新型复合物Li…HF,Li…FH,Li…H2O和Li…NH3的一阶超极化率的从头算理论研究

在MP2/6-311 G(2df,2pd)水平上优化得到了几种小型碱金属—极性分子复合物的结构,利用有限场方法[HF,MP2,MP3,MP4(SDQ)]在15种基组上分别计算了它们的偶极矩(μ),极化率(α0),各向异性极化率(Δα)和一阶超极化率(β0).在MP4(SDQ)/6-311 G(2df,2pd)理论水平上,各复合物分子一阶超极化率分别为:Li…HF,β0=3957.575 a.u.;Li…FH,β0=12939.614 a.u.;Li…NH3,β0=34881.899a.u.;Li…H2O,β0=39820.410 a.u..而分子HF,NH3,H2O的一阶超极化率的值分别为1.224 a.u.,35.560 a.u.,20.130 a.u..结果表明,复合物分子中的额外电子对分子非线性光学性质有巨大的贡献.     

Formation Mechanism and Binding Energy for Regular Tetrahedral Structure of Li4

The formation mechanism for the regular tetrahedral structure of Li4 cluster is proposed. The curve of the total energy versus the separation R between the two nuclei has been calculated by using the method of Gou‘s modified arrangement channel quantum mechanics (MACQM). The result shows that the curve has a minimal energy of-29.8279 a.u. at R=14.50 a0. When R approaches infinity the total energy of four lithium atoms has the value of-29.7121 a.u. So the binding energy of Li4 with respect to four lithium atoms is the difference of 0.1158 a.u.for the above two energy values. Therefore the binding energy per atom for Li4 is 0.029 a.u., or 0.7878 eV, which is greater than the binding energy per atom of 0.453 eV for Li2, the binding energy pcr atom of 0.494 eV for Li3 and the binding energy per atom of 0.632 eV for Li5 calculated previously by us. This means that the Li4 cluster may be formed stably in a regular tetrahedral structure of side length R=14.50 a0 with a greater binding energy.     

Formation Mechanism and Binding Energy for Regular Octahedral Structure of Li6 Cluster

The formation mechanism for the regular octahedral structure of Liscluster is proposed. The curve of the total energy versus the separation R between any two neighboring nuclei has been calculated by using the method of Gou＇s modified arrangement channel quantum mechanics （MACQM）. The result shows that the curve has a minimal energy of -44.736 89 a.u. at R = 5.07a0. When R approaches infinity, the total energy of six lithium atoms has the value of -44.568 17 a.u. So the binding energy of Li6 with respect to six lithium atoms is 0.1687 a.u. Therefore, the binding energy per atom for Li6 is 0.028 12 a.u., or 0.7637 eV, which is greater than the binding energy per atom of 0.453 eV for Li2 and the binding energy per atom of 0.494 eV for Li3 calculated in our previous work. This means that the Li6 cluster may be formed in a regular octahedral structure with a greater binding energy.     

Formation Mechanism and Binding Energy for Body-Centred Regular Icosahedral Structure of Li13 Cluster

The formation mechanism for the body-centred regular icosahedral structure of Li13 cluster is proposed. The curve of the total energy versus the separation R between the nucleus at the centre and nuclei at the apexes for this structure of Li13 has been calculated by using the method of Gou＇s modified arrangement channel quantum mechanics （MACQM）. The result shows that the curve has a minimal energy of-96.951 39 a.u. at R = 5.46ao. When R approaches to infinity, the total energy of thirteen lithium atoms has the value of-96.564 38 a.u. So the binding energy of Lii3 with respect to thirteen lithium atoms is 0.387 01 a.u. Therefore the binding energy per atom for Lii3 is 0.029 77 a.u. or 0.810 eV, which is greater than the binding energy per atom of 0.453 eV for Li2, 0.494 eV for Li3, 0.7878 eV for Li4. 0.632 eV for Lis, and 0.674 eV for Liv calculated by us previously. This means that the Li13 cluster may be formed stably in a body-centred regular icosahedral structure with a greater binding energy.     

Formation Mechanism and Binding Energy for Body-Centred Regular Octahedral Structure of Li7 Cluster

The formation mechanism for the body-centred regular octahedral structure of Li7 cluster is proposed. The curve of the total energy versus the separation R between the nucleus at the centre and nuclei at the apexes for this structure of Li7 has been calculated by using the method of Gou＇s modified arrangement channel quantum mechanics （MACQM）. The result shows that the curve has a minimal energy of-52.169 73 a.u. at R = 5.06ao. When R approaches infinity, the total energy of seven lithium atoms has the value of-51.996 21 a.u. So the binding energy of Li7 with respect to seven lithium atoms is 0.173 52 a.u. Therefore the binding energy per atom for Li7 is 0.024 79 a.u. or 0.674 eV, which is greater than the binding energy per atom of 0.453 eV for Li2, the binding energy per atom of 0.494 eV for Li3 and the binding energy per atom of 0.632 eV for Li5 calculated previously by us. This means that the Li7 cluster may be formed stably in a body-centred regular octahedral structure with a greater binding energy.     

Formation Mechanism and Binding Energy for Equilateral Triangle Structure of Li3 Cluster

The formation mechanism for the equilateral triangle structure of Li3 cluster is proposed. The curve of the total energy versus the interatomic distance for this structure has been calculated by using the method of Gou‘s Modified Arrangement Channel Quantum Mechanics. The result shows that the curve has a minimal energy of-22.338 60 a.u at R = 5.82 a0. The total energy of Li3 when R approaches ∞ has the value of-22.284 09 a.u. This is also the total energy of three lithium atoms dissociated from Li3. The difference value of 0.0545 08 a.u. for the above two energy values is the dissociation energy of Li3 cluster, which is also its binding energy. Therefore the binding energy per lithium atom for Li3 is 0.018 169 a.u. = 0.494 eV, which is greater than the binding energy of 0.453 eV per atom for Li2 calculated in a previous work. This means that the Li3 cluster may be formed in the equilateral triangle structure of side length R = 5.82a0 stably with a stronger binding from the symmetrical interaction among the three lithium atoms.     

Formation Mechanism and Binding Energy for Regular Tetrahedral Structure of Li4

The formation mechanism for the regular tetrahedral structure of Li4 cluster is proposed. The curve of the total energy versus the separation R between the two nuclei has been calculated by using the method of Gou＇s modified arrangement channel quantum mechanics （MACQM）. The result shows that the curve has a minimal energy of-29.8279 a.u. at R = 14.50 ao. When R approaches infinity the total energy of four lithium atoms has the value of-29.7121 a.u. So the binding energy of Li4 with respect to four lithium atoms is the difference of 0.1158 a.u.for the above two energy values. Therefore the binding energy per atom for Lh is 0.020 a.u., or 0.7878 eV, which is greater than the binding energy per atom of 0.453 eV for Li2, the binding energy per atom of 0.494 eV for Lia and the binding energy per atom of 0.632 eV for Li5 calculated previously by us. This means that the Li4 cluster may be formed stably in a regular tetrahedral structure of side length R = 14.50 ao with a greater binding energy.     

Li9团簇体心立方结构的形成机理和结合能

本文提出了Li9团簇体心立方结构的形成机理,并对此结构的总能量随中心原子到顶点原子间核间距R的变化用芶氏改进的排列通道量子力学方法(MACQM)进行了计算。结果显示曲线在R = 4.77 a0处有一极小值 -67.160922 a.u.,这表明Li9团簇的体心立方结构是可能稳定存在的。在R趋于无穷大时这9个锂原子的总能量为 -66.852240 a.u.,所以形成Li9的总结合能为0.308682 a.u.。因此Li9 团簇的原子平均结合能是0.034298 a.u.或0.933 eV,它大于我们过去计算的Li5团簇正四面体中心结构的原子平均结合能0.632 eV、Li7 团簇正八面体中心结构的原子平均结合能0.674 eV和Li13 团簇正二十面体中心结构的原子平均结合能0.810 eV。故在体心正多面体结构Lin (n= 5 ,7,9,13)中,Li9的体心立方结构有最大的原子平均结合能,这也许是碱金属晶体的晶胞取体心立方结构的一个原因。     

Formation Mechanism and Binding Energy for Equilateral Triangle Structure of Li3 Cluster

The formation mechanism for the equilateral triangle structure of Lia cluster is proposed. The curve of the total energy versus the interatomic distance for this structure has been calculated by using the method of Gou＇s Modified Arrangement Channel Quantum Mechanics. The result shows that the curve has a minimal energy of-22.338 60 a.u at R = 5.82 ao. The total energy of Lia when R approaches co has the value of-22.284 09 a.u. This is also the total energy of three lithium atoms dissociated from Lia. The difference value of 0.0545 08 a.u. for the above two energy values is the dissociation energy of Li3 cluster, which is also its binding energy. Therefore the binding energy per lithium atom for Lia is 0.018 169 a.u. = 0.494 eV, which is greater than the binding energy of 0.453 eV per atom for Li2 calculated in a previous work. This means that the Li3 cluster may be formed in the equilateral triangle structure of side length R = 5.82ao stably with a stronger binding from the symmetrical interaction among the three lithium atoms.     

Resonant charge transfer in slow Li~+–Li(2s) collision

The resonant charge transfer process for Li+–Li(2s) collision is investigated by the quantum-mechanical molecular orbital close-coupling(QMOCC) method and the two-center atomic-orbital close-coupling(AOCC) method in an energy range of 1.0 e V/u–104e V/u. Accurate molecular structure data and charge transfer cross sections are given. Both the allelectron model(AEM) and one-electron model(OEM) are used in the QMOCC calculations, and the discrepancies between the two models are analyzed. The OEM calculation can also give a reliable prediction of the cross sections for energies below 1 ke V/u.     

Formation Mechanism and Binding Energy for Icosahedral Central Structure of He1+3 Cluster

The formation mechanism for the icosahedral central structure of the He1 13 cluster is proposed and its total energy curve is calculated by the method of a Modified Arrangement Channel Quantum Mechanics. The energy is the function of separation R between two nuclei at the center and an apex of the icosahedral central structure. The result of the calculation has shown that the curve has a minimal energy -37.5765 (a.u.) at R = 2.70ao. The binding energy of He 13 with respect to He 12He was calculated to be 1.4046 a.u. This means that the cluster of He 13 may be formed in an icosahedral central structure with strong binding energy.     

Formation Mechanism and Binding Energy for Regular Octahedral Structure of Li6 Cluster

The formation mechanism for the regular octahedral structure of Li₆ cluster is proposed. The curve of the total energy versus the separation R between any two neighboring nuclei has been calculated by using the method of Gou's modified arrangement channel quantum mechanics (MACQM). The result shows that the curve has a minimal energy of -44.736 89 a.u. at R = 5.07a₀. When R approaches infinity, the total energy of six lithium atoms has the value of -44.568 17 a.u. So the binding energy of Li₆ with respect to six lithium atoms is 0.1687 a.u. Therefore, the binding energy per atom for Li₆ is 0.028 12 a.u., or 0.7637 eV, which is greater than the binding energy per atom of 0.453 eV for Li₂ and the binding energy per atom of 0.494 eV for Li₃ calculated in our previous work. This means that the Li₆ cluster may be formed in a regular octahedral structure with a greater binding energy.     

He+2团簇的形成机理与结合能计算

当He+离子与He原子相互作用时, 由于一个电子往返运动于两核之间形成单电子键, 从而使He+与He结合成为具有较强键能的He+2.根据此形成机理, 采用简单的变分波函数, 计算了He+2基态的能量曲线.结果显示,当核间距为1.74 a 0时, 能量有一极小值-0.090 14 a.u.(以He++He能量为零起始计算).从而得到He+ 2离子结合能为0.090 14 a.u., 这与实验结果0.090 96 a.u.符合得相当好, 比有的理论计算值更接近实验结果.     

Formation Mechanism and Binding Energy for Icosahedral Central Structure of He13^＋ Cluster

The formation mechanism for the icosahedral central structure of the He13^ cluster is proposed and its total energy curve is calculated by the method of a Modified Arrangement Channel Quantum Mechanics. The energy is the function of separation R between two nuclei at the center and an apex of the icosahedral central structure. The result of the calculation has shown that the curve has a minimal energy -37.5765 (a.u.) at R=2.70ao. The binding energy of He13^ with respect to He^ 12He was calculated to be 1.4046 a.u. This means that the cluster of He13^ may be formed in an icosahedral central structure with strong binding energy.     

The Formation Mechanism and Binding Energy for the Octahedral Central Structure of the He7^＋ Cluster

The formation mechanism for the octahedral central structure of the He7^ cluster is proposed and its total energy curve is calculated by the method of a modified arrangement channel quantum mechanics (MACQM). The energy is a function of separation R between two nuclei at the center and an apex of the octahedral central structure. The result of the calculation shows that the curve has a minimM energy -19.7296 a.u. at R = 2.40α0. The binding energy of He7^ with respect to He^ 6He was calculated to be 0.6437 a.u. This means that the duster of He7^ may be formed in the stable octahedral central structure with R=2.40 α0.     

能量修正的Glauber模型对中能反应总截面的影响

叙述了对Glauber模型中的透射系数进行半经验的能量修正,并利用该修正模型计算了^12—14C,⁶Li,⁷Be,⁸B+¹²C和⁶Li,⁷Be,⁸B+⁹Be以及²⁰Ne+¹²C,¹²C+²⁷Al等系统的激发函数(能区范围10—1000MeV/u),经与实验值比较,能量修正的Glauber理论计算值能够很好地描述中能条件下的反应总截面实验测量值.