双原子分子振动对热力学性质的影响

本文在分析了双原子分子振动能级的完备性和有限性及其对统计计算带来的影响的基础上,借助代数（AM）方法得到的双原子分子振动能级完全集合,采用量子力学统计系综方法,讨论了双原子分子振动能量对宏观热力学性质的统计贡献,并以氮气为例计算了相应的热力学函数和振动热容量．结果表明,真实的双原子分子振动能级是有限的;确定最高振动量子数和振动能级完全集合是正确进行统计分析的基础和关键;考虑振动能级的完备性和有限性后,只能导致数值解而不是解析解,所得的结果优于谐振子模型的解析结果,与实验数据吻合得很好．     

Vibrational structure theory: new vibrational wave function methods for calculation of anharmonic vibrational energies and vibrational contributions to molecular properties

A number of recently developed theoretical methods for the calculation of vibrational energies and wave functions are reviewed. Methods for constructing the appropriate quantum mechanical Hamilton operator are briefly described before reviewing a particular branch of theoretical methods for solving the nuclear Schr?dinger equation. The main focus is on wave function methods using the vibrational self-consistent field (VSCF) as starting point, and includes vibrational configuration interaction (VCI), vibrational M?ller-Plesset (VMP) theory, and vibrational coupled cluster (VCC) theory. The convergence of the different methods towards the full vibrational configuration interaction (FVCI) result is discussed. Finally, newly developed vibrational response methods for calculation of vibrational contributions to properties, energies, and transition probabilities are discussed.     

Two-dimensional infrared spectral signature and hydration of the oxalate dianion

Ultrafast vibrational spectra of the aqueous oxalate ion in the region of its carboxylate asymmetric stretch modes show novel relaxation processes. Two-dimensional infrared vibrational echo spectra and the vibrational dynamics obtained from them along with measurements of the anisotropy decay provide a picture in which the localization of the oxalate vibrational excitation onto the carboxylate groups occurs in ~450 fs. Molecular dynamics simulations are used to characterize the vibrational dynamics in terms of dihedral angle motion between the two carboxylate planes and solvation dynamics. The localization of the oxalate vibrational excitation onto the carboxylates is induced by the fluctuations in the carboxylate vibrational frequencies which are shown by theory and experiment to have a similar correlation time as the anisotropy decay.     

Separation of the vibrational,rotational, and translational motions of polyatomic molecules using curvilinear vibrational coordinates

A new method is suggested for separating the vibrational, rotational, and translational motions of polyatomic molecules using curvilinear vibrational coordinates that are linear with respect to the natural vibrational coordinates. It is shown that, in this case, Coriolis interactions between the vibrational and rotational motions are absent. The solutions of the anharmonic vibrational-rotational problems in the curvilinear and linear vibrational coordinates are compared. The absence of Coriolis interactions between the vibrational and rotational motions in the curvilinear vibrational coordinates is proved numerically. The same conclusion is additionally supported by calculations of the anharmonic vibrational energy levels for the H₂O, H₂S, NO₂, SO₂, and ClO₂ molecules in the linear and curvilinear vibrational coordinates using the Hamiltonian designed in the curvilinear vibrational coordinates with and without Coriolis vibrational-rotational interactions. Volgograd Pedagogical University. Translated fromZhurnal Strukturnoi Khimii, Vol. 36, No. 2, pp. 239–254, March–April, 1995. Translated by I. Izvekova     

On the interpretation of vibrational relaxation measurements

The relative relaxation rates of vibrational level populations following establishment of a Boltzmann vibrational distribution by rapid vibration—vibration energy transfer are shown to depend on the nature and extent of the departure from equilibrium. The only kinetic information obtainable under such conditions is τ, the relaxation time of the vibrational energy. The implications for interpretation of laser-induced vibrational fluorescence measurements are emphasized.     

Automatic generation of force fields and property surfaces for use in variational vibrational calculations of anharmonic vibrational energies and zero-point vibrational averaged properties

An automatic and general procedure for the calculation of geometrical derivatives of the energy and general property surfaces for molecular systems is developed and implemented. General expressions for an n-mode representation are derived, where the n-mode representation includes only the couplings between n or less degrees of freedom. The general expressions are specialized to derivative force fields and property surfaces, and a scheme for calculation of the numerical derivatives is implemented. The implementation is interfaced to electronic structure programs and may be used for both ground and excited electronic states. The implementation is done in the context of a vibrational structure program and can be used in combination with vibrational self-consistent field (VSCF), vibrational configuration interaction (VCI), vibrational Moller-Plesset, and vibrational coupled cluster calculations of anharmonic wave functions and calculation of vibrational averaged properties at the VSCF and VCI levels. Sample calculations are presented for fundamental vibrational energies and vibrationally averaged dipole moments and frequency dependent polarizabilities and hyperpolarizabilities of water and formaldehyde.     

Variational calculation of vibrational linear and nonlinear optical properties

A variational approach for reliably calculating vibrational linear and nonlinear optical properties of molecules with large electrical and/or mechanical anharmonicity is introduced. This approach utilizes a self-consistent solution of the vibrational Schrodinger equation for the complete field-dependent potential-energy surface and, then, adds higher-level vibrational correlation corrections as desired. An initial application is made to static properties for three molecules of widely varying anharmonicity using the lowest-level vibrational correlation treatment (i.e., vibrational M?ller-Plesset perturbation theory). Our results indicate when the conventional Bishop-Kirtman perturbation method can be expected to break down and when high-level vibrational correlation methods are likely to be required. Future improvements and extensions are discussed.     

Molecular vibrations of methane molecules in the structure I clathrate hydrate from ab initio molecular dynamics simulation

Vibrational frequencies of guest molecules in clathrate hydrates reflect the molecular environment and dynamical behavior of molecules. A detailed understanding of the mechanism for the vibrational frequency changes of the guest molecules in the clathrate hydrate cages is still incomplete. In this study, molecular vibrations of methane molecules in a structure I clathrate hydrate are calculated from ab initio molecular dynamics simulation. The vibrational spectra of methane are computed by Fourier transform of autocorrelation functions, which reveal distinct separation of each vibrational mode. Calculated symmetric and asymmetric stretching vibrational frequencies of methane molecules are lower in the large cages than in the small cages (8 and 16 cm(-1) for symmetric and asymmetric stretching, respectively). These changes are closely linked with the C-H bond length. The vibrational frequencies for the bending and rocking vibrational modes nearly overlap in each of the cages.     

Anharmonic vibrational probe for N-methylacetamide in different micro-environments

In the present study, anharmonic vibrational properties of the amide modes in N-methylacetamide (NMA), a model molecule for peptide vibrational spectroscopy, are examined by DFT calculations. The 3N-6 normal mode frequencies, diagonal and off-diagonal anharmonicities are evaluated by means of the second order vibrational perturbation theory (VPT2). Good performance of B3LYP/6-31+G** is found for predicting vibrational frequencies in comparison with gas phase experimental data. The amide vibrational modes are assigned through potential energy distribution analysis (PED). The solvation effect on the amide vibrational modes is modeled within the PCM method. From gas phase to polar solvents, red shifts are observed for both harmonic and anharmonic vibrational frequency of amide I mode while the CO bond length increases upon the solvent polarity. Cubic and quartic force constants are further calculated to evaluate the origin of the anharmonicity for the amide I mode of NMA in different micro-environments.     

Approximate inclusion of four-mode couplings in vibrational coupled-cluster theory

The vibrational coupled cluster (VCC) equations are analyzed in terms of vibrational Mo?ller-Plesset perturbation theory aiming specifically at the importance of four-mode couplings. Based on this analysis, new VCC methods are derived for the calculation of anharmonic vibrational energies and vibrational spectra using vibrational coupled cluster response theory. It is shown how the effect of four-mode coupling and excitations can be efficiently and accurately described using approximations for their inclusion. Two closely related approaches are suggested. The computational scaling of the so-called VCC[3pt4F] method is not higher than the fifth power in the number of vibrational degrees of freedom when up to four-mode coupling terms are present in the Hamiltonian and only fourth order when only up to three-mode couplings are present. With a further approximation, one obtains the VCC[3pt4] model which is shown to scale with at most the fourth power in the number of vibrational degrees of freedom for Hamiltonians with both three- and four-mode coupling levels, while sharing the most important characteristics with VCC[3pt4F]. Sample calculations reported for selected tetra-atomic molecules as well as the larger dioxirane and ethylene oxide molecules support that the new models are accurate and useful.     

Comment on the effect of internal energy on the rate of formation of NO+ by the reaction of O++N2

The effects of translational and vibrational energy on the rate of formation of NO⁺ are compared using the translational and vibrational excitation functions. The effects of simultaneous variation of translational, rotational and vibrational energy are assessed by comparing rates as a function of total reactant center of mass energy.     

Collective vibrations in cluster models for semiconductor surfaces: vibrational spectra of acetylenyl and methylacetylenyl functionalized Si(111)

The geometries and harmonic vibrational frequencies of the acetylenyl and methylacetylenyl functionalized Si(111) surfaces are investigated using quantum chemical calculations. The vibrational spectra are computed using a previously introduced method whereby the collective vibrational modes that correspond to the vibrations of the infinite periodic system are derived from modest sized cluster models. Our predictions should be useful for the interpretation of the experimental spectra when they become available. The symmetry elements of the methylacetylenyl Si(111) surface that are derived from the space group of the optimized structure and a vibrational mode resulting from photon-adsorbate coupling are explored.     

High-resolution waveguide terahertz spectroscopy of partially oriented organic polycrystalline films

We have characterized the terahertz (THz) vibrational spectroscopy of organic polycrystalline thin films using the new experimental technique of waveguide terahertz time domain spectroscopy (waveguide THz-TDS). The organic materials used in this study are tetracyanoquinodimethane (TCNQ) and 1,3-dicyanobenzene (13DCB). For each material, a thin film is cast onto one of the inner surfaces of a metal parallel plate waveguide (PPWG), followed by measurement of the low-frequency vibrational spectrum using waveguide THz-TDS. The vibrational spectra of the waveguide films are compared to corresponding vibrational spectra of standard pellet samples made by dispersing the organic solid in transparent polyethylene. We show how the waveguide films produce significantly narrower THz vibrational line shapes and reveal additional spectral lines that are obscured by inhomogeneous broadening effects in the pellet samples. When TCNQ waveguide films are cooled to 77 K, vibrational line widths as sharp as 25-30 gigahertz (0.83-1.0 cm(-1)) at the full width at half-maximum are observed, which are among the narrowest far-infrared line widths measured for this material. The origin of the line-narrowing effect for the waveguide films is the suppression of inhomogeneous broadening due to the planar ordering of the film on the waveguide surface. The TCNQ waveguide films are further characterized using optical microscopic evaluation to understand how film morphology affects the THz vibrational spectrum. X-ray diffraction is used to determine the orientation of the polycrystalline TCNQ films on the PPWG surface and to qualitatively explain the different vibrational line strengths observed for the ordered waveguide film relative to the random pellet.     

On the preference for vibrational energy in diatomic dissociation

Recent measurements of dissociation and relaxation rates, and of dissociation induction times, are shown to indicate very serious depletion of vibrational state populations during thermal dissociation. The large measured dissociation rates are then only compatible with dissociation from low vibrational states, i.e., there can be at most a very weak bias favoring vibrational excitation in thermal dissociation. It is suggested that dissociation from low vibrational states is assisted by rotational excitation.     

Correlating the vibrational spectra of structurally related molecules: A spectroscopic measure of similarity

Using catastrophe theory and the concept of a mutation path, an algorithm is developed that leads to the direct correlation of the normal vibrational modes of two structurally related molecules. The mutation path is defined by weighted incremental changes in mass and geometry of the molecules in question, which are successively applied to mutate a molecule into a structurally related molecule and thus continuously converting their normal vibrational spectra from one into the other. Correlation diagrams are generated that accurately relate the normal vibrational modes to each other by utilizing mode‐mode overlap criteria and resolving allowed and avoided crossings of vibrational eigenstates. The limitations of normal mode correlation, however, foster the correlation of local vibrational modes, which offer a novel vibrational measure of similarity. It will be shown how this will open new avenues for chemical studies. © 2017 Wiley Periodicals, Inc.     

Low-energy dissociative recombination in small polyatomic molecules

Indirect dissociative recombination of low-energy electrons and molecular ions often occurs through capture into vibrationally excited Rydberg states. Properties of vibrational autoionization, the inverse of this capture mechanism, are used to develop some general ideas about the indirect recombination process, and these ideas are illustrated by examples from the literature. In particular, the Δv = -1 propensity rule for vibrational autoionization, i.e., that vibrational autoionization occurs by the minimum energetically allowed change in vibrational quantum numbers, leads to the prediction of thresholds in the dissociative recombination cross sections and rates at the corresponding vibrational thresholds. Capture into rotationally excited Rydberg states is also discussed in terms of recent low-temperature studies of the dissociative recombination of H(3)(+).     

Quantum mechanical predictions of chiroptical vibrational properties

The developments in quantum mechanical calculations of vibrational circular dichroism, vibrational Raman optical activity, and vibrational contributions to optical rotation are summarized. Further developments needed in each of these areas are pointed out. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Vibrational contributions to indirect spin-spin coupling constants calculated via variational anharmonic approaches

Zero-point vibrational contributions to indirect spin-spin coupling constants for N2, CO, HF, H2O, C2H2, and CH4 are calculated via explicitly anharmonic approaches. Thermal averages of indirect spin-spin coupling constants are calculated for the same set of molecules and for C2X4, X = H, F, Cl. Potential energy surfaces have been calculated on a grid of points and analytic representations have been obtained by a linear least-squares fit in a direct product polynomial basis. Property surfaces have been represented by a fourth-order Taylor expansion around the equilibrium geometry. The electronic structure calculations employ density functional theory, and vibrational contributions to indirect spin-spin coupling constants are calculated employing vibrational self-consistent-field and vibrational configuration-interaction methods. The performance of vibrational perturbation theory and various approximate variational calculations are discussed. Thermal averages are computed by state-specific and virtual vibrational self-consistent-field methods.