Coupled cluster

Coupled cluster theory is the most robust way of introducing dynamic electron correlation into the wavefunction and the CCSD(T) method (coupled cluster singles doubles perturbative triples) is often referred to as the gold standard of quantum chemistry due to its excellent accuracy in computing reliable energies of molecules that are qualitatively well described by a single reference wavefunction.

- Any coupled cluster calculation is much more basis set sensitive than a DFT calculation and thus either requires large basis sets or extrapolation techniques. More recently, the development of explicitly correlated coupled cluster F12 methods is becoming useful to reduce basis set dependency.

- The severe scaling of coupled cluster methods has been a major research problem in recent years. This has led to the development of local correlation methods and ORCA features the domain-based local pair natural orbital (DLPNO) CC methods that allows coupled cluster calculations to be performed on larger systems than ever before. It builds on the local pair natural orbital (LPNO) methodology. As DLPNO is the recommended choice nowadays (for both closed-shell and open-shell systems), LPNO is no longer documented here (see manual).

Note that ORCA uses the frozen core approximation by default in coupled cluster calculations. While this approximation generally works well it is important to understand how the frozen core is defined in ORCA and to understand limitations of the approximation. See frozen core page for more.

Regular CCSD(T)

! CCSD(T) cc-pVTZ

If the coupled cluster CCSD iterations do not converge within the default 50 iterations, the maximum number can be modified. Do not change this to a very high number, however. If the coupled cluster iterations have trouble converging there is probably something exotic about the electronic structure that should be analyzed.

This may be indicative of a bad reference wavefunction or multiconfigurational character but sometimes the convergence settings just need to be modified a little bit to aid convergence.

! CCSD(T) cc-pVTZ

%mdci
maxiter 100
end

For tricky convergence cases modifying the DIIS parameters, such as MaxDIIS (max DIIS vectors stored) or the levelshift often works:

! CCSD(T) cc-pVTZ
%mdci
MaxDIIS 25 # Increasing the number of DIIS vectors be stored. Default is 7
Lshift X # Modifying the level shift in coefficents update. Default is 0.2
end

Open-shell CCSD(T)

There are different ways of doing a CCSD(T) calculation on an open-shell system. One could do the CCSD(T) calculation directly on an UHF determinant (UHF-UCCSD(T) ), this is the default for canonical CCSD(T) but may not be the most accurate one due to spin contamination in the UHF orbitals.

! CCSD(T) cc-pVTZ

Another option is to transform the UHF orbitals to QRO orbitals, removing much of the spin contamination. This is the default for DLPNO-CCSD(T) (see later) and is generally recommended.

! CCSD(T) cc-pVTZ UNO
%mdci
UseQROs true
end

Yet another option would be to perform first an ROHF calculation, transform the ROHF orbitals to unrestricted spinorbitals without iterations and then perform the CCSD calculation. This gives in my experience (RB) very similar results to the QRO approach above as both approaches remove the spin contamination in the orbitals.

! ROHF cc-pVDZ xyzfile
%base "rohf"
* xyz -1 2
coordinates
*
$new_job

! UHF cc-pVDZ noiter
%base "uhf"
*xyzfile -1 2
$new_job
! CCSD(T) cc-pVDZ noiter
%base "ccsdt"
*xyzfile -1 2

DLPNO-CCSD(T)

A "/C" auxiliary basis set is required as RI is used for integral transformations.

! DLPNO-CCSD(T) cc-pVTZ cc-pVTZ/C TIGHTSCF

Open-shell DLPNO-CCSD(T)
Note that in open-shell DLPNO-CCSD(T) calculations, QRO orbitals are used automatically to transform the UHF alpha/beta sets to a single alpha set.

With the previous LPNO methodology one had to make sure to calculate all species in a reaction as open-shell (with UHF) if one species was open-shell, as the closed-shell LPNO and open-shell LPNO methods were not directly compatible (a few terms in UHF-LPNO-CCSD were omitted). In the new open-shell DLPNO methodology this is no longer necessary. A new high-spin open-shell version of DLPNO-CC is available in ORCA 4.0. This now enables use of the DLPNO-CC methodology to neutral radical, anion radicals, transition metal complexes etc. In the new code PNOs are generated in the framework of semi-canonical NEVPT2 instead of the unrestricted MP2 that was previously used. This enables smooth convergence to RHF-MP2 in the closed-shell limit, hence the closed-shell and open-shell DLPNO-CC equations are now analogous.

Any DLPNO calculation requires consistent amount of memory, (approx. 6Gb in the example), Note that the MaxCore values is PER CORE, hence a parallel job will allocate #cores x MaxCore memory. This job would request 4*6GB= 24GB of memory, hence the computing node needs to have that much physical memory.

DLPNO-CCSD(T) is compatible with RIJCOSX to speed up the HF step. It is also possible to use RIJK.

! DLPNO-CCSD(T) cc-pVTZ cc-pVTZ/C RIJCOSX def2/J TIGHTSCF

Coupled cluster density and properties

Molecular properties at the coupled cluster level requires access to the coupled cluster density. The coupled cluster density is more complicated than in SCF methods, the linearized CCSD density is automatically calculated in CCSD calculations. For regular CCSD unrelaxed coupled cluster density is also available as is a density from orbital-optimized coupled cluster theory (OOCCD) which should be close to a fully relaxed coupled cluster density.

Note: Unrelaxed densities are not available for CCSD(T).

%mdci
density none, linearized, unrelaxed, orbopt
end

DLPNO-CCSD lambda equations are nowadays available in ORCA that provides access to coupled cluster molecular properties within the DLPNO scheme.

Explicit correlation: CCSD-F12

Todo...