Yang, W, *Ab initio approach for many-electron systems without invoking orbitals: An integral formulation of density-functional theory*,
Physical Review A, vol. 38 no. 11
(1988),
pp. 5494-5503 [doi] .
**Abstract:**

*A new approach for the calculation of ground states of many-electron systems is proposed via an integral formulation of the Hohenberg-Kohn-Sham density-functional theory. Only equations for the total electron density are involved; orbitals are not employed. Exchange and correlation effects are incorporated. In place of the set of single-electron equations, the total electron density is explicitly expressed in terms of the Kohn-Sham effective local potential through multidimensional integrations. The development is based on the first-order density matrix as obtained from the one-body Greens function in polygonal and Fourier path-integral representations. This might open up the possibility of ab initio calculations for molecules with very many electrons. It also provides explicit solutions to two long-standing problems: electron kinetic energy and momentum density as functionals of the total electron density. The formulation can also be used in calculations for general fermions. © 1988 The American Physical Society.*