Incremental embedding: A density matrix embedding scheme for molecules.

Area of Science:

• Quantum chemistry
• Computational chemistry
• Electronic structure theory

Background:

• Accurate electronic structure methods face high computational scaling challenges.
• Traditional fragment embedding methods struggle with systems requiring division across chemical bonds.
• Recent density matrix embedding theory and Schmidt decomposition methods show promise but have limitations for realistic systems.

Purpose of the Study:

• To develop a novel fragment embedding scheme for accurate electronic structure calculations.
• To overcome limitations of existing methods regarding system partitioning and site specification.
• To introduce a method that allows arbitrary overlapping fragments without defining special sites.

Main Methods:

• Developed a new Schmidt decomposition-based embedding scheme named incremental embedding.
• Allows combination of arbitrary overlapping fragments.
• Forms a convergent hierarchy where accuracy increases with fragment size.

Main Results:

• Incremental embedding successfully combines overlapping fragments without needing edge site information.
• The method exhibits a convergent hierarchy, improving accuracy with larger fragments.
• Computational scaling is lower than most correlated wave function methods at initial levels.
• Demonstrated rapid convergence and recovery of static correlation in small molecules using small basis sets.

Conclusions:

• Incremental embedding provides a scalable and accurate approach for electronic structure calculations.
• The method is applicable to realistic molecular systems, overcoming limitations of previous embedding techniques.
• Offers a promising avenue for studying complex chemical systems with high accuracy and reduced computational cost.