Hartree-Fock calculation of the harmonic force constants and equilibrium geometry of formaldehyde

Using the force method, complete sets of harmonic force constants have been obtained for formaldehyde from Hartree-Fock wavefunctions. The agreement with experiment is considered particularly satisfying for the off-diagonal constants. This holds not only for a near-Hartree-Fock Gaussian basis set but also for a small but polarized 7, 3/3/1 basis set. The value even of such a small calculation is underlined by frequencies calculated from force constants corrected for almost systematic errors in the diagonal constants. Experimental force fields are critically examined, and an explanation for the surprisingly large coupling between CO and CH stretching is indicated.     

Constrained force constants for octahedral molecules

A set of constrained force constants has been derived from experimental vibrational frequency data for eighty three octahedral molecules. Superimposing the condition that the larger value for f_d—f_dd′ be used when f_dα—f_dα″ is a maximum on the six equations relating vibrational frequencies to force constants generates a seventh. This provides a uniform set of results for all 83 molecules. The values of the force constants have a simple rationale in terms of chemical bonding theory. Some preliminary calculations for SF₆ show that these force constants are suitable for use in generating reliable molecular dynamical trajectory data.     

Quantum chemical calculation of force constants and vibrational spectra

As a result of the development of direct derivative methods and improved computational facilities, ab initio quantum chemical calculations have become an increasingly important source of information for the determination of molecular force constants. Within the Hartree-Fock (H-F) SCF model and using moderate size basis sets such calculations are now economically feasible for molecules of up to 2o–3o atoms. At this level of theory, harmonic diagonal force constants are overestimated by 1o–3o%, corresponding to 5–15% in the frequencies. However, the largely systematic errors can be accounted for by simple empirical corrections. The resulting SQM (Scaled Quantum Mechanical) force fields are probably the most reliable ones available at present for larger molecules. Calculated infrared intensities are semi-quantitatively correct. Beyond the H-F model, large scale calculations including electron correlation give great improvements in the force constants, but there are still residual errors of a few percent.     

Separated internal force constants for the ethylene and ethane molecules and their use for calculation of the force field for the propylene molecule

We consider the question of separation of linear combinations of force constants for ethylene and ethane. Introduction of a perturbation into the matrix of the kinematic coefficients allows us to solve the inverted vibrational problem using the matrix method of successive approximations without eliminating dependent coordinates. Such an approach makes it possible to obtain a sufficient system of equations for determining the separated internal force constants. The separated internal force constants determined for ethylene and ethane are used to calculate the force field for propylene. The calculated separated internal force constants for propylene reproduce its vibrational spectrum and the spectrum or propylene-d₆ with average deviation from experimental frequencies of 8 cm^–1. The numerical influence coefficients for stretching vibrations of the C-H bond are linearly related to the lengths of these bonds.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 22, No. 1, pp. 118–122, Janauary–February, 1986.     

Ab initio MO calculation of force constants and dipole derivatives for the formamide dimer. An estimation of hydrogen-bond force constants

Ab initio SCF MO calculations (with the 4-31G basis set) have been carried out to determine the equilibrium geometry, vibrational frequencies, dipole-moment derivatives, and force constants for intermolecular modes of the formamide dimer and its d₄ and d₆ derivatives. The results are correlated with monomer calculations and experimental data for crystalline formamide.     

Approximate calculation of thermodynamic instability constants of complex compounds

A Debye-Hückel type equation is proposed for calculating thermodynamic instability constants from measurements at a single, sufficiently high, ionic strength, in solutions containing NaClO₄. The applicability of this equation to instability constants of complexes of different composition and charge is shown.     

Calculation of force constants and vibrational frequencies of octahedral MX6 molecules

The vibrational frequencies of some octahedral species ([SbX₆]⁻, [SbX₆]³⁻, [NbX₆]⁻, [NbX₆]²⁻, [TaX₆]⁻, [TaX₆]²⁻; X = F, Cl, Br, I) have been calculated by means of six extrapolated molecular force constants using some linear relations between the force constants and the reciprocal radii of the ligands. A statistical treatment of these correlations allowed the calculation of error limits for a probability of 90%. The computations of the force constants and vibrational frequencies were based on the GF-matrix method.     

The calculation of indirect nuclear spin-spin coupling constants in large molecules

We present calculations of indirect nuclear spin-spin coupling constants in large molecular systems, performed using density functional theory. Such calculations, which have become possible because of the use of linear-scaling techniques in the evaluation of the Coulomb and exchange-correlation contributions to the electronic energy, allow us to study indirect spin-spin couplings in molecules of biological interest, without having to construct artificial model systems. In addition to presenting a statistical analysis of the large number of short-range coupling constants in large molecular systems, we analyse the asymptotic dependence of the indirect nuclear spin-spin coupling constants on the internuclear separation. In particular, we demonstrate that, in a sufficiently large one-electron basis set, the indirect spin-spin coupling constants become proportional to the inverse cube of the internuclear separation, even though the diamagnetic and paramagnetic spin-orbit contributions to the spin-spin coupling constants separately decay as the inverse square of this separation. By contrast, the triplet Fermi contact and spin-dipole contributions to the indirect spin-spin coupling constants decay exponentially and as the inverse cube of the internuclear separation, respectively. Thus, whereas short-range indirect spin-spin coupling constants are usually dominated by the Fermi contact contribution, long-range coupling constants are always dominated by the negative diamagnetic spin-orbit contribution and by the positive paramagnetic spin-orbit contribution, with small spin-dipole and negligible Fermi contact contributions.     

Molecular vibrational constants of some simple polyatomic molecules : Valence force constants and compliance constants of some halogenated methanes, silanes and germanes

The valence force constants and compliance constants of twenty-six halogenated methanes, silanes and germanes of symmetry C_3v and C_2v are reported. Correlations have been found between the primary force constants and the nature of the central atom and of the halogen, and the number of attached halogen atoms. Relationships have also been confirmed between the force and compliance constants and the bond lengths and strengths.     

Calculation of the force constants of molecules by means of the Hellmann-Feynman theorem

The force constants of the molecules LiH, BH, and H₂O have been calculated by means of the Hellmann-Feynman theorem on the basis of the Hartree-Fock-Roothan wave functions in the one-determinant approximation. The results obtained have been compared with the results previously calculated on the basis of the same functions by means of the virial theorem.     

Vibrational frequencies and force constants of N2O4 in complexes with molecules of different solvents determined by Raman spectra andAb initio calculation

The Raman spectra of N₂O₄ solutions in organic solvents have been recorded. The frequencies ofv ₁,v ₂, andv ₃ bands of N₂O₄ increase with increasing solvent electron-donor properties. Especially large changes ofv ₃ N-N stretching band have been observed (254.5 cm^–1 in n-hexane, 276.5 cm^–1 in 1,4-dioxane). The ab initio calculations have shown that the interaction between N₂O₄ and electron-donor molecules causes an increase of N-N and N-O stretching and O-N-O bending force constants of N₂O₄ in agreement with the results of Raman study.     

Some considerations on the force constants of bond-bond interaction in simple triatomic molecules

The force constants of bond-bond interaction in simple triatomic molecules have been discussed on the basis of a simple molecular orbital theory. It has been shown that the force constant of highly delocalized-bond molecule tends to take a large positive value, while that of highly localizedbond molecule a negative value. It is therefore suggested that the sign of the force constant is a good measure of the electron localization or delocalization in a molecule.     

Ab initio computation of force constants: Part VI. Applications of the force relaxation method for geometry optimization

Techniques to improve the computational efficiency of the force relaxation method are discussed. Force constants for fragments in previously computed smaller molecules can be transferred to construct a guess force constant matrix. Additional force constants that may be needed can be computed by a procedure which uses only one additional force calculation per diagonal force constant required. A scaling technique to improve convergence on the optimized geometry is discussed.     

Quantum-chemical study of the force constants of CH bonds in molecules with three-membered rings

We have considered the effect of the completeness of the basis set on the accuracy of nonempirical calculations of force constants (K_CH). We have studied the trends in the value of K_CH as a function of the nature of the hetero-atom in saturated and unsaturated rings. On the basis of estimated values of the orbital strengths conclusions have been drawn about the substantial contributions from the inner MO in determining K_CH. A relation has been obtained and analyzed between K_CH and the gradient of the electric field at the proton. Comparison with the previously established relation between K_CH and the ²J_CH SSIC [spin-spin interaction constants] has led to conclusions about the common character of the electronic interactions which determine the characteristics listed.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 25, No. 4, pp. 399–406, July–August, 1989.