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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.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 form 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 RC-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:
- coupled cluster method /
- carbon-containing triatomic molecules /
- equilibrium geometry /
- electron affinities
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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.
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^ - $.
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 RC-O/Å 1.167 1.163 1.162 1.162 ${\text{CO}}_2^ - $ RC-O/Å 1.237 1.232 1.231 1.230 ∠OCO/($ °) $ 137.6 137.7 137.8 137.9 OCS RC-O/Å 1.163 1.159 1.158 1.158 RC-S/Å 1.571 1.567 1.566 1.565 OCS– RC-O/Å 1.214 1.210 1.209 1.208 RC-S/Å 1.710 1.705 1.703 1.701 ∠OCS/($ °) $ 136.5 136.4 136.5 136.5 CS2 RC-S/Å 1.562 1.558 1.557 1.555 $ {\text{CS}}_{2}^{{ - }} $ RC-S/Å 1.641 1.636 1.634 1.633 ∠SCS/($ °) $ 143.3 143.5 143.6 143.7 
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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 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] 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]
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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 –0.541a)/–0.544b) –0.565a)/–0.568b) 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.
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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 0.448a)/0.443b) 0.425a)/0.420b) 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] Note: a)Q5-CBS+ΔCV+ΔDK+ΔZPE result. b)TQ5-CBS+ΔCV+ΔDK+ΔZPE result.
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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 –0.012a)/–0.016b) –0.034a)/–0.038b) 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.
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