Open-shell coupled cluster theories

Spin unrestricted (RHF-UCCSD) and partially spin restricted (RHF-RCCSD) open-shell coupled cluster theories as described in J. Chem. Phys. 99, 5219 (1993) (see also erratum, 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, 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, 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 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, 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 [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


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.