Theoretical analysis of weak adjacent substituent effect on the overtone intensities of XH (X = C, O) stretching vibrations

Hirokazu Takahashi, Satoshi Yabushita

Research output: Contribution to journalArticle

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Abstract

It is known that the overtone intensities of some set of OH and CH stretching vibrations show only a weak dependence on the adjacent substituent, in sharp contrast to the much stronger dependence of their fundamental intensities. To understand this characteristic, we calculated the fundamental and overtone intensities of the Δv = 1-6 transitions for the OH stretching of alcohols and acids and the CH stretching of hydrocarbons with different types of hybridization. Based on the local-mode model, from the three components of the dipole moment function (DMF) of each molecule, a one-component effective DMF that recovered about 95% of the total intensity for the Δv = 1-6 transitions was constructed and expressed as a sixth-order polynomial of the bond displacement ΔR, with the leading expansion coefficients M 1, M2, and M3 for the linear, quadratic, and cubic terms, respectively. When these coefficients for each molecule were represented as points in the coordinate system O-M1M 2M3, the points for some set of molecules were found to lie on a straight line. Interestingly, the line had a direction cosine such that the resultant transition moments exhibited a small substituent dependence of the overtone intensities. Moreover, the slope of the line could be well approximated by the Morse exponential parameter and the bond distance. These characteristics of the DMFs can be rationalized by using the calculated transition moments and the wave function expansion method with the eigenfunction of the Morse potential. It was also verified by the quasiclassical method of Medvedev that these characteristics of the DMFs are the intrinsic reason for the weak substituent dependence of the overtone intensities. It is emphasized that the graphical representation of the DMF parameters provides a comprehensive tool for discussing various aspects of vibrational intensities.

Original languageEnglish
Pages (from-to)5491-5502
Number of pages12
JournalJournal of Physical Chemistry A
Volume117
Issue number26
DOIs
Publication statusPublished - 2013 Jul 3

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Dipole moment
Stretching
harmonics
vibration
Molecules
Morse potential
dipole moments
Wave functions
Hydrocarbons
Eigenvalues and eigenfunctions
Alcohols
Polynomials
methylidyne
Acids
moments
molecules
expansion
coefficients
eigenvectors
polynomials

ASJC Scopus subject areas

  • Physical and Theoretical Chemistry

Cite this

Theoretical analysis of weak adjacent substituent effect on the overtone intensities of XH (X = C, O) stretching vibrations. / Takahashi, Hirokazu; Yabushita, Satoshi.

In: Journal of Physical Chemistry A, Vol. 117, No. 26, 03.07.2013, p. 5491-5502.

Research output: Contribution to journalArticle

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