Short-range correlation in molecular physics: The basis set problem and the correlation hole.

摘要

The greatest limitation of computational chemistry is the need to solve the Schrodinger equation in a basis set. Because the cost of correlated electronic structure calculations grows rapidly with the size of the basis set while the accuracy does not, predictive correlated calculations are at present feasible only in small molecules. The rapid growth of cost with the number of basis functions is essentially inevitable, but the slow growth of accuracy is not. Rather, this slow growth of accuracy is due to the expansion of the many-electron wavefunction in products of one-electron functions. Because there is a cusp in the wavefunction at the coalescence of electrons which is not properly described in any finite one-particle basis set, this expansion is slowly convergent.; Since the need for large basis sets is caused chiefly by the improper description of the wavefunction for small interelectronic separations, a clever treatment of this regime should obviate the need for large basis sets. By doing so, it would be possible to perform rather accurate correlated calculations for much larger systems than can be studied at present.; Density Functional Theory avoids these difficulties because the object of interest is the electronic density, which is a one-electron function and thus readily described in a single-particle basis set. Since the correlation energy is taken from an analytic model, moreover, so long as the model used properly describes the electronic cusp, Density Functional Theory can provide a route towards treating short-range correlation in a manner which is both accurate and basis set insensitive. Fortunately, the underlying approximation of most current functionals is the local density approximation, in which short-range correlation is treated very accurately.; Therefore, in this work we propose a technique which makes use of the accurate local density approximation for the short-range correlation but which uses the reliable basis set expansion for the remainder. The proposed model, as we will show in what follows, is both conceptually and computationally straightforward, and points the way to ameliorating the need for large basis sets in attaining accurate correlated results.