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

A deterministic alternative to the full configuration interaction quantum Monte Carlo method