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

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

Polyynes (C_2nH₂) show the unusually strong π_g + π_u combination bands in the infrared absorption spectra. We calculated them as the first overtone of the local CCH bending; the strong intensities are interpreted as a consequence of the large-amplitude bending vibration of the acidic acetylenic hydrogen combined with the size-dependent π electron conjugation. Our theoretical calculations show that the absorption intensity increases steadily and their increase rate is gradually slowed down by increasing the number of acetylene units up to n = 9. However, the calculated vibrational wavenumber converges quickly in agreement with the experimental observation. The second-order electron density deformation caused by the local CCH bending was analyzed using the linear response functions, including the linear and nonlinear contributions, to explain the n dependence. The easily polarizable π electron density caused two kinds of deformation-dominant but dark δ_xx-yy type and minor but bright σ type. Both of them exhibit interesting zigzag sign alternations, consistent with the law of alternating polarity of Coulson and Longuet-Higgins. The electron density polarization in these intra- and interacetylene units induces a large axial component molecular dipole moment, contributing to the intensity that increases with n. The difference between the curvilinear and rectilinear bending coordinates is interpreted within the present theoretical scheme.

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

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.

Breakthrough Potential in Near-Infrared Spectroscopy: Spectra Simulation. A Review of Recent Developments

Near-infrared (12,500–4,000 cm⁻¹; 800–2,500 nm) spectroscopy is the hallmark for one of the most rapidly advancing analytical techniques over the last few decades. Although it is mainly recognized as an analytical tool, near-infrared spectroscopy has also contributed significantly to physical chemistry, e.g., by delivering invaluable data on the anharmonic nature of molecular vibrations or peculiarities of intermolecular interactions. In all these contexts, a major barrier in the form of an intrinsic complexity of near-infrared spectra has been encountered. A large number of overlapping vibrational contributions influenced by anharmonic effects create complex patterns of spectral dependencies, in many cases hindering our comprehension of near-infrared spectra. Quantum mechanical calculations commonly serve as a major support to infrared and Raman studies; conversely, near-infrared spectroscopy has long been hindered in this regard due to practical limitations. Advances in anharmonic theories in hyphenation with ever-growing computer technology have enabled feasible theoretical near-infrared spectroscopy in recent times. Accordingly, a growing number of quantum mechanical investigations aimed at near-infrared region has been witnessed. The present review article summarizes these most recent accomplishments in the emerging field. Applications of generalized approaches, such as vibrational self-consistent field and vibrational second order perturbation theories as well as their derivatives, and dense grid-based studies of vibrational potential, are overviewed. Basic and applied studies are discussed, with special attention paid to the ones which aim at improving analytical spectroscopy. A remarkable potential arises from the growing applicability of anharmonic computations to solving the problems which arise in both basic and analytical near-infrared spectroscopy. This review highlights an increased value of quantum mechanical calculations to near-infrared spectroscopy in relation to other kinds of vibrational spectroscopy.

Anharmonic calculations of frequencies and intensities of OH stretching vibrations of (R)-1,3-butanediol conformers in the fundamentals and first overtones by density functional theory

The frequencies and absorption intensities of the five kinds of conformers of 1,3-butanediol with the same carbon skeleton (GG') were calculated by anharmonic calculation for the fundamentals and first overtones of OH stretching vibrations. The four kinds of conformers form intramolecular hydrogen bonds and one conformer did not. Intramolecular hydrogen bond formation shifted the frequency of fundamental and first overtone of H-bonding OH stretching vibration to the lower frequency. The absorption intensities of the fundamentals as well as the vibrational anharmonicities increased upon hydrogen bond formation, while the intensities of first overtones decreased. The differences of conformers were clearly seen in the frequencies of the first overtones of free OH.

Effects of intermolecular interactions on absorption intensities of the fundamental and the first, second, and third overtones of OH stretching vibrations of methanol and t-butanol‑d9 in n-hexane studied by visible/near-infrared/infrared spectroscopy

Visible (Vis), near-infrared (NIR) and IR spectra in the 15,600-2500cm^-1 region were measured for methanol, methanol-d₃, and t-butanol-d₉ in n-hexane to investigate effects of intermolecular interaction on absorption intensities of the fundamental and the first, second, and third overtones of their OH stretching vibrations. The relative area intensities of OH stretching bands of free and hydrogen-bonded species were plotted versus the vibrational quantum number using logarithm plots (V=1-4) for 0.5M methanol, 0.5M methanol‑d₃, and 0.5M t-butanol-d₉ in n-hexane. In the logarithm plots the relative intensities of free species yield a linear dependence irrespective of the solutes while those of hydrogen-bonded species deviate significantly from the linearity. The observed results suggest that the modifications in dipole moment functions of the OH bond induced by the formation of the hydrogen bondings change transient dipole moment, leading to the deviations of the dependences of relative absorption intensities on the vibrational quantum number from the linearity.

Absorption intensity changes and frequency shifts of fundamental and first overtone bands for OH stretching vibration of methanol upon methanol–pyridine complex formation in CCl4: analysis by NIR/IR spectroscopy and DFT calculations

The first overtone of the OH stretching mode of the OH–N hydrogen bond of the methanol–pyridine complex was observed.

Interpretation of semiclassical transition moments through wave function expansion of dipole moment functions with applications to the OH stretching spectra of simple acids and alcohols

Semiclassical description of molecular vibrations has provided us with various computational approximations and enhanced our conceptual understanding of quantum mechanics. In this study, the transition moments of the OH stretching fundamental and overtone intensities (Δv = 1-6) of some alcohols and acids are calculated by three kinds of semiclassical methods, correspondence-principle (CP) approximation, quasiclassical approximation, and uniform WKB approximation, and their respective transition moments are compared to those by the quantum theory. On the basis of the local mode picture, the one-dimensional potential energy curves and the dipole moment functions (DMFs) were obtained by density functional theory calculations and then fitted to Morse functions and sixth-order polynomials, respectively. It was shown that both the transition energies and the absorption intensities derived in the semiclassical methods reproduced their respective quantum values. In particular, the CP approximation reproduces the quantum transition moments if the formula given by Naccache is used for the action integral value. On the basis of these semiclassical results, we present a picture to understand the small variance in the overtone intensities of these acids and alcohols. Another important result is the ratios of semiclassical-to-quantum transition moment are almost independent of the applied molecules even with a great molecular variance of the DMFs, and they depend only on the nature of the semiclassical approximations and the quantum number. The difference between the semiclassical and quantum transition moments was analyzed in terms of a hitherto unrecognized concept that the Fourier expansion of the time dependent DMF in the CP treatment is a kind of the wave function expansion method using trigonometric functions as the quotient functions. For a Morse oscillator, we derive the analytic and approximate expressions of the quotient functions in terms of the bond displace coordinate in both the CP and the quantum mechanical frameworks and discuss the methodological dependence of the calculated transition moments. As a byproduct, we have found a simple derivation of the DMF expression first derived by Timm and Mecke long time ago.