Parameterized Configuration Interaction

The Parameterized Configuration Interaction (PCI-X) method simply takes the correlation energy and scales it by a constant factor X (typical value 1.2), i.e. it is assumed that the given combination of method and basis set recovers a constant fraction of the correlation energy. 

Blomberg, M. R. A., Siegbahn, P. E. M., Svensson, M., 1996, Comparisons of Results From Parameterized Configuration Interaction (PCI-80) and From Hybrid Density Functional Theory With Experiments for First Row Transition Metal Compounds , J. Chem. Phys., 104, 9546. 

GB = gas-phase basicity ICR = ion cyclotron resonance PA = proton affinity PCI = parameterized configuration interaction. 

A more widely used approach for organic molecules is based on second-order perturbation theory. Here the dipolar contribution to the field induced charge displacement is calculated by inclusion of the optical field as a perturbation to the Hamiltonian. Since the time dependence of the field is included here, dispersion effects can be accounted for. In this approach the effect of the external field is to mix excited state character into the ground state leading to charge displacement and polarization. The accuracy of this method depends on the parameterization of the Hamiltonian in the semi-empirical case, the extent to which contributions from various excited states are incorporated into the calculation, and the accuracy with which those excited states are described. This in turn depends on the nature of the basis set and the extent to which configuration interaction is employed. This method is generally referred to as the sum over states (SOS) method. 

The Linnett model is not parameterized as the Pearson and Miedema models are and bond enthalpies cannot be calculated from atomic data. However, it is strong on molecular structures and provides a simple (but qualitative) explanation for them without the need for much resonance and configuration interaction. 

It is important to note that, at each level of coupled-cluster theory, we include through the exponential parameterization of Eq. (28) all possible determinants that can be generated within a given orbital basis, that is, all determinants that enter the FCI wave function in the same orbital basis. Thus, the improvement in the sequence CCSD, CCSDT, and so on does not occur because more determinants are included in the description but from an improved representation of their expansion coefficients. For example, in CCS theory, the doubly-excited determinants are represented by ]HF), whereas the same determinants are represented by (T2 + Tf) HF) in CCSD theory. Thus, in CCSD theory, the weight of each doubly-excited determinant is obtained as the sum of a connected doubles contribution from T2 and a disconnected singles contribution from Tf/2. This parameterization of the wave function is not only more compact than the linear parameterization of configuration-interaction (Cl) theory, but it also ensures size-extensivity of the calculated electronic energy. 

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