The Unitary Group Adapted State Universal Multireference Coupled Cluster (UGA-SUMRCC) theory, recently developed by us (J. Chem. Phys.2012, 137, 074104), contains exactly the right number of linearly independent cluster operators. This avoids any redundancy of the excitation manifold in a way exactly paralleling the traditional spin-orbital based SUMRCC. The choice of the linearly independent cluster operators inducing the same change of orbital occupancy becomes increasingly cumbersome if we go over to the cases of active CSFs with more than two active quasiparticles. In the present development, we explore several aspects of the UGA-SUMRCC theory: (a) The first is a variant where we have deliberately incorporated redundancy of the cluster amplitudes to simplify the working equations and have shown that it can serve as a very good approximation to the parent UGA-SUMRCC theory for states with more than two valence occupancies. This in turn suggests that it could be a useful avenue to pursue for arbitrary mh-np situation since the working equations assume simpler algebraic structure in such cases. (b) The analyses of the aspects of size extensivity are known to involve greater complexity if they involve various reduced density matrices (RDMs), since the RDMs are not size-extensive quantities. We have presented the proof for UGA-SUMRCC starting from equations containing h-p RDMs via a decomposition involving products of size-extensive cumulants and argue that it has relevance for general cases beyond the h-p model spaces. (c) A useful extension of UGA-SUMRCC lies in formulating the theory for direct calculations of energy differences of spectroscopic interest such as excitation energies, ionization potentials, and electron affinities relative to a closed shell ground state, thus providing attractive alternatives to other allied methods such as SAC-CI, CC-LRT, EOM-CC, STEOM-CC, or ADC. This extension, called UGA-based Quasi-Fock MRCC by us, also leads to exact cancellation of common correlation terms between the initial and final states. Taking a cue from the hierarchical development in Fock-space theories but keeping in mind the advantages of a state-universal (equivalently called a valence specific) theory, our formulation proposes a spin-adapted, accurate, and compact scheme for studying such energy differences. Our results demonstrate superior performance of the method as compared to EOM-CC.
We introduce a Lagrangian implementation of the full coupled-cluster reduction [Xu et al., Phys. Rev. Lett. 121, 113001 (2018)], that is, a selected coupled-cluster (CC) based on an arbitrary-order full CC expansion using direct commutator expansions. In this method, the screening for the products of cluster amplitudes plays a central role to reduce the computational cost for the nonlinear commutator operations, while the convergence of the total energy in the standard energy expression is not rapid with tightening the threshold. The new implementation using Lagrangian is robust, containing error only quadratic to those of amplitudes, allowing a much larger screening threshold. We demonstrate the performance of the new implementation by investigating the calculations of N2 and C6H6. The accuracy and applicability are also demonstrated for the potential energy curve of H2O in comparison with conventional quantum chemical methods.
We consider a fermionic system for which there exist a single-reference configuration-interaction (CI) expansion of the ground-state wave function that converges, albeit not necessarily rapidly, with the increasing number of particle-hole excitations. For such systems, we show that, whenever the coefficients of Slater determinants (SD) with $l\ensuremath{\le}k$ excitations can be defined with a number of free parameters ${N}_{\ensuremath{\le}k}$ bounded polynomially in
k, the ground-state energy
E only depends on a small fraction of all the wave function parameters and is the solution of equations of the coupled-cluster (CC) form. This generalizes the standard CC method, for which ${N}_{\ensuremath{\le}k}$ is bounded by a constant. Based on that result and low-rank tensor decompositions (LRTD), we discuss two possible extensions of the CC approach for wave functions with general polynomial bound for ${N}_{\ensuremath{\le}k}$. The most straightforward of those extensions uses the LRTD to represent the amplitudes of the CC cluster operator
T which, unlike in the CC case, is not truncated with respect to number of excitations, and the energy and tensor parameters are given by a LRTD-adapted version of standard CC equations. The LRTD can also be used to directly parametrize the wave function coefficients, which involves different equations of the CC form. We derive those equations for the coefficients of SD's with $l\ensuremath{\le}4$ excitations, using the CC exponential wave function ansatz with a different type of excitation operator, and a representation of the Hamiltonian in terms of excited particle and hole operators. To complete the proposed computational methods, we construct compact tensor representations of coefficients, or
T amplitudes, using superpositions of tree tensor networks which take into account different possible types of entanglement between excited particles and holes. Finally, we discuss why the proposed CC extensions are theoretically applicable at larger coupling strengths than those treatable by the standard CC method.