Presentation of Molecular Force Fields in Terms of Dimensionless Coordinates

It is suggested that force fields calculated for polyatomic molecules may be presented in dimensionless coordinates, ξ (=R/R_e, where R is internal coordinate and Re is the equilibrium value of corresponding bond distance or angle). Stretching force constants when presented in dimensionless coordinates show interesting trends. It is found that whereas the force constants in terms of internal coordinates, F_ii vary widely for bonds with different atoms in the series Z-H (Z:C, Si, Ge), Y-H (Y:N, P, As, Sb, O, S), X-H (X:F, Cl, Br, I), X-C etc, the corresponding force constants in dimensionless coordinates, Φ_ii are same within the limits of experimental errors. It is felt that such force constants may have better prospects of transferability between related molecules and may be helpful in making the normal coordinate analysis easier to some extent.     

Molecular Force Field of Methanol

Abstract

Normal coordinate analysis was carried out on the vapor phase Raman and i.r. spectral data of methanol and its deuterated species to determine a vibrational force field. Based on the results of calculations, the 25-parameter molecular force field was analyzed and compared with the earlier studies and the vibrational band assignments were discussed in terms of the vibrational mode mixings, particularly, in the wavenumber region below 1500 cm^?1.     

Conformational Analysis of 2, 3, 3-Trimethylhexane

Infrared and Raman spectra were obtained for 2, 3, 3-trimethylhexane and were interpreted with the aid of normal coordinate calculations. It was concluded that this compound exists in three molecular conformations, but a fourth conformer may exist. Vibrational assignments were made for the three conformers.     

Vibrational Spectra,Normal Coordinate Calculations,and Molecular Mechanics Calculations for 2, 3, 3-Trimethyl-1-Butene

Infrared and Raman spectra were obtained for 2, 3, 3-trimethyl-1-butene, and a vibrational assignment was made with the aid of normal coordinate calculations. Molecular mechanics calculations were also made to determine molecular parameters of the stable conformation. Values for the force constants of a forty-one parameter modified valence force field were obtained that will be used for other 2-methyl-1-alkenes that contain substituted methyl groups.     

CF_3D非谐性常数的测定

本文报道了CF_3D红外光谱的实验测定。利用包含基频、泛频及组合频的方程直接获得了五个CF_3D定非谐性常数     

Conformational Analysis of 2-Methylhexane and 3-Methylhexane

Abstract

Infrared spectra were obtained for 2-methylhexane and 3-methylhexane, and were interpreted with the aid of normal coordinate calculations. It was shown that 2-methylhexane exists in three conformations. Evidence for the presence of three conformations of 3-methylhexane is presented, but a fourth conformer probably exists. Transferred force constant values resulted in an overall average difference between observed and calculated wavenumbers of 4.3 cm^?1, or 0.5%, for seven conformers of these two compounds.     

Elastic Constants of Superconducting MgB2 from Molecular Dynamics Simulations with Shell Model

The elastic constants of superconducting MgB₂ are calculated using a molecular dynamics method (MD) with shell model. The lattice parameters, five independent elastic constants, equations of state (EOS), Debye temperature, and bulk modulus of MgB₂ are obtained. Meanwhile, the dependence of the bulk modulus B, the lattice parameters a and c, and the unit cell volume V on the applied pressure are presented. It is demonstrated that the method introduced here can well reproduce the experimental results with a reasonable accuracy.     

AlB2弹性常数的第一性原理计算

利用基于局域密度近似框架下的第一原理平面波赝势方法,结合HGH型相对论分析赝势,对AlB2的晶格参数和弹性常数进行了计算.结果显示:当晶格参数c和a的比率c/a为1.084时,具有最稳定的几何结构,与实验值及其他理论得到的计算值相符合.     

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.     

Studies on dissociation energies of diatomic molecules using vibrational spectroscopic constants

New analytical expression and numerical approach are suggested to calculate dissociation energies De of diatomic molecular states using an extreme value method (EVM). Studies on some electronic states of OH, BH, N2, Br2, ClF and CO molecules show that the accuracy of the EVM dissociation energies depends on the number of correct vibrational constants used in the calculations. The convergence qualities of De are suggested to be an alternative physical criterion to measure the qualities of the various sets of vibrational constants from different literature for the same diatomic state.     

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.     

Evaluation of photoelastic constants from first-order Raman intensities of MgF2

A formalism to connect first-order Raman intensities of MgF₂ and its photoelastic constants is developed by developing a method of writing internal coordinates in terms of displacement gradientsu _ij which are not symmetric. It is found that for crystals containing only one line inA ₁ species, the ratiosP ₁₃/P ₃₃ and (P ₁₁ +P ₁₂)/P ₃₁ can be directly evaluated from the intensities, without having to derive the intensity formulae; while (P ₁₁ +P ₁₂)/P ₁₃ is independent of the intensities as well as the refractive index of the crystal. It is a function of only the dimensional parameters. In this crystal, since the speciesB _1g andB _2g also contain only one line each, the ratio (P ₁₁ −P ₁₂)/P ₆₆ can also be directly obtained from the intensities.     

A theoretical study on the mechanism and dynamics of reactions (CF3)2CHOCH2F/(CF3)2CHOCHF2 with OH radical

The information related with the mechanism of reactions (CF₃)₂CHOCH₂F + OH (R1) and (CF₃)₂CHOCHF₂ + OH (R2) was explored theoretically at the BMC-CCSD//BMK/6-311 + G(d,p) level. Based on the optimised structures, energies, and other information, the rate constants were evaluated by the canonical variational transition-state theory with small curvature tunneling contributions in a temperature range of 220–2000 K. For each reaction, there are both hydrogen-abstraction and displacement channels. In addition, more than one hydrogen atom can be abstracted. The relationship between hydrogen abstraction and displacement, between different hydrogen-abstraction channels, and between reactions R1 and R2 are elucidated.     

Anharmonic force constants of GaSb from the measured third order elastic constants at 300°K

The third-order elastic constants of single crystal GaSb are determined using ultrasonic pulse interferometer at 10 MHz. The constants at 300°K, in units of 10¹¹ N.m.⁻², are C_l11 = ™ 4 ·75 ± 0·06 C₁₄₄ = + 0·50 ± 0·25 C₁₁₃ = ™ 3 ·08 ± 0·02 C₁₆₆ = ™ 2·16 ± 0·13 C₁₂₃ = ™ 0 ·44 ± 0·29 C₄₅₆ = ™ 0·25 ± 0·15 These constants are used to evaluate the three anharmonic first and second neighbour force constants based on modified Keating’s model. The constants are (in units of 10¹¹ N.m⁻²)γ=− 2·406;δ=0·407;ε=−0·222.     

超导体MgB2弹性常数的第一原理计算

利用全势线性muffin-tin轨道(FP-LMTO)方法, 结合在密度泛函理论框架下的广义梯度近似, 研究了六角密堆积结构超导体MgB2的晶格参数, 弹性常数, 以及体积模量及其对压强的微分. 计算结果显示当晶格参数c和a的比率c/a大约为1.138时, MgB2的结构最稳定.本文所得到的计算结果与实验值及其他作者利用不同方法得到的计算值相符合.     

Revisiting Noether's Theorem on constants of motion

In this paper we revisit Noether's theorem on the constants of motion for Lagrangian mechanical systems in the ODE case, with some new perspectives on both the theoretical and the applied side. We make full use of invariance up to a divergence, or, as we call it here, Bessel-Hagen (BH) invariance. By recognizing that the Bessel-Hagen (BH) function need not be a total time derivative, we can easily deduce nonlocal constants of motion. We prove that we can always trivialize either the time change or the BH-function, so that, in particular, BH-invariance turns out not to be more general than Noether's original invariance. We also propose a version of time change that simplifies some key formulas. Applications include Lane-Emden equation, dissipative systems, homogeneous potentials and superintegrable systems. Most notably, we give two derivations of the Laplace-Runge-Lenz vector for Kepler's problem that require space and time change only, without BH invariance, one with and one without use of the Lagrange equation.     

Normal Coordinate Analysis of 3-Bromo-1,3-Dinitroazetidine

Abstract

The infrared spectrum of 3-bromo-1,3-dinitroazetidine was interpreted with the aid of normal coordinate calculations. A seventy-two parameter modified valence field was used in those calculations, and the observed wave numbers were fit with an average error of 2.5 cm^?1. An assignment of the bands in terms of symmetry coordinates is given. Many of the force constants were transferred to 1-acetyl-3,3-dinitroazetidine to aid in normal coordinate calculations for that compound.     

VPT2+K spectroscopic constants and matrix elements of the transformed vibrational Hamiltonian of a polyatomic molecule with resonances using Van Vleck perturbation theory

Vibrational levels of polyatomic molecules are analysed with Van Vleck perturbation theory to connect experimental energy levels to computed molecular potential energy surfaces. Vibrational matrix elements are calculated from a quartic potential function via second-order Van Vleck perturbation theory, a procedure that treats both weak and strong interactions among vibrational states by approximately block-diagonalising the vibrational Hamiltonian. A clear and complete derivation of anharmonic and resonance constants as well as general expressions for both on- and off-diagonal matrix elements of the transformed Hamiltonian is presented. The equations are written in partial fraction form and as a constant multiplied by a harmonic oscillator matrix element to facilitate removing the effect of strongly interacting resonant states both in analytical formulae and in computer code. The derived equations are validated numerically, and results for the isotopomers of formaldehyde (H₂CO, HDCO, D₂CO) are included. The implications of the equations on zero-point energy calculations and experimental fits are discussed. The VPT2+K method is defined by these results for use in fitting and calculating vibrational energy levels.     

一种获取双原子分子的转动常数的方法

本文给出了对于任何双原子分子或双原子自由基分子,由其振动常数结合RKR方程、结合从头计算,获得势能曲线及其转动常数的方法.并对CN的基态和激发态进行了计算,结果与实验值符合得非常一致.A