臺灣博碩士論文加值系統

因為一般密度泛函的自我作用誤差 (self-interaction errors) 在水的 hemibond 結構特別大，造成一般的密度泛函無法成功地將 (H 2 O)2+ 的 hemibond 結構，游離成 H2O 與 H2O + 。故分子束縛能的定義 (用 (H 2 O)2+ 的能量扣掉 H2O 與 H2O+ 的能量)，對 (H2O)2+ 來說，並不全面適用：即使一些密度泛函能給出正
確的 (H2O)2+ hemibond 結構的束縛能，但在計算此結構的游離曲線時，會給出較淺的位能；更甚者，許多密度泛函會預測該結構的游離曲線上，會出現一個屏障。出現這個屏障，是完全不合理的。這對想要用這些密度泛函來做分子動力學 (Molecular Dynamics) 的人來說，會造成非常嚴重的後果。因為用這些密度泛函算出來的 (H2O)2+ ，只要越過該屏障，很容易就會游離。為了比較不同的密度泛函在 (H2O)2+ 的表現，我們提供了三種不同的標準：(1) 分子束縛能。(2)
(H2O)2+ 的兩種構型與它們之間的過渡態，這三者之間的相對能量差。(3) 各種不同密度泛函，預測 (H2O)2+ 的游離曲線。我們發現，在這三個標準之中，平均表現最好的，莫屬 wB97X-2(LP) 了。此外，我們也解釋了：為何長距離修正的密度泛函 (long-range corrected hybrid functionals)，不若一般的全域密度泛函(global
hybrid functionals) 一樣，會錯誤地預測 (H2O)2+ 的游離曲線上，有一個假的屏障。

The reason why many exchange correlation functionals fail to give correct binding energies for the hemibonding structures of the ionized water clusters can be traced back to the dissociation behaviors of the hemibonded systems predicted by the exchange correlation functionals, since nearly most of the exchange-correlation functionals cannot predict that the hemibonded structure of the water dimer radical cation will dissociate into H2O and H2O+. Thus, the definition of the binding energies is unfair somehow: Although the previous suggested functionals such as BH&HLYP and MPW1K can give accurate equilibrium binding energies of the hemibonding structure, they fail to predict the correct dissociation limits. This will result in a potential curve which is too shallow. Thus, the hemibonded structure calculated by those functionals is much easier to dissociate than it actually should be. Therefore we propose three different criteria to reexamine the water dimer radi-cal cation: (i) The binding energies, (ii) the relative energies between the conformers of the ionized water dimer and (iii) the dissociation behaviors predicted by various exchange correlation functionals. We find that the functional which behaves well all over these three criteria is the wB97X-2 functional. Reasons that LC hybrid functionals generally work better than conventional density functionals for hemibonded systems is also explained in this work.

1 Introduction 7
2 The Hartree-Fock Theory 10
3 Density Functional Theory 13
3.1 The Kohn-Sham Scheme 13
3.2 The Exchange-Correlation Functionals 15
3.2.1 The Local Density Approximation (LDA) 15
3.2.2 The Generalized Gradient Approximations (GGAs) 15
3.2.3 The Hybrid Functionals 16
4 Results and Discussion 17
4.1 Criterion I: Binding Energies 17
4.2 Criterion II: Relative energies 19
4.3 Criterion III: Dissociation behavior 21
5 Summary and Conclusions 37
Bibliography 39

[1] B. C. Garrett; et al., Chem. Rev., 2005, 105, 355.
[2] J. A. LaVerne and S. M. Pimblott, J. Phys. Chem. A, 2000, 104, 9820.
[3] A. Furuhama, M. Dupuis and K. Hirao, Phys. Chem. Chem. Phys., 2008, 10,
2033-2042.
[4] L. Angel and A. J. Stace, Chem. Phys. Lett., 2001, 345, 227.
[5] R. N. Barnett and U. Landman, J. Phys. Chem. A, 1997, 101, 164.
[6] F. Dong, S. Heinbuch, J. J. Rocca and E. R. Bernstein, J. Chem. Phys., 2006,
124, 224319.
[7] G. H. Gardenier, M. A. Johnson and A. B. McCoy, J. Phys. Chem. A, 2009,
113, 4772.
[8] K. Mizuse, J.-L. Kuo and A. Fujii, Chem. Sci., 2011, 2, 868 DOI: 10.1039/
c0sc00604a.
[9] M. Sodupe, J. Bertran, L. Rodríguez-Santiago and E. J. Baerends, J. Phys.
Chem. A, 1999, 103, 166.
[10] J. Gräfenstein, E. Kraka and D. Cremer, Phys. Chem. Chem. Phys., 2004, 6,
1096.
[11] P. Hohenberg and W. Kohn, Phys. Rev., 1964, 136, B864.
[12] W. Kohn and L. J. Sham, Phys. Rev., 1965, 140, A1133.
[13] A. D. Becke, J. Chem. Phys., 1993, 98, 1372.
[14] H. M. Lee and K. S. Kim, J. Chem. Theory Comput., 2009, 5, 976.
[15] Q. Cheng, F. A. Evangelista, A. C. Simmonett, Y. Yamaguchi and H. F. Schae-
fer, J. Phys. Chem. A, 2009, 113, 13779.
[16] C. Møller and M. S. Plesset, Phys. Rev., 1934, 46, 618.
[17] A. D. Becke, Phys. Rev. A, 1988, 38, 3098.
[18] C. Lee, W. Yang and R. G. Parr, Phys. Rev. B, 1988, 37, 785.
[19] J. P. Perdew, K. Burke and M. Ernzerhof, Phys. Rev. Lett., 1996, 77, 3865.
[20] Y. Zhao and D. G. Truhlar, J. Chem. Phys., 2006, 125, 194101.
[21] A. D. Becke, J. Chem. Phys., 1997, 107, 8554.
[22] A. D. Becke, J. Chem. Phys., 1993, 98, 5648.
[23] C. Adamo and V. Barone, J. Chem. Phys. 110, 6158 (1999).
[24] Y. Zhao and D. G. Truhlar, Theor. Chem. Acc., 2008, 120, 215.
[25] Y. Zhao, N. E. Schultz and D. G. Truhlar, J. Chem. Phys., 2005, 123, 161103.
[26] A. D. Becke, J. Chem. Phys., 1993, 98, 1372.
[27] Y. Zhao, N. E. Schultz and D. G. Truhlar, J. Chem. Theory Comput., 2006, 2,
364.
[28] Y. Zhao and D. G. Truhlar, J. Phys. Chem. A, 2006, 110, 13126.
[29] J.-D. Chai and M. Head-Gordon, J. Chem. Phys., 2008, 128, 084106.
[30] J.-D. Chai and M. Head-Gordon, Phys. Chem. Chem. Phys., 2008, 10, 6615.
[31] J.-D. Chai and M. Head-Gordon, J. Chem. Phys., 2009, 131, 174105.
[32] J.-D. Chai and M. Head-Gordon, Chem. Phys. Lett., 2008, 467, 176.
[33] S. Grimme, J. Chem. Phys., 2006, 124, 034108.
[34] R. A. Kendall and H. A. Früchtl, Theor. Chem. Acc., 1997, 97, 158.
[35] Y. Shao, L. Fusti-Molnar, Y. Jung, J. Kussmann, C. Ochsenfeld, S. T. Brown,
A. T. B. Gilbert, L. V. Slipchenko,S. V. Levchenko, D. P. O’Neill, R. A. Distasio
Jr., R. C. Lochan, T. Wang, G. J. O. Beran, N. A. Besley, J. M., Herbert, C.
Y. Lin, T. Van Voorhis, S. H. Chien, A. Sodt, R. P. Steele, V. A. Rassolov,
P. E. Maslen, P. P. Korambath, R. D. Adamson, B. Austin, J. Baker, E. F. C.
Byrd, H. Dachsel, R. J. Doerksen, A. Dreuw, B. D. Dunietz, A. D. Dutoi, T. R.
Furlani, S. R. Gwaltney, A. Heyden, S. Hirata, C.-P. Hsu, G. Kedziora, R. Z.
Khalliulin, P. Klunzinger, A. M. Lee, M. S. Lee, W. Liang, I. Lotan, N. Nair, B.
Peters, E. I. Proynov, P. A. Pieniazek, Y. M. Rhee, J. Ritchie, E. Rosta, C. D.
Sherrill, A. C. Simmonett, J. E. Subotnik, H. L. Woodcock III, W. Zhang, A. T.
Bell, A. K. Chakraborty, D. M. Chipman, F. J. Keil, A. Warshel, W. J. Hehre,
H. F. Schaefer III, J. Kong, A. I. Krylov, P. M. W. Gill and M. Head-Gordon,
Phys. Chem. Chem. Phys., 2006, 8, 3172.
[36] Y.-S. Lin, C.-W. Tsai, G.-D. Li and J.-D. Chai, J. Chem. Phys., 2012 136,
154109.
[37] J. Gräfenstein, E. Kraka and D. Cremer, J. Chem. Phys., 2004, 120, 524.
[38] P. M. W. Gill, R. D. Adamson and J. A. Pople, Mol. Phys., 1996, 88, 1005.
[39] J.-D. Chai and S.-P. Mao, Chem. Phys. Lett., 2012, 538, 121.