Metrics
2 Record Views
Journal article
Vibrational spectrum of a 1D oscillator: The quantum, the Wigner, and the classical ways
Journal of the Chinese Chemical Society (Taipei), Vol.70(3), pp.495-510
03/30/2023
Web of Science ID: WOS:000877523800001
Abstract
Infrared spectra have been used in many chemical applications, and theoretical calculations have been useful for analyzing these experimental results. While quantum mechanics is used for calculating the spectra for small molecules, classical mechanics is used for larger systems. However, a systematic understanding of the similarities and differences between the two approaches is not clear. Previous studies focused on peak position and relative intensities of the spectra obtained by various quantum and classical methods, but here, we included “absolute” intensities in the evaluation. The infrared spectrum of a one‐dimensional (1D) harmonic oscillator (HO) and Morse oscillator were examined using four treatments: quantum, Wigner, truncated Wigner, and classical microcanonical treatments. For a 1D HO with a linear dipole moment function (DMF), the quantum and Wigner treatments give nearly the same spectra. On the other hand, the truncated Wigner underestimates the fundamental transition's intensity by half. In the case of cubic DMF, the truncated Wigner and classical methods fail to reproduce the relative intensity between the fundamental and second overtone transitions. Unfortunately, all the Wigner and classical methods fail to agree with the quantum results for a Morse oscillator with just 1% anharmonicity.
We calculated the vibrational spectra of simple one‐dimensional systems using quantum, semiclassical, and classical methods to understand if the dipole autocorrelation function of classical propagation methods can reproduce the quantum propagation method.
Related links
Details
- Title
- Vibrational spectrum of a 1D oscillator
- Publication Details
- Journal of the Chinese Chemical Society (Taipei), Vol.70(3), pp.495-510
- Resource Type
- Journal article
- Publisher
- Wiley‐VCH Verlag GmbH & Co. KGaA
- Number of pages
- 16
- Grant note
- National Science and Technology Council, Taiwan: 111-2113-M-001 -049 -, 111-2639-M-A49 -001 -ASP
National Science and Technology Council, Taiwan, Grant/Award Numbers: 111-2113-M-001 -049 -, 111-2639-M-A49 -001 -ASP
- Copyright
- © 2022 Chemical Society Located in Taipei and Wiley-VCH GmbH.
- Identifiers
- WOS:000877523800001; 99381548017606600
- Academic Unit
- Chemistry; Hal Marcus College of Science and Engineering
- Language
- English