Low-order tensor approximations for electronic wave functions: Hartree-Fock method with guaranteed precision.

Area of Science:

• Computational Chemistry
• Quantum Mechanics
• Numerical Analysis

Background:

• Finite element methods (FEM) face challenges with high storage and computational costs as system complexity increases.
• Existing Hartree-Fock (HF) implementations often require substantial resources, limiting their application to larger systems.

Purpose of the Study:

• To develop a novel formulation of the Hartree-Fock (HF) method utilizing an adaptive multiresolution basis set of spectral element type.
• To mitigate the computational and storage burdens associated with traditional FEM in quantum chemistry.

Main Methods:

• Implementation of HF method using low-order tensor approximations for operators and wave functions.
• Avoidance of explicit storage of the full-dimensional wave function.
• Utilizing spectral element basis sets for adaptive multiresolution analysis.

Main Results:

• Demonstrated microhartree precision for systems up to 14 electrons without full wave function storage.
• Low-order tensor approximation reduced storage for one-electron methods, with a modest cost increase.
• Preliminary tests on two-electron wave functions suggest a 50-fold reduction in storage requirements.

Conclusions:

• The developed approach offers significant storage savings and computational efficiency for HF calculations.
• This method makes correlated two-electron methods feasible on modern workstations with guaranteed precision.
• The formulation paves the way for more efficient quantum mechanical simulations of larger and more complex systems.