Properties and application of the reduced isotopic product rule for molecular vibration frequencies

The well-known approximate separation of low molecular vibrational frequencies from high frequencies has in the past been combined with the Redlich-Teller isotopic product rule to split the latter into separate rules for the high and for the low frequencies (reduced isotopic product rules). A number of variants and properties of these rules are discussed, along with some modifications applicable when redundant coordinates are involved. A discussion is given of the use of nonbonded distances instead of the related bond angles, and the employment of computer programs which calculate normal frequencies from postulated force constants. A comparison is made of the relative advantages of using these reduced product rules for testing assignments of observed vibration frequencies as opposed to the use of frequencies or frequency product ratios calculated from transferred force constants. Finally benzene, ethylene, methyl isocyanide, and cyclohexane are worked out as examples and some suggestions made of possible remaining uncertainties in the assigned fundamental frequencies.     

Zone center frequencies of the orthorhombic NdMnO3 perovskite

A short range force constant model has been applied for the first time to investigate the phonons in NdMnO₃ perovskite in the orthorhombic phase. The calculations with nine stretching and eight bending force constants provide good agreement for the observed Raman frequencies. The infrared frequencies have been assigned for the first time.     

Study on the force field of pyrite

A normal coordinate treatment is made for pyrite on the basis of a Urey-Bradley force field. The i.r. frequencies used in the calculation have been reported by Verble and Wallis and the Raman frequencies by Ushioda. The values obtained for the Fe-S and S-S force constants are discussed.     

A lattice dynamical investigation of the Raman and the infrared frequencies of the cubic Y2Ru2O7 pyrochlore

A short-range force constant model has been applied for the first time to investigate the Raman and the infrared frequencies in Y₂Ru₂O₇ pyrochlore in its cubic phase of space group Fd3m. The calculations of zone center phonons have been made with four stretching and three bending force constants. The calculated values of Raman and infrared frequencies are in good agreement with the observed ones.     

Quantum-mechanical calculation of the frequencies of the normal vibrations and intensities of the IR and Raman bands of pyridine N-oxide

The frequencies of the normal vibrations and the intensities of the bands in the IR and Raman spectra of pyridine N-oxide and three of its isotopomers are calculated with the density functional theory by using the Becke exchange and Lee-Yang-Parr correlation functionals with the 6?311+G(d, p) basis set. The scaling of the force constants in independent natural coordinates is performed. The force field of pyridine N-oxide in independent symmetry coordinates is obtained. A new assignment of the frequencies of some vibrations in the isotopomers is proposed. On the basis of the calculated frequencies and intensities, the vibrational IR and Raman spectra of pyridine N-oxide are modeled.     

Force constants from intensity analysis of molecules CH3Cl and CD3Cl

The secular equation (GF - Eλ)L = 0 contains more force constants than can be calculated from the equations formulated using the frequencies. For a 3 × 3 matrix, there are 6 force constants but only 3 frequencies. Attempts were made by others to estimate all the 6 constants to satisfy the frequencies and Coriolis constants and rotation distortion constants. However, many attempts are not made in these estimations to satisfy the intensities. A full complement of equations is derived to evaluate all the force constants combining the intensity equationsI =L’A withLL’ =G and evaluated the force constants ofA ₁ species of CH₃Cl and CD₃Cl. A simple analysis of a 2 × 2 matrix shows thatF ₁₂/F ₂₂=G ₁₂ ⁻¹ /G ₂₂ ⁻¹ as reported earlier.     

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.     

Formic acid anhydride: Matrix infrared spectra of five isotopic species,vibrational analysis,empirical and ab initio harmonic force field and thermodynamic functions

Argon matrix infrared spectra of formic acid anhydride (CHOOCHO, CDOOCHO, CDOOCDO, and CH¹⁸O¹⁸OCH¹⁸O) are presented. Assignments and normal coordinate analysis yield valence force constants (VFF I) reflecting a significant dependence on the conformation of the formyl groups. A similar dependence is borne out by force constants obtained from an ab initio SCF treatment. The quantum chemical force constants qualitatively confirm Badger's rule. It is shown that a second valence force field (VFF II) may be found which is in qualitative agreement with the quantum chemical force constants and also reproduces the observed frequencies just as well as VFF I. The stretching force constants appear to be enhanced for bonds which are trans to another bond.     

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.     

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.     

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.     

Lattice dynamics of wurtzite-type crystals—II

We evaluated, in the preceding paper, the effective ionic charge and electronic polarizability for wurtzite-type crystals on the basis of the polarizable-ion model given by Born and Huang. With use of the quantities so evaluated, we here estimated the short-range force constants from observed frequencies, elastic constants, and piezoelectric constants after simplifying Born and Huang's procedures. The resulting set of force constants can reproduce the observed data except for the piezoelectric constants. This poor reproduction of the piezoelectric constants is due to the fact that the long-range force is emphasized in the polarizable-ion model.     

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.     

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.     

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.     

Use ofD J,DJK constants for the unique fixing of intramolecular forces inXY 3 pyramidal molecules

A mathematical formalism is developed to evaluate all the possible sets of intramolecular force fields fitting fundamental vibrational frequencies and centrifugal distortion constants in the case ofXY ₃ pyramidal type molecules. The method is applied to PF₃ molecule as an example. It is found that there exist as many as four sets of force field fitting all the above experimental data. A few general criteria are suggested to eliminate the suprious sets, thus making further experimental data unnecessary to fix the true physical force field.     

Consistent shell model parameters for the rocksalt structure alkali halides

A set of shell model parameters for the rocksalt structure alkali halides is presented in which the shell charges and polarization force constants are taken to be crystal independent properties. The high and low frequency dielectric constants and the transverse optic frequencies for the whole family of crystals are reproduced with high accuracy.     

On the lattice dynamics of AgGaS2

Summary The vibrational spectrum and one-phonon density of states of a chalcopyrite crystal AgGaS₂ are calculated in an extended Keating’s model with two-bond-stretching and one-bond-bending force constants. Three charges of ions and three force constants are determined by a least-square fitting to experimental frequencies of long-wave phonons taken from Raman-scattering experiments. The calculated constant-volume specific heat, Debye temperature and elastic constants, of AgGaS₂ are in agreement with the experimental data of other authors.     

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.     

Anharmonic analysis of the vibrational states of pyrimidine by the density functional method

The quartic force field of pyrimidine is calculated in the approximation of the hybrid density functional B3LYP/6-31G(d). On the basis of this force field, the IR spectrum of pyrimidine in the range 250–3800 cm^?1 is interpreted. The Darling-Dennison and Fermi resonances are taken into account and their spectral manifestations are analyzed. A combined method for the anharmonic analysis of the vibrational states of polyatomic molecules that employs the theoretical anharmonicity constants and experimental frequencies is proposed. The method ensures a higher prediction accuracy.