Exact matrix product state representation and convergence of a fully correlated electronic wavefunction in the infinite-basis limit

In this paper we present the exact representation of a fully correlated electronic wavefunction as the single-particle basis approaches completeness. It consists of a half-infinite chain of matrices of exponentially increasing size. The complete basis limit is illustrated numerically using the density-matrix renormalization-group method by computing the core-valence entanglement in the C-2 ground state in increasing subsets of cc-pVTZ and pVQZ bases until convergence is reached.