高等学校化学学报 ›› 2021, Vol. 42 ›› Issue (7): 2218.doi: 10.7503/cjcu20210119
应富鸣,计辰儒,苏培峰,吴玮
收稿日期:
2021-02-26
出版日期:
2021-07-10
发布日期:
2021-04-12
基金资助:
YING Fuming, JI Chenru, SU Peifeng, WU Wei()
Received:
2021-02-26
Online:
2021-07-10
Published:
2021-04-12
Contact:
WU Wei
E-mail:weiwu@xmu.edu.cn
Supported by:
摘要:
提出了一种杂化多组态密度泛函新方法——λ-DFCAS. 在λ-DFCAS方法中, 电子相关能被分为静态和动态相关能. 静态相关能由多组态波函数方法完全活性空间自洽场(CASSCF)得到, 而动态相关能由密度泛函理论方法描述. 两种相关能的杂化比例由一个可调节的参数λ控制. 参数λ的取值取决于分子体系的多组态特性, 在0~1之间变化, 从而使得λ-DFCAS可以应用于各种强相关分子体系. 该方法能够以与CASSCF相当的计算代价获得接近完全活性空间二阶微扰(CASPT2)的计算精度, 并具备了大小一致性.
中图分类号:
TrendMD:
应富鸣, 计辰儒, 苏培峰, 吴玮. 基于完全活性空间自洽场的杂化多组态密度泛函方法λ-DFCAS. 高等学校化学学报, 2021, 42(7): 2218.
YING Fuming, JI Chenru, SU Peifeng, WU Wei. λ-DFCAS: A Hybrid Density Functional Complete Active Space Self Consistent Field Method. Chem. J. Chinese Universities, 2021, 42(7): 2218.
Species | ASb | BFsc | Time cost/s | ||
---|---|---|---|---|---|
CASSCF | CASPT2 | λ?DFCAS | |||
F2 | (2,2) | 70 | 0.5 | 0.7 | 1.3 |
C2 | (8,8) | 70 | 3.4 | 4.7 | 4.4 |
Reaction (Ⅵ) | (10,9) | 88 | 16.9 | 26.1 | 18.8 |
Reaction (Ⅴ) | (10,9) | 192 | 639.9 | 809.2 | 695.1 |
Reaction (Ⅲ) | (17,13) | 127 | 2337.8 | 7561.2 | 2379.8 |
Table 1 Time costs for F2, C2 and TSs of reactions(Ⅲ), (Ⅴ) and (Ⅵ) by CASSCF, CASPT2 and λ?DFCASa
Species | ASb | BFsc | Time cost/s | ||
---|---|---|---|---|---|
CASSCF | CASPT2 | λ?DFCAS | |||
F2 | (2,2) | 70 | 0.5 | 0.7 | 1.3 |
C2 | (8,8) | 70 | 3.4 | 4.7 | 4.4 |
Reaction (Ⅵ) | (10,9) | 88 | 16.9 | 26.1 | 18.8 |
Reaction (Ⅴ) | (10,9) | 192 | 639.9 | 809.2 | 695.1 |
Reaction (Ⅲ) | (17,13) | 127 | 2337.8 | 7561.2 | 2379.8 |
Species | AS | Equilibrium distance/nm | ||||||||
---|---|---|---|---|---|---|---|---|---|---|
Expt.[ | VBSCF | CASSCF | B3LYP | CASPT2 | dc?DFVB[ | hc?DFVB[ | λ?DFVB[ | λ?DFCAS | ||
MUE | 0.0020 | 0.0019 | 0.0007 | 0.0006 | 0.0010 | 0.0010 | 0.0013 | 0.0012 | ||
H2 | (2,2) | 0.0741 | 0.0015 | 0.0014 | 0.0002 | 0.0004 | 0.0008 | 0.0007 | 0.0004 | 0.0008 |
HF | (2,2) | 0.0917 | -0.0003 | -0.0001 | 0.0005 | 0.0007 | -0.0010 | -0.0011 | -0.0009 | -0.0004 |
C2 | (8,8) | 0.1243 | 0.0012 | 0.0012 | 0.0004 | 0.0000 | -0.0010 | -0.0014 | -0.0001 | 0.0004 |
N2 | (6,6) | 0.1098 | -0.0003 | -0.0011 | -0.0007 | 0.0006 | -0.0009 | -0.0008 | -0.0005 | 0.0005 |
F2 | (2,2) | 0.1412 | 0.0065 | 0.0057 | -0.0016 | 0.0013 | 0.0104 | -0.0009 | -0.0404 | 0.0039 |
Table 2 Equilibrium distances of diatomic molecules*
Species | AS | Equilibrium distance/nm | ||||||||
---|---|---|---|---|---|---|---|---|---|---|
Expt.[ | VBSCF | CASSCF | B3LYP | CASPT2 | dc?DFVB[ | hc?DFVB[ | λ?DFVB[ | λ?DFCAS | ||
MUE | 0.0020 | 0.0019 | 0.0007 | 0.0006 | 0.0010 | 0.0010 | 0.0013 | 0.0012 | ||
H2 | (2,2) | 0.0741 | 0.0015 | 0.0014 | 0.0002 | 0.0004 | 0.0008 | 0.0007 | 0.0004 | 0.0008 |
HF | (2,2) | 0.0917 | -0.0003 | -0.0001 | 0.0005 | 0.0007 | -0.0010 | -0.0011 | -0.0009 | -0.0004 |
C2 | (8,8) | 0.1243 | 0.0012 | 0.0012 | 0.0004 | 0.0000 | -0.0010 | -0.0014 | -0.0001 | 0.0004 |
N2 | (6,6) | 0.1098 | -0.0003 | -0.0011 | -0.0007 | 0.0006 | -0.0009 | -0.0008 | -0.0005 | 0.0005 |
F2 | (2,2) | 0.1412 | 0.0065 | 0.0057 | -0.0016 | 0.0013 | 0.0104 | -0.0009 | -0.0404 | 0.0039 |
Species | AS | Vibrational frequency/cm-1 | ||||||||
---|---|---|---|---|---|---|---|---|---|---|
Expt.[ | VBSCF | CASSCF | B3LYP | CASPT2 | dc?DFVB[ | hc?DFVB[ | λ?DFVB[ | λ?DFCAS | ||
MUE | 170 | 113 | 57 | 30 | 93 | 187 | 232 | 79 | ||
H2 | (2,2) | 4401 | -179 | -173 | 18 | 43 | -92 | 197 | 354 | -110 |
HF | (2,2) | 4138 | -220 | -8 | -13 | -26 | 122 | 349 | 199 | 96 |
C2 | (8,8) | 1855 | 87 | -13 | 24 | 43 | 135 | 210 | -114 | -45 |
N2 | (6,6) | 2359 | 173 | 153 | 91 | -39 | -32 | 91 | -138 | -37 |
F2 | (2,2) | 917 | -191 | -219 | 139 | 0 | -85 | 87 | 353 | 109 |
Table 3 Vibrational frequencies of diatomic molecules*
Species | AS | Vibrational frequency/cm-1 | ||||||||
---|---|---|---|---|---|---|---|---|---|---|
Expt.[ | VBSCF | CASSCF | B3LYP | CASPT2 | dc?DFVB[ | hc?DFVB[ | λ?DFVB[ | λ?DFCAS | ||
MUE | 170 | 113 | 57 | 30 | 93 | 187 | 232 | 79 | ||
H2 | (2,2) | 4401 | -179 | -173 | 18 | 43 | -92 | 197 | 354 | -110 |
HF | (2,2) | 4138 | -220 | -8 | -13 | -26 | 122 | 349 | 199 | 96 |
C2 | (8,8) | 1855 | 87 | -13 | 24 | 43 | 135 | 210 | -114 | -45 |
N2 | (6,6) | 2359 | 173 | 153 | 91 | -39 | -32 | 91 | -138 | -37 |
F2 | (2,2) | 917 | -191 | -219 | 139 | 0 | -85 | 87 | 353 | 109 |
Species | AS | BDE/(kJ·mol-1) | ||||||||
---|---|---|---|---|---|---|---|---|---|---|
Expt.[ | VBSCF | CASSCF | B3LYP | CASPT2 | dc?DFVB[ | hc?DFVB[ | λ?DFVB[ | λ?DFCAS | ||
MUE | 106.7 | 110.9 | 24.7 | 20.1 | 46.9 | 20.9 | 14.6 | 17.2 | ||
H2 | (2,2) | 458.1 | -61.1 | -59.4 | 15.5 | -13.8 | 39.3 | 7.1 | -2.5 | -12.6 |
HF | (2,2) | 591.2 | -115.9 | -115.5 | -10.9 | -7.9 | -20.5 | -13.8 | 8.4 | -13.0 |
C2 | (8,8) | 619.2 | -22.6 | -22.6 | -74.9 | 7.9 | 120.1 | -36.8 | -42.3 | -47.7 |
N2 | (6,6) | 956.0 | -244.3 | -265.7 | 13.0 | 57.7 | 13.8 | -34.3 | -17.2 | -5.9 |
F2 | (2,2) | 159.8 | -89.5 | -91.2 | 9.6 | 12.6 | -41.4 | -12.6 | 3.3 | -6.7 |
Table 4 BDEs of diatomic molecules*
Species | AS | BDE/(kJ·mol-1) | ||||||||
---|---|---|---|---|---|---|---|---|---|---|
Expt.[ | VBSCF | CASSCF | B3LYP | CASPT2 | dc?DFVB[ | hc?DFVB[ | λ?DFVB[ | λ?DFCAS | ||
MUE | 106.7 | 110.9 | 24.7 | 20.1 | 46.9 | 20.9 | 14.6 | 17.2 | ||
H2 | (2,2) | 458.1 | -61.1 | -59.4 | 15.5 | -13.8 | 39.3 | 7.1 | -2.5 | -12.6 |
HF | (2,2) | 591.2 | -115.9 | -115.5 | -10.9 | -7.9 | -20.5 | -13.8 | 8.4 | -13.0 |
C2 | (8,8) | 619.2 | -22.6 | -22.6 | -74.9 | 7.9 | 120.1 | -36.8 | -42.3 | -47.7 |
N2 | (6,6) | 956.0 | -244.3 | -265.7 | 13.0 | 57.7 | 13.8 | -34.3 | -17.2 | -5.9 |
F2 | (2,2) | 159.8 | -89.5 | -91.2 | 9.6 | 12.6 | -41.4 | -12.6 | 3.3 | -6.7 |
Reaction | AS | Reaction barrier/(kJ·mol-1) | |||||
---|---|---|---|---|---|---|---|
CASSCF | CASPT2 | λ?DFCAS | PBE | B3LYP | Expt. | ||
MUE | 36.0 | 9.6 | 11.7 | 38.5 | 14.2 | ||
(Ⅰ) | (4,3) | 13.0 | 29.7 | -7.9 | -28.9 | -13.4 | 138.1[ |
(Ⅱ) | (6,6) | 77.0 | 0.8 | 6.7 | -51.0 | -8.4 | 97.5[ |
(Ⅲ) | (17,13) | 52.7 | 2.9 | -28.9 | -24.7 | -16.7 | 71.5[ |
(Ⅳ) | (17,13) | 59.0 | -20.1 | -20.1 | -120.1 | -36.8 | 344.3[ |
(Ⅴ) | (10,9) | 7.5 | -9.6 | 4.2 | -26.8 | -18.0 | 56.1[ |
(Ⅵ) | (10,9) | 23.8 | -2.5 | -14.2 | -9.6 | -2.1 | 201.3[ |
(Ⅶ) | (10,9) | 19.2 | 0.8 | 0.8 | -7.9 | 3.8 | 137.2[ |
Table 5 Computational barriers of chemical reactions*
Reaction | AS | Reaction barrier/(kJ·mol-1) | |||||
---|---|---|---|---|---|---|---|
CASSCF | CASPT2 | λ?DFCAS | PBE | B3LYP | Expt. | ||
MUE | 36.0 | 9.6 | 11.7 | 38.5 | 14.2 | ||
(Ⅰ) | (4,3) | 13.0 | 29.7 | -7.9 | -28.9 | -13.4 | 138.1[ |
(Ⅱ) | (6,6) | 77.0 | 0.8 | 6.7 | -51.0 | -8.4 | 97.5[ |
(Ⅲ) | (17,13) | 52.7 | 2.9 | -28.9 | -24.7 | -16.7 | 71.5[ |
(Ⅳ) | (17,13) | 59.0 | -20.1 | -20.1 | -120.1 | -36.8 | 344.3[ |
(Ⅴ) | (10,9) | 7.5 | -9.6 | 4.2 | -26.8 | -18.0 | 56.1[ |
(Ⅵ) | (10,9) | 23.8 | -2.5 | -14.2 | -9.6 | -2.1 | 201.3[ |
(Ⅶ) | (10,9) | 19.2 | 0.8 | 0.8 | -7.9 | 3.8 | 137.2[ |
Reaction | Reaction energy/(kJ·mol-1) | |||||
---|---|---|---|---|---|---|
CASSCF | CASPT2 | λ?DFCAS | PBE | B3LYP | Expt. | |
MUE | 10.0 | 24.3 | 10.9 | 51.0 | 25.5 | |
(Ⅰ) | 18.8 | 46.0 | 38.5 | 55.6 | 50.6 | 446.0[ |
(Ⅲ) | 6.3 | 23.0 | 8.8 | 95.4 | 20.1 | -272.4[ |
(Ⅵ) | 4.6 | 3.3 | -14.6 | 1.7 | 5.9 | 64.0[ |
Table 6 Chemical reaction energies by various methods*
Reaction | Reaction energy/(kJ·mol-1) | |||||
---|---|---|---|---|---|---|
CASSCF | CASPT2 | λ?DFCAS | PBE | B3LYP | Expt. | |
MUE | 10.0 | 24.3 | 10.9 | 51.0 | 25.5 | |
(Ⅰ) | 18.8 | 46.0 | 38.5 | 55.6 | 50.6 | 446.0[ |
(Ⅲ) | 6.3 | 23.0 | 8.8 | 95.4 | 20.1 | -272.4[ |
(Ⅵ) | 4.6 | 3.3 | -14.6 | 1.7 | 5.9 | 64.0[ |
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