四原子分子中Majorana算子矩阵元的新计算公式

李代数方法在研究双原子分子、三原子分子振－转光谱及相关问题等方面已被证明是一种有效方法[‘－0,并被成功推广到多原子分子[’－门．构造代数哈密顿量是此方法的关键,这就要求选择合适的     

三原子分子振转激发态成簇现象理论研究

在只考虑弯曲振动与总角动量的耦合,而冻结伸缩振动的模型下,采用Jacobi多项式作为弯曲振动的基函数,用严格的变分法研究了H~2O分子的振转激发态的成簇现象。本文计算了H~2O分子的振转能级和函数,研究了振动激发态下转动高激发态中出现的成簇态。     

三原子分子振转激发态成簇现象理论研究

在只考虑弯曲振动与总角动量的耦合,而冻结伸缩振动的模型下,采用Jacobi多项式作为弯曲振动的基函数,用严格的变分法研究了H_2O分子的振转激发态的成簇现象.本文计算了H_2O分子的振转能级和函数,研究了振动激发态下转动高激发态光谱中出现的成簇态.     

双原子分子振转激发态

发展了一种较简便的方法来计算双原子分子的振转激发态。原则上,该方法可以给出同数值积分方法一样精确的结果。作为例子, 给出了H_2的162个振转激发态的准确能级和波函数。     

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。     

求解弱相互作用分子A-BC的振转能级和波函数的SCF-CI方法

给出了一种计A－BC型弱相互作用分子体系的分子间振转激发态的自洽场-组态相互作用(SCF－CI)方法. 首先使用SCF方法代化径向伸缩振动和弯曲振动的基函数,再用CI方法确定精确的振转激发态能级. 在求解-维的伸缩振动SCF方程时,采用Numerov－Johnson算法在给定区间上求解获得振动波函数的数值解. 具体计算了Ar－HCI和Ar－N₂体系的振转激发态的能级以验证该方法. 结果表明,本方法可用较少的组态就能获得可与其它大计算量的方法具有相比拟的精度的结果.     

次氟酸分子的势能函数及其振动光谱的同位素效应的理论研究

用三原子振动激发态的变分计算程序(TRIATOM)精确计算次氟酸分子H¹⁶OF的振动激发态的能级以及次氯酸分子中的H和O分别被D和¹⁸O取代后的H¹⁸OF,D¹⁶)OF和D¹⁸OF的同位素效应,理论计算值与已有的实验结果吻合较好。预测了一些尚未观测到的谱线频率及同位素效应,并确立了一个同位素位移的加和规则。     

次氟酸分子的势能函数及其振动光谱的同位素效应的理…

用三原子振动激发态的变分计算程序（ＴＲＩＡＴＯＭ）精确计算次氟酸分子Ｈ＾１６ＯＦ的振动激发态的能级以及次氯酸分子中的Ｈ和Ｏ分别被Ｄ和＾１８Ｏ取代后Ｈ＾１８ＯＦ，Ｄ＾１６Ｏｆ和Ｄ＾１８ＯＦ的同位素效应，理论计算值与已有的实验结果吻合较好，预测了一些尚水观测到的谱线频率及同位素效应，并确立了一个同位素位移的加和规则。     

确定三原子分子势能面的SCF-CI方法

建议根据振动高激发态的实验能级确定三原子分子势能面的SCF-CI方法.此法中使用键长-键角内坐标系下的SCF-CI方法来精确地计算振动高激发态的能级及其对势能参数的一阶微分,并使用LMF算法来优化势能参数.为验证此方法,优化了水分子的势能面,计算出水分子的振动高激发态能级与70个观测到的振动能级相比较,标准偏差为1.15cm~(-1).     

Lie代数方法在线形三原子分子转动谱计算中的应用

利用动力学群U₁(4)ÄU₂(4)的对称性质以及相应的Lie代数给出了描写线形三原子分子振转谱的Hamilton量. 在考虑了振转相互作用后, 所得上述Hamilton量本征值的表达式具有在光谱分析计算中常用的项值方程的形式. 利用此表达式拟合观察线位可以得到分子的振转常数. 作为算例, 对N₂O及HCN分子(02⁰0-01¹0)ν₂红外跃迁谱带的转动能级进行了拟合分析, 所得均方根误差分别为0.00001和0.0014 cm^-1.     

A procedure of determining potential energy surfaces of triatomic molecules from inversion of spectroscopic data

In this paper,we have suggested an iterative procedure of optimization of the linearparameters in an analytic potential energy function for a triatomic molecule,by combining both variational and second order perturbation methods.The most important feature of this procedure is that the objective function is an analytical expression which can be optimized easily.The application to the water molecule is presented.     

An SCF-CI method for determining the potential energy surface of a triatomic molecule

A self-consistent-field (SCF)-configuration interaction (CI) (SCF-CI) method for determining the potential energy surface of a triatomic molecule from the observed vibrational band origins has been suggested. By this method, the SCF-CI procedure in the internal coordinates is used to calculate the vibrational bond origins and their first derivatives with respect to parameters in the potential energy function using the exact vibrational Hamiltonian, and the optimizer LMF in the nonlinear-squares problem is employed to optimize parameters in the potential energy function. This approach is used to optimize the potential energy function of the water molecule. The standard deviation of this fitting to the 70 observed band origins is 1.154cm-1.     

On the variational solution of the coupled breathing rotation-vibration of a spherical top molecule

On the basis of the solutions of the isotropic 3-D harmonic oscillator, we show how to evaluate the matrix elements for the coupled rotation-vibration of the totally symmetric breathing mode of a rotating spherical top molecule, whereby the anharmonic potential energy is expanded in a power series of r. It is shown also how to obtain the ro-vibrational spectrum when used in conjunction with the variational method to obtain eigenvalues.     

On the variational solution of morphed molecular potential in a diatomic molecule

The general one-dimensional potential energy function, including centrifugal distortion, for a diatomic molecule is morphed with a series of Morse-like functions for each of the rotational quantum numbers $J$ . For each of the morphed potential, explicit formulae for the matrix elements of the complete energy matrix, on the basis of the solutions of the one-dimensional harmonic oscillator, are given and these may be used in connection with the variational procedure to solve the corresponding vibrational Schrödinger equation. From the set of vibrational levels $\{\text{ E}_\mathrm{vJ}\}, J = 0, 1, 2,{\ldots }$ the ro-vibrational transitions can be deduced.     

Variational calculation of vibrational energies of triatomic molecules using SCF optimized modes

A self-consistent field optimization of the vibrational coordinates for nonlinear triatomic molecules is presented. The optimal coordinates are obtained by making a three-dimensional rotational transformation of the normal modes and determining the rotation angles as those for which the SCF energy is stationary. The utility of the optimized coordinates in full variational calculations of vibrational energies is studied for the molecules of H₂O, O₃, H₂D⁺, H₂T⁺, and D₂T⁺. For H₂O and O₃, the optimization procedure leads to the local mode representation. It is shown that the use of the optimal coordinates in variational calculations allows a large reduction of the dimension of the Hamiltonian matrix to be diagonalized in order to reach convergence.     

On the use of optimal internal vibrational coordinates for symmetrical bent triatomic molecules

The use of generalized internal coordinates for the variational calculation of excited vibrational states of symmetrical bent triatomic molecules is considered with applications to the SO2, O3, NO2, and H2O molecules. These coordinates depend on two external parameters which can be properly optimized. We propose a simple analytical method to determine the optimal internal coordinates for this kind of molecules based on the minimization with respect to the external parameters of the zero-point energy, assuming only quadratic terms in the Hamiltonian and no quadratic coupling between the optimal coordinates. The optimal values of the parameters thus obtained are shown to agree quite well with those that minimize the sum of a number of unconverged energies of the lowest vibrational states, computed variationally using a small basis function set. The unconverged variational calculation uses a basis set consisting of the eigenfunctions of the uncoupled anharmonic internal coordinate Hamiltonian. Variational calculations of the excited vibrational states for the four molecules considered carried out with an increasing number of basis functions, also evidence the excellent convergence properties of the optimal internal coordinates versus those provided by other normal and local coordinate systems.     

Ab initio vibration and ro-vibrational spectrum of the 1A1 state of He2Si2+

The low-lying ro-vibrational states for the ground electronic state (1A1) of HeSi2+ have been calculated using an ab initio variational solution of the nuclear Schr?dinger equation. A 96 point CCSD(T)/cc-pCVQZ potential energy surface (PES) has been calculated and a Ogilvie-Padé (3,6) potential energy function has been generated. This force field was embedded in the Eckart-Watson Hamiltonian from which the vibrational and ro-vibrational eigenfunctions and eigenenergies have been variationally calculated. A 70 point QCISD/aug-cc-pCVTZ discrete dipole moment surface (DMS) was calculated and a 5th order power series expansion (in terms of the two bond lengths and the included bond angle) has been generated. Absolute line intensities have been calculated and are presented for some of the most intense transitions between the vibrational ground state and the low-lying ro-vibrational states of this ion.     

An analytical computation of Christoffel symbols for reaction coordinate and trajectory treatments under internal coordinates

We examine the Hessian matrix of the potential energy under internal coordinates. We report all Christoffel symbols which exist for molecules if we use the known coordinates such as bond distances, bond angles, torsion angles, and out-of-plane angles. We use as an example triatomic HCN in an extended geometry.     

Treating singularities present in the Sutcliffe-Tennyson vibrational Hamiltonian in orthogonal internal coordinates

Two methods are developed, when solving the related time-independent Schrodinger equation (TISE), to cope with the singular terms of the vibrational kinetic energy operator of a triatomic molecule given in orthogonal internal coordinates. The first method provides a mathematically correct treatment of all singular terms. The vibrational eigenfunctions are approximated by linear combinations of functions of a three-dimensional nondirect-product basis, where basis functions are formed by coupling Bessel-DVR functions, where DVR stands for discrete variable representation, depending on distance-type coordinates and Legendre polynomials depending on angle bending. In the second method one of the singular terms related to a distance-type coordinate, deemed to be unimportant for spectroscopic applications, is given no special treatment. Here the basis set is obtained by taking the direct product of a one-dimensional DVR basis with a two-dimensional nondirect-product basis, the latter formed by coupling Bessel-DVR functions and Legendre polynomials. With the basis functions defined, matrix representations of the TISE are set up and solved numerically to obtain the vibrational energy levels of H3+. The numerical calculations show that the first method treating all singularities is computationally inefficient, while the second method treating properly only the singularities having physical importance is quite efficient.