三原子分子的喇曼散射

利用U(5)群链描述三原子分子振转谱的对称性质,并用群论方法计算了CO_2分子喇曼散射的跃迁矩阵元,给出了它的振动与转动喇曼散射截面.结果与实验较好地符合.     

Fluids of general hard triatomic molecules

The second, third, and fourth virial coefficients, B_i , of a fluid of general symmetric hard triatomic molecules (fused hard spheres) have been calculated both numerically and theoretically for a variety of potential parameters. It has been found that: (i) for B₂ a valency angle ω_c exists such that for ω>w_c, B ₂ is independent of ω, (ii) B ₃ is very flat for ω>w_c, and (iii) B ₄ exhibits a maximum at ω～π/2. Theoretical calculations employing an assigned convex body fit very well the second and fairly well the third virial coefficients, but fail for the fourth except in the case of a linear molecule.     

Orbital angular momentum in triatomic molecules

The effects of electronic angular momentum in triatomic linear molecules are considered. An effective vibronic hamiltonian is derived and second order energy level expressions are obtained for the bending levels in an electronic Π state. The formulae allow for the anharmonicity of the bending potentials and for the variation of the expectation value <L_z > with bond angle; effects of electron spins are also included. The vibronic levels predicted by the analytic expressions are compared with those calculated using a full matrix treatment of the orbital angular momentum; it is shown that they are far more accurate than the levels predicted by the formulae currently available in the literature. The relationship between the anharmonic corrections and the deviation of <L_z > from unity is discussed in terms of an electrostatic interaction between linear molecule states of different symmetry.     

Potential energy surface intersections for triatomic molecules

The different types of surface intersection which may occur in linear configurations of triatomic molecules are reviewed, particularly with regard to the way in which the degeneracy is split as the molecule bends. The Renner-Teller effect in states of symmetry Π, Δ, Φ, etc., and intersections between Σ and Π, Σ and Δ, and Π and Δ states are discussed. A general method of modelling such intersecting potential surfaces is proposed, as a development of the model previously used by Murrell and Carter and co-workers for single-valued surfaces. Some of the lower energy surfaces of H₂O, NH₂, O₃, C₃, and HNO are discussed as examples.     

Time-dependent local-to-normal mode transition in triatomic molecules

Time-evolution of the vibrational states of two interacting harmonic oscillators in the local mode scheme is presented. A local-to-normal mode transition (LNT) is identified and studied from temporal perspective through time-dependent frequencies of the oscillators. The LNT is established as a polyad-breaking phenomenon from the local standpoint for the stretching degrees of freedom in a triatomic molecule. This study is carried out in the algebraic representation of bosonic operators. The dynamics of the states are determined via the solutions of the corresponding nonlinear Ermakov equation and a local time-dependent polyad is obtained as a tool to identify the LNT. Applications of this formalism to H₂O, CO₂, O₃ and NO₂ molecules in the adiabatic, sudden and linear regime are considered.     

Effective volumes of hard homonuclear nonlinear triatomic molecules

Expressions to determine effective molecular volumes for nonlinear hard homonuclear triatomic molecules are derived. They are used, in combination with an equation of state previously proposed for hard-body molecular fluids, to reproduce accurately the existing simulation data for this kind of fluid, covering a wide fange of bond angles.     

Analytical potentials for triatomic molecules from spectroscopic data

Orthogonal internal coordinates are defined which have useful properties for constructing the potential energy functions of triatomic molecules with two or three minima on the surface. The coordinates are used to obtain ground state potentials of ClOO and HOF, both of which have three minima.     

Analytical potentials for triatomic molecules from spectroscopic data

A general procedure has been developed for constructing analytical potential functions for triatomic molecules which have more than one minimum, these minima not necessarily being related by symmetry. Explicit potentials have been derived for the ground states of HO₂, SO₂ and ClO₂. For HO₂ a linear hydrogen bonded structure O-H----O is predicted as a metastable species. In the case of SO₂ a second minimum corresponding to the species SOO is predicted and ab initio calculations at the SCF MO double-zeta level have been made to establish the geometry and energy of this. For ClO₂ it has been assumed that the spectroscopically observed states of OClO and ClOO are separate minima on the same surface.     

Centrifugal distortion in weakly bound linear triatomic molecules

A simple formula is derived for the centrifugal distortion constant of a linear triatomic molecule in which one of the chemical bonds is much weaker than the other. The derivation is in complete analogy with the standard semiclassical diatomic derivation and results in the equation $\text{D}{}_{\mathrm{J}}\text{= [}\text{4B}{}_{\mathrm{e}}{}^3\text{(hv)}{}^2\text{][1 ? (}\text{B}{}_{\mathrm{e}}\text{b}{}_{\mathrm{e}}\text{)]}$, where B_e, ν, and b_e are, respectively, the triatomic rotational constant, the low stretching frequency, and the rotational constant of the strongly bound diatomic part of the triatomic molecule.     

Lasers on overtone transitions of carbon monoxide molecule

The experimental and theoretical study of lasers working on the first vibrational overtone of the CO molecule is reviewed. A theoretical model of the active medium of the CO laser and its verification are presented. The CO laser operation in a wide spectral range (2.5–4.2 μm) that spans the atmospheric transparency window is demonstrated in the review of experimental works. It is shown that the overtone CO laser can serve as an effective mid-IR source for atmospheric spectroscopy, long-distance transportation of laser radiation, remote laser sensing, etc.     

Analytical potentials for triatomic molecules from spectroscopic data

A method is described for constructing analytical potentials for the ground states of stable triatomic species from spectroscopic data. The method leads to potentials which reproduce both the equilibrium and asymptotic properties of the molecule. Application of the method to H₂O leads to a potential surface which agrees with known experimental and theoretical data. For example, the predicted reaction coordinate for the C _2v insertion of O(¹D) into H₂ is in good agreement with published calculations.     

Quantum telecommunication based on atomic cascade transitions

A quantum repeater at telecommunications wavelengths with long-lived atomic memory is proposed, and its critical elements are experimentally demonstrated using a cold atomic ensemble. Via atomic cascade emission, an entangled pair of 1.53 microm and 780 nm photons is generated. The former is ideal for long-distance quantum communication, and the latter is naturally suited for mapping to a long-lived atomic memory. Together with our previous demonstration of photonic-to-atomic qubit conversion, both of the essential elements for the proposed telecommunications quantum repeater have now been realized.     

Vibration-rotation theory and isotopic substitution in nonlinear triatomic molecules

In the interpretation of high-resolution data it is helpful to be able to relate the experimentally determined molecular constants, such as rotational constants, centrifugal distortion constants, and vibration-rotation interaction constants of a given molecule to those of its isotopically substituted variants. Results concerning the symmetric nonlinear triatomic molecule (XYX) have been given through the second order of approximation by previous workers. In this paper, extensions of the work to the fourth order of approximation and to the nonsymmetric nonlinear triatomic molecule (XYZ) are considered. These extensions are found to increase the algebraic complexity of the problem considerably, and results can generally be given in implicit form only. The approach used is one that emphasizes the isotopic invariants of the problem, i.e., those expressions which remain unchanged when applied to the various isotopic modifications of a given molecule under the assumption that the molecular force field and the molecular geometry remain unchanged under isotopic substitution.     

Quantum cascade transitions in nanostructures

In this article we review the physical characteristics of quantum cascade transitions (QCTs) in various nanoscopic systems. The quantum cascade laser which utilizes such transitions in quantum wells is a brilliant outcome of quantum engineering that has already demonstrated its usefulness in various real-world applications. After a brief introduction to the background of this transition process, we discuss the physics behind these transitions in an externally applied magnetic field. This has unravelled many intricate phenomena related to intersubband resonance and electron relaxation modes in these systems. We then discuss QCTs in a situation where the quantum wells in the active regions of a quantum cascade structure are replaced by quantum dots. The physics of quantum dots is a rapidly developing field with its roots in fundamental quantum mechanics, but at the same time, quantum dots have tremendous potential applications. We first present a brief review of those aspects of quantum dots that are likely to be reflected in a quantum-dot cascade structure. We then go on to demonstrate how the calculated emission peaks of a quantum-dot cascade structure with or without an external magnetic field are correlated with the properties of quantum dots, such as the choice of confinement potentials, shape, size and the low-lying energy spectra of the dots. Contents PAGE 1 Introduction 456 2 Intersubband transitions in quantum wells 458 3 Quantum cascade transitions 462 3.1. Basic principles 462 3.1.1. Minibands and minigaps 464 3.1.2. Vertical transitions 464 3.1.3. GaAs/AlGaAs quantum cascade lasers 464 3.1.4. QCLs based on superlattice structures 465 3.1.5. Type-II quantum cascade lasers 466 3.1.6. Recent developments 466 3.2. Applications: sense-ability and other qualities 466 4 Quantum cascade transitions in novel situations 467 4.1. External magnetic field 467 4.1.1. Parallel magnetic field 468 4.1.2. Many-body effects: depolarization shift 470 4.1.3. The role of disorder 471 4.1.4. Tilted magnetic field 475 4.2. Magneto-transport experiments and phonon relaxation 479 4.3. Magneto-optics experiment and phonon relaxation 484 5 A brief review of quantum dots 485 5.1. From three- to zero-dimensional systems 485 5.2. Making the dots 487 5.2.1. Lithographic patterning 487 5.2.2. Self-assembled quantum dots 488 5.3. Shell filling in quantum dots 489 5.4. Electron correlations: spin states 490 5.5. Anisotropic dots 491 5.6. Influence of an external magnetic field 491 5.6.1. The Fock diagram 491 5.6.2. The no-correlation theorem 492 5.6.3. Correlation effects and magic numbers 492 5.6.4. Spin transitions 493 5.7. Quantum dots in novel systems 494 5.8. Potential applications of quantum dots 494 5.8.1. Single-electron transistors (SETs) 494 5.8.2. Single-photon detectors 494 5.8.3. Single-photon emitters 495 5.8.4. Quantum-dot lasers 495 6 Quantum cascade transitions in quantum-dot structures 496 6.1. Quantum dots versus quantum wells 496 6.2. QCT with rectangular dots 497 6.2.1. Vertical transitions 500 6.2.2. Diagonal transitions 501 6.3. QCT in a parabolic dot 504 6.4. Magnetic field effects on intersubband transitions 506 6.5. Mid-IR luminescence from a QD cascade device 512 7 Summary and open questions 513 Acknowledgements 515 References 515     

Bifurcation in the rotational spectra of nonlinear symmetric triatomic molecules

A microscopic theory is proposed for bifurcation in the rotational spectra of nonlinear AB₂-type molecules. The theory is based on a study of small-amplitude vibrational and precessional motion near the stationary states of a rotating molecule. Bifurcation leads to the formation of fourfold clusters of levels in the upper parts of the rotational multiplets, disruption of the symmetry of the molecule, and a transition from normal to local valence vibrations. The role of the centrifugal force of inertia in the development of these effects is clarified. Bifurcation and the accompanying phenomena are studied in the hydride molecules H₂O, H₂S, H₂Se, and H₂Te using empirical molecular potentials. Zh. éksp. Teor. Fiz. 112, 1239–1256 (October 1997)     

Ab initio calculations of vibrational energies and wave-functions of triatomic molecules

A method is developed for the ab initio treatment of non-infinitesimal vibrations of triatomic molecules. The orientation of the moving system of axes fixed to the molecule is defined in a way that differs somewhat from that normally used. The transformation from internal coordinates into normal coordinates is accomplished by a combined diagonalization and numerical integration procedure; the vibrational functions themselves are expanded into products of one-dimensional harmonic oscillator functions. The method is applied to the calculation of vibrational levels of two states in HCN and deviation from the results obtained using the uncoupled harmonic approximation is discussed.     

Vibrational chaotic dynamics in triatomic molecules: A comparative study

Within Lie algebraic model, the vibrational chaotic dynamics in triatomic molecules are studied. The molecules of H₂S, NO₂, and O₃ are sampled to explore the dynamical differences between the local and normal mode molecules. The comprehensive effects of the local and normal mode vibrations, resonances and chaos on the dynamical entanglement are studied. The results demonstrate that the resonances as well as chaos can promote the evolution of dynamical entanglement.     

Vibrational energies for triatomic molecules using a semi-classical trajectory method

Previously proposed, semi-classical quantization conditions are further examined and then used to calculate low-lying vibrational energy levels of SO₂ and H₂O. Results are compared with variational quantum-mechanical results, using various realistic analytic potentials.     

Non-empirical calculation of spin-orbit coupling constants for some linear triatomic molecules

Higher-order sum rules of the form , are derived for the rotatory strengths of randomly oriented and oriented molecules. In randomly oriented molecules R ⁽ⁿ⁾ = 0 for one-electron systems when n<5, whereas R ⁽⁰⁾=R ⁽²⁾=R ⁽⁴⁾=0 for many-electron systems. In oriented molecules R ⁽ⁿ⁾=0 for one-electron systems when n<3, whereas R ⁽⁰⁾=R ⁽²⁾=0 for many-electron systems. The remaining non-vanishing R ⁽ⁿ⁾ can all be evaluated as diagonal matrix elements of the ground-state wave-function. The resulting expressions are applied to the one-electron model of Condon, Altar and Eyring, and to the coupled oscillator model of Born, Oseen and Kuhn. It is found that the rotatory strengths of the latter model do not fulfil some of the general sum rules. The reason for this discrepancy is discussed. Finally the implications of the present results for the controversy of one-electron versus coupled oscillator models are discussed, and it is proposed that the non-vanishing moments be used as ‘chirality indices’ for specific ground-state wave-functions.