Single determinant N-representability and the kernel energy method applied to water clusters

Area of Science:

• Quantum Chemistry
• Computational Chemistry
• Theoretical Chemistry

Background:

• The Kernel energy method (KEM) offers accurate energy calculations for large molecules by analyzing molecular subsets (kernels).
• KEM's computational cost scales more favorably than full molecule methods.
• However, KEM-derived energies do not inherently satisfy the variational theorem.

Purpose of the Study:

• To extend KEM for generating a full molecule, single-determinant, N-representable one-body density matrix.
• To ensure the resulting density matrix satisfies the variational theorem.
• To improve the accuracy of KEM energy calculations and address theoretical limitations.

Main Methods:

• A kernel expansion for the one-body density matrix was defined, analogous to KEM's energy expansion.
• The density matrix was converted into a normalized projector using Clinton's algorithm.
• The method was applied to clusters of 3 to 20 water molecules.

Main Results:

• The extended KEM successfully generated a single-determinant N-representable one-body density matrix.
• The resulting density matrix corresponds to a quantum mechanically valid wavefunction that satisfies the variational theorem.
• Energies calculated using the extended method were more accurate than standard KEM results.
• All violations of the variational theorem were resolved.

Conclusions:

• The extended KEM provides a robust method for obtaining N-representable density matrices in quantum chemical calculations.
• This approach enhances energy accuracy and ensures adherence to fundamental quantum mechanical principles like the variational theorem.
• The developed N-representability framework is relevant for applications in quantum crystallography.