The combined use of SCF-MO calculations and experimental data in the evaluation of quadratic force fields: MOCIC potential functions for fluoroform,methyl acetylene,and methyl cyanide

A semiempirical method combining SCF-MO calculations and limited vibrational data has been employed to evaluate the completely general quadratic potential fields of fluoroform, methyl acetylene, and acetonitrile. MOCIC (molecular orbital constraint using interaction coordinates) potential fields are presented for gas phase molecules of intermediate size. Here general harmonic force fields or excellent approximations utilizing extensive experimental data are available as standards. A statistical evaluation of the interaction potentials shows that there is some improvement in going from MNDO or ab initio SCF-MO force fields to the MOCIC functions which reliably reproduce the off-diagonal vibrational potential constants in most instances. The MOCIC primary compliants are excellent approximations of their vibrational counterparts, as expected. Comparison of the calculated isotopic frequencies, Coriolis coupling constants, and centrifugal distortion constants for the SCF-MO, MOCIC, and vibrational spectroscopic potential fields with the corresponding experimental values also shows MOCICs reliability for molecules with many interaction potentials. There is substantial improvement in the calculated isotopic frequency shifts and centrifugal distortion constants in going from SCF-MO to MOCIC functions.     

The emprical general harmonic force field of ethane

A total of 175 spectroscopic data, accumulated from 10 isotopic species of ethane, are used to define all 22 parameters of the harmonic potential function within narrow limits. Before calculation, numerous Fermi resonances have been identified and quantified through infrared and Raman spectroscopic studies of CH₃CD₃ and its ¹³C isotopic species. This is an essential prerequisite to such an investigation, without which a self-consistent empirical data set cannot be achieved from which to determine physically meaningful force constants. Comparison of the empirical force constants with those predicted by scaled ab initio calculations shows an excellent degree of correspondence in all force constants, and confirms that both approaches can lead to essentially identical results. Calculated values of spectroscopic data of reliable quality are listed. These should be of value to future spectroscopic investigation of isotopic ethanes and for resolving the many resonance perturbations which are present.     

Ground state rotational parameters and fundamental vibration frequencies for isotopically substituted diboranes

The present spectroscopic structural information on diborane derives from infrared studies of B₂H₆ and B₂D₆ species only. Due to the impossibility of selective isotopic substitution in diborane, and the consequent coexistence of a number of isotopic species in any partially deuterated sample, the most probable source of further structural information of quality will be from microwave studies of asymmetrically deuterated species. To assist in the assignment of the overlapping spectra that will occur, accurate rotation and quartic distortion constants are presented for the ground states of all isotopic diboranes in terms of existing zero-point average structural parameters and isotopic changes in these calculated through the harmonic potential function. Sets of fundamental anharmonic vibration frequencies are calculated in order that interference from low-lying vibrations with significant populations at ambient temperatures may be anticipated.     

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.     

Sextic force field of nitrous oxide

The sextic force field in the curvilinear internal coordinates has been studied for the nitrous oxide molecule from the spectroscopic data of ¹⁴N₂¹⁶O, ¹⁴N¹⁵N¹⁶O, and ¹⁵N¹⁴N¹⁶O. The bands below 6600 cm⁻¹ have been used. The force constants in the internal coordinates are converted to those in dimensionless normal coordinates by two successive transformations. The vibration Hamiltonian matrix for each symmetry species of a given isotopic species has been constructed from the harmonic oscillator basis functions, and it is then diagonalized numerically to give the vibrational energy levels and the wavefunctions. The latter have been used for the evaluation of ratational constants. The least-squares refinement has been very successful in the present study, and it is shown that the general quartic force field supplemented by the quintic and sextic stretching diagonal force constants estimated from the Morse function, provided that the terms up to sextic are kept in the dimensionless normal coordinate space, well reproduces the spectroscopic constants such as the vibrational levels, rotational constants, l-type doubling constants, and centrifugal distortion constants. The spectroscopic constants of the isotopic molecules which are excluded from the refinement process are also in good agreement with the computed ones. The bond dissociation energies of the NN and NO bonds estimated from the present results have been critically examined.     

Quadratic potential functions for the boron trihalides

General quadratic compliance constants have been evaluated for the boron trihalides using frequency data and Coriolis coupling constants obtained from a variety of sources. Coriolis data from band contour analysis are too imprecise to help determine the E′ symmetry potential constants. Solutions obtained using Cyvin's Coriolis constants appear to be reasonable on the basis of trends in the valence compliants and interaction displacement coordinates. The semiempirical SCF-MO scheme MNDO has been employed to establish prior constraints of the interaction displacement coordinates in the estimate of the quadratic potential constants for BF₃ and BCl₃.     

Simultaneous Determination of Force Constants and Dipole Moment Derivatives of Methane

The expressions of the effective Hamiltonian and dipole moment spectroscopic parameters in the tetrahedral formalism are used simultaneously to fit the force field and dipole moment derivatives of the methane molecule. Data, the so-called “observed parameters,” are the values of the spectroscopic parameters determined from the frequencies and line strengths analyses. The ambiguities of most parameters (in the polyad scheme) are treated consistently with the Hamiltonian reduction chosen in the frequency analyses. As an illustration, the method is applied to the tetrahedralXY₄isotopic species only. The quadratic and cubic force field constants have been determined in addition to the linear and six of the seven quadratic dipole moment derivatives. The observed parameters are reproduced with a standard deviation of 4%. The results are compared with previous works and it is moreover shown that the introduction of the dipole moment data removes some correlations between the force constants.     

Anharmonic force field of acetylene

The harmonic and anharmonic force field of acetylene has been determined in a least-squares calculation from recently determined data on the spectroscopic constants of various isotopic species (including the vibrational l-doubling constant). A general quadratic and cubic force field was used, but a constrained quartic force field containing only 8 of the 23 possible quartic constants. The results are discussed and compared with earlier work.     

基于核运动效应下的H同位素双原子分子的解析势能函

在加入核运动效应修正下的Born-Oppenheimer近似电子能量的基础上, 采用QCISD(T)/ aug-cc-pvqz方法计算出H同位素双原子分子（H₂, HD, HT, D₂, DT,T₂）的势能函数参数, 获得体现H同位素分子质量差异下的势能函数。 并在此基础上导出H同位素分子的力常数和光谱数据。 同时对于OH, OD和OT分子采用QCISD/aug-cc-pvtz方法计算, 同样获得了这些分子对应的势能函数、 力常数和光谱数据。Based on the correction of the electron energy under Born Oppenheimer approximation using nuclear motion effect, the parameters of potential energy functions for hydrogen isotopic diatomic molecules (H₂, HD,HT,D₂, DT,T₂) are calculated with QCISD (T) method and aug-cc-pvqz basis set,and those potential energy functions that indicate the differences from the masses of hydrogen isotopic atoms are obtained. The force constants and spectroscopic data of those molecules are calculated as well. The potential energy functions, force constants, and spectroscopic data of the isotopic diatomic molecules OH, OD,and OT are also derived using QCISD method and aug-cc-pvtz basis set.     

The Degenerate Vibrations of BCl3, BBr3 and BI3 with Application of Keating Coordinates

The experimental works of vibrational spectroscopy and normal coordinate analyses for BCl₃, BBr₃ and BI₃ are reviewed extensively. Harmonic force fields of the E' species are produced using isotopic frequencies and Coriolis constants as additional data, respectively. The usefulness of Keating coordinates versus valence coordinates as basis of force field approximations is discussed. The conclusions are not unequivocal, but they go in favour of the Keating coordinates when the reliability of the different computations is taken into account. Boron trichloride is treated specifically in some detail. Final force fields are proposed for the title molecules with the aid of the mass influence on Coriolis constants.     

On the calculation of force constants using isotopic frequencies by parametric method: Application to systems of (3×3) order

A method is proposed for the determination of angle parameters for ONF, ONCl and ONBr, utilising the isotopic frequencies of two isotopically substituted molecules. The force constants, Coriolis coupling constants, inertia defect, mean amplitudes of vibration and rotational distortion constants were also calculated and compared with literature values.     

Calculation of force constants and mean amplitudes of vibration of octahedral XY6 molecules using frequencies and zeta constants

Expressions involving vibrational frequencies, Coriolis coupling constants and masses of the atoms of the molecule that are invariant under symmetrical isotopic substitutions are derived for octahedral XY₆ molecules following the method given by Jagannathan and others. These invariants are used to calculate the force constants, compliance constants and mean amplitudes of vibration of 13 molecules of XY₆-type.     

Methyl cianide: Spectroscopic studies of isotopically substituted species,and the harmonic potential function

The infrared gas-phase spectra of CH₃CN, ¹³CH₃CN, CH₃¹³CN, CH₃C¹⁵N, CD₃CN, and CD₃¹³CN have been studied in detail, in order to determine accurately the fundamental vibration frequency displacements on heavy isotopic substitution. A number of important Fermi resonances have been identified, and treated quantitatively. The unperturbed fundamental frequencies and heavy isotopic displacements form a self-consistent set of data, which, together with Coriolis zeta and centrifugal distortion constants, enable the harmonic potential function of methyl cyanide to be determined with only one constraint. A comparison between the latter and results from an ab initio calculation reveals disagreement in the values of two interaction constants, which seem well outside our experimental error. Infrared frequencies in crystalline films of CD₃CN and CD₃¹³CN at 78 K are also reported.     

The vapor phase Raman spectra,Raman band contour analyses,Coriolis coupling constants,and e-species force constants of the molecules SPF3, FCCl3, and BrCCl3

The vapor phase Raman spectra of the molecules SPF₃, FCCl₃, and BrCCl₃ have been recorded at pressures of up to 1 atm over the fundamental frequency regions. The Raman band contours of the e-species fundamentals have been analyzed to yield first-order Coriolis coupling constants from which, together with the fundamental frequencies, e-species force constants of the general harmonic potential function have been evaluated. The results for thiophosphoryltrifluoride are compared with those deduced previously on the basis of infrared band contour analyses.     

CH2+, NH2+和HBr2+的解析势能函数

对于有势能极大和势能极小的带两个单位正电荷的双原子分子,王藩侯和朱正和两位教授曾提出了一个六参数的解析势能函数用于描述该系统.本文将以基态的CH2 ,NH2 和HBr2 为例,对该函数进行详细的讨论.对CH2 ,NH2 和HBr2 分别采用MP3/6-311 G**,CISD/6-311 G**和CID/LanL1dz进行了大量的单点计算,根据这些点作出了它们的势能曲线,并采用最小二乘法进行拟合,拟合出了该势能函数的六个参数.在此基础上计算出了力常数和光谱数据.     

The vapour phase Raman spectra,Raman band contour analyses,Coriolis coupling constants,and e-species force constants for the molecules HCF3, ClCF3, BrCF3, and ICF3

The vapour phase Raman spectra of the molecules HCF₃, ClCF₃, BrCF₃, and ICF₃ have been recorded at pressures of up to 1 atmosphere over the fundamental frequency regions. The Raman band contours of the e-species fundamentals have been analysed to yield first-order Coriolis coupling constants from which, together with the fundamental frequencies, e-species force constants of the general harmonic potential function have been evaluated. One force field was found for fluoroform, but two different ones were found for the molecules ClCF₃, BrCF₃ and ICF₃.     

Gas phase vibrational fundamentals and vib-rotational parameters of AsCl3

Contour simulation of the gas phase infrared fundamental bands of AsCl₃ 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.     

Anharmonic effects on lattice resonant modes of impure metallic crystals

The effect of lattice anharmonicity on the resonant modes of dilute impurities for Au-Cu, Au-Ag and W-Cr metallic systems are studied from the poles of the double time temperature dependent impure Green’s function of these crystals. The third order force constants used in the present work are derived assuming the systems to obey the Lennard-Jones potential. The inclusion of lattice anharmonicity has been found to increase the resonant frequency which depends upon the mass defect, force constant change parameter and the impurity concentration terms. Some interesting features about the phase shift and the change in width of the vibrational spectrum are reported at room temperature for the isotopic defects and the defects interacting with host atoms. The results are found to be in qualitative agreement with the experiments on the systems considered.     

Force field calculation for inplane vibrations of ethylene usingcndo/Force method

cndo/Force method is used to evaluate redundancy-free internal valence force field (rfivff) for inplane vibrations of ethylene. The bending force constants, the stretch-band and bend-bend interaction force constants are predicted reasonably well in magnitude and sign by this method; whereas stretching force constants and stretch-stretch interactions are overestimated. Initial force field is set up by transferring stretching force constants from structurally-related molecules and including the rest of the force constants fromcndo force field. The field so constructed is subjected to refinement by the least square method. A total of 64 vibrational frequencies of C₂H₄, C₂D₄, C₂H₂D₂ and their¹³C isotopic modifications are used to determine force field containing 15 parameters. The final force field is found to be reasonable on the basis of frequency fits, potential energy distribution and band assignments.     

完全活性空间自洽场方法对NO分子基态势能函数的研究

利用MOLPRO从头算程序包, 选用完全活性空间自洽场(CASSCF)方法并选取cc-pVTZ, cc-pVQZ, cc-pV5Z和cc-pV6Z基组, 计算了NO分子基态的平衡核间距与谐振频率, 从中优选出cc-pV5Z基组进行单点能扫描, 并将扫描结果用最小二乘法拟合得到4参数、5参数、6参数和7参数的Murrell-Sorbie势能函数. 通过比较由势能函数计算出的光谱数据, 最终确定6参数的结果最好. 最后, 利用拟合出的解析势能函数, 通过求解径向Schrödinger方程, 得到了NO分子基态J=0时的全部38个振动态的振动能级、经典转折点、惯性转动常数以及6个离心畸变常数.