We demonstrate the existence of different density-density functionals designed to retain selected properties of the many-body ground state in a noninteracting solution starting from the standard density functional theory ground state. We focus on diffusion quantum Monte Carlo applications that require trial wave functions with optimal Fermion nodes. The theory is extensible and can be used to understand current practices in several electronic structure methods within a generalized density functional framework. The theory justifies and stimulates the search of optimal empirical density functionals and effective potentials for accurate calculations of the properties of real materials, but also cautions on the limits of their applicability. The concepts are tested and validated with a near-analytic model.
The quantum
N-electron structure problem is expressed as a classical
N-body structure problem plus a quantum many-body problem with a reduced number of variables. This forms the foundation of a method for solving the electronic structure problem using
k-electron distribution functions instead of many-electron wave functions. The method represents a unified approach to the entire hierarchy of generalized density-functional theories, beginning with standard density-functional theory
(k=1) and pair density-functional theory
(k=2) and culminating in an exact treatment of the entire
N-electron system
(k=N).
A framework for developing new approximate electronic structure methods is presented, in which the correlation energy of a many-electron system in the ground state is computed as in the single-reference second-order many-body perturbation theory but with the reference one-body Hamiltonian modified by additional (generally non-local) potentials which are universal functionals of the Hartree-Fock density. The existence of such functionals that reproduce the exact correlation energy justifies the search for approximate models which may overcome some important deficiencies of the traditional density-functional methods and also perform better than the usual low-order wavefunction methods.