  An efficient excited state method, named xCDFCI, in the configuration
interaction framework, is proposed. xCDFCI extends the unconstrained nonconvex
optimization problem in coordinate descent full configuration
interaction~(CDFCI) to a multicolumn version, for low-lying excited states
computation. The optimization problem is addressed via a tailored coordinate
descent method. In each iteration, a determinant is selected based on an
approximated gradient, and coefficients of all states associated with the
selected determinant are updated. A deterministic compression is applied to
limit memory usage. We test xCDFCI applied to H2O and N2 molecules under the
cc-pVDZ basis set. For both systems, five low-lying excited states in the same
symmetry sector are calculated together with the ground state. xCDFCI also
produces accurate binding curves of carbon dimer in the cc-pVDZ basis with
chemical accuracy, where the ground state and four excited states in the same
symmetry sector are benchmarked.
