Vibrational Distortion Research Articles

Quadrupolar spin relaxation mechanisms for 235U in liquid UF6

The nuclear spin lattice relaxation time is calculated for 235U situated at the center of an octahedral 235UF6 molecule. Vibrational distortion, collisional deformation, and electric fields induced by neighbouring hexadecapole moments are considered as possible mechanisms that could account for the observed 235U quadrupolar relaxation rate. The efficiency of these mechanisms in causing relaxation is discussed by comparing the calculated value with the experimentally determined one.

A systematic study of molecular vibrational anharmonicity and vibration—rotation interaction by self-consistent-field higher-derivative methods. Asymmetric top molecules

Recently developed analytic third-derivative methods for self-consistent-field (SCF) wavefunctions have made it possible to theoretically determine a number of anharmonic molecular properties, including vibration—rotation interaction constants, vibrational anharmonic constants, fundamental vibrational frequencies, sextic centrifugal distortion constants, and rotational constants which include zero-point vibrational and centrifugal distortion corrections. Application has been made here to a variety of asymmetric top molecules including H 2O, H 2S, H 2CO, HCO, CH 2( 3B 1), CH 2( 1A 1), CH 2( 1B 1), C 2H 4, and several isotopomers. The formulas employed for the various spectroscopic constants are those derived from standard spectroscopic perturbation theory. For most of these molecules the anharmonic molecular constants which are available from experiments are well reproduced theoretically using a double-zeta plus polarization (DZP) basis set. Particularly good agreement is found for fundamental vibrational frequencies obtained by combining configuration interaction singles and doubles (CISD) harmonic frequencies with SCF anharmonic corrections within the same basis set. This work also provides insight into the applicability of standard spectroscopic perturbation theory to such molecules. Moreover, the methods used here are immediately applicable to molecules significantly larger than those studied here.

Thermal disruption of the inherent structure of simple liquids

Short range order in liquids formally may be viewed as an inherent structure (amorphous particle packings) that has been smeared by thermally induced vibrational distortions. In order to study these distortions, we have employed molecular-dynamics computer simulation, with steepest-descent quenching to potential energy minima, for a model system resembling liquefied noble gases. A typical multidimensional path connecting the liquid configuration to its quench packing is found to be tortuous and characteristic of substantial anharmonicity. In this respect, thermodynamically stable liquids differ qualitatively from crystals and low- temperature amorphous solids. On the basis of evidence from quench path geometry, and by observing how particle pairs redistribute as a result of the quench, an hierarchical domain clustering picture emerges to characterize vibrational anharmonicity in liquids.

Noncontinuum solvent effects upon the intrinsic free-energy barrier for electron-transfer reactions

A phenomenological electrochemical approach is outlined by which noncontinuum contributions to the outer-shell intrinsic barrier to electron transfer, ..delta..G/sub os//sup */, resulting from specific reactant-solvent interactions can be estimated from the measured dependence of the formal potential upon the molecular and structural properties of the solvent. A simplified derivation, based on electrochemical half-reactions, of the conventional dielectric continuum expression is given in order to clarify the physical origins of the outer-shell intrinsic barrier and to identify likely additional noncontinuum components. Numerical calculations for amine and other redox couples involving specific ligand-solvent interactions indicate that the noncontinuum contributions to ..delta..G/sub os//sup */ for both homogeneous and electrochemical exchange reactions can be surprisingly small (typically approximately less than or equal to 1-2 kcal mol/sup -1/) even when the thermodynamics of ion solvation are in severe disagreement with the dielectric continuum (Born) predictions. An additional noncontinuum component associated with vibrational distortions of outer-shell solvent may be significant for multicharged aquo complexes and other reactants engaging in strong ligand-solvent hydrogen bonding. 50 references, 3 figures, 1 table.

Coupled channel distorted wave method of atom–molecule reactive scattering: Application to p a r a to o r t h o hydrogen molecule conversion

We present a three dimensional coupled channel distorted wave approach of the atom–molecule reactive scattering. The full entrance channel wave functions are obtained from the inelastic vibrational and rotational close-coupling approximation, and reactive cross sections are evaluated with those wave functions employing the transition matrix (T matrix) method. Therefore, in contrast to the previous adiabatic distorted wave model of the reactive scattering, the present method allows for the target molecule to be dynamically distorted following the motion of the incident atom. The formulation of the approach and efficient computational procedures for obtaining the reactive T matrix elements are presented. The reactive scattering cross sections and the rate constants of the H+H2 para to ortho hydrogen molecule conversion have been evaluated to illustrate the computational aspects of the present method. The wave function obtained from the rotational close-coupling approximation yields better results on the reactive cross section than that from the pure vibrational coupling. The wave function computed from the simultaneous vibrational and rotational close-coupling approximation results in the most accurate cross section. This indicates that in order to obtain accurate results with the T matrix method, the simultaneous vibrational and rotational distortions of the target molecule should be considered when approximating the full entrance channel wave function. The differential cross section and the rotational distribution of the product molecule calculated from the present coupled channel distorted wave scheme are qualitatively similar to those obtained from the previous adiabatic distorted wave method; however, the magnitude of the cross sections from the present theory is larger than the previous ones. This might arise from the fact that the vibrational distortion of the target in the previous adiabatic distorted wave model is not sufficiently large. The present approach is shown to account for all major features of the reactive scattering in the H3 system.

Transferability of bond polar parameters: interpretation of infrared intensities in acetylene, propyne and 3-butyne

The infrared band intensities of acetylene, propyne and 2-butyne are interpreted in terms of bond polar parameters. The intensity parameters are defined as derivatives of the total molecular dipole moment with respect to linear and angular coordinates, associated with individual bond vibrational distortions. The values and the transferability of the bond polar parameters in the molecules examined are discussed.

Analytic radial dependence of diatomic electronic structure constants in terms of the vibration-rotation spectroscopic data

A direct procedure is proposed for investigating the internuclear distance dependence of diatomic structure constants (fine structure, spin rotation, etc.) from the vibration-rotation spectroscopic data. Starting from previous results concerning an elaborate solution of the anharmonic oscillator model wave equation, analytic relations are obtained allowing the determination of the radial form of any electronic parameter in terms of the measured values of its associated vibrational and first centrifugal distortion constants or, alternatively, of its vibrational constants alone. These relations are valid for any electronic state. Several applications are considered and discussed.

The effect of anharmonic vibration and centrifugal distortion on nuclear shielding in linear triatomic molecules: NNO and CO2

The temperature dependence of the mean bond displacement in linear triatomic molecules NNO and CO2 have been determined using the well-established anharmonic force fields for these molecules. The results are applied to explain the temperature dependence of the nuclear shielding observed in the zero-pressure limit for the 15N and 13C nuclei in 15N15NO and 13CO2. By fitting the observed σ0(T)−σ0(300 K) for T=250–350 K, empirical values of (∂σ/∂Δr)e=−220 ppm/Å (CO2), −1030 ppm/Å (NN*O), and −5190 ppm/Å (N*NO) are obtained. These derivatives are discussed in comparison to similar molecular types. The average shielding for the vibrational states (000) and (0110) are calculated for both 15N nuclei in NNO and compared with values obtained from experimental spin-rotational constants. The empirical derivatives are also used to calculate NMR isotope shifts from the mass-dependent 〈Δr〉.

Bond polar parameters from integrated infrared intensities

Abstract Bond polar parameters have been defined as derivatives of the total molecular dipole moment with respect to linear and angular coordinates associated with individual bond vibrational distortions, and obtained via transformation of the experimental dipole moment derivatives. In the present paper further advances in theoretical approach were presented. New type of angular bond coordinates are introduced and the number of intensity parameters reduced.

Gas phase vibrational fundamentals and vib-rotational parameters of AsCl 3

Contour simulation of the gas phase infrared fundamental bands of AsCl 3 led to estimated values for the first-order Coriolis constants, the vibrational frequencies, and the relative values of the vibrational transition moments. Improved values of the six independent force constants of a general quadratic force field were determined on the basis of the observed frequencies, mean amplitudes of vibration, and Coriolis and centrifugal distortion constants. The potential energy distribution over the normal modes is reported.

Preparation and characterization of strontium formate dihydrate

AbstractLarge single crystals of strontium formate dihidrate of high opticalquality have been grown from aqueous solutions by slow cooling from 50 °C to 20 °C. A thermogravimetric study is carried out in order to study the kinetic parameters and associated mechanism of the dehydration process. Raman vibrational assignments and a qualitative description of the normal modes are proposed. Two non‐equivalent formate and water arrangements with different degrees of vibrational distortion are established.

Vibrationally induced nuclear spin relaxation of quadrupolar nuclei

Nuclear spin relaxation times are calculated for quadrupolar nuclei situated at the center of octahedral and tetrahedral molecules. Vibrational distortion of such a molecule generates an electric field gradient at the center, which does not average to zero when the molecule is in an excited state of a degenerate vibration. The electric field gradient causes quadrupolar relaxation because of randomness in the vibrational state of the molecule. The theory relates the nuclear spin relaxation time to constants derived from the high resolution infrared spectrum of the molecule in the gas phase.

Parametric analysis of infrared intensities

A parametric model of the intensities in the infrared spectra employing molecular polar parameters related with vibrational distortions of separate valence bonds is described. The parameters represent derivatives of the Cartesian components of the total dipole moment with respect to linear and angular coordinates describing the changes in length and orientation of each bond in a molecule. Matrix formulation is used throughout the mathematical procedure. The analysis results in determination of bond parametric vectors from the intensities of stretching modes, and bond parametric (3×3) matrices from the intensities of deformation modes. The application of the model in the interpretation of experimental infrared intensity data is discussed.

Hidden structure in liquids

The canonical partition function for classical many-body systems is transformed so that the temperature-independent packing statistics and the thermal excitations are uniquely separated. This requires classification of particle configurations according to multidimensional potential-energy minima that can be reached by steepest-descent paths (quenches). Such classifications have been constructed for several starting configurations in the solid, fluid, and coexistence phases of the two-dimensional Gaussian core model. These quenches reveal a remarkable degree of polycrystalline order hidden within the fluid phase by vibrational distortion, and that order appears to have a large correlation length. The results suggest that melting hinges upon defect softening in the quenched packings, and a crude theory of melting for the Gaussian core model is developed in the Appendix.

Ground vibrational inertia defect and centrifugal distortion constants of octahedral XY6 molecules and ions

The general inertia defect of nonplanar XY6 type of molecules and ions has been evaluated for the first time by applying the method suggested by Herschbach and Laurie. The centrifugal distortion constants have also been calculated for the above system.

Vibrationally induced nuclear quadrupole coupling in tetrahedral and octahedral molecules

Hyperfine splittings arising from the presence of a quadrupolar nucleus at the center of a molecule belonging to the point group Td or Oh (e.g., 189OsO4 or 235UF6) are symmetry forbidden to a high degree of approximation. Nevertheless, quadrupole splittings can be induced by either vibrational or rotational distortions of the molecule, i.e., by distortions similar to those responsible for inducing electric dipole moments in Td molecules. Such hyperfine splittings have recently been observed in several laboratories using laser saturation spectroscopy. In this paper we investigate theoretically the quadrupole splittings induced by excitation of doubly and triply degenerate vibrations in Td and Oh molecules. We find that much of the vibration–rotation formalism already present in the methane literature can be applied with only minor changes to the induced-quadrupole-coupling problem, and that rather simple theoretical relationships can be derived between the quadrupole splitting and the tetrahedral or octahedral vibration–rotation splitting of a given level. Values for the scalar and tensor contribution to the quadrupole coupling constant have been derived from the experimental data for 189OsO4 reported by Bordé et al.

A model for parametric analysis of the intensities in the infrared spectra

A model for parametric analysis of IR intensities based on the use of molecular polar parameters related with vibrational distortions of separate bonds is described. The parameters represent derivatives of the total dipole moment with respect to coordinates describing the changes in the length and orientation of each bond in a molecule. The mathematical procedure is given using matrix representation. The analysis results in determination of bond polar vectors obtained from the intensities of stretching modes, and bond polar (3×3) matrices calculated from the intensities of deformation modes. The rotational contributions to the intensities in the case of polar molecules are explicitly considered. An example of application is presented in detail.

Formation and microwave spectrum of the 2Σ-radical barium-monofluoride

The microwave spectrum of gaseous barium monofluoride (BaF) has been measured in the frequency range from 76.8 to 103.6 and from 270.2 to 285.2 GHz. Molecules were produced in a number of different high temperature reactions and in a low temperature flame. Five rotational transitions ( J + 1, N + 1, υ) « ( J, N, υ) have been measured with vibronic quantum numbers up to 4 for 138Ba 19F. For 136Ba 19F only υ = 0 lines were observed. This large range of quantum numbers allowed a precise determination of vibrational and centrifugal distortion effects. For 138Ba 19F the following molecular constants were derived: Y 01 = 6491.3962(11)MHz, Y 11 = −34.8831(11)MHz, Y 21 = 15.93(22)kHz, Y 02 = −5.5250(11)kHz, Y 12 = 9.43(95)Hz, λ (SR) e = 80.984(19)MHz, α λ = 58.4(73)kHz, δ λ = 112(17)Hz. Potential and vibrational constants were calculated from the Dunham coefficient. The constant α λ is a factor of seven smaller than expected from theoretical considerations. Transitions of the 136Ba 19F isotopic species can be calculated within the experimental accuracy from these constants using mass relations.

OD Stretching Vibrations in Deuterated Potassium Ferrocyanide Trihydrate

AbstractDeuterated and isotopically dilute single crystals of K4Fe(CN)6. 3 D2O are investigated using low temperature Raman spectra. The work involves an attempt to asses the origin of the numerious OD modes using the isotope dilution technique. An estimate of the magnitude of the intra‐ and intermolecular interactions in formation of OD stretchings is made from available experimental data. Three crystallographically nonequivalent water molecules with different extent of vibrational distortion are established in the ferroelectric phase of the crystal.

Force field studies of some XY3 planar molecules and ions

AbstractRedington and Aljibury's parametric method has been applied to study the force fields of some XY3 planar molecules and ions. Interatomic force constants and interaction force constants were calculated. Other molecular constants like coriolis coupling constants, mean amplitudes of vibration and centrifugal distortion constants were calculated and found to agree with the available literature values.