Molecular structure of the boron(III) oxide molecule in the SCF approximation

The potential surface for the boron(III) oxide (B₂O₃) ground state has been calculated in restricted HF approximation with a minimal STO—3G basis set. The equilibrium geometry has C_2v symmetry; the corresponding structural parameters are as follows: r(O_i—B₁)= 1.241 Å; r(B_i—O)= 1.341 Å ; ∠B₁QB₂ = 142° and ǒO₁B₁O = 177°. Calculations were also carried out using the SCF-Xα approach for two configurations of B₂O₃ with C_2v and D_∞h symmetry.     

Energy bands: Chern numbers and symmetry

Energy bands formed by rotation–vibrational states of molecules in the presence of symmetry and their qualitative modifications under variation of some control parameters are studied within the semi-quantum model. Rotational variables are treated as classical whereas a finite set of vibrational states is considered as quantum. In the two-state approximation the system is described in terms of a fiber bundle with the base space being a two-dimensional sphere, the classical phase space for rotational variables. Generically this rank 2 complex vector bundle can be decomposed into two complex line bundles characterized by a topological invariant, the first Chern class. A general method of explicit calculation of Chern classes and of their possible modifications under variation of control parameters in the presence of symmetry is suggested. The construction of iso-Chern diagrams which split the space of control parameters into connected domains with fixed Chern numbers is suggested. A detailed analysis of the rovibrational model Hamiltonian for a D₃ invariant molecule possessing two vibrational states transforming according to the two-dimensional irreducible representation is done to illustrate non-trivial restrictions imposed by symmetry on possible values of Chern classes.     

Reduced effective Hamiltonians for degenerate vibrational states of methane-type molecules

The ambiguity of effective Hamiltonians for the fundamental degenerate states of the methane-type molecules is studied. The transformations of these Hamiltonians to reduced forms which include only empirically determinable parameters are suggested. The set of parameters fitted by Champion and Pierre for the ν₄ band of CH₄ (J. Mol. Spectrosc.79, 225–280 (1980)) is found to be related to the set of parameters of Husson and Poussigue (J. Phys.32, 859–865 (1971)) by the unitary transformation of the effective Hamiltonian.     

The hydrogen atom in a superstrong magnetic field

A new method for energy-level calculations of the H-atom in a superstrong magnetic field is proposed. The method is based on perturbation theory. The finite-difference technique is used to solve the resulting equations.     

Generating functions for effective hamiltonians. Symmetry,topology, combinatorics

Recent developments associated with old technique of generating functions and invariant theory which I have started to apply to molecular problems due to my collaboration with Yu.F. Smirnov about 25 years ago are discussed. Three aspects are presented: the construction of diagonal in polyad quantum number effective resonant vibrational Hamiltonians using the symmetrized Hadamard product; the decomposition of the number of state generating function into regular and oscillatory contributions and its relation with Todd polynomials and topological characterization of energy bands; qualitative aspects of resonant oscillators and fractional monodromy as one of new generalizations of Hamiltonian monodromy.     

Ab initio study of molecular structure and internal rotation in methyldicyanophosphine and methyldiisocyanophosphine. The Raman spectrum of methyldicyanophosphine and its interpretation with the use of scaling ofab initio force fields

The equilibrium geometric parameters and structures of transition states of internal rotation for the molecules of methyldicyanophospine MeP(CN)₂ and its isocyano analog MeP(NC)₂ were calculated by the RHF and MP2 methods with the 6–31G^* and 6–31G^** basis sets. At the MP2 level, the total energy of cyanide is −35 kcal mol⁻¹ lower than that of isocyanide and the barriers to internal rotation of methyl group for MeP(CN)₂ and MeP(NC)₂ are 2.2 and 2.7 kcal mol⁻¹, respectively. For both molecules, the one-dimensionalab initio potential functions of internal rotation approximated by a truncated Fourier series were used to determine the frequencies of torsional transitions by solving direct vibrational problems for a non-rigid model. The Raman spectrum of crystalline MeP(CN)₂ was recorded in the range 3500–50 cm⁻¹. The vibrational spectra of this compound were interpreted by scalingab initio force fields calculated by the RHF and MP2 method. The vibrational spectrum of methyldiisocyanophosphine was predicted with the use of the obtained scale factors. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 9, pp. 1703–1714, September, 1998.     

Equilibrium conformation of dimethylaminodichlorophosphine molecule: the use of the results of quantum-chemical calculations and spectroscopic measurements in the analysis of gas-phase electron diffraction data

Geometric parameters and force fields of two stable isomers of dimethylaminodichlorophosphine molecule, a gauche-conformer with C₁ symmetry (A) and anti-conformer with C _s symmetry (D), resulting from internal rotation about the P—N bond, were calculated in the RHF/6-31G* approximation. Using the scaled quantum-chemical force field for the most stable conformer A, the first reliable interpretation of the vibrational spectra of the light and perdeuterated isotopomers of dimethylaminodichlorophosphine was obtained. The root-mean-square vibrational amplitudes, harmonic and anharmonic vibrational corrections, and centrifugal distortion corrections were also calculated. Structural analysis of electron diffraction data was performed with consideration of nonlinear kinematic effects at the first-order level of perturbation theory. The experimental values of the equilibrium geometric parameters were estimated. The results obtained suggest a nonplanar equilibrium configuration of the amino group in the dimethylaminodichlorophosphine molecule.     

Spectra of tensor operators adapted to nonstandard basis. Qualitative features of clustering

Spectra of irreducible tensor operators for the chain of group G ? O(3) are investigated from the qualitative point of view. Conditions are found for clustering of the eigenvalues of tensor operators in the high-J limit. Approximate formulas are proposed which permit the calculation of the relative positions of the clusters. Centrifugal distortion of spherical tops, crystal-field splitting, and low-frequency bending vibrations of nonrigid molecules composed of an atom and rigid symmetrical core are considered as physical examples. Clustering of the F^(kJJ′) coefficients of Moret-Bailly are qualitatively explained as well.     

Vibration—rotation hamiltonian for nonrigid triatomic molecules with diatomic rigid core

Several semi-rigid model hamiltonians are constructed for calculation of the vibration—rotation spectra of nonrigid triatomic molecules with diatomic rigid core. The models proposed are applicable to molecules with an elliptical nonrigid trajectory. This means that the potential energy surface corresponding to the interaction between the external atom and rigid core possesses minima close to elliptical surface. Such molecules as MCN (M = Li, Na, K) are appropriate examples.