MOLPRO

26 OPEN-SHELL COUPLED CLUSTER THEORIES 195
26 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 (1993) 5219 (see also erratum, J. Chem.
Phys., 112 (2000) 3106) are available in MOLPRO. In both cases a high-spin RHF reference
wavefunction is used. No coupled cluster methods based on UHF orbitals are implemented in
MOLPRO (the only correlation method in MOLPRO which uses UHF orbitals is UMP2). 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 is 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.
Perturbative triples corrections are computed as follows:
RCCSD(T), UCCSD(T)
RCCSD[T], UCCSD[T]
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).
corrections are computed without contributions of single excitations
(sometimes called CCSD+T(CCSD)) .
triples corrections are computed as defined by M. J. O. Deegan and
P. J. Knowles, Chem. Phys. Letters 227 (1994) 321.
In fact, 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
ENERGC
ENERGT(1)
ENERGT(2)
ENERGT(3)
total energy for method specified in the input.
total CCSD energy without triples.
total CCSD(T) energy.
total CCSD[T] energy.
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) 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.