Levy Constrained Search in Fock Space: An Alternative Approach to Noninteger Electron Number

doi:10.3866/PKU.WHXB201711071

Abstract

Abstract:

By extending the Levy wavefunction constrained search to Fock Space, one can define a wavefunction constrained search for electron densities in systems having noninteger number of electrons. For pure-state v-representable densities, the results are equivalent to what one would obtain with the zero-temperature grand canonical ensemble. In other cases, the wavefunction constrained search in Fock space presents an upper bound to the grand canonical ensemble functional. One advantage of the Fock-space wavefunction constrained search functional over the zero-temperature grand-canonical ensemble constrained search functional is that certain specific excited states (i.e., those that are not ground-state v-representable) are the stationary points of the Fock-space functional. However, a potential disadvantage of the Fock-space constrained search functional is that it is not convex.

Key words: Density functional theory, Levy constrained search functional, Fock space, Fractional electron number, Excited-state density functional theory, Universal density functional, Zero temperature grand canonical ensemble, Convexity

Paul W. AYERS,Mel LEVY. Levy Constrained Search in Fock Space: An Alternative Approach to Noninteger Electron Number[J]. Acta Phys. -Chim. Sin. 2018, 34(6), 625-630. doi: 10.3866/PKU.WHXB201711071

References

1	Hohenberg P. ; Kohn W. Phys. Rev. 1964, 136, B864.
2	Parr R. G. ; Yang W. Density-Functional Theory of Atoms and Molecules Oxford UP: New York, NY, USA, 1989.
3	Kohn W. ; Becke A. D. ; Parr R. G. J. Phys. Chem. 1996, 100, 12974.
4	Kohn W. Rev. Mod. Phys. 1999, 71, 1253.
5	Levy M. Proc. Natl. Acad. Sci. USA 1979, 76, 6062.
6	Levy M. ; Perdew J. P. The Constrained Search Formulation of Density Functional Theory. In Density Functional Methods in Physics, NATO ASI Series (Series B: Physics), Vol. 123; Dreizler, R. M., da Providência, J. Eds. Springer: Boston, MA, USA.
7	Perdew J. P. ; Levy M. Phys. Rev. B 1985, 31, 6264.
8	Gorling A. Phys. Rev. A 1996, 54, 3912.
9	Gorling A. Phys. Rev. A 1999, 59, 3359.
10	Levy M. In On Time-Independent Density-Functional Theories for Excited States, Proceedings of the 1st International Workshop Electron Correlation and Material Properties 1999, 299- 308.
11	Levy M. ; Nagy A. Phys. Rev. Lett. 1999, 83, 4361.
12	Levy M. ; Nagy A. Phys. Rev. A 1999, 59, 1687.
13	Nagy A. ; Levy M. Phys. Rev. A 2001, 63, 052502.
14	Nagy A. ; Levy M. Ayers P. W. Time-Independent Theory for a Single Excited State. In Chemical Reactivity Theory: A Density Functional View; Chattaraj, P. K., Ed. Taylor and Francis: Boca Raton, FL, USA, 2009, 121.
15	Ayers P. W. ; Levy M. Phys. Rev. A 2009, 80, 012508.
16	Ayers P. W. ; Nagy A. ; Levy M. Phys. Rev. A 2012, 85, 042518.
17	Ayers P. W. ; Levy M. ; Nagy A. J. Chem. Phys. 2015, 143 (19), 4.
18	Evangelista F. A. ; Shushkov P. ; Tully J. C. J. Phys. Chem. A 2013, 117 (32), 7378.
19	Glushkov V. N. ; Assfeld X. J. Chem. Phys. 2010, 132, 204106.
20	Glushkov V. N. ; Levy M. J. Chem. Phys. 2007, 126, 174106.
21	Miranda-Quintana R. A. ; Gonzalez M. M. Int. J. Quantum Chem. 2013, 113 (22), 2478.
22	Ayers P. W. Variational Principles for Understanding Chemical Reactions. Ph.D. Dissertation University of North Carolina: Chapel Hill, NV, USA, 2001.
23	Perdew J. P. ; Parr R. G. ; Levy M. ; Balduz J. L. , Jr. Phys. Rev. Lett. 1982, 49, 1691.
24	Zhang Y. K. ; Yang W. T. Theor. Chem. Acc. 2000, 103, 346.
25	Yang W. T. ; Zhang Y. K. ; Ayers P. W. Phys. Rev. Lett. 2000, 84, 5172.
26	Ayers P. W. J. Math. Chem. 2008, 43, 285.
27	Liu S. B. Acta Phys. -Chim. Sin. 2009, 25, 590.
28	Ayers P. W. ; Anderson J. S. M. ; Bartolotti L. J. Int. J. Quantum Chem. 2005, 101, 520.
29	Johnson P. A. ; Bartolotti L. J. ; Ayers P. W. ; Fievez T. ; Geerlings P. Charge Density and Chemical Reactivity: A Unified View from Conceptual DFT. In Modern Charge Density Analysis; Gatti, C., Macchi, P. Eds. Springer: New York, NY, USA, 2012, 715- 764.
30	De Proft F. ; Geerlings P. ; Ayers P. W. The conceptual Density Functional Theory Perspective of Bonding. In The Chemical Bond: Fundamental Aspects of Chemical Bonding; Shaik, S., Frenking, G., Eds. Wiley: Darmstadt, Germany, 2014, 1, 233- 270.
31	Gazquez J. L. J. Mex. Chem. Soc. 2008, 52, 3.
32	Geerlings P. ; De Proft F. ; Langenaeker W. Chem. Rev. 2003, 103, 1793.
33	Heidar-Zadeh F. ; Miranda-Quintana R. A. ; Verstraelen T. ; Bultinck P. ; Ayers P. W. J. Chem. Theory Comp. 2016, 12 (12), 5777.
34	Heidar-Zadeh F. ; Richer M. ; Fias S. ; Miranda-Quintana R. A. ; Chan M. ; Franco-Perez M. ; Gonzalez-Espinoza C. E. ; Kim T. D. ; Lanssens C. ; Patel A. H. G., et al. Chem. Phys. Lett. 2016, 660, 307.
35	Liu S. B. ; Schauer C. K. ; Pedersen L. G. J. Chem. Phys. 2009, 131, 164107.
36	Ayers P. W. ; Parr R. G. ; Pearson R. G. J. Chem. Phys. 2006, 124, 194107.
37	Chattaraj P. K. ; Ayers P. W. ; Melin J. Phys. Chem. Chem. Phys. 2007, 9, 3853.
38	Ayers P. W. Faraday Discuss. 2007, 135, 161.
39	Chattaraj P. K. ; Ayers P. W. J. Chem. Phys. 2005, 123, 086101.
40	Kutzelnigg W. J. Chem. Phys. 1985, 82 (9), 4166.
41	Kutzelnigg W. ; Koch S. J. Chem. Phys. 1983, 79 (9), 4315.
42	Kutzelnigg W. J. Chem. Phys. 1982, 77 (6), 3081.
43	Kutzelnigg W. Quantum chemistry In Fock Space. In Aspects of Many-Body Effects in Molecules and Extended Systems; Mukherjee, D., Ed., Springer-Verlag: Berlin, Germany, 1989, 35- 68.
44	Kutzelnigg W. J. Chem. Phys. 1984, 80 (2), 822.
45	Stone M. H. Linear Transformations in Hilbert Space American Mathematical Society: New York, NY, USA, 1932, 15
46	Eschrig H. The Fundamentals of Density Functional Theory Eagle: Leipzig, Germany, 2003.
47	Eschrig H. Phys. Rev. B 2010, 82, 205120.
48	Malek A. M. ; Balawender R. arXiv:1310.6918 2013.
49	Malek A. ; Balawender R. J. Chem. Phys. 2015, 142, 054104.
50	Franco-Perez M. ; Ayers P. W. ; Gazquez J. L. Theor. Chem. Acc. 2016, 135 (8), 199.
51	Franco-Perez M. ; Ayers P. W. ; Gazquez J. L. ; Vela A. J. Chem. Phys. 2015, 143 (24), 244117.
52	Franco-Perez M. ; Gazquez J. L. ; Ayers P. W. ; Vela A. J. Chem. Phys. 2015, 143 (15), 154103.
53	Miranda-Quintana R. A. ; Ayers P. W. J. Chem. Phys. 2016, 144 (24), 244112.
54	Bochicchio R. C. ; Miranda-Quintana R. A. ; Rial D. J. Chem. Phys. 2013, 139 (19), 191101.
55	Franco-Perez M. ; Heidar-Zadeh F. ; Ayers P. W. ; Gazquez J. L. ; Vela A. Phys. Chem. Chem. Phys. 2017, 19 (18), 11588.
56	Gyftopoulos E. P. ; Hatsopoulos G. N. Proc. Natl. Acad. Sci. USA 1965, 60, 786.
57	Ayers P. W. ; Yang W. Density Functional Theory. In Computational Medicinal Chemistry for Drug Discovery; Bultinck, P., de Winter, H., Langenaeker, W., Tollenaere, J. P. Eds. Dekker: New York, NY, USA, 2003, 571- 616.
58	Ayers P. W. ; Levy M. Theor. Chem. Acc. 2000, 103, 353.
59	Valone S. M. J. Chem. Phys. 1980, 73, 4653.

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