Localized-muffin-tin-orbital basis for atomic-cluster calculations within the local-density formalism

A new approach for solving the Hohenberg-Kohn-Sham density-functional equations for atomic clusters of moderate size and arbitrary symmetry is described. A basis set is introduced in the spirit of the LCMTO (linear combination of muffin-tin orbitals) method of Andersen with a ($\phi , \dot{\phi }$) form inside each atomic sphere. However, advantageous features of the conventional linear-combination-of-atomic-orbitals method are brought in by introducing only atomiclike orbital tails in the region outside the spheres. The "common-$\kappa$" approximation and cellular partitioning of the LCMTO approach are abandoned; with this approach it becomes necessary to carry out some three-dimensional integrations. Techniques are introduced which allow all integrals contributing to the secular matrix and total energy to be evaluated either semianalytically or by the Gaussian integration of smooth functions. Preliminary results for ${\mathrm{H}}_2$ and ${\mathrm{O}}_2$ demonstrate the practicality of the scheme.