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

AYERS Paul W.1,*(),LEVY Mel2,3,4,*()

1. 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
• 收稿日期:2017-09-25 发布日期:2018-03-20
• 通讯作者: AYERS Paul W.,LEVY Mel E-mail:ayers@mcmaster.ca;mlevy@tulane.edu

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

Paul W. AYERS1,*(),Mel LEVY2,3,4,*()

1. 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
• Received:2017-09-25 Published:2018-03-20
• Contact: Paul W. AYERS,Mel LEVY E-mail:ayers@mcmaster.ca;mlevy@tulane.edu

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.

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.