Please wait a minute...
Frontiers of Chemistry in China

ISSN 1673-3495

ISSN 1673-3614(Online)

CN 11-5726/O6

Front Chem Chin    0, Vol. Issue () : 269-279    https://doi.org/10.1007/s11458-011-0256-3
RESEARCH ARTICLE
Calculations of ionization energies and electron affinities for atoms and molecules: A comparative study with different methods
Neil Qiang SU1, Igor Ying ZHANG1,2, Jianming WU2(), Xin XU1,2
1. State Key Laboratory of Physical Chemistry of Solid Surfaces; College for Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, China; 2. Shanghai Key Laboratory of Molecular Catalysis and Innovative Materials, MOE Laboratory for Computational Physical Science, Department of Chemistry, Fudan University, Shanghai 200433, China
 Download: PDF(463 KB)   HTML
 Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks
Abstract

In the present work, we examined the performance of 36 density functionals, including the newly developed doubly hybrid density functional XYG3 (Y. Zhang, X. Xu, and W. A. Goddard III, Proc. Natl. Acad. Sci, USA, 2009, 106, 4963), to calculate ionization energies (IEs) and electron affinities (EAs). We used the well-established G2-1 set as reference, which contains 14 atoms and 24 molecules for IE, along with 7 atoms and 18 molecules for EA. XYG3 leads to mean absolute deviations (MADs) of 0.057 and 0.080 eV for IEs and EAs, respectively, using the basis set of 6–311+ G(3df,2p). In comparison with some other functionals, MADs for IEs are 0.109 (B2PLYP), 0.119 (M06-2X), 0.159 (X3LYP), 0.161 (PBE), 0.162 (B3LYP), 0.165 (PBE0), 0.173 (TPSS), 0.200 (BLYP), and 0.215 eV (LC-BLYP). MADs for EAs are 0.090 (X3LYP), 0.090 (B2PLYP), 0.102 (PBE), 0.103 (M06-2X), 0.104 (TPSS), 0.105 (BLYP), 0.106 (B3LYP), 0.126 (LC-BLYP), and 0.128 eV (PBE0).

Keywords ionization energy      electron affinity      DFT      XYG3      B3LYP     
Corresponding Author(s): WU Jianming,Email:jianmingwu@fudan.edu.cn   
Issue Date: 05 December 2011
 Cite this article:   
Neil Qiang SU,Igor Ying ZHANG,Jianming WU, et al. Calculations of ionization energies and electron affinities for atoms and molecules: A comparative study with different methods[J]. Front Chem Chin, 0, (): 269-279.
 URL:  
https://academic.hep.com.cn/fcc/EN/10.1007/s11458-011-0256-3
https://academic.hep.com.cn/fcc/EN/Y0/V/I/269
SpeciesExpt.BLYPB3LYPPBEPBE0TPSSTPSShM06-LM06-2XXYG3MP2QCISD(T)
Li5.39-0.13-0.23-0.18-0.17-0.10-0.090.36-0.01-0.070.040.03
Be9.320.340.200.320.340.250.250.440.250.170.500.03
B8.3-0.33-0.44-0.37-0.34-0.45-0.44-0.31-0.02-0.150.020.07
C11.26-0.15-0.29-0.28-0.26-0.19-0.19-0.18-0.07-0.06-0.010.06
N14.540.03-0.13-0.20-0.17-0.13-0.13-0.26-0.030.03-0.070.04
O13.61-0.56-0.55-0.46-0.25-0.42-0.34-0.25-0.11-0.060.280.20
F17.42-0.32-0.34-0.26-0.06-0.020.04-0.07-0.140.010.100.15
CH412.620.250.060.240.220.240.230.090.050.010.070.06
NH310.180.06-0.010.010.150.210.240.11-0.020.060.030.12
OH13.01-0.18-0.23-0.160.010.090.130.03-0.040.000.090.15
H2O12.620.070.000.030.170.220.260.170.020.04-0.070.13
HF16.040.00-0.06-0.030.140.160.210.130.040.02-0.130.09
Na5.14-0.21-0.28-0.21-0.14-0.03-0.010.64-0.01-0.060.070.05
Mg7.650.02-0.080.030.110.110.120.14-0.120.020.310.07
Al5.980.11-0.04-0.09-0.11-0.17-0.170.110.200.060.180.06
Si8.150.210.04-0.05-0.07-0.07-0.080.100.160.090.120.06
P10.490.310.110.00-0.04-0.02-0.03-0.040.180.090.030.06
S10.36-0.05-0.19-0.07-0.04-0.10-0.080.17-0.050.040.420.27
Cl12.970.06-0.10-0.010.010.010.020.11-0.030.040.250.26
SiH4110.330.090.300.200.170.15-0.060.280.000.210.11
PH10.150.17-0.02-0.10-0.14-0.12-0.13-0.050.040.010.040.06
PH29.820.06-0.12-0.17-0.20-0.18-0.20-0.050.01-0.040.070.08
PH39.870.150.030.090.140.140.150.060.120.080.210.11
HS10.370.05-0.10-0.020.010.010.020.09-0.010.010.210.18
H2S(2B1 cation)10.470.200.040.090.120.120.130.140.030.060.140.17
H2S(2A1 cation)12.780.300.120.220.200.191.730.220.150.070.140.16
HCl12.750.170.000.060.070.090.090.07-0.010.020.080.17
C2H211.40.280.160.160.250.310.320.300.140.01-0.080.10
C2H410.510.230.150.100.230.280.310.200.210.080.020.06
CO14.010.10-0.130.140.080.150.120.33-0.040.01-0.180.12
N2 (2Σ cation)15.580.22-0.270.20-0.180.190.040.08-0.570.200.270.13
N2 (2Π cation)16.70.270.070.150.160.290.280.23-0.03-0.12-0.320.13
O212.07-0.40-0.79-0.38-0.68-0.41-0.53-0.59-0.82-0.160.35-0.11
P210.530.390.210.180.170.160.16-0.25-0.54-0.07-0.080.13
S29.360.08-0.23-0.10-0.29-0.16-0.23-0.10-0.25-0.040.140.08
Cl211.50.430.110.340.150.300.220.28-0.060.010.110.14
ClF12.660.330.050.290.160.270.210.23-0.080.050.030.16
SC11.330.06-0.110.030.030.040.040.27-0.01-0.07-0.690.05
Tab.1  Experimental ionization energies (IEs, eV) at 0 K and theoretical errors for the G2-1 Set (38 systems)
MAD b)AD c)RMS d)Max+ e)Max - f)
1st RungSVWN0.663-0.6630.698NAg)-1.15 (F→F+)
SVWN50.224-0.1750.2690.30 (Be→Be+)-0.56(O2O2+)
2nd RungBLYP0.2000.0780.2400.43(Cl2Cl2+)-0.56 (O→O+)
PBE0.161-0.0040.2000.34(Cl2Cl2+)-0.46 (O→O+)
PW910.165-0.0590.2090.29(Cl2Cl2+)-0.53 (O→O+)
BPW910.2290.0640.3771.71 (H2S→H2S + 2A1)-0.46 (O→O+)
BP860.231-0.0400.3671.60 (H2S→H2S + 2A1)-0.63 (O→O+)
HCTH4070.245-0.0830.3801.57 (H2S→H2S + 2A1)-0.61 (N→N+)
LC-BLYP0.215-0.1490.2980.26 (Be→Be+)-0.92(O2O2+)
3rd RungM06-L0.1930.0770.2390.64 (Na→Na+)-0.59(O2O2+)
TPSS0.1730.0370.2050.31(C2H2C2H2+)-0.45 (B→B+)
VSXC0.1920.0460.3461.64 (H2S→H2S + 2A1)-0.33 (N→N+)
tHCTH0.220-0.0230.3651.62 (H2S→H2S + 2A1)-0.50 (Mg→Mg+)
4th RungB3LYP0.162-0.0870.2260.20 (Be→Be+)-0.79(O2O2+)
X3LYP0.159-0.0400.2140.24 (Be→Be+)-0.76(O2O2+)
PBE00.165-0.0010.2040.34 (Be→Be+)-0.68(O2O2+)
B3PW910.159-0.0560.2080.32 (Be→Be+)-0.72(O2O2+)
B3P860.616-0.6160.646NAg)-1.28(O2O2+)
BHHLYP0.2130.0760.2810.47(C2H4C2H4+)-0.99(O2O2+)
TPSSh0.2140.0740.3471.73 (H2S→H2S + 2A1)-0.53(O2O2+)
O3LYP0.1410.0370.1800.30(SiH4SiH4+)-0.57(O2O2+)
B980.130-0.0240.1780.24 (Be→Be+)-0.71(O2O2+)
HSE060.1660.0040.2060.34 (Be→Be+)-0.68(O2O2+)
CAM-B3LYP0.165-0.0970.2380.22(P2P2+)-0.85(O2O2+)
LC-ωPBE0.194-0.1110.2550.29 (Be→Be+)-0.70(O2O2+)
B97-10.1300.0150.1690.29 (Be→Be+)-0.62(O2O2+)
B97-D0.1610.0570.2000.35(Cl2Cl2+)-0.52(O2O2+)
ωB97X0.1350.0070.1870.46 (Be→Be+)-0.63(O2O2+)
ωB97X-D0.132-0.0060.1870.49 (Be→Be+)-0.67(O2O2+)
M06-2X0.119-0.0110.1960.28(SiH4SiH4+)-0.82(O2O2+)
M060.1590.0270.2110.39 (Be→Be+)-0.76(O2O2+)
5th RungXYG30.0570.0100.0750.20(N2N2+,2g)-0.16(O2O2+)
MC3BB0.1200.0700.1500.42 (Be→Be+)-0.40(O2O2+)
B2PLYP0.1090.0490.1300.31 (Be→Be+)-0.31(O2O2+)
B2PLYP-D0.1100.0540.1310.31 (Be→Be+)-0.31(O2O2+)
B2GP-PLYP0.1010.0500.1230.33 (Be→Be+)-0.31(O2O2+)
Ab initioHF1.0050.9541.1351.82 (Be→Be+)-0.84(O2O2+)
UMP20.1630.0770.2180.50 (Be→Be+)-0.69 (CS→CS+)
MP4SDQ0.1500.1160.1730.33 (S→S+)-0.38 (CS→CS+)
QCISD(T)0.1110.1060.1250.27 (S→S+)-0.11 (CS→CS+)
Tab.2  Statistic theoretical errors for ionization energies (IEs, eV) at 0 K for the G2-1 Set (38 systems)
Fig.1  Histogram of deviations (Expt. – Calc.) for 38 ionization energies (IEs) in the G2-1 set. Each vertical bar represents deviations in a 0.1 eV range.
SpeciesExpt.BLYPB3LYPPBEPBE0TPSSTPSShM06-LM06-2XXYG3MP2QCISD(T)
C1.26-0.06-0.10-0.29-0.14-0.17-0.12-0.070.020.130.010.06
CH1.24-0.08-0.12-0.29-0.15-0.14-0.10-0.010.010.070.010.10
CH20.65-0.16-0.13-0.110.110.110.170.130.160.060.220.13
CH30.080.050.060.010.220.190.250.200.140.160.170.20
NH0.38-0.13-0.07-0.100.180.160.240.160.180.120.190.23
NH20.740.000.04-0.030.230.170.250.300.130.06-0.050.16
O1.46-0.24-0.14-0.200.140.050.170.180.150.110.140.22
OH1.83-0.010.06-0.030.290.190.290.370.240.07-0.110.19
F3.4-0.16-0.06-0.140.220.070.190.280.250.08-0.140.16
O20.44-0.06-0.120.040.160.040.090.260.070.070.210.13
NO0.02-0.23-0.30-0.22-0.14-0.19-0.16-0.10-0.09-0.030.190.08
CN3.820.00-0.210.00-0.050.060.030.18-0.17-0.07-0.78-0.00
Si1.380.190.06-0.08-0.06-0.03-0.020.040.140.120.030.04
P0.75-0.12-0.19-0.10-0.01-0.07-0.030.07-0.080.050.370.23
S2.08-0.02-0.11-0.060.030.000.030.08-0.020.050.210.20
Cl3.620.05-0.06-0.030.040.030.05-0.06-0.030.000.020.16
SiH1.280.150.03-0.10-0.07-0.04-0.040.130.100.110.110.10
SiH21.120.07-0.05-0.15-0.13-0.10-0.090.150.070.070.140.12
SiH31.440.100.020.040.130.130.150.250.160.120.260.13
PH1.00-0.01-0.09-0.050.040.030.060.070.020.050.210.17
PH21.260.100.010.020.100.100.120.130.050.070.140.15
SH2.310.08-0.02-0.010.080.070.090.120.000.040.060.15
PO1.090.03-0.17-0.12-0.20-0.11-0.140.07-0.090.050.150.09
S21.660.16-0.010.100.080.100.090.31-0.020.070.160.16
Cl22.39-0.36-0.45-0.23-0.20-0.27-0.26-0.28-0.16-0.180.040.02
Tab.3  Experimental electron affinities (EAs, eV) at 0 K and theoretical errors for the G2-1 Set (25 systems)
MAD b)AD c)RMS d)Max+ e)Max - f)
1st RungSVWN0.750-0.7500.766NAg)-1.15 (F←F-)
SVWN50.289-0.2890.269NAg)-0.63 (F←F-)
2nd RungBLYP0.105-0.0260.1350.19 (Si←Si-)-0.36 (Cl2←Cl2-)
PBE0.102-0.0860.1330.10 (S2←S2-)-0.29 (C←C-)
PW910.133-0.1280.1640.06 (S2←S2-)-0.33 (C←C-)
BPW910.094-0.0600.1230.12 (S2←S2-)-0.27 (C←C-)
BP860.211-0.2110.232NAg)-0.39 (Cl2←Cl2-)
HCTH4070.167-0.1560.2130.12 (O2←O2-)-0.47 (Cl2←Cl2-)
LC-BLYP0.126-0.0380.1630.22 (CH3←CH3-)-0.38 (CN←CN-)
3rd RungM06-L0.1600.1180.1860.37 (OH←OH-)-0.28 (Cl2←Cl2-)
TPSS0.1040.0150.1220.19 (OH←OH-)-0.27 (Cl2←Cl2-)
VSXC0.104-0.0170.1480.25 (O2←O2-)-0.54 (Cl2←Cl2-)
tHCTH0.109-0.0970.1540.08 (O2←O2-)-0.42 (Cl2←Cl2-)
4th RungB3LYP0.106-0.0840.1440.06 (OH←OH-)-0.45 (Cl2←Cl2-)
X3LYP0.090-0.0350.1230.12 (OH←OH-)-0.40 (Cl2←Cl2-)
PBE00.1280.0360.1460.29 (OH←OH-)-0.20 (Cl2←Cl2-)
B3PW910.103-0.0300.1260.17 (OH←OH-)-0.29 (Cl2←Cl2-)
B3P860.595-0.5950.604NAg)-0.83 (Cl2←Cl2-)
BHHLYP0.2480.1980.2850.58 (OH←OH-)-0.29 (Cl2←Cl2-)
TPSSh0.1300.0530.1530.29 (OH←OH-)-0.26 (Cl2←Cl2-)
O3LYP0.1080.0680.1230.25 (O2←O2-)-0.19 (Cl2←Cl2-)
B980.078-0.0040.1030.17 (OH←OH-)-0.29 (Cl2←Cl2-)
HSE060.1260.0340.1450.28 (OH←OH-)-0.23 (Cl2←Cl2-)
CAM-B3LYP0.103-0.0520.1350.12 (Si←Si-)-0.36 (Cl2←Cl2-)
LC-ωPBE0.125-0.0060.1470.28 (CH3←CH3-)-0.28 (PO←PO-)
B97-10.0810.0290.0990.20 (OH←OH-)-0.23 (Cl2←Cl2-)
B97-D0.081-0.0040.1160.17 (S2←S2-)-0.39 (Cl2←Cl2-)
ωB97X0.0830.0090.1060.17 (Si←Si-)-0.25 (CN←CN-)
ωB97X-D0.079-0.0130.1000.15 (OH←OH-)-0.22 (Cl2←Cl2-)
M06-2X0.1030.0510.1260.25 (F←F-)-0.17 (CN←CN-)
M060.0950.0480.1160.24 (SiH2←SiH2-)-0.23 (NO←NO-)
5th RungXYG30.0800.0580.0900.16 (CH3←CH3-)-0.18 (Cl2←Cl2-)
MC3BB0.1750.1320.1880.29 (NH←NH-)-0.26 (CN←CN-)
B2PLYP0.0900.0560.1020.17 (CH3←CH3-)-0.22 (Cl2←Cl2-)
B2PLYP-D0.0910.0560.1040.17 (CH3←CH3-)-0.23 (Cl2←Cl2-)
B2GP-PLYP0.1140.0830.1240.21 (CH3←CH3-)-0.19 (CN←CN-)
Ab initioHF1.1481.1481.2832.21 (F←F-)NAg)
UMP20.1660.0790.2240.37 (P←P-)-0.78 (CN←CN-)
MP4SDQ0.2080.1750.2290.36 (NH←NH-)-0.41 (CN←CN-)
QCISD(T)0.1350.1350.1480.23 (NH←NH-)NAg)
Tab.4  Statistic theoretical errors for electron affinities (EAs, eV) at 0 K for the G2-1 Set (25 systems)
Fig.2  Histogram of deviations (Expt. – Calc.) for 25 electron affinities (EAs) in the G2-1 set. Each vertical bar represents deviations in a 0.1 eV range.
1 Lias, S. G.; Bartmess, J. E., http://webbook.nist.gov/chemistry/ion (retrieved Oct. 19, 2011)
2 Parr, R. G.; Yang, W., Density Functional Theory of Atoms and Molecules , Oxford University Press, New York, 1989
3 Chemical Reactivity Theory, A Density Functional View, Ed. Chattaraj, P. K., CRC Press, Taylor & Francis Group, New York, 2009
4 Pearson, R. G., Chemical Hardness. Wiley-VCH, Weinheim, Germany, 1997
5 Geerlings, P.; De Proft, F.; Langenaeker, W., Chem. Rev. 2003, 103, 1793-1873
doi: 10.1021/cr990029p
6 Mulliken, R. S., J. Chem. Phys. 1934, 2, 782-793
doi: 10.1063/1.1749394
7 Ayers, P. W., J. Math. Chem. 2008, 43, 285-303
doi: 10.1007/s10910-006-9195-5
8 Parr, R. G.; Pearson, R. G., J. Am. Chem. Soc. 1983, 105, 7512-7516
doi: 10.1021/ja00364a005
9 Parr, R. G.; Szentpaly, L. V.; Liu, S., J. Am. Chem. Soc. 1999, 121, 1922-1924
doi: 10.1021/ja983494x
10 Yokojima, S.; Yoshiki, N.; Yanoi, W.; Okada, A., J. Phys. Chem. B 2009, 113, 16384-16392
doi: 10.1021/jp9054582
11 Smalo, H. S.; Astrand, P. O.; Ingebrigtsen, S., IEEE Trans. Dielectr. Electr. Insul. 2010, 17, 733-741
doi: 10.1109/TDEI.2010.5492245
12 Steenken, S.; Telo, J. P.; Novais, H. M.; Candeias, L. P., J. Am. Chem. Soc. 1992, 114, 4701-4709
doi: 10.1021/ja00038a037
13 Khistyaev, K.; Bravaya, K. B.; Kamarchik, E.; Kostko, O.; Ahmed, M.; Krylov, A. I., Faraday Discuss. 2011, 150, 313-330
doi: 10.1039/c0fd00002g
14 Vijayaraj, R.; Subramanian, V.; Chattaraj, P. K., J. Chem. Theory Comput. 2009, 5, 2744-2753
doi: 10.1021/ct900347f
15 Fayet, G.; Joubert, L.; Rotureau, P.; Adamo, C., Chem. Phys. Lett. 2009, 467, 407-411
doi: 10.1016/j.cplett.2008.11.033
16 Pandey, P. P.; Gupta, A. K.; Singh, P. P., Asian J. Chem. 2008, 20, 6417-6434
17 Thanikaivelan, P.; Subramanian, V.; Rao, J. R.; Nair, B. U., Chem. Phys. Lett. 2000, 323, 59-70
doi: 10.1016/S0009-2614(00)00488-7
18 Stanton, J. F.; Gauss, J., J. Chem. Phys. 1999, 111, 8785-8788
doi: 10.1063/1.479673
19 Kemeny, A. E.; Francisco, J. S.; Dixon, D. A.; Feller, D., J. Chem. Phys. 2003, 118, 8290-8295
doi: 10.1063/1.1565317
20 Parthiban, S.; Martin, J. M. L., J. Chem. Phys. 2001, 114, 6014-6029
doi: 10.1063/1.1356014
21 Pople, J. A.; Head-Gordon, M.; Fox, D. J.; Raghavachari, K.; Curtiss, L. A., J. Chem. Phys. 1989, 90, 5622-5629
doi: 10.1063/1.456415
22 Curtiss, L. A.; Raghavachari, K.; Trucks, G. W.; Pople, J. A., J. Chem. Phys. 1991, 94, 7221-7230
doi: 10.1063/1.460205
23 Curtiss, L. A.; Raghavachari, K.; Redfern, P. C.; Rassolov, V.; Pople, J. A., J. Chem. Phys. 1998, 109, 7764-7776
doi: 10.1063/1.477422
24 Curtiss, L. A.; Redfern, P. C.; Raghavachari, K., J. Chem. Phys. 2007, 126, 84108-84112
doi: 10.1063/1.2436888
25 Montgomery, J. A. Jr; Frisch, M. J.; Ochterski, J. W.; Petersson, G. A., J. Chem. Phys. 1999, 110, 2822-2827
doi: 10.1063/1.477924
26 Wood, G. P. F.; Radom, L.; Petersson, G. A.; Barnes, E. C.; Frisch, M. J.; and Montgomery, Jr. J. A., J. Chem. Phys . 2006, 125, 094106/1-16
27 Curtiss, L. A.; Raghavachari, K.; Redfern, P. C.; Pople, J. A., J. Chem. Phys. 1998, 109, 42-55
doi: 10.1063/1.476538
28 Rienstra-Kiracofe, J. C.; Tschumper, G. S.; Schaefer, H. F.; Nandi, S.; Ellison, G. B., Chem. Rev. 2002, 102, 231-282
doi: 10.1021/cr990044u
29 Zhang, H. Y.; Sung, Y. M.; Wang, X. L., Chem. Euro. J. 2003, 9, 502-508
doi: 10.1002/chem.200390052
30 Joanteguy, S.; Pfister-Guillouzo, G.; Chermette, H., J. Phys. Chem. A 1999, 103, 3505-3511
doi: 10.1021/jp984494m
31 Becke, A. D., Phys. Rev. A 1988, 38, 3098-3100
doi: 10.1103/PhysRevA.38.3098
32 Lee, C. T.; Yang, W. T.; Parr, R. G., Phys. Rev. B 1988, 37, 785-789
doi: 10.1103/PhysRevB.37.785
33 Perdew, J. P., Phys. Rev. B 1986, 33, 8822-8824
doi: 10.1103/PhysRevB.33.8822
34 Perdew, J. P.; Wang, Y., Phys. Rev. B 1992, 45, 13244-13249
doi: 10.1103/PhysRevB.45.13244
35 Slater, J. C., Quamtum Theory of Molecules and Solids , v.4, McGraw-Hill, New York, 1974
36 Vosko, S. H.; Wilk, L.; Nusair, M., Can. J. Phys. 1980, 58, 1200-1211
doi: 10.1139/p80-159
37 Becke, A. D., J. Chem. Phys. 1993, 98, 5648-5652
doi: 10.1063/1.464913
38 Stephens, P. J.; Devlin, F. J.; Chabalowski, C. F.; Frisch, M. J., J. Phys. Chem. 1994, 98, 11623-11627
doi: 10.1021/j100096a001
39 Van Voorhis, T.; Scuseria, G. E., J. Chem. Phys. 1998, 109, 400-410
doi: 10.1063/1.476577
40 Tao, J.; Perdew, J.; Staroverov, V.; and Scuseria, G., Phys. Rev. Lett . 2003, 91, 146401/1-4
41 Zhao, Y.; and Truhlar, D. G., J. Chem. Phys . 2006, 125, 194101/1-18
42 Boese, A. D.; Handy, N. C., J. Chem. Phys. 2002, 116, 9559-9569
doi: 10.1063/1.1476309
43 Schmider, H. L.; Becke, A. D., J. Chem. Phys. 1998, 108, 9624-9631
doi: 10.1063/1.476438
44 Iikura, H.; Tsuneda, T.; Yanai, T.; Hirao, K., J. Chem. Phys. 2001, 115, 3540-3544
doi: 10.1063/1.1383587
45 Vydrov, O. A.; Heyd, J.; Krukau, A.; and Scuseria, G. E., J. Chem. Phys . 2006, 125, 074106/1-9
46 Yanai, T.; Tew, D.; Handy, N. C., Chem. Phys. Lett. 2004, 393, 51-57
doi: 10.1016/j.cplett.2004.06.011
47 Chai, J. D.; and Head-Gordon, M., J. Chem. Phys . 2009, 131, 174105/1-13
48 Chai, J. D.; and Head-Gordon, M., J. Chem. Phys . 2008, 128, 084106/1-15
49 Chai, J. D.; Head-Gordon, M., Phys. Chem. Chem. Phys. 2008, 10, 6615-6620
doi: 10.1039/b810189b
50 Grimme, S., J. Comput. Chem. 2006, 27, 1787-1799
doi: 10.1002/jcc.20495
51 Schwabe, T.; Grimme, S., Phys. Chem. Chem. Phys. 2007, 9, 3397-3406
doi: 10.1039/b704725h
52 Zhang, Y.; Xu, X.; Goddard, W. A. III, Proc. Natl. Acad. Sci. U.S.A. 2009, 106, 4963-4968
doi: 10.1073/pnas.0901093106
53 Zhao, Y.; Lynch, B. J.; Truhlar, D. G., J. Phys. Chem. A 2004, 108, 4786-4791
doi: 10.1021/jp049253v
54 Grimme, S., J. Chem. Phys . 2006, 124, 034108/1-16
55 Karton, A.; Tarnopolsky, A.; Lamère, J. F.; Schatz, G. C.; Martin, J. M. L., J. Phys. Chem. A 2008, 112, 12868-12886
doi: 10.1021/jp801805p
56 Zhang, I. Y.; Luo, Y.; and Xu, X., J. Chem. Phys . 2010, 132, 194105/1-11
57 Zhang, I. Y.; Luo, Y.; and Xu, X., J. Chem. Phys . 2010, 133, 104105/1-12
58 Zhang, I. Y.; Wu, J. M.; Xu, X., Chem. Commun. 2010, 46, 3057-3070
doi: 10.1039/c000677g
59 Furche, F.; and Perdew, J. P., J. Chem. Phys . 2006, 124, 044103/1-27
60 Perdew, J.; Burke, K.; Ernzerhof, M., Phys. Rev. Lett. 1996, 77, 3865-3868
doi: 10.1103/PhysRevLett.77.3865
61 Boese, A. D.; Handy, N. C., J. Chem. Phys. 2001, 114, 5497-5503
doi: 10.1063/1.1347371
62 Becke, A. D., J. Chem. Phys. 1993, 98, 1372-1377
doi: 10.1063/1.464304
63 Xu, X.; Goddard, W. A. III, Proc. Natl. Acad. Sci. U.S.A. 2004, 101, 2673-2677
doi: 10.1073/pnas.0308730100
64 Xu, X.; Zhang, Q. S.; Muller, R. P.; and Goddard III, W. A., J. Chem. Phys . 2005, 122, 014105/1-14
65 Adamo, C.; Barone, V., J. Chem. Phys. 1999, 110, 6158-6169
doi: 10.1063/1.478522
66 Ernzerhof, M.; Scuseria, G. E., J. Chem. Phys. 1999, 110, 5029-5036
doi: 10.1063/1.478401
67 Cohen, A. J.; Handy, N. C., Mol. Phys. 2001, 99, 607-615
doi: 10.1080/00268970010023435
68 Xu, X.; Goddard, W. A. III, J. Phys. Chem. 2004, 108, 8495-8504
doi: 10.1021/jp047428v
69 Hamprecht, F. A.; Cohen, A.; Tozer, D. J.; Handy, N. C., J. Chem. Phys. 1998, 109, 6264-6271
doi: 10.1063/1.477267
70 Staroverov, V. N.; Scuseria, G. E.; Tao, J.; Perdew, J. P., J. Chem. Phys. 2003, 119, 12129-12137
doi: 10.1063/1.1626543
71 Krukau, A. V.; Vydrov, O. A.; Izmaylov, A. F.; and Scuseria, G. E., J. Chem. Phys . 2006, 125, 224106/1-5
72 Zhao, Y.; Truhlar, D. G., Theor. Chem. Acc. 2008, 120, 215-241
doi: 10.1007/s00214-007-0310-x
73 Zhang, I. Y.; Xu, X., Int. Rev. Phys. Chem. 2011, 30, 115-160
doi: 10.1080/0144235X.2010.542618
74 Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; Nakatsuji, H.; Caricato, M.; Li, X.; Hratchian, H. P.; Izmaylov, A. F.; Bloino, J.; Zheng, G.; Sonnenberg, J. L.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Vreven, T.; Montgomery, J. A. Jr; Peralta, J. E.; Ogliaro, F.; Bearpark, M.; Heyd, J. J.; Brothers, E.; Kudin, K. N.; Staroverov, V. N.; Kobayashi, R.; Normand, J.; Raghavachari, K.; Rendell, A.; Burant, J. C.; Iyengar, S. S.; Tomasi, J.; Cossi, M.; Rega, N.; Millam, J. M.; Klene, M.; Knox, J. E.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Martin, R. L.; Morokuma, K.; Zakrzewski, V. G.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Dapprich, S.; Daniels, A. D.; Farkas, O.; Foresman, J. B.; Ortiz, J. V.; Cioslowski, J.; Fox, D. J., Gaussian 09 , Revision B.01; Gaussian, Inc.: Wallingford, CT, 2009.
75 Knoll, E. H.; Friesner, R. A., J. Phys. Chem. B 2006, 110, 18787-18802
doi: 10.1021/jp0619888
76 Huber, K. P.; Herzberg, G. H., Molecular Spectra and Molecular Structure, IV. Constants of Diatomic Molecules , van Nostrand-Reinhold, New York, 1979
77 Ding, X. L.; Wu, J. M.; Xu, X., Chem. J. Chin. Univ. 2008, 29, 396-398
78 R?sch, N.; Trickey, S. B., J. Chem. Phys. 1997, 106, 8940-8941
doi: 10.1063/1.473946
79 Galbraith, J. M.; Schaefer, H. F. III, J. Chem. Phys. 1996, 105, 862-864
doi: 10.1063/1.471933
80 Jensen, F., J. Chem. Theory Comput. 2010, 6, 2726-2735
doi: 10.1021/ct1003324
81 Zhang, I. Y.; Wu, J. M.; Luo, Y.; Xu, X., J. Comput. Chem. 2011, 32, 1824-1838
doi: 10.1002/jcc.21764
82 Zhang, I. Y.; Wu, J. M.; Luo, Y.; Xu, X., J. Chem. Theory Comput. 2010, 6, 1462-1469
doi: 10.1021/ct100010d
[1] Ruizhou ZHANG, Xiaohong LI, Xianzhou ZHANG. Molecular structure and vibrational spectra of phenobaraitone by density functional theory and ab initio hartree-Fock calculations[J]. Front Chem Chin, 2011, 6(4): 358-366.
[2] Asadollah FARHADI, Mohammad Ali TAKASSI. Applying density functional theory on tautomerism in 3,4-dihydropyrimidin-2(1H)-ones[J]. Front Chem Chin, 2011, 6(2): 142-146.
[3] Jie LIU, Zhenyu GUO, Jin SUN, Wanzhen LIANG. Theoretical studies on electronic spectroscopy and dynamics with the real-time time-dependent density functional theory[J]. Front. Chem. China, 2010, 5(1): 11-28.
[4] Xiaohong LI, Ruizhou ZHANG, Xiangdong YANG, . QSAR study on fluoroquinolones as antibacterial agents active for Pseudomonas aeruginosa[J]. Front. Chem. China, 2010, 5(1): 80-87.
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed