An alternative hierarchy of electron correlation beyond the electron pair approximation

Area of Science:

• Quantum Chemistry
• Computational Physics

Background:

• Coupled cluster theory is a standard method for electronic structure calculations.
• Traditional coupled cluster with singles and doubles (CCSD) and triples (CCSDT) methods can be computationally expensive due to a large number of parameters.

Purpose of the Study:

• To develop a hierarchy of more computationally efficient coupled cluster approximations.
• To introduce the semigeneralized singles and doubles (CCSGSD) and generalized singles and doubles (CCGSD) ansätze.
• To explore the parameter scaling of these new methods.

Main Methods:

• The study extends the Nakatsuji theorem to construct a hierarchy of coupled cluster approximations.
• It introduces specific operator types for the CCSGSD and CCGSD ansätze.
• The constrained coupled cluster ansatz with singles, doubles, and triples (CCCSDT) is presented as a realization of CCSGSD.

Main Results:

• The CCSGSD ansatz includes operators of the types a(ab)(ic) and a(ka)(ij).
• The CCGSD ansatz utilizes a more complete basis of operators.
• The CCCSDT approximation requires fewer parameters (O(nm^3)) compared to traditional CCSDT (O(n^3m^3)) for large systems.

Conclusions:

• The proposed hierarchy offers a more parameter-efficient route to high-accuracy electronic structure calculations.
• The derivation of a linear system for the CCCD[T] approximation and discussion of solution strategies are presented.