Minimax variational approach to the relativistic two-electron problem

Simplified Dirac--Coulomb Equations

“…After executing the Kronecker product, the DC Hamiltonian may be expressed in the form of (cf. [14,15,27,28])…”

“…explicitly correlated functions. Such approaches which are not based on the one-electron approximation were applied to the DC equation in a very limited way [14][15][16][17][18][19]. The present formulation of reduced DC Hamiltonians aims in the application of such approaches in very accurate relativistic calculations of several electron systems.…”

Analytically Solving the Relativistic Dirac-Coulomb Equation for Atoms and Molecules

“…Another problem that often appears in the relativistic field is the variational instability and collapse. Though some studies using kinetic and other balances [7,8] were reported, there seems to be no established method. It was impressive that Pestka and Karwowski closed their important chapter of the Rychlewski's book in 2003 [7] by noting ''The Hylleraas CI approach to solving the Dirac-Coulomb eigenvalue problem is still in its infancy.…”

“…. 4 N ) and when an arbitrary variation of satisfies ĈĤ ÿ E ; (8) then this has the structure of the exact wave function. Proof: When we define Ĥ ÿ E , is a column vector of the elements n n 1 .…”

“…Another method of avoiding the variational collapse is to ensure kinetic balance, etc. on the basis functions [7,8,10]. From the DE, we obtain a relation connecting small and large components as S cp=E ÿ V c 2 L .…”