Are natural orbitals useful for generating an efficient expansion of the wave function?

Abstract

We investigate whether the natural orbitals (NOs) minimize $\Vert \Psi -\Phi {\Vert }^2$, where $\Psi$ is a wave function and $\Phi$ is a full configuration interaction (CI) approximation to $\Psi$ in a truncated basis. We will show that the NOs rarely provide the optimal orbitals for $\Phi$, except when (1) there are only two particles or (2) only one basis function is removed in the case of fermions. Further, we will show that the CI expansion coefficients of $\Psi$ and $\Phi$ are identical up to a global scaling factor and demonstrate how the NOs can be used to generate the orbitals that minimize $\Vert \Psi -\Phi {\Vert }^2$.

8 pages, 5 figures

References in corpus (3)

• Natural occupation numbers: When do they vanish?
• Long-range interactions and the sign of natural amplitudes in two-electron systems
• Optimal multi-configuration approximation of an N-fermion wave function

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• Optimal Orbital Selection for Full Configuration Interaction (OptOrbFCI): Pursuing the Basis Set Limit under a Budget
• Strong-field absorption and emission of radiation in two-electron systems calculated with time-dependent natural orbitals
• Natural orbitals in multiconfiguration calculations of hyperfine structure parameters
• Optimal Slater-determinant approximation of fermionic wave functions
• Time-dependent renormalized-natural-orbital theory applied to laser-driven H${}_2^{+}$
• Invertibility of the retarded response functions for initial mixed states: application to one-body reduced density matrix functional theory
• Elucidating the molecular orbital dependence of the total electronic energy in multireference problems
• Structure of the first order Reduced Density Matrix in three electron systems: A Generalized Pauli Constraints assisted study