where Ψ CI 0 is the cardinality (the number of non-zero elements) of the CI vector. The goal of selected CI methods is to find the solution to Eq. (3) where k is the maximum number of determinants to be considered in the sCI problem. The value of k is a userdefined parameter, and will depend on the particular system and the desired accuracy. If k is equal to the dimension of all possible determinants for a problem, the solution to Eq. ( ) is equivalent to the FCI problem. Ultimately, this problem can be viewed as a special instance of a combinatorial optimization problem, akin to the knapsack problem or the traveling salesman problem. Given a subset of possible determinants to include, what is the optimal combination of determinants that minimizes the expected value of the Hamiltonian?