O2分子B3u-态势能曲线的从头计算

李晨曦; 郭迎春; 王兵兵

doi:10.7498/aps.66.103101

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摘要

B3u-态是O2的最强的三重跃迁（B3u-X3g-） Schumann-Runge（SR）带的上态，SR吸收带在保护地球、阻止紫外辐射等方面起着关键作用.SR连续带的光解离是平流层O原子及O3的主要来源，掌握详细准确的O2分子的电子态势能曲线，有助于对这些光谱现象的深入理解.本文通过MOLPRO 软件，采用包含Davison修正的内收缩的多参考组态相互作用（icMRCI+Q）方法，对O2的B3u-态的势能曲线进行了计算，采用的多参考组态函数来自完全活性空间自洽场计算.首先，采用共价组态构成多参考组态，对和B3u-态对称性相同的四个态进行了态平均计算，发现B3u-态不存在双势阱结构，文献（Spectrochimica Acta Part A： Molecular and Biomolecular Spectroscopy 2014 124 216）中双势阱的产生是根的振荡（root flipping）造成的，即B3u- 态的势能曲线在核间距约为0.2 nm处跳变到能量相近的23 态的势能曲线上.本文中的态平均计算避免了这种根的振荡.接着，采用完全活性空间组态相互作用的方法计算B3u- 态的势能曲线，通过改变活性空间的轨道组成，发现带有2u轨道电子布居的里德伯组态对B3u-态的束缚态的特征的出现是必不可少的.最后，通过将2u轨道加入到活性空间中，实现将相关的里德伯组态加入到多参考组态，对B3u-态的势能曲线进行了icMRCI+Q计算，得到相较于以往的理论计算与实验值更加相近的势能曲线以及光谱常数.本文探讨里德伯组态贡献的过程为如何确定多参考组态相互作用计算中的参考组态、提高理论计算的准确度提供了可以借鉴的途径.

关键词:

作者及机构信息

1.
华东师范大学物理与材料科学学院, 上海 200241;

2.
中国科学院物理研究所, 凝聚态物理国家重点实验室, 光物理实验室, 北京 100190

通信作者: 郭迎春, ycguo@phy.ecnu.edu.cn

基金项目: 国家自然科学基金（批准号：11474348，61275128）资助的课题.

参考文献

[1]	Suzuki D, Kato H, Ohkawa M, Anzai K, Tanaka H, Vieira P, Campbell L, Brunger M J 2011 J. Chem. Phys. 134 064311
[2]	Krupenie P H 1972 J. Phys. Chem. Ref. Data 1 423
[3]	Lewis B R, Gibson S T, Slanger T G, Huestis D L 1999 J. Chem. Phys. 110 11129
[4]	Chiu S S, Cheung A S, Finch M, Jamieson M J, Yoshino K, Dalgarno A, Parkinson W H 1992 J. Chem. Phys. 97 1787
[5]	Lewis B R, Gibson S T, Dooley P M 1994 J. Chem. Phys. 100 7012
[6]	Lewis B R, Berzins L, Carver J H 1986 J. Quant. Spectrosc. Radiat. Transfer 36 209
[7]	Saxon R P, Liu B 1977 J. Chem. Phys. 67 5432
[8]	Buenker R J, Peyerimhoff S D, Peric M 1976 Chem. Phys. Lett. 42 383
[9]	Tatewaki H, Tanaka K, Sasaki F, Obara S, Ohno K, Yoshimine M 1979 Int. J. Quantum Chem. 15 533
[10]	Muller T, Dallos M, Lischka H, Dubrovay Z, Szalay P G 2001 Theor. Chem. Acc. 105 227
[11]	Liu H, Shi D S, Sun J F, Zhu Z L, Zhang S L 2014 Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 124 216
[12]	Langhoff S R, Davidson E R 1974 Mol. Int. J. Quantum Chem. 8 61
[13]	Werner H J, Knowles P J 1984 J. Chem. Phys. 82 5053
[14]	Knowles P J, Werner H J 1985 Chem. Phys. Lett. 115 259
[15]	Werner H J, Meyer W 1981 J. Chem. Phys. 74 5794
[16]	LeRoy R J 2002 University of Waterloo Chemical Physics Research Report CP-655
[17]	Woon D E, Dunning T H 1994 J. Chem. Phys. 100 2975
[18]	Halkier A, Helgaker T, Jrgensen P, Klopper W, Koch H, Olsen J, Wilson A K 1998 Chem. Phys. Lett. 286 243
[19]	Woon D E, Dunning Jr T H 1995 J. Chem. Phys. 103 4572
[20]	Jong W D, Harrison R J, Dixon D A 2001 J. Chem. Phys. 114 48
[21]	Kiljunen T, Eloranta J, Khriachtchev H K, Pettersson M, Rsnen M 2000 J. Chem.Phys. 112 7475
[22]	Yan B, Pan S P, Wang Z G, Yu J H 2005 Acta Phys. Sin. 54 5618 (in Chinese) [闫冰, 潘守甫, 王志刚, 于俊华 2005 物理学报 54 5618]
[23]	Minaev B F, Minaeva V A 2001 Phys. Chem. Chem. Phys. 3 720

施引文献

[1]	Suzuki D, Kato H, Ohkawa M, Anzai K, Tanaka H, Vieira P, Campbell L, Brunger M J 2011 J. Chem. Phys. 134 064311
[2]	Krupenie P H 1972 J. Phys. Chem. Ref. Data 1 423
[3]	Lewis B R, Gibson S T, Slanger T G, Huestis D L 1999 J. Chem. Phys. 110 11129
[4]	Chiu S S, Cheung A S, Finch M, Jamieson M J, Yoshino K, Dalgarno A, Parkinson W H 1992 J. Chem. Phys. 97 1787
[5]	Lewis B R, Gibson S T, Dooley P M 1994 J. Chem. Phys. 100 7012
[6]	Lewis B R, Berzins L, Carver J H 1986 J. Quant. Spectrosc. Radiat. Transfer 36 209
[7]	Saxon R P, Liu B 1977 J. Chem. Phys. 67 5432
[8]	Buenker R J, Peyerimhoff S D, Peric M 1976 Chem. Phys. Lett. 42 383
[9]	Tatewaki H, Tanaka K, Sasaki F, Obara S, Ohno K, Yoshimine M 1979 Int. J. Quantum Chem. 15 533
[10]	Muller T, Dallos M, Lischka H, Dubrovay Z, Szalay P G 2001 Theor. Chem. Acc. 105 227
[11]	Liu H, Shi D S, Sun J F, Zhu Z L, Zhang S L 2014 Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 124 216
[12]	Langhoff S R, Davidson E R 1974 Mol. Int. J. Quantum Chem. 8 61
[13]	Werner H J, Knowles P J 1984 J. Chem. Phys. 82 5053
[14]	Knowles P J, Werner H J 1985 Chem. Phys. Lett. 115 259
[15]	Werner H J, Meyer W 1981 J. Chem. Phys. 74 5794
[16]	LeRoy R J 2002 University of Waterloo Chemical Physics Research Report CP-655
[17]	Woon D E, Dunning T H 1994 J. Chem. Phys. 100 2975
[18]	Halkier A, Helgaker T, Jrgensen P, Klopper W, Koch H, Olsen J, Wilson A K 1998 Chem. Phys. Lett. 286 243
[19]	Woon D E, Dunning Jr T H 1995 J. Chem. Phys. 103 4572
[20]	Jong W D, Harrison R J, Dixon D A 2001 J. Chem. Phys. 114 48
[21]	Kiljunen T, Eloranta J, Khriachtchev H K, Pettersson M, Rsnen M 2000 J. Chem.Phys. 112 7475
[22]	Yan B, Pan S P, Wang Z G, Yu J H 2005 Acta Phys. Sin. 54 5618 (in Chinese) [闫冰, 潘守甫, 王志刚, 于俊华 2005 物理学报 54 5618]
[23]	Minaev B F, Minaeva V A 2001 Phys. Chem. Chem. Phys. 3 720

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O2分子B3u-态势能曲线的从头计算

1. 华东师范大学物理与材料科学学院, 上海 200241;

2. 中国科学院物理研究所, 凝聚态物理国家重点实验室, 光物理实验室, 北京 100190

通信作者: 郭迎春, ycguo@phy.ecnu.edu.cn

基金项目:

国家自然科学基金（批准号：11474348，61275128）资助的课题.

收稿日期: 2017-01-27

修回日期: 2017-03-15

刊出日期: 2017-05-05

摘要: B3u-态是O2的最强的三重跃迁（B3u-X3g-） Schumann-Runge（SR）带的上态，SR吸收带在保护地球、阻止紫外辐射等方面起着关键作用.SR连续带的光解离是平流层O原子及O3的主要来源，掌握详细准确的O2分子的电子态势能曲线，有助于对这些光谱现象的深入理解.本文通过MOLPRO 软件，采用包含Davison修正的内收缩的多参考组态相互作用（icMRCI+Q）方法，对O2的B3u-态的势能曲线进行了计算，采用的多参考组态函数来自完全活性空间自洽场计算.首先，采用共价组态构成多参考组态，对和B3u-态对称性相同的四个态进行了态平均计算，发现B3u-态不存在双势阱结构，文献（Spectrochimica Acta Part A： Molecular and Biomolecular Spectroscopy 2014 124 216）中双势阱的产生是根的振荡（root flipping）造成的，即B3u- 态的势能曲线在核间距约为0.2 nm处跳变到能量相近的23 态的势能曲线上.本文中的态平均计算避免了这种根的振荡.接着，采用完全活性空间组态相互作用的方法计算B3u- 态的势能曲线，通过改变活性空间的轨道组成，发现带有2u轨道电子布居的里德伯组态对B3u-态的束缚态的特征的出现是必不可少的.最后，通过将2u轨道加入到活性空间中，实现将相关的里德伯组态加入到多参考组态，对B3u-态的势能曲线进行了icMRCI+Q计算，得到相较于以往的理论计算与实验值更加相近的势能曲线以及光谱常数.本文探讨里德伯组态贡献的过程为如何确定多参考组态相互作用计算中的参考组态、提高理论计算的准确度提供了可以借鉴的途径.

关键词:

Ab initio calculation of the potential curve of B3u- state of O2

1.
School of Physics and Materials Science, East China Normal University, Shanghai 200241, China;

2.
Laboratory of Optical Physics, Beijing National Laboratory of Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China

Fund Project:

Project supported by the National Natural Science Foundation of China (Grant Nos. 11474348, 61275128).

Received Date: 27 January 2017

Accepted Date: 15 March 2017

Published Online: 05 May 2017

Abstract: The B3u- state of O2 molecule is an upper state of the most strongly allowed triplet-triplet (B3u-X3g-) absorption, the Schumann-Runge (SR) transition, which plays a crucial role in protecting the earth from suffering UV radiation. Photo-dissociation of O2 molecule in the SR transition is the major source of odd oxygen (O and O3) in the stratosphere. Comprehensive knowledge of the electronic states, especially their potential energy curves (PECs), is necessary to understand those phenomena. In this paper, we calculate the PEC of B3u- state of O2 by using the internally contracted multi-reference configuration interaction including Davison correction method, which is denoted by icMRCI+Q, and utilize the complete active space self-consistent field (CASSCF) function as a reference function. The calculation is implemented in the MOLPRO suite of codes. Firstly, we carry out the state-averaged (SA) calculation on the four lowest states, A'3u, B3u-, 23u and 23u- states, which are in the same irreducible representation of symmetric group. The active space of CASSCF consists of full valence space. The augmented correlation-consistent aug-cc-pV5Z basis set is used. The results show that the PEC of B3u- state does not displays double well structure, which is contradictory to Liu's result (Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 2014 124 216). By analyzing the PEC structure, we find that the double well of Liu's result comes from the root flipping, that is, the PEC interchange from B3u- state into 23u state. In our case the root flipping is avoided by the SA calculation. Secondly, in order to ensure that the most important configurations are included in the reference function, we calculate the PEC of B3u- state of O2 molecule at CASSCF/aug-cc-pVTZ level by changing the active space. We find that the bound well of the PEC will not appear unless the active space includes 2u orbital which is beyond the full valence space. That means that the Rydberg configurations including 2u orbital play a crucial role in forming the bound well. And the result is further improved by adding into the active space another two orbitals 4g and 4g whose orbital energies are both less than 2u. Finally, we add the Rydberg configurations into the multi-reference configuration function by putting 2u, 4g, 4u into the active space and then carry out the calculation at an icMRCI+Q/aug-cc-pVTZ level. The obtained B3u- state PEC and its spectroscopic constants are in good agreement with the experimental data compared with previous results. Moreover, the process we determine the reference configurations is useful for making accurate calculation at an MRCI level on other species.

Keywords:

B3u- state of O2 /
internally contracted multi-reference configuration interaction /
potential energy curve /
spectroscopic constants

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