  Development of exponentially scaling methods has seen great progress in
tackling larger systems than previously thought possible. One such technique,
full configuration interaction quantum Monte Carlo, is a useful algorithm that
allows exact diagonalization through stochastically sampling determinants. The
method derives its utility from the information in the matrix elements of the
Hamiltonian, along with a stochastic projected wave function, to find the
important parts of Hilbert space. However, the stochastic representation of the
wave function is not required to search Hilbert space efficiently, and here we
describe a highly efficient deterministic method to achieve chemical accuracy
for a wide range of systems, including the difficult Cr$_{2}$ dimer. In
addition our method also allows efficient calculation of excited state
energies, for which we illustrate with benchmark results for the excited states
of C$_{2}$.
