In this paper we perform a quantal density functional theory (Q-DFT) study of the hydrogen molecule in its ground state. In common with traditional Kohn-Sham density functional theory, Q-DFT transforms the interacting system as described by Schrodinger theory, to one of noninteracting fermions-the S system-such that the equivalent density, total energy, and ionization potential are obtained. The Q-DFT description of the S system is in terms of "classical" fields and their quantal sources that are quantum-mechanical expectations of Hermitian operators taken with respect to the interacting and S system wave functions. The sources, and hence the fields, are separately representative of all the many-body effects the S system must account for, viz. electron correlations due to the Pauli exclusion principle, Coulomb repulsion, and correlation-kinetic effects. The local electron-interaction potential energy of each model fermion is the work done to move it in the force of a conservative effective field that is the sum of the individual fields. The Hartree, Pauli, Coulomb, and correlation-kinetic energy components of the total energy are also expressed in virial form in terms of the corresponding fields. The highest occupied eigenvalue of the S system is the negative of the ionization potential energy. The Q-DFT analysis of the hydrogen molecule is performed employing the highly accurate correlated wave function of Kolos and Roothaan. (C) 2004 American Institute of Physics.