Variational mixed quantum/semiclassical simulation of dihalogen guest and rare-gas solid host dynamics

Abstract

A variational mixed quantum-semiclassical theory for the internal nuclear dynamics of a small molecule and the induced small-amplitude coherent motion of a low-temperature host medium is developed, tested, and used to simulate the temporal evolution of nonstationary states of the internal molecular and surrounding medium degrees of freedom. In this theory, termed the Fixed Vibrational Basis/Gaussian Bath (FVB/GB) method, the system is treated fully quantum mechanically while Gaussian wave packets are used for the bath degrees of freedom. An approximate time-dependent wave function of the entire model is obtained instead of just a reduced system density matrix, so the theory enables the analysis of the entangled system and bath dynamics that ensues following initial displacement of the internal-molecular (system) coordinate from its equilibrium position. The norm- and energy-conserving properties of the propagation of our trial wave function are natural consequences of the Dirac-Frenkel-McLachlan variational principle. The variational approach also stabilizes the time evolution in comparison to the same ansatz propagated under a previously employed locally quadratic approximation to the bath potential and system-bath interaction terms in the bath-parameter equations of motion. Dynamics calculations are carried out for molecular iodine in a 2D krypton lattice that reveal both the time-course of vibrational decoherence and the details of host-atom motion accompanying energy dissipation and dephasing. This work sets the stage for the comprehensive simulation of ultrafast time-resolved optical experiments on small molecules in low-temperature solids.

Quantum dynamics and spectroscopy of dihalogens in solid matrices. I. Efficient simulation of the photodynamics of the embedded I2Kr18 cluster using the G-MCTDH method

“…( 22) is 6; apart for of the terms a 05 q 5 1 and a 06 q 6 1 , all the other monomials have maximum order 4. In previous work, 46 a polynomial expansion of the potential was also found to be reliable to describe the same system.…”

“…The system-environment perspective of the G-MCTDH description is the same as in the Fixed Vibrational Basis/Gaussian Bath (FVB/GB) approach developed by Cina and coworkers [44][45][46] and successfully applied to the I 2 : Kr system. In the FVB/GB method a different ansatz is used: The energy eigenstates of the system are calculated and the time-dependent wavefunction is obtained by combining each eigenstate with one variationally evolving 'thawed' Gaussian wave packet (i. e. with time-dependent position and width).…”

“…A similar approach is the local coherent state approximation (LCSA) of Martinazzo et al, 42 in which the vibrational basis is replaced by a discrete variable representation (DVR). More recently, Kovac and Cina 43 , described the photodynamics of a I 2 Kr 6 model cluster using the fixed vibrational basis/Gaussian bath theory (FVB/GB), [44][45][46] in which the wavefunction for the system coordinate (the I-I stretch) is represented on a conventional basis of vibrational eigenstates, and each level is accompanied by a Gaussian wave packet describing the bath. In all of these approaches, the propagation is fully based on the time-dependent variational principle.…”

Simulating quantum thermodynamics of a finite system and bath with variable temperature

“…Quantum nanodevices can be imagined whose performance may depend on considerations similar to those here. Molecular systems interacting with small baths are being investigated in calculations of entanglement dynamics and spectroscopic signals [7,8]. Recently [9][10][11], work on molecular "quantum chaos" is being conceptualized as a venue for the exploration of contemporary ideas about the foundations of quantum thermodynamics, to which we turn next.…”

A quantum mechanical insight into SN2 reactions: Semiclassical initial value representation calculations of vibrational features of the Cl−⋯CH3Cl pre-reaction complex with the VENUS suite of codes

“…This approach can be applied to other existing chemical dynamics codes and semiclassical methods have shown a good balance between feasibility and quantum accuracy. 2,[9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24] Secondly, we aim at describing how SC-IVR may be employed to shed some light on the mechanism of nucleophilic reactions from a quantum mechanical point of view. More specifically, we look at the importance of vibrational couplings in promoting an SN2 reaction, and the role played by anharmonic effects, which are neglected by the commonly employed harmonic approximation.…”