Data and Description for Fixed Vibrarional Basis/ Baussian Bath Theory
Fixed Vibrational Basis/Gaussian Bath theory (FVB/GB) is developed by Cina group to simulate small molecule dynamics in low-temperature media (J. Chem. Phys. 2007, 127, 114502; J. Phys. Chem. A. 2011, 115, 3980). It takes advantage of a timescale separation between the system and bath, but does not make an adiabatic approximation. The system is treated fully quantum mechanically and the system eigen vectors are found and used as basis to expand the overall nuclear ket of the sample. Because the bath motions are often indirectly driven by the system vibration to small amplitude in typical ultrafast optical experiments, it is appropriate to make an approximate, Gaussian ansatz for the bath wave packets. A variational approach is adopted to obtain equations of motion for the bath wave-packet parameters. The overall nuclear ket is then written in terms of the time-dependent parameters, which enables one to calculate any physical observable from the sample.
To apply variational FVB/GB, we consider a realistic model consisting of a 2D lattice with 25 atoms: one iodine molecule and 23 krypton atoms. The total potential is taken to be a sum of pair-wise atom-atom interactions. Periodic boundary conditions are adopted in order to mimic the presence of the infinite bulk surrounding our model system. The size of the period square box is 18.558 angstroms. The equilibrium configuration is obtained by carrying out a cooling simulation. Excluding two zero-frequency modes, we have 48 normal modes. The normal coordinate of the highest-frequency mode is taken to be the system coordinate, while the remaining 47 internal normal coordinates are taken to constitute the bath coordinates. The orthogonal matrix being used to transform Cartesian to normal coordinates enables one to write the total potential energy function in terms of the system coordinate and a 47-element bath-coordinate vector. It is then easy to decompose the potential function into system, bath, and interaction potentials. For the system, we keep the full potential. And we make a Taylor expansion of the bath and system-bath interaction potentials, and keep terms up to fourth order. Coefficients can, in principle, be obtained by using a finite-difference method. As a practical alternative, we simply fit the multidimensional bath (and system-bath interaction) potentials to polynomials in the bath (or system and bath) coordinates. There are as many as 447,910 coefficients and terms in the Taylor expansion. These coefficients can be found here.