On the determination of equilibrium geometries and potential functions of simple polyatomic molecules from electron diffraction

The degree to which current electron diffraction (ED) techniques allow reliable determination of equilibrium geometries and potential functions of simple molecular systems is studied. Special attention is paid to the choice of the model potential function in the diffraction analysis. The main calculations were performed using accurate diffraction data on SO₂ and SF₆ available from the literature. Routine electron diffraction data on PbCl₂ and PbBr₂ obtained at Moscow University were also treated and found to be reasonably informative regarding bond stretching anharmonicity. Compelling evidence has been presented that any unfavorable situation in the ED analysis of equilibrium geometries and force fields of molecules can be substantially improved by augmenting scattering observations with reliable inferences from vibrational spectroscopy data. This useful cooperation of techniques is shown to be most powerful in efforts to solve equilibrium geometries and molecular dynamics.In addition, numerical simulation experiments were carried out with CO₂ and SO₂ as samples. It is shown that the high-temperature and hot-molecule techniques of electron diffraction may yield valuable information on anharmonicity.     

The harmonic force fields of BF3, SnCl4 SbBr3 obtained by the joint use of electron diffraction and vibrational spectroscopy data

The recently developed technique of joint analysis using electron diffraction and vibrational spectroscopy data for determining molecular force fields is demonstrated for the sample molecules BF₃ and SnCl₄. The technique is based on harmonic force constants being the common parameters in the interpretational methods of both components. The general harmonic force field of SbBr₃ is refined in this way using electron diffraction and recently available gas-phase spectroscopic frequencies of vibration.     

Effects of Vibrational Nonequilibrium on the Chemistry of Two-Temperature Nitrogen Plasmas

A new two-temperature chemical kinetics model for nitrogen plasmas is presented. The model is used together with the vibrationally-specific collisional-radiative model to study the effects of vibrational nonequilibrium distributions on the chemical composition of two-temperature atmospheric pressure nitrogen plasmas. It is found that over a wide range of conditions the vibrational levels follow Boltzmann distributions and that the vibrational temperature T_v is well approximated by gas temperature T_g at low electron number densities and by electron temperature T_e at high electron number densities. This result suggests that simple kinetic models with two-temperature rate coefficients can be used to reliably model nonthermal plasmas. The calculation also yields a surprising result that, for a given constant gas temperature, the steady-state electron number density exhibits an S-shaped dependence on the electron temperature. This S-shaped behavior is caused by competing ionization, charge transfer reactions, two-body dissociative recombination, and three-body electron recombination reactions, and therefore is characteristic of molecular plasmas.     

Alkali metal intercalated titanate nanotubes: A vibrational spectroscopy study

Alkali metal (Li⁺, Na⁺, K⁺) intercalated titanate nanotubes have been studied by vibrational spectroscopy (Raman and FT-infrared), X-ray diffraction, and electron microscopy. The vibrational spectroscopic data shown that the most affected vibrational mode is that related to Ti-O bond whose oxygen is not shared among the TiO₆ units of the framework structure. A correlation between vibrational frequency shifts and intercalated metal was found, thus showing that vibrational spectroscopy is very useful for probing metal intercalated titanate nanotubes. Our results provide good evidences that the structure of titanate layers in titanate nanotube, a subject of long debate in the literature, is similar to trititanates (like Na₂Ti₃O₇).     

Estimation of equilibrium structure and anharmonicity by use of changes in the rz structure by isotopic substitution and vibrational excitation: I. General formulation and application to OCl2

A general formulation is presented on the differences in the average (r_z) structure caused by isotopic substitution and vibrational excitation; the differences in the average structure for both bonded and nonbonded atomic pairs are represented as linear combinations of quadratic average values of the Cartesian displacement coordinates. This method is applicable to a joint analysis of spectroscopic and electron diffraction data so that the equilibrium geometrical parameters and effective anharmonic constants for polyatomic molecules can be estimated even when only a limited number of rotational constants for isotopic species and vibrationally excited states are available. Its application to OCl₂ molecule as an example is discussed.     

Quantum-chemical calculations and electron diffraction study of the equilibrium molecular structure of vitamin K3

The equilibrium molecular structure of 2-methyl-1,4-naphthoquinone (vitamin K₃) having C _s symmetry is experimentally characterized for the first time by means of gas-phase electron diffraction using quantum-chemical calculations and data on the vibrational spectra of related compounds.     

Effects of anharmonicity of molecular vibrations on the diffraction of electrons: Part III. Predictive models

It has long been known how to relate anharmonic vibrational distribution functions to scattered electron intensities when deriving molecular parameters from gas-phase electron diffraction patterns. What has been lacking is a convenient procedure for estimating the characteristic asymmetry parameters of radial distribution functions for polyatomic molecules, particularly in the case of non-bonded internuclear distances. In the present work alternative models of bond distribution functions are discussed briefly and a plausible model is proposed for geminal non-bonded distances. Numerical examples are worked out for the ground-states of CO₂, CS₂, H₂O, and D₂O. Variations of the asymmetry parameters of SO₂ and SF₆ with temperature are examined. It is shown that the effect of asymmetry can become quite large at elevated temperatures.     

The microwave spectrum of trimethyl silyl isocyanate (CH3)3SiNCO

The microwave spectrum of trimethyl silyl isocyanate has been investigated in the region 26.5–40 GHz. The spectrum belonging to the ground vibrational state is characteristic of a symmetric top indicating that the equilibrium configuration of the SiNCO chain is either linear or very nearly so. The ground state B₀ value is 1203.83 MHz which is consistent with the structure observed for SiH₃NCO. The ground state transitions are accompanied by many vibrational satellites belonging to the lowest bending mode whose frequency was estimated to be 64 ± 15 cm⁻¹. These results are consistent with electron diffraction results from which the SiNC angle is deduced to be ≈ 150°.     

Molekülstruktur von gasförmigem 1,5-diazabicyclo-[3.3.0] octan(DABCO)

The molecular structure of DABCO was studied by vibrational spectroscopy and by gas phase electron diffraction. The infrared and Raman spectra indicate C₂ symmetry for DABCO, excluding conformational models of higher or lower symmetry. According to the diffraction data the most reasonable conformation is a twisted cis-exo-exo-form. Experimental bond distances (r_a) and bond angles (∠_a) are listed above. The dihedral angle ψ between the C₂N-groups was fo und to be 37.9 ± 3.3°.     

Combined vibrational,conformational and electron diffraction studies of 2,2,6-trimethylcyclohexanone

The molecular structure of 2,2,6-trimethylcyclohexanone was studied by electron diffraction in the vapor phase combined with auxiliary vibrational and conformational calculations, r_a = 1.535 ± 0.004 and r_a = 1.108 ± 0.015 were found for the average C-H and C-C bonds, respectively, from data taken at both the Oslo and Arkansas electron diffraction units. Five local conformational energy minima (2 rigid (chair) and 3 flexible (boat) ones) were found for the molecule. Data analysis revealed that, at 70° C, the vapors of the compound contained essentially one conformer in a chair form with two of the three methyl-substituents in equatorial positions. Molecular mechanics results based on different force fields taken from the literature were compared, and found to be in fair agreement.     

Surfactant Assisted Hydrothermal Synthesis of Superparamagnetic ZnFe<Subscript>2</Subscript>O<Subscript>4</Subscript> Nanoparticles as an Efficient Visible-Light Photocatalyst for the Degradation of Organic Pollutant

Super paramagnetic ZnFe₂O₄ nanoparticles were prepared by a surfactant assisted (ethylamine) hydrothermal method along with heat treatment. The nanoparticles were characterized by X-ray diffraction, Fourier transform infrared spectroscopy, high resolution scanning electron microscopy, Transmission electron microscopy, vibrating sample magnetometer and diffuse reflectance spectra technique. From the analyses, influence of calcination temperature on the structural, vibrational, morphological, magnetic and optical properties of ZnFe₂O₄ nanoparticles were investigated. The ZnFe₂O₄ nanoparticles with an average particle size of 17 nm showed high photocatalytic activity in the degradation of methylene blue (90 %). This work demonstrates that ZnFe₂O4 can be used as a potential monocomponent in visible-light photocatalysis for the degradation of organic pollutants. Furthermore, the products were super paramagnetic and could be conveniently separated within 15 min and recycled by using simple magnet, which is very beneficial for the degradation of organic pollutants.     

Structure and energy studies of Β-diketonates. 4. vibrational characteristics of Y(DPM)3 and Y(DPM)2

The vibrational problem for the Y(DPM)₃ and Y(DPM)₂ molecular forms that are present in the overheated vapor of yttrium tris-dipivaloylmethanate is solved. For this purpose, the experimental Raman spectra of Y(DPM)₃ solutions are interpreted. The force field of the Y(DPM)₂ radical is estimated on the basis of the force constants determined for Y(DPM)₃. Rms vibrational amplitudes and corrections for perpendicular displacements to the internuclear distances of the two molecular forms needed for interpreting electron diffraction data are calculated. Translated fromZhurnal Struktumoi Khimii, Vol. 38, No. 3, pp. 470–479, May–June, 1997.     

Hexamethylenetetramine (urotropine) C6H12N2: Interpreting the vibrational spectra of -d0 and -d12 isotopomers by scaling the quantum-chemical force field

The equilibrium structure and quadratic and cubic force fields of the urotropine molecule are calculated at the MP2 (full)/cc-pVTZ level. Pulay scaling of the quadratic force field allows unambiguous interpretation of the vibrational spectra of -d₀ and -d₁₂ urotropines. A reliable matrix for the quadratic force constants of urotropine is obtained which may be used to determine the parameters of the equilibrium structure of the urotropine molecule by means of gas-phase electron diffraction.     

High temperature electron diffraction investigation and the bending vibrational frequency of cobalt (II) chloride

The structure of CoCl₂ was studied by high-temperature gas electron diffraction. The linear shrinkage effect was determined in particular and compared to values calculated by spectroscopical methods. By this approach the v₂ vibrational frequency was determined to be 78 ± 8 cm ^?1, which is significantly larger than a previous estimate from the literature. The present; value is fairly well compatible with a recent matrix-isolation infrared frequency, viz. 94 cm^?1.     

The molecular geometry of iron trifluoride from electron diffraction and a reinvestigation of aluminum trifluoride

The molecular geometry of iron trifluoride has been determined at 1260 K by gas-phase electron diffraction. Use of a platinum envelope during the experiment prevented the iron trifluoride sample from partial reduction otherwise observed at high temperatures. The molecular geometry of aluminum trifluoride has been reinvestigated at 1300 K. The electron diffraction results for both AlF₃ and FeF₃ are compatible with planar bond configuration (D _3h symmetry) with bond lengths (r _g ): Al-F 1.630±0.003 Å and Fe-F 1.763±0.004 Å. Experimental vibrational frequencies support the notion of planarity for aluminum trifluoride. There is no such additional spectroscopic evidence available for iron trifluoride.     

Application of the effective harmonic oscillator method to computing the thermal averages for a system of coupled anharmonic oscillators

By treating the Hamiltonian for coupled oscillators with polynomial anharmonicity by the Gibbs-Bogoliubov inequality, the effective harmonic oscillator (EHO) method is developed and applied to computing the thermal averages for polyatomic molecules. Practical utility is demonstrated with calculations of electron diffraction quantities, namely the distance r_a and amplitude l, and of the vibrational partition functions for CO₂, CS₂, SO₂ and H₂O from spectroscopic data on the force fields. The results are compared with those in the literature obtained by more accurate techniques. A comparison of r_a and l was also made with the results of electron diffraction measurements.     

Spectroscopic calculations of electron diffraction parameters of diatomic molecules

Using spectroscopic data, the electron diffraction parameters r_g and l_e for the iodine and oxygen molecules are calculated at various temperatures by numerical diagonalization of the vibrational hamiltonian matrix and by the density matrix approach. The results are discussed and compared with available experimental data. A comparison is also made with the results of second-order perturbation calculations for iodine reported in the literature.     

Molecular structure of C(SiCl<Subscript>3</Subscript>)<Subscript>4</Subscript> tetrakis-(trichlorosilyl)methane

Methods of quantum chemistry and gas phase electron diffraction (at a temperature of 303±5 K) are applied to determine parameters of the geometric configuration of C(SiCl₃)₄ tetrakis(trichlorosilyl)methane. Frequencies of the vibrational spectrum are calculated. The value of the internal rotation barrier of SiCl₃ groups relative to the Si-C bond is 148.7 kJ/mol.     

Molecular Structure of BiBr3: An Electron Diffraction Study

The molecular structure of BiBr₃ was determined by gas-phase electron diffraction. The principal geometrical parameters are r (Bi—Br) = 2.567 ± 0.005 Å and _221D;Br—Bi—Br = 98.6 ± 0.2°. The force field of the molecule was obtained by a normal coordinate analysis utilizing both experimental vibrational frequencies and electron diffraction mean amplitudes of vibration. The variation of bond lengths and bond angles within the Group 15 trihalides is consistent with the expected trend, except that all bismuth trihalide bond angles appear to be somewhat large.     

Chemical mechanism of surface‐enhanced raman scattering spectrum of pyridine adsorbed on Ag cluster: Ab initio molecular dynamics approach

The surface‐enhanced Raman scattering (SERS) spectrum of pyridine adsorbed on Ag₂₀ cluster (pyridine‐Ag₂₀) at room temperature is calculated by performing ab initio molecular dynamics simulations in connection with a Fourier transform of the polarizability autocorrelation function to investigate the static chemical enhancement behind the SERS spectrum. The five enhanced vibrational modes of pyridine, namely, υ_6a, υ₁, υ₁₂, υ_9a, and υ_8a, can be assigned and identified by using a new analytical scheme, namely, single‐frequency‐pass filter, which is based on a Fourier transform filtering technique. To understand the factors evoking the enhancement in the SERS spectrum, the dynamic properties of molecular structures and charges for both of the free pyridine and adsorbed pyridine are analyzed. The calculated results indicate that the vibrational amplitudes of adsorbed pyridine are enhanced due to both of the electron transfer from pyridine to Ag₂₀ cluster and the softening of pyridine bond. In addition, the N‐Ag stretching within pyridine‐Ag₂₀ will couple with these five vibrational modes of pyridine. Consequently, the electron transfer between pyridine and Ag₂₀ cluster induced by different molecular vibrational modes prompts the redistribution of electron density of pyridine. These factors collectively cause the noticeable change in polarizability during molecular vibrations and hence result in the enhancement of Raman peaks. © 2013 Wiley Periodicals, Inc.