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
1. [1]
  Xu Huang , Kai-Yin Wu , Chao Su , Lei Yang , Bei-Bei Xiao . Metal-organic framework Cu-BTC for overall water splitting: A density functional theory study. Chinese Chemical Letters, 2025, 36(4): 109720-. doi: 10.1016/j.cclet.2024.109720
2. [2]
  Xinyu Ren , Hong Liu , Jingang Wang , Jiayuan Yu . Electrospinning-derived functional carbon-based materials for energy conversion and storage. Chinese Chemical Letters, 2024, 35(6): 109282-. doi: 10.1016/j.cclet.2023.109282
3. [3]
  Maitri Bhattacharjee , Rekha Boruah Smriti , R. N. Dutta Purkayastha , Waldemar Maniukiewicz , Shubhamoy Chowdhury , Debasish Maiti , Tamanna Akhtar . Synthesis, structural characterization, bio-activity, and density functional theory calculation on Cu(Ⅱ) complexes with hydrazone-based Schiff base ligands. Chinese Journal of Inorganic Chemistry, 2024, 40(7): 1409-1422. doi: 10.11862/CJIC.20240007
4. [4]
  Uttam Pandurang Patil . Porous carbon catalysis in sustainable synthesis of functional heterocycles: An overview. Chinese Chemical Letters, 2024, 35(8): 109472-. doi: 10.1016/j.cclet.2023.109472
5. [5]
  Aolei Tan , Xiaoxiao Ma . Exploring the functional roles of small-molecule metabolites in disease research: Recent advancements in metabolomics. Chinese Chemical Letters, 2024, 35(8): 109276-. doi: 10.1016/j.cclet.2023.109276
6. [6]
  Tianze Wang , Junyi Ren , Dongxiang Zhang , Huan Wang , Jianjun Du , Xin-Dong Jiang , Guiling Wang . Development of functional dye with redshifted absorption based on Knoevenagel condensation at 1-site in phenyl[b]-fused BODIPY. Chinese Chemical Letters, 2024, 35(6): 108862-. doi: 10.1016/j.cclet.2023.108862
7. [7]
  Guiyang Zheng , Xuelian Kang , Haoran Ye , Wei Fan , Christian Sonne , Su Shiung Lam , Rock Keey Liew , Changlei Xia , Yang Shi , Shengbo Ge . Recent advances in functional utilisation of environmentally friendly and recyclable high-performance green biocomposites: A review. Chinese Chemical Letters, 2024, 35(4): 108817-. doi: 10.1016/j.cclet.2023.108817
8. [8]
  Zeyu Jiang , Yadi Wang , Changwei Chen , Chi He . Progress and challenge of functional single-atom catalysts for the catalytic oxidation of volatile organic compounds. Chinese Chemical Letters, 2024, 35(9): 109400-. doi: 10.1016/j.cclet.2023.109400
9. [9]
  Jiajing Wu , Ru-Ling Tang , Sheng-Ping Guo . Three types of promising functional building units for designing metal halide nonlinear optical crystals. Chinese Journal of Structural Chemistry, 2024, 43(6): 100291-100291. doi: 10.1016/j.cjsc.2024.100291
10. [10]
  Xin Li , Wanting Fu , Ruiqing Guan , Yue Yuan , Qinmei Zhong , Gang Yao , Sheng-Tao Yang , Liandong Jing , Song Bai . Nucleophiles promotes the decomposition of electrophilic functional groups of tetracycline in ZVI/H₂O₂ system: Efficiency and mechanism. Chinese Chemical Letters, 2024, 35(10): 109625-. doi: 10.1016/j.cclet.2024.109625
11. [11]
  Lilin Song , Mengru Sun , Yuqing Song , Feng Zhang , Bei Zhao , Hairong Zeng , Jinhui Shi , Huixin Liu , Shanshan Zhao , Tian Tian , Heng Yin , Guangbo Ge . Rationally engineered IR-783 octanoate as an enzyme-activatable fluorogenic tool for functional imaging of hNotum in living systems. Chinese Chemical Letters, 2024, 35(11): 109601-. doi: 10.1016/j.cclet.2024.109601
12. [12]
  Xixian Sun , Shengke Li , Ruibing Wang , Leyong Wang . Functional macrocyclic arenes with active binding sites inside cavity for biomimetic molecular recognition. Chinese Chemical Letters, 2025, 36(4): 110806-. doi: 10.1016/j.cclet.2024.110806
13. [13]
  Qingyun Hu , Wei Wang , Junyuan Lu , He Zhu , Qi Liu , Yang Ren , Hong Wang , Jian Hui . High-throughput screening of high energy density LiMn_1-xFe_xPO₄ via active learning. Chinese Chemical Letters, 2025, 36(2): 110344-. doi: 10.1016/j.cclet.2024.110344
14. [14]
  Haodong Wang , Xiaoxu Lai , Chi Chen , Pei Shi , Houzhao Wan , Hao Wang , Xingguang Chen , Dan Sun . Novel 2D bifunctional layered rare-earth hydroxides@GO catalyst as a functional interlayer for improved liquid-solid conversion of polysulfides in lithium-sulfur batteries. Chinese Chemical Letters, 2024, 35(5): 108473-. doi: 10.1016/j.cclet.2023.108473
15. [15]
  Hengying Xiang , Nanping Deng , Lu Gao , Wen Yu , Bowen Cheng , Weimin Kang . 3D core-shell nanofibers framework and functional ceramic nanoparticles synergistically reinforced composite polymer electrolytes for high-performance all-solid-state lithium metal battery. Chinese Chemical Letters, 2024, 35(8): 109182-. doi: 10.1016/j.cclet.2023.109182
16. [16]
  Boyuan Hu , Jian Zhang , Yulin Yang , Yayu Dong , Jiaqi Wang , Wei Wang , Kaifeng Lin , Debin Xia . Dual-functional POM@IL complex modulate hole transport layer properties and interfacial charge dynamics for highly efficient and stable perovskite solar cells. Chinese Chemical Letters, 2024, 35(7): 108933-. doi: 10.1016/j.cclet.2023.108933
17. [17]
  Haitao Yin , Liang Meng , Li Li , Jiamu Xiao , Longrui Liang , Nannan Huang , Yansong Shi , Angang Zhao , Jingwen Hou . Polydopamine-modified biochar supported polylactic acid and zero-valent iron affects the functional microbial community structure for 1,1,1-trichloroethane removal in simulated groundwater. Chinese Chemical Letters, 2025, 36(1): 110313-. doi: 10.1016/j.cclet.2024.110313
18. [18]
  Yong Shu , Xing Chen , Sai Duan , Rongzhen Liao . How to Determine the Equilibrium Bond Distance of Homonuclear Diatomic Molecules: A Case Study of H₂. University Chemistry, 2024, 39(7): 386-393. doi: 10.3866/PKU.DXHX202310102
19. [19]
  Yong-Fang Shi , Sheng-Hua Zhou , Zuju Ma , Xin-Tao Wu , Hua Lin , Qi-Long Zhu . From [Ba3S][GeS4] to [Ba3CO3][MS4] (M = Ge, Sn): Enhancing optical anisotropy in IR birefringent crystals via functional group implantation. Chinese Journal of Structural Chemistry, 2025, 44(1): 100455-100455. doi: 10.1016/j.cjsc.2024.100455
20. [20]
  Yang Qin , Jiangtian Li , Xuehao Zhang , Kaixuan Wan , Heao Zhang , Feiyang Huang , Limei Wang , Hongxun Wang , Longjie Li , Xianjin Xiao . Toeless and reversible DNA strand displacement based on Hoogsteen-bond triplex. Chinese Chemical Letters, 2024, 35(5): 108826-. doi: 10.1016/j.cclet.2023.108826

Get Citation

PDF

XML

Metrics

PDF Downloads(7)
Abstract views(227)
HTML views(13)

通讯作者: 陈斌, bchen63@163.com

1.
沈阳化工大学材料科学与工程学院沈阳 110142