Developments and applications of computational infrared spectroscopy in non-bonded systems: Quantal and classical systems

Abstract

Infrared (IR) spectroscopy, responding to molecular vibrations, is one of the most important tools in understanding the behavior of molecules. For complex systems, because of the relatively dense spectra lines, it could be very difficult to assign IR spectra merely by experience, an instance of which is non-bonded system. For middle-size system, theory and computation, however, can handle part of this problem by construct the potential energy surfaces (PESs) of system following a nuclear motion calculation classic or quantum mechanically. For large-size non-bonded system, although it is hard to calculate the properties of the whole system directly, by decomposing the system into quasi-isolated parts, the spectra can be calculated from the first principle using some approximations, which belong to the toolchain of computational spectroscopy. In this review, we recall some of these methodology based on perturbation theory. (1) In the research of van der Waals complexes, intramolecular vibrations are separated from intermolecular motion via Born-Oppenheimer approximation and first order Rayleigh-Schrodinger perturbation theory. For the ground and first excited state of the chromophores, rigid body intermolecular PESs are build including the relative orientation of the rigid molecules. Based on the intermolecular PESs, rotation and intermolecular radial stretching are treated using Discrete Variable Representation/Finite Basis Representation (DVR/FBR) fully quantum mechanically. The rovibrational spectra are then obtained by the gap between energy levels and the transition dipole moments. (2) Spectroscopy of quantum clusters, where chromophores molecules are caged in helium or hydrogen molecules solvent, are another important topic where perturbation theory and quantum simulation get involved. As previous systems, accurate two-body intermolecular PESs are also needed. The potential of the system is then represented by the many-body expansion, often truncated at two-body term. Quantum effect of the rigid molecules is simulated by finite temperature Path Integral Monte Carlo (PIMC) method. Worm operator is used to take exchange phenomena of the boson into account. Rotation of the chromophore molecule and the boson exchange were found to be very important in the simulation of quantum clusters. By studying IR spectra of quantum cluster, microscopic superfluidity was discovered and confirmed. (3) In bulk system like solution and biological systems, computation of IR spectra remains a challenge. The birth of quantum vibrational perturbation (QVP) theory gives an opportunity of considering the quantum effect and the chemical environment in the same scheme. Regular molecular dynamics simulation (MD) is executed to deal with the solvent fluctuation, and then quantal molecular vibration of chromophore is calculated via DVR quantum solver based on low dimensional cut of intramolecular vibrational coordinate. At each MD step, the instantaneous vibration frequencies are computed by perturbation theory. This mixed quantum mechanical/classic mechanical, or quasi-classical MD simulation will generate the instantaneous frequencies as function of time. Using line shape theory for quasi-classical MD, the spectra line of such system can be obtained. All three situations rely on perturbation theory more or less, which can be very computationally efficient. Because the main part of the IR transition gap can be corrected by experimental data, these methods can focus on transition frequency shift without considering error canceling artifact. In the future, systems containing stronger secondary bond need more efforts in the development of calculation methodology. Kinetic coupling is also an interesting topic to be developed in the coming days. Besides, the new proceeding in electronic structure theory helps a lot in the computational IR spectroscopy.