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

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

FINZELKati. ^, ,
BULTINCKPatrick.

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

通讯作者: FINZELKati., Kati.Finzel@UGent.be

摘要: 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.

关键词:

English

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
Accepted Date: 19 October 2017
Revised Date: 27 September 2017
Available Online: 15 June 2018
Fund Project:
The project was supported by the Fund for Scientific Research in Flanders (FWO-Vlaanderen) for Research Grant G021115N

Abstract: 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.

Key words:

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
2. [2]
  Karasiev, V.; Sjostrom, T.; Trickey, S. B. Computer Phys. Commun. 2014, 185, 3240. 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
4. [4]
  Ghosh, S.; Suryanarayana, P. J. Comput. Phys. 2016, 307, 634. doi: 10.1016/j.jcp.2015.12.027
5. [5]
  Thomas, L. H. Proc. Cambridge Philos. Soc. 1927, 23, 542. doi: 10.1017/S0305004100011683
6. [6]
  Fermi, E. Zeitschrift für Physik 1928, 48, 73. doi: 10.1007/BF01351576
7. [7]
  Hohenberg, P.; Kohn, W. Phys. Rev. B 1964, 136, 864. 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
9. [9]
  Ayers, P. W.; Liu, S. Phys. Rev. A 2007, 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
11. [11]
  Kryachko, E. S.; Ludeña, E. V. Phys. Rep. 2014, 544, 123. doi: 10.1016/j.physrep.2014.06.002
12. [12]
  von Weizsäcker, C. F. Z. Phys. 1935, 96, 431. 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
15. [15]
  Murphy, D. R. Phys. Rev. A 1981, 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
17. [17]
  Fuentealba, P.; Reyes, O. Chem. Phys. Lett. 1995, 232, 31. 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
19. [19]
  Lee, D.; Constantin, L. A.; Perdew, J. P.; Burke, K. J. Chem. Phys. 2009, 130, 034107. 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
22. [22]
  Ghiringhelli, L. M.; Delle Site, L. Phys. Rev. B 2008, 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
24. [24]
  Trickey, S.; Karasiev, V. V.; Vela, A. Phys. Rev. B 2011, 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
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
29. [29]
  Waber, J. T.; Cromer, D. T. J. Chem. Phys. 1965, 42, 4116. doi: 10.1063/1.1695904
30. [30]
  Weinstein, H.; Politzer, P.; Srebrenik, S. Theor. Chim. Acta 1975, 38, 159. 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
32. [32]
  Yang, W. Phys. Rev. A 1986, 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
35. [35]
  Levy, M.; Ou-Yang, H. Phys. Rev. A 1988, 38, 625. doi: 10.1103/PhysRevA.38.625
36. [36]
  Nagy, A. Acta Phys. Hung. 1991, 70, 321. doi: 10.1007/BF03054145
37. [37]
  Nagy, A.; March, N. H. Int. J. Quantum Chem. 1991, 39, 615. doi: 10.1002/qua.560390408
38. [38]
  Nagy, A.; March, N. H. Phys. Chem. Liq. 1992, 25, 37. doi: 10.1080/00319109208027285
39. [39]
  Holas, A.; March, N. H. Int. J. Quantum Chem. 1995, 56, 371. 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
41. [41]
  Nagy, A. Chem. Phys. Lett. 2008, 460, 343. doi: 10.1016/j.cplett.2008.05.077
42. [42]
  Nagy, A. Int. J. Quantum Chem. 2010, 110, 2117. doi: 10.1002/qua.22497
43. [43]
  Nagy, A. J. Chem. Phys. 2011, 135, 044106. doi: 10.1063/1.3607313
44. [44]
  Finzel, K. Int. J. Quantum Chem. 2015, 115, 1629. doi: 10.1002/qua.24986
45. [45]
  Finzel, K. J. Chem. Phys. 2016, 144, 034108. doi: 10.1063/1.4940035
46. [46]
  Finzel, K. Theor. Chem. Acc. 2016, 135, 87. doi: 10.1007/s00214-016-1850-8
47. [47]
  Finzel, K. Int. J. Quantum Chem. 2016, 116, 1261. 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
49. [49]
  Finzel, K.; Ayers, P. W. Int. J. Quantum Chem. 2017, 117, E25364. doi: 10.1002/qua.25364
50. [50]
  Finzel, K.; Baranov, A. I. Int. J. Quantum Chem. 2016, 117, 40. 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
53. [53]
  Bartolotti, L. J.; Acharya, P. K. J. Chem. Phys. 1982, 77, 4576. 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
55. [55]
  Kohut, S. V.; Ryabinkin, I. G.; Staroverov, V. N. J. Chem Phys. 2014, 140, 18A535. doi: 10.1063/1.4871500
56. [56]
  Slater, J. C. Phys. Rev. 1951, 81, 385. doi: 10.1103/PhysRev.81.385
57. [57]
  Görling, A. Phys. Rev. A 1992, 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
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
61. [61]
  Slater, J. C. Phys. Rev. 1969, 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
63. [63]
  Perdew, J. P.; Burke, K.; Wang, Y. Phys. Rev. B 1996, 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
65. [65]
  Van Voorhis, T.; Scuseria, G. E. J. Chem. Phys. 1998, 109, 400. 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
67. [67]
  Becke, A. D. J. Chem. Phys. 1993, 98, 5648. doi: 10.1063/1.464913

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沈阳化工大学材料科学与工程学院沈阳 110142

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

通讯作者: FINZELKati., Kati.Finzel@UGent.be

English

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

Corresponding author: FINZEL Kati., Kati.Finzel@UGent.be

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

通讯作者: FINZELKati., Kati.Finzel@UGent.be

English

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

Corresponding author: FINZEL Kati., Kati.Finzel@UGent.be

CCS Chemistry：嵌段共聚物自组装成 “三明治”二维有机材料，实现纳米级压力传感功能

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CCS Chemistry：工作高效不疲劳，只须让催化剂动起来

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