Crystal lattice dynamics of ZnGeP2 and AgGaS2 in hard ion model

A calculation is made of the long-wavelength phonon spectrum of ZnGeP₂ and AgGaS₂ in the hard ion model. The parameters of short-range forces and dynamic charges are found by comparing the theory with the experimental data on infrared absorption and Raman scattering of light. The elastic and piezoelectric constants are calculated. The available experimental data are discussed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 3–10, May, 1980.     

Energy band structure of the compounds AgGaS2, AgGaSe2, and AgGaTe2

Using the pseudopotential method the energy-band structure of the compounds AgGaS₂, AgGaSe₂, AgGaTe₂ is calculated. Calculations are performed with and without consideration of the displacement of anion atoms not changing the crystalline-lattice symmetry. It is established that anion displacement affects the conduction band only slightly and has a more significant effect on the valence band. Available experimental data are evaluated on the basis of the calculations performed.     

A study on the GVFF of CHF3, CH2F2, and CH3F

The complete GVFF of CHF₃, CH₂F₂, and CH₃F has been calculated from self-consistent-field ab initio energies, using a 4–31 G basis set. The larger part of the interaction force constants is close to those of the best available force fields from experimental data. Only one interaction term in CH₃F and the interaction force constants of the A₁ species in CH₂F₂ differ appreciably from the experimental ones. Using constraints from the ab initio studies we have improved the GVFF of CH₃F and CH₂F₂. It is shown that all comparable stretch-stretch interaction terms are of the same order of magnitude in the three molecules. The sign of all stretch/bend force constants are in accordance with those predicted by the hybrid orbital force field.     

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.     

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.     

A combined empirical-ab initio determination of the general harmonic force field of ketene

The general harmonic force field (GHFF) of ketene has been determined through a joint empirical-ab initio investigation. Perturbations in the infrared spectra of all isotopic species render experimental frequency data of limited discriminatory value in the empirical determination. Microwave/infrared determined quartic distortion constants are found to be mutually incompatible, both within and between isotopic species. The sensitivity of the distortion constants to truncation and constraints made in their determination is established in order to make a realistic estimate of their reliability in the force constant calculations. Ab initio calculations performed at various different levels of sophistication predict consistent values for interaction constants, some of which are markedly different from previously reported empirical values. The joint empirical-ab initio GHFF reproduces all observed and perturbation-corrected data well over five isotopic species. Coriolis interaction constants are calculated for ketene-H₂, -HD, and -D₂, which will be of assistance to future analyses, particularly of the strongly interacting four-level systems below 1000 cm⁻¹. Scaled ab initio force constants, calculated around the experimental ground state geometry as reference, are in excellent agreement with the empirical values, with one exception, which arises due to neglect of configuration interaction.     

Lattice dynamical study of Sr2B′UO6 (B′=Ni, Co) double perovskites

A short range force constant model has been used within the normal coordinate analysis framework for the first time to investigate the lattice dynamics of Sr₂B′UO₆ (B′=Ni, Co) double perovskites having space group P2_1/n. The zone centre phonons have been calculated with ten stretching force constants and eight bending force constants in the nickel compound and ten stretching and nine bending force constants in cobalt compound. The theoretically obtained values of Raman and infrared wave numbers exhibit a satisfactory agreement with the experimental values. A complete assignment of these frequencies to specific modes has also been made.     

Pure rotational spectrum, ab initio anharmonic force field, and equilibrium structure of silyl chloride

The ground state rotational spectra of H₃Si³⁵Cl, H₃Si³⁷Cl, and D₃Si³⁵Cl have been measured from the microwave to the submillimeterwave ranges and accurate rotational parameters have been determined. For H₃Si³⁷Cl, they are in good agreement with the values obtained from the ground state combination differences. The quadratic, cubic, and semi-diagonal quartic force field has been calculated at the MP2 level of theory employing a basis set of polarized valence quadruple-zeta quality. This force field has been used to predict the spectroscopic constants. The calculated values are found to be in good agreement with the available experimental data. The equilibrium structure has been derived from the experimental ground state rotational constants and either the ab initio or the experimental rovibrational interaction parameters. These experimental and semi-experimental structures are in excellent agreement with the ab initio equilibrium geometry.     

A lattice dynamical investigation for the Raman and the infrared frequencies of Bi2W2O9

Studies on infrared and Raman-active phonons in the Aurivillius ferroelectric Bi₂W₂O₉ were performed theoretically. The Raman and infrared phonons were calculated by applying a short-range force constant model using normal coordinates having space group Pna2₁. Sixteen stretching, two repulsive and seventeen bending force constants were used for the calculations of the zone center phonons. The calculated Raman and infrared wavenumbers are in very good agreement with the experimental ones in the literature. Potential energy distribution for this compound has also been investigated for the contribution of each force constant towards the Raman and the infrared wavenumbers.     

用从头算方法研究GeCl2分子的非谐振力场和光谱常数

用从头算方法的MP2和CCSD（T）方法结合cc-pVTZ基组计算了二氯化锗同位素（⁷⁰GeCl₂、⁷²GeCl₂和⁷⁶GeCl₂）分子的平衡结构、光谱常数和非谐振力场.二氯化锗的几何结构、转动常数、振转相互作用常数、谐频、非谐振常数、四次和六次离心畸变常数、三次和四次力常数的计算结果与实验结果符合较好,二氯化锗分子的同位素效应较小,可能的原因是Ge同位素的质量变化相对较小.两种方法计算的结果均与实验结果符合,但CCSD（T）方法比MP2计算结果的偏差稍大一些,可能的原因是CCSD（T）方法在描述过共价Cl原子的电子相关时不够充分.     

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.     

Lattice dynamics of ZnGeP2 and AgGaS2 in a tensor-charge model

A tensor-charge model is developed for the lattice dynamics of the ternary compounds A²B⁴C ₂ ⁵ and A¹B³C ₂ ⁶ . The long-wavelength phonon frequencies are calculated for ZnGeP₂ and AgGaS₂ crystals. The tensor-charge parameters are determined by comparing the theoretical and experimental values of the infrared intensities of active frequencies. In the crystal ZnGeP₂, the tensor charges of the zinc and phosphorus are found to be close to the isotropic charges of the point-ion model, while the tensor charge of germanium is very different from the point-ion charge. In the AgGaS₂ crystal, the tensor charges of all the atoms differ appreciably from the point-ion charges. The results are discussed from the point of view of the chemical bond.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 40–44, September, 1980.     

Calculation of vibrational structure in the core and valence esca spectra of CO and N2

The vibrational excitations in the core and valence ESCA bands of CO and N₂ have been investigated by means of Franck—Condon (FC) analysis. FC factors obtained from optimized geometries and from the force constants of the neutral ground and ionized states are compared with those obtained from calculated ionized-state energy gradients. Geometries, force constants, and energy gradients are calculated both from frozen-orbital energies and from OS RHF wavefunctions. The differences between the results of the methods employed are discussed in the light of experimental data.     

Ground state rotational spectrum,K = 3 splittings,ab initio anharmonic force field and equilibrium structure of trifluoroamine

The submillimetre-wave spectrum of ¹⁴NF₃ has been measured and the ground state rotational spectrum has been reanalysed, including the K=3 splittings. The quadratic, cubic and semidiagonal quartic force field has been calculated at the CCSD(T) level of theory employing a basis set of at least polarized valence triple-zeta quality. This force field has been used to predict the spectroscopic constants, including the parameters specific to the doubly degenerate vibrational states. The calculated values are found to be in good agreement with the available experimental data. The equilibrium structure has been derived from the experimental ground state rotational constants and either the ab initio or the experimental rovibrational interaction parameters. These experimental and semiexperimental structures are in excellent agreement with the ab initio equilibrium geometry.     

Ab initio anharmonic force field and equilibrium structure of vinyl bromide

The quadratic, cubic, and semi-diagonal quartic force field of vinyl bromide has been calculated at the MP2 level of theory employing a basis set of triple-ζ quality including a relativistic pseudopotential on bromine. A semi-experimental equilibrium structure has been derived from experimental ground state rotational constants and rovibrational interaction parameters calculated from the ab initio force field. This structure is in excellent agreement with the ab initio structure calculated at the CCSD(T) level of theory using a basis set of quadruple-ζ quality and an offset correction. The experimental mass-dependent r_m structures are also determined and their accuracy is discussed.     

Calculation of molecular geometries and force constants from CNDO wavefunctions by the force method

The semi-empirical quantum chemical calculation of molecular geometries and force constants by the usual energy hypersurface method rapidly becomes impractical as the size of the molecule increases. Here we show that the application of the force method to semi-empirical wavefunctions makes an economic and simple calculation of molecular geometries and force constants possible. Problems which are virtually insoluble by the classical method, such as full geometry optimization in large molecules, can be solved this way.

The calculation of forces as exact negative derivatives of the total SCF energy is given for CNDO wavefunctions. Two geometry optimization schemes are discussed ; it is concluded that a steepest descent method is the most practical in semi-empirical calculations. As an example the fully optimized equilibrium geometry of pyrrole has been determined. Except for the CH and NH bond lengths, the calculated geometry agrees almost perfectly with the experimental one.

The calculation of force constants from the forces is discussed. The force constants of CH₄ and H₂O have been determined, including the interaction ones. The signs and magnitudes of the stretch-bend interaction constants agree with experiment.     

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.     

Ab initio anharmonic force field and equilibrium structure of propene

The quadratic, cubic and semi-diagonal quartic force field of propene has been calculated at the MP2 level of theory employing a basis set of triple-ζ quality. A semi-experimental equilibrium structure has been derived from experimental ground state rotational constants and rovibrational interaction parameters calculated from the ab initio force field. This structure is in excellent agreement with the ab initio structure calculated at the CCSD(T) level of theory using a basis set of quintuple-ζ quality and a core correlation correction. The experimental mass-dependent r_m structures are also determined and their accuracy is discussed. The use of isolated CH stretching frequencies is shown to be a good method to determine CH bond length.     

Experimental and theoretical X-ray K-spectra of sulfur of zincblende-based compounds AgGaS2-CdGa2S4-InPS4

The K-edge X-ray absorption spectrum of sulfur in AgGaS₂, CdGa₂S₄, and InPS₄ was investigated both experimentally and theoretically. The lattices of these compounds can be represented as chalcopyrite with various amounts of defectiveness. The spectra were obtained with an experimental resolution about 0.2 eV. To obtain the theoretical absorption spectrum, the FEFF7 high order multiple scattering code was used. The clusters considered contained 80-87 atoms; up to 624 multiple-scattering paths of the photoelectron were taken into account, with the highest order scattering equal to 6. A very good correspondence between the theoretical and experimental spectra was achieved when the energy dependent exchange energy was calculated according to the Dirac-Hara approximation.     

Evidence for slow exchange in E.S.R. spectra of nitroxide biradicals

Force constants have been calculated for H₂NF and HNF₂ from ab initio Hartree-Fock wavefunctions by the force method, using 7s3p/1 gaussian basis sets. The force field of HNF₂, obtained from a combination of the theoretical results with the experimental frequencies, can be considered as the most reliable one at present. Previous force fields are discussed critically. From a full optimization the predicted geometry of H₂NF is: NF = 1·399 Å, NH = 1·018 Å, HNF = 102·9° and HNH = 105·9°.