Symmetry coordinates of nonrigid molecules

Motivated by Altmann’s definition of symmetry groups of nonrigid molecules, Wigner’s method of obtaining the symmetry coordinates of a molecule is extended to nonrigid molecules with free internal rotations. The molecule BF₂ CH₃ is exemplified.     

Morphometric approach to the solvation free energy of complex molecules

We show that the solvation free energy of a complex molecule such as a protein can be calculated using only four geometrical measures of the molecular structure and corresponding thermodynamical coefficients. We compare results from this morphometric approach to those obtained by an elaborate statistical-mechanical theory in liquid state physics for a large variety of different structures of protein G and find excellent agreement. Since the computational time is drastically reduced, the new approach provides a practical and efficient way for calculating the solvation free energy which can be employed when this quantity has to be calculated for a large number of structures, as in a simulation study of protein folding.     

Quantum theory of energy exchange in direct encounters of polyatomic molecules with nonrigid surfaces

Recently developed effective mass theory of vibrational, rotational and translational energy exchange in molecular collisions is extended naturally to polyatomic molecules colliding with nonrigid surfaces. Considering the processes where the short-range forces are of prevailing importance, we transform the Hamiltonian into the form which enables us to eliminate the coordinates which are cyclic in the limit of zero range forces and can thus be expected to be approximately ignorable when forces are of short, but finite, range. Instead of three rotational and three translational coordinates we are thus left with one only relevant generalized coordinate. The mass corresponding to this coordinate can easily be calculated; it depends on the mass and the moments of inertia of the molecule, and on the segment of the potential surface on which the system evolves. The motion of the only relevant generalized coordinate is then quantized. The inelastic scattering problem is treated within first-order in the distorted wave expansion. In the cases where this may be expected to be inadequate, more advanced approximation schemes developed in scattering theory could be applied as well. The excitations of bulk phonons and also of vibrational modes localized on the surface are included in the theory. As an application, energy transfer in collisions of CO₂ molecules with Pt and Ag surfaces is studied (since this is the experimentally most studied case involving molecules of more than two atoms), and the results are compared with the experiments and with the recent semiclassical stochastic trajectory calculations in which the transfer of vibrational energy to rotations is neglected and the solid's vibrations are treated by a quasiclassical approximation. Excellent agreement was found between the present theory and the trajectory calculations mentioned for all three gas temperatures considered (290, 580 and 1160 K) in the case of small change in vibrational energy and high surface temperature, i.e., under the conditions where the agreement between the two methods could possibly be expected because of the approximations involved.     

DNA分子能带结构与电子态研究

DNA分子链内的巡游电子数与其结构和位形密切相关，可变的电子数会导致这类软物质费米面处能带结构的变化.在紧束缚近似下，计入电子 晶格的相互作用，计算了DNA分子不同巡游电子数下的能带结构及态密度，对碱基对不同排列情况下DNA分子可能的电属性进行了讨论. 关键词： DNA 态密度 电晶相互作用     

On the relation between the energy level classification of a nonrigid molecule and the symmetry of its equilibrium configurations

The problem of changes in the energy level classification of a nonrigid molecule upon a change in its equilibrium configurations, in the case in which different possible geometries of such configurations correspond to different point groups, is considered for the example of the nonrigid dimethylacetylene molecule CH₃C₂CH₃ in the ground electronic state.     

Symmetry properties of the effective hamiltonians of some nonrigid molecules

Group-theoretical methods are used to identify the nonvanishing parameters and establish relations between them in the effective Hamiltonians which describe rotation and motion with large amplitude. The cases considered are 1) bending vibration in molecules of the type XY₂ and XYZ and 2) inversion vibration in pyramidal molecules of the type XY₃. For the latter type of molecule, the symmetry properties of the parameters in the effective centrifugal Hamiltonian for quasidegenerate inversion states are investigated. The general form of this Hamiltonian and its symmetry properties are established and studied in an arbitrary order in the small parameter.Translated from Izvestiya Vysshikh Uchebnykh Zavednii, Fizika, No. 2, pp. 22–26, February, 1981.     

A symmetry-based approach to the effective Hamiltonian for symmetric top molecules in degenerate vibronic states

The effective Hamiltonian for a symmetric top molecule in a degenerate vibronic state is obtained. Included in this Hamiltonian are the rotational, spin-rotational, spin-orbit coupling and electronic spin-spin interactions. The terms of the Hamiltonian are expressed as the product of molecular ‘constants,’ rotational angular momentum operators, and symmetry operators. A formalism is derived, and tables included, to determine whether or not a symmetry operator vanishes for a given vibronic state of a particular molecular symmetry. In this way, one can easily obtain all the non-vanishing Hamiltonian terms for a particular application.     

Rotational energy levels of symmetric top molecules in 2 E states

Expressions are derived for the rotational energy levels of a symmetric top molecule in a ² E state which take into account a spin-orbit interaction and vibronic Jahn-Teller interactions. Some group theoretical aspects of the Jahn-Teller problem for a general symmetric top molecule are discussed. In addition, the overall selection rules and formulae for the relative intensities of rotational lines in a ² A-² E transition are derived and the possibility of applying them to two recently published experimental examples is considered.     

Transformation of the effective rotational Hamiltonian of nonrigid X 2 Y molecules

The transformation of the effective rotational Hamiltonian H of nonrigid X ₂ Y molecules to the form having a minimum number of diagonals in the basis of rotational functions of a symmetric top is discussed. Such a transformation is a generalization of the reduction transformation performed for the polynomial effective Hamiltonian H. It is shown that in the general case the transformation substantially changes the form of the initial Hamiltonian, which restricts the region of applicability (J<J*) of the reduced Hamiltonian represented in a class of elementary functions in terms of angular momentum operators. The values of the rotational quantum number J* are estimated for the (000) ground and (010) vibrational states of the H₂O molecule.     

New approach to surface ionization and drift-tube spectroscopy of organic molecules

A new physical model of ionization of organic molecules from the class of amines on the oxidized surface of transition metals is suggested. According to this model, the process involves the capture of protons or hydroxyl groups forming on the oxide surface upon water molecule adsorption. The adequacy of the model is demonstrated experimentally with test amines, such as Novocaine (procaine), bencaine, Dimedrol (diphenylhydramine), etc. A theory of drift motion of ion beams that includes the space charge effect is proposed. It is shown that the quantity P _i=μj/ε₀ v _g ² (where μ is the ion mobility, j is the ion current density, ɛ₀ is the permittivity, and v _g is the longitudinal velocity of an ionized gas) plays the role of perveance for intense drift ion beams. A new type of drift-tube spectrometer that uses an ion source due to surface ionization is developed.     

An extended Lennard-Jones potential energy function for diatomic molecules: Application to ground electronic states

A new simple analytical diatomic potential energy function that can be considered an extension of the prototypical Lennard-Jones model is proposed and tested. Five- and six-parameter models are considered and these can be easily constructed from widely available low-order vibrational-rotational constants and the dissociation energy. Accuracy tests are carried out on the ground electronic states of sixteen diatomic molecules. The proposed six-parameter function is found to be more accurate than other available few-parameter analytical models for the diatomic potential energy, and has accuracy comparable to that of modern high-level ab initio functions.     

One method of describing the transfer of energy of the kinetic degrees of freedom to the electronic states of molecules

An analysis is made of the process of transferring the kinetic energy of highly excited vibrational terms of a molecule to an electronic state of one of its constituent atoms. This is done by utilizing a wave equation for the effective wave functions of the atom, corresponding to mixed states, in which the velocity of this atom relative to the neighboring atoms in the molecule enters as a parameter. An expression is found for the excitation probability in the case of a hydroge-like atom in the resonant approximation. State University, Omsk. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 20–26, September, 1996.     

Depolarized light scattering studies of the orientational motion in liquids of nonrigid molecules

We report depolarized Rayleigh spectra, HV, of diphenyl ether (DPE) and 1,3 diphenyl-1,3 tetramethyldisiloxane (PMS) in the temperature range of 276 to 353 K using Fabry-Perot interferometry. We have associated the single Lorentzian HV spectra with molecular reorientation in DPE and intramolecular rotation in flexible PMS under slipping boundary conditions.     

Classification of the states of nonrigid molecular systems with continuous axial symmetry groups

Construction of the stationary state classification is considered for nonrigid molecular systems whose geometrical symmetry of internal dynamics is determined by continuous axial groups. The construction is based on the methods of symmetry group chains.     

Extension of the Local Approach to excited states of molecules

The Local Approach for the calculation of electronic correlation energies in molecules is generalized to excited states. Within the Local Approach correlated states are obtained by applying a local projection operator on the Hartree-Fock ground state or simple reference states, which are used as zeroth order approximations for the excited states, respectively. In the case of excited states one has in addition to require the correlated states to be orthogonal on the states lower in energy. This is done by using Schmidt's orthogonalization. The method is applied to a simple model of the H₆-ring for which an exact solution is available. The results obtained are of comparable quality as for the ground state.     

GeS分子基态和低激发态的势能曲线与光谱性质

本文以aug-cc-pv5Z为基组, 采用考虑Davidson修正的多参考组态相互作用方法(MRCI+Q)得到了GeS分子基态(X¹Σ⁺)和5个低激发态(1¹Σ, 1¹Δ, A¹Π, 1⁵Σ⁺, 2⁵Σ⁺)的势能曲线. 计算结果表明: 2⁵Σ⁺态为排斥态, 其余5个态为束缚态; 6个态有着共同的离解通道, 离解极限均为Ge(³P)+S(³P). 利用计算得到的势能曲线得了X¹Σ⁺, 1¹Σ^-, 1¹Δ, A¹Π和1⁵Σ⁺态的垂直跃迁能T_e, 平衡键长R_e, 离解能D_e, 谐振频率ω_e, 非谐性常数ω_ex_e及平衡位置的电偶极矩. X¹Σ⁺态的R_e 为2.034 Å, D_e 为5.728 eV, ω_e为571.73 cm^-1, ω_ex_e为1.6816 cm^-1, 平衡位置的电偶极矩为1.9593 Debye. 激发态1¹Σ, 1¹Δ, A¹Π, 1⁵Σ⁺的T_e 依次为25904.81, 26209.22, 32601.19, 43770.26 cm^-1; R_e依次为2.313, 2.322, 2.188, 2.8790 Å; D_e依次为2.524, 2.487, 1.694, 0.3036 eV, ω_e依次为358.90, 353.08, 376.32, 134.96 cm^-1; ω_ex_e依次为1.2421, 1.2151, 1.6608, 1.9095 cm^-1; 平衡位置的电偶极矩依次为1.3178, 1.4719, 1.5917, -1.9785 Debye. 通过求解核运动的薛定谔方程得到了J=0时X¹Σ⁺, 1¹Σ^-, 1¹Δ, A¹Π和1⁵Σ⁺态前30个振动态的振动能级G_v和分子常数B_v, 得到的结果和已有的实验值及其他理论值符合较好.