Difference Dedicated Configuration Interaction

7 Make a rough estimate of the total number of determinants in the MR-CISD wave function for a system with 74 electrons, 154 orbitals and a CAS(2,2)CI reference wave function. Calculate the percentage of 2h-2p excitations in the MR-CISD wave function (neglect the Ih, Ip, Ih-lp, 2h and 2p excitations, they give rise to a very small number of determinants). 

The justification for eliminating the 2h-2p determinants relies on second-order perturbation theory in its quasi-degenerate formulation as exposed in Chap. 1. Although it can be done for an arbitrary number of unpaired electrons, we will elaborate the 2-electrons/2-orbitals case for simplicity. The model space is spanned by the neutral and ionic determinants 

For the contribution of Pr, the second matrix element in the numerator is zero because the determinants on the left and the right of the operator have more than two different columns, and the same occurs for the first matrix element in the 4 s contribution. This eliminates any second-order perturbation contribution fl om the 2h-2p determinants to the off-diagonal elements of the model space. 

8 Write down the second-order contribution of Pq to Pi H ff l), where pQ arises from a double excitation from orbital h to orbital p acting on the ionic determinant Pl = hhbb. Argue that this contribution is equal to zero. 

On the contrary, the diagonal elements do have a contribution from the 2h-2p excitations. Continuing with the external determinants Pr and 0s, it is easily shown that the former only contributes to and the latter to 0j H 0j) 

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Ab initio DDCI2 (difference-dedicated configuration interaction) calculations seem to provide accurate estimations of the magnetic exchange coupling constants, as demonstrated for the doubly azido-bridged nickel(II) dimer [Ni2(terpy)2(/i-l,l-N3)2]2+.2133... 

Cl methods [21] add a certain number of excited Slater determinants, usually selected by the excitation type (e.g. single, double, triple excitations), which were initially not present in the CASSCF wave function, and treat them in a non-perturbative way. Inclusion of additional configurations allows for more degrees of freedom in the total wave function, thus improving its overall description. These methods are extremely costly and therefore, are only applicable to small systems. Among this class of methods, DDCI (difference-dedicated configuration interaction) [22] and CISD (single- and double excitations) [21] are the most popular. 

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