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.     

Heteronuclear diatomic force constants clarified through perturbation theory II

A simple relationship between the heteronuclear diatomic force constant (K(AB)) and the homonuclear diatomic force constants (K(AA), K(BB)), which was proposed in a previous report, has been improved through the second-order perturbation theory as K(AB) = zeta3(K(AA) x K(BB))(1/2); zeta = (R(AA) x R(BB))(1/2)/R(AB) where zeta denotes the correction factor in which R(AB), R(AA), and R(BB) are the equilibrium internuclear distances of diatomic molecules AB, AA, and BB, respectively. To test the above expression, a large number of heteronuclear diatomic force constants have been calculated and compared with those obtained from normal coordinate analyses as well as ab initio quantum mechanical methods (Gaussian 98W). We have found that the above modified expression better reproduces the force constants of most heteronuclear diatomic molecules than the previous expression. It is therefore expected that the expression may also be applied to the prediction of stretching force constants between heteronuclear diatomics in various polyatomic molecules.     

Use of the virial theorem to calculate the molecular force constants of diatomic hydrides

The possibility of using the virial theorem to calculate the coefficients of the potential function for diatomic hydrides on the basis of the Fock-Roothaan wave function in the closed electron shell approximation has been demonstrated in relation to the LiH, BH, CH, NH, and OH molecules.     

Universal scaling features of spectroscopic constants for diatomic systems

Based on a new criterion that was proposed to search for the universality of spectroscopic constants for bound ground-state diatomics [R. H. Xie and P. S. Hsu, Phys. Rev. Lett. 96, 243201 (2006)], we have found universal scaling relations between spectroscopic constants of diatomic systems with s-, p-, and d-type valence-shell constituents. Our study suggests a useful empirical approach for the prediction of molecular spectroscopic constants.     

An attempt to decompose the force constants for some diatomic molecules by the derivatives of the electronic kinetic energy

The force constants for several diatomic molecules were calculated by the derivatives of the electronic kinetic energy within the restricted Hartree–Fock formalism. The uniform scaling procedure was utilized in order to satisfy the virial theorem. The decomposition of the force constant was performed by partitioning the derivatives of the kinetic energy in several ways.     

Calculation of vibrational constants of diatomic molecules

We apply Wigner's effective-harmonic-oscillator (EHO) function with the Morse potential to the calculation of vibrational constants of diatomic molecules. A one-particle system is described by the operator representation of Wigner's function. We find the EHO parameters both for a single molecule and for an equilibrium ensemble of molecules. We obtain numerical values of the constants for the iodine molecule.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 24, No. 4, pp. 485–487, July–August, 1988.     

Chiral force constants: Recommendations for the presentation of internal coordinate force constants

Some force constants associated with the internal coordinates that sense handedness or chirality can have opposite signs in the enantiomers of chiral molecules. Examples of such force constants include interaction force constants between a torsional and stretching or bending internal coordinates. The sign reversal for these force constants in the enantiomers of chiral molecules or in opposite-handed molecular segments is best recognized by labeling them as chiral force constants. Recognition of chiral force constants suggests that certain guidelines are to be followed in the presentation of internal coordinate force constants. © 1993 by John Wiley & Sons, Inc. © John Wiley & Sons, Inc.     

A correlation of excited state rotational constants for diatomic molecules

The concepts of “orbital stress” and “transition stress” are defined and applied to N₂, N⁺₂, CO, and CO⁺. The bond lengths and rotational constants of excited electronic states are related to the transition stress, and the response of the electrons and nuclei to the transition stress is shown to be a molecular property, essentially independent of the electronic configuration or state.     

Pseudo-exact force constants from coriolis coupling constants

A method has been developed to calculate Pseudo-Exact Force Constants from ζ-constants after truncating a higher dimensional secular equation with the High Low Frequency Separation Method (PE-HFS and PE-LFS method). A procedure to reduce the C-matrix is presented and the conditions for the applicability will be discussed. The present method is applicable to many cases where only one ζ-constant can be measured (e.g., if some band contours are disturbed and prevent the determination of all ζ-values). It is also possible to get excellent starting force constants for a least square programme in cases where sufficient data are known. The effectiveness of the different first order ζ-constants in fixing the force constants has been pointed out. The pseudo ζ sum rule for the truncated secular equation is also discussed. A proof for the sign rule for ζ-constants for xzy₃ (C_3v) type molecules [ζ(δ_as(XY₃)) < 0 and ζ(?_r(XY₃)) > 0] is given.     

Millimeter-wave rotational spectrum and molecular constants of diatomic gallium bromide

Gas-phase spectra of four isotopic species of GaBr have been detected in the millimeter wavelength region. The molecules were produced by a flame reaction of gallium and bromine at 1000° C. From the rotational spectra molecular constants have been determined for ⁶⁹Ga⁷⁹Br,⁶⁹Ga⁸¹Br,⁷¹Ga⁷⁹Br,⁷¹Ga⁸¹Br. The equilibrium internuclear distance is r_e = 2.3524907(82).     

Millimeter-wave rotational spectrum and molecular constants of diatomic gallium iodide

The gas-phase molecular spectrum of Gal has been detected in the millimeter wavelength region. The molecules are produced by vapourising a mixture of gallium and lead iodide into an evaculated cell. Analysis of the observed rotational transitions yields the following molecular parameters for ⁶⁹Ga¹²⁷I: Y₀₁ = 1706.89645(83) MHz, Y₁₁ = −5.68714(53) MHz, Y₂₁ = 6.329(43) kHz, Y₀₂ = −0.472713(60) kHz, Y₁₂ = 0.472(38) Hz, ω_e = 216.38 cm⁻¹, ω_e^x_e= 0.471 cm⁻¹, and for ⁷¹Ga¹²⁷I: y₀₁ = 1675.72004(71) MHz, Y₁₁ = −5.53277(57) MHz, Y₂₁ = 5.995(34) kHz, Y₀₂ = −0.455700(51) kHz, y₁₂ = 0.522(40) Hz, ω_e = 214.37 cm⁻¹, and ω_e^x_e = 0.458 cm⁻¹. The equilibrium internuclear distance obtained for Gal is r_e = 2.574667(12) Å.     

Atomic multipoles and perpendicular electrostatic forces in diatomic and planar molecules

Current methods for assigning atomic multipoles focus on reproduction of the molecular electrostatic potential. Another aspect of electrostatic interaction, which is usually overlooked, is the forces that an external electric field exerts on the nuclei of a molecule. In a self-consistent theory, both the electrostatic potential and force should be accounted for. However, in general it is not easy to meet this requirement for the force. For planar molecules, though, a formal solution is available in terms of atomic multipoles that are extracted from the molecular multipolar tensors. These Force-Related (FR) atomic multipoles are discussed in detail for some typical diatomics and planar polyatomics, and are shown to provide a solid uniform framework for treating both aspects of the electrostatics. In contrast, the commonly used potential-derived charges (i.e., the atomic charges obtained by fitting the electrostatic potential) can yield large deviations with respect to electrostatic forces on the nuclei, even when the electrostatic potential is very well reproduced.     

Vibrational modes and force constants ofp-bromotoluene

The characteristic features of the normal vibrational modes ofp-bromotoluene were calculated; the assignments of spectral bands reported previously were corrected. The force constants of the molecule were estimated in terms of the model of the unified valence and force field.     

Millimeter-wave rotational transitions and molecular constants of the diatomic silver iodide

In the 280 GHz region four rotational transitions of both isotopic species of AgI in vibrational states up to v = 2 have been measured. The analysis including frequencies of former observations in the 10 GHz region resulted in improved and new Dunham parameters Y_kl. From these data values of the vibrational constants ω_e and ω_ex_e have been deduced.     

Application of the spline-function method to determination of potential constants for diatomic molecules

We describe a new technique for calculating force constants for diatomic molecules, making significnat use of approximate information on derivatives of the function of the total energy of the molecule given in tables. The proposed procedure is applied to determine the potential constants for the LiH molecule.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 21, No. 1, pp. 98–101, January–February, 1985.