Development and pilot molecular applications of the uncoupled state-specific MRCC (UC-SS-MRCC) theory

Perturbative triples correction to domain-based local pair natural orbital variants of Mukherjee's state specific coupled cluster method

In this article we report an implementation of the perturbative triples correction to Mukherjee's state-specific multireference coupled cluster method based on the domain-based pair natural orbital approach (DLPNO-MkCC). We tested the performance of DLPNO-MkCCSD(T) in calculations involving tetramethyleneethane and isomers of naphthynes. These tests show that more than 97% of triples energy was recovered with respect to the canonical MkCCSD(T) method, which together with the DLPNO-MkCCSD part accounts for about 99.70-99.85% of the total correlation energy. The applicability of the method was demonstrated on calculations of singlet-triplet gaps for several large systems: triangulene, dynemicin A, and a beryllium complex.

Aspects of Size-Consistency of Orbitally Noninvariant Size-Extensive Multireference Perturbation Theories: A Case Study Using UGA-SSMRPT2 as a Prototype

Profiling a potential energy surface (PES), all the way to dissociate a molecular state into particular fragments and to display real or avoided crossings, requires a multireference description and the maintenance of size-consistency. The many body methods, which suit this purpose, should thus be size-extensive. Size-extensive theories, which are invariant with respect to transformation among active orbitals are, in principle, size-consistent. Relatively cheaper size-extensive theories, which do not possess this invariance, can still be size-consistent if the active orbitals are localized on the asymptotic fragments. Such methods, if perturbative in nature, require the use of an unperturbed Hamiltonian, which has orbital invariance with respect to the transformation within active, core, and virtual orbitals. The principal focus of this paper is to numerically realize size-consistency with localized active orbitals using our recently developed orbitally noninvariant Unitary Group Adapted State Specific Multireference second order Perturbation Theory (UGA-SSMRPT2) as a prototype method. Our findings expose certain generic potential pitfalls of size-extensive but orbitally noninvariant MRPT theories, which are mostly related to the inability of reaching proper localized active orbitals in the fragments due to the artifacts of the orbital generation procedure. Despite the invariance of the zeroth order CAS function, lack of invariance of the MRPT itself then leads to size-inconsistency. In particular, reaching symmetry broken fragment active orbitals is an issue of concern where suitable state-averaging might ameliorate the problem, but then one has to abandon full orbital optimization. Additionally, there can be situations where the orbitals of the fragment reached as an asymptote of the supermolecule are not the same as those obtained from the optimization of the fragments individually and will require additional transformation. Moreover, for a certain PES, one may either abandon the use of optimized orbitals for that state to preserve proper symmetry and degeneracy in the fragment orbitals or be satisfied with the use of optimized orbitals, which generate broken symmetric orbitals in the fragmentation limit. All these pathologies are illustrated using the PES of various electronic states of multiply bonded systems like N2, C2H2, HCN, C2, and O2. Subject to such proviso, the UGA-SSMRPT2 turns out to be an excellent theory for studying the PES leading to fragmentation of strongly correlated systems satisfying the requirements of size-consistency with localized active orbitals. An unexpected spin-off of our studies is the realization that the size-inextensive MRMP2, which bears a close structural similarity with our theory, might under certain situations display size-consistency. We analyze this feature concretely in our paper. Our studies may serve as a benchmark for monitoring numerically the size-consistency of any state specific multireference theory which is size-extensive but not invariant with respect to transformation of active orbitals.

Diagnosis of the performance of the state-specific multireference coupled-cluster method with different truncation schemes

We have tested the linked version of a iterative (partial) triples correction for the Jeziorski-Monkhorst ansatz based state-specific multireference coupled cluster (SS-MRCC) approach with singles and doubles (SD) excitations [abbreviated as SS-MRCCSDT-1a and SS-MRCCSDT-1a+d]. The assessments of SS-MRCCSDT-1a and SS-MRCCSDT-1a+d schemes have been performed on the ground potential energy surface (PES) of P4, Li(2),Be(2) systems which demand the MR description, and on study of the excitation energy between the ground and first excited state for P4 system. Illustrations in the isomerization of cyclobutadiene also show the power of the schemes. One of the designed features of the SS-MRCCSDT-n methods introduced here is that they do not require storage of the triples amplitudes. In the entire range of geometries, we found a definite improvement provided by SS-MRCC with SDT-1a and SDT-1a+d schemes over the standard SD one. In the nondegenerate regions of PES, the closeness of the performance of the single-reference CC to the SS-MRCC methods increases after inclusion of even partial triple excitations. Generally, the performance of the SS-MRCCSDT-1a+d approach is closer to the corresponding full configuration interaction (FCI) one than to the SS-MRCCSDT-1a specially in the degenerate geometries (as is evident from nonparallelism error). The deviation from FCI for the first excited state of the P4 model using various SS-MRCC theories with different truncation schemes obtained by converging on the second root of the effective Hamiltonian has also been reported. We also compare our results with the current generation state-of-the-art single and multireference CC calculations to envisage the usefulness of the present approach. Initial implementation indicates that the SS-MRCCSDT-n formalism can provide not only reliable excitation energies and barrier height even when used in a relatively small model space, but also offers a considerable promise in generating the entire energy surface with low nonparallelity error.