Ab initio study of the force constants of inorganic molecules ONF and NF3

The force constants of ONF and NF₃ have been determined from Hartree-Fock ab initio wavefunctions by the force method. Three different Gaussian basis sets, ranging from 7s3p augmented with functions on the bonds to 5s2p, were used for ONF. Only the smallest basis was applied to NF₃. The results show remarkable agreement with experiment, especially for the coupling constants. The NF stretching force constant is greatly overestimated in calculations with the 5s2p basis. The calculated force field makes it possible to exclude sets of force constants which are unphysical but compatible with the experimental data. The results show that even calculations with 5s2p basis sets can contribute to the determination of force fields.The experimental value of the $\text{ON}\text{β}$ coupling constant in ONF ranges between 0.27 and 0.54 mdyn; our calculations corroborate the higher value. An estimation of the calculated molecular geometries is given.     

Boron Trifluoride: Application of the Keating Bendings to the Degenerate Vibrations

The harmonic force field of the E' species of BF₃ is studied. The Keating force field (KFF) is defined in analogy with the familiar VFF and CFF. In this connection three different coordinate sets are introduced. All of them contain bond stretchings. In addition, the valence coordinates include ordinary (Decius') bendings, the central coordinates nonbond stretchings, and Keating coordinates the Keating's bendings.

The experimental data of vibrational frequencies and Coriolis constants are reviewed extensively, as well as previous normal coordinate analyses. The different coordinate sets are tested for their usefulness as basis of force field approximations. For this purpose two different sets of experimental data are applied. The general conclusion goes in favour of the Keating coordinates.     

The harmonic force field and ground-state average structure of allene

Existing spectroscopic data for allene-H₄, -D₄, and -1,1-D₂ are improved and augmented by gas-phase Raman and solid-phase infrared studies. A number of ¹³C vibration frequencies are identified in natural abundance by each technique. A total of 58 input data enable 22 of the 23 force field parameters to be determined, the ¹³C frequency shift data removing the ambiguity of choice between two sets of A₁ and B₂ species force constants. The remaining interaction force constant is constrained to the predicted ab initio value of Botschwina and Pulay. The force field is used to determine the ground-state average (r_z) structure of allene. Observed trends in the H-D isotopic effects on the r_z structures of ethylene, allene, and ketene are in accordance with those expected.     

The computed force constants and vibrational spectra of cubane

The geometry, complete harmonic force field, and dipole moment derivatives of cubane, C₈H₈, have been calculated at the Hartree-Fock level using a 4–21 Gaussian basis set. The infrared and Raman spectra of cubane and four deuterated derivatives were calculated and compared with previously observed spectra. A set of five scale factors for the calculated force constants was then derived by least-squares fitting of the fundamental vibrational frequencies calculated from the scaled force field to the frequencies obtained by direct experimental measurement. The resulting scaled quantum-mechanical (SQM) force field, containing 73 unique elements, is believed to give an accurate representation of the harmonic vibrational potential of cubane. In most cases, the spectral assignments previously made from purely empirical considerations were confirmed, but a few corrections are proposed. The only major alteration is for an A_2u mode revised to appear at 1030 cm^?1 in the undeuterated molecule. Coriolis constants and approximate infrared intensities are also calculated.     

Theoretical prediction of vibrational spectra: The out-of-plane force field and vibrational spectra of pyridine

The harmonic force field for the out-of-plane vibrations of pyridine has been calculated from ab initio Hartree-Fock wavefunctions obtained with a 4–21 basis set of contracted Gaussians. To account for systematic errors, the calculated force constants were scaled, using only two independent sclae factors which were transferred unchanged from benzene. The resulting scaled quantum mechanical force field, which is strictly a priori in that it is not based on any experimental data on pyridine, predicts the 64 out-of-plane fundamental frequencies of pyridine and its deuterated isotopomers of C_2v symmetry with a mean deviation from experiment of only 8.5 cm^?1. Addition of polarization functions to the basis set for the nitrogen atom and refinement of the two scale factors by fitting them to the observed pyridine spectra produce no significant improvement in the fit. Assignments of the vibrational spectra are discussed.     

Microwave spectrum and molecular force field of tetratomic C2v molecules: NO2Cl

The rotational constants and quartic centrifugal distortion constants for NO₂³⁵Cl and NO₂³⁷Cl have been determined from an analysis of rotational transitions in the microwave and millimeter wave regions between 8.2–40 and 90–120 GHz, respectively.The values of the in-plane force constants in the general harmonic potential field have been obtained by combination of infrared and microwave data. Vibrational frequencies of ¹⁴NO₂Cl and ¹⁵NO₂Cl, inertia defects of NO₂³⁵Cl in the excited vibrational states v₃ = 1 and v₅ = 1, and first-order centrifugal distortion constants of NO₂³⁷Cl are the experimental data used in the least-squares fitting determination of force constants.     

Phonon dispersion relations of the A15 compound Nb3Sb

We have calculated the phonon dispersion relations of the A15 compound Nb₃Sb using an angular force model approach, the analysis being restricted to third neighbour interactions only. The force constants have been evaluated by fitting them to the measured values ofphonons at the zone centre. Good agreement has been observed between theory and the available experimental results. It has been inferred that the angular forces are not of significant importance between different atoms (Nb-Sb). The physical aspects for the same are discussed.     

A precise solution of the rotation bending Schrödinger equation for a triatomic molecule with application to the water molecule

In this paper we report the results of improving the non-rigid bender formulation of the rotation-vibration Hamiltonian of a triatomic molecule [see A. R. Hoy and P. R. Bunker, J. Mol. Spectrosc., 52, 439 (1974)]. This improved Hamiltonian can be diagonalized as before by a combination of numerical integration and matrix diagonalization and it yields rotation-bending energies to high values of the rotational quantum numbers. We have calculated all the rotational energy levels up to J = 10 for the (v₁, v₂, v₃) states (0, 0, 0) and (0, 1, 0) for both H₂O and D₂O. By least squares fitting to the observations varying seven parameters we have refined the equilibrium structure and force field of the water molecule and have obtained a fit to the 375 experimental energies used with a root mean square deviation of 0.05 cm^?1. The equilibrium bond angle and bond length are determined to be 104.48° and 0.9578 Å respectively. We have also calculated these energy levels using the ab initio equilibrium geometry and force constants of Rosenberg, Ermler and Shavitt [J. Chem. Phys., 65, 4072 (1976)] and this is then the first complete ab initio calculation of rotation-vibration energy levels of high J in a polyatomic molecule to this precision. the rms fit of these ab initio energies to the experimental energies for the H₂O molecule is 2.65 cm^?1.     

An Improved Anharmonic Force Field of Difluoromethanimine, F2C NH

The anharmonic force field of difluoromethanimine, F₂C NH, has been reinvestigated theoretically using a coupled-cluster singles and doubles approach, augmented for structural optimization and harmonic force field by a contribution of connected triple excitations, CCSD(T). The cubic and quartic force constants have been obtained by numerical derivatives computed from analytical quadratic force constants calculated by second-order Møller-Plesset perturbation theory, MP2. The quadratic force constants and the equilibrium structure of F₂C NH have then been scaled by a global least-squares fitting procedure to the spectroscopic data and parameters experimentally determined for this molecule. This force field, obtained in the internal coordinates space and therefore valid for all isotopomers of difluoromethanimine, yields a complete set of spectroscopic molecular constants providing a critical assessment of the experimental rotational and centrifugal distortion constants, fundamentals, overtones, and combination bands determined so far for F₂C NH. In addition, the final force field can be used to make predictions of all important vibrational and rotational parameters which should be accurate and useful for new spectroscopic investigations.     

Methanol and deuterated species: Infrared data,valence force field,rotamers, and conformation

New infrared measurements of gaseous and matrix-isolated methanol and 7 deuterated species are presented and analyzed. A revised assignment for the species CH₃OH(D) and CD₃OH(D) is used to determine 15 significant parameters of a valence force field by a converged simultaneous least-squares adjustment to 44 observed fundamentals. The respective frequencies calculated for the rotamers of CH₂DOH(D) and CHD₂OH(D) turn out to be a valid prediction as they are used to assign 78 observed fundamentals of the species with partially deuterated methyl groups. The values of the 15 force constant parameters are refined by including all 122 observed fundamentals. The force field contains significant deviations from local C_3v symmetry of the methyl group. Such an asymmetry, in the CH-stretching diagonal part, produces a difference of about 10 cm^?1 in the zero point energy of symmetric and asymmetric rotamers of the species with partially deuterated methyl groups. Calculations based on equilibrium structures with and without methyl tilt yield better agreement with observed data in the nontilted case. A preliminary calculation of relative intensities reproduces the major effects of isotopic substitution and rotational isomerism. Experimental evidence for the staggered conformation is obtained from a comparison of observed data with calculated results based on staggered and eclipsed models.     

Computer simulation of stoichiometric hydroxyapatite: Structure and substitutions

A force field for the modeling of hydroxyapatite; Ca₁₀(PO₄)₆OH₂ (HAP) is established based upon transferable potentials. Ca-O, P-O and O-O potentials were transported from those previously published for fluorapatite and based on single crystal experimental data. The interactions of hydroxyl oxygen with calcium and phosphate were re-scaled by fitting to experimental data for CaO and AlPO₄, respectively, to account for the reduction in the oxygen charge from −2.0 to −1.426. Force field accuracy is tested by comparing the calculated and experimental values for the cell constant and atom positions in the unit cell. The elastic constants and bulk modulus calculated for HAP are in close agreement with the experimental results. The potentials were also used to calculate the compressibility data of HAP and fluorapatite, and these results also agree with the published experimental data. Using formal charges for metal cations allows modeling the complete solid solution of Cd-Ca hydroxyapatite with a good accuracy.     

Lattice vibration analysis of cryolite A3B′X6 and elpasolite A3BB′X6 compounds. A force constant calculation of Sr2ZnTeO6

A normal coordinate treatment of crystals with general formula A₃B′X₆ and A₂BB′X₆ with cubic structure (space group F_m3m) is made with the G-F matrix method. A modified valence force field is assumed to give a set of ten force constants for calculating all fundamental vibrations in the k = 0 approximation.     

Crystal field at the impurity center sites in ionic crystals

Perturbation theory is developed for second-quantized operators in a basis of partly nonorthogonal orbitals. This method may be helpful in carrying out ab initio calculations of the parameters of the crystal field at the impurity center sites. As an illustration, when estimating the crystal field parameters for Yb³⁺: KZnF₃, some fitting parameters are calculated using this method. The results agree well with experimental data, which indicates that this theory shows considerable promise.     

Uniqueness of methyl fluoride force field

The uniqueness of the general harmonic force field of methyl fluoride is analyzed. The analysis is applicable to other methyl halides as well. Through the compliance scheme, it is seen that by supplementing the data employed by Aldous and Mills (i.e., vibrational frequencies ω_i, Coriolis coupling constants ζ_i and the centrifugal stretching constants D_J, D_JK of CH₃F and CD₃F molecules), with the frequencies of A′ or A″ species of either CH₂DF or CD₂HF, the force field is uniquely determined. The addition of any other extra data including the ¹²CH₃F¹³CH₃F isotopic shifts only makes the determination of the force field parameters more precise.     

Atypical intensity distribution in the Raman spectrum of 9,10-anthraquinone

The structure, the frequencies of the normal vibrations, and the absolute intensities of the bands in the IR and Raman spectra of 9,10-anthraquinone and its four symmetrical isotopomers are calculated in terms of the DFT/B3LYP method with the 6-31G(d) basis set. The effective harmonic force field of 9,10-anthraquinone is found by the Pulay method. A technique for directly obtaining the effective force fields without using experimental data on the frequencies of fundamental vibrations is proposed. An atypical intensity distribution in the Raman spectrum of 9,10-anthraquinone between two totally symmetric A _g and two nontotally symmetric B _3g vibrations is found. A new interpretation of these four experimentally observed vibrational Raman bands is proposed.     

Method for fitting crystal field parameters and the energy level fitting for Yb3+ in crystal Sc2O3

<正>A method to compute the numerical derivative of eigenvalues of parameterized crystal field Hamiltonian matrix is given,based on the numerical derivatives the general iteration methods such as Levenberg-Marquardt,Newton method, and so on,can be used to solve crystal field parameters by fitting to experimental energy levels.With the numerical eigenvalue derivative,a detailed iteration algorithm to compute crystal field parameters by fitting experimental energy levels has also been described.This method is used to compute the crystal parameters of Yb~(3+) in Sc_2O_3 crystal, which is prepared by a co-precipitation method and whose structure was refined by Rietveld method.By fitting on the parameters of a simple overlap model of crystal field,the results show that the new method can fit the crystal field energy splitting with fast convergence and good stability.     

The anharmonic force fields of PH3, PHF2, PF3, PH5, and H3PO

The cubic and quartic force fields of the title compounds are determined from ab initio SCF calculations using 6-31G^** and TZP/TZ2P basis sets. The computed geometries, vibration-rotation interaction constants, l-doubling constants, anharmonicity constants, and vibrational wavenumbers are compared with the available experimental data, especially for PH₃ and PF₃. Many experimentally unknown spectroscopic constants are predicted. A scaling procedure based on calculated harmonic and anharmonic force fields is proposed for predicting the vibrational wavenumbers of unknown molecules such as PH₅.     

Millimeter wave spectra of P35Cl3 in vibrationally excited states

The millimeter wave rotational spectra of P³⁵Cl₃ have been recorded for the excited vibrational states v₂ = 1 and v₄ = 1. The analysis of the latter yields ξ₄₄^c = ?0.738(12) and resolves a dilemma in fitting the harmonic force field.     

Vibrational properties of single-wall BC3 nanotubes

The phonon dispersions of single-wall BC₃ nanotubes with any chirality are calculated within a symmetry-based force constant model of the lattice dynamics. Based on the non-symmorphic symmetry group of the BC₃ tubes, the symmetries and number of the Raman- and infrared-active modes at Γ point of the one-dimensional Brillouin zone are given. The neighbor atom-atomic interaction force constants are recalculated by fitting them to the experimental phonon energy-dispersion curves of honeycomb BC₃ sheet. The frequencies of the optically active modes are presented as the function of diameters and chiralities for BC₃ tubes. The obtained phonon density-of-states spectra, phonon dispersion relations, and vibrational patterns of the zone-center phonons are presented and discussed in detail. The calculated frequencies of infrared-active modes are compared with the experimental values reported in the literature. The results provide comprehensive information about the vibrational properties of the BC₃ tubes and shed light on the interpretation of Raman scattering and infrared spectroscopies.     

Infrared band contour analysis and molecular constants of SPF3 and NSF3

Infrared spectra of gaseous SPF₃ and NSF₃ have been recorded at various temperatures. The band contours of the E fundamentals were analyzed by computer simulation taking into account the dependence of the rotational constants on the vibrational state. The ζ values together with centrifugal distortion constants (only for SPF₃) and isotope shifts Δν_i(³²S/³⁴S) were used as additional data in force constant calculations. CNDO calculations have been carried out to distinguish between two sets of force constants for the E block of NSF₃. An interpretation of the calculated stretch-stretch interaction force constants, f_rR, is given. Anharmonicity constants X₄₆ for SPF₃ and NSF₃ were determined.