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.     

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.     

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.     

用类氧原子波函数计算H7^—团簇正八体中心结构的能量曲线

选用类氧原子波函数,在单中心球模型近似下,利用变分法计算了Ｈ７＾－团簇正八面体中心结构的能量曲线。结果表明,当中心Ｈ原子核能顶角Ｈ原子核之间的距离Ｒ＝１．５８ａ０时,体系能量有一极小值－４．０８９９４５３ｈ．ａ．ｕ．。这表明Ｈ７的正八面体中心结构是可能稳定存在的。计算结果与用ＭＡＣＱＭ法计算的结果基本相符,表明提出的物理模型及其计算方法是合理的。     

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 He3+ Cluster

The formation mechanism for the equilateral triangle structure of the He3 cluster is proposed. The curveof the total energy versus the internuclear distance R for this structure has been calculated by the method of a modifiedarrangement channel quantum mechanics. The result shows that the curve has a minimal -7.81373 a.u at 1 = 1.55 a0.The binding energy of He3 with respect to He He He was calculated to be 0.1064 a.u. (about 2.89 eV). This meansthat the He3 cluster may be formed in the equilateral triangle structure stably by the interaction of He with two heliumatoms.     

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。     

THE MACQM CALCULATION OF THE TOTAL ENERGY CURVE FOR THE ICOSAHEDRAL CENTRAL STRUCTURE OF THE CLUSTER H_13~-

ＴＨＥＭＡＣＱＭＣＡＬＣＵＬＡＴＩＯＮＯＦＴＨＥＴＯＴＡＬＥＮＥＲＧＹＣＵＲＶＥＦＯＲＴＨＥＩＣＯＳＡＨＥＤＲＡＬＣＥＮＴＲＡＬＳＴＲＵＣＴＵＲＥＯＦＴＨＥＣＬＵＳＴＥＲＨ－１３ＺｈａｎｇＪｉａｎｐｉｎｇ＊ＬｉＰｉｎｇＧｏｕＱｉｎｇｑｕａｎＩｎｓｔ...     

THE MACQM CALCULATION OF THE TOTAL ENERGY CURVE OF THE BODY-CENTERED CUBIC STRUCTURE OF THE H_9~- CLUSTER

ＴＨＥＭＡＣＱＭＣＡＬＣＵＬＡＴＩＯＮＯＦＴＨＥＴＯＴＡＬＥＮＥＲＧＹＣＵＲＶＥＯＦＴＨＥＢＯＤＹ－ＣＥＮＴＥＲＥＤＣＵＢＩＣＳＴＲＵＣＴＵＲＥＯＦＴＨＥＨ－９ＣＬＵＳＴＥＲＧｏｕＱｉｎｇｑｕａｎＺｈａｎｇＪｉａｎｐｉｎｇＬｉＰｉｎｇＩｎｓｔｉｔｕ...     

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.     

用类O原子波函数对H+9团簇的体心立方结构与能量的研究

在单中心球模型近似下,选用类O原子解析函数,用变分法计算了H+9团簇体心立方结构与能量。结果表明当中心氢原子核到顶角氢原子核之间的距离R=1.97a0时,体系能量有一极小值E=-4.376h0(a0=0.529177×10-10m,h0=27.2eV)。这表明H+9团簇的体心立方结构是稳定的结构,H+9团簇是存在的。     

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.     

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.     

用类Li原子波函数对H52+团簇的正四面体中心结构与能量的研究

在单中心球模型近似下,选用类Li原子解析波函数,用变分法计算了H52 团簇正四面体中心结构与能量.结果表明当中心氢原子核到顶角氢原子核之间的距离R=1.93a0时,体系能量有一极小值E=-4.3792 Hartree(a0=0.529177×10-10m,1 Hartree=27.2 eV).这表明H52 团簇的正四面体中心结构是稳定的结构,H52 团簇是可能存在的.     

The MACQM Calculation of the Total Energy Curve for the Equilateral Triangle Structure of H3+ Cluster

Considering that the cluster H₃⁺ can be formed from the interaction of H⁺ with two hydrogen atoms, a modified arrangeLent channel quantum mechanics method has been used to calculate the total energy curve for the equilateral triangle structure of H₃⁺. The result shows that the curve has a minimal energy -1.2306 a.u. at the internuclear distance R = 1.97ao = 1.04 Å. This bond length is in good agreement with the experimental value of R = 0.98 ± 0.02 Å.     

The MACQM Calculation for the BInding Energy of the Equilateral Triangle Structure of H3^— Cluster

Considering that the equilateral triangle structure of H3^- cluster can be formed from the interaction of H^- with two hydrogen atoms,a modified arrangement channel quantum mechanics method has been used to calculate the total energy curve for this structure,The result shows that the cureve has a minimal energy-1.6672 a.u.at an internuclear distance of 1.77a0,so its dissociation energy(binding energy)is D(H^- H H)=0.1395,a.u.This means that the cluster H3^- may be formed in an equilateral triangle structure with a bond length of 1.77α0.     

H^—5的正四面体中心和正方形中心构型能量的理论计算

文中用ＭＡＣＱＭ（ｍｏｄｉｆｉｅｄａｒａｎｇｅｍｅｎｔｃｈａｎｎｅｌｑｕａｎｔｕｍｍｅｃｈａｎｉｃｓ）方法计算了负离子团簇Ｈ－５的正四面体中心和正方形中心构型的能量随中心原子核到顶角原子核间距离Ｒ变化的曲线。计算得知，两种构型均在Ｒ＝１．５５ａ０时有能量极小值Ｅ正四面体中心＝－２．７８９９ａ．ｕ．，Ｅ正方形中心＝－２．７５３９ａ．ｕ．。说明Ｈ－５的这两种结构都可能存在，但正四面体中心结构较为稳定。     

Li2基态结合能的MACQM计算

本文采用改进的排列通道量子力学方法(MACQM),对Li2基态势能曲线进行了计算,结果表明:在核间距R=5.05a0处,能量有极小值-14.88937a.u,由此得到Li2基态结合能为0.0333a.u,所得结果与实验值符合得很好.     

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.     

H9^＋团簇的体心立方结构与能量的理论计算

此文利用单电子在中心氢原子核与周围每个氢原子核之间形成单电子键的共振模型来划分通道，将改进的排列通道量子力学方法推广应用于Ｈ９＋的体心立方结构与能量的理论计算。结果发现，当中心与周围顶角问距Ｒ０＝１．９０ａ０时，总能量有一极小值－４．３０８ｈ．ａ．ｕ，表明Ｈ９＝的体心立方结构是稳定存在的。此外，Ｈ９团簇电离时体积要发生膨胀，大约膨胀到原来的１．５倍。