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Acta Physico-Chimica Sinca  2017, Vol. 33 Issue (6): 1130-1139    DOI: 10.3866/PKU.WHXB201703221
ARTICLE     
Fitting and Extrapolation of Configuration Interaction Energies in Complete Active Space
Jing-Si CAO,Fei-Wu CHEN*()
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Abstract  

Configuration interaction calculation in complete active space is related to the numbers of active electrons and orbitals. However, configuration interaction energy is not a monotonically decreasing function of these two variables. Thus, the numbers of active electrons and orbitals are not proper variables to extrapolate the configuration interaction energy. In order to address this problem, we defined a new variable:maximum number of unoccupied orbitals in the complete active space. We performed a series of configuration interaction calculations on singlet, doublet, and triplet molecules, and simulated their ground state energies with the number of active electrons and the number of maximum unoccupied orbitals. The mean square root errors of these simulations were on the order of 10-6. The accuracy of the extrapolated energies was better than that of MP4 and than that of CCSD for small molecules. The extrapolated full configuration interaction energies were very close to the energy values of full configuration interactions. Furthermore, the extrapolated energies were exploited to optimize the bond distances of several diatomic molecules and to compute harmonic vibrational frequencies. Their accuracies were better than that of the complete active space self-consistent field.



Key wordsComplete active space      Active electron      Active orbital      Energy extrapolation      Bond length      Harmonic vibrational frequency     
Received: 02 December 2016      Published: 22 March 2017
MSC2000:  O641  
Fund:  National Natural Science Foundation of China(21173020);National Natural Science Foundation of China(21473008)
Corresponding Authors: Fei-Wu CHEN     E-mail: chenfeiwu@ustb.edu.cn
Cite this article:

Jing-Si CAO,Fei-Wu CHEN. Fitting and Extrapolation of Configuration Interaction Energies in Complete Active Space. Acta Physico-Chimica Sinca, 2017, 33(6): 1130-1139.

URL:

http://www.whxb.pku.edu.cn/10.3866/PKU.WHXB201703221     OR     http://www.whxb.pku.edu.cn/Y2017/V33/I6/1130

Fig 1 Diagram of E vs the maximum number of unoccupied orbitals Mmax of CH4
Fig 2 Diagram of E vs the number of active electron Nele of CH4
MoleculeNele = 2Nele = 4Nele = 6Nele = 8Nele = 10R2-M aSe-M b
CH4?40.195727?40.222980?40.258960?40.299640?40.3008370.99730.6583 × 10?6
H2O?75.995708?76.025908?76.076865?76.118908?76.1194500.99081.8218 × 10?6
HF?99.994106?100.022484?100.076012?100.113805?100.1146770.99450.9384 × 10?6
HCl?460.040777?460.050411?460.075289?460.094432?460.0947110.99550.0410 × 10?6
C2H4?78.036773?78.051796?78.086919?78.127227?78.1370240.99470.4622 × 10?6
N2H4?111.097151?111.113767?111.137168?111.185411?111.2053070.98300.5837 × 10?6
O3?224.203067?224.225559?224.264612?224.310388?224.3664410.97590.3973 × 10?6
Cl2?918.865005?918.871332?918.879059?918.888453?918.9320420.99270.0135 × 10?6
Table 1 Extrapolated energies (hartree) of singlet molecules and fitting parameters
MoleculeB3LYPMP2MP4CCSDExtra.*FCI
CH4?39.973539?39.802466?39.816872?39.855656?40.300837?40.300835
H2O?75.868653?75.821248?75.925882?75.817822?76.119450?76.120838
HF?100.267014?100.058036?99.988922?100.071557?100.114677?100.114307
C2H4?77.791740?77.491723?77.497659?77.603125?78.138748**
N2H4?111.151725?111.057303?110.957610?111.067759?111.249844**
HCl?460.647716?460.076776?459.987620?460.112090?460.096813**
Cl2?920.217791?919.130112?918.968190?919.162674?918.957751**
O3?224.952575?224.568669?224.229338?224.662578?224.391424**
Table 2 Energies (hartree) of singlet molecules calculated with six methods
Fig 3 Diagram of E vs the maximum number of unoccupied orbitals Mmax of MgH
Fig 4 Diagram of E vs the maximum number of unoccupied orbitals Mmax of O2
MoleculeNele = 3Nele = 5Nele = 7Nele = 9Nele = 11R2-M aSe-M b
doublet
CH?38.278501?38.316570?38.317560_d_d0.99542.5961 × 10?6
NH2?55.551240?55.592851?55.633837?55.635109_d0.98112.9242 × 10?6
MgH?200.155490?200.155730?200.156500?200.157750?200.1582500.98940.1459 × 10?6
CN_c?92.267993?92.327288?92.366993?92.3680980.97921.3202 × 10?6
NO_c?129.259794?129.319029?129.362475?129.4071960.98550.9284 × 10?6
MoleculeNele = 2Nele = 4Nele = 6Nele = 8Nele = 10R2-M aSe-M b
triplet
CH2?38.910163?38.937379?38.980092?38.981150_d0.99421.0792 × 10?6
NH?54.942410?54.972083?55.011873?55.012792_d0.99671.1471 × 10?6
OH+?74.946500?74.976967?75.015879?75.016735_d0.99870.4998 × 10?6
PH?341.097250?341.112110?341.132901?341.133321?341.1339790.99420.0476 × 10?6
SiH2_c?289.846197?289.873244?289.873604?289.8745410.98460.3962 × 10?6
NF?153.730305?153.761556?153.791543?153.833042?153.8939670.99390.3777 × 10?6
O2_c?149.563901?149.625447?149.688563?149.7315430.98690.6808 × 10?6
Table 3 Extrapolated energies (hartree) of multiplet molecules and fitting parameters
MoleculeUB3LYPUMP2UMP4UCCSDExtra.*FCI
doublet
CH?38.374599?38.245978?38.220027?38.278615?38.317560?38.317560
NH2?55.606183?55.438307?55.420849?55.502775?55.635109?55.634553
MgH?200.582497?200.127416?200.121352?200.140603?200.158250?200.158250
CN?92.454861?92.200641?92.132753?92.245942?92.374824**
NO?129.658134?129.156903?129.078059?129.217100?129.407196**
triplet
CH2?38.897733?38.738979?38.714131?38.792961?38.981150?38.981093
NH?55.108368?54.966748?54.921893?54.990677?55.012793?55.013001
OH+?75.154984?74.972583?74.916438?75.003497?75.016735?75.016885
PH?341.828742?341.320647?341.246246?341.350612?341.135901?341.135910
NF?154.306964?153.979267?153.865934?154.006754?153.931458**
SiH2?290.359061?289.875054?289.829758?289.899624?289.874660**
O2?150.048948?149.940643?149.821090?149.722662?149.779525**
Table 4 Energies (hartree) of multiplet molecules calculated with six methods
MoleculeHFNaHCHMgHNHOH+
singletdoublettriplet
re(HF/6-31G)0.92081.91741.10661.75091.00011.0070
re(MP2/6-31G)0.94701.92941.13661.77051.05221.0454
re(CASSCF/6-31G)0.94901.95651.14031.80251.02341.0413
re(Extra.)a0.94951.95411.12851.80061.03601.0346
re(Exp)b0.91681.88741.11991.72971.03621.0289
we(HF/6-31G)4149.431186.192957.201549.733441.703242.45
we(MP2/6-31G)3788.681143.412790.251460.383220.162976.43
we(CASSCF/6-31G)3746.701068.142638.141333.523034.043011.83
we(Extra.)a3750.871074.362808.411356.973019.553108.53
we(Exp)b4138.301172.202858.501495.203282.273113.37
Table 5 Comparison of the bond length (re, 10-10 m) and harmonic frequency (we, cm-1) calculated with four methods
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