Relaxation of Small Molecules: an ab initio Study

The formation mechanism for the equilateral triangle structure of the He3^ cluster is proposed.The curve of the total energy versus the internuclear distance R for this structure has been caclulated by the method of a modified arrangement channel quantum mechanics,The result shows that the curve has a minimal -7.81373 a.u.at R=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 means that the He3^ cluster may be formed in the equilateral triangle structure stable by the interaction of He^ with two helium atoms.     

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 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.     

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.     

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 totalenergy curve is calculated by the method of a modified arrangement channel quantum mechanics (MACQM). The energyis a function of separation R between two nuclei at the center and an apex of the octahedral central structure. The resultof the calculation shows that the curve has a minimal energy -19.7296 a.u. At R = 2.40 α0. The binding energy of He7 with respect to He 6He was calculated to be 0.6437 a.u. This means that the cluster of He7 may be formed in thestable octahedral central structure with R = 2.40 α0.     

The formation mechanism and the binding energy the body—centred regular tetrahedral structure of He5^＋

We propose the formation mechanism of the body-centred regular tetrahedral structure of the He5^ cluster,The total energy curve for this structure has been calculated by using a modified arrangement channel quantum mechanics method.The result shows that a minimal energy of -13.9106 a.u.occurs at a separation of 1.14a0 between the nucleus at the centre and nuclei at the apexes.Therefore we obtain the binding energy of 0.5202a .u.for this structure.This means that the He5^ cluster may be stable with a high binding energy in a body-centred regular tetrahedral structure.     

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 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 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.     

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.     

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.     

H3正三角形和H4正四面体结构的变分计算

采用改进排列通道量子力学(Modified Arrangement Channel Quantum Mechanics,简称MACQM)方法和变分法,计算了H₃体系正三角形和H₄体系的正四面体结构的能量曲线.当H₃体系原子核的间距R=1.74a₀,波函数变分参数α=1.03时,体系能量有最低值-1.58161 a.u.;当H₄体系原子核的间距R=1.60a₀,波函数变分参数α=1.07时,体系能量有最低值-2.28097 a.u.,这表明H₃体系的正三角形构型和H₄的正四面体结构是可以稳定存在的.     

H4^＋团簇离子两种结构的能量曲线计算

此文认为在一定的条件下,Ｈ４＾＋团簇可能由一个氢核与三个氢原子相互作用而形成对称性较高的平面正三角形中心结构或正四面体结构。用ＭＡＣＱＭ方法,本文计算了这两种构型的能量曲线。结果表明：平面正三角形中心结构在中心原子核与顶角原子核间距离为２．１９ａ０时,体系出现能量极小值－１．６４８４ａ．ｕ．;正四面体结构在核间距为１．９２ａ０时,体系有一能量极小值－１．７７７７ａ．ｕ．。这说明Ｈ４＾＋的这两种结构     

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.     

Study of ion desorption induced by a resonant core-level excitation of condensed H2O using Auger electron photo-ion coincidence (AEPICO) spectroscopy combined with synchrotron radiation

Ion desorption induced by a resonant excitation of O 1s of condensed amorphous H₂O has been studied by total ion and total electron yield spectroscopy, nonderivative Auger electron spectroscopy (AES) and Auger electron photo-ion coincidence (AEPICO) spectroscopy. The spectrum of total ion yield divided by total electron yield exhibits a characteristic threshold peak at hν = 533.4 eV, which is assigned to the 4a₁ ← O 1s resonant transition. The AES at the 4a₁ ← O 1s resonance is interpreted as being composed of the spectator-AES of the surface H₂O, and the normal-AES of the bulk H₂O, where the 4a₁ electron is delocalized before Auger transitions. H⁺ is found to be the only ion species in AEPICO spectra measured at the 4a₁ ← O 1s resonance and at the O 1s ionization (hν = 560 eV). The electron kinetic energy dependence of the AEPICO yield (AEPICO yield spectrum) at the 4a₁ ← O 1s resonance is found to be greatly different from that at the O 1s ionization. The peak positions of the AEPICO yield spectrum at the 4a₁ ← O 1s resonance are found to correspond to those of the spectator-AES of the surface H₂O, which is extracted from the AES at the 4a₁ ← O 1s resonance. Furthermore, the AEPICO yield is greatly enhanced at the 4a₁ ← O 1s resonance as compared with that at the O 1s ionization. On the basis of these results, a spectator-Auger-stimulated ion desorption mechanism and/or ultra-fast ion desorption mechanism are concluded to be responsible for the H⁺ desorption at the 4a₁ ← O 1s resonance. The enhancement of the H⁺ yield is ascribed to the O---H anti-bonding character of the 4a₁ orbital.     

The Role of a1(1260) in π-p→a1-(1260)p and π-p→π-ρ0p Reactions Near Threshold

We report on a theoretical study of the π^-p→a₁^-(1260) p and π^-p→π^-ρ⁰p reactions near threshold within an effective Lagrangian approach. The production process is described by t-channel ρ⁰ meson exchange. For the π^-p→π^-ρ⁰p reaction, the final π^-ρ⁰ results from the decay of the a₁(1260) resonance, which is assumed as a dynamically generated state from the K^*K and ρπ coupled channel interactions. We calculate the total cross section of the π^-p→a₁^-(1260)p reaction. It is shown that, with the coupling constant of the a₁(1260) to ρπ channel obtained from the chiral unitary theory and a cut off parameter Λρ~1.5 GeV in the form factors, the experimental measurement can be reproduced. Furthermore, the total and differential cross sections of π^-p→a₁^-(1260)p→π^-ρ⁰p reaction are evaluated, and it is expected that our model calculations can be tested by future experiments. These reactions are important for the study of the a₁(1260) resonance and would provide further constraints on the properties of the a₁(1260) state.