Tensor decomposition in post-Hartree-Fock methods. I. Two-electron integrals and MP2.

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Theoretical Physics

Background:

• Post-Hartree-Fock (HF) methods are computationally intensive, requiring significant storage and processing power for accurate electronic structure calculations.
• Conventional algorithms face challenges in handling large multidimensional tensors representing integrals and wavefunction parameters.

Purpose of the Study:

• To present a novel approximation for post-HF methods using tensor decomposition techniques.
• To reduce the computational effort and storage requirements of quantum chemistry algorithms.
• To enable rigorous truncation and error estimation in electronic structure calculations.

Main Methods:

• Application of tensor decomposition in the canonical product tensor format.
• Representing multidimensional tensors as expansions in one-dimensional vectors.
• Implementation details include decomposition of two-electron integrals, AO-MO transformation, and MP2 energy calculations.

Main Results:

• Storage reduction to O(d·R·n) and computational effort reduction to O(R(2)·n) for tensors in canonical format.
• Demonstrated scaling of decomposition rank with system size (N) for AO integrals (O(N^1.8)), MO integrals (O(N^1.4)), and MP2 t(2)-amplitudes (O(N^1.2)).
• Achieved MP2 energy accuracy in the mHartree range with a specified error bound (ε = 10^-2).

Conclusions:

• Tensor decomposition offers a promising approach to drastically decrease computational cost and storage in post-HF methods.
• The method allows for efficient handling of large systems and provides a pathway for developing more scalable quantum chemistry algorithms.
• Potential for extension to more complex methods like coupled cluster theory.