  We present an efficient \textit{ab initio} method for calculating the
electronic structure and total energy of strongly correlated electron systems.
The method extends the traditional Gutzwiller approximation for one-particle
operators to the evaluation of the expectation values of two particle operators
in a full many-electron Hamiltonian. The method is free of adjustable Coulomb
parameters, and has no double counting issues in the calculation of total
energy, and has the correct atomic limit. We demonstrate that the method
describes well the bonding and dissociation behaviors of the hydrogen and
nitrogen clusters. We also show that the method can satisfactorily tackle great
challenging problems faced by the density functional theory recently discussed
in the literature. The computational workload of our method is similar to the
Hartree-Fock approach while the results are comparable to high-level quantum
chemistry calculations.
