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

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

AYERS Paul W. ^1,, ,
LEVY Mel ^2,3,4,,

1.
Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario L8S 4M1, Canada
2.
Department of Physics, North Carolina A & T State University, Greensboro, NC 27411, USA
3.
Department of Chemistry, Duke University, Durham, NC 27708, USA
4.
Department of Chemistry, Tulane University, New Orleans, LA 70118, USA

Corresponding author: AYERS Paul W., ayers@mcmaster.ca LEVY Mel, mlevy@tulane.edu
Received Date: 25 September 2017
Revised Date: 2 November 2017
Accepted Date: 2 November 2017
Available Online: 7 June 2017

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.
1. [1]
  Hohenberg, P.; Kohn, W. Phys. Rev. 1964, 136, B864. doi: 10.1103/PhysRev.136.B864 doi: 10.1103/PhysRev.136.B864
2. [2]
  Parr, R. G.; Yang, W. Density-Functional Theory of Atoms and Molecules; Oxford UP: New York, NY, USA, 1989.
3. [3]
  Kohn, W.; Becke, A. D.; Parr, R. G. J. Phys. Chem. 1996, 100, 12974. doi: 10.1021/jp960669l doi: 10.1021/jp960669l
4. [4]
  Kohn, W. Rev. Mod. Phys. 1999, 71, 1253. doi: 10.1103/RevModPhys.71.1253 doi: 10.1103/RevModPhys.71.1253
5. [5]
  Levy, M. Proc. Natl. Acad. Sci. USA 1979, 76, 6062. doi: 10.1073/pnas.76.12.6062 doi: 10.1073/pnas.76.12.6062
6. [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. doi: 10.1007/978-1-4757-0818-9_2 doi: 10.1007/978-1-4757-0818-9_2
7. [7]
  Perdew, J. P.; Levy, M. Phys. Rev. B 1985, 31, 6264. doi: 10.1103/PhysRevB.31.6264 doi: 10.1103/PhysRevB.31.6264
8. [8]
  Gorling, A. Phys. Rev. A 1996, 54, 3912. doi: 10.1103/PhysRevA.54.3912 doi: 10.1103/PhysRevA.54.3912
9. [9]
  Gorling, A. Phys. Rev. A 1999, 59, 3359. doi: 10.1103/PhysRevA.59.3359 doi: 10.1103/PhysRevA.59.3359
10. [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; pp. 299-308.
11. [11]
  Levy, M.; Nagy, A. Phys. Rev. Lett. 1999, 83, 4361. doi: 10.1103/PhysRevLett.83.4361 doi: 10.1103/PhysRevLett.83.4361
12. [12]
  Levy, M.; Nagy, A. Phys. Rev. A 1999, 59, 1687. doi: 10.1103/PhysRevA.59.1687 doi: 10.1103/PhysRevA.59.1687
13. [13]
  Nagy, A.; Levy, M. Phys. Rev. A 2001, 63, 052502. doi: 10.1103/PhysRevA.63.052502 doi: 10.1103/PhysRevA.63.052502
14. [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; p. 121.
15. [15]
  Ayers, P. W.; Levy, M. Phys. Rev. A 2009, 80, 012508. doi: 10.1103/PhysRevA.80.012508 doi: 10.1103/PhysRevA.80.012508
16. [16]
  Ayers, P. W.; Nagy, A.; Levy, M. Phys. Rev. A 2012, 85, 042518. doi: 10.1103/PhysRevA.85.042518 doi: 10.1103/PhysRevA.85.042518
17. [17]
  Ayers, P. W.; Levy, M.; Nagy, A. J. Chem. Phys. 2015, 143 (19), 4. doi: 10.1063/1.4934963 doi: 10.1063/1.4934963
18. [18]
  Evangelista, F. A.; Shushkov, P.; Tully, J. C. J. Phys. Chem. A 2013, 117 (32), 7378. doi: 10.1021/jp401323d doi: 10.1021/jp401323d
19. [19]
  Glushkov, V. N.; Assfeld, X. J. Chem. Phys. 2010, 132, 204106. doi: 10.1063/1.3443777 doi: 10.1063/1.3443777
20. [20]
  Glushkov, V. N.; Levy, M. J. Chem. Phys. 2007, 126, 174106. doi: 10.1063/1.2733657 doi: 10.1063/1.2733657
21. [21]
  Miranda-Quintana, R. A.; Gonzalez, M. M. Int. J. Quantum Chem. 2013, 113 (22), 2478. doi: 10.1002/qua.24486 doi: 10.1002/qua.24486
22. [22]
  Ayers, P. W. Variational Principles for Understanding Chemical Reactions. Ph.D. Dissertation, University of North Carolina: Chapel Hill, NV, USA, 2001.
23. [23]
  Perdew, J. P.; Parr, R. G.; Levy, M.; Balduz, J. L., Jr. Phys. Rev. Lett. 1982, 49, 1691. doi: 10.1103/PhysRevLett.49.1691 doi: 10.1103/PhysRevLett.49.1691
24. [24]
  Zhang, Y. K.; Yang, W. T. Theor. Chem. Acc. 2000, 103, 346. doi: 10.1007/s002149900021 doi: 10.1007/s002149900021
25. [25]
  Yang, W. T.; Zhang, Y. K.; Ayers, P. W. Phys. Rev. Lett. 2000, 84, 5172. doi: 10.1103/PhysRevLett.84.5172 doi: 10.1103/PhysRevLett.84.5172
26. [26]
  Ayers, P. W. J. Math. Chem. 2008, 43, 285. doi: 10.1007/s10910-006-9195-5 doi: 10.1007/s10910-006-9195-5
27. [27]
  Liu, S. B. Acta Phys. -Chim. Sin. 2009, 25, 590. doi: 10.3866/PKU.WHXB20090332 doi: 10.3866/PKU.WHXB20090332
28. [28]
  Ayers, P. W.; Anderson, J. S. M.; Bartolotti, L. J. Int. J. Quantum Chem. 2005, 101, 520. doi: 10.1002/qua.20307 doi: 10.1002/qua.20307
29. [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; pp. 715-764.
30. [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; Vol. 1, pp. 233-270.
31. [31]
  Gazquez, J. L. J. Mex. Chem. Soc. 2008, 52, 3.
32. [32]
  Geerlings, P.; De Proft, F.; Langenaeker, W. Chem. Rev. 2003, 103, 1793. doi: 10.1021/cr990029p doi: 10.1021/cr990029p
33. [33]
  Heidar-Zadeh, F.; Miranda-Quintana, R. A.; Verstraelen, T.; Bultinck, P.; Ayers, P. W. J. Chem. Theory Comp. 2016, 12 (12), 5777. doi: 10.1021/acs.jctc.6b00494 doi: 10.1021/acs.jctc.6b00494
34. [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. doi: 10.1016/j.cplett.2016.07.039 doi: 10.1016/j.cplett.2016.07.039
35. [35]
  Liu, S. B.; Schauer, C. K.; Pedersen, L. G. J. Chem. Phys. 2009, 131, 164107. doi: 10.1063/1.3251124 doi: 10.1063/1.3251124
36. [36]
  Ayers, P. W.; Parr, R. G.; Pearson, R. G. J. Chem. Phys. 2006, 124, 194107. doi: 10.1063/1.2196882 doi: 10.1063/1.2196882
37. [37]
  Chattaraj, P. K.; Ayers, P. W.; Melin, J. Phys. Chem. Chem. Phys. 2007, 9, 3853. doi: 10.1039/b705742c doi: 10.1039/b705742c
38. [38]
  Ayers, P. W. Faraday Discuss. 2007, 135, 161. doi: 10.1039/b606877d doi: 10.1039/b606877d
39. [39]
  Chattaraj, P. K.; Ayers, P. W. J. Chem. Phys. 2005, 123, 086101. doi: 10.1063/1.2011395 doi: 10.1063/1.2011395
40. [40]
  Kutzelnigg, W. J. Chem. Phys. 1985, 82 (9), 4166. doi: 10.1063/1.448859 doi: 10.1063/1.448859
41. [41]
  Kutzelnigg, W.; Koch, S. J. Chem. Phys. 1983, 79 (9), 4315. doi: 10.1063/1.446313 doi: 10.1063/1.446313
42. [42]
  Kutzelnigg, W. J. Chem. Phys. 1982, 77 (6), 3081. doi: 10.1063/1.444231 doi: 10.1063/1.444231
43. [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; pp. 35-68.
44. [44]
  Kutzelnigg, W. J. Chem. Phys. 1984, 80 (2), 822. doi: 10.1063/1.446736 doi: 10.1063/1.446736
45. [45]
  Stone, M. H. Linear Transformations in Hilbert Space; American Mathematical Society: New York, NY, USA, 1932; Vol. 15.
46. [46]
  Eschrig, H. The Fundamentals of Density Functional Theory. Eagle: Leipzig, Germany, 2003.
47. [47]
  Eschrig, H. Phys. Rev. B 2010, 82, 205120. doi: 10.1103/PhysRevB.82.205120 doi: 10.1103/PhysRevB.82.205120
48. [48]
  Malek, A. M.; Balawender, R. arXiv:1310.6918 2013.
49. [49]
  Malek, A.; Balawender, R. J. Chem. Phys. 2015, 142. 054104. doi: 10.1063/1.4906555 doi: 10.1063/1.4906555
50. [50]
  Franco-Perez, M.; Ayers, P. W.; Gazquez, J. L. Theor. Chem. Acc. 2016, 135 (8), 199. doi: 10.1007/s00214-016-1961-2 doi: 10.1007/s00214-016-1961-2
51. [51]
  Franco-Perez, M.; Ayers, P. W.; Gazquez, J. L.; Vela, A. J. Chem. Phys. 2015, 143 (24), 244117. doi: 10.1063/1.4938422 doi: 10.1063/1.4938422
52. [52]
  Franco-Perez, M.; Gazquez, J. L.; Ayers, P. W.; Vela, A. J. Chem. Phys. 2015, 143 (15), 154103. doi: 10.1063/1.4932539 doi: 10.1063/1.4932539
53. [53]
  Miranda-Quintana, R. A.; Ayers, P. W. J. Chem. Phys. 2016, 144 (24), 244112. doi: 10.1063/1.4953557 doi: 10.1063/1.4953557
54. [54]
  Bochicchio, R. C.; Miranda-Quintana, R. A.; Rial, D. J. Chem. Phys. 2013, 139 (19), 191101. doi: 10.1063/1.4832495 doi: 10.1063/1.4832495
55. [55]
  Franco-Perez, M.; Heidar-Zadeh, F.; Ayers, P. W.; Gazquez, J. L.; Vela, A. Phys. Chem. Chem. Phys. 2017, 19 (18), 11588. doi: 10.1039/c7cp00224f doi: 10.1039/c7cp00224f
56. [56]
  Gyftopoulos, E. P.; Hatsopoulos, G. N. Proc. Natl. Acad. Sci. USA 1965, 60, 786.
57. [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; pp. 571-616.
58. [58]
  Ayers, P. W.; Levy, M. Theor. Chem. Acc. 2000, 103, 353. doi: 10.1007/s002149900093 doi: 10.1007/s002149900093
59. [59]
  Valone, S. M. J. Chem. Phys. 1980, 73, 4653. doi: 10.1063/1.440656 doi: 10.1063/1.440656
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