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Coupled Cluster Methods

TeraChem includes a variety of coupled cluster methods for describing dynamic electron correlation. These include methods that exploit tensor hypercontraction and rank-reduction, leading to \(O(N^4)\) scaling for CCSD, compared to the usual \(O(N^6)\) scaling of CCSD in conventional codes. Analytic gradients are not currently implemented for any of the coupled cluster methods implemented in TeraChem, so these methods are suitable primarily for energy evaluation (gradients can only be obtained by numerical differentation).

A summary of the coupled cluster methods available:

  • Ground State Methods
    • CCSD - coupled cluster with single and double excitations
    • CCSD(T) - CCSD with perturbative triple excitations
    • CC2 - second order approximate coupled cluster
  • Excited State Methods
    • EOM-EE-CCSD - equation-of-motion excitation energy CCSD
    • EOM-IP-CCSD - equation-of-motion ionization potential CCSD
    • EOM-CVS-CCSD - equation-of-motion core-valence-separation CCSD
    • EOM-CVS-IP-CCSD - equation-of-motion core-valence-separtion ionization potential CCSD
    • EOM-EE-CC2 - equation-of-motion excitation energy CC2

All coupled cluster methods in TeraChem use the Cholesky decomposition of the two-electron integrals:

\[ (ij|kl) = \sum_P L_{ij,P}L_{kl,P} \]

This does not lead to any scaling reduction, but does make the calculation much faster because of reduced I/O requirements.

There are several keywords pertaining to the Cholesky Decomposition and are therefore relevant to any coupled cluster method in terachem.

Summary of Cholesky Decomposition keywords

Keyword Type Default Description
ccbox_cd_thresh float 1.0e-6 Accuracy threshold for Cholesky Decomposition of integrals
ccbox_cholesky string "cpu" Whether to use the CPU or GPU Cholesky Decomposition routine
ccbox_cd_max integer INT_MAX (= 2147483647 for 32-bit integers) Maximum allowable size of Cholesky factorization
ccbox_cd_threall double 1.0e-14 Threshold to neglect shell pairs in Cholesky Decomposition
ccbox_cd_threspdp double 0.0 SPDP threshold in Cholesky Decomposition

Usually the default Cholesky Decomposition parameters are a reasonable choice, but for large systems a looser CD threshold may be necessary.

There are also several general keywords that govern any coupled cluster calculation in TeraChem.

Summary of general keywords

Keyword Type Default Description
ccbox_frozen_core integer 0 Number of orbitals which are "frozen," i.e. doubly occupied in all included determinants
ccbox_scratch_dir string /tmp Directory where scratch files for CC will be stored
ccbox_no_disk boolean false Store all CC arrays in memory, rather than writing to temporary disk storage?
ccbox_timings string "no" Print detailed timings for CC calculation?