EOM-CCSD

Model (I) Evaluate properties by Eqn. (8). This is the EOM-CCSD scheme originally implemented. 

In this case, of course. A is not consistent with the stationary condition of Eqn. (1). Model (II) eliminates an apparent unlinked term, so is not completely size-extensive. On the other hand, the models (IT) and (III) do not contain any unlinked terms and are therefore exactly extensive. However, unlike EOM-CCSD itself, none of these models is exact for two-electron systems. 

Table 2 shows transition moments calculated by the different EOM-CCSD models. As has been discussed above, the right-hand transition moment 9 is size intensive but the left-hand transition moment 9 in model I and model II is not size intensive. Model II is much improved as far as size intensivity is concerned because of the elimination of the apparent unlinked terms. The apparent unlinked terms are a product of the size-intensive quantity ro and size-extensive quantities and therefore are size extensive. The difference between the values of model I and model II, as summarized in the fifth column, reveals strict size extensivity. Complete elimination of unlinked diagrams by using A amplitudes brings strict size intensivity for the transition moment and therefore the transition probabilities calculated by model III are strictly size intensive. 

EOM-CCSD without apparent unlinked terms. The numbers in the parenthesis ar increments from N-1. 

Table 3 Second Order Properties Calculated by EOM-CCSD Methods...

Concerning the VEE, we have chosen, as standard references for comparison, the EOM-CCSD results from Stanton et al. [56] and from Comeau and Bartlett [57]. Results from other very efficient state-of-the-art methods such as Exponentially Generated Cl or the now widely used CASPT2 could also have been used. In general, these are methods from which mean errors in VEE less than 0.2 eV might be expected provided that the basis set used is at least of split-valence plus polarization quality and it is augmented in a well-conditioned way to account for Rydberg states. 

All of the calculations have been performed at the experimental equilibrium distance R = 1.128 A, in order to enable a proper comparison with the EOM-CCSD reference. In so far as there are neither largely interacting excited states nor special reasons for expecting a breakdown of the Born Oppenheimer approximation, great changes in the MAE are not expected if one takes the (SC) SDCI ground state equilibrium value for Re which is Re = 1.140 A (very close to the CCSD value, as expected Cfr. table 1). We have performed a separate calculation of the whole set of VEE with the aug-cc-pVDZ basis set at the Rg distance, in any case. The results have not been included in table II for the sake of clarity, but the total MAE values where 2.34 eV for the MR-SDCI and 0.17 eV for (SC)2mR-SDCI. 

SDCI (SC)2- SDCI MR- SDCI (SC)2 MR-SDCE SDCI (SC) - SDCl MR- SDCI (scy MR-SDCl EOM- CCSD ... 

Pecul calculated the 1J(3He,3He) coupling in ,154 i.e., one of the weakest bonded van der Waals complexes, using full Cl46 and EOM-CCSD methods.44,155 158 She found that in this complex the FC term of such coupling decreases exponentially with the d(He-He) distance being He, 3He) 22 Hz, for d(He He) = 4 au and falling below 0.1 Hz for d(He-He) = 7 au. Pecul concluded that the main FC coupling pathway is the overlap between the electronic clouds of both helium atoms and that its efficiency does not depend on whether this corresponds to an attractive or repulsive interaction. Similarly, Pecul et al.159 carried out calculations based on... 

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