Vibrations of excited molecules at combination and difference frequencies

In the context of the theory of molecular vibrations, by applying the direct product operation of matrices, an equation for the vibrations of vibrationally excited molecules at combination and difference frequencies is obtained. From the solution of this equation, elements of vibration patterns and expressions that can be used for the study of changes in the molecular structural parameters and the coefficients of kinematic interactions are determined. The formulas obtained are applied to the calculation of the anharmonic electro-optical parameters of the molecules of water H₂O and its two isotopes H₂ ¹⁷O and H₂ ¹⁸O. These calculations are performed in terms of the semiempirical quantum-chemical CNDO/2 method and by numerical differentiation of dipole moment functions by employing a cubic spline approximation.     

Variational calculation of low-lying and excited vibrational levels of the water molecule

The variational method of calculating vibrational energy levels for triatomic molecules has been extended to determine the lowest 22 levels for H₂O, using an analytic form for the potential surface developed by Sorbie and Murrell. In addition, complete ab initio calculations of the fundamental frequencies for H₂O have been carried out using extensive configuration interaction forms for the potential. They are predicted to be 3720, 1629, and 3807 cm^?1, to be compared with experimental values of 3656, 1597, and 3754 cm^?1. Also discussed is how the variational method may be extended to allow the calculation of vibrational energy levels for larger molecules.     

Satellite phenomena in the X-ray photoelectron spectra of lanthanide trihydroxides

Using the direct CI method perturbation corrections to the Koopmans ionization energies have been obtained up to order 10 for the molecules CN^? and H₂O. The results are compared with those from the fully converged CI and B_k-type calculations. The convergence of the perturbation series is found to be quite slow although substantial improvement is possible using a variation-perturbation method.     

BS2和BS2-分子的红外光谱和Jahn-Teller效应

Laser ablated boron atoms have been reacted with hydrogen sulfide and the reaction products condensed with argon at 4 K, which gave BS₂, BS₂^-, HSBS, and HBS molecules. Reagent isotopic substitution (H₂S, H₂³⁴S, D₂S, ¹⁰B, ¹¹B) and variation of boron and hydrogen sulfide concentrations have been used to identify the major products. Both BS₂^- and BS₂ were identified as linear molecules with no significant difference in the structure parameters, but the B-S anti-symmetric stretching vibration of BS₂ is significantly lower than that of BS₂^-, which is ascribed to pseudo Jahn-Teller effect. Theoretical calculation was employed to have an insight into the interaction nature of the bonds in the corresponding products.     

Theoretical study of efficiency of metal cations (Mg+, Ca+, and Ag+) for effective hydrogen storage

The interaction between the metal cations and H₂ molecule has been investigated using dispersion-corrected and -uncorrected hybrid density functional and CCSD(T) methods in conjunction with the correlation consistent triple-ζ quality basis sets for the storage of the H₂ molecule. The molecular properties, potential energy surfaces, stability, binding energy and well-depth have been computed for the metal cation–dihydrogen (M⁺–H₂, M = Mg, Ca, and Ag) complexes in the gas phase. The results obtained by the dispersion-corrected hybrid density functional B2PLYP-D method agree very well with the earlier experimental and theoretical results wherever available. Different components of the interaction energy have been estimated by the symmetry adapted perturbation theory (SAPT) to get physical insight into the interaction energy. Among the three complexes, only Ag⁺–H₂ is the most stable complex and it accumulates more H₂ molecules as the interaction between the metal cation Ag⁺ and the H₂ molecule is the greatest.     

Penning ionization electron spectroscopy of H2O,D2O,H2S and SO2

Electron energy peak shifts and peak shapes were determined in the ionization of H₂O, D₂O, H₂S and SO₂ by Ne(³P₂) and He(2¹S, 2³S) metastable atoms. The shifts are large, especially in ionization of H₂O and D₂O into the ionic ground state and are probably mostly due to chemical interaction during the collision.In a previous paper the electron energy distribution curves for ionization of CO, HCl, HBr, N₂O, NO₂, CO₂, COS and CS₂ by helium, neon and argon metastables and the characteristics of this ionization were described¹. In this paper the series of triatomic molecules was extended to the molecules H₂O, D₂O, H₂S and SO₂. Because all these molecules have considerable dipole moments it could be expected that the peak shifts might be enhanced as compared with other triatomic molecules.     

Crystal field investigations of Yb(C2H5SO4)3. 9H2O and Er: YA1G

Using the spectroscopically derived crystal field parameters for Yb(C₂H₅SO₄)₃. 9H₂O and Er³⁺: YA1G, the temperature dependence of Schottky specific heat, paramagnetic susceptibility, magnetic anisotropy and μ_eff has been calculated over a temperature range 5–400°K. The hyperfine interaction parameters for ¹⁷¹Yb³⁺, ¹⁷³Yb³⁺ and ¹⁶⁷Er³⁺ systems are also obtained and in turn used to estimate the nuclear specific heat. The nice agreement obtained for susceptibility and specific heat of Yb(C₂H₅SO₄)₃. 9H₂O at very low temperatures confirms the accuracy of CEF parameters employed and the neglect of exchange interaction. However, for Er³⁺: YA1G, the CEF parameters are adequate to explain the bulk thermal and magnetic properties but not the g-values.     

The fluctuation hypothesis of hydrogen bonding

To describe the distortion perturbations of the water molecules in solutions the quantum-mechanical method of partial oscillators has been developed. This method allows one to separate in a simple manner two types of influences on vibrations of OH oscillators, viz. the intermolecular perturbations resulting in the different strengths of hydrogen bonds and intramolecular coupling between stretching vibrations. Here the coupling is treated quite strictly, whereas the intermolecular perturbations are introduced phenomenologically. The calculation of the distribution of distortions among molecules in liquid H₂O and D₂O induced by non-equivalency of the two hydrogen bonds of the water molecule has been made on the basis of the method developed, and the parameters of the mean statistical molecule have been found from the experimental spectrum of HOD. The depolarization ratios of vibrations in Raman spectra of the mean statistical molecules H₂O and D₂O have been computed as an illustration of the possibilities of the proposed calculation method. All the estimates show that the stretching oscillators of H₂O and D₂O molecules are significantly coupled in spite of the great distortion of the symmetry of water molecules in the liquid state.     

EPR studies of Gd3+-doped Ce2(SO4)3.8H2O and La2(SO4)3.9H2O single crystals

EPR spectra of Gd³⁺-doped Ce₂(SO₄)₃.8H₂O and La₂(SO₄)₃.9H₂O single crystals have been measured with an X-band spectrometer at room and low temperatures. The absolute signs of spin Hamiltonian parameters have been determined for the La₂(SO₄)₃.9H₂O host from intensities of lines at liquid helium temperature; for the Ce₂(SO₄).8H₂O host the lines broaden considerably below 60 K, not permitting the determination of absolute signs of spin Hamiltonian parameters. The data are analysed using a rigourous least-squares procedure, fitting simultaneously all lines obtained for several orientations of the external magnetic field. The zero-field splittings have been computed for both the hosts. The characteristics of EPR spectra of Gd³⁺ in these hosts are compared with those obtained in other rare-earth trisulphate octahydrate hosts.     

Vibrational Spectra and Structure of Potassium Alum Kal(SO4)2·12[(H2O) x (D2O)1−x ]

The IR spectra and polarization Raman spectra of Kal(SO₄)₂·12(H₂O) and Kal(SO₄)₂·12[H₂O)_0.3(D₂O)_0.7] crystals at 93 K and room temperature have been obtained experimentally. The vibrational spectra of structural elements of potassium alum — the complexes [Al(H₂O)₆ ³⁺ and [Al(D₂O)₆]³⁺ — have been calculated. The vibrational spectra have been interpreted based on the calculation and factor-group analysis data. The spectral data obtained point to the fact that, in the crystals considered, the sulfate ions are partially disordered and there exist two crystallographically different types of water molecules.     

<Superscript>27</Superscript>Al NMR Study of the Structure and Dynamics of Natrolite

The temperature dependences of nuclear magnetic resonance and magic angle spinning nuclear magnetic resonance spectra of ²⁷Al nuclei in natrolite (Na₂Al₂Si₃O₁₀· 2H₂O) have been studied. The influence of water molecules and sodium ions mobility on the shape of the ²⁷Al NMR spectrum and framework dynamics have been discussed The temperature dependences of the spin–lattice relaxation times T₁ of ²⁷Al nuclei in natrolite have also been studied. It has been shown that the spin–lattice relaxation of the ²⁷Al is governed by the electric quadrupole interaction with the crystal electric field gradients modulated by translational motion of H₂O molecules in the natrolite pores. The dipolar interactions with paramagnetic impurities become significant as a relaxation mechanism of the ²⁷Al nuclei only at low temperatures (<270 K).     

Relative intensities in x-ray photoelectron spectra. Part VI. The spectra of He(I), He(II), Y Mζ and Zr Mζ

The 2s- and 2p-electron photoionization cross-sections at photon energies up to 190 eV have been calculated, using the RPAE method for averaged configurations of the C, N, O and Ne atoms. The RPAE method ensures a more accurate relation between the cross-sections, 2s/2p, than that obtained using the Hartree—Fock method. Within the framework of the Gelius—Siegbahn model, but with the use of theoretical atomic cross-sections, we have calculated the photoionization cross-sections for He(I), He(II), Y Mζ, Zr Mζ for CH₄, C₂H₆, C₃H₈, C₂H₄, C₂H₂, NH₃, H₂O, CN^?, N₂, CO, CO₂, N₂O and NO₂^? molecules. For CO, N₂, CO₂, N₂O and H₂O molecules, a comparison is made between the theoretical and experimental cross-sections for hν < 60 eV. The calculated absolute and relative values of the molecular-orbital cross-sections are in reasonable agreement with experiment, especially at hν ? 40 eV. The calculations correctly reproduce the change in intensities under the transition He(I) → He(II). We have shown that our calculations have a significant advantage over those performed using the PW and OPW approximations. It is shown for NO, N₂, CO, H₂O, CH₄, NH₃ and N₂O molecules that the total photoionization cross-section calculated taking into account the real structure of the molecular orbitals is in better agreement with the experimental photoabsorption cross-section than is the sum of the cross-sections for the atoms in a molecule.     

Thermal parameters of MgSO4·7H2O and NiSO4·7H2O crystals added with urea and thiourea

Pure and impurity-added (with urea and thiourea) MgSO₄·7H₂O and NiSO₄·7H₂O single crystals were grown by the free-evaporation method from aqueous solutions. Density was measured by the flotation method. X-ray diffraction data were collected for powder samples and used for the estimation of thermal parameters like Debye-Waller factor, mean-square amplitude of vibration, Debye temperature and Debye frequency. The thermal parameters do not vary in a particular order with respect to impurity concentration, which could be attributed to the random disturbance created by the impurity molecules in the hydrogen-bonding system of the MgSO₄·7H₂O and NiSO₄·7H₂O lattices.     

Die Eigenschwingungen des Metall-Hydratkomplexes in BeSO4·4H2O und BeSO4·4D2O

Infrared reflection spectra of single crystals of BeSO₄·4H₂O and BeSO₄·4D₂O have been obtained in polarized light at 300°K and at 14°K in the region between 4000 cm^?1 and 300 cm^?1. By a Kronig-Kramers analysis, the frequencies of the infrared active transitions have been calculated. These transitions are attributed to internal vibrations of the water molecules and sulfate ions and, in the region between 1000 cm^?1 and 300 cm^?1, especially to internal and external vibrations of the tetrahedral Be⁺⁺·4aqu-complexes. The vibrational modes of these complexes consist of a superposition of translational and librational modes of the water molecules and translational modes of the central Be⁺⁺-ion. The vibrational frequencies and normal modes of this complex have been calculated in a central-force model, and force-constants have been determined by fitting the calculated frequencies to the observed spectra. The calculations have shown that the modes, which comprise mainly translational motions of the water molecules, are strongly coupled with librational motions of the water molecules. On the other hand, there exist pure librational modes with practically no admixture of translational motions. The optimum sets of force constants for the BeSO₄·4H₂O crystal and the BeSO₄·4D₂O crystal differ in a manner which can be understood under the assumption that the dimensions of the Be(D₂O)₄ complex are about 0.1 Å larger than those of the Be(H₂O)₄ complex. Some arguments supporting this conclusion will be discussed.     

Photoluminescence study of new lanthanide complexes with benzeneseleninic acids

New lanthanide complexes with benzeneseleninic (ABSe) and 4-chloro-benzeneseleninic (ABSeCl) acids have been synthesized and characterized by elemental analysis, infrared and UV–visible spectroscopies. The emission spectra of the trivalent europium complexes presented the typical electronic ⁵D₀→⁷F_J transitions of the ion (J=0–4). The ground-state geometries of the europium complexes have been calculated by using the Sparkle/AM1 model. From these results, the 4f–4f intensity parameters and energies of the ligand singlet and triplet excited states have been obtained. The lower emission quantum yield for the [Eu(ABSe)₃(H₂O)₂](H₂O)₂ compound, as compared to the [Eu(ABSeCl)₃(H₂O)₂] one, can be associated to the higher numbers of water molecules, in the first and second coordination spheres, that contribute to the luminescence quenching. The [Eu(ABSe)₃(H₂O)₂](H₂O)₂ complex presents an intermediate state whose energy difference with respect to the first excited singlet state is resonant with three phonons from the water molecules, favouring a multiphonon relaxation process from the singlet state followed by a fast internal conversion process; this effect is less pronounced in the complex with the ABSeCl ligand. The luminescence decay curves of the gadolinium complexes indicate that the level responsible for the intramolecular energy transfer process has a triplet character for both compounds. The nephelauxetic effect in these compounds was investigated under the light of a recently proposed covalency scale based on the concept of overlap polarizability of the chemical bond.     

Synthesis,spectroscopic and structural characterisation of two p-nitrobenzamide compounds: experimental and DFT study

The title molecules, N-(1,5-dimethyl-3-oxo-2-phenyl-1H-3-(2H)-pyrazolyl)4-nitrobenzamide (C₁₈H₁₆N₄O₄·H₂O) (I) and 2,2-dimethyl-3-(4-nitrobenzoyl)-5-(phenylamino)-2,3-dihydro-1,3,4-thiyadiazole (C₁₇H₁₆N₄O₃S) (II), were prepared and characterised by ¹H NMR, ¹³C NMR, infrared spectroscopy (IR) and structural X-ray diffraction (XRD) techniques. The molecular geometries, vibrational frequencies of the title compounds in the ground state have been calculated by using the density functional theory (DFT) method with 6-31G(d) basis set, and compared with the experimental data. The calculated results showed that the optimised geometries from the DFT method agree with the X-ray structures well for both compounds. Theoretical calculations of harmonic vibration frequencies are in good agreement with experimental results. To determine conformational flexibility, the molecular energy profiles of the title compounds were obtained. Besides, molecular electrostatic potential (MEP), frontier molecular orbitals (FMO) analysis and thermodynamic properties of the title compounds were investigated by theoretical calculations.     

Overtone vibrations of molecules

A vibrational equation for overtones is derived by applying the direct multiplication of matrices in the framework of the molecular vibration theory. The relationships determining the characteristics of the overtone vibration mode and expressions describing the changes in the structural and geometric molecular parameters are obtained by solving the deduced equation. The electro-optical parameters of the overtones 2ν_s, 3ν_s, 4ν_s, and 5ν_s(s=3, 4) of a methane molecule are calculated from the deduced relationships using the semiempirical quantum-mechanical CNDO/2 method and numerical differentiation with cubic spline functions.     

Collisional broadening and shifting of the 211-202 transition of H2O, H2O, H2O by atmosphere gases

Broadening and shifting of the 2₁₁-2₀₂ transition of H₂¹⁶O, H₂¹⁷O, H₂¹⁸O by pressure of water, nitrogen and oxygen were precisely measured at room temperature using spectrometer with radio-acoustic detection of absorption. Shift parameters for all studied lines as well as broadening parameters of H₂¹⁷O, H₂¹⁸O lines were measured for the first time. Comparison of obtained results with previously known experimental and theoretical data is presented.     

Thermochemistry,bond energies and internal rotor barriers of methyl sulfinic acid,methyl sulfinic acid ester and their radicals

Sulfur–Oxygen containing hydrocarbons are formed in oxidation of sulfides and thiols in the atmosphere, on aerosols and in combustion processes. Understanding their thermochemical properties is important to evaluate their formation and transformation paths. Structures, thermochemical properties, bond energies, and internal rotor potentials of methyl sulfinic acid CH₃S(?O)OH, its methyl ester CH₃S(?O)OCH₃ and radicals corresponding to loss of a hydrogen atom have been studied. Gas phase standard enthalpies of formation and bond energies were calculated using B3LYP/6‐311G (2d, p) individual and CBS‐QB3 composite methods employing work reactions to further improve accuracy of the ${\Delta} _{{\bf f}} H_{{\bf 298}}^{{\bf o}} $ . Molecular structures, vibration frequencies, and internal rotor potentials were calculated. Enthalpies of the parent molecules CH₃S(?O)OH and CH₃S(?O)OCH₃ are evaluated as ?77.4 and ?72.7 kcal mol^?1 at the CBS? QB3 level; Enthalpies of radicals C^?H₂? S(?O)? OH, CH₃? S^?(?O)₂, C^?H₂? S(?O)? OCH₃ and CH₃? S(?O)? OC^?H₂ (CBS‐QB3) are ?25.7, ?52.3, ?22.8, and ?26.8 kcal mol^?1, respectively. The CH₃C(?O)O—H bond dissociation energy is of 77.1 kcal mol^?1. Two of the intermediate radicals are unstable and rapidly dissociate. The CH₃S(?O)? O. radical obtained from the parent CH₃? S(?O)? OH dissociates into methyl radical (${\bf CH}_{{\bf 3}}^{{\bf .}} $ ) plus SO₂ with endothermicity (ΔH_rxn) of only 16.2 kcal mol^?1. The CH₃? S(?O)? OC^?H₂ radical dissociates into CH₃? S^?=O and CH₂=O with little or no barrier and an exothermicity of ?19.9 kcal mol^?1. DFT and the Complete Basis Set‐QB3 enthalpy values are in close agreement; this accord is attributed to use of isodesmic work reactions for the analysis and suggests this combination of B3LYP/work reaction approach is acceptable for larger molecules. Copyright © 2010 John Wiley & Sons, Ltd.