Citation: FINZEL Kati., BULTINCK Patrick.. The Influence of the Exchange-Correlation Functional on the Non-Interacting Kinetic Energy and Its Implications for Orbital-Free Density Functional Approximations[J]. Acta Physico-Chimica Sinica, ;2018, 34(6): 650-655. doi: 10.3866/PKU.WHXB201710251 shu

The Influence of the Exchange-Correlation Functional on the Non-Interacting Kinetic Energy and Its Implications for Orbital-Free Density Functional Approximations

FINZEL Kati. ^, ,
BULTINCK Patrick.

Department of Inorganic and Physical Chemistry, Ghent University, 281 Krijgslaan, 9000 Ghent, Belgium

Corresponding author: FINZEL Kati., Kati.Finzel@UGent.be
Received Date: 25 August 2017
Revised Date: 27 September 2017
Accepted Date: 19 October 2017
Available Online: 15 June 2017
Fund Project: The project was supported by the Fund for Scientific Research in Flanders (FWO-Vlaanderen) for Research Grant G021115N

In this work it is shown that the kinetic energy and the exchange-correlation energy are mutual dependent on each other. This aspect is first derived in an orbital-free context. It is shown that the total Fermi potential depends on the density only, the individual parts, the Pauli kinetic energy and the exchange-correlation energy, however, are orbital dependent and as such mutually influence each other. The numerical investigation is performed for the orbital-based non-interacting Kohn-Sham system in order to avoid additional effects due to further approximations of the kinetic energy. The numerical influence of the exchange-correlation functional on the non-interacting kinetic energy is shown to be of the order of a few Hartrees. For chemical purposes, however, the energetic performance as a function of the nuclear coordinates is much more important than total energies. Therefore, the effect on the bond dissociation curve was studied exemplarily for the carbon monoxide. The data reveals that, the mutual influence between the exchange-correlation functional and the kinetic energy has a significant influence on bond dissociation energies and bond distances. Therefore, the effect of the exchange-correlation treatment must be considered in the design of orbital-free density functional approximations for the kinetic energy.
- Density functional approximation,
- Density functional approximation,
- Kinetic energy functional,
- Exchangecorrelation functional,
- Bond dissociation energy,
- Bond distance
1. [1]
  Ho, G. S.; Lignères, V. L.; Carter, E. A. Comput. Phys. Comm. 2008, 179, 839. doi: 10.1016/j.cpc.2008.07.002 doi: 10.1016/j.cpc.2008.07.002
2. [2]
  Karasiev, V.; Sjostrom, T.; Trickey, S. B. Computer Phys. Commun. 2014, 185, 3240. doi: 10.1016/j.cpc.2014.08.023 doi: 10.1016/j.cpc.2014.08.023
3. [3]
  Lehtomäki, J.; Makkonen, I.; Caro, M. A.; Harju, A.; Lopez-Acevedo, O. J. Chem. Phys. 2014, 141, 234102. doi: 10.1063/1.4903450 doi: 10.1063/1.4903450
4. [4]
  Ghosh, S.; Suryanarayana, P. J. Comput. Phys. 2016, 307, 634. doi: 10.1016/j.jcp.2015.12.027 doi: 10.1016/j.jcp.2015.12.027
5. [5]
  Thomas, L. H. Proc. Cambridge Philos. Soc. 1927, 23, 542. doi: 10.1017/S0305004100011683 doi: 10.1017/S0305004100011683
6. [6]
  Fermi, E. Zeitschrift für Physik 1928, 48, 73. doi: 10.1007/BF01351576 doi: 10.1007/BF01351576
7. [7]
  Hohenberg, P.; Kohn, W. Phys. Rev. B 1964, 136, 864. doi: 10.1103/PhysRev.136.B864 doi: 10.1103/PhysRev.136.B864
8. [8]
  Kohn, W.; Sham, L. J. Phys. Rev. A 1965, 140, 1133. doi: 10.1103/PhysRev.140.A1133 doi: 10.1103/PhysRev.140.A1133
9. [9]
  Ayers, P. W.; Liu, S. Phys. Rev. A 2007, 75, 022514. doi: 10.1103/PhysRevA.75.022514 doi: 10.1103/PhysRevA.75.022514
10. [10]
  Ludeña, E. V.; Illas, F.; Ramirez-Solis, A. Int. J. Mod. Phys. B 2008, 22, 4642. doi: 10.1142/S0217979208050395 doi: 10.1142/S0217979208050395
11. [11]
  Kryachko, E. S.; Ludeña, E. V. Phys. Rep. 2014, 544, 123. doi: 10.1016/j.physrep.2014.06.002 doi: 10.1016/j.physrep.2014.06.002
12. [12]
  von Weizsäcker, C. F. Z. Phys. 1935, 96, 431. doi: 10.1007/BF01337700 doi: 10.1007/BF01337700
13. [13]
  Kirzhnits, D. A. Sov. Phys. JETP 1957, 5, 64.
14. [14]
  Hodges, C. H. Can. J. Phys. 1973, 51, 1428. doi: 10.1139/p73-189 doi: 10.1139/p73-189
15. [15]
  Murphy, D. R. Phys. Rev. A 1981, 24, 1682. doi: 10.1103/PhysRevA.24.1682 doi: 10.1103/PhysRevA.24.1682
16. [16]
  Lee, H.; Lee, C.; Parr, R. G. Phys. Rev. A 1991, 44, 768. doi: 10.1103/PhysRevA.44.768 doi: 10.1103/PhysRevA.44.768
17. [17]
  Fuentealba, P.; Reyes, O. Chem. Phys. Lett. 1995, 232, 31. doi: 10.1016/0009-2614(94)01321-L doi: 10.1016/0009-2614(94)01321-L
18. [18]
  Tran, F.; Wesolowski, T. A. Int. J. Quantum Chem. 2002, 89, 441. doi: 10.1002/qua.10306 doi: 10.1002/qua.10306
19. [19]
  Lee, D.; Constantin, L. A.; Perdew, J. P.; Burke, K. J. Chem. Phys. 2009, 130, 034107. doi: 10.1063/1.3059783 doi: 10.1063/1.3059783
20. [20]
  Karasiev, V.; Chakraborty, D.; Trickey, S. B. Many-Electron Approaches in Physics, Chemistry and Mathematic; Delle Site, L.; Bach, V. Eds.; Springer Verlag: Heidelberg, Germany, 2014; pp. 113-134.
21. [21]
  Karasiev, V.; Trickey, S. B. Adv. Quantum Chem. 2015, 71, 221. doi: 10.1016/bs.aiq.2015.02.004 doi: 10.1016/bs.aiq.2015.02.004
22. [22]
  Ghiringhelli, L. M.; Delle Site, L. Phys. Rev. B 2008, 77, 073104. doi: 10.1103/PhysRevB.77.073104 doi: 10.1103/PhysRevB.77.073104
23. [23]
  Ghiringhelli, L. M.; Hamilton, I. P.; Delle Site, L. J. Chem. Phys. 2010, 132, 014106. doi: 10.1063/1.3280953 doi: 10.1063/1.3280953
24. [24]
  Trickey, S.; Karasiev, V. V.; Vela, A. Phys. Rev. B 2011, 84, 075146. doi: 10.1103/PhysRevB.84.075146 doi: 10.1103/PhysRevB.84.075146
25. [25]
  Wang, Y. A.; Carter, E. A. Theoretical Methods in Condensed Phase Chemistry; Schwarz, S. D. Ed.; Kluwer: New York, NY, USA, 2000; pp. 117--184.
26. [26]
  Shin, I.; Carter, E. A. J. Chem. Phys. 2014, 140, 18A531. doi: 10.1063/1.4869867 doi: 10.1063/1.4869867
27. [27]
  Ayers, P. W.; Lucks, J. B.; Parr, R. G. Acta Chimica et Physica Debrecina 2002, 34, 223.
28. [28]
  Bartell, L. S.; Brockway, L. O. Phys. Rev. 1953, 90, 833. doi: 10.1103/PhysRev.90.833 doi: 10.1103/PhysRev.90.833
29. [29]
  Waber, J. T.; Cromer, D. T. J. Chem. Phys. 1965, 42, 4116. doi: 10.1063/1.1695904 doi: 10.1063/1.1695904
30. [30]
  Weinstein, H.; Politzer, P.; Srebrenik, S. Theor. Chim. Acta 1975, 38, 159. doi: 10.1007/BF00581473 doi: 10.1007/BF00581473
31. [31]
  Schmider, H.; Sagar, R.; Smith, V. H., Jr. Can. J. Chem. 1992, 70, 506. doi: 10.1139/v92-072 doi: 10.1139/v92-072
32. [32]
  Yang, W. Phys. Rev. A 1986, 34, 4575. doi: 10.1103/PhysRevA.34.4575 doi: 10.1103/PhysRevA.34.4575
33. [33]
  Dreizler, R. M.; Gross, E. K. U. Density Functional Theory; Springer Verlang: Berlin Heidelberg, Germany, 1990.
34. [34]
  March, N. H. Phys. Lett. A 1986, 113, 476. doi: 10.1016/0375-9601(86)90123-4 doi: 10.1016/0375-9601(86)90123-4
35. [35]
  Levy, M.; Ou-Yang, H. Phys. Rev. A 1988, 38, 625. doi: 10.1103/PhysRevA.38.625 doi: 10.1103/PhysRevA.38.625
36. [36]
  Nagy, A. Acta Phys. Hung. 1991, 70, 321. doi: 10.1007/BF03054145 doi: 10.1007/BF03054145
37. [37]
  Nagy, A.; March, N. H. Int. J. Quantum Chem. 1991, 39, 615. doi: 10.1002/qua.560390408 doi: 10.1002/qua.560390408
38. [38]
  Nagy, A.; March, N. H. Phys. Chem. Liq. 1992, 25, 37. doi: 10.1080/00319109208027285 doi: 10.1080/00319109208027285
39. [39]
  Holas, A.; March, N. H. Int. J. Quantum Chem. 1995, 56, 371. doi: 10.1002/qua.560560423 doi: 10.1002/qua.560560423
40. [40]
  Amovilli, C.; March, N. H. Int. J. Quantum Chem. 1998, 66, 281. doi: 10.1002/(SICI)1097-461X(1998)66:4 <281::AID-QUA3>3.0.CO;2-R doi: 10.1002/(SICI)1097-461X(1998)66:4<281::AID-QUA3>3.0.CO;2-R
41. [41]
  Nagy, A. Chem. Phys. Lett. 2008, 460, 343. doi: 10.1016/j.cplett.2008.05.077 doi: 10.1016/j.cplett.2008.05.077
42. [42]
  Nagy, A. Int. J. Quantum Chem. 2010, 110, 2117. doi: 10.1002/qua.22497 doi: 10.1002/qua.22497
43. [43]
  Nagy, A. J. Chem. Phys. 2011, 135, 044106. doi: 10.1063/1.3607313 doi: 10.1063/1.3607313
44. [44]
  Finzel, K. Int. J. Quantum Chem. 2015, 115, 1629. doi: 10.1002/qua.24986 doi: 10.1002/qua.24986
45. [45]
  Finzel, K. J. Chem. Phys. 2016, 144, 034108. doi: 10.1063/1.4940035 doi: 10.1063/1.4940035
46. [46]
  Finzel, K. Theor. Chem. Acc. 2016, 135, 87. doi: 10.1007/s00214-016-1850-8 doi: 10.1007/s00214-016-1850-8
47. [47]
  Finzel, K. Int. J. Quantum Chem. 2016, 116, 1261. doi: 10.1002/qua.25169 doi: 10.1002/qua.25169
48. [48]
  Finzel, K.; Ayers, P. W. Theor. Chem. Acc. 2016, 135, 255. doi: 10.1007/s00214-016-2013-7 doi: 10.1007/s00214-016-2013-7
49. [49]
  Finzel, K.; Ayers, P. W. Int. J. Quantum Chem. 2017, 117, E25364. doi: 10.1002/qua.25364 doi: 10.1002/qua.25364
50. [50]
  Finzel, K.; Baranov, A. I. Int. J. Quantum Chem. 2016, 117, 40. doi: 10.1002/qua.25312 doi: 10.1002/qua.25312
51. [51]
  Parr, R. G.; Yang, W. Density-Functional Theory of Atoms and Molecules; Oxford University Press: New York, NY, USA, 1989.
52. [52]
  Levy, M.; Perdew, J. P. Phys. Rev. A 1985, 32, 2010. doi: 10.1103/PhysRevA.32.2010 doi: 10.1103/PhysRevA.32.2010
53. [53]
  Bartolotti, L. J.; Acharya, P. K. J. Chem. Phys. 1982, 77, 4576. doi: 10.1063/1.444409 doi: 10.1063/1.444409
54. [54]
  Ryabinkin, I. G.; Kananenka, A. A.; Staroverov, V. N. Phys. Rev. Lett. 2013, 111, 074112. doi: 10.1103/PhysRevLett.111.013001 doi: 10.1103/PhysRevLett.111.013001
55. [55]
  Kohut, S. V.; Ryabinkin, I. G.; Staroverov, V. N. J. Chem Phys. 2014, 140, 18A535. doi: 10.1063/1.4871500 doi: 10.1063/1.4871500
56. [56]
  Slater, J. C. Phys. Rev. 1951, 81, 385. doi: 10.1103/PhysRev.81.385 doi: 10.1103/PhysRev.81.385
57. [57]
  Görling, A. Phys. Rev. A 1992, 46, 3753. doi: 10.1103/PhysRevA.46.3753 doi: 10.1103/PhysRevA.46.3753
58. [58]
  Görling, A.; Ernzerhof, M. Phys. Rev. A 1995, 51, 4501. doi: 10.1103/PhysRevA.51.4501 doi: 10.1103/PhysRevA.51.4501
59. [59]
  Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.; Burant, J. C.; et al. Gaussian 16, Revision A.03; Gaussian, Inc.: Wallingford, CT, USA, 2016.
60. [60]
  Woon, D. E.; Dunning, T. H. J. J. Chem. Phys. 1993, 98, 1358. doi: 10.1063/1.464303 doi: 10.1063/1.464303
61. [61]
  Slater, J. C. Phys. Rev. 1969, 179, 28. doi: 10.1103/PhysRev.179.28 doi: 10.1103/PhysRev.179.28
62. [62]
  Perdew, J. P.; Chevary, J. A.; Vosko, S. H.; Jackson, K. A.; Pederson, M. R.; Singh, D. J.; Fiolhais, C. Phys. Rev. B 1992, 46, 6671. doi: 10.1103/PhysRevB.46.6671 doi: 10.1103/PhysRevB.46.6671
63. [63]
  Perdew, J. P.; Burke, K.; Wang, Y. Phys. Rev. B 1996, 54, 16533. doi: 10.1103/PhysRevB.54.16533 doi: 10.1103/PhysRevB.54.16533
64. [64]
  Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. Rev. Lett. 1996, 77, 3865. doi: 10.1103/PhysRevLett.77.3865 doi: 10.1103/PhysRevLett.77.3865
65. [65]
  Van Voorhis, T.; Scuseria, G. E. J. Chem. Phys. 1998, 109, 400. doi: 10.1063/1.476577 doi: 10.1063/1.476577
66. [66]
  Perdew, J. P.; Ruzsinszky, A.; Gábor, I.; Constantin, A. L.; Sun, J. Phys. Rev. Lett. 2009, 103, 026403. doi: 10.1103/PhysRevLett.103.026403 doi: 10.1103/PhysRevLett.103.026403
67. [67]
  Becke, A. D. J. Chem. Phys. 1993, 98, 5648. doi: 10.1063/1.464913 doi: 10.1063/1.464913
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