Multireference correlation in long molecules with the quadratic scaling density matrix renormalization group

Area of Science:

• Computational Chemistry
• Quantum Mechanics
• Materials Science

Background:

• Accurately describing electron correlation is crucial for understanding molecular properties.
• Traditional methods struggle with large systems due to high computational cost.
• Multireference correlations present a significant challenge in quantum chemistry.

Purpose of the Study:

• To develop an efficient algorithm for calculating multireference correlations in large molecular systems.
• To achieve an exact characterization of correlation with reduced computational scaling.
• To demonstrate the algorithm's performance on model systems like polyenes and hydrogen chains.

Main Methods:

• A local ab initio density matrix renormalization group (DMRG) algorithm was devised.
• The method utilizes integral screening to reduce computational cost.
• The algorithm scales quadratically with system size without requiring correlation domains.

Main Results:

• The algorithm achieves exact correlation energies (Full Configuration Interaction) with high precision (1-10 microE(h)).
• It successfully correlates up to 100 electrons in 100 active orbitals.
• The method's scaling, convergence, and robustness were demonstrated on polyenes and hydrogen chains.
• Exact energies for the metal-insulator transition in hydrogen chains were obtained.

Conclusions:

• The local ab initio DMRG algorithm provides an accurate and efficient method for large-scale electronic structure calculations.
• This approach overcomes limitations of conventional quantum chemical methods for systems with strong electron correlation.
• The developed algorithm enables precise studies of phenomena like metal-insulator transitions.