Binding of atoms and stability of molecules in Hartree and Thomas-Fermi type theories. Part 3 : Binding of neutral subsystems

This paper is the third of a series devoted to the study of the binding of atoms, molecules and ions and of the stability of general molecular systems including molecular ions, in the context of Hartree and Thomas-Fermi type theories. For Thomas-Fermi-von WeizsOcker or Thomas-Fermi-Dirac-von Weizsacker models, we prove here that neutral systems can be bound and in view of the results shown in the preceding parts this yields the stability of arbitrary molecules (general neutral molecular systems). For the Hartree and Hartree-Fock models, we prove that neutral planar systems can be bound and this yields the stability of arbitrary tetraatomic molecules for instance. Various variants and extensions are also considered.

[1]  P. Lions On Hartree and Hartree-Fock equations in atomic and nuclear physics , 1989 .

[2]  Pierre-Louis Lions,et al.  Binding of atoms and stability of molecules in Hartree and Thomas-Fermi type theories. Part 2 : Stability is equivalent to the binding of neutral subsystems , 1993 .

[3]  Elliott H. Lieb,et al.  The Thomas—Fermi—von Weizsäcker Theory of Atoms and Molecules , 1981 .

[4]  Lagrange Multipliers, Morses Indices and Compactness , 1990 .

[5]  Pierre-Louis Lions,et al.  The concentration-compactness principle in the Calculus of Variations , 1985 .

[6]  E. Lieb,et al.  Universal nature of van der Waals forces for Coulomb systems. , 1986, Physical review. A, General physics.

[7]  Barry Simon,et al.  The Hartree-Fock theory for Coulomb systems , 1977 .

[8]  Elliott H. Lieb,et al.  A Relation Between Pointwise Convergence of Functions and Convergence of Functionals , 1983 .

[9]  E. Lieb Thomas-fermi and related theories of atoms and molecules , 1981 .

[10]  Elliott H. Lieb,et al.  Minimum action solutions of some vector field equations , 1984 .

[11]  Pierre-Louis Lions,et al.  Solutions of Hartree-Fock equations for Coulomb systems , 1987 .

[12]  P. Lions The concentration-compactness principle in the calculus of variations. The locally compact case, part 1 , 1984 .

[13]  P. Lions,et al.  Hartree-Fock theory in nuclear physics , 1986 .

[14]  I. Ekeland Nonconvex minimization problems , 1979 .

[15]  E. Lieb,et al.  The Thomas-Fermi theory of atoms, molecules and solids , 1977 .

[16]  Edward Teller,et al.  On the Stability of Molecules in the Thomas-Fermi Theory , 1962 .