Abstract
A ring approximation within an internally contracted multireference (MR) Coupled Cluster (CC) framework is worked out and tested. Derivation of equations utilizes MR based, generalized normal ordering and the corresponding generalized Wick-theorem (MR-GWT). Contractions among cluster operators are avoided by adopting a normal ordered exponential ansatz. The original version of the MR ring CC doubles (MR-rCCD) equations [Á. Szabados and Á. Margócsy, Mol. Phys. 115, 2731 (2017)] is rectified in two aspects. On the one hand, over-completeness of double excitations is treated by relying on the concept of frames. On the other hand, restriction on the maximal cumulant rank is lifted from two to four. This is found essential for obtaining reliable correlation corrections to the energy. The MR function underlying the approach is provided by the Generalized Valence Bond (GVB) model. The pair structure of the reference ensures a fragment structure of GVB cumulants. This represents a benefit when evaluating cumulant contractions appearing as a consequence of MR-GWT. In particular, cumulant involving terms remain less expensive than their traditional, pair-contracted counterpart, facilitating an O(N6) eventual scaling of the proposed MR-rCCD method. Pilot applications are presented for covalent bond breaking, deprotonation energies, and torsional potentials.
Highlights
Coupled cluster (CC) theory is remarkably successful in capturing dynamical correlation effects when describing the electronic structure of molecular systems.[1]
Results on the symmetric OH bond stretch of the H2O molecule are shown in Figs. 2 and 3. This example is similar to the single OH bond stretch in that ring CC doubles (rCCD) yields a greater portion of electron correlation than the extended RPA (ERPA) correction
A hump is again present on the Generalized Valence Bond (GVB)-rCCD total energy curve on the order of a mEh peaking at around 3 Å
Summary
Coupled cluster (CC) theory is remarkably successful in capturing dynamical correlation effects when describing the electronic structure of molecular systems.[1]. The wave operator of Eq (1) introduces difficulties in MR generalized Wicktheorem (MR-GWT)[25,27,34,35] based matrix element evaluation, leading to a tremendous blow-up in the number and complexity of the contractions to derive and implement. One of the difficulties common to icMR-CC formulations irrespective of the parametrization of the wave operator is the redundancy among excited functions. Cumulant based truncation is occasionally avoided by transcribing the MR-GNO form of operators into normal order with respect to a genuine vacuum, following MR-GWT based manipulations, just for the purpose of matrix element evaluation by the ordinary Wick-theorem.[49,55,61]. A common trait of the here proposed icMR-rCCD method and previously reported geminal based correlation schemes is the inherent utilization of the two-electron fragment structure of the reference. Since we shall be concerned solely with internally contracted theory, the “ic” designation is omitted from acronyms further on
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