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BeC分子基态和低激发态光谱性质和解析势能函数

张计才 孙金锋 施德恒 朱遵略

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BeC分子基态和低激发态光谱性质和解析势能函数

张计才, 孙金锋, 施德恒, 朱遵略

Spectroscopic properties and analytical potential energy function of ground and low-lying excited states of BeC moleule

Zhang Ji-Cai, Sun Jin-Feng, Shi De-Heng, Zhu Zun-Lue
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  • BeC是一个具有丰富低激发电子态的分子, 本文基于动态权重完全活性空间自冾场方法获得的参考波函数, 采用多参考组态相互作用方法对BeC分子进行高精度的从头计算, 获得了BeC分子$ {{\rm{X}}^3} {{\text{Σ}} ^ - } $, ${\rm{A}}^3 {\text{Π}}$, $ {{\rm{b}}^1} {{\text{Δ}} } $, ${{\rm{c}}^1} {\text{Π}}$$ {{\rm{d}}^1}{{\text{Σ}} ^ + } $共5个电子态的势能曲线. 为了获得精确的光谱结果, 在计算中考虑了标量相对论效应修正, 并把相互作用能外推至完全基组极限. 在此基础上获得了这些态的光谱常数和偶极距, 以及一些允许跃迁的跃迁偶极距、弗兰克-康登因子和辐射寿命. 最后, 通过扩展的Rydberg函数拟合获得了基态势能曲线精确的解析表达式.
    Diatomic molecule BeC has a complex electronic structure with a large number of low-lying excited states that are all strongly bound electronic states. Thus, the BeC molecule has the abundant spectral information. In this work, the potential energy curves and wavefunctions of $ {{\rm{X}}^3} {{\text{Σ}} ^ - } $, ${\rm{A}}^3 {\text{Π}}$, $ {{\rm{b}}^1} {{\text{Δ}} } $, ${{\rm{c}}^1} {\text{Π}}$ and $ {{\rm{d}}^1}{{\text{Σ}} ^ + } $ states of the BeC molecule are calculated by using the internally contracted multi-reference configuration interaction (MRCI) approach, which is based on the use of a dynamically weighted complete active space self-consistent field (DW-CASSCF) procedure. To improve the reliability and accuracy of calculation, the scalar relativistic corrections and the extrapolation of potential energy to the complete basis set limit are taken into account. On the basis of the calculated potential energy curves and wavefunctions, the spectroscopic constants (Te, Re, ${\omega _{\rm{e}}}$, ${\omega _{\rm{e}}}{x_{\rm{e}}}$, ${\omega _{\rm{e}}}{y_{\rm{e}}}$, Be, ${\alpha _{\rm{e}}}$, and De) and permanent dipole moments of those states are determined, the results of which are in good agreement with the existing available experimental and theoretical values. The obtained permanent dipole moments indicate that the electrons transfer from Be to C and the polarity for molecule is $ {\rm{B}}{{\rm{e}}^{{\text{δ}} + }}{{\rm{C}}^{{\text{δ}} - }}$. The transition properties of the spin-allowed ${\rm{A}}^3 {\text{Π}}$$ {{\rm{X}}^3} {{\text{Σ}} ^ - } $, ${{\rm{c}}^1} {\text{Π}}$$ {{\rm{b}}^1} {{\text{Δ}} } $, ${{\rm{c}}^1} {\text{Π}}$$ {{\rm{d}}^1}{{\text{Σ}} ^ + } $ transitions are predicted, including the transition dipole moments, Franck-Condon factors, and radiative lifetimes. The radiative lifetimes for the ${\rm{A}}^3 {\text{Π}}$$ {{\rm{X}}^3} {{\text{Σ}} ^ - } $ transitions are predicated to be at a $ {{\text{µ}}\rm{ s}}$ level, and the good agreement with previous theoretical values is found. Radiative lifetimes for ${{\rm{c}}^1} {\text{Π}}$$ {{\rm{b}}^1} {{\text{Δ}} } $ and ${{\rm{c}}^1} {\text{Π}}$$ {{\rm{d}}^1}{{\text{Σ}} ^ + } $ transitions are also evaluated at the levels of $ {{\text{µ}}\rm{ s}}$ and ms, respectively. The PEC for the ground state is fitted into accurate analytical potential energy functions by using the extended-Rydberg potential function.
      通信作者: 张计才, jicaiz@htu.cn
    • 基金项目: 国家自然科学基金(批准号: 61275132, 11274097)资助的课题.
      Corresponding author: Zhang Ji-Cai, jicaiz@htu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 61275132, 11274097).
    [1]

    Borodin D, Doerner R, Nishijima D, Kirschner A, Kreter A, Matveev D, Galonska A, Philipps V 2011 J. Nucl. Mater. 415 219Google Scholar

    [2]

    Conn R W, Doerner R P, Won J 1997 Fusion Eng. Des. 37 481

    [3]

    Chen M D, Li X B, Yang J, Zhang Q E, Au C T 2006 Int. J. Mass Spectrom. 253 30Google Scholar

    [4]

    Chen M D, Li X B, Yang J, Zhang Q E 2006 J. Phys. Chem. A 110 4502

    [5]

    Zhang C J 2006 J. Mol. Struc.: Theochem. 759 201Google Scholar

    [6]

    Barker B J, Antonov I O, Merritt J M, Bondybey V E, Heaven M C, Dawes R 2012 J. Chem. Phys. 137 214313Google Scholar

    [7]

    Wright J S, Kolbuszewski M 1993 J. Chem. Phys. 98 9725Google Scholar

    [8]

    Borin A C, Ornellas F R 1993 J. Chem. Phys. 98 8761Google Scholar

    [9]

    da Silva C O, Teixeira F E C, Azevedo, J A T, Da Silva E C, Nascimento M A C 1996 Int. J. Quant. Chem. 60 433Google Scholar

    [10]

    Pelegrini M, Roberto-Neto O, Ornellas F R, Machado F B C 2004 Chem. Phys. Lett. 383 143Google Scholar

    [11]

    Wells N, Lane I C 2011 Phys. Chem. Chem. Phys. 13 19036Google Scholar

    [12]

    Koch W, Frenking G, Gauss J, Cremer D, Sawaryn A, Schleyer P V R 1986 J. Am. Chem. Soc. 108 5732Google Scholar

    [13]

    Fioressi S E, Binning Jr R C, Bacelo D E 2014 Chem. Phys. 443 76Google Scholar

    [14]

    Patrick A D, Williams P, Blaisten-Barojas E 2007 J. Mol. Struc.: Theochem. 824 39Google Scholar

    [15]

    Ghouri M M, Yareeda L, Mainardi D S 2007 J. Phys. Chem. A 111 13133Google Scholar

    [16]

    Midda S, Das A K 2004 J. Mol. Spectrosc. 224 1Google Scholar

    [17]

    Borin A C, Ornellas F R 1995 Chem. Phys. 190 43Google Scholar

    [18]

    Borin A C, Ornellas F R A 1995 J. Mol. Struc.: Theochem 335 107Google Scholar

    [19]

    Teberekidis V I, Kerkines I S K, Carsky P, Tsipis C A, Mavridis A 2005 Int. J. Quant. Chem. 102 762Google Scholar

    [20]

    Deskevich M P, Nesbitt D J, Werner H J 2004 J. Chem. Phys. 120 7281Google Scholar

    [21]

    Dawes R, Jasper A W, Tao C, Richmond C, Mukarakate C, Kable S H, Reid S A 2010 J. Phys. Chem. Lett. 1 641Google Scholar

    [22]

    Werner H J, Knowles P J 1988 J. Chem. Phys. 89 5803Google Scholar

    [23]

    Knowles P J, Werner H J 1988 Chem. Phys. Lett. 145 514Google Scholar

    [24]

    Werner H J, Knowles P, Knizia G, Manby F R, Schütz M, Celani P, Korona T, Lindh R, Mitrushenkov A, Rauhut G 2010 Molpro Version 2010.1: A Package of ab initio Programs

    [25]

    Peterson K A, Wilson A K, Woon D E, Dunning Jr T H 1997 Theor. Chem. Acc. 97 251Google Scholar

    [26]

    Woon D E, Dunning Jr T H 1995 J. Chem. Phys. 103 4572Google Scholar

    [27]

    Prascher B P, Woon D E, Peterson K A, Dunning T H, Wilson A K 2011 Theor. Chem. Acc. 128 69Google Scholar

    [28]

    Karton A, Martin J M L. 2006 Theor. Chem. Acc. 115 330Google Scholar

    [29]

    Halkier A, Helgaker T, Jørgesen P, Klopper W, Koch H, Olsen J, Wilson A K 1998 Chem. Phys. Lett. 286 243Google Scholar

    [30]

    Nakajima T, Hirao K 2000 J. Chem. Phys. 113 7786Google Scholar

    [31]

    Fedorov D G, Nakajima T, Hirao K 2003 J. Chem. Phys. 118 4970Google Scholar

    [32]

    Paulovic J, Nakajima T, Hirao K, Lindh R, Malmqvist P Å 2003 J. Chem. Phys. 119 798Google Scholar

    [33]

    NIST, Atomic Spectra Database, see http://www.nist.gov/pml/data/asd.cfm (2012)

    [34]

    Haris K, Kramida A, 2017 Astrophys. J. Suppl. S. 233 16Google Scholar

    [35]

    LeRoy R J 2010 LEVEL 8.0: A Computer Program for Solving the Radial Schrödinger Equation for Bound and Quasibound Levels, Chemical Physics: Research Report CP-663 (Ontario: University of Waterloo)

    [36]

    Herzberg G. 1950 Molecular Spectra and Molecular Structure I. Spectra of Diatomic Molecules(New York: Van Nostrand Reinhold) p658

    [37]

    Murrel J N, Carter S, Farantos S C, Huxley P, Varandas A J C 1984 Molecular Potential Energy Functions (Wiley: Chichester, U. K.) p9

    [38]

    7D-Soft High Technology, Inc. 1st Opt User Manual (V.6.0) Beijing, People’s Republic of China, 2014

  • 图 1  BeC分子5个电子态的势能曲线(1 Hartree = 2625.4984 kJ/mol)

    Fig. 1.  Potential energy curves of five states of BeC molecule (1 Hartree = 2625.4984 kJ/mol).

    图 2  BeC分子5个电子态的偶极矩(1 Debye = 3.336 × 10–30 C·m)

    Fig. 2.  Dipole moments of five electronic states of BeC(1 Debye = 3.336 × 10–30 C·m).

    图 3  BeC分子基态的Mulliken电荷分布

    Fig. 3.  Mulliken population for the ground state BeC molecule.

    图 4  跃迁偶极距曲线

    Fig. 4.  Transition dipole moment curves.

    表 1  BeC分子6个态的离解极限关系

    Table 1.  Dissociation relationship of six electronic states of BeC molecule.

    原子态 $ {\text{Λ}}{\text{-}}{\rm S}$态 相对能量/cm–1
    本文 (无Q) 本文 (+Q) 实验值[34]
    Be(1Sg)+C(3Pg) $ {{\rm{X}}^3} {{\text{Σ}} ^ - } $, ${\rm{A}}^3 {\text{Π}}$ 0 0
    Be(1Sg)+C(1Dg) $ {{\rm{b}}^1} {{\text{Δ}} } $, ${{\rm{c}}^1} {\text{Π}}$, $ {{\rm{d}}^1}{{\text{Σ}} ^ + } $ 10124.12 10169.70 10192.66
    Be(1Sg)+C(1Sg) ${2^1}{{\text{Σ}} ^ + } $ 21679.58 21581.62 21648.03
    下载: 导出CSV

    表 2  BeC分子$ {{\rm{X}}^3}{\text{Σ}} $, ${{\rm{A}}^3}{\text{Π}}$, $ {{\rm{b}}^1} {{\text{Δ}} } $, ${{\rm{c}}^1} {\text{Π}}$$ {{\rm{d}}^1}{{\text{Σ}} ^ + } $等5个态的光谱参数

    Table 2.  Spectroscopic constants of the five states of BeC molecule.

    Te/cm–1Re/nm${\omega _{\rm{e}}}$/cm–1$ {\omega _{\rm{e}}}{x_{\rm{e}}} $/cm–1102${\omega _{\rm{e}}}$уe/cm–1Be/cm–1$ {10^3}{\alpha _{\rm{e}}}$/cm–1De/eV
    ${{{\rm{X}}^3}{\text{Σ}}^- } $00.1673918.087.35017.871.178315.6442.1873
    Cal. [6]00.1661937.99.61.19
    Cal. [7]00.16939052.04
    Cal. [8]00.16679518.421.1832.39
    Cal. [10]00.168392511.252.14
    Cal. [19]00.16802.04
    ${{\rm{A}}^3}{\text{Π}}$8916.350.1771772.748.692199.891.051828.3671.0777
    Cal. [7]9033.410.17990.92
    Cal. [8]94660.175676414.691.07521.16
    Cal. [10]89610.179187426.261.03
    $ {{\rm{b}}^1}{\text{Δ}} $7823.390.1675933.508.3017.561.171416.7002.4408
    Cal. [7]8872.100.16939042.27
    Cal. [8]87320.16689567.61.17572.63
    $ {{\rm{c}}^1}{\text{Π}} $10909.210.1760834.807.1389.201.055114.3652.0933
    Cal. [7]11291.760.17788181.97
    Cal. [8]116180.17588476.941.06122.24
    $ {{\rm{d}}^1}{{\text{Σ}} ^ + } $12139.140.16698936.2117.553126.981.176416.0001.9060
    Cal. [7]12582.240.16939051.81
    Cal. [8]135790.1679557.31.17322.02
    注: Cal. 为理论计算值.
    下载: 导出CSV

    表 3  ${{\rm{A}}^3}{\text{Π}}$$ {{\rm{X}}^3} {{\text{Σ}} ^ - } $, ${{\rm{c}}^1}{\text{Π}}$$ {{\rm{b}}^1} {{\text{Δ}} } $, $ {{\rm{d}}^1}{{\text{Σ}} ^ + } $${{\rm{c}}^1}{\text{Π}}$跃迁的弗兰克-康登因子

    Table 3.  Franck-condon factor for ${{\rm{A}}^3}{\text{Π}}$$ {{\rm{X}}^3} {{\text{Σ}} ^ - } $, ${{\rm{c}}^1}{\text{Π}}$$ {{\rm{b}}^1}{{\text{Δ}} } $, $ {{\rm{d}}^1}{{\text{Σ}} ^ + } $${{\rm{c}}^1}{\text{Π}}$ transitions.

    $\nu '$—$ \nu ''$FC$\nu '$—$ \nu ''$FC$\nu '$—$ \nu ''$FC$\nu '$—$ \nu ''$FC$\nu '$—$ \nu ''$FC$\nu '$— $ \nu ''$FC
    ${\rm{A}}^3 {\text{Π}}$—${\rm{X}}^3 {\text{Σ}}^-$
    0—00.54390—10.36531—00.30491—20.41431—30.16702—00.1080
    2—10.26602—30.36012—40.22763—20.16543—40.29083—50.2691
    4—20.17634—50.22554—60.29935—30.15615—60.16395—70.3216
    6—30.10706—40.12736—60.13396—70.10526—80.33486—90.1183
    7—40.10957—50.10007—70.16187—90.33427—100.1531
    ${{\rm{c}}^1}{\text{Π}}$ —${{\rm{b}}^1}{\text{Δ}}$
    0—00.62370—10.31531—00.27011—10.17401—20.39991—30.1368
    2—10.26892—30.34702—40.23223—10.15183—20.18033—40.2122
    3—50.29644—20.18944—40.10274—50.10454—60.30424—70.1238
    5—30.16345—50.14355—70.31386—30.12366—40.12686—60.1567
    6—80.29687—40.12897—70.14957—90.26908—50.12198—80.1212
    8—100.23809—110.202510—120.1699
    ${{\rm{d}}^1}{\text{Σ}}$—${{\rm{c}}^1}{\text{Π}}$
    0—00.61640—10.27171—00.32321—10.16931—20.26172—10.4016
    2—30.16992—40.18503—10.39013—20.35133—50.15104—20.2362
    4—30.21564—40.10734—60.10685—30.30145—40.10115—50.1501
    6—40.31096—60.16137—40.12927—50.31757—70.14428—50.1801
    8—60.29458—80.10549—60.21929—70.261210—70.256310—80.2265
    下载: 导出CSV

    表 4  ${\rm{A}}^3 {\text{Π}}$, $ {{\rm{b}}^1} {{\text{Δ}} } $, ${{\rm{c}}^1}{\text{Π}}$$ {{\rm{d}}^1}{{\text{Σ}} ^ + } $态几个振动能级的辐射寿命

    Table 4.  Radiative lifetime of the vibrational energy levels for ${\rm{A}}^3 {\text{Π}}$, $ {{\rm{b}}^1} {{\text{Δ}} } $, ${{\rm{c}}^1} {\text{Π}}$ and $ {{\rm{d}}^1}{{\text{Σ}} ^ + } $states.

    跃迁辐射寿命$/{{\text{μ}}{\rm{ s}}}$
    $\nu '$ = 0$\nu '$ = 1$\nu '$ = 2$\nu '$ = 3$\nu '$ = 4$\nu '$ = 5$\nu '$ = 6$\nu '$ = 7
    ${\rm{A}}^3 {\text{Π}}$—${{\rm{X}}^3}{{\text{Σ}} ^ - }$14.6614.6414.4613.8212.9912.1611.6511.31
    Cal.[10]14.014.515.6
    ${{\rm{c}}^1} {\text{Π}}$—$ {{\rm{b}}^1} {{\text{Δ}} } $191.10166.59161.38159.48151.88176.09197.32239.85
    ${{\rm{c}}^1} {\text{Π}}$—$ {{\rm{d}}^1}{{\text{Σ}} ^ + } $2730.001010.00630.00460.00380.00330280.00230.00
    下载: 导出CSV

    表 5  BeC分子基态解析势能函数参数值

    Table 5.  The values for the analytic parameters for the ground state of BeC molecule.

    参数C1C2C3C4C5
    参数值4.5847206886.8251733754.9797806622.0123720551.900852427
    参数C6C7C8C9C10
    参数值–5.415648763–6.03351734512.82526525–6.0864348930.939009741
    下载: 导出CSV
  • [1]

    Borodin D, Doerner R, Nishijima D, Kirschner A, Kreter A, Matveev D, Galonska A, Philipps V 2011 J. Nucl. Mater. 415 219Google Scholar

    [2]

    Conn R W, Doerner R P, Won J 1997 Fusion Eng. Des. 37 481

    [3]

    Chen M D, Li X B, Yang J, Zhang Q E, Au C T 2006 Int. J. Mass Spectrom. 253 30Google Scholar

    [4]

    Chen M D, Li X B, Yang J, Zhang Q E 2006 J. Phys. Chem. A 110 4502

    [5]

    Zhang C J 2006 J. Mol. Struc.: Theochem. 759 201Google Scholar

    [6]

    Barker B J, Antonov I O, Merritt J M, Bondybey V E, Heaven M C, Dawes R 2012 J. Chem. Phys. 137 214313Google Scholar

    [7]

    Wright J S, Kolbuszewski M 1993 J. Chem. Phys. 98 9725Google Scholar

    [8]

    Borin A C, Ornellas F R 1993 J. Chem. Phys. 98 8761Google Scholar

    [9]

    da Silva C O, Teixeira F E C, Azevedo, J A T, Da Silva E C, Nascimento M A C 1996 Int. J. Quant. Chem. 60 433Google Scholar

    [10]

    Pelegrini M, Roberto-Neto O, Ornellas F R, Machado F B C 2004 Chem. Phys. Lett. 383 143Google Scholar

    [11]

    Wells N, Lane I C 2011 Phys. Chem. Chem. Phys. 13 19036Google Scholar

    [12]

    Koch W, Frenking G, Gauss J, Cremer D, Sawaryn A, Schleyer P V R 1986 J. Am. Chem. Soc. 108 5732Google Scholar

    [13]

    Fioressi S E, Binning Jr R C, Bacelo D E 2014 Chem. Phys. 443 76Google Scholar

    [14]

    Patrick A D, Williams P, Blaisten-Barojas E 2007 J. Mol. Struc.: Theochem. 824 39Google Scholar

    [15]

    Ghouri M M, Yareeda L, Mainardi D S 2007 J. Phys. Chem. A 111 13133Google Scholar

    [16]

    Midda S, Das A K 2004 J. Mol. Spectrosc. 224 1Google Scholar

    [17]

    Borin A C, Ornellas F R 1995 Chem. Phys. 190 43Google Scholar

    [18]

    Borin A C, Ornellas F R A 1995 J. Mol. Struc.: Theochem 335 107Google Scholar

    [19]

    Teberekidis V I, Kerkines I S K, Carsky P, Tsipis C A, Mavridis A 2005 Int. J. Quant. Chem. 102 762Google Scholar

    [20]

    Deskevich M P, Nesbitt D J, Werner H J 2004 J. Chem. Phys. 120 7281Google Scholar

    [21]

    Dawes R, Jasper A W, Tao C, Richmond C, Mukarakate C, Kable S H, Reid S A 2010 J. Phys. Chem. Lett. 1 641Google Scholar

    [22]

    Werner H J, Knowles P J 1988 J. Chem. Phys. 89 5803Google Scholar

    [23]

    Knowles P J, Werner H J 1988 Chem. Phys. Lett. 145 514Google Scholar

    [24]

    Werner H J, Knowles P, Knizia G, Manby F R, Schütz M, Celani P, Korona T, Lindh R, Mitrushenkov A, Rauhut G 2010 Molpro Version 2010.1: A Package of ab initio Programs

    [25]

    Peterson K A, Wilson A K, Woon D E, Dunning Jr T H 1997 Theor. Chem. Acc. 97 251Google Scholar

    [26]

    Woon D E, Dunning Jr T H 1995 J. Chem. Phys. 103 4572Google Scholar

    [27]

    Prascher B P, Woon D E, Peterson K A, Dunning T H, Wilson A K 2011 Theor. Chem. Acc. 128 69Google Scholar

    [28]

    Karton A, Martin J M L. 2006 Theor. Chem. Acc. 115 330Google Scholar

    [29]

    Halkier A, Helgaker T, Jørgesen P, Klopper W, Koch H, Olsen J, Wilson A K 1998 Chem. Phys. Lett. 286 243Google Scholar

    [30]

    Nakajima T, Hirao K 2000 J. Chem. Phys. 113 7786Google Scholar

    [31]

    Fedorov D G, Nakajima T, Hirao K 2003 J. Chem. Phys. 118 4970Google Scholar

    [32]

    Paulovic J, Nakajima T, Hirao K, Lindh R, Malmqvist P Å 2003 J. Chem. Phys. 119 798Google Scholar

    [33]

    NIST, Atomic Spectra Database, see http://www.nist.gov/pml/data/asd.cfm (2012)

    [34]

    Haris K, Kramida A, 2017 Astrophys. J. Suppl. S. 233 16Google Scholar

    [35]

    LeRoy R J 2010 LEVEL 8.0: A Computer Program for Solving the Radial Schrödinger Equation for Bound and Quasibound Levels, Chemical Physics: Research Report CP-663 (Ontario: University of Waterloo)

    [36]

    Herzberg G. 1950 Molecular Spectra and Molecular Structure I. Spectra of Diatomic Molecules(New York: Van Nostrand Reinhold) p658

    [37]

    Murrel J N, Carter S, Farantos S C, Huxley P, Varandas A J C 1984 Molecular Potential Energy Functions (Wiley: Chichester, U. K.) p9

    [38]

    7D-Soft High Technology, Inc. 1st Opt User Manual (V.6.0) Beijing, People’s Republic of China, 2014

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出版历程
  • 收稿日期:  2018-09-11
  • 修回日期:  2018-12-19
  • 上网日期:  2019-03-01
  • 刊出日期:  2019-03-05

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