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

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

AYERSPaul W. ^{1,
,} ,
LEVYMel ^{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

通讯作者: AYERSPaul W., ayers@mcmaster.ca
LEVYMel, mlevy@tulane.edu

摘要: 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.

关键词:

Density functional theory
/ Levy constrained search functional
/ Fock space
/ Fractional electron number
/ Excited-state density functional theory
/ Universal density functional
/ Zero temperature grand canonical ensemble
/ Convexity

English

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
Accepted Date: 02 November 2017
Revised Date: 02 November 2017
Available Online: 15 June 2018

Abstract: 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.

Key words:

Density functional theory
/ Levy constrained search functional
/ Fock space
/ Fractional electron number
/ Excited-state density functional theory
/ Universal density functional
/ Zero temperature grand canonical ensemble
/ Convexity

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沈阳化工大学材料科学与工程学院沈阳 110142

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

通讯作者: AYERSPaul W., ayers@mcmaster.ca
LEVYMel, mlevy@tulane.edu

English

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

Corresponding author: AYERS Paul W., ayers@mcmaster.ca LEVY Mel, mlevy@tulane.edu

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中国化学会秘书处

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

通讯作者: AYERSPaul W., ayers@mcmaster.ca LEVYMel, mlevy@tulane.edu

English

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

Corresponding author: AYERS Paul W., ayers@mcmaster.ca LEVY Mel, mlevy@tulane.edu

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

CCS Chemistry：颜徐州、鲍哲南： 你的皮肤可能是一片SPMs

CCS Chemistry：工作高效不疲劳，只须让催化剂动起来

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CCS Chemistry：金黄色葡萄球菌醛基脱氢酶是如何识别特异性底物的？

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通讯作者: 陈斌, bchen63@163.com

中国化学会秘书处

通讯作者: AYERSPaul W., ayers@mcmaster.ca
LEVYMel, mlevy@tulane.edu

CCS Chemistry：颜徐州、鲍哲南：你的皮肤可能是一片SPMs