Can optimized effective potentials be determined uniquely?

• DOI: 10.1063/1.1381013
• Publication Date: 2002-07-26T12:44:22Z
• Authors: So Hirata; Stanislav Ivanov; Ireneusz Grabowski; Rodney J. Bartlett; Kieron Burke; James D. Talman
• Keywords: Kernel (algebra)

Local (multiplicative) effective exchange potentials obtained from the linear-combination- of-atomic-orbital (LCAO) optimized potential (OEP) method are frequently unrealistic in that they tend to exhibit wrong asymptotic behavior (although formally should have correct behavior) and also assume unphysical rapid oscillations around nuclei. We give an algebraic proof that, with infinity of orbitals, kernel OEP integral equation has one only singularity associated a constant hence determines local uniquely, provided we impose some appropriate boundary condition upon potential. When number orbitals is finite, however, ill-posed it infinite solutions. circumvent this problem by projecting function space accessible thereby making unique. The observed numerical problems are, therefore, primarily due slow convergence projected respect size expansion basis set for orbitals. Nonetheless, judicious choice sets, obtain accurate atoms molecules LCAO procedure, which significant improvements over or gradient-corrected functionals Slater Krieger–Li–Iafrate scheme offers better approximations method.