含碳三原子分子结构与电子亲和能的计算

单石敏; 连艺; 徐海峰; 闫冰

doi:10.7498/aps.73.20231871

摘要

本文分别采用单、双和微扰处理三激发耦合簇方法与自旋非限制的开壳层耦合簇方法对CO₂, OCS, CS₂及其对应阴离子${\text{CO}}_2^ - $, ${\mathrm{OC}}{{\mathrm{S}}^ - }$, $ {\mathrm{C}}{\text{S}}_2^ - $进行高精度的从头算研究. 我们计算了这些分子在一系列相关一致基组aug-cc-pV(X+d)Z (X = T, Q, 5) 以及完全基组极限下的基态平衡几何结构, 并研究了芯-价电子相关与标量相对论效应的影响, 计算结果与已有文献报道结果吻合较好. 基于计算的几何结构, 获得了中性分子CO₂, OCS, CS₂的绝热电子亲和能, 系统考察了不同基组以及零点能修正对这些分子电子亲和能的影响, 给出了考虑各种修正下3种分子准确的电子亲和能. 本文将丰富含碳三原子分子的光谱常数和电子亲和能等分子参数的信息, 可为实验光谱研究提供重要参考.

关键词:

Abstract

The accurate measurement and calculation of molecular electron affinity has been a hot topic. The existing theoretical study does not consider the effects of different basic sets, or various correlation effects or zero point energy correction. In addition, there are some deviations of calculation results from experimental measurements. Therefore, we conduct a high-level ab initio study on the electron affinities of CO₂, OCS, CS₂ and their corresponding anions $ {\text{CO}}_{2}^{{ - }} $, OCS^–, $ {\text{CS}}_{2}^{{ - }} $ by adopting the coupled cluster with singles and doubles (triples) (CCSD(T)), spin-unrestricted open-shell coupled cluster with singles and doubles (triples) (UCCSD(T)), respectively. The equilibrium geometries of the ground states of these molecules are calculated under a series of extended correlation consistent basis sets aug-cc-pV (X+d)Z (X = T, Q, 5) and complete basis set extrapolation (CBS) limit. The effects of core-valence (CV) electron correlation and scalar relativistic (SR) on equilibrium geometry of the ground state are studied, and our results are compared with previous experimental observations and theoretical data. Our calculations are in good agreement with the previous results. It is found that the calculations of equilibrium geometries of these molecules tend to converge. It is noted that the scalar relativistic effect has little influence on the equilibrium structure of the neutral molecule, but it has more significant influence on the bond angle of $ {\text{CS}}_{2}^{{ - }} $.With the increase of atomic number, the core-valence correlation effect exerts a more remarkable influence on the equilibrium structures of ground states of CS₂ and $ {\text{CS}}_{2}^{{ - }} $ molecules except for R_C-S of OCS^–. Based on accurate structures, the adiabatic energy values of neutral molecules CO₂, OCS, CS₂ by CCSD(T) method and those of $ {\text{CO}}_{2}^{{ - }} $, OCS^–, $ {\text{CS}}_{2}^{{ - }} $ by using UCCSD(T) and spin-restricted open-shell coupled cluster with singles and doubles (triples) (RCCSD(T)) are calculated, respectively. And finally, the adiabatic electron affinities (EAs) of the neutral molecules CO₂, OCS, CS₂ are obtained. The effects of different basis sets, CBS, correlation effects and zero-point energy correction on the EA values of these molecules are investigated. It is found that both the scalar relativistic effect and the core-valence correlation effect affect the EAs of neutral molecules, and the core-valence correlation effect has a more significant effect on the EA value. The results show that the correlation effect has more significant influence on the adiabatic EA than the equilibrium structure of the ground state of neutral molecules. Based on the CBS+ΔCV+ΔDK+ΔZPE calculation, accurate EA information is acquired. Our results of EA values are within the experimental error. This work will enrich the information about spectral constants and electron affinities of carbon-containing triatomic molecules, and provide an important reference for experimental spectral analysis.

Keywords:

作者及机构信息

1.
中北大学半导体与物理学院, 太原　030051

2.
吉林大学原子与分子物理研究所, 长春　130012

通信作者: 徐海峰, xuhf@jlu.edu.cn ; 闫冰, yanbing@jlu.edu.cn

基金项目: 国家自然科学基金(批准号: 11874177, 12174148, 12274178)和山西省基础研究计划(批准号: 202203021212116)资助的课题.

Authors and contacts

1.
School of Semiconductors and Physics, North University of China, Taiyuan 030051, China

2.
Institute of Atomic and Molecular Physics, Jilin University, Changchun 130012, China

Corresponding author: Xu Hai-Feng, xuhf@jlu.edu.cn ; Yan Bing, yanbing@jlu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11874177, 12174148, 12274178) and the Fundamental Research Program of Shanxi Province, China (Grant No. 202203021212116).

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参考文献

[1]	Rienstra K J C, Tschumper G S, Schaefer H F, Nandi S, Ellison G B 2002 Chem. Rev. 102 231 Google Scholar
[2]	Cahen D, Kahn A 2003 Adv. Mater. 15 271 Google Scholar
[3]	Ru P B, Bi E, Zhang Y, Wang Y B, Kong W Y, Tang W T, Zhang P, Wu Y Z, Chen W, Yang X D, Chen H, Han L Y 2020 Adv. Energy Mater. 10 1903487 Google Scholar
[4]	Compton R N, Reinhardt P W, Cooper C D 1975 J. Chem. Phys. 63 3821 Google Scholar
[5]	Holroyd R A, Cangwer T E, Allen A O 1975 Chem. Phys. Lett. 31 520 Google Scholar
[6]	Surber E, Sanov A 2002 J. Chem. Phys. 116 5921 Google Scholar
[7]	Chen E C M, Wentworth W E 1983 J. Phys. Chem. 87 45 Google Scholar
[8]	Hughes B M, Lifshitzt C, Tiernan T O 1973 J. Chem. Phys. 59 3162 Google Scholar
[9]	Oakes J M, Barney Ellison G 1986 Tetrahedron. 42 6263 Google Scholar
[10]	Schiedt J, Weinkauf R 1997 Chem. Phys. Lett. 274 18 Google Scholar
[11]	Misaizu F, Tsunoyama H, Yasumura Y, Ohshimo K, Ohno K 2004 Chem. Phys. Lett. 389 241 Google Scholar
[12]	Cavanagh S J, Gibson S T, Lewis B R 2012 J. Chem. Phys. 137 144304 Google Scholar
[13]	Herzberg G 1966 Molecular Spectra & Molecular Structure III (Polyatomic Molecules) (New York: Van Nostrand Reinhold) p145
[14]	Hartman K O, Hisatsune I C 1966 J. Chem. Phys. 44 1913 Google Scholar
[15]	Ovenall D W, Whiffen D H 1961 Mol. Phys. 4 135 Google Scholar
[16]	Lahaye J G, Vandenhaute R, Fayt A 1987 J. Mol. Spectrosc. 123 48 Google Scholar
[17]	Suzuki I 1975 Bull. Chem. Soc. Jpn. 48 1685 Google Scholar
[18]	Bennett J E, Mile B, Thomas A 1967 Trans. Faraday Soc. 63 262 Google Scholar
[19]	Yu D, Rauk A, Armstrong D A 1992 J. Phys. Chem. 96 6031 Google Scholar
[20]	Gutsev G L, Bartlett R J, Compton R N 1998 J. Chem. Phys. 108 6756 Google Scholar
[21]	Barsotti S, Sommerfeld T, Ruf M W, Hotop H 2004 Int. J. Massspectrom. 233 181
[22]	Pacansky J, Wahlgren U, Bagus P S 1975 J. Chem. Phys. 62 2740 Google Scholar
[23]	Yoshioka Y, Schaefer H F, Jordan K D 1981 J. Chem. Phys. 75 1040 Google Scholar
[24]	Surber E, Ananthavel S P, Sanov A 2002 J. Chem. Phys. 116 1920 Google Scholar
[25]	Joachim W H, Knowles P J, Knizia G, Manby F R, Schütz M 2012 Wiley Interdiscip. Rev. : Comput. Mol. Sci. 2 242 Google Scholar
[26]	Bartlett R J, Watts J D, Kucharski S A, Noga J 1990 Chem. Phys. Lett. 165 513 Google Scholar
[27]	Dunning T H, Peterson K A, Wilson A K 2001 J. Chem. Phys. 114 9244 Google Scholar
[28]	Fellera D, Peterson K A, Daniel C T 2006 J. Chem. Phys. 124 054107 Google Scholar
[29]	Fellera D, Peterson K A 2007 J. Chem. Phys. 126 114105 Google Scholar
[30]	Peterson K A, Woon D E, Dunning T H 1994 J. Chem. Phys. 100 7410 Google Scholar
[31]	Dunning T H 1989 J. Chem. Phys. 90 1007 Google Scholar
[32]	Reiher M, Wolf A 2004 J. Chem. Phys. 121 2037 Google Scholar
[33]	Wolf A, Reiher M, Hess B A 2002 J. Chem. Phys. 117 9215 Google Scholar
[34]	Peterson K A, Dunning T H 2002 J. Chem. Phys. 117 10548 Google Scholar
[35]	Lu T, Chen F W 2012 J. Comput. Chem. 33 580 Google Scholar

施引文献

图 1 (a) CO₂基态分子轨道图; (b) OCS基态分子轨道图; (c) CS₂基态分子轨道图

Fig. 1. (a) Molecular orbital of the ground state of CO₂; (b) molecular orbital of the ground state of OCS; (c) molecular orbital of the ground state of CS₂.

下载: 全尺寸图片幻灯片

图 2 (a) $ {\text{CO}}_2^ - $基态分子轨道图; (b) $ {\mathrm{OC{S}}^ - } $基态分子轨道图; (c) $ {\mathrm{C}}{\text{S}}_2^ - $基态分子轨道图

Fig. 2. (a) Molecular orbital of the ground state of $ {\text{CO}}_2^ - $; (b) molecular orbital of the ground state of $ {\mathrm{OC{S}}^ - } $; (c) molecular orbital of the ground state of $ {\mathrm{C}}{\text{S}}_2^ - $.

下载: 全尺寸图片幻灯片

表 1 CO₂, OCS, CS₂及其阴离子在不同基组与CBS极限下基态的键长与键角

Table 1. Equilibrium bond distance and bond angle of the ground state of CO₂, OCS, CS₂ and the corresponding anions as a function of different basis sets and CBS limit.

		AV(T+d)Z	AV(Q+d)Z	AV(5+d)Z	CBS
CO₂	R_C-O/Å	1.167	1.163	1.162	1.162
${\text{CO}}_2^ - $	R_C-O/Å	1.237	1.232	1.231	1.230
	∠OCO/(°)	137.6	137.7	137.8	137.9
OCS	R_C-O/Å	1.163	1.159	1.158	1.158
	R_C-S/Å	1.571	1.567	1.566	1.565
${\mathrm{OCS}}^{ - } $	R_C-O/Å	1.214	1.210	1.209	1.208
	R_C-S/Å	1.710	1.705	1.703	1.701
	∠OCS/(°)	136.5	136.4	136.5	136.5
CS₂	R_C-S/Å	1.562	1.558	1.557	1.555
$ {\text{CS}}_{2}^{{ - }} $	R_C-S/Å	1.641	1.636	1.634	1.633
	∠SCS/(°)	143.3	143.5	143.6	143.7

下载: 导出CSV

表 2 CO₂, OCS, CS₂及其应阴离子在不同关联效应下基态的键长与键角

Table 2. Equilibrium bond distance and bond angle of the ground state of CO₂, OCS, CS₂ and the corresponding anions as a function of different correlation effect.

		本工作计算结果				其他计算结果	实验结果
		CBS	ΔCV	ΔDK	Total	其他计算结果	实验结果
CO₂	R_C-O/Å	1.162	–0.002	0	1.160	1.143 ^[19]/1.179^[19]/1.1614 ^[20]/1.164^[20]/1.167 ^[21]	1.162 ^[13]
$ {\text{CO}}_{2}^{{ - }} $	R_C-O/Å	1.230	–0.002	0	1.228	1.225^[19]/1.256^[19]/1.230^[20]/1.233^[20]/1.237^[21]	1.25 ^[14]
	∠OCO/(°)	137.9	0.1	0	138.0	135^[19]/134.2 ^[19]/137.9 ^[20]/137.7 ^[20]/136.7 ^[21]	134 ^[15]
OCS	R_C-O/Å	1.158	–0.002	0	1.156	1.158 ^[20]/1.161 ^[20])/1.163 ^[21]	1.156 ^[16]
	R_C-S/Å	1.565	–0.003	0	1.562	1.566 ^[20]/1.563 ^[20]/1.575 ^[21]	1.561 ^[16]
${\mathrm{OCS}}^{ - } $	R_C-O/Å	1.208	–0.002	0	1.206	1.208 ^[20]/1.209 ^[20]/1.213 ^[21]	—
	R_C-S/Å	1.701	–0.005	0	1.696	1.704 ^[20]/1.707 ^[20]/1.716 ^[21]	—
	∠OCS/(°)	136.5	0.1	0	136.6	136.5 ^[20]/136.3 ^[20]/136.2 ^[21]	—
CS₂	R_C-S/Å	1.555	–0.003	0	1.552	1.558 ^[20]/1.557 ^[20]/1.565 ^[21]	1.556 ^[17]
$ {\text{CS}}_{2}^{{ - }} $	R_C-S/Å	1.633	–0.004	0	1.629	1.635 ^[20]/1.630 ^[20]/1.646 ^[21]	—
	∠SCS/(°)	143.7	0.2	–0.1	143.8	144 ^[20]/145.2 ^[20]/142.7 ^[21]	141 ^[18]

下载: 导出CSV

表 3 CO₂分子的绝热电子亲和能以及与以往理论和实验数据对比

Table 3. Adiabatic electron affinity of CO₂ compared to previous theoretical and experimental data.

	绝热电子亲和能/eV
	UCCSD(T)	RCCSD(T)
AV(T+d)Z	–0.631	–0.654
AV(Q+d)Z	–0.630	–0.653
AV(5+d)Z	–0.624	–0.648
Q5-CBS	–0.616	–0.640
TQ5-CBS	–0.619	–0.643
ΔCV	–0.012
ΔDK	–0.003
ΔZPE	0.090
Total	–0.541^a)/–0.544^b)	–0.565^a)/–0.568^b)
Experiment	–0.6 ± 0.2 ^[4]/–0.44±0.2 ^[5]
Calculation	–0.36 ^[22]/–0.669 ^[20]/–0.544 ^[21]
注: ^a)Q5-CBS+ΔCV+ΔDK+ΔZPE result. ^b)TQ5-CBS+ΔCV+ΔDK+ΔZPE result.

下载: 导出CSV

表 5 CS₂分子的电子亲和能以及与以往理论和实验数据对比

Table 5. Adiabatic electron affinity of CS₂ compared to previous theoretical and experimental data.

	绝热电子亲和能/eV
	UCCSD(T)	RCCSD(T)
AV(T+d)Z	0.359	0.337
AV(Q+d)Z	0.399	0.377
AV(5+d)Z	0.407	0.384
Q5-CBS	0.417	0.394
TQ5-CBS	0.412	0.389
ΔCV	–0.013
ΔDK	–0.009
ΔZPE	0.053
Total	0.448 ^a)/0.443 ^b)	0.425 ^a)/0.420 ^b)
Experiment	0.6 ± 0.1 ^[7]/≤0.8 ^[10]/0.58±0.05 ^[11]/ 0.5525(13) ^[12]
Calculation	0.406 ^[20]/0.382 ^[20]/0.457 ^[21]/0.54 ^[11]
注: ^a)Q5-CBS+ΔCV+ΔDK+ΔZPE result. ^b)TQ5-CBS+ΔCV+ΔDK+ΔZPE result.

下载: 导出CSV

表 4 OCS分子的电子亲和能以及与以往理论和实验数据对比

Table 4. Adiabatic electron affinity of OCS compared to previous theoretical and experimental data.

	绝热电子亲和能/eV
	UCCSD(T)	RCCSD(T)
AV(T+d)Z	–0.098	–0.119
AV(Q+d)Z	–0.073	–0.095
AV(5+d)Z	–0.069	–0.091
Q5-CBS	–0.062	–0.0839
TQ5-CBS	–0.066	–0.0876
ΔCV	–0.016
ΔDK	–0.004
ΔZPE	0.070
Total	–0.012 ^a)/–0.016 ^b)	–0.034 ^a)/–0.038 ^b)
Experiment	0.46±0.2 ^[4]/–0.04 ^[6]
Calculation	–0.007 ^[21]/–0.059±0.061 ^[24]
注: ^a)Q5-CBS+ΔCV+ΔDK+ΔZPE result. ^b)TQ5-CBS+ΔCV+ΔDK+ΔZPE result.

下载: 导出CSV

[1]	Rienstra K J C, Tschumper G S, Schaefer H F, Nandi S, Ellison G B 2002 Chem. Rev. 102 231 Google Scholar
[2]	Cahen D, Kahn A 2003 Adv. Mater. 15 271 Google Scholar
[3]	Ru P B, Bi E, Zhang Y, Wang Y B, Kong W Y, Tang W T, Zhang P, Wu Y Z, Chen W, Yang X D, Chen H, Han L Y 2020 Adv. Energy Mater. 10 1903487 Google Scholar
[4]	Compton R N, Reinhardt P W, Cooper C D 1975 J. Chem. Phys. 63 3821 Google Scholar
[5]	Holroyd R A, Cangwer T E, Allen A O 1975 Chem. Phys. Lett. 31 520 Google Scholar
[6]	Surber E, Sanov A 2002 J. Chem. Phys. 116 5921 Google Scholar
[7]	Chen E C M, Wentworth W E 1983 J. Phys. Chem. 87 45 Google Scholar
[8]	Hughes B M, Lifshitzt C, Tiernan T O 1973 J. Chem. Phys. 59 3162 Google Scholar
[9]	Oakes J M, Barney Ellison G 1986 Tetrahedron. 42 6263 Google Scholar
[10]	Schiedt J, Weinkauf R 1997 Chem. Phys. Lett. 274 18 Google Scholar
[11]	Misaizu F, Tsunoyama H, Yasumura Y, Ohshimo K, Ohno K 2004 Chem. Phys. Lett. 389 241 Google Scholar
[12]	Cavanagh S J, Gibson S T, Lewis B R 2012 J. Chem. Phys. 137 144304 Google Scholar
[13]	Herzberg G 1966 Molecular Spectra & Molecular Structure III (Polyatomic Molecules) (New York: Van Nostrand Reinhold) p145
[14]	Hartman K O, Hisatsune I C 1966 J. Chem. Phys. 44 1913 Google Scholar
[15]	Ovenall D W, Whiffen D H 1961 Mol. Phys. 4 135 Google Scholar
[16]	Lahaye J G, Vandenhaute R, Fayt A 1987 J. Mol. Spectrosc. 123 48 Google Scholar
[17]	Suzuki I 1975 Bull. Chem. Soc. Jpn. 48 1685 Google Scholar
[18]	Bennett J E, Mile B, Thomas A 1967 Trans. Faraday Soc. 63 262 Google Scholar
[19]	Yu D, Rauk A, Armstrong D A 1992 J. Phys. Chem. 96 6031 Google Scholar
[20]	Gutsev G L, Bartlett R J, Compton R N 1998 J. Chem. Phys. 108 6756 Google Scholar
[21]	Barsotti S, Sommerfeld T, Ruf M W, Hotop H 2004 Int. J. Massspectrom. 233 181
[22]	Pacansky J, Wahlgren U, Bagus P S 1975 J. Chem. Phys. 62 2740 Google Scholar
[23]	Yoshioka Y, Schaefer H F, Jordan K D 1981 J. Chem. Phys. 75 1040 Google Scholar
[24]	Surber E, Ananthavel S P, Sanov A 2002 J. Chem. Phys. 116 1920 Google Scholar
[25]	Joachim W H, Knowles P J, Knizia G, Manby F R, Schütz M 2012 Wiley Interdiscip. Rev. : Comput. Mol. Sci. 2 242 Google Scholar
[26]	Bartlett R J, Watts J D, Kucharski S A, Noga J 1990 Chem. Phys. Lett. 165 513 Google Scholar
[27]	Dunning T H, Peterson K A, Wilson A K 2001 J. Chem. Phys. 114 9244 Google Scholar
[28]	Fellera D, Peterson K A, Daniel C T 2006 J. Chem. Phys. 124 054107 Google Scholar
[29]	Fellera D, Peterson K A 2007 J. Chem. Phys. 126 114105 Google Scholar
[30]	Peterson K A, Woon D E, Dunning T H 1994 J. Chem. Phys. 100 7410 Google Scholar
[31]	Dunning T H 1989 J. Chem. Phys. 90 1007 Google Scholar
[32]	Reiher M, Wolf A 2004 J. Chem. Phys. 121 2037 Google Scholar
[33]	Wolf A, Reiher M, Hess B A 2002 J. Chem. Phys. 117 9215 Google Scholar
[34]	Peterson K A, Dunning T H 2002 J. Chem. Phys. 117 10548 Google Scholar
[35]	Lu T, Chen F W 2012 J. Comput. Chem. 33 580 Google Scholar

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