A time averaged semiclassical approach to IR spectroscopy

Abstract

We propose a new semiclassical approach to the calculation of molecular IR spectra. The method employs the time averaging technique of Kaledin and Miller upon symmetrization of the quantum dipole–dipole autocorrelation function. Spectra at high and low temperatures are investigated. In the first case, we are able to point out the possible presence of hot bands in the molecular absorption line shape. In the second case, we are able to reproduce accurate IR spectra as demonstrated by a calculation of the IR spectrum of the water molecule, which is within 4% of the exact intensity. Our time averaged IR spectra can be directly compared to time averaged semiclassical power spectra as shown in an application to the CO2 molecule, which points out the differences between IR and power spectra and demonstrates that our new approach can identify active IR transitions correctly. Overall, the method features excellent accuracy in calculating absorption intensities and provides estimates for the frequencies of vibrations in agreement with the corresponding power spectra. In perspective, this work opens up the possibility to interface the new method with the semiclassical techniques developed for power spectra, such as the divide-and-conquer one, to get accurate IR spectra of complex and high-dimensional molecular systems.

A Perspective on the Investigation of Spectroscopy and Kinetics of Complex Molecular Systems with Semiclassical Approaches

“…In quantum mechanical terms this is the Fourier transform of a trace σ ( ω ) = 1 2 π ∫ − ∞ + ∞ normale − i ω t T r [ e − β Ĥ Q μ̂ e i Ĥ t / ℏ μ̂ e − i Ĥ t / ℏ ] d t where Q is the quantum partition function of the system, β = 1/ T is the Boltzmann constant, μ̂ is the electric dipole operator, and Ĥ is the vibrational Hamiltonian operator. The corresponding IR absorption spectrum (α(ω)) at temperature T is obtained as α ( ω ) = ω ( 1 − e − β ℏ ω ) σ ( ω ) Demonstration of how to work out a time averaged expression for σ(ω), and therefore α(ω), with some relevant applications to some molecules is the object of a recent paper . What is important to notice in this Perspective is that this new approach opens up the possibility to adopt the same techniques developed for SC power spectra (i.e., MC SCIVR, DC SCIVR, and AS SCIVR) for calculation of IR spectra.…”

“…Demonstration of how to work out a time averaged expression for σ(ω), and therefore α(ω), with some relevant applications to some molecules is the object of a recent paper. 63 What is important to notice in this Perspective is that this new approach opens up the possibility to adopt the same techniques developed for SC power spectra (i.e., MC SCIVR, DC SCIVR, and AS SCIVR) for calculation of IR spectra. In this way, semiclassical IR spectra are potentially envisioned to be available in the near future for biomolecules, solvated systems, and materials at the same level of accuracy already demonstrated for power spectra.…”