====== Open-shell coupled cluster theories ======

Spin unrestricted (''RHF-UCCSD'') and partially spin restricted (''RHF-RCCSD'') open-shell coupled cluster theories as described in [[https://dx.doi.org/10.1063/1.465990|J. Chem. Phys.]] **99**, 5219 (1993) (see also [[http://dx.doi.org/10.1063/1.480886|erratum]], [[https://dx.doi.org/10.1063/1.480886|J. Chem. Phys.]] **112**, 3106 (2000)) are available in Molpro. In both cases a high-spin ''RHF'' reference wavefunction is used. Coupled cluster methods based on UHF orbitals are implemented in Molpro for a number of methods as well, including ''CCD'',''CCSD'', ''CCSD(T)'',''MP2-4'', ''CISD'' and ''DCSD''. 

In the description that follows, the acronyms ''RCCSD'' and ''%% UCCSD%%'' are used, but the theories should normally be referred to as ''RHF-RCCSD'', ''RHF-UCCSD'', in order to distinguish them from alternative ansätze based on spin-unrestricted orbitals. The program will accept either the full or abbreviated acronyms as input commands.

In the ''RCCSD'' theory certain restrictions among the amplitudes are introduced, such that the linear part of the wavefunction becomes a spin eigenfunction (this is not the case in the ''UCCSD'' method, even if an ''RHF'' reference function is used). At present, the implementation of ''RCCSD'' is only preliminary, and no CPU time is saved by as compared to ''UCCSD''. However, improved algorithms, as described in the above publication, are currently being implemented, and will be available in the near future.

The input and the options are exactly the same as for closed-shell ''CCSD'', except that ''RCCSD'' or ''UCCSD'' are used as keywords. By default, the open-shell orbitals are the same as used in the ''RHF'' reference function, but this can be modified using ''OCC'', ''CLOSED'', and ''WF'' cards.

Distinguishable cluster calculations can be performed using ''RDCSD'' or ''UDCSD'' commands. The SCS correction is calculated as defined by D. Kats, [[https://dx.doi.org/10.1080/00268976.2017.1417646|Mol. Phys.]] **116**, 1435 (2018).

Perturbative triples corrections are computed as follows:

  * **''%%RCCSD(T), UCCSD(T)%%''** triples corrections are computed as defined by J. D. Watts, J. Gauss and R. J. Bartlett, [[https://dx.doi.org/10.1063/1.464480|J. Chem. Phys.]] **98**, 8718 (1993).
  * **''%%RCCSD[T], UCCSD[T]%%''** corrections are computed without contributions of single excitations [sometimes called CCSD+T(CCSD)]. These slightly differ from the [T] corrections defined by [[https://dx.doi.org/10.1063/1.464480|Watts et al.]] in that the contributions from $X^{ijk}_{abc}$ are not included.
  * **''%%RCCSD-T, UCCSD-T%%''** triples corrections are computed as defined by M. J. O. Deegan and P. J. Knowles, [[https://dx.doi.org/10.1016/0009-2614(94)00815-9|Chem. Phys. Lett.]] **227**, 321 (1994).

All three contributions are always computed and printed. The following variables are used to store the results (here ''CCSD'' stands for either ''UCCSD'' or ''RCCSD''):

  * **''ENERGY''** total energy for method specified in the input.
  * **''ENERGC''** total ''CCSD'' energy without triples.
  * **''%%ENERGT(1)%%''** total ''%%CCSD(T)%%'' energy.
  * **''%%ENERGT(2)%%''** total ''%%CCSD[T]%%'' energy.
  * **''%%ENERGT(3)%%''** total ''CCSD-T'' energy.

It should be noted that in open-shell cases the triples energy slightly depends on the treatment of core orbitals. In Molpro pseudo-canonical alpha and beta spin orbitals %%[%%[[http://dx.doi.org/10.1016/S0009-2614(91)85118-G|Chem. Phys. Lett.]] **186**, 130 (1991)] are generated by block-diagonalizing the corresponding Fock matrices in the space of valence orbitals, leaving frozen core orbitals untouched. Some other programs include the frozen core orbitals in the canonicalization and transformation. Because of core-valence mixing this leads to slightly different energies. Neither of the two methods can be regarded as better or more justified — it is just a matter of definition. However, the method in Molpro is more efficient since the subsequent integral transformation involves only valence orbitals and no core orbitals.

Spin-unrestricted coupled cluster calculations using UHF orbitals can be done using the input options

<code>
uhf
uccsd|uccsd(t)|ucisd|ump2|ump3|ump4
</code>

The spin-unrestricted coupled cluster code can also handle spin-restricted references, yet, by default the restricted open-shell coupled cluster code is executed when the previous SCF calculation was of RHF type. In order to force the execution of the unrestricted code one can set the option ''UHF_UCCSD=1'' to the ''UCCSD'' command. It should be noted, however, that there is little to choose between the two different codes performance wise for RHF references.

==== Open-Shell Coupled cluster calculation on CN ====

<code - examples/cn_rccsd-t.inp>
geometry={c;n,c,r}
r=2.2
{rhf;
occ,5,1,1;
closed,4,1,1;
wf,13,1,1}
rccsd-t
</code>