capacity, and other canonical averages for a series of quartic potentials, showing good agreement with the quantum results.