The analysis of rovibrational motion equations of a diatomic molecule in the linear regime

The motion equations of diatomic molecules are here extended from the absolute vibrational case to a more general and real rotational and vibrational (rovibrational) case. The rovibrational Hamiltonian is heuristically formed by substituting the respective number and angular momentum operators for the vibrational and rotational quantum numbers in the energy eigenvalues of a diatomic molecule which was first introduced by Dunham. The motion equations of observable quantities such as the position and linear momentum are then determined by implementing the well-known Heisenberg relation in quantum mechanics. We face with the second-order imaginary differential equations for describing the temporal variations of the relative position and the linear momentum of two oscillating atoms, which are coupled in the x–y horizontal plane. The possible rovibrational oscillations are distinguished by the three quantum numbers n, l and m associated with the energy and angular momentum quantities. It is finally demonstrated that the simultaneous solutions of rovibrational equations satisfy the energy conservation during all quantised oscillations of a diatomic molecule in space.     

Classical study of the rovibrational dynamics of a polar diatomic molecule in static electric fields

We study the classical dynamics of a polar diatomic molecule in the presence of a strong static homogeneous electric field. Our full rovibrational investigation includes the interaction with the field due to the permanent electric dipole moment and the polarizability of the molecule. Using the LiCs molecule as a prototype, we explore the stability of the equilibrium points and their bifurcations as the field strength is increased. The phase space structure and its dependence on the energy and field strength are analyzed in detail. We demonstrate that depending on the field strength and on the energy, the phase space is characterized either by regular features or by small stochastic layers of chaotic motion.     

用预言振转跃迁谱线的新公式研究AuO分子电子跃迁P支的高激发态发射谱线

本文在孙卫国等建立的预测双原子分子高转动激发态的 振转跃迁能谱的解析物理公式的基础上, 增加了该公式推导时被省略的高阶转动项H_v对能级的贡献, 获得了包含此高阶小项的预测双核体系高转动激发态的振转跃迁谱线的新表达式. 使用该新公式对AuO分子P支发射跃迁光谱的研究表明: 加入高阶转动常数H_v后的新公式所预言的振转跃迁 谱线的精度比不包含H_v 的公式给出的结果提高了约一个数量级. 因此, 更加有力地表明了使用多重差分法建立的这类物理公式在预言实 验未给出的物理数据方面的正确性和有效性. 关键词： AuO H_v')" href="#">转动常数H_v P支谱线')" href="#">P支谱线 多重差分法     

用代数方法精确研究HF分子B1Σ的振转能谱

基于代数方法(algebraic method)可以获得双原子分子的包含最高振动能级在内的所有高阶振动能级的精确数值这一事实,又提出了一种新的代数方法(algebraic method 2)来精确研究双原子分子电子态的振转能谱和转动常数. 以HF分子的B¹Σ电子态为例,应用algebraic method 2方法研究了该电子态的振动量子数从ν=0到ν=10的所有振转能谱,获得了与实验值符合得非常好的理论结果. 关键词： 代数方法 双原子分子 振转能级     

精确预言双原子分子Q线系高振转激发态的跃迁谱线

用多重差分的方法,从双原子分子跃迁谱线的普遍表达式出发,已经建立起了预言双原子分子P线系高激发振转跃迁谱线的解析物理公式。采用同样的方法,充分利用现有实验条件下测定的部分振转跃迁谱线数据,文章建立了预言双原子分子Q线系高激发振转跃迁谱线的物理公式。使用该公式和一组经过物理筛选的(15条)精确的实验跃迁谱线,研究了IrN分子A1Π—X1Σ+跃迁系统中(4,1),(3,1)跃迁带的Q支发射光谱。结果表明,该公式不仅很好地重复了所有已知的实验光谱数据,且正确预言了实验没有获得的很多高转动量子态的未知发射谱线,从而提供了一种新的预言高转动量子态的未知跃迁谱线的物理方法。     

Semiempirical study of perturbations of the Landé g factors of the electronic-vibrational-rotational levels of hydrogen: I. Theory

Theoretical analysis of perturbations of the Landé g factors of the electronic-vibrational-rotational levels of a diatomic molecule is performed for the case of interactions between electronic states whose number is arbitrary finite and that are not limited by the smallness of the parameter describing these interactions, with regard for the interaction of rovibrational states with an arbitrary finite number of vibrational-rotational levels of individual perturbing electronic states. The spin-multiplet interaction between rovibrational states was disregarded. As a result of general consideration, formulas are obtained for the g factors of rovibrational levels for the following cases: (i) mutual perturbation of a pair of levels; (ii) an nl complex of terms; and (iii) the interaction between an arbitrary number of vibrational-rotational levels of electronic states (whose number is also not limited) considered in the first order of the perturbation theory. The formulas obtained are given in the form of dependences on differences in observed (perturbed) values of rovibrational terms and matrix elements of vibrational wave functions dependent on the internuclear distance, which, in turn, are matrix elements of the electron wave functions of different operators that take into account the interaction between the electrons and nuclei of a molecule. The possibilities of using the obtained expressions in semiempirical study of perturbations and of determining the absolute dependences of the g factors of rovibrational levels of the electronic states of diatomic molecules (in particular, the hydrogen molecule) on the vibrational and rotational quantum numbers are analyzed.     

Influence of Environmental Parameters on the Stability of the DNA Molecule

Fluctuations in viscosity within the cell nucleus have wide limits. When a DNA molecule passes from the region of high viscosity values to the region of low values, open states, denaturation bubbles, and unweaving of DNA strands can occur. Stabilization of the molecule is provided by energy dissipation—dissipation due to interaction with the environment. Separate sections of a DNA molecule in a twisted state can experience supercoiling stress, which, among other things, is due to complex entropic effects caused by interaction with a solvent. In this work, based on the numerical solution of a mechanical mathematical model for the interferon alpha 17 gene and a fragment of the Drosophila gene, an analysis of the external environment viscosity influence on the dynamics of the DNA molecule and its stability was carried out. It has been shown that an increase in viscosity leads to a rapid stabilization of the angular vibrations of nitrogenous bases, while a decrease in viscosity changes the dynamics of DNA: the rate of change in the angular deviations of nitrogenous bases increases and the angular deformations of the DNA strands increase at each moment of time. These processes lead to DNA instability, which increases with time. Thus, the paper considers the influence of the external environment viscosity on the dissipation of the DNA nitrogenous bases’ vibrational motion energy. Additionally, the study on the basis of the described model of the molecular dynamics of physiological processes at different indicators of the rheological behavior of nucleoplasm will allow a deeper understanding of the processes of nonequilibrium physics of an active substance in a living cell to be obtained.     

Classical dynamics of polar diatomic molecules in external fields

In this paper, we present the study of the global classical dynamics of a rigid diatomic molecule in the presence of combined electrostatic and nonresonant polarized laser fields. In particular, we focus on the collinear field case, which is an integrable system because the z-component P_φ of the angular momentum is conserved. The study involves the complete analysis of the stability of the equilibrium points, their bifurcations and the evolution of the phase flow as a function of the field strengths and P_φ. Finally, the influence of the bifurcations on the orientation of the quantum states is studied.     

Mechanism of angular momentum exchange between molecules and Laguerre-Gaussian beams

We derive the interaction Hamiltonian between a diatomic molecule and a Laguerre-Gaussian beam under the assumption of a small spread of the center of mass wave function of the molecule in comparison with the beam waist. Considering the dynamical variables of the center of mass, vibrational, rotational, and electronic motion, we show that, within the electronic dipole approximation, the orbital angular momentum of the field couples with the rotational and electronic motion. The changes in the transition probabilities and selection rules induced by the field orbital angular momentum and the applicability of the derived interaction mechanisms for polyatomic molecules are discussed.     

Rovibrational dynamics of the RbCs molecule in static electric fields. Classical study

We study the classical dynamics of the RbCs molecule in the presence of a static electric field. Under the Born–Oppenheimer approximation, we perform a rovibrational investigation which includes the interaction of the field with the molecular polarizability. The stability of the equilibrium points and the phase space structure of the system are explored in detail. We find that, for strong electric fields or for energies close to the dissociation threshold, the molecular polarizability causes relevant effects on the system dynamics.     

Computer simulation of a diatomic molecule dissolved in a monatomic fluid—Correlation functions,band shapes,and relaxation times

Four N₂-Ar ‘solute-solvent’ systems representing different temperatures and densities were simulated on a computer by the molecular dynamics technique. From the data for each system, the dipole, angular velocity, force-on-the-bond, and P ₂ correlation functions were calculated. These functions were used to determine rovibrational infra-red and Raman band-shapes, and N.M.R. relaxation times for quadrupolar, magnetic dipole-dipole and spin-rotation relaxation mechanisms. The P ₂ and dipole correlation functions were compared with those calculated by Gordon from experimental data. The lack of agreement was examined to determine restrictions on the application of Gordon's method for obtaining these correlation functions. Also, the band shapes were compared with the experimental data to help determine these restrictions. The N.M.R. relaxation times were examined for temperature dependence and for dominant contributions to the total relaxation time. The force-on-the-bond correlation function was found to require an extra term that takes into account the average force field to which the N₂ molecule is subjected. A three-parameter model for rotational diffusion of a diatomic molecule is tested and compared with existing models.     

A close look at the motion of C60 on gold

In this paper, we have studied the motion of buckminsterfullerene (C₆₀) on a gold surface by analyzing its potential energy and using classical molecular dynamics method. The results can be employed to investigate the motion of C₆₀-based nanocars which have been made in recent years. For this purpose, we have studied the translational and rotational motions of C₆₀ molecule independently. First, we have calculated the potential energy of a C₆₀ molecule on a gold surface in different orientations and positions and employed this data to predict fullerene motion by examining its potential energy. Then we have simulated the motion of C₆₀ at different temperatures using classical molecular dynamics methods. Specifying the regime of the motion at different temperatures is one of main goals of this paper. We have found that the rotational motion of C₆₀ molecule on the gold substrate, was easier than its sliding (translational) motion. Also, the regime of motion of fullerene depended on temperature. The results demonstrate that three different regimes of motion, dependent on temperature, could be observed: rare jumps to adjacent cells, frequent jumps, and continuous motion. Employing the results of this paper not only helps to understand the C₆₀ motion on the gold surface but also provides an appropriate tool for realizing motion of the thermally-driven fullerene-based nanocars.     

Interaction of translational and rotational modes of a molecular impurity in two-dimensional atomic crystals

The interaction between the translational and rotational degrees of freedom of a diatomic homonu-clear molecule that executes a motion at the site of a two-dimensional close-packed atomic matrix located on a close-packed atomic substrate (a molecular substitutional impurity in the crystal field of the two-dimensional lattice of a solidified rare gas) is investigated theoretically. The relationships describing the effective dynamic properties of an impurity rotator in the presence of translational excitations of its center of inertia are derived in the framework of consistent procedures on the basis of the Lagrangian (the functional-integral method) and Hamiltonian (the canonical-transformation method) formalisms. The inclusion of the translational-rotational interaction leads to a radical change in the inertial properties of the molecule. This manifests itself in a change in the form of the operator for the rotational kinetic energy as compared to the corresponding expression for a free rotator. The inertia tensor components for the molecule become functions of molecular orientation, and the molecule, in terms of rotational motion, transforms into a “parametric rotator” whose effective kinetic energy is represented as a generalized quadratic form of the angular momentum (or the angular velocity) components with a symmetry corresponding to the symmetry of the external crystal field. The translational-rotational interaction also results in the renormalization of the parameters of the crystal potential without a change in its initial form.     

Investigation of the dynamics of angular motion and construction of algorithms for controlling the angular momentum of spacecraft using a magnetic attitude control system

The problem of controlling the angular momentum of spacecraft using magnetic attitude control systems interacting with the Earth’s magnetic field is considered. A mathematical model for the angular motion dynamics of a spacecraft has been constructed. An approach to determining the parameters of the control law for a spacecraft attitude control and stabilization system that ensures angular momentum dissipation is proposed.     

Discrete hydrodynamics: Numerical results for the soft-sphere viscosity

Numerical calculations have been done of the viscosity of the soft-sphere liquid, using a new molecular dynamics technique. It is based on a formulation of hydrodynamics which is discrete in space and time, and exactly renormalizable. The present data turn out to be sufficient to estimate the viscosity, but determination of the full equations of motion (and therefore renormalization) requires further calculations using a smaller discrete time interval; these are presently under way. The present results indicate that this method is more than 100 times more efficient than previous (Green-Kubo or nonequilibrium molecular dynamics) methods. This suggests that the discrete formulation is the most natural way to approach hydrodynamics.     

Dynamics of a crystal containing a molecular impurity—II. Molecular vibrations included

The dynamics of a crystal containing a molecular impurity is discussed with allowance for the effects of internal vibrations of the molecule. Cartesian co-ordinates are introduced to describe internal vibrations, angular oscillations and centre of mass motions of the impurity, and the displacements of the atoms of the host crystal. Next the Hamiltonian is set up and the equations of motion derived. In this process, use is made of Dirac brackets when dealing with coordinates having redundancy and constraints. From the dynamical matrix, some of the familiar results of the crystal-field approximation are recovered. The application of the partitioning technique is then discussed, and finally comparison is made with results of other approaches.