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     

Laser Raman and infrared spectra and normal coordinate analysis of CH3MCl3 (M  Si and Ge)

The vibrational spectroscopic data, including i.r., far-i.r. and Raman spectra, of methyltrichlorosilane CH₃SiCl₃ and methyltrichlorogermane CH₃GeCl₃ have been recorded. All the observed vibrational bands are assigned to vibrational modes. The normal modes of vibration were analysed and calculated and a force field for each of the two compounds is calculated.     

Quantum mechanical study of electronic transitions in collinear atom—diatom collisions

Quantum mechanical calculations are reported for model, nonreactive, collinear collision systems composed of the H₂ diatom and the halogen atom X = F, Cl, Br or I. The model involves two electronic potential energy surfaces, obtained in a diatomics-in-molecules formulation, that correspond asymptotically to the two spin-orbit states of X. On each surface the calculations include as many vibrational states of H₂ as are asymptotically allowed, up to a limiting number of five. The first two collision systems, FH₂ and ClH₂, are characterized by electronic splittings much smaller than any vibrational spacing included in the diatom spectrum, and as a result they show a high degree of vibrational elasticity with essentially all transition activity testricted to spin—orbit switching in the halogen. This pattern is broken for BrH₂ collisions, where the near-equality between electronic and vibrational quanta apparently leads to a resonant exchange of energy between the two modes. The greater spinorbit splitting in iodine (～ 2 vibrational quanta) results in largely elastic behavior in IH₂ collisions for both vibrational and electronic transitions. A modified Massey criterion is exhibited for some of the FH₂ and BrH₂ transitions.     

Vibrational relaxation of ethylene oxide and ethylene oxide-rare-gas mixtures

The collision-induced vibrational energy relaxation of ethylene oxide (C₂H₄O) was studied by means of laser-induced fluorescence. The time-dependent population of the vibrational modes v₃ and v₅/v₁₂ was measured after excitation of CH-stretching vibrations near 3000 cm^?1. Rate constants for the vibrational energy transfer by collisions with C₂H₄O and the rare gases are deduced, and a simplified model for the vibrational relaxation of C₂H₄O is discussed.     

Rates of vibrational and dissociative excitation of diatomic molecules in atom-molecule collisions in a hot gas

Vibrational relaxation and dissociation in O₂-Ar at low O₂ contents are considered. The populations of the vibrational levels are found as functions of time. The vibrational relaxation time and the dissociation rate constant at 3000 to 20 000 K are calculated. The relaxation equation for the vibrational energy per unit volume in the presence of dissociation is considered.     

Time-dependent close coupling for vibrational excitation in three dimensions: Application to H+ - H2

Impact parameter calculations for the non-reactive H⁺ + H₂ (n_i = 0) → H⁺ + H₂ (n_f) collision are reported for energies 10 eV ? E_cm ? 200 eV describing the rotational motion of the molecule in the sudden limit. The time-dependent Schrödinger equation for the vibrational motion has been solved by close coupling techniques expanding the vibrational wavefunction into both harmonic and numerically exact H₂ bound states. The convergence in vibrational basis sets, where up to six vibrational levels are considered, becomes worse with decreasing energy and increasing inelasticity. Furthermore, the harmonic wavefunctions are not suitable over a large range of energies to calculate proper cross sections. The various integral and differential cross sections have been compared with the classical results of Giese and Gentry.     

Inversion Vibrational Energy Levels of PH3+(X2A2") Calculated by a New Two-dimension Variational Method

A new 2-D variational method is proposed to calculate the vibrational energy levels of the symmetric P-H stretching vibration (v1) and the symmetric umbrella vibration (inversion vibration) (v2) of PH₃⁺(X²A₂") that has the tunneling effect. Because the symmetric internal Cartesian coordinates were employed in the calculations, the kinetic energy operator is very simple and the inversion vibrational mode is well characterized. In comparison with the often used 1-D model to calculate the inversion vibrational energy levels, this 2-D method does not require an assumption of reduced mass, and the interactions between the v1 and v2 vibrational modes are taken into consideration. The calculated vibrational energy levels of PH₃⁺ are the first reported 2-D calculation, and the average deviation to the experimental data is less than 3 cm^-1 for the first seven inversion vibrational energy levels. This method has also been applied to calculate the vibrational energy levels of NH₃. The application to NH₃ is less successful, which shows some limitations of the method compared with a full dimension computation.     

Ab initio computation of vibrational relaxation rate coefficients for the collisions of CO2 with helium and neon atoms

Ab initio calculations of rate coefficients are reported for the vibrational relaxation of CO₂ molecules in collision with helium and neon atoms. Self consistent-field computations have been performed to parameterise simple three-dimensional potential energy functions which have been used in vibrational close-coupling, rotational infinite-order-sudden calculations of rate coefficients. Excellent agreement is obtained between the calculated and experimental rate coefficients for the deactivation of the (01₁0) vibrational level in the He + CO₂ system at temperatures of 300 K and above. The ab initio predictions of rate coefficients for relaxation of CO₂ vibrational levels such as (10⁰0) and (02⁰0) should be useful in computer simulations of CO₂ lasers.     

Variational calculations on the vibrational level structure of S0 HDCO

We perform converged high precision variational calculations to determine the frequencies of the vibrational levels in S₀ HDCO, extending up to 5000 cm^?1 of vibrational excitation energy. For these calculations we use our specific vibrational method (recently employed for studies on H₂CO and D₂CO), consisting of a combination of a search/selection algorithm and a Lanczos iteration procedure and based on the Martin, Lee, Taylor potential energy surface for formaldehyde. The calculated level structure is compared to the recently measured frequencies by Ellsworth et al. in order to improve their assignments and further clarify the vibrational mixing pattern and vibrational resonances in HDCO that are very different from the other more symmetric formaldehyde species H₂CO and D₂CO studied recently.     

Potential energy functions of polyatomic molecules

A direct method is proposed for determining polyatomic potential energy functions, expressed in terms of normal coordinates, which yield a given set of vibrational excitation energies. The method is a modification of the semiclassical technique for computing vibrational energy levels of Percival and Pomphrey. The technique is used to derive potential functions for the NO₂, SO₂ and ClO₂ molecules. With these potentials twenty two higher vibrational excitations energies have been predicted for these molecules and these results differ from the experimental values by at most 3 cm^?1. The computed potential functions are not unique despite the apparent accuracy of the vibrational energy levels. Comparison with the RKR method indicates that the present method must be extended to include rotational perturbations.     

Large configuration interaction calculations of nuclear spin-spin coupling constants: III. Vibrational effects in ammonia

Large configuration interaction calculations of the proton—proton coupling constant for several geometrical configurations of the ammonia molecules are reported. The analytical expressions for the energy surface and the coupling constant as functions of two cartesian displacement coordinates are fitted to the calculated values. The potential is used for the calculation of the vibrational wavefunctions for ¹⁵NH₃ and ¹⁵ND₃ species and the vibrational averaging of the coupling constant is carried out using these functions. Though the value of the coupling constants shows a very strong geometry dependence, the vibrational corrections are found to be small. A possible correlation of the proton—proton coupling constant with an angular parameter in the NH₂ group in RNH₂ compounds is indicated.     

Crystal field effects on the ground and lowest excited triplet states of benzene isotopes in a borazine host crystal

The phosphorescence spectra of the C₆H₆C₆H₅D₁p-C₆H₄D₂symp-C₆H₃D₃, C₆D₆ and ¹³CC₅D in a borazine host crystal are analyzed at high resolution. The spectral lines are sharp (～2 cm^?1 wide) indicating that the impurity molecules occupy a unique site in the borazine lattice which is probably substitutional. The phonon sidebands are weak,giving clean, well-resolved spectra much like those of isotopic mixed crystals. In contrast, however, the crystal field effects on the ground state vibrational levels are much smaller than those found for isotopic mixed crystals. The gas-to-crystal shifts are very small, the vibrational degeneracies are not removed and orientational splittings are only observable for a few select vibrational levels. For most vibrational levels and for the derivation of selection rules one can asume the effective crystal site symmetry to be D_3d. The data provide the first conclusive evidence that the splitting observed in the benzene phosphorescence spectrum results from a distortion of the molecule when excited to the zeroth vibrational level of the T₁ state. Furthermore, the data suggest that the distortion is intrinsic in nature (i.e.,is not caused by the crystal field).     

丙氨酸二肽分子二级结构与振动光谱特性

利用从头算方法探索蛋白质模型分子——丙氨酸二肽的二级结构布居特性以及体系势能变化. 引入对分子结构敏感的振动探针(酰胺振动吸收带), 借助其光谱表象, 寻求振动光谱参数与分子结构之间的联系. 研究结果表明: 丙氨酸二肽分子处于C_7eq构型(Φ/Ψ=-80°/80°)时具有最低能量值, 且分子易形成β折叠、PP_II、C₅及C₇等能量较低的稳定构型. 通过简正模式分析, 得到分子3N-6 个振动模式的吸收光谱, 并通过势能分布分析方法对分子骨架上酰胺振动吸收带的特征振动模式进行了指认. 重点考察分子骨架上酰胺-I带振动光谱参数与分子构型变化之间的相关性, 建立振动光谱参数与蛋白质二级结构之间的联系, 为在化学键水平上研究蛋白质的结构及其发挥作用的机制提供科学依据.     

Anab initio potential energy surface and dynamics calculations for vibrational excitation of I2 by He

We present newab initio calculations of the interaction potential and the elastic and inelastic cross sections for He scattering by I₂. The electronic structure calculations of the interaction potential are based on an extensive one-electron basis set (triple zeta plus ad set on each I, ans function plus ap set at the I₂ bond center, and quadruple zeta plus twop sets on He), a two-configuration-SCF orbital set, and a configuration interaction calculation based on all single and double excitations out of the two-configuration reference space. The calculations are performed at 16He-I₂ distances for nine combinations of I₂ vibrational displacement and orientation. A new form of analytic representation is presented that is particularly well suited to efficient and accurate fitting ofab initio interaction potentials that include vibrational displacements. Scattering calculations are performed by the vibrational close-coupling, rotational-infinite-order-sudden approximation with a converged vibrational basis.     

Quantal transition probabilities from classical trajectories: Application to the collinear reactive H + Cl2 system

Moments of the classically computed distribution of products vibrational energy are employed to generate a discrete vibrational state distribution. The built-in convergence criterion of the method is discussed and demonstrated. Comparison is made with the quantal results for the collinear H + Cl₂ reaction and with the experimental results for the H + F₂ reaction.     

Density functional studies of AnF6 (An=U,Np, and Pu) and UF6−nCln (n=1–6) using hybrid functionals: geometries and vibrational frequencies

We have compared the performance of widely used hybrid functionals for calculating the bond lengths and harmonic vibrational frequencies of AnF₆ (An=U, Np, and Pu) and UF_6?nCl_n (n=1–6) molecules using “small‐core” relativistic effective core potentials and extended basis sets. The calculated spectroscopic constants compare favorably with experimental data for the bond lengths (average error ≤ 0.01 Å) and vibrational frequencies (average error ≤ 7 cm^?1) of the AnF₆ molecules. The experimental vibrational frequencies of the stretching modes were available for most of the UF_6?nCl_n (n=1–6) molecules. The calculated vibrational frequencies are in good agreement with the experimental data to within 4.6 cm^?1 and 7.6 cm^?1 for selected Becke1 and Lee, Yang, Parr (B1LYP), and Becke3 and Perdew, Wang (B3PW91) functionals, respectively. We conclude that one can predict reliable geometries and vibrational frequencies for the unknown related systems using hybrid density functional calculations with the RECPs. The geometries and vibrational frequencies of the UF_6?nCl_n (n=1–6) molecules that have not been determined experimentally are also presented and discussed. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 2010–2017, 2001     

Anharmonic Vibrational Motions In C<Subscript>60</Subscript>: A Potential Energy Surface Derived From Vibrational Self-Consistent Field Calculations

A potential energy surface (PES) is developed for C₆₀ designed to describe vibrational motions valid in the anharmonic limit. The PES is based on a previously existing one that is fit to the harmonic fundamentals and is then modified to generate anharmonicity of all orders and in all terms, but without additional fitted parameters. The resulting Cartesian vibrational motions are decomposed into normal modes, and the anharmonic expansion coefficients are calculated including 2-mode couplings and up to 4th order. The resulting PES is used in a vibrational self-consistent field (VSCF) algorithm to calculate the anharmonically corrected fundamental frequencies. The parameters are then fit to fundamental infrared and Raman frequencies. While it is not possible to assign combination and overtone transitions with sufficient experimental accuracy, conclusions about the effects of anharmonic vibrational coupling in C₆₀ are described.     

Vibrational Distributions of N2 (A3∑+u) in the nitrogen afterglow

Absolute populations of the lowest six vibrational levels of N₂ (A³∑⁺_u) have been measured under various conditions in the Lewis-Rayleigh afterglow of nitrogen for the first time. These vibrational distributions are interpreted in terms of a simple kinetic model which permits the evaluation of rate constants for vibrational relaxation of the A-state levels by V-V energy transfer to ground state nitrogen molecules.     

Vibrational relaxation in SO2

SSH—Tanczos calculations are carried out to estimate the energy transfer probabilities and the slow vibrational relaxation time in SO₂ in the temperature range 300–2000 K. The theoretical results suggest a series process below 1000 K, and a complex series/parallel process above that temperature for the vibrational relaxation in SO₂. The theoretical results are compared with the known experimental data.     

Molecular analysis of water clusters: Calculation of the cluster structures and vibrational spectrum using density functional theory

Density functional theory (DFT) is applied to obtain absorption spectra at THz frequencies for molecular clusters of H₂O. The vibrational modes of the clusters are calculated. Coupling among molecular vibrational modes explains their spectral features associated with THz excitation. THz excitation is associated with vibrational frequencies which are here calculated within the DFT approximation of electronic states. This is done for both isolated molecules and collections of molecules in a cluster. The principal result of the paper is that a crystal-like cluster of 38 water molecules together with a continuum solvent background is sufficient to replicate well the experimental vibrational frequencies.