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# 4.6.7 PARI-K Fast Exchange Algorithm

(February 4, 2022)

PARI-K733 is an algorithm that significantly accelerates the construction of the exchange matrix in Hartree-Fock and hybrid density functional theory calculations with large basis sets. The speedup is made possible by fitting products of atomic orbitals using only auxiliary basis functions found on their respective atoms. The PARI-K implementation in Q-Chem is an efficient MO-basis formulation similar to the AO-basis formulation of Merlot et al.774 PARI-K is highly recommended for calculations using basis sets of size augmented triple-zeta or larger, and should be used in conjunction with the standard RI-J algorithm for constructing the Coulomb matrix.1191 The exchange fitting basis sets of Weigend1191 (cc-pVTZ-JK and cc-pVQZ-JK) are recommended for use in conjunction with PARI-K. The errors associated with the PARI-K approximation appear to be only slightly worse than standard RI-HF.774

PARI_K

PARI_K
Controls the use of the PARI-K approximation in the construction of the exchange matrix
TYPE:
LOGICAL
DEFAULT:
FALSE Do not use PARI-K.
OPTIONS:
TRUE Use PARI-K.
RECOMMENDATION:
Use for basis sets aug-cc-pVTZ and larger.