A new four-parameter empirical potential energy function for diatomic molecules

A new empirical four-parameter function is proposed for the construction of potential curves of 15 stable states of diatomic molecules. The parameters are evaluated in terms of experimentally known spectroscopic constants. On comparing its performance with other functions, the proposed function is found to be simple and reliable for a wide range of molecules.      

双荷电双原子分子的新解析势能函数

提出了能更好反映双荷电双原子分子势能曲线特点的新解析势能函数，并推导出了相应的二、三、四阶力常数计算公式；作为新函数的应用实例，给出了BH2+, He22+ 和HF2+等分子离子的解析势能函数，力常数和光谱数据。     

The infinite-volume ground state of the Lennard-Jones potential

We consider a finite chain of particles in one dimension, interacting through the Lennard-Jones potential. We prove the ground state is unique, and approaches uniform spacing in the infinite-particle limit.Research supported in part by NSF grant MCS 78-01520.     

用能量自洽法研究异核双原子分子的势能曲线

用研究双原子分子解析势能函数的新方法——ECM方法进一步研究了一些异核双原子分子的电子基态和激发态：CIF分子的A３Π1和B0＋(３Π)态，CH分子的X２Π态，BH分子的X1Σ＋态，XeO分子的d1Σ＋态，LaF分子的X1Σ＋态，Li7D分子的X1Σ＋态，NaRb分子的X1Σ＋态，KRb分子的(2)3Σ＋和21Π态等.获得的势能曲线表明，ECM势能很好地符合Rydberg-Klein-Rees(RKR)值，得到了比Morse势，huxley-Murrell-Sorbie(HMS)势更令人满意的结果.而且在分子渐近区和分子离解区域，ECM方法还能得到RKR可能缺乏的可靠物理数据. 关键词： 能量自洽 双原子分子 势能函数 电子态     

A new Morse ring-shaped potential for diatomic molecules

Using the Pekeris approximation, the Schrödinger equation is solved analytically for the Morse plus a novel angle-dependent potential. The generalized parametric Nikiforov–Uvarov method is used to obtain energy eigenvalues and corresponding eigenfunctions. We present the effect of the angle-dependent part on radial solutions, and some numerical results for diatomic molecules are also given.     

Rotation and vibration of diatomic molecule oscillator with hyperbolic potential function

The explicit expressions of energy eigenvalues and eigenfunctions of bound states for a three-dimensional diatomic molecule oscillator with a hyperbolic potential function are obtained approximately by means of the hypergeometric series method. Then for a one-dimensional system, the rigorous solutions of bound states are solved with a similar method. The eigenfunctions of a one-dimensional diatomic molecule oscillator, expressed in terms of the Jacobi polynomial, are employed as an orthonormal basis set, and the analytic expressions of matrix elements for position and momentum operators are given in a closed form.     

Studies on the analytical potential energy function of diatomic molecular ion XY~+ using variational method

It is well-known that the accurate behavior of potential energy function of molecular ion plays an important role in the studies such as solution chemistry, atmosphere chemistry, nebular medium, plasma physics, and gun powder, etc.[1, 2]. The values of potential energy function of diatomic molecular ion could significantly influence the optical efficiency of laser pump using ion vapors as working substrate[3]. The ionic potential is very important for the studies on low-energy ion-atom collisi…     

Accurate vibrational energy spectra and dissociation energies of some diatomic electronic states

An algebraic method (AM) used to study the full vibrational spectra of diatomic systems, and an analytical formula used to calculate accurate molecular dissociation energies are applied to study the full vibrational spectra and molecular dissociation energies of some electronic states of homonuclear and heteronuclear diatomic molecules and diatomic ions. Studies show that the AM method and the analytical expression are reliable and economical physical methods for studying full vibrational spectra and molecular dissociation energies of diatomic electronic systems theoretically. They are particularly useful for those diatomic systems whose high-lying vibrational energies may not be available.      

同核双原子分子离子的势能研究

使用作者最近建立的研究双原子分子离子精确势能的离子能量自洽法(ECMI),对碱金属、氟、氧的同核双原子分子离子的以下电子态进行了研究:Na2 的X2∑g 态,Li2 的X2∏u态,F2 的A2Пu态,F2 的X2∏g,和O2 的A2∏u态.将获得的ECMI势能曲线与用其他理论方法得到的势能曲线进行的比较表明,ECMI得到了这些态的最好势能,而且ECMI势不仅能获得平衡核间距附近的精确势能,还能得到其他方法往往难以得到的双原子分子离子渐进区和离解区的正确势能.     

赝自旋对称性条件下四参量双原子分子势中相对论粒子的束缚态

在赝自旋对称性条件下,严格求解了四参量双原子分子势中运动粒子的s波Klein-Gordon方程和Dirac方程,并给出了相应的束缚态能谱和相对论性波函数.     

PuNO分子结构与势能函数

本文运用密度泛函理论的B3LYP方法, 对钚原子应用LANL2DZ收缩价基函数, 氮、氧原子采用AUG-cc-pVTZ基函数, 分别对PuN, PuO, NO和PuNO体系进行了结构优化, 得到PuNO分子最稳构型为C_∞v (Pu-N-O), 电子态为⁶Σ^- (基态), 平衡核间距R_ON=0.12257 nm, R_NPu=0.22951 nm, 离解能D_e=8.10537 eV. 同时优化得到PuNO 分子存在两种亚稳态平衡构型分别为C_∞v (Pu-O-N), ⁶Σ^- (电子态)和C_s (O-Pu-N), A" (电子态), 以及分子体系相应的力学常数等. 拟合出PuN, PuO 和NO 分子的Murrell-Sorbie势能函数, 并使用多体项展式理论得到了PuNO分子的分析势能函数, 其等值势能图准确再现了PuNO分子最稳态构型及两个亚稳态构型的离解能和结构特性, 由此讨论了该分子体系的势能面静态特征.     

AuZn和AuAl分子基态与低激发态的势能函数与热力学性质

用密度泛函理论B3LYP方法计算研究AuZn和AuAl分子基态与低激发态的结构与势能函数,导出分子的光谱数据.结果表明,AuZn和AuAl分子基态分别为X²Σ和X¹Σ,基态与低激发态的势能函数均可用Murrell-Sorbie函数来表达.AuZn分子低激发态a⁴Σ的绝热激发能为43529kJ/mol,AuAl分子低激发态a³Σ的绝热激发能为19991kJ/mol.计算固体AuZn和AuAl的内能和熵时,近似以气体分子的电子能和振动能代替固体分子的内能,用电子熵和振动熵代替固体分子的熵.在此近似下,计算得到AuZn和AuAl基态与低激发态固态分子生成反应热力学性质与温度的关系. 关键词： AuZn和AuAl B3LYP 热力学性质 势能函数     

氢化物双原子分子势能曲线的能量自洽法研究

使用能量自洽法较系统地研究了部分氢化物及其同位素双原子分子的一些电子基态和激发态的势能：NaH，RbH分子的X1Σ+态，同位素分子HF和DF，H35Cl和D35Cl，6LiH，6LiD和7LiH的Ｘ１Σ+态，BH分子的a3Π,b3Σ-激发态，CH分子的A2Δ激发态和BeH分子的A2Π激发态.不仅得到了与基于实验的Rydberg-Klein-Rees势能或Inverted Perturbation Approach值或Configuration Interaction理论数据符合得很好的势能，而且获得了其他 关键词： 能量自洽 势能函数 氢化物     

双原子离子部分电子态的离解能的精确研究

本文使用基于微扰理论的代数方法(AM),研究了双原子离子F2+的X2Ⅱg,CO+的X2∑+,O2+的A2Ⅱu,BeH+的X1∑+四个电子态的离解能,然后使用最近提出的新公式计算了这些电子态的离解能,并分别与离解能的实验值进行了比较.研究结果表明:使用新公式得到的分子离解能与实验值更加接近;同时AM和新公式相结合的理论方法也适用于双原子离子体系.     

Studies on the full vibrational energy spectra for some electronic states of diatomic molecular ions XY+

The first accurate studies on the vibrational spectroscopic constants and the corresponding full vibrational energy spectra of some electronic states of diatomic molecular ions XY⁺ were performed using algebraic method(AM). The AM is applied on the X¹Σ⁺ state of BeH⁺, the X²Σ⁺ state of CO⁺, the X²Π_g state of F ₂ ⁺ , the A²Π_u state of O ₂ ⁺ and the X²Σ _g ⁺ state of Li ₂ ⁺ . The results show that AM can generate accurate vibrational spectroscopic constants as well as accurate full vibrational energy spectra by using some accurate experimental vibrational energies, and that the AM vibrational energies are better than other theoretical data. __________ Translated from Chinese Journal of Atomic and Molecular Physics, 2005, 22 (4) (in Chinese)     

双原子离子部分电子态的离解能的精确研究

本文使用孙卫国提出的基于微扰理论的代数方法(AM),研究了双原子离子F2+的X2Πg,CO + 的X2Σ+, O2+的A2Πu ,BeH +的X1Σ+ 四个电子态的离解能,然后使用最近提出的新公式计算了这些电子态的离解能,并分别与离解能的实验值进行了比较．研究结果表明：使用新公式得到的分子离解能与实验值更加接近;同时AM和新公式相结合的理论方法也适用于双原子离子体系。     

NiH2分子的结构及其势能函数

应用群论及原子分子反应静力学方法推导了NiH2分子基态的电子态及其离解极限,在MP2/6-311G水平上,优化出NiH2(3Δg)分子稳定构型为D∞h,其平衡核间距Re=0.157 3 nm、∠HNiH=180.00°,同时计算出振动频率:对称伸缩振动频率ν1=2 000 cm-1,弯曲振动频率ν2=721 cm-1和反对称伸缩振动频率ν3=1 875 cm-1.在此基础上,使用多体项展式理论方法,导出了基态NiH2分子的全空间解析势能函数,该势能函数准确地再现了NiH2(D∞h)平衡结构.     

Studies on the analytical potential energy function of diatomic molecular ion XY<Superscript>+</Superscript> using variational method

A new analytical potential energy function for diatomic molecular ion XY⁺ is proposed based on the energy consistent method (ECM). The Coulomb potential included in the new ionic potential contains multipole corrections, converges quickly and is variationally, changeable. The new potential and the ECM are applied to variationally studying the potential energies of eight electronic states of several diatomic molecular ions: the A²π state of CO⁺, the X²∑_g⁺ state of Li₂⁺, the X²∑_g⁺ state of He₂⁺, the 1²∏_u state of Na₂⁺, the A²∏_u state of N₂⁺, the X¹∑⁺ state of KrH⁺, the X²∑⁺ state of SiO⁺ and the A²π state of SO⁺ ion. The present results agree excellently with the experiment-based Rydberg-Klein-Rees (RKR) potentials, and are superior to the commonly used Huxley-Murrell-Sorbie (HMS) analytical potentials, and are better in some cases than some quantum mechanicalab initio potentials in the ionic asymptotic and dissociation regions.     

BeH,BeD,BeT分子基态(X~2Σ~ )的结构与势能函数

采用量子力学从头算方法,运用二次组态相互作用QCISD(T)/aug-cc-pVTZ和电子相关单双耦合簇CCSD(T)/6-311 G(3df,2pd)研究了BeH,BeD,BeT分子基态的结构与势能函数,计算出了这些分子的光谱数据(ωe,ωeχe,Be,αe,De),结果与实验光谱数据吻合较好。这表明上述分子基态的势能函数可用经修正的Murrell-Sorbie c6函数来表示.     

A diatomic network model for electronic states of bulk,surface and thin films

This paper reports our investigations on an exactly solvable network model of solids. General properties of diatomic lattices, in particular the dispersion relations for the energy levels, the structure of the energy bands and the density of states for bulk, surface and thin films are compared with the corresponding properties of the monatomic lattices which we have previously reported. For a thin film of finite thickness, we present a simple but informative method of analyzing Van Hove singularities in the density of states. Effects due to the inclusion of second neighbor interactions are also studied. Calculations are exact and the method has apparent advantages over other methods of discussing similar problems.