V.I. Pupyshev

Structure and vibrational assignment of gouche-1,3-butadiene

Abstract The completely optimized structures and harmonic force fields of the s-trans(anti) - and gouche -isomers of 1,3-butadiene have been computed at the ab initio Hartree—Fock level using the 6·31G basis set. The gouche dihedral angle was found to be 34.8° from the planar s-cis(syn) -configuration of the 1,3-butadiene molecule. Seven scale factors for correcting the theoretical force constants of the trans -isomer were calculated from the experimental frequencies of light and heavy trans -1,3-butadienes. The correction of the gouche -butadiene force field was then carried out using these scale factors, and the vibrational problems were solved for gouche forms of C 4 H 6 , CD 2 CHCHCD 2 , C 4 D 6 , 13 CH 2 CHCH 13 CH 2 , and 12 CH 2 CHCHCH 2 . The total assignment of the experimental vibrational frequencies of these isotopomers is given. The conclusion drawn is that the quantum mechanical geometry and the scaled quantum mechanical force field correctly simulate the structure and the experimental frequencies of the butadiene gouche -conformer.

The Lenz vector in the confined hydrogen atom problem

Abstract A general criterion for the degeneracy of states of the hydrogen atom placed in a spherical impenetrable box of radius R is formulated on the basis of the Lenz vector formalism. The reasons for the elimination of the Coulomb degeneracy typical of the conventional hydrogen atom problem and for the non-conservation of the Lenz vector are discussed. The explanation of the simultaneous degeneracy of some energy levels (e.g. 2s and 3d, 3s and 4d, etc. at R =2 au) is given.

Exact Relations for Confined One-Electron Systems

Publisher Summary This chapter describes integrals of motion and boundary value problems. The chapter describes the mutual connections among the commutation relations and exponential transformations, for example, in the context of Hausdorfs relations. The coordinate transformation is a standard method for the analysis of boundary value problems. An important type of commutation relation is naturally connected with the scaling procedure. The possibility of using the virial/hypervirial relations for approximate wavefunctions depends on the form and nature of the classes of approximate functions. The chapter considers the one-parameter family of regions Ω (λ) and the corresponding boundary value problems, and also presents the main results concerning the energy changes with region modifications. Perturbation theory can be used to describe the splitting of electron energy levels for a hydrogen atom under small shifts from the center of an impenetrable spherical cavity, for example, it is demonstrated that first-order perturbation theory shows that for any s -state, the position of the atom in the center corresponds to a minimum.

Ab initio structures and vibrational analysis of two planar configurations of 1,3,5-hexatriene

Abstract The geometrical parameters of the tTt -hexatriene-1,3,5 and tCt -hexatriene-1,3,5 molecules have been computed at the RHF/6–31G level. The structures of both molecules are found to be planar in this approximation. The force fields of these molecules were calculated at the HF/6–31G//HF/6–31G level. The vibrational analyses of both molecules and their 2,3,4,5-tetradeuteroanalogues made it possible to refine the assignment of some experimental vibrational frequencies. The calculated mean amplitudes of vibrations of the non-deuterated molecules are compared with the experimental ones.

Perturbation theory for the hydrogen atom in a spherical cavity with off-centre nucleus

The problem of a hydrogen atom in an impenetrable spherical cavity of small radius R is considered on the basis of the first-order perturbational treatment of the electron-nucleus interaction taking explicit account of the boundary condition. An approximate analytic expression is derived for the electronic energy as a function of the shift of the nucleus off the centre. The estimations obtained are in good qualitative and semiquantitative agreement with the results of the finite-difference calculations. Some general features of the energy dependences are discussed qualitatively.

Hidden symmetry in the confined hydrogen atom problem

The classical counterpart of the well-known quantum mechanical model of a spherically confined hydrogen atom is examined in terms of the Lenz vector, a dynamic variable featuring the conventional Kepler problem. It is shown that a conditional conservation law associated with the Lenz vector is true, in fair agreement with the corresponding quantum problem previously found to exhibit a hidden symmetry as well.

Potential function of internal rotation for isoprene from ab initio calculations and experimental data

Abstract Ab initio computations of the potential energy curve of internal rotation around the central single CC bond of isoprene have been performed at the Hartree—Fock level with a 3·21G basis set. The similarity of the slope of the curve obtained and the potential energy curve calculated for a more complete basis set ( 7s3p/4s2p ) [Kavana-S2ebo, J. Mol. Struct. 106 (1984) 259] is discussed. The values of the Pitzer function F (φ), its Fourier expansion coefficients, and coefficients of the potential energy expansion were calculated from data given in the above reference. The correction of the potential energy expansion coefficients was carried out from frequencies of torsional “hot” bands of isoprene and torsional overtone of its second rotational isometric form. It was shown that the isoprene second isomer is realized as a gauche -form. The potential energy expansion coefficients were obtained as follows: V 1 = 399.9, V 2 = 1330.22, V 3 = 781.8 and V 4 = −175.8 cm −1 .

The iterative consistency method and its geometric interpretation

Abstract Features of the iterative procedure which allows one to find a particular solution of the molecular force field, on the basis of the vibrational spectra of two isotopically substituted molecules, are considered, with the aid of a geometric interpretation of the equations used.

Transferability of quantum mechanical force field scale factors between conjugated hydrocarbons

The transferability of scale factors (empirical corrections) for quantum mechanical force fields among closely related molecules is tested for the related hydrocarbons, ethylene, 1,3-butadiene, and 1,3,5-hexatriene and their isotopomers. The agreement demonstrated here between the fundamental vibrational frequencies calculated from the scaled quantum mechanical force fields and the experimental frequencies of these molecules confirms this transferability. The advantage of combining quantum mechanical calculations of force constants with empirical scale factors for the accurate prediction of force fields and vibrational frequencies in the analysis of the incomplete experimental spectra of the rotamers of these hydrocarbons is stressed.

Molecular hydrogen 3s,d 3Λg+ complex revisited

The rovibronic term values, Lande factors, and radiative properties of all bound levels in the 3s,d 3Λg+ complex of H2, D2, and HD are evaluated in the framework of fully ab initio channel-coupling approach. The modified multichannel quantum-defect theory is employed to transform highly accurate ab initio Born–Oppenheimer electronic matrix elements borrowed from a literature to their diabatic counterparts avoiding explicit consideration of radial coupling effects. The radiative lifetimes of the most critical levels in the H2 complex are remeasured by a delayed coincidence method. The accuracy of the predicted term values, Lande factors, transition probabilities and experimental lifetimes is sufficient to indicate the sources of disagreement in existing theory and experimental data.