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# 6.12.5 Local Pair Models for Valence Correlations Beyond Doubles

(July 14, 2022)

Working with Prof. Head-Gordon at Berkeley, John Parkhill has developed implementations for pair models which couple 4 and 6 electrons together quantitatively. Because these truncate the coupled cluster equations at quadruples and hextuples respectively they have been termed the “Perfect Quadruples” and “Perfect Hextuples” models. These can be viewed as local approximations to CASSCF. The PQ and PH models are executed through an extension of Q-Chem’s coupled cluster code, and several options defined for those models will have the same effects although the mechanism may be different (CC_DIIS_START, CC_DIIS_SIZE, CC_DOV_THRESH, CC_CONV, etc.).

In the course of implementation, the non-local coupled cluster models were also implemented up to ${\hat{T}}_{6}$. Because the algorithms are explicitly sparse their costs relative to the existing implementations of CCSD are much higher (and should never be used in lieu of an existing CCMAN code), but this capability may be useful for development purposes, and when computable, models above CCSDTQ are highly accurate. To use PQ, PH, their dynamically correlated “+SD” versions or this machine generated cluster code set: METHOD = MGC.

MGC_AMODEL

MGC_AMODEL
Choice of approximate cluster model.
TYPE:
INTEGER
DEFAULT:
Determines how the CC equations are approximated:
OPTIONS:
0 Local Active-Space Amplitude iterations (pre-calculate GVB orbitals with your method of choice (RPP is good)). 7 Optimize-Orbitals using the VOD 2-step solver. (Experimental-only use with MGC_AMPS = 2, 24 ,246) 8 Traditional Coupled Cluster up to CCSDTQPH. 9 MR-CC version of the Pair-Models. (Experimental)
RECOMMENDATION:
None

MGC_NLPAIRS

MGC_NLPAIRS
Number of local pairs on an amplitude.
TYPE:
INTEGER
DEFAULT:
None
OPTIONS:
Must be greater than 1, which corresponds to the PP model. 2 for PQ, and 3 for PH.
RECOMMENDATION:
None

MGC_AMPS

MGC_AMPS
Choice of Amplitude Truncation
TYPE:
INTEGER
DEFAULT:
None
OPTIONS:
2$\leq$ n $\leq$ 123456, a sorted list of integers for every amplitude which will be iterated. Choose 1234 for PQ and 123456 for PH
RECOMMENDATION:
None

MGC_LOCALINTS

MGC_LOCALINTS
Pair filter on an integrals.
TYPE:
LOGICAL
DEFAULT:
FALSE
OPTIONS:
Enforces a pair filter on the 2-electron integrals, significantly reducing computational cost. Generally useful for more than 1 pair locality.
RECOMMENDATION:
None

MGC_LOCALINTER

MGC_LOCALINTER
Pair filter on an intermediate.
TYPE:
LOGICAL
DEFAULT:
FALSE
OPTIONS:
Any nonzero value enforces the pair constraint on intermediates, significantly reducing computational cost. Not recommended for $\leq$ 2 pair locality
RECOMMENDATION:
None