Séminaire LCPQ
Salle de séminaire IRSAMC
In this talk, I will discuss the formulations and implementations of State-Specific (SS) and State-Universal (SU) Multi-reference Coupled Cluster (MRCC) theories, which are explicitly unitary group-adapted (UGA) and thus do not suffer from spin-contamination. We will refer to them as UGA-SSMRCC and UGA-SUMRCC respectively. We propose a new multi-exponential cluster Ansatz analogous to but different from the one suggested by Jeziorski and Monkhorst (JM). Unlike the JM Ansatz, our choice involves spin-free unitary generators for the cluster operators and we replace the traditional exponential structure for the wave-operator by a suitable normal ordered exponential. I will sketch the consequences of choosing our Ansatz, which leads to fully spin-free finite power series structure of the ‘direct term’ of the MRCC equations. The UGA-SUMRCC and UGA-SSMRCC equations both follow from projection equations onto virtual functions reached from every model function. For the UGA-SUMRCC formalism, there are no redundancies for the cluster amplitudes, while the UGA-SSMRCC requires suitable sufficiency conditions to arrive at a well-defined set of equations for the cluster amplitudes. In the UGA-SSMRCC, I will introduce two distinct and inequivalent sufficiency conditions and discuss their pros and cons. The UGA-SUMRCC and UGA-SSMRCC equations are manifestly connected and hence size-extensive. I will also discuss another approximant to the UGA-SSMRCC, where the number of cluster amplitudes can be drastically reduced by internal contraction of the two-body inactive cluster amplitudes. These are the most numerous. This is referred to as the ICID-UGA-SSMRCC method . Redeeming features of the UGA-based formalisms of ours (a) the ability to treat strong orbital relaxation effects and (b) easy access to the direct computation of energy differences. Both will be exemplified by typical applications which will cover core ionization potentials and core-excited states. Pilot numerical results will be presented to indicate the promise and the efficacy of all the three methods for two-electron problems as well as for systems with more that two-electrons in the active space. For the UGA-SSMRCC method, the effect of localization and size-consistency will also be demonstrated. Finally, we will also indicate our recent attempts to go beyond these strategies.