钯、钇、氢体系的团簇结构和分子势能函数
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摘要
过渡金属团簇特别是钯(Pd)及其掺杂团簇,是近年来令人感兴趣的团簇之一,由于其独特的物理和化学性质而被广泛地应用于催化反应和材料吸附中。例如钯(Pd)及钯钇(Pd-Y)合金渗氢材料应用在氢(同位素)的纯化与分离、氢能源利用技术中高纯氢的提取、工业生产中氢的分离与回收,对开发清洁的氢能源具有重要意义。本文采用量子力学中密度泛函(DFT)B3LYP方法和相对论有效原子实模型(RECP)、应用Gaussian98W程序,对钯氢、钇氢、钯钇以及钯钇氢小团簇的分子结构、势能函数进行了计算。在此基础上对Pd_n(n=2-9)、Pd_nH(n=1-9)、Pd_nY(n=1-9)和Pd_nYH(n=1-9)团簇的基态结构、能级和电子性质的变化规律进行系统地研究。首次利用团簇的“软球模型”理论解释了Pd_n(n=2-9)的基态结构。
1.计算了PdH、YH、PdY、PdH_2、YH_2和PdYH团簇分子的结构。在原子分子反应静力学基础上,根据分子电子状态构造的群论原理,确定了钯、钯钇、钯氢、钇氢和钯钇氢小团簇分子的基电子状态,导出了PdH、YH和PdY双原子分子的Murrell-Sorbie势能函数,在此基础上推导出光谱项常数和力常数。利用多体项展式理论方法,首次导出PdH_2、YH_2和PdYH三原子团簇分子的解析势能函数,并绘出了其等值势能面图。各分子的等值势能面图准确地再现了其平衡构型及能量关系。
2.采用相对论有效原子实势理论(RECP)和密度泛函理论(DFT)方
The clusters of palladium and yttrium are one of the clusters that have come to attention in recent years. This is because their special physical and chemical property. The palladium and the alloy of palladium and yttrium are used as the catalyst in chemical reaction and sorbing material widely. Because hydrogen is easy absorbed by them, palladium and alloy of palladium and yttrium are used in purification and separation of hydrogen.In this paper, the molecular structure and potential energy function of small clusters of palladium, yttrium and hydrogen have been calculated by use of the density function theory (DFT) Becke 3LYP method with relativistic effective core potential (RECP) and Gaussian98W program. On this basis, the ground-state structure, energy level distribution and the electronic properties of cluster of Pdn ( n=2-9), PdnH ( n=1-9), PdnY( n=1-9)and PdnYH( n=1-9) are researched systematically. It is the first time to use the "soft ball model" theory of cluster to explain the structure of Pdn (n=2-8).Firstly, the cluster molecules structures for PdH、YH、 PdY、 PdH2、 YH2 and PdYH are calculated At the base of the atomic and molecular reaction statics, according to the group theory principle of electron state construction of molecule, the electronic state of the small cluster molecule are determined. Results show that the ground electronic states for PdH、YH、 PdY、 PdH2、 YH2 and PdYH are PdH (X2∑+)、 YH (X1∑+)、PdY (X2∑+)、PdH2
YH2 (X2A1) and PdYH (X1A') respectively, and the corresponding reasonable dissociation limits.The Murrell-Sorbie potential energy function curves of diatomic molecule of PdH、 YH and PdY have been obtained, then the spectral datum and force constants have been derived. The analytic potential energy functions for ground states of PdH2 (X1A1)、YH2 (X2A1) 和 PdYH (X1A') molecules are derived by many-boy expansion method, then their equivalence potential energy curves are drawn. The equivalence potential energy curves of PdH2 show its stable structure characteristics and energy relation of PdH2, and discuss the static characteristic of potential energy section of Pd (1Sg) + H (2Sg) + H (2Sg). There is one saddle point on these reaction channels, namely energy threshold; ppears. The equivalence potential energy curves of YH2 show its stable structure characteristics and energy relation, and discuss the static characteristic ofpotential energy section of Y(2Dg)+ H(2Sg)+ H(2Sg). There is no saddle point on these reaction channels, namely no energy threshold appears. The equivalence potential energy curves of PdYH show its stable structure characteristics and energy relation, and discuss the static characteristic of potential energy section of Pd(1Sg) + Y (2Dg) + H (2Sg). There is no saddle point on these reaction channels, namely no energy threshold appears.Secondly, we use the B3LYP/LANL2DZ method of density function theory to research the stability of the ground state structure of clusters Pdn (n=2-9) and PdnH (n=1-9), the Fermi level, ionization potentials and electron affinities and so on, systematically.The research result of clusters Pdn (n=2-9) indicate that the ground state structure of cluster Pdn(n≥4)is spatial structure. This mass there are no many-body interactions and it's same with Yclusters. One of the most striking features of Pd clusters is that the stability of electron state 3 is big than the stability of electron state 1. The ground electron states of all clusters Pd,, (n=2-9) is three. Another striking feature is that "odd-even" alternations and "magic numbers" effect do not exist in all of them. According to Koopmanns theorem, the value of HLGs (HOMO-LUMO gaps) indicates the transition ability of electron from occupying orbital to empty one, and represent the ability of participating in the chemical reaction of molecule to a certain extent The HLGs of clusters Pdn (n=2-9) is change small gradually from n=2 to 9.
The ability of participating in the chemical reaction of molecule is strong gradually. The ability of participating in the chemical reaction is same with the clusters YnThe research result of cluster PdnH (n=1-9) indicate that "odd-even" alternations and "magic numbers" effect exist in all of them, the cluster PdnH demonstrates: higher the Fermi levels while n is even number. The ability of participating in the chemical reaction of molecule is strong; or vice versa while n is odd. According to Koopmanns theorem, The negative values of level of HOMO stand for the first ionization potential of the cluster, the level of LUMO is about equal with the electronic affinities in the value, the value of HLGs (HOMO-LUMO gaps) indicates the transition ability of electron from occupying orbital to empty one, and represent the ability of participating in the chemical reaction of molecule to a certain extent. HOMO energies of cluster PdnH are higher fora n=1 to 9, shows that the cluster is easier to gain electrons gradually. The HLG of cluster PdnH is small from n=1 to 9, shows that the chemical activation is stronger gradually, then the frequency of probable electronic transition spectrum reduces.Compare cluster PdnH with relevant cluster Pd,,, the electronic properties of doped cluster PdnH is same direction as cluster P4 Cluster PdnH is easier to loss electrons. The ability of loss electrons is stronger gradually from n=1 to 9 for all the two clusters. The chemical activation of cluster PdnH is stronger with relevant cluster Pdn while n is odd number, the chemical activation is same or little stronger while n is even number.Then, it's the first time to use the B3LYP/LANL2DZ method of density function theory to research the stability of the ground state structure of cluster PdnY (n=1-9) and PdYnH(n=1-9), the Fermi level, ionization potentials and electron affinities and so on, systematically.The research result of cluster PdnY (n=1-9) indicate that the chemical activation is weaker gradually from n=1 to 7 and is little stronger gradually from n=7 to 9.Compare cluster PdnY with relevant cluster Pdn+1, the chemical activation of cluster PdnY is stronger with relevant cluster Pdn+1 with the exception of cluster s Pd6Y and Pd7Y and more stronger while n=1 to 5. HOMO and LUMO energies of cluster PdnY are also higher with relevant cluster Pdn+1 while n=1 to 5 and 8. According to Koopmanns theorem, cluster PdnY
relatively easier to loss electrons with the exception of cluster s Pd6Y and Pd7Y.The research result of cluster PdnYH(n=1-9) indicate that the chemical activation is weaker gradually from n=1 to 3, then the frequency of probable electronic transition spectrum increase; and is little stronger gradually from n=3 to 9, then the frequency of probable electronic transition spectrum reduces.Compare cluster PdnYH with relevant cluster PdnY, HOMO energies of cluster PdnY H are lower and LUMO energies of cluster PdnYH are higher with relevant cluster PdnY. According to Koopmanns theorem, cluster PdnYH relatively easier to gain electrons with the exception of clusters PdnY. Oppositional cluster PdnY relatively easier to loss electrons.In the last section of the papwe, density functional (B3LYP method with relativistic effective core potential (RECP) has been used to optimize the structures of PdH and YH molecules. The electronic and vibrational energy or entropy of the molecules is assumed to be the corresponding values of their solid states, and the △Hθ、 △Gθ、 △Sθ and hydrogen equilibrium pressure of different temperatures are obtained by this approximation. The results show that the PdH(s) heat of formation is 32.05kJ mol-1, which is near the value of experiment 37.3 kJmol-1, and the YH heat of formation is 70.21KJ mol-1.
1.计算了PdH、YH、PdY、PdH_2、YH_2和PdYH团簇分子的结构。在原子分子反应静力学基础上,根据分子电子状态构造的群论原理,确定了钯、钯钇、钯氢、钇氢和钯钇氢小团簇分子的基电子状态,导出了PdH、YH和PdY双原子分子的Murrell-Sorbie势能函数,在此基础上推导出光谱项常数和力常数。利用多体项展式理论方法,首次导出PdH_2、YH_2和PdYH三原子团簇分子的解析势能函数,并绘出了其等值势能面图。各分子的等值势能面图准确地再现了其平衡构型及能量关系。
2.采用相对论有效原子实势理论(RECP)和密度泛函理论(DFT)方
The clusters of palladium and yttrium are one of the clusters that have come to attention in recent years. This is because their special physical and chemical property. The palladium and the alloy of palladium and yttrium are used as the catalyst in chemical reaction and sorbing material widely. Because hydrogen is easy absorbed by them, palladium and alloy of palladium and yttrium are used in purification and separation of hydrogen.In this paper, the molecular structure and potential energy function of small clusters of palladium, yttrium and hydrogen have been calculated by use of the density function theory (DFT) Becke 3LYP method with relativistic effective core potential (RECP) and Gaussian98W program. On this basis, the ground-state structure, energy level distribution and the electronic properties of cluster of Pdn ( n=2-9), PdnH ( n=1-9), PdnY( n=1-9)and PdnYH( n=1-9) are researched systematically. It is the first time to use the "soft ball model" theory of cluster to explain the structure of Pdn (n=2-8).Firstly, the cluster molecules structures for PdH、YH、 PdY、 PdH2、 YH2 and PdYH are calculated At the base of the atomic and molecular reaction statics, according to the group theory principle of electron state construction of molecule, the electronic state of the small cluster molecule are determined. Results show that the ground electronic states for PdH、YH、 PdY、 PdH2、 YH2 and PdYH are PdH (X2∑+)、 YH (X1∑+)、PdY (X2∑+)、PdH2
YH2 (X2A1) and PdYH (X1A') respectively, and the corresponding reasonable dissociation limits.The Murrell-Sorbie potential energy function curves of diatomic molecule of PdH、 YH and PdY have been obtained, then the spectral datum and force constants have been derived. The analytic potential energy functions for ground states of PdH2 (X1A1)、YH2 (X2A1) 和 PdYH (X1A') molecules are derived by many-boy expansion method, then their equivalence potential energy curves are drawn. The equivalence potential energy curves of PdH2 show its stable structure characteristics and energy relation of PdH2, and discuss the static characteristic of potential energy section of Pd (1Sg) + H (2Sg) + H (2Sg). There is one saddle point on these reaction channels, namely energy threshold; ppears. The equivalence potential energy curves of YH2 show its stable structure characteristics and energy relation, and discuss the static characteristic ofpotential energy section of Y(2Dg)+ H(2Sg)+ H(2Sg). There is no saddle point on these reaction channels, namely no energy threshold appears. The equivalence potential energy curves of PdYH show its stable structure characteristics and energy relation, and discuss the static characteristic of potential energy section of Pd(1Sg) + Y (2Dg) + H (2Sg). There is no saddle point on these reaction channels, namely no energy threshold appears.Secondly, we use the B3LYP/LANL2DZ method of density function theory to research the stability of the ground state structure of clusters Pdn (n=2-9) and PdnH (n=1-9), the Fermi level, ionization potentials and electron affinities and so on, systematically.The research result of clusters Pdn (n=2-9) indicate that the ground state structure of cluster Pdn(n≥4)is spatial structure. This mass there are no many-body interactions and it's same with Yclusters. One of the most striking features of Pd clusters is that the stability of electron state 3 is big than the stability of electron state 1. The ground electron states of all clusters Pd,, (n=2-9) is three. Another striking feature is that "odd-even" alternations and "magic numbers" effect do not exist in all of them. According to Koopmanns theorem, the value of HLGs (HOMO-LUMO gaps) indicates the transition ability of electron from occupying orbital to empty one, and represent the ability of participating in the chemical reaction of molecule to a certain extent The HLGs of clusters Pdn (n=2-9) is change small gradually from n=2 to 9.
The ability of participating in the chemical reaction of molecule is strong gradually. The ability of participating in the chemical reaction is same with the clusters YnThe research result of cluster PdnH (n=1-9) indicate that "odd-even" alternations and "magic numbers" effect exist in all of them, the cluster PdnH demonstrates: higher the Fermi levels while n is even number. The ability of participating in the chemical reaction of molecule is strong; or vice versa while n is odd. According to Koopmanns theorem, The negative values of level of HOMO stand for the first ionization potential of the cluster, the level of LUMO is about equal with the electronic affinities in the value, the value of HLGs (HOMO-LUMO gaps) indicates the transition ability of electron from occupying orbital to empty one, and represent the ability of participating in the chemical reaction of molecule to a certain extent. HOMO energies of cluster PdnH are higher fora n=1 to 9, shows that the cluster is easier to gain electrons gradually. The HLG of cluster PdnH is small from n=1 to 9, shows that the chemical activation is stronger gradually, then the frequency of probable electronic transition spectrum reduces.Compare cluster PdnH with relevant cluster Pd,,, the electronic properties of doped cluster PdnH is same direction as cluster P4 Cluster PdnH is easier to loss electrons. The ability of loss electrons is stronger gradually from n=1 to 9 for all the two clusters. The chemical activation of cluster PdnH is stronger with relevant cluster Pdn while n is odd number, the chemical activation is same or little stronger while n is even number.Then, it's the first time to use the B3LYP/LANL2DZ method of density function theory to research the stability of the ground state structure of cluster PdnY (n=1-9) and PdYnH(n=1-9), the Fermi level, ionization potentials and electron affinities and so on, systematically.The research result of cluster PdnY (n=1-9) indicate that the chemical activation is weaker gradually from n=1 to 7 and is little stronger gradually from n=7 to 9.Compare cluster PdnY with relevant cluster Pdn+1, the chemical activation of cluster PdnY is stronger with relevant cluster Pdn+1 with the exception of cluster s Pd6Y and Pd7Y and more stronger while n=1 to 5. HOMO and LUMO energies of cluster PdnY are also higher with relevant cluster Pdn+1 while n=1 to 5 and 8. According to Koopmanns theorem, cluster PdnY
relatively easier to loss electrons with the exception of cluster s Pd6Y and Pd7Y.The research result of cluster PdnYH(n=1-9) indicate that the chemical activation is weaker gradually from n=1 to 3, then the frequency of probable electronic transition spectrum increase; and is little stronger gradually from n=3 to 9, then the frequency of probable electronic transition spectrum reduces.Compare cluster PdnYH with relevant cluster PdnY, HOMO energies of cluster PdnY H are lower and LUMO energies of cluster PdnYH are higher with relevant cluster PdnY. According to Koopmanns theorem, cluster PdnYH relatively easier to gain electrons with the exception of clusters PdnY. Oppositional cluster PdnY relatively easier to loss electrons.In the last section of the papwe, density functional (B3LYP method with relativistic effective core potential (RECP) has been used to optimize the structures of PdH and YH molecules. The electronic and vibrational energy or entropy of the molecules is assumed to be the corresponding values of their solid states, and the △Hθ、 △Gθ、 △Sθ and hydrogen equilibrium pressure of different temperatures are obtained by this approximation. The results show that the PdH(s) heat of formation is 32.05kJ mol-1, which is near the value of experiment 37.3 kJmol-1, and the YH heat of formation is 70.21KJ mol-1.
引文
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