Improved molecular constants for the and states of NaH

Improved molecular constants for the and states of the NaH molecule are presented. NaH molecules are produced by reactive scattering of H and Na₂ in a crossed beam experiment. High vibrational levels (6 9) of the NaH molecules are predominantly populated. Their excitation spectrum in the range has been measured using a new variant of Doppler spectroscopy. The transition frequencies involving the vibrational levels 2 8 in the and 6 9 in the state have been determined with an accuracy of better than . Using also previously published data a new set of molecular constants for the and state is derived. In particular, the vibrational dependence of the rotational constants B, D and H as well as some of v”-v' band origins for and is determined. The transition frequencies measured here or published previously are reproduced by these new coefficients with an accuracy of 0.1 cm^-1 [rms value] with a maximum deviation of 0.4 cm^-1. New RKR potential energy curves have been calculated up to the turning points of the levels v” = 9 in the state and v' = 25 in the state. Received 21 August 1999     

Ergodicity in computer simulation of quantum dissipative processes

The ergodicity principle in quantum theory is employed for elaboration of a new quantum trajectory technique which is used for numerical simulation of quantum dissipative systems. With this purpose the density matrix of a quantum system is represented as a sum over an ensemble of quantum states in time intervals. The method is employed for computations of a quantum anharmonic oscillator.     

可激发气体分子声弛豫过程振动模式能量转移速率计算

研究可激发气体中振动模式能量转移速率和声弛豫过程形成的关系,将单一气体Tanczos弛豫方程理论[J.Chem.Phys.25,439(1956)]扩展应用于混合气体中振动模式的振动-振动(V-V)和振动-平动(V-T)能量转移速率的计算。在室温下CO₂,CH₄,CL₂,N₂和O₂组成的多种混合气体中,振动模式能量转移速率的计算结果表明:对于多个振动模式所形成的声复合弛豫过程,各振动模式的声激发能可由V-V能量转移相互耦合后传递给具有最快V-T转移速率的最低振动频率振动模式,再通过该振动模式的V-T转移退激发形成主弛豫过程。这种选择最快转移路径的声激发量弛豫方式,造成了大多数可激发气体中声弛豫吸收谱的实测数据只存在一个吸收峰的现象。从而提供了一个可通过计算微观振动能量转移速率分析混合气体声弛豫过程形成机理的理论模型。      

Calculation of vibrational energy transition rates in acoustic relaxation processes for excitable gas molecules

To research the correlation between vibrational energy transition rates and acoustic relaxation processes in excitable gases, the vibrational relaxation theory provided by Tanczos [J.Chem. Phys. 25, 439(1956)] is applied to calculate the energy transition rates of VibrationalVibrational(V-V) and Vibrational-Translational(V-T) energy transfer in gas mixtures. The results of calculation for the multi-relaxation processes in various gas mixtures, consisting of carbon dioxide, methane, chlorine, nitrogen, and oxygen at room temperature, demonstrate that the acoustic energy stagnated in every vibrational mode is coupled with each other through V-V energy exchanges. The vibrational excitation energy will relax through the V-T de-excitation path of the lowest mode because of its fastest V-T transition rate, resulting in that only one absorption peak can be measured for most of excitable gas mixtures. Thus, an effective model is provided to analyze how the vibrational energy transition rates affect the characteristics of acoustic relaxation processes and acoustic propagation in excitable gas mixtures.     

Theoretical study of the molecular properties of benzyl azide, 2-, 3- and 4-methyl benzyl azide

Ab initio and density functional calculations have been performed to study the benzyl azide, 2-, 3- and 4-methyl benzyl azides. Several molecular properties, such as conformational equilibrium, optimal geometry, and vibrational frequencies, have been computed for these molecules. Ionisation energies were also computed.     

Vibration analog of a superradiant quantum transition

A vibrational analog of the superradiant quantum transition (SQT) in a classical system of weakly bound oscillators of van der Pole-Duffing (self-generators), in which the coupling element is a linear oscillator, is described. Such an analog is a strongly modulated oscillatory process of almost complete periodic energy exchange between the generators. This type of mode is alternative to nonlinear normal modes (NNM) and close in its character to limiting phase trajectories (LPTs), which have been introduced recently as applied to conservative systems, but in contrast to them, as the attractor. It is shown that the necessary condition of the transition to intense energy exchange in the classical system is the instability of one of the NNMs similarly to that when the condition of the superradiant transition is the instability of the ground state in a quantum model.     

NO分子宏观气体热力学性质的理论研究

采用量子统计系综理论,研究了基态NO分子宏观气体摩尔熵、摩尔内能、摩尔热容等热力学性质.首先应用课题组前期建立的变分代数法(variational algebraic method, VAM)计算获得了基态NO分子的完全振动能级,得到的VAM振动能级作为振动部分,结合欧拉-麦克劳林渐进展开公式的转动贡献,应用于经典的热力学与统计物理公式中,从而计算得到了1000-5000 K温度范围内NO宏观气体的摩尔内能、摩尔熵和摩尔热容.将不同方法计算得到的摩尔热容结果分别与实验值进行比较,结果表明基于VAM完全振动能级获得的结果优于其他方法获得的理论结果.振动部分采用谐振子模型对无限能级求和计算热力学性质的方法有一定的局限性,应当使用有限的完全振动能级进行统计求和.     

Dissociation Energies of Diatomic Molecules

Molecular dissociation energies of 10 electronic states of alkali molecules of KH, ^7LiD, ^7 LiH, ^6LiH, NaK, NaLi and NaRb are studied using the highest three accurate vibrational energies of each electronic state, and an improved parameter-free analytical formula which is obtained starting from the LeRoy Bernstein vibrational energy expression near the dissociation limit. The results show that as long as the highest three vibrational energies are accurate, the current analytical formula will give accurate theoretical dissociation energies De^theory, which are in excellent agreement with the experimental dissociation energies De^expt.     

Radiative transitions in highly ionised silicon-like ions

Transition energies, oscillator strengths and transition probability values for radiative transitions have been calculated for the highly ionised atoms of Si isoelectronic sequence from Mn¹¹⁺ to Kr²²⁺ for the singly excited states up to principal quantum number n = 7. Time-dependent coupled Hartree-Fock (TDCHF) theory has been used to estimate such transition properties. Most of the results for the oscillator strengths and transition probabilities are new. Transition energies agree reasonably well with available spectroscopic values. Received 25 January 2000 and Received in final form 24 October 2000     

Torsional barriers and nonlinear optical properties of 2-, 3-, 4-phenylpyridine molecules

The torsional barriers and nonlinear optical properties for all phenylpyridine molecules were calculated by using Hartree-Fock (HF) theory and Becke three-parameter functional (B3LYP) hybrid approaches within the density functional theory framework with the 6-31++G(d, p) basis set, and via the GAUSSIAN 98W. The torsional barrier computations show that dihedral angle between the two rings increases with the number of H-H vicinal interactions and torsional barriers with dihedral angles for 3-, 4-phenylpyridines are too similar for both HF and B3LYP level calculations. Also, HOMO-LUMO energy gaps, polarizabilities, anisotropy of polarizabilities, and static hyperpolarizabilities are calculated as a function of dihedral angle between benzene and pyridine rings. The study reveals that the phenylpyridines show very low nonlinear optical properties. The calculated torsional barrier, equilibrium dihedral angle and molecular dipole moment results for these molecules were compared with available experimental and other results determining from different computational methods.     

碰撞诱导离解(CID)(Ⅰ)——含时量子理论

本文采用含时量子力学微扰理论研究了分子碰撞诱导离解(CID)动力学过程。分子系统具有Morse振子和分子间指数排斥相互作用势的类型。所建立的分析理论公式能方便地用来讨论有关CID过程的各种物理化学问题。以(I₂,He)分子系统为例所进行的计算表明,在总能量一定的条件下,分子振动能比相对平动能更有效地促进CID过程的进行。而且,除必须克服离解能量势垒外,CID过程并没有额外的动力学阈值限制。 关键词：     

Mn22+离子1s22s-1s2np的偶极跃迁能和振子强度

用全实加关联方法计算了类锂Mn22 离子1s22s-1s2np(2≤n≤9)的偶极跃迁能和振子强度.1s2np(2≤n≤9)态的精细结构通过计算自旋-轨道与自旋-其他轨道相互作用算符的期待值确定.依据单通道量子亏损理论,确定了Rydberg系列1s2np的量子数亏损.从而可以用这些作为能量的缓变函数的量子亏损,实现对任意高激发态(n≥10)的能量的可靠预言.将这些分立态振子强度与单通道量子亏损理论相结合,得到在电离阈附近束缚态-束缚态跃迁振子强度以及束缚态-连续态跃迁的振子强度密度,从而将Mn22 离子的这一重要光谱特性的理论预言外推到整个能域.     

The environment-induced-superselection model of the large-molecules conformational stability and transitions

The large molecules lie in the “border territory" between the “quantum" and the “classical". To which extent one should employ the classical or quantum-mechanical methods in describing their behavior is an open issue. To this end, the problem of the large-molecules conformational stability and transitions is typical. While the small or medium-size molecules are successfully described by the quantum mechanical methods, the large-molecules conformational transitions are usually investigated classically. However, the problem of the origin of stability of the large-molecules conformations remains open. In this paper, we offer a solution-in-principle for both the large-molecules conformational stability and transitions yet in the context of the quantum decoherence theory. Actually, we apply the “environment-induced superselection rules" theory that naturally answers both of the problems, and, in a sense, offers a unifying picture for the molecules in a solution. Generality of our approach stems from the generality of the decoherence theory. So, our approach is a qualitative theoretical program alternating the point of view to the large-molecules dynamics: while ultimately being the quantum-mechanical systems, the large molecules in a solution may still exhibit the (approximately) classical behavior of their conformational degrees of freedom.     

Cr~(21+)离子1s~23d-1s~2nf的跃迁能和偶极振子强度(英文)

用全实加关联方法计算了类锂Cr21+离子1s23d-1s2nf(4≤n≤9)的跃迁能和1s2nf(n≤9)态的精细结构.在类氢近似下估算了对能量的高阶相对论修正.依据量子亏损理论,确定了Rydberg系列1s2nf的量子数亏损.据此可以实现对任意高激发态(n≥10)的能量的可靠预言.计算了Cr21+离子1s23d-1s2nf(4≤n≤9)跃迁的振子强度.与量子亏损理论相结合,得到该离子从1s23d态到电离阈附近高激发束缚态间的偶极跃迁振子强度以及到相应连续态跃迁的振子强度密度,从而将Cr21+离子的这一重     

Parity chain and parity chain breaking in the two-level cavity quantum electrodynamics system

We investigate the transitions between energy levels and parity symmetry in an effective two-level polar molecule system strongly coupled with a quantized harmonic oscillator. By the dressed-state perturbation theory,the transition diagrams between the dressed-state energy levels are presented clearly and show that the odd(even) parity symmetry is broken by the permanent dipole moment(PDM) of the polar molecules. By the analytical and numerical methods, we find that when the coupling strength and the PDM increase, the more frequency components are induced by the counter-rotating terms and PDM.     

Equations-of-motion approach to quantum mechanics: application to a model phase transition

We present a generalized equations-of-motion method that efficiently calculates energy spectra and matrix elements for algebraic models. The method is applied to a five-dimensional quartic oscillator that exhibits a quantum phase transition between vibrational and rotational phases. For certain parameters, 10 x 10 matrices give better results than obtained by diagonalizing 1000 x 1000 matrices.     

On the geometric quantization of the ro-vibrational motion of homonuclear diatomic molecules

In the framework of geometric quantization we extend the harmonic oscillator rules to rotation and vibration of molecules. First, the geometric quantization of the rigid rotor is introduced. The novelty is that we found an explicit relation giving the impulse along the third axes, which takes discrete values and found that it depends not only on the principal quantum number, but also on the orbital and magnetic quantum numbers. Geometric quantization is further extended to the class of vibrational (damped) systems. The theory is sought as mathematical requirement, which can be traced in the analysis of integrable systems. It is shown that properties of the critical points of the momentum map can be the key to the integrability. A $C^{⁎}$ isomorphism of the momentum map between the Lie algebra of physical observables and that of the harmonic oscillator induces the geometric quantization on former. We show how the method works, taking into account the Lennard-Jones' potential, which characterizes the interaction between molecules. A second example shows a physical system having the energy levels depending on the magnitude of the frequencies.