Graphical Transition Moment Decomposition and Conceptual Density Functional Theory Approaches to Study the Fundamental and Lower-Level Overtone Absorption Intensities of Some OH Stretching Vibrations

Abstract

The investigation of electron density migrations caused by molecular structure changes is of central importance in various fields of chemistry. To address this topic in general and to study absorption intensities of vibrations, we analyze sensitive dipole moment functions (DMFs) of a molecule by combining the linear response function of conceptual DFT and bond dipoles separated by the quantum theory of atoms in molecules with a graphical transition moment decomposition scheme. The fundamental intensities of OH stretching vibrations depend strongly on the substituents but only weakly on the molecular conformations. Interestingly, in some alcohols, completely opposite trends have been observed for the lower-level overtone intensities: a weak substituent dependence but a stronger conformation dependence. It is well known that the formation of a hydrogen-bonded complex increases the OH stretching fundamental intensity, but less well known is the decrease in their overtone intensities. To investigate these characteristics comprehensively, we calculated their intensities (Δv = 1, 2, and 3) for conformers of ethanol and trifluoroethanol (TFE) and hydrogen-bonded phenol (PhOH) systems via the DFT method in the local mode model for the OH stretching coordinate ΔR. Their first and second derivatives of the electron density with respect to ΔR were calculated and interpreted using their bond moments. For ethanol and TFE, the OH, CC, and CH bond moments were found to make an important contribution to the molecular DMF derivatives parallel to the OH bond. The OH bond contributes only to the first derivative of DMF, and its conformational dependence is determined by the magnitude of the charge polarization of each structure. The electron density derivatives in the CC bond region were largely maintained during the internal rotation; thus, their conformation-dependent contributions were expressed by a geometrical factor of the CC bond direction. The CH bond at the antiperiplanar position of the OH bond was found to make a remarkably large contribution to the second derivative of DMF in the gauche conformer. The importance of electron density migration on substituents was also identified in the hydrogen-bonded phenol, in which the π-electron density change on the aromatic ring was clearly shown. This migration creates the DMF derivatives both perpendicular and parallel to the OH bond and strongly affects the absorption intensities. In all the cases, some bond moments on the substituents contribute to the first and second DMF derivatives in a structure-dependent manner, thus explaining their stereoelectronic effects.

Selection of the Effective Characteristic Spectra Based on the Chemical Structure and Its Application in Rapid Analysis of Ethanol Content in Gasoline

“…Gasoline is mainly composed of hydrocarbons, and changes in the absorption strength of the C–H bond were not apparent, whereas changes in the absorption strength of the O–H bond were apparent. In the characteristic absorption spectra of ethanol, the spectra ranged from 6060.171 to 7141.113 cm –1 , covering the first overtone of O–H stretching. − The absorption peaks in the region from 4661.104 to 5000.515 cm –1 are related to the combined absorption frequency of the O–H stretching and bending vibrations. , The spectral range from 6450.422 to 7407.241 cm –1 resulted from the first overtone of the combination band from C–H + C–H and C–H + C–C stretching; , and the spectral range from 5660.050 to 6001.389 cm –1 corresponds to the first overtone of C–H stretching . The absorption peaks in the region from 8300.121 to 8500.682 cm –1 are caused by the second overtone of C–H from the methyl group, , while the peaks below 6060.171 cm –1 contain the first overtone from aromatic C–H stretching .…”

Size-Dependent πg + πu Combination Band Intensities of Polyynes C2nH2 (n = 1–9) Analyzed by the Local CCH Bending and the Linear Response Functions

“…However, such a sum-over-state expansion method typically yields a slow convergence with fluctuation errors. Details of the real space change δρ­( r ) caused by the perturbative change in the nuclear attractive potential δ v ( r ′) by molecular vibrations can be analyzed quantitatively using the linear response function of the conceptual density functional theory (DFT), − as demonstrated by us recently . Dipole moment derivative calculations using the linear response function of DFT are considered to be the analytical derivative calculations using the perturbed Hartree–Fock scheme, − and thus have variational stability.…”

“…Details of the real space change δρ(r) caused by the perturbative change in the nuclear attractive potential δv(r′) by molecular vibrations can be analyzed quantitatively using the linear response function of the conceptual density functional theory (DFT), 34−37 as demonstrated by us recently. 38 Dipole moment derivative calculations using the linear response function of DFT are considered to be the analytical derivative calculations using the perturbed Hartree−Fock scheme, 39−41 and thus have variational stability. Most studies have applied a notion of linear response to computing atom-condensed charges by integrating δρ(r) over each atom.…”