Citation: NAGY Ágnes. Phase Space View of Ensembles of Excited States[J]. Acta Physico-Chimica Sinica, ;2018, 34(5): 492-496. doi: 10.3866/PKU.WHXB201709221 shu

Phase Space View of Ensembles of Excited States

NAGY Ágnes ^,

Department of Theoretical Physics, University of Debrecen, H-4002 Debrecen, Hungary

Corresponding author: NAGY Ágnes, anagy@phys.unideb.hu
Received Date: 11 August 2017
Revised Date: 31 August 2017
Accepted Date: 31 August 2017
Available Online: 22 May 2017
Fund Project: The project was supported by the National Research, Development and Innovation Fund of Hungary, Financed under the 123988 Funding Scheme

The density functional theory and its extension to ensembles of excited states can be formalized as thermodynamics. However, these theories are not unique because one of their key quantities, the kinetic energy density, can be defined in several ways. Usually, the everywhere positive gradient form is applied; however, other forms are also acceptable, provided they integrate to the true kinetic energy. Recently, a kinetic energy density of the ground-state theory maximizing the information entropy has been proposed. Here, ensemble kinetic energy density, leading to extremum information entropy, is derived via constrained search. The corresponding ensemble temperature is found to be constant.
- Ensemble of excited states,
- Kinetic energy density,
- Constrained search,
- Ensemble temperature
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]
  Gunnarsson, O.; Lundqvist, B. I. Phys. Rev. B 1976, B13, 4274.doi: 10.1103/PhysRevB.13.4274
3. [3]
  Gunnarsson, O.; Jonson M.; Lundqvist, B. I. Phys. Rev. B 1979, 20, 3136. doi: 10.1103/PhysRevB.20.3136
4. [4]
  von Barth, U. Phys. Rev. A 1979, 20, 1693.doi: 10.1103/PhysRevA.20.1693 doi: 10.1103/PhysRevA.20.1693
5. [5]
  Theophilou, A.K. J. Phys. C 1978, C12, 5419.doi: 10.1088/0022-3719/12/24/013 doi: 10.1088/0022-3719/12/24/013
6. [6]
  Gross, E. K. U.; Oliveira, L.N.; Kohn, W. Phys. Rev. A 1988, 37, 2805. doi: 10.1103/PhysRevA.37.2805
7. [7]
  Gross, E. K. U.; Oliveira, L.N.; Kohn, W. Phys. Rev. A 1988, 37, 2809. doi: 10.1103/PhysRevA.37.2809
8. [8]
  Gross, E. K. U.; Oliveira, L.N.; Kohn, W. Phys. Rev. A 1988, 37, 2821. doi: 10.1103/PhysRevA.37.2821
9. [9]
  Nagy, Á. Phys. Rev. A 1990, 42, 4388.doi: 10.1103/PhysRevA.42.4388 doi: 10.1103/PhysRevA.42.4388
10. [10]
  Nagy, Á. J. Phys. B 1991, 24, 4691.doi: 10.1088/0953-4075/24/22/008 doi: 10.1088/0953-4075/24/22/008
11. [11]
  Nagy, Á.; Andrejkovics, I. J. Phys. B 1994, 27, 233.doi: 10.1088/0953-4075/27/2/002 doi: 10.1088/0953-4075/27/2/002
12. [12]
  Nagy, Á. Int. J. Quantum. Chem. 1995, 56, 225.doi: 10.1002/qua.560560406 doi: 10.1002/qua.560560406
13. [13]
  Nagy, Á. J. Phys. B 1996, 29, 389. doi: 10.1088/0953-4075/29/3/007 doi: 10.1088/0953-4075/29/3/007
14. [14]
  Nagy, Á. Int. J. Quantum. Chem. 1995, 29 (Suppl.), 297.doi: 10.1002/qua.560560833 doi: 10.1002/qua.560560833
15. [15]
  Nagy, Á. Adv. Quantum. Chem. 1997, 29, 159.doi: 10.1016/S0065-3276(08)60268-3 doi: 10.1016/S0065-3276(08)60268-3
16. [16]
  Nagy, Á. Phys. Rev. A 1994, 49, 3074.doi: 10.1103/PhysRevA.49.3074 doi: 10.1103/PhysRevA.49.3074
17. [17]
  Nagy, Á. Int. J. Quantum. Chem. 1998, 69, 247.doi: 10.1002/(SICI)1097-461X(1998)69:3<247::AIDQUA4>3.0.CO;2-V doi: 10.1002/(SICI)1097-461X(1998)69:3<247::AIDQUA4>3.0.CO;2-V
18. [18]
  Görling, A. Phys. Rev. A 1996, 54, 3912.doi: 10.1103/PhysRevA.54.3912 doi: 10.1103/PhysRevA.54.3912
19. [19]
  Görling, A.; Levy, M. Phys. Rev. B 1993, 47, 13105.doi: 10.1103/PhysRevB.47.13105
20. [20]
  Görling, A.; Levy, M. Phys. Rev. A 1994, 50, 196.doi: 10.1103/PhysRevA.50.196
21. [21]
  Görling, A.; Levy, M. Int. J. Quantum. Chem. 1995, 29 (Suppl.), 93. doi: 10.1002/qua.560560810
22. [22]
  Nagy, Á. Int. J. Quantum. Chem. 1998, 70, 681.doi: 10.1002/(SICI)1097-461X(1998)70:4/5<681::AIDQUA14>3.0.CO;2-5 doi: 10.1002/(SICI)1097-461X(1998)70:4/5<681::AIDQUA14>3.0.CO;2-5
23. [23]
  Levy, M.; Nagy, Á. Phys. Rev. Lett. 1999, 83, 4361.doi: 10.1103/PhysRevLett.83.4361 doi: 10.1103/PhysRevLett.83.4361
24. [24]
  Nagy, Á.; Levy, M. Phys. Rev. A 2001, 63, 052502.doi: 10.1103/PhysRevA.63.052502 doi: 10.1103/PhysRevA.63.052502
25. [25]
  Ayers, P. W.; Levy, M.; Nagy, Á. Phys. Rev. A 2012, 85, 042518.doi: 10.1103/PhysRevA.85.042518 doi: 10.1103/PhysRevA.85.042518
26. [26]
  Ayers, P. W.; Levy, M.; Nagy, Á. J. Chem. Phys. 2015, 143, 191101.doi: 10.1063/1.4934963 doi: 10.1063/1.4934963
27. [27]
  Gross E. U. K., Dobson J. F., Petersilka M.. Density Functional Theory. In Topics in Current Chemistry; Nalewajski R., Ed.[J]. Springer-Verlag: Heidelberg, Germany, 1996,Vol. 81p. 81.
28. [28]
  Casida M. F.. Recent Advances in the Density Functional Methods. in Recent Advances in Computational Chemistry; Chong D. P., Ed.[J]. World Scientific: Singapore, 1996,Vol. 1p. 155.
29. [29]
  Ghosh, S. K.; Berkowitz, M.; Parr, R. G. Proc. Natl. Acad. Sci. USA 1984, 81, 8028. doi: 10.1073/pnas.81.24.8028 doi: 10.1073/pnas.81.24.8028
30. [30]
  Ghosh S. K.; Parr, R. G. Phys.Rev. A 1986, 34, 785.doi: 10.1103/PhysRevA.34.785 doi: 10.1103/PhysRevA.34.785
31. [31]
  Ghosh, S. K.; Berkowitz, M. J. Chem. Phys. 1985, 83, 2976.doi: 10.1063/1.449846 doi: 10.1063/1.449846
32. [32]
  Parr, R. G.; Rupnik, K.; Ghosh, S. K. Phys. Rev. Lett. 1986, 56, 1555. doi: 10.1103/PhysRevLett.56.1555 doi: 10.1103/PhysRevLett.56.1555
33. [33]
  Lee, C.; Parr, R. G. Phys. Rev. A 1987, 35, 2377.doi: 10.1103/PhysRevA.35.2377 doi: 10.1103/PhysRevA.35.2377
34. [34]
  Rong, C. Y.; Lu, T.; Chattaraj P. K.; Liu, S. B. Indian J. Chem. A 2014, 53, 970.
35. [35]
  Gadre, S. R.; Bendale, R. D. Int. J. Quant. Chem. 1985, 28, 311.doi: 10.1002/qua.560280212 doi: 10.1002/qua.560280212
36. [36]
  Gadre, S. R.; Sears, S. B.; Chakravorty, S. J.; Bendale, R. D. Phys. Rev. A 1985, 32, 2602. doi: 10.1103/PhysRevA.32.2602 doi: 10.1103/PhysRevA.32.2602
37. [37]
  Gadre, S. R. Phys. Rev. A 1984, 30, 620.doi: 10.1103/PhysRevA.30.620 doi: 10.1103/PhysRevA.30.620
38. [38]
  Gadre, S. R.; Kulkani, S. A.; Shrivastava, I. H. Chem. Phys. Lett. 1990, 166, 445. doi: 10.1016/0009-2614(90)85058-K doi: 10.1016/0009-2614(90)85058-K
39. [39]
  Gadre, S. R.; Bendale, R. D.; Gejii, S. P. Chem. Phys. Lett. 1985, 117, 138. doi: 10.1016/0009-2614(85)85222-2 doi: 10.1016/0009-2614(85)85222-2
40. [40]
  Nagy, Á.; Parr, R. G. Proc. Ind. Acad. Sci. Chem. Sci. 1984, 106, 217.
41. [41]
  Nagy, Á.; Parr, R. G. J. Mol. Struct. (Theochem) 2000, 501, 101.doi: 10.1016/S0166-1280(99)00418-2 doi: 10.1016/S0166-1280(99)00418-2
42. [42]
  Nagy, Á.; Parr, R. G. Int. J. Quantum Chem. 1996, 58, 323.doi: 10.1002/(SICI)1097-461X(1996)58:4<323::AIDQUA1>3.0.CO;2 doi: 10.1002/(SICI)1097-461X(1996)58:4<323::AIDQUA1>3.0.CO;2
43. [43]
  Nagy, Á. Proc. Ind. Acad. Sci. (Chem. Sci) 1994, 106, 251.
44. [44]
  Nagy Á.. Reviews of Modern Quantum Chemistry; Sen, K. D. Ed[J]. World Scientific: Singapore, 2002,Vol. Ⅰp. 413.
45. [45]
  Nagy, Á. J. Mol. Struct. Theochem 2010, 943, 48.doi: 10.1016/j.theochem.2009.10.010 doi: 10.1016/j.theochem.2009.10.010
46. [46]
  Nagy, Á. Indian J. Chem. A 2014, 53, 965.
47. [47]
  Nagy, Á. Int. J. Quantum Chem. 2017, 117, e5396.doi: 10.1002/qua.25396 doi: 10.1002/qua.25396
48. [48]
  Levy, M. Proc. Natl. Sci. USA 1979, 76, 6002.
49. [49]
  Lieb, H. Int. J. Quantum Chem. 1982, 24, 243.doi: 10.1002/qua.560240302 doi: 10.1002/qua.560240302
1. [1]
  Peizhe Li , Qiaoling Liu , Mengyu Pei , Yuci Gan , Yan Gong , Chuchen Gong , Pei Wang , Mingsong Wang , Xiansong Wang , Da-Peng Yang , Bo Liang , Guangyu Ji . Chlorogenic acid supported strontium polyphenol networks ensemble microneedle patch to promote diabetic wound healing. Chinese Chemical Letters, 2024, 35(8): 109457-. doi: 10.1016/j.cclet.2023.109457
2. [2]
  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
3. [3]
  Xin Li , Ling Zhang , Yunyan Fan , Shaojing Lin , Yong Lin , Yongsheng Ying , Meijiao Hu , Haiying Gao , Xianri Xu , Zhongbiao Xia , Xinchuan Lin , Junjie Lu , Xiang Han . Carbon interconnected microsized Si film toward high energy room temperature solid-state lithium-ion batteries. Chinese Chemical Letters, 2025, 36(2): 109776-. doi: 10.1016/j.cclet.2024.109776
4. [4]
  Lingfeng Zheng , Chengyuan Lv , Wenlin Cai , Qingze Pan , Zuokai Wang , Wenkai Liu , Jiangli Fan , Xiaojun Peng . A single-component LED excited enone photoinitiator for colorless and transparent antibacterial film preparation. Chinese Chemical Letters, 2025, 36(4): 109922-. doi: 10.1016/j.cclet.2024.109922
5. [5]
  Dan-Ying Xing , Xiao-Dan Zhao , Chuan-Shu He , Bo Lai . Kinetic study and DFT calculation on the tetracycline abatement by peracetic acid. Chinese Chemical Letters, 2024, 35(9): 109436-. doi: 10.1016/j.cclet.2023.109436
6. [6]
  Supphachok Chanmungkalakul , Syed Ali Abbas Abedi , Federico J. Hernández , Jianwei Xu , Xiaogang Liu . The dark side of cyclooctatetraene (COT): Photophysics in the singlet states of “self-healing” dyes. Chinese Chemical Letters, 2024, 35(8): 109227-. doi: 10.1016/j.cclet.2023.109227
7. [7]
  Gang Hu , Chun Wang , Qinqin Wang , Mingyuan Zhu , Lihua Kang . The controlled oxidation states of the H₄PMo₁₁VO₄₀ catalyst induced by plasma for the selective oxidation of methacrolein. Chinese Chemical Letters, 2025, 36(2): 110298-. doi: 10.1016/j.cclet.2024.110298
8. [8]
  Dian-Xue Ma , Yu-Wu Zhong . Achieving highly-efficient room-temperature phosphorescence with a nylon matrix. Chinese Journal of Structural Chemistry, 2024, 43(9): 100391-100391. doi: 10.1016/j.cjsc.2024.100391
9. [9]
  Ruilong Geng , Lingzi Peng , Chang Guo . Dynamic kinetic stereodivergent transformations of propargylic ammonium salts via dual nickel and copper catalysis. Chinese Chemical Letters, 2024, 35(8): 109433-. doi: 10.1016/j.cclet.2023.109433
10. [10]
  Ling Tang , Yan Wan , Yangming Lin . Lowering the kinetic barrier via enhancing electrophilicity of surface oxygen to boost acidic oxygen evolution reaction. Chinese Journal of Structural Chemistry, 2024, 43(11): 100345-100345. doi: 10.1016/j.cjsc.2024.100345
11. [11]
  Meng Shan , Yongmei Yu , Mengli Sun , Shuping Yang , Mengqi Wang , Bo Zhu , Junbiao Chang . Bifunctional organocatalyst-catalyzed dynamic kinetic resolution of hemiketals for synthesis of chiral ketals via hydrogen bonding control. Chinese Chemical Letters, 2025, 36(1): 109781-. doi: 10.1016/j.cclet.2024.109781
12. [12]
  Hui Liu , Xiangyang Tang , Zhuang Cheng , Yin Hu , Yan Yan , Yangze Xu , Zihan Su , Futong Liu , Ping Lu . Constructing multifunctional deep-blue emitters with weak charge transfer excited state for high-performance non-doped blue OLEDs and single-emissive-layer hybrid white OLEDs. Chinese Chemical Letters, 2024, 35(10): 109809-. doi: 10.1016/j.cclet.2024.109809
13. [13]
  Yunfei Shen , Long Chen . Gradient imprinted Zn metal anodes assist dendrites-free at high current density/capacity. Chinese Journal of Structural Chemistry, 2024, 43(10): 100321-100321. doi: 10.1016/j.cjsc.2024.100321
14. [14]
  Zhilong Xie , Guohui Zhang , Ya Meng , Yefei Tong , Jian Deng , Honghui Li , Qingqing Ma , Shisong Han , Wenjun Ni . A natural nano-platform: Advances in drug delivery system with recombinant high-density lipoprotein. Chinese Chemical Letters, 2024, 35(11): 109584-. doi: 10.1016/j.cclet.2024.109584
15. [15]
  Longsheng Zhan , Yuchao Wang , Mengjie Liu , Xin Zhao , Danni Deng , Xinran Zheng , Jiabi Jiang , Xiang Xiong , Yongpeng Lei . BiVO₄ as a precatalyst for CO₂ electroreduction to formate at large current density. Chinese Chemical Letters, 2025, 36(3): 109695-. doi: 10.1016/j.cclet.2024.109695
16. [16]
  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
17. [17]
  Na Wang , Wang Luo , Huaiyi Shen , Huakai Li , Zejiang Xu , Zhiyuan Yue , Chao Shi , Hengyun Ye , Leping Miao . Crystal engineering regulation achieving inverse temperature symmetry breaking ferroelasticity in a cationic displacement type hybrid perovskite system. Chinese Chemical Letters, 2024, 35(5): 108696-. doi: 10.1016/j.cclet.2023.108696
18. [18]
  Kun Zhang , Ni Dan , Dan-Dan Ren , Ruo-Yu Zhang , Xiaoyan Lu , Ya-Pan Wu , Li-Lei Zhang , Hong-Ru Fu , Dong-Sheng Li . A small D-A molecule with highly heat-resisting room temperature phosphorescence for white emission and anti-counterfeiting. Chinese Journal of Structural Chemistry, 2024, 43(3): 100244-100244. doi: 10.1016/j.cjsc.2024.100244
19. [19]
  Linjing Li , Wenlai Xu , Jianyong Ning , Yaping Zhong , Chuyue Zhang , Jiane Zuo , Zhicheng Pan . Revealing the intrinsic mechanisms for accelerating nitrogen removal efficiency in the Anammox reactor by adding Fe(II) at low temperature. Chinese Chemical Letters, 2024, 35(8): 109243-. doi: 10.1016/j.cclet.2023.109243
20. [20]
  Shiqi Peng , Yongfang Rao , Tan Li , Yufei Zhang , Jun-ji Cao , Shuncheng Lee , Yu Huang . Regulating the electronic structure of Ir single atoms by ZrO₂ nanoparticles for enhanced catalytic oxidation of formaldehyde at room temperature. Chinese Chemical Letters, 2024, 35(7): 109219-. doi: 10.1016/j.cclet.2023.109219

Get Citation

PDF

XML

Metrics

PDF Downloads(11)
Abstract views(445)
HTML views(18)

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