The multifacet graphically contracted function method. I. Formulation and implementation.

Area of Science:

• Quantum Chemistry
• Computational Chemistry
• Electronic Structure Theory

Background:

• The computationally intensive nature of electronic structure calculations limits the scope of achievable chemical system modeling.
• Existing methods like the single-facet graphically contracted function (GCF) expansion have limitations in accuracy and efficiency for complex systems.

Purpose of the Study:

• To present the fundamental formulation of the multifacet generalization of the graphically contracted function (MFGCF) electronic structure method.
• To analyze the computational efficiency and accuracy of the MFGCF method for various chemical applications.

Main Methods:

• Formulation of the MFGCF method, including handling linear dependency and parameter redundancy.
• Computation of reduced density matrices, Hamiltonian, and spin-density matrices.
• Calculation of optimization gradients for single-state and state-averaged electronic structure calculations.
• Efficient computation of configuration state function and Slater determinant expansion coefficients.
• Analysis of computational scaling for energy and gradient computations, showing an O(N(2)n(4)) dependency.

Main Results:

• The MFGCF method demonstrates efficient computation of electronic structures with a favorable scaling.
• Applications to challenging chemical systems (N2, H8, H2O dissociation, Be insertion into H2) show results comparable to exact full-CI values.
• The method's performance is validated against the previous single-facet GCF expansion form.

Conclusions:

• The MFGCF method provides a computationally efficient and accurate approach for electronic structure calculations.
• Its formulation and implementation offer a significant advancement for modeling complex chemical phenomena.
• The method's efficiency is attributed to the utilization of dense matrix-matrix product computational kernels.