BH2的分子结构和势能函数

采用密度泛函理论(DFT)的B3P86方法和相对论有效原子实势理论模型(RECP),对BH2,BH2+和BH2-分子进行了优化,得到这些分子基态的电子状态分别是2A′,3A′,3A".计算也得到了BH2的分子结构和势能函数,它的离解能是7.752eV,BH2分子具有C2V对称性;由微观可逆性原理,判断了BH2分子的离解极解;并且导出了BH2分子的多体项展式势能函数,其势能面等值图展现了H-B-H的结构,这些结果可以用于BH2分子的微观反应动力学.     

Calculation of the Peierls-Yoccoz translational mass for Hartree-Fock wave functions

The Peierls-Yoccoz projection method for translation is applied to Hartree-Fock wave functions constructed on a mesh for ${}^4\text{He}$ and ${}^{16}\text{O}$. As expected, the mass parameters differ from the nuclear masses, indicating a breaking of galilean invariance.     

A single-parameter trial wave function for the mixed valence ground state

The mixed valence trial ground state suggested by Stevens and Brandow is reconsidered in the case of two electrons per atom. The wellknown difficulties due to nonorthogonality are resolved by expanding the trial state in an orthonormal basis. The expansion coefficients are determinants composed of Bloch phase factors, as in the Gutzwiller method. Studying first the limiting case of the Kaplan-Mahanti strongly localized ground state in the Brandow formalism, we derive rules for a simplified handling of the determinants; this opens the way to the more complicated weakly localized ground state. This is handled by expressing theN variational parameters of the Brandow formalism through a single one, the hybridization temperature . The ground state energy is a well-behaved function of the hybridization matrix elementV. The valence and the shift of the Fermi level are calculated to lowest order inV. The band occupation numbers follow a Fermi distribution at temperature V. We argue that the ground state is insulating, with thed-electrons localized into large Wannier-type orbitals centered on the respectivef-holes, as envisaged by Stevens.     

Introduction of the electron repulsion into the molecular orbital wave function

The total MO wave function of a π-electron system contains covalent, total ionic and mixed parts. Taking the electron repulsions explicitly into account, the individual contribution of the parts are revaluated. The ω technique of Streitwieser is critically discussed and reformulated, disinguishing between odd and even numbered ω-electron systems. ω=0·5 (instead of Streitwieser's ω=1·4) fits the experimental data of ethylene reasonably well. This improved ω technique is used for taking the electron repulsions into account.

The new method is applied to ethylene, butadiene, benzene, hexatriene, the allyl cation, the allyl radical and the allyl anion. A substantial improvement of the total π electron energy is achieved.     

BeF2分子基态势能函数研究

利用密度泛函理论（DFT）B3LYP/aug-cc-PVTZ方法对BeF和BeF2分子进行计算, BeF分子的基态电子态为X2Σ+,平衡核间距Re=0.1367 nm,BeF2分子最稳定构型为D∞h构型,基态电子态为X1Σg+,离解能De=13.4 eV。利用最小二乘法拟合了BeF分子基态的Murrell-Sorbie势能函数,并得到其光谱数据与力常数。结合全局多体项展式方法,导出了基态BeF2分子基态势能函数的解析表达式,该函数准确反映了BeF2分子的结构以及静态反应特征,这些结果为进一步探索BeF2的微观分子反应动力学提供了基础。     

BH2的分子结构和势能函数

采用密度泛函理论(DFT)的B3P86方法和相对论有效原子实势理论模型(RECP)，对BH₂，BH₂⁺和BH₂^-分子进行了优化，得到这些分子基态的电子状态分别是²A′，³A′，³A″. 计算也得到了BH₂的分子结构和势能函数，它的离解能是7.752eV，BH₂分子具有C_{2V关键词： 2}')" href="#">BH₂ 分子结构 势能函数     

SiO2分子的基态(X1A1)结构与分析势能函数

应用群论及原子分子反应静力学方法推导了SiO2分子的电子态及其离解极限,采用B3P86方法,在6-311G**水平上,优化出SiO2基态分子稳定构型为单重态的C2V构型,其平衡核间距Re=RSi-O=0.1587 nm,∠OSiO=111.2°,能量为-440.4392 a.u..同时计算出基态的简正振动频率:对称伸缩振动频率v(B2)=945.4cm-1,弯曲振动频率v(A1)=273.5 cm-1和反对称伸缩振动频率v(A1)=1362.9cm-1.在此基础上,使用多体项展式理论方法,导出了基态SiO2分子的全空间解析势能函数,该势能函数准确再现了SiO2(C2V)平衡结构.     

SiF2基态分子的结构与势能函数

运用Gaussian03软件包,采用密度泛函理论中的B3P86 方法,结合6-311++G**(3df,3pd)基组对基态SiF2分子的平衡电子结构和谐振频率进行了优化计算,得到了其稳定结构为C2v构型.SiF2基态电子态为X1A1,平衡核间距RSi-F=0.1061nm,键角αF-Si-F=100.6762°,离解能 De=13.8eV.应用多体项展式理论推导了基态SiF2分子的解析势能函数,其等值势能图准确地再现了SiF2分子的平衡构型特征和能量变化.     

Radial matrix elements and dipole moment function for the ground state of CO

Radial matrix elements 〈vJ|x^k|v′J′〉 for k = 0–5, v = 0–12, |v′- v| = 0–4, and J up to 150 have been calculated for CO using accurate wavefunctions obtained from the numerical solution of the Schrödinger equation with a second-order RKR potential curve. These are used in conjunction with a model dipole moment function (a Padé approximant which has the correct united and separated atom limits and R^?4 long-range behavior) to analyze the experimental intensity data. For all the levels considered, we conclude that an adequate representation of the dipole moment function is provided by a five-term power series expansion. This simplifies the computation of dipole moment matrix elements, typical results of which are presented to illustrate the dependence on the rotational and vibrational quantum numbers.     

基态S3分子的结构与解析势能函数

本文采用Gaussian03 B3P86方法,在6-311 G(3d2f)基组水平上,对S3分子进行几何优化理论计算,计算结果表明S3分子基态1A1最稳定的构型为C2V构型,其离解能为10.8372 eV,能量最小值为-1193.19946 a.u.,计算还得到了谐振频率、力常数,计算结果与实验值符合得很好.在此基础上利用多体展式理论方法得到了S3分子的解析势能函数和等值势能图,势能函数正确反映了S3分子的构型与能量变化.     

完全活性空间自洽场方法对NO分子基态势能函数的研究

利用MOLPRO从头算程序包, 选用完全活性空间自洽场(CASSCF)方法并选取cc-pVTZ, cc-pVQZ, cc-pV5Z和cc-pV6Z基组, 计算了NO分子基态的平衡核间距与谐振频率, 从中优选出cc-pV5Z基组进行单点能扫描, 并将扫描结果用最小二乘法拟合得到4参数、5参数、6参数和7参数的Murrell-Sorbie势能函数. 通过比较由势能函数计算出的光谱数据, 最终确定6参数的结果最好. 最后, 利用拟合出的解析势能函数, 通过求解径向Schrödinger方程, 得到了NO分子基态J=0时的全部38个振动态的振动能级、经典转折点、惯性转动常数以及6个离心畸变常数.     

HNO分子基态的结构与解析势能函数研究

应用群论及原子分子反应静力学的方法, 导出了HNO分子基态电子态和合理的离解极限.利用优选出的密度泛函理论B3LYP方法结合6-311G **优化计算了HNO分子基态的平衡结构和谐振频率.计算结果表明基态HNO分子稳定态为C_S构型,电子组态为X¹A',平衡核间距分别为R_H-N=0.1065 nm,R_N-O=0.1200 nm,键角∠H-N-O=108.60°,离解能D_e=15.379 eV.基态简正振动频率分别为:弯曲振动频率ν₁=1575.6351 cm^-1,对称伸缩振动频率ν₂=1673.2890 cm^-1,反对称伸缩振动频率ν₃=2837.7856 cm^-1.在此基础上,应用多体项展式理论导出了基态HNO分子的全空间解析势能函数,该势能函数等值势能图准确再现了HNO分子平衡结构和离解能. 关键词： 势能函数 光谱常数 密度泛函方法     

Electromagnetic and weak constraints on the ground state wave functions of C and N

The nuclear wave functions of the A = 13 ground state isodoublet system are analysed by constraining them (within the 1p shell) to fit the best available electromagnetic and weak data. It is found that the wave functions are dominated by only two basis states of the possible five, with a greater degree of configuration mixing than that predicted by Cohen-Kurath. The use of these phenomenological wave functions to study ¹³C(γ, π⁻)¹³N_g.s. at low energies gives better agreement with data than using Cohen-Kurath wave functions but a factor of three enhancement still persists.     

Nonadiabatic effects in the ground state of the hydrogen molecule

A sum-over-states procedure is used in the ab initio evaluation of the matrix elements needed for a nonadiabatic treatment of the ground electronic state of H₂. Bunker's (J. Mol. Spectrosc.42, 478 (1972)) semiempirical value for the nonadiabatic parameter l₁ = 0.130 ± 0.006 is in agreement with the present calculation, which therefore supports the interpretation of the difference between theoretical adiabatic and experimental vibrational energies as being due to nonadiabatic effects. The same techniques are used to evaluate the expectation value of $\text{?}{}^2\text{?R}{}^2$ in the H₂ ground electronic state. Finally, it is pointed out that an average energy denominator used in several recent treatments of nonadiabatic effects in H₂ is in error by roughly a factor of two. The correct average energy denominator reflects that the sums have large contributions from states in the electronic continuum.     

用遗传算法研究一维光晶格中玻色凝聚气体基态波函数

以Gross-Pitaevskii（G-P）平均场能量泛函为目标函数,运用遗传算法研究一维光晶格系统中玻色凝聚气体的基态性质,提出了求解系统波函数的一种新方法.通过优化计算,对当前常用的托马斯-费米近似和高斯近似模型进行修正和讨论,并给出最优基态波函数. 关键词： 玻色凝聚气体 遗传算法 波函数     

SiF$lt;sub$gt;2$lt;/sub$gt;基态分子的结构与势能函数

运用Gaussian03软件包,采用密度泛函理论中的B3P86 方法,结合6-311++G^**（3df,3pd） 基组对基态SiF₂分子的平衡电子结构和谐振频率进行了优化计算,得到了其稳定结构为C_2v构型.SiF₂基态电子态为X¹A₁,平衡核间距R_Si—F=0.1061　nm,键角α_F—Si—F=100.6762°,离解能D_e=13.8　eV.应用多体项展式理论推导了基态SiF₂分子的解析势能函数,其等值势能图准确地再现了SiF₂分子的平衡构型特征和能量变化. 关键词： 2')" href="#">SiF₂ Murrell-Sorbie函数 多体项展式理论     

SiO2分子的基态(X1A1)结构与分析势能函数

应用群论及原子分子反应静力学方法推导了SiO₂分子的电子态及其离解极限，采用B3P86方法，在6-311G^**水平上,优化出SiO₂基态分子稳定构型为单重态的C_2V构型，其平衡核间距R_e=R_Si—O=0.1587 nm,∠OSiO＝111.2°,能量为-440.4392 a.u..同时计算出基态的简正振动频率:对称伸缩振动频率ν(B₂)=945.4cm^-1，弯曲振动频率ν(A₁)=273.5 cm^-1和反对称伸缩振动频率ν(A₁)=1362.9cm^-1.在此基础上，使用多体项展式理论方法，导出了基态SiO₂分子的全空间解析势能函数，该势能函数准确再现了SiO₂(C_2V)平衡结构.     

Continuum bound state and transition matrix of the scattering wave function for projected Yamaguchi potential

The presence of a continuum bound state for the nucleon-nucleon (nn) scattering by a nonlocal potential in which Yamaguchi potential enters as an attractive part is examined. It is well-known that an extra node in the radial wave function is directly related to the existence of a continuum bound state in the scattering spectrum. The extra nodes of the wave functions occur in conjunction with the zeros of the Fredholm determinants associated with the physical and regular wave functions of the radial equation for the nonlocal potential. Here we have observed that the extra nodes also occur in conjunction with the zeros of the transition matrix.