Solutions to quasi-relativistic multi-configurative HartreeFock equations in quantum chemistry

C. Argaez; M. Melgaard

doi:10.1016/j.na.2011.08.038

Solutions to quasi-relativistic multi-configurative HartreeFock equations in quantum chemistry

C. Argaez, M. Melgaard^*

^*Corresponding author for this work

Science Institute

Research output: Contribution to journal › Article › peer-review

8 Citations (Scopus)

Abstract

We establish the existence of infinitely many distinct solutions to the multi-configurative HartreeFock type equations for N-electron Coulomb systems with quasi-relativistic kinetic energy -α- ²Δ^xn+α-⁴-α-² for the nth electron. Finitely many of the solutions are interpreted as excited states of the molecule. Moreover, we prove the existence of a ground state. The results are valid under the hypotheses that the total charge ^Ztot of K nuclei is greater than N-1 and that ^Ztot is smaller than a critical charge ^Zc. The proofs are based on a new application of the LionsFangGhoussoub critical point approach to nonminimal solutions on a complete analytic HilbertRiemann manifold, in combination with density operator techniques.

Original language	English
Pages (from-to)	384-404
Number of pages	21
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	75
Issue number	1
DOIs	https://doi.org/10.1016/j.na.2011.08.038
Publication status	Published - Jan 2012

Bibliographical note

Funding Information:
The research of the second author is supported by a Stokes Award (SFI) , grant 07/SK/M1208 .

Funding Information:
The first author acknowledges support by grant O9-RFP-MTH23 , Science Foundation Ireland (SFI) .

Other keywords

Abstract critical point theory
Density operator techniques
Multiple solutions
PalaisSmale sequences
Semilinear elliptic equations

Access to Document

10.1016/j.na.2011.08.038

Cite this

@article{d93141a4e5ef4439bc926c7dd90a5dc2,

title = "Solutions to quasi-relativistic multi-configurative HartreeFock equations in quantum chemistry",

abstract = "We establish the existence of infinitely many distinct solutions to the multi-configurative HartreeFock type equations for N-electron Coulomb systems with quasi-relativistic kinetic energy -α- 2Δxn+α-4-α-2 for the nth electron. Finitely many of the solutions are interpreted as excited states of the molecule. Moreover, we prove the existence of a ground state. The results are valid under the hypotheses that the total charge Ztot of K nuclei is greater than N-1 and that Ztot is smaller than a critical charge Zc. The proofs are based on a new application of the LionsFangGhoussoub critical point approach to nonminimal solutions on a complete analytic HilbertRiemann manifold, in combination with density operator techniques.",

keywords = "Abstract critical point theory, Density operator techniques, Multiple solutions, PalaisSmale sequences, Semilinear elliptic equations",

author = "C. Argaez and M. Melgaard",

note = "Funding Information: The research of the second author is supported by a Stokes Award (SFI) , grant 07/SK/M1208 . Funding Information: The first author acknowledges support by grant O9-RFP-MTH23 , Science Foundation Ireland (SFI) . ",

year = "2012",

month = jan,

doi = "10.1016/j.na.2011.08.038",

language = "English",

volume = "75",

pages = "384--404",

journal = "Nonlinear Analysis, Theory, Methods and Applications",

issn = "0362-546X",

publisher = "Elsevier Ltd.",

number = "1",

}

TY - JOUR

T1 - Solutions to quasi-relativistic multi-configurative HartreeFock equations in quantum chemistry

AU - Argaez, C.

AU - Melgaard, M.

N1 - Funding Information: The research of the second author is supported by a Stokes Award (SFI) , grant 07/SK/M1208 . Funding Information: The first author acknowledges support by grant O9-RFP-MTH23 , Science Foundation Ireland (SFI) .

PY - 2012/1

Y1 - 2012/1

N2 - We establish the existence of infinitely many distinct solutions to the multi-configurative HartreeFock type equations for N-electron Coulomb systems with quasi-relativistic kinetic energy -α- 2Δxn+α-4-α-2 for the nth electron. Finitely many of the solutions are interpreted as excited states of the molecule. Moreover, we prove the existence of a ground state. The results are valid under the hypotheses that the total charge Ztot of K nuclei is greater than N-1 and that Ztot is smaller than a critical charge Zc. The proofs are based on a new application of the LionsFangGhoussoub critical point approach to nonminimal solutions on a complete analytic HilbertRiemann manifold, in combination with density operator techniques.

AB - We establish the existence of infinitely many distinct solutions to the multi-configurative HartreeFock type equations for N-electron Coulomb systems with quasi-relativistic kinetic energy -α- 2Δxn+α-4-α-2 for the nth electron. Finitely many of the solutions are interpreted as excited states of the molecule. Moreover, we prove the existence of a ground state. The results are valid under the hypotheses that the total charge Ztot of K nuclei is greater than N-1 and that Ztot is smaller than a critical charge Zc. The proofs are based on a new application of the LionsFangGhoussoub critical point approach to nonminimal solutions on a complete analytic HilbertRiemann manifold, in combination with density operator techniques.

KW - Abstract critical point theory

KW - Density operator techniques

KW - Multiple solutions

KW - PalaisSmale sequences

KW - Semilinear elliptic equations

UR - http://www.scopus.com/inward/record.url?scp=80053935469&partnerID=8YFLogxK

U2 - 10.1016/j.na.2011.08.038

DO - 10.1016/j.na.2011.08.038

M3 - Article

AN - SCOPUS:80053935469

SN - 0362-546X

VL - 75

SP - 384

EP - 404

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

IS - 1

ER -

Solutions to quasi-relativistic multi-configurative HartreeFock equations in quantum chemistry

Abstract

Bibliographical note

Other keywords

Access to Document

Fingerprint

Cite this