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.     

Separated Product Rules for High and Low Frequencies in Isotopic Molecules

Separation of high and low frequencies is a known approximation in the theory of molecular vibrations. Accordingly the Teller-Redlich product rule for isotopic frequencies splits into separated product rules. A theorem states that the approximate frequency ratios for the high and low frequencies when multiplied together give the exact ratio for the whole set of frequencies. The theorem is illustrated by numerical computations for H₂S₂/D₂S₂ and proved mathematically for special cases as well as the general case.     

Rotational spectrum of ONCl in the (0, 0, 1) and (0, 1, 0) vibrational states and “b” type spectrum in the ground state. Comparison of force field obtained by different combinations of experimental data

From the rotational spectrum of ONCl in (0, 0, 1) and (0, 1, 0) excited vibrational states the inertia defects in these states have been determined. The “b” type rotational spectrum in the ground state has also been measured allowing the determination of Δ⁰ and of all the first-order centrifugal distortion constants.It is shown that by using differences of inertia defects Δ₂ and Δ₃ together with centrifugal distortion constants which do not involve the planarity relations and with harmonic vibrational frequencies of two isotopic species, the harmonic vibrational frequencies of two other isotopic species can be satisfactorily predicted.By using only inertia defects differences Δ₂ and Δ₃ as extra data, a definite choice can be made among the three sets of force constants which equally well reproduce the harmonic frequencies of four isotopic species.     

Infrared spectra of matrix isolated BH3NH3, BD3ND3, and BH3ND3

The infrared spectra of ammonia-borane, BH₃NH₃, and two of its deuterated isotropic species, BD₃ND₃ and BH₃ND₃, isolated in argon matrix at liquid hydrogen temperature have been measured. Well resolved bands for these three isotopic species have been observed for all the fundamentals. A complete frequency assignment based on C₃v molecular symmetry has been made. A set of force constants have been calculated from the data for the two isotopes BH₃NH₃ and BD₃ND₃ using a valence force field. The agreement between experiment and frequencies calculated from these force constants for the mixed isotopic species, BH₃ND₃, substantiates the present assignment.     

Cartesian Dynamics of Simple Molecules IV Centrosymmetric Linear Quadratomics

A simple spring model for molecular vibrations, which uses Cartesian co-ordinates for both longitudinal and transverse displacements, is applied to centrosymmetric linear quadratomic molecules, such as cyanogen and acetylene and its halogenated derivatives. Analytical expressions for the three stretching and two bending mode frequencies are obtained in terms of five independent force constants. By substitution of Raman and infrared frequencies, values of these force constants are obtained and briefly discussed. The validity of the model is confirmed by the satisfactory agreement between calculated and observed frequencies of isotopic species.     

Cartesian Dynamics of Simple Molecules VI Centrosymmetric Linear Pentatomics

A simple spring model for molecular vibrations, which uses Cartesian co-ordinates for both longitudinal and transverse displacements, is applied to centresymmetric linear pentatomic molecules such as carbon suboxide and carbon subsulphide. Analytical expressions for the four stretching and three bending mode frequencies are derived in terms of seven independent force constants. By substitution of Raman and infrared frequencies, values of these force constants are obtained and briefly discussed. Eigenvectors of the normal modes and eigenfrequencies of various isotopic species are also calculated.     

Pyrolysis of amines: Infrared spectrum of methyleneimine

Methyleneimine was detected in the gas phase by a moderately high resolution infrared spectrometer as one of the intermediate species produced by a pyrolysis of amines. Observed vibrational frequencies of some isotopic derivatives have been combined with the ab initio values to reach a most reliable force constants set. Some other spectroscopic parameters, involving geometrical parameters and dipole moment derivatives, have also been calculated ab initio and compared with the observation. Its half-life in our experimental apparatus was about 10 min, which is much longer than the previously reported values, 0.1 or 10 sec.     

Cartesian Dynamics of Simple Molecules. IX. Pyramidal Quadratomics (C3v Symmetry)

The vibrations of pyramidal AB₃ type molecules with C_3v symmetry are analyzed in terms of Cartesian co-ordinates, and analytical expressions for the four normal mode frequencies are derived as functions of two stretching and two bending force constants. Optimized values of these force constants are obtained for a number of tri-hydride and tri-halide molecules by substitution of available spectroscopic and geometric data. The physical validity of the model is confirmed by comparing the calculated and observed frequencies of several isotopic species.     

The application of the matrix method of successive approximations to the calculation of the force constants of tetramethylmethane

A study is made of the applicability of the matrix method of successive approximations to the calculation of force constants under conditions of insufficient experimentally measured vibrational frequencies using as an example the molecule tetramethylmethane and its deuteron modifications. A solution is guaranteed by fixing some of the force constants in each approximation. A procedure is proposed for the selection of the force constants to be fixed, and the assignment of values to them. The force constants obtained in this way completely satisfactorily reproduce the experimental vibration frequencies.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, No. 7, pp. 59–62, July, 1971.     

Formate anion: The physical force field

Unequivocal assignments for all of the vibrational modes of the formate ion have been made from isotopic shifts measured in the Fourier transform infrared and Raman spectra of polycrystalline samples of the sodium salts of HCO₂^?, H¹³CO₂^?, DCO₂^?, and D¹³CO₂^?. Literature frequencies for DCO¹⁸O^? and DC¹⁸O₂^? have been added to the above results for the unique determination of the 10 force constants in the general harmonic force field. Product rule relations among the harmonic frequencies are shown to interfere seriously with the determination of the physical force field by the standard normal coordinate computation. The least-squares refinement is found to be particularly sensitive to identified types of anharmonic error in the frequencies. Refinements characterized as Φ^aH and Φ^aD improve reliability by elimination of the deuterium isotopic shift for νCH. The physical force field is interpreted in terms of the geometric and electronic structure.     

A reduced dimensionality model of torsional vibrations in star molecules

The torsional vibrations of star molecules are studied with a reduced dimensionality model. In this model, the molecule is described by two equivalent sets of lumped inertial cylinders and vibrational frequencies are predicted by solution of the coupled equations of motion. Force constants are determined by including them as free parameters in the model and fitting the computed frequencies to their analogs as determined using full normal coordinate analysis at the HFSCF level of theory. Best agreement between the methods occurs when torsional force constants are included for the first two layers of the molecule. This reveals that non-bonded torsional interactions are important in the vibrational dynamics of these systems. Further insight is afforded by an analysis of why simple harmonic oscillator models are sufficient for modeling some related systems but fail to reproduce the trend in global mode frequencies for saturated aliphatic star molecules. The analysis reveals that the origin of this failure lies in backbone flexibility in these branched polymeric systems.     

A transferable valence force field for polyatomic molecules: A scheme for a series of molecules containing CO groups

The definition of a transferable valence force field is given for a series of molecules containing CO groups, including pyruvic acid, acetone, acetic acid, methyl acetate, formic acid and methyl formate. Its main characteristics might be applied to any other molecule or group of molecules. The limitation of the force fields through transferability requirements opens expectations for a strong data reduction. A set of 144 force constants is adjusted to 308 frequencies and 232 shifts of 61 isotopic modifications. The good fit achieved (rms-deviation: 6.38 and 1.26 cm^?1 for frequencies and shifts, respectively) suggests the present type of constraining to be very valuable. Furthermore, systematic trends concerning magnitudes and signs of distinct types of force constants as well as good agreement with ab initio values in the case of formic acid indicate physical significance. A PED-characterization of the fundamentals of the main parent species is given. In the case of methyl acetate the calculations suggest a revision of published assignments.     

The microwave and millimeter-wave spectra of hypochlorous acid

To permit atmospheric monitoring of the molecule, the microwave spectra of two isotopic species of hypochlorous acid, HOCl, have been measured in the frequency range 8–650 GHz. Three b-type branches and an a-type Q branch have all been measured for the first time; improved measurements have been made for the a-type R branches. The analysis has included combination differences of earlier high-resolution infrared spectra to give accurate values for all rotational constants, five quartic and five higher degree centrifugal distortion constants, as well as the chlorine nuclear quadrupole and spin-rotation coupling constants. From the Stark effect, accurate values have also been obtained for both components of the molecular dipole moment. A table of transition frequencies of potential use in atmospheric monitoring is presented.     

An ab initio study of the harmonic and anharmonic force field and fundamental vibrational frequencies of performic acid

The harmonic and anharmonic force fields and fundamental vibrational frequencies of cis-cis and cis-trans performic acid are studied ab initio in the 4-31G basis set using geometries fully optimized at this level. The frequencies predicted for the cis-cis conformer are compared with those derived from spectroscopic observations on the most stable form. An extensive comparison is made between the changes in diagonal and off-diagonal quadratic and cubic force constants, and diagonal stretching quartic constants, in going from the chain to the ring structure in performic and formic acid, and features which these changes have in common are seen to support the view that there is a hydrogen bonding type of interaction in trans-formic acid despite its unfavorable geometry.     

Cartesian Dynamics of Simple Molecules X Linear Quadratomics (C∞v Symmetry)

The vibrations of linear ABC₂ type molecules with C_∞V point group are analysed in terms of Cartesian co-ordinates. Algebraic expressions for the three stretching and two bending normal mode frequencies are derived in terms of longitudinal and transverse force constants, atomic masses and bond lengths. Values of non-valence interaction parameters are transferred from A₂B₂ (D_∞h) molecules, and values of the principal force constants are adjusted to reproduce the observed frequencies for a number of asymmetric halogen derivatives of acetylene. Normal mode frequencies of various isotopic species are also calculated. The nature of the computed eigenvectors for these molecules is briefly discussed. It is found that the carbon-carbon and carbon-hydrogen valence interactions remain approximately constant for these molecules, whereas the carbon-halogen bonds show a weakening trend with increasing halogen mass.     

The microwave spectrum,harmonic force field,and structure of carbonyl chlorofluoride,OCCIF

Rotational spectra of three isotopic species of carbonyl chlorofluoride, OCCIF, have been extensively measured, and have been analyzed for rotational constants, quartic centrifugal distortion constants, and chlorine nuclear quadrupole coupling constants. Ab initio calculations of the harmonic force field have been made using several different sets of basis functions, and their relative cost efficiency has been assessed. The measured distortion constants have been combined with vibrational wavenumbers (both from the literature and from the present work) and with the ab initio force constants to refine the force field. Ground state effective (r₀) and average (r_z) structures have been evaluated for the molecule.     

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.     

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.     

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.     

The Harmonic and Anharmonic Force Fields of Nitrosyl Halides

Harmonic and anharmonic symmetry force constants matrices have been calculated using a stepwise coupling method for the twelve isotopic species of nitrosyl fluoride, chloride and bromide. The valence force fields derived from the above matrices were used to recalculate the normal frequencies and the potential energy distribution among force constants. The valence force fields are compared with others previously reported obtained by different methods.