Finite Basis Set Disease

Other charge distributions, e.g., a finite hard sphere or a Fermi-type nuclear model, are also used. The coupling of the upper and lower components of the wavefunction via 5,p,- requires either kinetically balanced basis sets or the imposal of appropriate boundary conditions in order to avoid the so-called finite basis set disease. 

We now return to the problem of formulating the Dirac equation in the algebraic approximation and avoiding the so-called finite basis set disease by considering applications to one-electron systems. Applications to many-electron systems are discussed in Section VIII.E. We shall first of all consider the minimum basis set description of one-electron systems and then describe extended basis set calculations. 

DHF calculations on molecules using finite basis sets require considerably more computational effort than the corresponding nonrelativistic calculations and cause several problems due to the presence of the Dirac one-particle operator. It is therefore desirable to find (approximate) relativistic Hamiltonians for many-electron systems which are not plagued by unboundedness from below and therefore do not cause problems like the variational collapse at the self-consistent field level or the Brown-Ravenhall disease at the configuration interaction level. It is also desirable to find forms in which the quality of a matrix representation of the kinetic energy is more stable than for the Dirac Hamiltonian, i.e., forms which are not affected by the finite basis set disease . 

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