四原子分子振转相互作用的Lie代数方法

利用Lie代数方法研究了四原子分子振转相互作用，在代数框架内首次给出四 原子分子振转相互作用的张量算子非对角矩阵元的表达式，利用这些表达式对线型 四原子分子HCCF振转相互作用的l-doubling进行了计算。     

构造SO~2分子势能面的李代数方法

把李代数方法得到的SO~2分子的代数Hamiltonian,利用相干态基经典化并找到一个新的变换,将分子的键角引入,而得到SO~2分子的势能面。由该势能面计算的解离能,所给出的势能面的立体图和相应的等高线以及力常数与其他方法给出的相一致。该方法可以推广到多原子分子及反应体系。     

乙酸甲酯在强激光场下的电离

强场下分子的电离与解离研究是一个新的研究领域 .分子内的分子实与价电子之间的库仑场强度为 108 V· cm－ 1量级 .通常激光的电场强度远小于这个量级 ,因此可以采用微扰理论来解释分子在激光场中的电离与解离 .如果激光场的功率密度达到 1013 W· cm－ 2以上 ,其电场强度就能到 8.7× 107 V· cm－ 1以上 ,达到甚至超过分子内的电场强度 .此时微扰理论已经不太适用 ,分子的电离机理及研究方法将有所不同 [1－ 5].　　关于强场电离与解离的理论没有统一的解释 [2,3].在强场下通常用 Keldysh因子γ来判断原子的电离方式 [6]：其中ω 0为激…     

反应碰撞的动力学李代数描述

提出一种李代数方法描述分子反应碰撞问题．给出了含有主要动力学参量的S-矩阵元、分子碰撞跃迁几率以及反应体系能量统计平均值随时间演化的解析表达式．讨论了一个简单排斥势场中的原子-双原子分子共线反应体系，以阐明这种新方法的要点。     

双原子分子振动对热力学性质的影响

本文在分析了双原子分子振动能级的完备性和有限性及其对统计计算带来的影响的基础上,借助代数（AM）方法得到的双原子分子振动能级完全集合,采用量子力学统计系综方法,讨论了双原子分子振动能量对宏观热力学性质的统计贡献,并以氮气为例计算了相应的热力学函数和振动热容量．结果表明,真实的双原子分子振动能级是有限的;确定最高振动量子数和振动能级完全集合是正确进行统计分析的基础和关键;考虑振动能级的完备性和有限性后,只能导致数值解而不是解析解,所得的结果优于谐振子模型的解析结果,与实验数据吻合得很好．     

表面增强喇曼光谱检测卟啉单分子膜

利用轴向配位作用将5,10,15－20－四苯基钴（Ⅱ）卟啉（CoTPP)固定在4－巯基吡啶自组装膜表面上,形成CoTPP单分子膜,通过组装金纳米粒子的方法,成功地获得了膜中CoTPP分子的喇曼光谱。研究结果表明,CoTPP分子是通过钴原子与氮原子之间的配位作用与巯基吡啶分子结合的,且其分子平面与基底表面近似平行。     

1N组态金属配合物的光谱强度

本文在假拟原子壳模型的分子场近似下,应用Wigner-Racah代数方法,按照配位场理论的弱场及中间场偶合图象讨论了过渡金属配合物的电子光谱,导出了适用于任意组态l~N和任意对称性GG并涉及电偶极、电四极与磁偶极跃迁的有关矩阵元、谱线强度、跃迁几率以及振子强度公式。     

非线性三原子分子高激发振动态的理论研究: Lie代数方法

利用Ｌｉｅ代数方法研究了弯曲三原子分子的振动高激发态能谱，并以ＳＯ_２为例， 拟合 ３０条光谱能级得到的 ＲＭＳ误差是 １．６６ ｃｍ~－１．结果表明，所得到的分子 Ｈａｍｉｌｔｏｎｉａｎ 的代数展开式可以很好地再现实验能级，它预测了ＳＯ_２分子振动总量子数达１０的全部 振动能级．从得到的该代数Ｈａｍｉｌｔｏｎｉａｎ还可以得到势能面等．     

NO双分子和二聚体与Cu2作用的理论计算

采用密度泛函理论(DFT)中的B3LYP方法，在Lanl2DZ基组下，对NO双分子和二聚体与铜原子簇相互作用的结构进行了研究. 结果表明，NO可以在铜表面相邻的两个铜原子上形成稳定的双分子吸附和二聚体吸附，而在双分子吸附形式中NO以氮原子吸附在铜上的构型最稳定，且顶点吸附的稳定性不如非顶点吸附形式.在二聚体吸附形式中， N－N键被加强，而N－O键被削弱的程度大于双分子吸附形式，说明二聚体的形成有利于NO在金属铜表面的直接分解.同时电荷布居分析表明，单重态的二聚体与铜作用时，铜原子上的平均电荷达到0.66 e,说明在这种吸附形式中铜被离子化的倾向较大，而且这种吸附形式最有利于NO的分解.这些结果说明NO经二聚体形式在铜表面直接催化分解是可行的.     

反式-5,1O,15-三芳基-5,1O,15-三羟基-1-氢-三苯并[a,f,k]三茚的合成与从头算结构分析

合成了两个具有三个羟基的新型主体分子反式－5,10,15－三芳烃－5,10,15－三羟基－1－氢－三苯并[a,f,k]三茚（芳基分别为苯基和－萘基）,并通过从头算对其及其异构体的结构进行了分析,结果发现当芳基为苯基时,其顺式异构体分子印环中所有原子不完全处于共平面,而其反式异构体和1－萘基的顺反异构体均处于共平面。     

SO(4)群链的广义耦合系数和耦合张量算子矩阵元的计算

证明了群链(Ⅰ)和(Ⅲ)的广义耦合系数和耦合张量算子矩阵元的一般计算公式,应用该公式计算了Majorana算子矩阵元,从而验证了一般矩阵元公式推导的正确性.     

Analogy between real irreducible tensor operator and molecular two-particle operator

. Molecular matrix elements of a physical operator are expanded in terms of polycentric matrix elements in the atomic basis by multiplying each by a geometrical factor. The number of terms in the expansion can be minimized by using molecular symmetry. We have shown that irreducible tensor operators can be used to imitate the actual physical operators. The matrix elements of irreducible tensor operators are easily computed by choosing rational irreducible tensor operators and irreducible bases. A set of geometrical factors generated from the expansion of the matrix elements of irreducible tensor operator can be transferred to the expansion of the matrix elements of the physical operator to compute the molecular matrix elements of the physical operator. Two scalar product operators are employed to simulate molecular two-particle operators. Thus two equivalent approaches to generating the geometrical factors are provided, where real irreducible tensor sets with real bases are used. Received: 3 September 1996 / Accepted: 19 December 1996     

Improved treatment for matrix elements of spin-dependent operators

In this paper a general method for the evaluation of the matrix elements of spin-dependent operators is proposed to improve the treatment primitively suggesteed by Cooper and Musher. This approach is largely based on the recent results which the present authors have achieved in the representation theory for the inner- and outer-product reduction of the symmetric group. It is shown that the so-called outer-product coupling coefficients (OPCC ) can be used to generalize the method for constructing the irreducible tensor operators of group S_n. Together with the use of inner-product coupling coefficients (IPCC ), an expression for the matrix elements of spin-dependent operators is presented as the product of a Racah coefficient for S_n and a reduced matrix element which can be expressed in terms of IPCC, OPCC , and the related integrals. The treatment for one- and two-electron spin-dependent operators is discussed in detail.     

Unitary group approach to the many-electron problem. II. Adjoint tensor operators for U(n)

In this paper we present a derivation of the U(n) adjoint coupling coefficients for the representations appropriate to many-electron systems. Since the states of a many-fermion system are to comprise the totally antisymmetric Nth rank tensor representation of U(2n), the work of this paper enables the matrix elements of the U(2n) generators to be evaluated directly in the U(n) × U(2) (i.e., spin orbit) basis using their transformation properties as adjoint tensor operators. A connection between the adjoint coupling coefficients, as derived in this paper, and the matrix elements of certain (spin independent) two-body operators is also presented. This indicates that in CI calculations, one may obtain the matrix elements of spin-dependent operators from the known matrix elements of certain spin-independent two-body operators. In particular this implies a segment-level formula for the matrix elements of the U(2n) generators in the spin-orbit basis.     

Matrix elements in configuration interaction calculations

A method is proposed for the calculation of matrix elements among various states of atoms. A set of tensor operators is the only entity in the formalism, and all formulas involve merely the vacuum expectation values of these tensor operators and the recoupling transformation coefficients. Some numerical examples are given for the Coulomb interaction matrix elements.     

Addendum to superfine and hyperfine structures in the ν3 band of 32SF6: Evidence for a tensor spin-vibration interaction in spherical tops

We give a first demonstration of a tensor spin-vibration interaction in the triply degenerate vibrationally excited state of a molecule. The corresponding coupling constant for ³²SF₆ has been found to be equal to ?6.75 kHz from a theoretical fit of the hyperfine structures of P(4)F₁ and of the R(29)F₁²F₂¹ cluster in the ν₃ band around 10 μm. We also gave a more accurate value of the tensor spin-rotation coupling constant, c_d, and the values of the reduced matrix elements of the relevant nuclear spin operators.     

Unitary group tensor operator algebras for many-electron systems: II. One- and two-body matrix elements

Relying on our earlier results in the unitary group Racah-Wigner algebra, specifically designed to facilitate quantum chemical calculations of molecular electronic structure, the tensor operator formalism required for an efficient evaluation of one- and two-body matrix elements of molecular electronic Hamiltonians within the spin-adapted Gel'fand-Tsetlin basis is developed. Introducing the second quantization-like creation and annihilation vector operators at the unitary group [U(n)] level, appropriate two-box symmetric and antisymmetric irreducible tensor operators as well as adjoint tensors are defined and their matrix elements evaluated in the electronic Gel'fand-Tsetlin basis as single products of segment values. Using these tensor operators, the matrix elements of one- and two-body components of a general electronic Hamiltonian are found. Explicit expressions for all relevant quantities pertaining to at most two-column irreducible representations that are required in molecular electronic structure calculations are given. Relationships with other approaches and possible future extensions of the formalism to partitioned bases or spin-dependent Hamiltonians are discussed.On leave from: Department of Chemistry, Xiamen University, Xiamen, Fujian, PR China.     

Vibration-rotation interactions between overtone and combination levels of asymmetric-top molecules: application to the infrared spectroscopy of formaldehyde and ketene

The conventional vibration-rotation Hamiltonian for an asymmetric-top molecule is rewritten by expanding the elements of the inverse inertial tensor about the equilibrium molecular geometry. The approach allows the identification of terms in the Hamiltonian that couple states differing by two, three, or four vibrational quanta and hence the calculation of dimensioned Coriolis xi coupling coefficients for interacting fundamental, overtone, and combination levels. The matrix elements that result from the application of the expanded Hamiltonian depend upon the harmonic vibrational wave numbers, equilibrium moments of inertia, Coriolis zeta parameters, and the derivatives of the elements of the inertial tensor matrix with respect to each of the normal coordinates. The Coriolis coupling coefficients may be calculated through evaluation of the summations that result from the appropriate terms. The validity of the approach is demonstrated through the calculation of coupling coefficients for interacting levels in formaldehyde and ketene. The uncertainty in the calculated values of the coupling coefficients is typically better than +/-6%, although the values calculated for interactions that involve low-frequency vibrational modes are less reliable. Comparisons are made between the calculated values and experimental results.     

Theory of two shells of atomic electrons using non-orthogonal radial orbitals

A theory for handling non-orthogonal radial orbitals of two shells of atomic electrons based on the mathematical apparatus of irreducible tensor operators is presented. The general expressions for one- and two-electron operator matrix elements are given.     

Spherical particle in Poiseuille flow between planar walls

We study a spherical mesoparticle suspended in Newtonian fluid between plane-parallel walls with incident Poiseuille flow. Using a two-dimensional Fourier transform technique we obtain a symmetric analytic expression for the Green tensor for the Stokes equations describing the creeping flow in this geometry. From the matrix elements of the Green tensor with respect to a complete vector harmonic basis, we obtain the friction matrix for the sphere. The calculation of matrix elements of the Green tensor is done in large part analytically, reducing the evaluation of these elements to a one-dimensional numerical integration. The grand resistance and mobility matrices in Cartesian form are given in terms of 13 scalar friction and mobility functions which are expressed in terms of certain matrix elements calculated in the spherical basis. Numerical calculation of these functions is shown to converge well and to agree with earlier numerical calculations based on boundary collocation. For a channel width broad with respect to the particle radius, we show that an approximation defined by a superposition of single-wall functions is reasonably accurate, but that it has large errors for a narrow channel. In the two-wall geometry the friction and mobility functions describing translation-rotation coupling change sign as a function of position between the two walls. By Stokesian dynamics calculations for a polar particle subject to a torque arising from an external field, we show that the translation-rotation coupling induces sideways migration at right angles to the direction of fluid flow.