Cusp-driven cause of determinant-scaling in the UCI ansatz

Determine whether the observed increase—approximately linear with the number of basis functions—of the number of Slater determinants required to achieve fixed accuracy in a given basis for the Unconstrained Configuration Interaction (UCI) ansatz is caused by the short-distance electron-electron and electron-nucleus cusp conditions of the continuum-space wave function as the continuum limit is approached.

Background

The paper introduces the Unconstrained Configuration Interaction (UCI) ansatz, a variational wavefunction formed by a sum of non-orthogonal Slater determinants optimized via an efficient quadratic energy optimization. In studying LiH across multiple basis-set sizes (6 to 146 orbitals), the authors observe an approximate collapse of the energy-error curves when plotted against the ratio of the number of determinants to basis size m, suggesting that the number of determinants needed for fixed error scales roughly linearly with m.

The authors explicitly conjecture that this scaling may be driven by the short-distance cusp conditions inherent to the continuum-space electronic wave function. Since sums of Slater determinants cannot represent the cusp exactly in the continuum limit, this conjecture proposes a mechanistic explanation for the observed scaling as the basis set increases.