Sparsity of the wavefunction from the generalized Pauli exclusion principle

Area of Science:

• Quantum Chemistry
• Computational Physics
• Electronic Structure Theory

Background:

• Electron occupations in quantum states are governed by generalized Pauli constraints (GPCs), which generalize the Pauli exclusion principle.
• These GPCs define the boundary of valid one-electron reduced density matrices (1-RDMs) derivable from N-electron wavefunctions.

Purpose of the Study:

• To investigate the sparsity of Slater-determinant wavefunctions as a condition for their 1-RDMs to saturate GPCs.
• To explore the accuracy and applicability of sparse wavefunction Ansätze for various electronic systems.

Main Methods:

• Analyzing the conditions under which sparse wavefunctions saturate GPCs.
• Employing sparse wavefunctions with natural orbitals from full configuration interaction.
• Performing calculations on systems including the boron isoelectronic sequence, N2+, hydrogen chains, and cyclic π systems.

Main Results:

• Sparse wavefunctions exactly saturate GPCs for 3 electrons in 6 or 8 orbitals.
• For larger systems, exact wavefunctions typically do not saturate GPCs, making sparse representations approximations.
• Optimization of sparse wavefunctions does not guarantee saturation of GPCs.

Conclusions:

• Wavefunction sparsity is a necessary but not sufficient condition for GPC saturation.
• The sparse wavefunction Ansatz provides an upper bound to the ground-state energy.
• The study assesses the quality of the sparse Ansatz by the correlation energy recovered in various chemical systems.