N2- and O2-broadening coefficients of C2H2 IR lines

Pressure-broadening parameters of six lines belonging to the ν₅ band of C₂H₂ in collision with N₂ have been measured with a tunable diode-laser spectrometer in order to complete up to J = 33 our earlier measurements (D. Lambot, G. Blanquet, and J. P. Bouanich, J. Mol. Spectrosc.136, 86–92 (1989)) on the broadening of C₂H₂ by N₂ and O₂ at 297 K. These N₂- and O₂-broadening coefficients have been first calculated on the basis of the Anderson-Tsao-Curnutte theory; in this approach, we show that the short-range interactions which contribute significantly to the linewidths are not correctly treated. Next, we consider the improved semiclassical model proposed by Robert and Bonamy. The intermolecular potential consists in the addition of the atom-atom interaction model to the quadrupolar interactions. The limited radial spherical harmonics expansion of the atom-atom potential, from which expressions for the differential cross section were derived, appears to be quite insufficient at short intermolecular distances. Therefore, we use a more accurate representation of this potential, avoiding an inadequate truncation and keeping the analytic expressions obtained by Bonamy and Robert. In the calculations we take into account the contributions derived from the radial functions U₀₀₀(r), U₂₀₀(r), and U₂₂₀(r), as well as from U₄₀₀(r). A theoretical expression is obtained for the U₄₀₀ contribution to the differential cross section. The results of the calculations arising from the exact radial expansion of the atom-atom potential appear to be significantly larger for high J lines than those arising from the truncated expansion. The latter results, which do not include adjustable atom-atom parameters, are in good agreement with experimental broadening coefficients for C₂H₂---O₂ and in reasonable agreement (except at large J values) for C₂H₂---N₂. It is also shown that the contributions to the linewidths derived from U₄₀₀ are rather small for C₂H₂---N₂ and more important for C₂H₂---O₂. Finally, by calculating the collisional linewidths of C₂H₂---N₂ and C₂H₂---O₂ at 200 K, we have predicted their temperature dependences.     

Long range C,N and H atom-atom potential parameters from ab initio dispersion energies for different azabenzene dimers

After comparing theoretically the atom-atom model with the multipole expansion for the dispersion energy, we derive atom-atom potential parameters for C, N and H contacts by fitting the atom-atom dispersion energies to the dispersion interactions calculated by an ab initio method for the following (aza)-benzene molecules: benzene, pyridine, pyridazine, pyrimidine, pyrazine, s-triazine and s-tetrazine. The data base for the fit consists of 1200 randomly chosen configurations for each azabenzene dimer. The optimized parameters for the carbon and hydrogen contacts in particular are not unique ; reasonably good fits are obtained with different parameter sets. A very simple rule, which relates the atom-atom potentials to the isotropic molecular C₆ dispersion coefficients, already leads to good estimates for the parameters. From the empirical parameter sets available in the literature the William-Govers set yields results which are close to our ab initio dispersion energies.     

Elastic Scattering of Electrons by a Cut-Off Coulomb Potential at Low Energies

Elastic scattering of electrons by cut-off Coulomb potential U_c(r) is investigated, where U_c(r) = 0, for r > r_c and U_c(r) = ?1/r + 1/r_c for r ≦ r_c. This is first considered in terms of classical, and later quantum mechanical (partial wave) methods in the low energy range 0 ≦ ? ? 1/r_c, where ? is the energy of the free electron. Scattering in this energy region displays a number of particular characteristics, such as back scattering, at certain energies. It can be concluded that some agreement does exist between the classical and quantum mechanical results.     

The mean squared torque in pure and mixed dense fluids

The mean squared torque on a molecule can be obtained from infra-red or Raman band moments, and provides a direct measure of the strength of the anisotropic intermolecular forces. The expression for the mean squared torque on a molecule of species α in a fluid mixture is given in terms of the intermolecular potential and the angular pair correlation functions. This relation is made tractable by introducing a perturbation expansion in powers of the anisotropic potential strength for the angular pair correlation functions. Monte Carlo calculations of the mean squared torque are presented for a liquid of linear molecules having dipolar, quadrupolar and anisotropic overlap interactions. Comparison of the perturbation expansion to second order with these ‘exact’ results shows good agreement for μ*=μ/(εσ³)^1/2 and Q*=Q/(εσ⁵)^1/2 values less than about 0·5, and for values of the dimensionless overlap constant |δ| less than about 0·2. Finally, experimental values of the mean squared torque for both pure and mixed liquids are compared to the Monte Carlo and to the perturbation theory results.     

Iterated Mayer expansion for classical gases at low temperatures

We derive iterated Mayer expansions for classical gases and establish recursive bounds which control their convergence. These bounds are useful for gases with two body forces which are strong and possibly attractive at distances that are short compared to their range. Our procedure is based on splitting the potential into pieces of decreasing strength and increasing range. This may be called a renormalization group treatment of a classical gas. We apply our results to Yukawa lattice gas models and obtain convergence of series expansions for the pressure for a range of parameters (temperature, fugacities, range of the interaction) that was inaccessible before. Application to 3-dimensionalU(1) lattice gauge theory (Coulomb gas,Z-ferromagnet) will be made elsewhere.Work supported in part by Deutsche Forschungsgemeinschaft     

Improved convergence of the ‘atoms in molecules’ multipole expansion of electrostatic interaction

We study the anisotropic electrostatic interaction with high rank multipoles (? = 5) for a set of 10 van der Waals complexes and 27 DNA base pairs. Multipoles are generated by the distributed multipole analysis (DMA) and by the topological quantum theory of ‘atoms in molecules’ (AIM). The convergence of the multipolar expansion of the interaction between topological atoms is improved by distributing the moments over extra off-nuclear sites via a shifting procedure. A clear theoretical distinction is made between partitioning and distributing. A substantial improvement in the convergence of the AIM multipole expansion is observed for the smaller van der Waals molecules. An AIM representation with extra sites on the bond midpoints performs as well as DMA with just nuclear sites. However, for the larger DNA base pairs no improvement follows from the introduction of extra sites with AIM. For these larger systems AIM and DMA expansions perform equivalently, provided that now DMA allows for extra sites. This work further encourages the development of a topological intermolecular force field.     

Intermolecular potential and equilibrium orientational states for dimers of non-polar molecules

The anisotropic intermolecular potential V(r ?₁ ?₂ ?) of two non-polar molecules, with its arbitrary coefficients represented by the functions of the intermolecular distance r, is formulated and analytically minimized in the angular variables ?₁, ?₂ and ? = ?₁ ??₂. In terms of multipole expansion, the explicit form of these coefficients is strictly specified by the constants of quadrupole, dispersion, and repulsive interactions of two non-polar molecules. These coefficients are also obtainable from basic orientational configurations computed by ab initio methods. As a result, the intermolecular potential V(r) can be found and equilibrium orientational states can be characterized at each value of r. An analysis of literature data for the H₂, N₂, and O₂ dimers together with ab initio calculations of V(r, ?₁, ?₂ ?) for the H₂ and N₂ dimers (performed by the MP2 and CCSD(T) methods with the cc-aug-pvqz basis set) demonstrate that the analytical form proposed for the angular dependence of V and the result of its minimization are helpful in revealing intermediate orientational phases in which angular variables change continuously with r, and the function V(r) has regions with a mild slope. One such phase with ?₁ = ?₂, ? = 0 has been found to correspond to the global minimum of the N₂ dimer.     

Ne-HBr复合物CCSD(T)势能面对转动非弹性分波截面的影响

利用非线性最小二乘法拟合在CCSD(T)/aug-cc-pVQZ理论水平下计算的相互作用能，得到了基态Ne-HBr复合物势能面的解析表达式.在此基础上，采用量子密耦方法计算了入射能量分别为40，60，80 和100meV时，Ne原子与HBr分子碰撞的分波截面，详细讨论了CCSD(T)势能面的长程吸引和短程各向异性相互作用对非弹性分波截面的影响.结果表明：(1)总非弹性分波截面主要来自j=0 →j′=1, 2跃迁.高J端的尾部极大是势能面长程吸引阱的贡献，主要来自j=0 →j′=1跃迁；低J端的主极大是短程排斥的贡献，主要来自j=0 →j′=2跃迁；极小值是短程排斥和长程吸引作用相互抵消的结果.(2)尽管不同入射能量时非弹性分波截面的峰值和极小值对应的总角动量量子数J各不相同，但它们对应于几乎相同的碰撞参数，取样势能面的相同部分.     

Translational and rotational motions of a diatomic molecule enclosed in a solid matrix

The hamiltonian for a molecule enclosed in a cavity may be written H = H ^R(θ) + H ^T(r) + U ^RT(θ, r), where θ and r denote the molecular orientation and the displacement of the centre of mass. The crystalline potential seen by the guest molecule can be explicitly calculated on the basis of atom-atom and electrostatic multipolar interactions, by using an nth-order gradient formula in the spherical representation. We take a N ₂ molecule encaged in β-quinol clathrate as our model system, and solve variationally the Schrödinger equation for H to clarify the translation-rotation coupling. Energy levels of H are obtained as a function of the height of the hindering potential for rotation, by modifying the strength of the electrostatic multipolar interaction. Three limiting cases of H ^R are important: (a) libration around the Z-axis, (b) free rotation, and (c) an oscillational rotation whose equilibrium orientation is perpendicular to the Z-axis. The constrained translation under consideration is an anharmonic and almost spherically symmetric oscillation. The Pauli principle must be applied to the eigenstate of H. Excepting the case (a), translational states of H are different for different nuclear spin species, and higher-order effects of U ^RT on these states are significant. For p-N₂, some modes of motion interchange if the rotational motion changes from case (a) to case (c). If the constraining potential for translation is steeper, the effect of U ^RT will become smaller. The anharmonicity involved in H ^T is not negligible in discussing this effect.     

Electron-electron double resonance in nitroxide radical solutions

All the pair interactions arising from the ground state H₂, N₂, CO₂, HF and LiH molecules are used as models for investigating the validity of the multipolar results (corresponding to the classical interaction of the permanent multipole moments of the interacting molecules) as a representation of the first-order Coulomb interaction energy. Charge overlap effects, the neglect of which are responsible for the misbehaviour of the multipolar results as the intermolecular distance R becomes small, are discussed as a function of the nature of the interacting molecules. Useful analytical formulae are presented which represent the numerical results. Some of the difficulties in using the multipolar results to represent the anisotropic part of a dimer potential are discussed in general and more specifically with respect to the evaluation of the mean square torque of nitrogen molecules.     

The δ-function expansion of the modified two-particle Ursell function of a hard-sphere fluid

The expansion of the modified two-particle Ursell functionU(r) of a hardsphere quantal fluid is obtained in terms of a series of derivatives of δ-function. This expansion has been used to expand the second virial co-efficientB ₂ of the fluid. The expansion is correct up to the fourth power in thermal wavelength and the terms of the order of λ⁸ and λ⁴ in the first expa nsion are new.     

Investigation of the stability of the inverse spectroscopic problem of diatomic molecules

The stability and convergence of the inverse spectroscopic problem is investigated for diatomic molecules in the¹ electron state for a potential representation by series in the Dunham variable z_d=(r-r_e)/r_e, the Ogilvie-Tipping z_ot=(r-r_e)/(r + r_e), the Simmond-Parr-Finlan z_S= (r-r_e)/r and the Tucker z_t=sign (p)[1 -(r_e/r)^P]. None among the representations under investigation was that which would give a significant systematic improvement in stability as compared with others. The convergence is related to the selection of the initial approximation in the method of least squares, and is practically independent of the functional form of the potential. For the Dunham representation the solutions of the inverse problem yield quantities close to the true values of the expansion coefficients.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 98–101, May, 1984.     

Perturbation theory for the radial distribution function

Perturbation theory is used to consider expansions for the radial distribution function, g ₂(r), of a fluid with a soft core. We consider the Lennard-Jones (12, 6) potential and divide it into repulsive and attractive regions. In the repulsive region we expand the function exp (β u(r))g ₂(r) about a hard sphere value. For the first-order contribution of the attractive region we consider a simple approximation to the exact analytical expression. The resulting g ₂(r) is accurate at densities below about ρσ ³=0·5.     

He-NO碰撞体系分波截面的理论计算

首先用Huxley势函数拟合在RCCSD(T)/aug-cc-pVTZ bf理论水平下计算的He-NO相互作用能数据,从而得到了He原子与NO分子相互作用各向异性势;然后用密耦近似方法计算了He-NO碰撞体系的总分波截面、弹性分波截面和非弹性分波截面,并总结了分波截面的变化规律.计算结果表明,拟合势较好地描述了He-NO系统相互作用的各向异性特征,利用碰撞体系分子间势的量子化学从头计算结果,可解决势能参数难以确定的问题,对进一步研究原子与分子碰撞机理有一定参考价值.     

On high-temperature expansions of the Hubbard model

We discuss the application of the high-temperature expansion method to the Hubbard model. We recalculate the expansion series of the susceptibility up to the sixth order in the transfer matrix element,t, in the strong correlation limit, and up to the fourth order int in case that the repulsive potential,U, is finite, butt/U 1. It is seen that the convergence of the series is very poor.     

A critical evaluation of isotropic potential functions for chlorine

A survey of many crystal structures shows that short intermolecular chlorine-chlorine contacts are anisotropic. This observation challenges the currently used potential function models which allow only for isotropic exp-6 and coulomb interactions. In this study the polymorphic p-dichlorobenzene DCB system is used to illustrate the difficulties encountered by relying on the isotropic atom-atom approximation. It is found that exp-6 potential functions cannot be extrapolated beyond the range of contacts used in their derivation. Addition of coulomb terms provides needed additional flexibility to the potential function but the derived C-Cl bond polarization is not found to be a constant of the molecule, i.e. the optimum value is not the same for each phase of DCB. Furthermore, no single exp-6 potential function could satisfy the structural constraints provided by the three phases of crystalline DCB and by hexachlorobenzene. These findings are typical of curve-fitting methods which employ an incorrect mathematical form for the curve and indicate the necessity of including anisotropic terms in the interaction potential.     

He原子和BH分子碰撞体系的转动激发能量转移

在碰撞体系He+BH的CCSD(T)二维势能面基础上,应用密耦方法,研究了 He+BH分子碰撞转动激发过程.计算了该体系的转动态-态激发的弹性和非弹性的微分和积分截面,分析了计算结果与势能面特征间的关系.结果表明: He原子以从H原子端共线形式碰撞BH分子对j=0→j'=2的激发最为有效;短程排斥对Δj=2的激发作用较大;态-态跃迁总截面出现振荡结构,长程部分分波只对j=0→j'=1的跃迁总截面有较大贡献,j'≥ 关键词： He+BH体系 转动激发 散射截面     

Flow equations and the strong-coupling expansion for the Hubbard model

Applying the method of continuous unitary transformations to a class of Hubbard models, we reexamine the derivation of thet/U expansion for the strong-coupling case. The flow equations for the coupling parameters of the higher order effective interactions can be solved exactly, resulting in a systematic expansion of the Hamiltonian in powers oft/U, valid for any lattice in arbitrary dimension and for general band filling. The expansion ensures a correct treatment of the operator products generated by the transformation, and only involves the explicit recursive calculation of numerical coefficients. This scheme provides a unifying framework to study the strong-coupling expansion for the Hubbard model, which clarifies and circumvents several difficulties inherent to earlier approaches. Our results are compared with those of other methods, and it is shown that the freedom in the choice of the unitary transformation that eliminates interactions between different Hubbard bands can affect the effective Hamiltonian only at ordert ³/U² or higher.     

Extension of the generalized multipole technique to anisotropic medias

This paper presents an extension of the generalized multipole technique (GMT) for 2D anisotropic scatterers. New expansions similar to the Bessel multipole expansion are derived for arbitrary anisotropic media. Numerical simulations prove the accuracy and the rapid convergence of these expansions. As the results obtained are extremely accurate, this technique is most helpful for the evaluation of reference solutions and for the understanding of the physical interaction of light with arbitrary anisotropic media.