掺杂小团簇Be_nLi和B_nNi的理论研究
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摘要
本文集中研究碱金属锂原子掺杂铍团簇和过渡金属镍原子掺杂硼团簇的结构和性质。团簇是几个到几十个甚至上千个原子或分子的聚集体。近来,团簇科学经历着前所未有的研究热潮。团簇作为一个巨大的物质宝库,人类对它的挖掘才刚刚开始,然而它所展现的财富,已经在科学界造成巨大的震撼。碳是人类最早认识的化学元素,随着C_(60)等碳簇的发现,人们对碳又有了新的认识,并因此开辟了一个全新的研究领域。从二十世纪90年代以来,投入C_(60)研究的科学家之多,涉及的学科面之广,发表的论文数之多,在科学史上是罕见的。而每一类新团簇的发现,都会兴起一波又一波的研究热潮。其实,C_(60)等富勒烯还只是碳簇的一种,其它结构形式的团簇,其它元素的团簇,以及更为丰富的多元团簇,都可能一一成为新的研究热点。
研究人员对于人们熟悉的铍、锂、硼、镍等元素所组成的团簇是十分感兴趣的,因为团簇的这些非同寻常的结构往往会导致某些奇妙的特性,通过广泛地研究,甚至具有工业生产的潜力。关于这些特性的研究,无论从基础研究还是从美学的角度来看,都是非常吸引人的。在过去的几十年中,谱学研究和理论研究的结合已经成为一个活跃的研究领域。大量的实验研究方面的进展,促进了较大尺寸的铍、锂、硼、镍等团簇的理论研究,这种理论和实验结合的研究方法加深了人们对团簇微观行为的物理图像和化学结构的理解。本文集中于碱金属锂原子掺杂铍团簇和过渡金属镍原子掺杂硼团簇的理论研究,研究结果可以概括为以下几个方面:
1.采用量子化学从头算的方法,在密度泛函B3LYP/6-31G(d)的水平上对BenLi(n=1-14)团簇的各种可能同分异构体进行了研究,找出其中的基态结构,并对这些基态结构进行了相对稳定性、振动频率、电子性质和极化率的分析。从几何构型看,随尺寸的增加Li原子趋向于BeN团簇的外围。计算结果表明n=4、9和13是BenLi团簇的幻数。随着尺寸的增加,能隙逐渐减小,s,p轨道杂化逐渐增强。掺杂锂原子后降低了BeN主团簇的平均结合能,增加了BeN主团簇的极化率。
2.通过基于密度泛函理论下的广义梯度近似(GGA)方法,选择Becke交换梯度修正和Perdew-Wang关联梯度修正,并采用带极化的双数值原子基组(DNP)对BnNi(n≤5)小团簇进行全部构型优化和磁性计算,确定了其基态结构。计算结果表明:BnNi(n≤5)小团簇基态结构的自旋多重度分别为2,1,2,1,2;B2Ni基态团簇较其近邻稳定; Ni原子掺入B团簇后增大了其结合能;Ni原子磁矩和团簇总磁矩随团簇尺寸增大而呈振荡趋势,B2Ni基态团簇和B4Ni基态团簇出现“磁矩淬灭”现象。
The dissertation is devoted to the study of formation and characterization of Li-doped BeN(N=2-15) and Ni-doped BN(N≤6) clusters. Clusters are aggregates of atoms or molecules ranging in size from two to tens of thousands of monomer units. Recently, cluster science has undergone an explosive growth in activity. The carbon is the chemical element which the humanity most early knew, along with the discovery of C_(60) and so on carbon clusters, enable the people also to have the new understanding to the carbon, and therefore opened a broad-new research area. Since the 1990s, the scientists which have invested the C_(60) research are so many, involves discipline is broad, the publication paper numbers are so many, in the scientific history is rare. But each kind of new cluster of discovery, can start a wave of the research upsurge. Actually, C_(60) and so on fuller alkene also is only a carbon cluster of one kind, other structural styles clusters, other elements clusters, as well as richer multi- element clusters, all is possible to become the new research hot spot.
The researchers are interested in the clusters regards beryllium, lithium, boron, nickel and so on element, because unusual structure will lead to fascinating properties, even to a potential for industrial application through extensive investigation. The study of the properties is often attractive from both the fundamental and the aesthetical points of view. Spectroscopic investigation of the clusters combined with theoretical study has become an active field of research in the last decades. Hand in hand with the advances in experimental studies, there has been much progress in efforts to derive theoretical models for larger clusters of beryllium, lithium, boron, nickel and so on element. The combined efforts of experimentalists and theoreticians have led to a detailed physical insight into the microscopic interactions that govern the structural and dynamic behavior of these clusters. In this thesis, we investigate the structures and properties of Li-doped BeN(N=2-15) and Ni-doped BN(N≤6) clusters using frst-principles quantum chemistry methods based on density functional theory (DFT). Main results and conclusion could be summarized in the following:
1. Density functional calculations have been carried out for Li-doped BeN (N=2-15) clusters at the B3LYP/6-31G(d) level. Geometry of various isomeric structures of the clusters were optimized and their energies were compared to find the most stable isomers. Based on the analysis of the theoretical results, the equilibrium geometries, vibrational frequencies, relative stability, the electronic properties and polarizabilities are discussed. The resulting geometries show that Li prefers to be on the periphery of Be clusters. The results indicate that size n=4、9 and 13 are magic numbers of the BenLi clusters. Along with the size increase, the gap gradually reduce, the s, p orbits hybridization gradually strengthens. Our calculations demonstrate that Li impurity decreases the binding energy per atom while increases the polarizabilities of BeN clusters. 2. The full geometry optimization and the magnetic property computation to the small clusters BnNi(n≤5) were performed using generalized gradient approximate (GGA) method based on the density functional theory, the Becke exchange gradient revision and the Perdew-Wang connection gradient revision were chosen, and the double numerical basis including p-polarization function (DNP) were used, and had determined their lowest energy structures. The computed results indicated that the spinning multiplicities of the lowest energy structures for small clusters BnNi(n≤5) respectively are 2, 1, 2,1, 2; After Ni-doped into the BN clusters to increase their average binding energy; The Ni atomic magnetic moment and total magnetic moment of clusters showing the oscillation tendency as increasing of clusters size.
研究人员对于人们熟悉的铍、锂、硼、镍等元素所组成的团簇是十分感兴趣的,因为团簇的这些非同寻常的结构往往会导致某些奇妙的特性,通过广泛地研究,甚至具有工业生产的潜力。关于这些特性的研究,无论从基础研究还是从美学的角度来看,都是非常吸引人的。在过去的几十年中,谱学研究和理论研究的结合已经成为一个活跃的研究领域。大量的实验研究方面的进展,促进了较大尺寸的铍、锂、硼、镍等团簇的理论研究,这种理论和实验结合的研究方法加深了人们对团簇微观行为的物理图像和化学结构的理解。本文集中于碱金属锂原子掺杂铍团簇和过渡金属镍原子掺杂硼团簇的理论研究,研究结果可以概括为以下几个方面:
1.采用量子化学从头算的方法,在密度泛函B3LYP/6-31G(d)的水平上对BenLi(n=1-14)团簇的各种可能同分异构体进行了研究,找出其中的基态结构,并对这些基态结构进行了相对稳定性、振动频率、电子性质和极化率的分析。从几何构型看,随尺寸的增加Li原子趋向于BeN团簇的外围。计算结果表明n=4、9和13是BenLi团簇的幻数。随着尺寸的增加,能隙逐渐减小,s,p轨道杂化逐渐增强。掺杂锂原子后降低了BeN主团簇的平均结合能,增加了BeN主团簇的极化率。
2.通过基于密度泛函理论下的广义梯度近似(GGA)方法,选择Becke交换梯度修正和Perdew-Wang关联梯度修正,并采用带极化的双数值原子基组(DNP)对BnNi(n≤5)小团簇进行全部构型优化和磁性计算,确定了其基态结构。计算结果表明:BnNi(n≤5)小团簇基态结构的自旋多重度分别为2,1,2,1,2;B2Ni基态团簇较其近邻稳定; Ni原子掺入B团簇后增大了其结合能;Ni原子磁矩和团簇总磁矩随团簇尺寸增大而呈振荡趋势,B2Ni基态团簇和B4Ni基态团簇出现“磁矩淬灭”现象。
The dissertation is devoted to the study of formation and characterization of Li-doped BeN(N=2-15) and Ni-doped BN(N≤6) clusters. Clusters are aggregates of atoms or molecules ranging in size from two to tens of thousands of monomer units. Recently, cluster science has undergone an explosive growth in activity. The carbon is the chemical element which the humanity most early knew, along with the discovery of C_(60) and so on carbon clusters, enable the people also to have the new understanding to the carbon, and therefore opened a broad-new research area. Since the 1990s, the scientists which have invested the C_(60) research are so many, involves discipline is broad, the publication paper numbers are so many, in the scientific history is rare. But each kind of new cluster of discovery, can start a wave of the research upsurge. Actually, C_(60) and so on fuller alkene also is only a carbon cluster of one kind, other structural styles clusters, other elements clusters, as well as richer multi- element clusters, all is possible to become the new research hot spot.
The researchers are interested in the clusters regards beryllium, lithium, boron, nickel and so on element, because unusual structure will lead to fascinating properties, even to a potential for industrial application through extensive investigation. The study of the properties is often attractive from both the fundamental and the aesthetical points of view. Spectroscopic investigation of the clusters combined with theoretical study has become an active field of research in the last decades. Hand in hand with the advances in experimental studies, there has been much progress in efforts to derive theoretical models for larger clusters of beryllium, lithium, boron, nickel and so on element. The combined efforts of experimentalists and theoreticians have led to a detailed physical insight into the microscopic interactions that govern the structural and dynamic behavior of these clusters. In this thesis, we investigate the structures and properties of Li-doped BeN(N=2-15) and Ni-doped BN(N≤6) clusters using frst-principles quantum chemistry methods based on density functional theory (DFT). Main results and conclusion could be summarized in the following:
1. Density functional calculations have been carried out for Li-doped BeN (N=2-15) clusters at the B3LYP/6-31G(d) level. Geometry of various isomeric structures of the clusters were optimized and their energies were compared to find the most stable isomers. Based on the analysis of the theoretical results, the equilibrium geometries, vibrational frequencies, relative stability, the electronic properties and polarizabilities are discussed. The resulting geometries show that Li prefers to be on the periphery of Be clusters. The results indicate that size n=4、9 and 13 are magic numbers of the BenLi clusters. Along with the size increase, the gap gradually reduce, the s, p orbits hybridization gradually strengthens. Our calculations demonstrate that Li impurity decreases the binding energy per atom while increases the polarizabilities of BeN clusters. 2. The full geometry optimization and the magnetic property computation to the small clusters BnNi(n≤5) were performed using generalized gradient approximate (GGA) method based on the density functional theory, the Becke exchange gradient revision and the Perdew-Wang connection gradient revision were chosen, and the double numerical basis including p-polarization function (DNP) were used, and had determined their lowest energy structures. The computed results indicated that the spinning multiplicities of the lowest energy structures for small clusters BnNi(n≤5) respectively are 2, 1, 2,1, 2; After Ni-doped into the BN clusters to increase their average binding energy; The Ni atomic magnetic moment and total magnetic moment of clusters showing the oscillation tendency as increasing of clusters size.
引文
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[1] Chen Y H, Zhang C R and Ma J, Density functional theory study on the structure and properties of MgmBn(m=1,2;n=1-4) clusters, Acta Phys. Sin. 2006 55(1): 0171 (in Chinese). [陈玉红,张才荣,马军,MgmBn(m=1,2;n=1-4)团簇结构与性质的密度泛函理论研究,物理学报 2006 55(1):0171]
[2] Yan S Y, The molecular structure and potential energy function of the ground state of BH2 molecule, Acta Phys. Sin. 2006 55(7):3408 (in Chinese). [阎世英, BH2的分子结构和势能函数, 物理学报 2006 55(7):3408]
[3] Ma W J, Wang Y B, Zhang J, Wu H S, Structure Characteristics and Stability of BmN (m=2-9) Clusters, Acta Phys. -Chim. Sin., 2007 23(2):169 (in Chinese). [马文瑾,王艳宾,张静,武海顺,BmN(m=2-9)团簇的结构特征与稳定性,物理化学学报 2007 23(2):169]
[4] Feng X J and Luo Y H, Structure and Stability of Al-Doped Boron Clusters by the Density-Functional Theory, J. Phys. Chem. A 2007 111: 2420.
[5] Chang Z W, Wang Q L and Luo Y H, Effects of spin multiplicity on atomic structure of titanium trimer, Acta Phys. Sin. 2006 55(9):4553 (in Chinese). [常志文,王清林,罗有华,自旋多重度对钛三聚体原子结构的影响,物理学报 2006 55(9):4553]
[6] Yan S Y and Zhu Z H, Spin polarization effect for Fe2 molecule, Chin. Phys. 2006 15(7):1517.
[7] Yan S Y and Zhu Z H, Spin polarization effect for Tc2 molecule , Chin. Phys. 2004 13(12):2053.
[8] Xie A D, Yan S Y, Zhu Z H and Fu Y B, Spin polarization effect for Os2 molecule, Chin. Phys. 2005 14(9):1808.
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[1] Gu G Y, Ding X L , Dai B, A theoretical study of the LaO clusters, J. At. Mol. Struct. 2005 22(04):0629 (in chinese). [顾广颐,丁迅雷,代 兵,团簇LaO的理论研究,原子与分子物理学报 2005 22(04):0629.]
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[9] Wang H Y , Li X B , Tang Y J , Chen X H, Wang Z Y, Zhu Z H, Structures and stabilities of AunXm (n + m=4, X =Cu, Al, Y) clusters, Acta Phys. Sin.2005 54(08):3565 (in Chinese). [王红艳,李喜波,唐永健,谌晓洪,王朝阳,朱正和,AunXm (n + m=4,X=Cu, Al, Y) 混合小团簇的结构和稳定性研究, 物理学报 2005 54(08):3565.]
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[14] Frisch M J, Trucks G W, Schlegel H B, Scuseria G E, Robb M A, Cheeseman J R, Montgomery J A, Jr, Vreven T, Kudin K N, Burant J C, Millam J M, Iyengar S S, Tomasi J, Barone V, Mennucci B, Cossi M, Scalmani G, Rega N, Petersson G A, Nakatsuji H, Hada M, Ehara M, Toyota K, Fukuda R, Hasegawa J, Ishida M, Nakajima T, Honda Y, Kitao O, Nakai H, Klene M, Li X, Knox J E, Hratchian H P, Cross J B, Adamo C, Jaramillo J, Gomperts R, Stratmann R E, Yazyev O, Austin A J, Cammi R, Pomelli C, Ochterski J W, Ayala P Y, Morokuma K, Voth G A, Salvador P, Dannenberg J J, Zakrzewski V G, Dapprich S, Daniels A D, Strain M C, Farkas O, Malick D K, Rabuck A D, Raghavachari K, Foresman J B, Ortiz J V, Cui Q, Baboul A G, Clifford S, Cioslowski J, Stefanov B B, Liu G, Liashenko A, Piskorz P, Komaromi I, Martin R L, Fox D J, Keith T, Al-Laham M A, Peng C Y, Nanayakkara A,Challacombe M, Gill P M W, Johnson B, Chen W, Wong M W, Gonzalez C, and Pople J A, Gaussian 03, Revision C.02, Gaussian, Inc., Wallingford CT, 2004.
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[1] Chen Y H, Zhang C R and Ma J, Density functional theory study on the structure and properties of MgmBn(m=1,2;n=1-4) clusters, Acta Phys. Sin. 2006 55(1): 0171 (in Chinese). [陈玉红,张才荣,马军,MgmBn(m=1,2;n=1-4)团簇结构与性质的密度泛函理论研究,物理学报 2006 55(1):0171]
[2] Yan S Y, The molecular structure and potential energy function of the ground state of BH2 molecule, Acta Phys. Sin. 2006 55(7):3408 (in Chinese). [阎世英, BH2的分子结构和势能函数, 物理学报 2006 55(7):3408]
[3] Ma W J, Wang Y B, Zhang J, Wu H S, Structure Characteristics and Stability of BmN (m=2-9) Clusters, Acta Phys. -Chim. Sin., 2007 23(2):169 (in Chinese). [马文瑾,王艳宾,张静,武海顺,BmN(m=2-9)团簇的结构特征与稳定性,物理化学学报 2007 23(2):169]
[4] Feng X J and Luo Y H, Structure and Stability of Al-Doped Boron Clusters by the Density-Functional Theory, J. Phys. Chem. A 2007 111: 2420.
[5] Chang Z W, Wang Q L and Luo Y H, Effects of spin multiplicity on atomic structure of titanium trimer, Acta Phys. Sin. 2006 55(9):4553 (in Chinese). [常志文,王清林,罗有华,自旋多重度对钛三聚体原子结构的影响,物理学报 2006 55(9):4553]
[6] Yan S Y and Zhu Z H, Spin polarization effect for Fe2 molecule, Chin. Phys. 2006 15(7):1517.
[7] Yan S Y and Zhu Z H, Spin polarization effect for Tc2 molecule , Chin. Phys. 2004 13(12):2053.
[8] Xie A D, Yan S Y, Zhu Z H and Fu Y B, Spin polarization effect for Os2 molecule, Chin. Phys. 2005 14(9):1808.
[9] Becke A D, Correlation energy of an inhomogeneous electron gas: A coordinate-space model, J. Chem. Phys. 1988 88(2):1053.
[10] Perdew J P and Wang Y, Accurate and simple analytic representation of the electron-gas correlation energy, Phys. Rev. B 1992 45(23):13244.
[11] (a)Delley B, From molecules to solids with the Dmol3 approach, J. Chem. Phys 2000 113:7756. (b)Delley B, An all-electron numerical method for solving the local density functional for polyatomic molecules, J. Chem. Phys. 1990 92:508.
[12] David R L, CRC Handbook of Chemistry and Physics, 79th (New York: CRC Press,Inc) 1998 51 and 80.
[13] Niu J, Rao B K, Jena P, Atomic and electronic structures of neutral and charged boron and boron-rich clusters, J. Chem. Phys. 1997 107:132.
[14] Yang C L, Zhu Z H, Wang R, Liu X Y, Analytical potential energy functions of the neutral and cationin B2, J. Mol. Struct.Theochem 2001 548:47.
[15] Deshpande M, Kanhere D G, Pandey R, Structures, energetics, and magnetic properties of NinB clusters with n=1–8,12, Phys. Rev. A 2005 71: 063202.
[16] Wu Z J, Density functional study of 3d-metal monoborides, J. Mol. Struct. Theochem 2005 728:167.
[17] Boustani Ihsan, Systematic ab initio investigation of bare boron clusters: Determination of the geometry and electronic structures of Bn(n=2 – 14), Phys. Rev. B. 1997 55(24):16426.
[18] Zhai H J and Wang L S, Photoelectron Spectroscopy and ab Initio Study of B3- and B4- Anions and Their Neutrals, J. Phys. Chem. A. 2003 107: 9319-9328.
[19] Li Q S and Ji H W, Structure and Stability of B5, B5+ and B5- Clusters, J. Phys. Chem. A. 2002 106:7042.
[20] Niu J, Rao B K, and Jena P,Atomic and electronic structures of neutral andcharged boron and boron-rich clusters,J. Chem. Phys. 1997 107 (1):132.
[21] Aihara Jun-ichi, Kanno Hideaki and Ishida Toshimasa, Aromaticity of Planar Boron Clusters Confirmed, J. AM. CHEM. SOC. 2005 127:13324.
[22] Ma J, Li Z H, Fan K N, Zhou M F, Density functional theory study of the B6; B6+; B6- and B62- clusters, Chem. Phys. Lett. 2003 372:708.
[23] Apsel S E, Emmert J W, Deng J and Bloomfield L A, Surface-enhanced magnetism in nikel clusters, Phys. Rev. Lett. 1996 76:1441.
[24] 段海明,团簇体系的第一性原理计算研究,中国科学院博士论文,2001.