An extended Lennard-Jones potential energy function for diatomic molecules: Application to ground electronic states

A new simple analytical diatomic potential energy function that can be considered an extension of the prototypical Lennard-Jones model is proposed and tested. Five- and six-parameter models are considered and these can be easily constructed from widely available low-order vibrational-rotational constants and the dissociation energy. Accuracy tests are carried out on the ground electronic states of sixteen diatomic molecules. The proposed six-parameter function is found to be more accurate than other available few-parameter analytical models for the diatomic potential energy, and has accuracy comparable to that of modern high-level ab initio functions.     

Perturbation and variational approach for the equation of state for hard-sphere and Lennard-Jones fluids

The present work uses the concept of a scaled particle along with the perturbation and variation approach, to develop an equation of state (EOS) for a mixture of hard sphere (HS), Lennard–Jones (LJ) fluids. A suitable flexible functional form for the radial distribution function G(R) is assumed for the mixture, with R as a variable. The function G(R) has an arbitrary parameter m and a different equation of state can be obtained with a suitable choice of m. For m = 0.75 and m = 0.83 results are close to molecular dynamics (MD) result for pure HS and LJ fluid respectively.     

On the limitations of the equation of state based on the Lennard-Jones potential

It is emphasized that any equation of state (EOS) based on the generalized Lennard-Jones potential or the Mie potential, suffers from two main shortcomings as pointed out by Stacey and Davis [2]. One of the shortcomings viz. the problem related to imaginary numbers for the exponents in the potential function, has been removed recently by Jiuxun [11] by using a relationship between the exponents. However, the modified EOS obtained by Jiuxun suffers from the second shortcoming viz. it gives lower values for −B ₀ B″₀, an important equation of state parameter related to the second pressure derivative of the bulk modulus. Values of B ₀ B″₀ obtained by Jiuxun are not consistent with those reported by Stacey and Davis.      

XY(H,Li, Na)分子基态的结构与势能函数

运用群论及原子分子反应静力学方法，推导了XY(H，Li，Na)分子基态的电子态及相应的离解极限.并采用密度泛函方法(B3LYP)和二次组态相互作用方法(QCISD)优化计算了XY(H，Li，Na)分子基态的平衡结构、振动频率和离解能.使用QCISD/6-311++G(3df,3pd)方法，对XY(H，Li，Na)分子基态进行了单点能扫描计算，采用最小二乘法拟合Murrell-Sorbie函数得到了相应的势能函数和与该基态相对应的光谱常数(B_e,α_e,ω_e和ω_eχ_e)，计算结果与实验数据符合得相当好. 关键词： 组态相关方法 基态 势能函数     

The symmetry of ground states under perturbation

We consider a two-body potential which has only periodic ground states and prove that it can be perturbed, by an arbitrarily small perturbation, so as to have only aperiodic ground states.Research supported in part by NSF grant MCS 78-01520-A01.     

OD、OT、DT分子基态的结构和解析势能函数

本文采用密度泛函方法(B3LYP)和组态相关方法(QCISD(T))优化计算了OD、OT、DT分子基态(X2Ⅱ)的平衡结构、振动频率和离解能.根据原子分子反应静力学原理.导出了OD、OT、DT分子基态(X2 Ⅱ)的合理离解极限,采用最小二乘法拟合Murrell-Sorbie函数得到了相应的势能函数和与该基态相对应的光谱常数(Be,ae,we和wexe),计算结果与实验数据符合得相当好.     

The ground state for sticky disks

It is proven that the ground state of the two-dimensional sticky potential is the triangular lattice.Research supported in part by NSF grant MCS 78-01520-A01.     

GaH(D,T)分子基态结构与势能函数

采用量子力学从头计算方法,运用单双取代二次组态相互作用和单双（三）取代二次组态相互作用并考虑基组6-311++G（3df,3pd）计算优化了GaH（D,T）分子基态X¹Σ⁺的结构和离解能.并采用最小二乘法拟合改进的Murrell-Sorbie函数得到了相应的势能函数.计算得到的光谱常数与实验光谱数据符合得很好. 关键词： GaH（D T）分子基态 势能函数 Murrell-Sorbie函数     

BiH(D,T)分子基态结构与势能函数

采用量子力学从头计算方法,运用单双取代二次组态相互作用和单双（三）取代二次组态相互作用并结合LanL2DZ基组,计算优化了BiH（D,T）分子基态X³Σ的结构和离解能.并采用最小二乘法拟合改进的Murrell-Sorbie 函数得到了相应的势能函数.计算得到的光谱常数与实验光谱数据符合很好. 关键词： BiH（D T）分子基态 势能函数 Murrell-Sorbie函数     

Structure and analytical potential energy function for the ground state of the BCx (x=0, －1)

In this paper, the electronic states of the ground states and dissociation limits of BC and BC- are correctly determined based on group theory and atomic and molecular reaction statics. The equilibrium geometries, harmonic frequencies and dissociation energies of the ground state of BC and BC- are calculated by using density function theory and quadratic CI method including single and double substitutions. The analytical potential energy functions of these states have been fitted with Murrell-Sorbie potential energy function from our ab initio calculation results. The spectroscopic data （αe, ωe and ωeχe） of each state is calculated via the relation between analytical potential energy function and spectroscopic data. All the calculations are in good agreement with the experimental data.     

CO基态的偶极矩的量化计算研究

运用MOLPRO软件,采用基组6-31G,6-31G(d),6-31G(2d,3f),aug-cc-pv5z,方法HF(Hartree-Fock)、CASSCF(完全活性空间自洽场)和MRCI(多参考组态相互作用),计算了CO的基态X1Σ+的偶极矩随核间距变化的12条曲线,与基于实验光谱数据的偶极矩在平衡位置的值以及在平衡位置的斜率进行了比较,结果表明,采用MRCI方法,aug-cc-pv5z基组的偶极矩曲线最为准确.平衡位置斜率的偏差小于1%.接着采用MRCI方法,aug-cc-pv5z基组计算得到了CO基态的势能曲线,进而通过求解核的薛定谔方程得到振动能级以及分子力常数,分子力常数与实验值符合的很好.     

热核物质中基态关联修正下的单核子势和核子有效质量

以有限温度Brueckner-Hartree-Fock(BHF)方法为基础，利用质量算子的空穴线展开，计算了不同温度和密度下的核物质中单核子势和核子有效质量，特别是研究和讨论了基态关联效应和三体核力贡献对热核物质中单核子势的影响. 研究表明，基态关联和三体核力对单核子势的密度和温度依赖性均有重要影响. 基态关联导致的重排修正具有排斥性，大大减弱了低动量区域单核子势的吸引性，而且基态关联效应对单核子势的贡献随密度增大而增强，随温度升高而减弱. 三体核力对基态关联的影响是导致单核子势中重排项贡献减小. 在高密 关键词： 有限温度BHF方法 质量算子空穴线展开 重排修正 单核子势 有效质量     

Influence of DC electric field on the Lennard-Jones potential and phonon vibrations of carbon nanotube on catalyst

Influence of DC electric field on carbon nanotube (CNT) growth in chemical vapor deposition is studied. Investigation of electric field effect in van der Waals interaction shows that increase in DC electric field raises the magnitude of attractive term of the Lennard-Jones potential. By using a theoretical model based on phonon vibrations of CNT on catalyst, it is shown that there is an optimum field for growth. Also it is observed that CNT under optimum electric field is longer than CNT in the absence of field. Finally, the relation between optimum DC electric field and type of catalyst is investigated and for some intervals of electric field, the best catalyst is introduced, which is very useful for experimental researches.     

Influence of temperature on ground state energy of bound polaron in asymmetric Gaussian potential quantum well in presence of electromagnetic field

By a combination method of Lee–Low–Pines unitary transformation method and Pekar-type variational method, the ground state energy (GSE) of the bound polaron is studied in the asymmetrical Gaussian potential quantum well considering the temperature and electromagnetic field. The impacts of the temperature and asymmetrical Gaussian potential, electromagnetic field and phonon–electron coupling upon the GSE are obtained. The results show that the GSE of the bound polaron not only oscillates as the temperature changes regardless of the electromagnetic field and asymmetrical Gaussian potential and Coulomb impurity potential (CIP) and electron–phonon coupling but also has different rules with the electromagnetic field and asymmetrical Gaussian potential and CIP and electron–phonon coupling at different temperature zones.     

OH分子基态（X2Π）的结构与势能函数

采用密度泛函理论的B3LYP方法和二次组态相互作用(QCISD(T))方法优化计算了OH分子基态(X²Π)的平衡结构、振动频率和离解能.根据原子分子反应静力学原理，导出了OH分子基态(X²Π)的合理离解极限，采用最小二乘法拟合Murrell-Sorbie函数得到了相应的势能函数和与该基态相对应的光谱常数(B_e，α_e，ω_e和ω_eχ_e)，计算结果与实验数据符合得相当好. 关键词： OH分子 2Π)')" href="#">基态(X²Π) 势能函数     

The study of magnetization of the spin system in the ground state

Within the framework of the effective-field theory with self-spin correlations and the differential operator technique, the ground state magnetizations of the biaxial crystal field spin system on the honeycomb lattices have been studied. The influences of the biaxial crystal field on the magnetization in the ground state have been investigated in detail.     

类硼离子基态的精细结构(英文)

以多电子精细结构哈密顿的球张量形式为基础,借助不可约张量理论,建立了类硼离子基态精细结构能量的解析表达式.完成了所有角向积分和自旋求和计算,使精细结构能量表示为若干个径向积分之和.在此基础上计算了类硼体系(Z=5~8)基态精细结构能量,计算结果与实验数据符合得较好.     

钾原子基态的定量证明

用原子实模型简化钾原子的哈密顿,把原子实极化和轨道贯穿视为微扰,用微扰法计算了钾原子的能量,定量证明了钾原子的基态是4s态．     

Perturbation and variational approach for the equation of state for hard-sphere and Lennardben Jones fluids

The present work uses the concept of a scaled particle along with the perturbation and variation approach, to develop an equation of state (EOS) for a mixture of hard sphere (HS), Lennard-Jones (LJ) fluids. A suitable flexible functional form for the radial distribution function G(R) is assumed for the mixture, with R as a variable. The function G(R) has an arbitrary parameter m and a different equation of state can be obtained with a suitable choice of m. For m= 0.75 and m= 0.83 results are close to molecular dynamics (MD) result for pure HS and LJ fluid respectively.     

氦原子基态能量的Roothaan-Hartree-Fock计算

采用包含两个斯莱特基的双ζ函数说明了利用自洽场法求解基态氦原子Roothaan-Hartree-Fock方程的数值过程,计算得基态能量为-2.862 568 Hartree.利用基态的对称性,提出了通过求解泊松方程来计算库仑算符的方法,给出了交叠矩阵和单电子算符的矩阵元,并对自洽的标准作了讨论.