EuC，EuC_2和YC分子的结构和稳定性的理论研究
摘要
本文利用量子力学处理分子问题的基本原理和方法,在相对论有效原子实势模型的基础上,应用量子化学通用的计算程序Gaussian 98 和Gamess 对稀有金属碳化物的结构和稳定性进行理论上的研究。
使用密度泛函方法和多组态自洽场方法对一碳化铕(EuC),二碳化铕(EuC_2)以及一碳化镱(YC)分子进行了理论研究,计算结果表明碳原子和铕原子能形成稳定的极性分子,应用两种方法都得到了上述三种分子的基态以及几个低激发态的电子态结构。参照本文计算所得结果以及文献中用同样方法计算的结果比较发现,铕的一碳化物和二碳化物比对应的镱的一碳化物和二碳化物稳定。这个结论在一定程度上可以解释现在人们用Eu/Ni 和Y/Ni 作双金属催化剂制备单壁碳纳米管时的一些实验现象。
Gaseous metal carbides have been extensively studiedboth in experiment and in theory, for example, the impurecarbide phase TcC has been shown to be superconducting at3.85K. And also, single-walled carbon nanotubes (SWNTs) have beenintensively studied for their interesting one-dimensional (1D) physicalproperties and for their high potential for technological application.Some addition of rare earth element to transition metal nickel, forexample, La, Ce, Tb and Lu, has showed good effect on the synthesisof SWNTs. Y/Ni has been reported to be an effective catalyst for thesynthesis of SWNTs, in shape contrast, Eu/Ni gives very low yield ofSWNTs in the as-grown samples. Though Y and Eu are all rare earthelement, the mechanism of the huge difference in the catalyticbehavior of synthesis of SWNTs is open to question. Some reportshave suggested that the RE carbides may be important precursors forthe growth of SWNTs. And further X-ray investigation on thearc-discharge cathode deposit showed that there is no Eu carbide butrich in Y carbide. In addition, TEM observation also showed that the
RE carbide is related to the SWNT bundles. Stimulated by this idea,we take the investigation about the Eu and Y carbide in theory tocompare their physical and chemistry properties and attempt to givesome explanation on the experimental results.
No previous theoretical investigations have been carried out onthe EuC and EuC2 molecules. In this study, density functional theoryand ab initio calculations have been performed on the basis ofrelativistic effective core potentials(RECPs) on various electronicstates of EuC , EuC2 and YC to investigate their structures, molecularparameters, vibrational frequencies, nature of bonding and stability.
In our work, the dissociation energies are calculated usingMCSCF method. The potential curves for the ground state ∑+ and 12excitated states12∏and 12∑—of EuC molecule converge into differentdissociation limit. That is to say, the ∑+ converges into Eu (8S) + C 12(3P), the ∏and 12 12∑—converge into C(1D)+ Eu (8S). Increasing or decreasing of Mulliken electric charge changes theintensity of chemical bond. The Mulliken population analysis of thethree molecules suggests charge transfer from rare earth element tocarbon resulting Eu+C—and Y+C—polar bonds. The charge transferfrom europium to carbon is more than yttrium to carbon for the EuCand YC molecules, respectively, that is to say, EuC is steadier than YCmolecule. On the other hand, the dissociation energy of EuC is higherthan that of YC molecule from our calculation results using MCSCFmethod, and the dissociation of EuC2 is almost double of the YC2
when the metallic atom is dissociated along the perpendicular bisectorof two carbon atoms. So we can conclude that the europium carbidesare steadier than the corresponding yittrium carbides. Most likely, it is more difficult for the formation of EuC moleculethan that of the YC molecule in the course of the synthesis of SWNTs.This results in the low yield of nanotubes in the case of Eu/Ni ascatalyst. This result is supported by a recent X-ray analysis on thehigh-temperature (2000 C) annealed mixture of graphite powder and oEu2O3. But once the EuC molecule is formed, it will be steadier thanYC molecule. At the same time, the amount of transfer of electriccharge only affects the stability other than the quantity of the formingrare earth carbides, which differs from some reports. Especially, in the process of calculation using MCSCF method, itis worthy pointing out that we should consider not only thecalculational precision of different active space but also the hardwarecondition of our computer. If the active space is too large, it is possibleto exceed the physical EMS memory of PC computer. This will resultsin the calculative assignment uncompleted. However, it is possible thatthe calculational results are not precise or even false if the active spaceis choosed unsuitable. For example, the active space is choosed(13e,17o)or even more large than(13e,12o)and(13e,16o) thatcan obtain the correct results for the high spin multiplicities of the EuCmolecule. But the results for the low multiplicities are close to that ofB3LYP when we choose the (13e,12o)and(13e,16o)active space. In the whole calculation process of our work, the REPs
使用密度泛函方法和多组态自洽场方法对一碳化铕(EuC),二碳化铕(EuC_2)以及一碳化镱(YC)分子进行了理论研究,计算结果表明碳原子和铕原子能形成稳定的极性分子,应用两种方法都得到了上述三种分子的基态以及几个低激发态的电子态结构。参照本文计算所得结果以及文献中用同样方法计算的结果比较发现,铕的一碳化物和二碳化物比对应的镱的一碳化物和二碳化物稳定。这个结论在一定程度上可以解释现在人们用Eu/Ni 和Y/Ni 作双金属催化剂制备单壁碳纳米管时的一些实验现象。
Gaseous metal carbides have been extensively studiedboth in experiment and in theory, for example, the impurecarbide phase TcC has been shown to be superconducting at3.85K. And also, single-walled carbon nanotubes (SWNTs) have beenintensively studied for their interesting one-dimensional (1D) physicalproperties and for their high potential for technological application.Some addition of rare earth element to transition metal nickel, forexample, La, Ce, Tb and Lu, has showed good effect on the synthesisof SWNTs. Y/Ni has been reported to be an effective catalyst for thesynthesis of SWNTs, in shape contrast, Eu/Ni gives very low yield ofSWNTs in the as-grown samples. Though Y and Eu are all rare earthelement, the mechanism of the huge difference in the catalyticbehavior of synthesis of SWNTs is open to question. Some reportshave suggested that the RE carbides may be important precursors forthe growth of SWNTs. And further X-ray investigation on thearc-discharge cathode deposit showed that there is no Eu carbide butrich in Y carbide. In addition, TEM observation also showed that the
RE carbide is related to the SWNT bundles. Stimulated by this idea,we take the investigation about the Eu and Y carbide in theory tocompare their physical and chemistry properties and attempt to givesome explanation on the experimental results.
No previous theoretical investigations have been carried out onthe EuC and EuC2 molecules. In this study, density functional theoryand ab initio calculations have been performed on the basis ofrelativistic effective core potentials(RECPs) on various electronicstates of EuC , EuC2 and YC to investigate their structures, molecularparameters, vibrational frequencies, nature of bonding and stability.
In our work, the dissociation energies are calculated usingMCSCF method. The potential curves for the ground state ∑+ and 12excitated states12∏and 12∑—of EuC molecule converge into differentdissociation limit. That is to say, the ∑+ converges into Eu (8S) + C 12(3P), the ∏and 12 12∑—converge into C(1D)+ Eu (8S). Increasing or decreasing of Mulliken electric charge changes theintensity of chemical bond. The Mulliken population analysis of thethree molecules suggests charge transfer from rare earth element tocarbon resulting Eu+C—and Y+C—polar bonds. The charge transferfrom europium to carbon is more than yttrium to carbon for the EuCand YC molecules, respectively, that is to say, EuC is steadier than YCmolecule. On the other hand, the dissociation energy of EuC is higherthan that of YC molecule from our calculation results using MCSCFmethod, and the dissociation of EuC2 is almost double of the YC2
when the metallic atom is dissociated along the perpendicular bisectorof two carbon atoms. So we can conclude that the europium carbidesare steadier than the corresponding yittrium carbides. Most likely, it is more difficult for the formation of EuC moleculethan that of the YC molecule in the course of the synthesis of SWNTs.This results in the low yield of nanotubes in the case of Eu/Ni ascatalyst. This result is supported by a recent X-ray analysis on thehigh-temperature (2000 C) annealed mixture of graphite powder and oEu2O3. But once the EuC molecule is formed, it will be steadier thanYC molecule. At the same time, the amount of transfer of electriccharge only affects the stability other than the quantity of the formingrare earth carbides, which differs from some reports. Especially, in the process of calculation using MCSCF method, itis worthy pointing out that we should consider not only thecalculational precision of different active space but also the hardwarecondition of our computer. If the active space is too large, it is possibleto exceed the physical EMS memory of PC computer. This will resultsin the calculative assignment uncompleted. However, it is possible thatthe calculational results are not precise or even false if the active spaceis choosed unsuitable. For example, the active space is choosed(13e,17o)or even more large than(13e,12o)and(13e,16o) thatcan obtain the correct results for the high spin multiplicities of the EuCmolecule. But the results for the low multiplicities are close to that ofB3LYP when we choose the (13e,12o)and(13e,16o)active space. In the whole calculation process of our work, the REPs
引文
[1] William A. Chupka, and Joseph Berkowitz, Clayton F. Giese and Mark G. Inghram, Thermodynamic studies of some gaseous metallic carbides, J. Phys. Chem., 1958, 62, 611.
[2] Douglas L. Strout and Michael B. Hall, Small Yttrium-Carbon clusters: rings are most stable, J. Phys. Chem., 1996, 100(46), 18007.
[3] 李赣,孙颖,汪小琳,高涛,朱正和,PuC 和PuC_2 的分子结构与势能函数, 物理化学学报, 2003, 19(4),356。
[4] Xi Li and Lai-Sheng Wang, Electronic structure and chemical bonding between the first row transition metals and C2: A photoelectron spectroscopy study of MC-2 (M=Sc, V, Cr, Mn, Fe, and Co), J. Chem. Phys., 1999, 111(18), 8389.
[5] S. Wel, B. C. Guo, J. Purnell, S. Buzza, and A. W. Castleman, Jr, Metallocarbohedrenes as a class of stable neutral clusters: Formation mechanism of M_8C_(12) (M=Ti and V), J. Phys. Chem., 1992, 96(11), 4166.
[6] Timothy C. Steimle, Robert R. Bousquet, Kei-ichi C, Namiki, and Anthony J. Merer, Rotational analysis of the A~2A_1 -X~2A_1 Band system of Yttrium dicarbide, YC2, Journal of Molecular Spectroscopy, 2002, 215, 10.
[7] I. R. Shein, and A. L. Ivanovskii, Electronic properties of the novel 18-K superconducting Y2C3 as compared with 4-K YC2 from first principles calculations, Solid State Communications, 2004, 131, 223.
[8] Hua-Jin Zhai, Lai-Sheng Wang, P. Jena, G. L. Gutsev and C. W. Bauschlicher, Competition between linear and cyclic structures in monochromium carbide clusters CrC-n and CrCn (n=2-8): A photoelectron spectroscopy and density functional study, J. Chem. Phys., 2004, 120(19) , 8996.
[9] G. Meloni, L. M. Thomson, and K. A. Gingerich, Structure and thermodynamic stability of the OsC and OsC2 molecules by theoretical calculations and by Knudsen cell mass spectrometry, J. Chem. Phys., 2001, 115(10), 4496.
[10] P. Jackson, G. E. Gadd, D. W. Mackey, H. van der Wall, and G. D. Willett, Density function investigation of various states of the molecules TcC, TcC2, ScC2, and YC2, J. Phys. Chem A., 1998, 102(45), 8941.
[11] Irene Shim, Karl A. Gingerich, All-electron ab initio investigations of the three lowest-lying electronic states of the RuC molecule. Chemical Physics Letters., 2000, 317, 338.
[12] Satish K. Gupta, Bianca M. Nappl, and Karl A. Gingerich, Thermodynamic stabilities of gaseous carbides of Iridium and platinum, J. Phys. Chem.,1981, 85(8), 971.
[13] Hang Tan, Muzhen Liao, K. Balasubramanian, Electronic states and potential energy curves of iridium carbide (IrC), Chemical Physics Letters., 1997, 280, 219.
[14] 周公度,段连运,《结构化学基础》,北京大学出版社,1999 年。
[15] Yoshihiro Kubozono,Takashi lnoue and S. Kashino Okayama University. E-mail:kubozono@cc.okayama-u.ac.jp.
[16] Zujin Shi, Toshiya Okazaki, Takashi Shimada, Toshiki Sugai, Kazutomo Suenaga, and Hisanori Shinohara, Selective High-Yield Catalytic Synthesis of Terbium Metallofullerenes and Single-Wall Carbon Nanotubes, J. Phys. Chem. B., 2003, 107(11), 2485.
[17] Houjin Huang and Shihe Yang, Relative Yields Endohedral Lanthanide Metallofullerenes by Arc Synthesis and Their Correlation with the Elution Behavior, J. Phys. Chem. B, 1998, 102(50), 10196.
[18] E.-J. Cho and S.-J.Oh, Surface valence transition in trivalent Eu insulating compounds observed by photoelectron spectroscopy, Phys. Rev. B., 1999, 59(24), 613.
[19] B. Fromme, V. Bocatius, and E. Kisker, Electron exchange in the f-f excitations of EuO, Phys. Rev. B., 2001, 64, 125114.
[20] Yoo Jin Kim, Myungkoo Suh, and Duk-Young Jung, Crystal structure and spectroscopic study of novel two-
and three-dimensional photoluminescent Eu(III)-adipate
compounds, Inorg. Chem., 2004, 43, 245.
[21] Stéphane Suárez, Daniel Imbert, Frédéric Gumy, Claude Piguet, and Jean-Claude G. Bünzli, Metal-Centered photoluminescence as a tool for detecting phase transitions inEuIII-and TbIII-Containing metallomesogens, Chem. Mater., 2004, 16, 3257.
[22] R. J. Gambino, R. R. Ruf, and P. Fumagalli, The role of vacancies in the magnetic and magneto-optic properties of Tb-doped EuO and EuS films, J. Appl. Phys., 1993, 73(10), 6109.
[23] Irene Margiolaki, Serena Margadonna, Kosmas Prassides, Thomas Hansen, Kenji Ishii, and Hiroyoshi Suematsu, Magnetic structure of the Europium fulleride ferromagnet Eu6C60, J. Am. Chem. Soc., 2002, 124, 11288.
[24] 唐敖庆,杨忠志,李前树, 《量子化学》,北京,科学出版社, 1982.
[25] D. Hartree, Calculations of structure. New York: Wiley, 1957.
[26] J. Sadlej, Semi-empirical methods of quantum chemistry. Chichester: Ellis Horwood, 1985.
[27] 徐光宪,黎乐民,王德民, 《量子化学基本原理和从头计算法》, 北京,科学出版社,1985.
[28] 江逢林,《量子化学原理》,上海, 复旦大学出版社, 1990.
[29] C. C. J. Roothaan, P. S. Bagus, Methods of molecular quantum mechanics. London: Academic Press, 1964.
[30] P. Hohenberg, W. Kohn, Inhomogeneous Electron Gas, Phys. Rev B., 1964, 136, 864.
[31] L. Kleinman, Exchage density-Functional gradient expansion, Phys. Rev. B, 1984, 30, 2223.
[32] F. Herman, J. P. Van Dyke, I. B. Orteburger, Improved Statistical Exchange Approximation for Inhomogeneous Many-Electron System, Phys. Rev. Lett., 1969, 22, 807.
[33] O. Gunnarsson, R. O. Jones, Density Functional Calculations for Atoms, Molecules and Clusters, Phys. Scr., 1980, 21, 394.
[34] A. D. Becke, Density-functional thermochemistry. III. The Role of Exact Exchange, J. Chem. Phys., 1993, 98, 5648.
[35] C. Lee, W. Yang, R. G. Parr, Development of the Colle–Salvetti Correlation-Energy Formula into a Functional of the Electron Density, Phys. Rev. B, 1988, 37, 785.
[36] P. Jeffrey Hay and Richard L. Martin, Theoretical studies of the structures and vibrational frequencies of actinide compounds using relativistic effective core potentials with Hartree-Fock and density functional methods: UF6, NpF6, and PuF6, J. Chem. Phys.,1998, 109(10), 3875.
[37] Li, Q.; Liu, X.-Y.; Gal. T.; Zhu, Z.-H.; Fu. Y.-B; Wang. X.-L. Acta Phy.-Chim. Sin. 2000.16(11), 987 (in Chinese) (李权,刘晓亚,高涛,朱正和,付依备,汪小琳,物理化学学 报,2000,16(11),987。)
[38] T. Ziegler, Approximate Density Functional Theory as a Practical Tool in Molecular Energetics and Dynamics, Chem. Rev., 1991, 91, 651.
[39] P. Mlynarski, D. R. Salahub, Local and nonlocal Density Functional Study of Ni4 and Ni5 Clusters. Models for the Chemisorption of Hydrogen on (111) and (100) Nickel Surfaces, J. Chem. Phys., 1991, 95, 6050.
[40] B. G. Johnson, P. M. W. Gill, The Performance of a Family of Density Functional Methods, J. Chem. Phys., 1993, 98, 5612.
[41] C. Lee, W. Yang, R. G. Parr, Development of the Colle–Salvetti Correlation-Energy Formula into a Functional of the Electron Density, Phys. Rev. B., 1988, 37, 785.
[42] J. P. Perdew, Y. Wang, Accurate and Simple Analytic Representation of the Electron-Gas Correlation Energy, Phys. Rev. B., 1992, 45, 13244.
[43] A. D. Becke, Correlation Energy of an Inhomogeneous Electron Gas: A Coordinate-Space Model, J. Chem. Phys., 1988, 88, 1053.
[44] P. Jeffrey Hay , Willard R. Wadt, Luis R. Kahn, and Franck W. Bobrowicz, Ab initio studies of AuH, AuCl, HgH and HgCl2 using relativistic effective core potentials, J. Chem. Phys., 1978, 69(3), 984.
[45] P. Jeffrey Hay and Willard R. Wadt, Ab initio effective core potentials for molecular calculations. Potentials for the transition metal atoms Sc to Hg, J. Chem. Phys., 1985, 82(1), 270.
[46] Walter J. Stevens, Harold Basch and Morris Krauss, Compact
[2] Douglas L. Strout and Michael B. Hall, Small Yttrium-Carbon clusters: rings are most stable, J. Phys. Chem., 1996, 100(46), 18007.
[3] 李赣,孙颖,汪小琳,高涛,朱正和,PuC 和PuC_2 的分子结构与势能函数, 物理化学学报, 2003, 19(4),356。
[4] Xi Li and Lai-Sheng Wang, Electronic structure and chemical bonding between the first row transition metals and C2: A photoelectron spectroscopy study of MC-2 (M=Sc, V, Cr, Mn, Fe, and Co), J. Chem. Phys., 1999, 111(18), 8389.
[5] S. Wel, B. C. Guo, J. Purnell, S. Buzza, and A. W. Castleman, Jr, Metallocarbohedrenes as a class of stable neutral clusters: Formation mechanism of M_8C_(12) (M=Ti and V), J. Phys. Chem., 1992, 96(11), 4166.
[6] Timothy C. Steimle, Robert R. Bousquet, Kei-ichi C, Namiki, and Anthony J. Merer, Rotational analysis of the A~2A_1 -X~2A_1 Band system of Yttrium dicarbide, YC2, Journal of Molecular Spectroscopy, 2002, 215, 10.
[7] I. R. Shein, and A. L. Ivanovskii, Electronic properties of the novel 18-K superconducting Y2C3 as compared with 4-K YC2 from first principles calculations, Solid State Communications, 2004, 131, 223.
[8] Hua-Jin Zhai, Lai-Sheng Wang, P. Jena, G. L. Gutsev and C. W. Bauschlicher, Competition between linear and cyclic structures in monochromium carbide clusters CrC-n and CrCn (n=2-8): A photoelectron spectroscopy and density functional study, J. Chem. Phys., 2004, 120(19) , 8996.
[9] G. Meloni, L. M. Thomson, and K. A. Gingerich, Structure and thermodynamic stability of the OsC and OsC2 molecules by theoretical calculations and by Knudsen cell mass spectrometry, J. Chem. Phys., 2001, 115(10), 4496.
[10] P. Jackson, G. E. Gadd, D. W. Mackey, H. van der Wall, and G. D. Willett, Density function investigation of various states of the molecules TcC, TcC2, ScC2, and YC2, J. Phys. Chem A., 1998, 102(45), 8941.
[11] Irene Shim, Karl A. Gingerich, All-electron ab initio investigations of the three lowest-lying electronic states of the RuC molecule. Chemical Physics Letters., 2000, 317, 338.
[12] Satish K. Gupta, Bianca M. Nappl, and Karl A. Gingerich, Thermodynamic stabilities of gaseous carbides of Iridium and platinum, J. Phys. Chem.,1981, 85(8), 971.
[13] Hang Tan, Muzhen Liao, K. Balasubramanian, Electronic states and potential energy curves of iridium carbide (IrC), Chemical Physics Letters., 1997, 280, 219.
[14] 周公度,段连运,《结构化学基础》,北京大学出版社,1999 年。
[15] Yoshihiro Kubozono,Takashi lnoue and S. Kashino Okayama University. E-mail:kubozono@cc.okayama-u.ac.jp.
[16] Zujin Shi, Toshiya Okazaki, Takashi Shimada, Toshiki Sugai, Kazutomo Suenaga, and Hisanori Shinohara, Selective High-Yield Catalytic Synthesis of Terbium Metallofullerenes and Single-Wall Carbon Nanotubes, J. Phys. Chem. B., 2003, 107(11), 2485.
[17] Houjin Huang and Shihe Yang, Relative Yields Endohedral Lanthanide Metallofullerenes by Arc Synthesis and Their Correlation with the Elution Behavior, J. Phys. Chem. B, 1998, 102(50), 10196.
[18] E.-J. Cho and S.-J.Oh, Surface valence transition in trivalent Eu insulating compounds observed by photoelectron spectroscopy, Phys. Rev. B., 1999, 59(24), 613.
[19] B. Fromme, V. Bocatius, and E. Kisker, Electron exchange in the f-f excitations of EuO, Phys. Rev. B., 2001, 64, 125114.
[20] Yoo Jin Kim, Myungkoo Suh, and Duk-Young Jung, Crystal structure and spectroscopic study of novel two-
and three-dimensional photoluminescent Eu(III)-adipate
compounds, Inorg. Chem., 2004, 43, 245.
[21] Stéphane Suárez, Daniel Imbert, Frédéric Gumy, Claude Piguet, and Jean-Claude G. Bünzli, Metal-Centered photoluminescence as a tool for detecting phase transitions inEuIII-and TbIII-Containing metallomesogens, Chem. Mater., 2004, 16, 3257.
[22] R. J. Gambino, R. R. Ruf, and P. Fumagalli, The role of vacancies in the magnetic and magneto-optic properties of Tb-doped EuO and EuS films, J. Appl. Phys., 1993, 73(10), 6109.
[23] Irene Margiolaki, Serena Margadonna, Kosmas Prassides, Thomas Hansen, Kenji Ishii, and Hiroyoshi Suematsu, Magnetic structure of the Europium fulleride ferromagnet Eu6C60, J. Am. Chem. Soc., 2002, 124, 11288.
[24] 唐敖庆,杨忠志,李前树, 《量子化学》,北京,科学出版社, 1982.
[25] D. Hartree, Calculations of structure. New York: Wiley, 1957.
[26] J. Sadlej, Semi-empirical methods of quantum chemistry. Chichester: Ellis Horwood, 1985.
[27] 徐光宪,黎乐民,王德民, 《量子化学基本原理和从头计算法》, 北京,科学出版社,1985.
[28] 江逢林,《量子化学原理》,上海, 复旦大学出版社, 1990.
[29] C. C. J. Roothaan, P. S. Bagus, Methods of molecular quantum mechanics. London: Academic Press, 1964.
[30] P. Hohenberg, W. Kohn, Inhomogeneous Electron Gas, Phys. Rev B., 1964, 136, 864.
[31] L. Kleinman, Exchage density-Functional gradient expansion, Phys. Rev. B, 1984, 30, 2223.
[32] F. Herman, J. P. Van Dyke, I. B. Orteburger, Improved Statistical Exchange Approximation for Inhomogeneous Many-Electron System, Phys. Rev. Lett., 1969, 22, 807.
[33] O. Gunnarsson, R. O. Jones, Density Functional Calculations for Atoms, Molecules and Clusters, Phys. Scr., 1980, 21, 394.
[34] A. D. Becke, Density-functional thermochemistry. III. The Role of Exact Exchange, J. Chem. Phys., 1993, 98, 5648.
[35] C. Lee, W. Yang, R. G. Parr, Development of the Colle–Salvetti Correlation-Energy Formula into a Functional of the Electron Density, Phys. Rev. B, 1988, 37, 785.
[36] P. Jeffrey Hay and Richard L. Martin, Theoretical studies of the structures and vibrational frequencies of actinide compounds using relativistic effective core potentials with Hartree-Fock and density functional methods: UF6, NpF6, and PuF6, J. Chem. Phys.,1998, 109(10), 3875.
[37] Li, Q.; Liu, X.-Y.; Gal. T.; Zhu, Z.-H.; Fu. Y.-B; Wang. X.-L. Acta Phy.-Chim. Sin. 2000.16(11), 987 (in Chinese) (李权,刘晓亚,高涛,朱正和,付依备,汪小琳,物理化学学 报,2000,16(11),987。)
[38] T. Ziegler, Approximate Density Functional Theory as a Practical Tool in Molecular Energetics and Dynamics, Chem. Rev., 1991, 91, 651.
[39] P. Mlynarski, D. R. Salahub, Local and nonlocal Density Functional Study of Ni4 and Ni5 Clusters. Models for the Chemisorption of Hydrogen on (111) and (100) Nickel Surfaces, J. Chem. Phys., 1991, 95, 6050.
[40] B. G. Johnson, P. M. W. Gill, The Performance of a Family of Density Functional Methods, J. Chem. Phys., 1993, 98, 5612.
[41] C. Lee, W. Yang, R. G. Parr, Development of the Colle–Salvetti Correlation-Energy Formula into a Functional of the Electron Density, Phys. Rev. B., 1988, 37, 785.
[42] J. P. Perdew, Y. Wang, Accurate and Simple Analytic Representation of the Electron-Gas Correlation Energy, Phys. Rev. B., 1992, 45, 13244.
[43] A. D. Becke, Correlation Energy of an Inhomogeneous Electron Gas: A Coordinate-Space Model, J. Chem. Phys., 1988, 88, 1053.
[44] P. Jeffrey Hay , Willard R. Wadt, Luis R. Kahn, and Franck W. Bobrowicz, Ab initio studies of AuH, AuCl, HgH and HgCl2 using relativistic effective core potentials, J. Chem. Phys., 1978, 69(3), 984.
[45] P. Jeffrey Hay and Willard R. Wadt, Ab initio effective core potentials for molecular calculations. Potentials for the transition metal atoms Sc to Hg, J. Chem. Phys., 1985, 82(1), 270.
[46] Walter J. Stevens, Harold Basch and Morris Krauss, Compact