Calculations of ionization energies and electron affinities for atoms and molecules: A comparative study with different methods

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

References

[1] Lias, S. G.; Bartmess, J. E., http://webbook.nist.gov/chemistry/ion (retrieved <month>Oct</month>. <day>19</day>, 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

[6] Mulliken, R. S., J. Chem. Phys.1934, 2, 782-793

[7] Ayers, P. W., J. Math. Chem.2008, 43, 285-303

[8] Parr, R. G.; Pearson, R. G., J. Am. Chem. Soc.1983, 105, 7512-7516

[9] Parr, R. G.; Szentpaly, L. V.; Liu, S., J. Am. Chem. Soc.1999, 121, 1922-1924

[10] Yokojima, S.; Yoshiki, N.; Yanoi, W.; Okada, A., J. Phys. Chem. B2009, 113, 16384-16392

[11] Smalo, H. S.; Astrand, P. O.; Ingebrigtsen, S., IEEE Trans. Dielectr. Electr. Insul.2010, 17, 733-741

[12] Steenken, S.; Telo, J. P.; Novais, H. M.; Candeias, L. P., J. Am. Chem. Soc.1992, 114, 4701-4709

[13] Khistyaev, K.; Bravaya, K. B.; Kamarchik, E.; Kostko, O.; Ahmed, M.; Krylov, A. I., Faraday Discuss.2011, 150, 313-330

[14] Vijayaraj, R.; Subramanian, V.; Chattaraj, P. K., J. Chem. Theory Comput.2009, 5, 2744-2753

[15] Fayet, G.; Joubert, L.; Rotureau, P.; Adamo, C., Chem. Phys. Lett.2009, 467, 407-411

[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

[18] Stanton, J. F.; Gauss, J., J. Chem. Phys.1999, 111, 8785-8788

[19] Kemeny, A. E.; Francisco, J. S.; Dixon, D. A.; Feller, D., J. Chem. Phys.2003, 118, 8290-8295

[20] Parthiban, S.; Martin, J. M. L., J. Chem. Phys.2001, 114, 6014-6029

[21] Pople, J. A.; Head-Gordon, M.; Fox, D. J.; Raghavachari, K.; Curtiss, L. A., J. Chem. Phys.1989, 90, 5622-5629

[22] Curtiss, L. A.; Raghavachari, K.; Trucks, G. W.; Pople, J. A., J. Chem. Phys.1991, 94, 7221-7230

[23] Curtiss, L. A.; Raghavachari, K.; Redfern, P. C.; Rassolov, V.; Pople, J. A., J. Chem. Phys.1998, 109, 7764-7776

[24] Curtiss, L. A.; Redfern, P. C.; Raghavachari, K., J. Chem. Phys.2007, 126, 84108-84112

[25] Montgomery, J. A. Jr; Frisch, M. J.; Ochterski, J. W.; Petersson, G. A., J. Chem. Phys.1999, 110, 2822-2827

[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

[28] Rienstra-Kiracofe, J. C.; Tschumper, G. S.; Schaefer, H. F.; Nandi, S.; Ellison, G. B., Chem. Rev.2002, 102, 231-282

[29] Zhang, H. Y.; Sung, Y. M.; Wang, X. L., Chem. Euro. J.2003, 9, 502-508

[30] Joanteguy, S.; Pfister-Guillouzo, G.; Chermette, H., J. Phys. Chem. A1999, 103, 3505-3511

[31] Becke, A. D., Phys. Rev. A1988, 38, 3098-3100

[32] Lee, C. T.; Yang, W. T.; Parr, R. G., Phys. Rev. B1988, 37, 785-789

[33] Perdew, J. P., Phys. Rev. B1986, 33, 8822-8824

[34] Perdew, J. P.; Wang, Y., Phys. Rev. B1992, 45, 13244-13249

[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

[37] Becke, A. D., J. Chem. Phys.1993, 98, 5648-5652

[38] Stephens, P. J.; Devlin, F. J.; Chabalowski, C. F.; Frisch, M. J., J. Phys. Chem.1994, 98, 11623-11627

[39] Van Voorhis, T.; Scuseria, G. E., J. Chem. Phys.1998, 109, 400-410

[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

[43] Schmider, H. L.; Becke, A. D., J. Chem. Phys.1998, 108, 9624-9631

[44] Iikura, H.; Tsuneda, T.; Yanai, T.; Hirao, K., J. Chem. Phys.2001, 115, 3540-3544

[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

[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

[50] Grimme, S., J. Comput. Chem.2006, 27, 1787-1799

[51] Schwabe, T.; Grimme, S., Phys. Chem. Chem. Phys.2007, 9, 3397-3406

[52] Zhang, Y.; Xu, X.; Goddard, W. A. III, Proc. Natl. Acad. Sci. U.S.A.2009, 106, 4963-4968

[53] Zhao, Y.; Lynch, B. J.; Truhlar, D. G., J. Phys. Chem. A2004, 108, 4786-4791

[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. A2008, 112, 12868-12886

[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

[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

[61] Boese, A. D.; Handy, N. C., J. Chem. Phys.2001, 114, 5497-5503

[62] Becke, A. D., J. Chem. Phys.1993, 98, 1372-1377

[63] Xu, X.; Goddard, W. A. III, Proc. Natl. Acad. Sci. U.S.A.2004, 101, 2673-2677

[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

[66] Ernzerhof, M.; Scuseria, G. E., J. Chem. Phys.1999, 110, 5029-5036

[67] Cohen, A. J.; Handy, N. C., Mol. Phys.2001, 99, 607-615

[68] Xu, X.; Goddard, W. A. III, J. Phys. Chem.2004, 108, 8495-8504

[69] Hamprecht, F. A.; Cohen, A.; Tozer, D. J.; Handy, N. C., J. Chem. Phys.1998, 109, 6264-6271

[70] Staroverov, V. N.; Scuseria, G. E.; Tao, J.; Perdew, J. P., J. Chem. Phys.2003, 119, 12129-12137

[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

[73] Zhang, I. Y.; Xu, X., Int. Rev. Phys. Chem.2011, 30, 115-160

[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. B2006, 110, 18787-18802

[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] Rösch, N.; Trickey, S. B., J. Chem. Phys.1997, 106, 8940-8941

[79] Galbraith, J. M.; Schaefer, H. F. III, J. Chem. Phys.1996, 105, 862-864

[80] Jensen, F., J. Chem. Theory Comput.2010, 6, 2726-2735

[81] Zhang, I. Y.; Wu, J. M.; Luo, Y.; Xu, X., J. Comput. Chem.2011, 32, 1824-1838

[82] Zhang, I. Y.; Wu, J. M.; Luo, Y.; Xu, X., J. Chem. Theory Comput.2010, 6, 1462-1469

Acknowledgments

This work was supported by the National Natural Science Foundation of China (Nos. 91027044, 20973138, 21133004), and the Ministry of Science and Technology of China (Nos. 2007CB815206, 2011CB808505).

RIGHTS & PERMISSIONS

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg