Correlation consistent configuration

E. A. Carter, W. A. Goddard, J. Chem. Phys. 88, 3132 (1988). Correlation-Consistent Configuration Interaction Accurate Bond Dissociation Energies from Simple Wave Functions. 

Carter EA, Goddard WA (1988) Correlation-consistent configuration-interaction - accurate bond-dissociation energies from simple wave-functions. J Chem Phys 88(5) 3132-3140... 

Figure 1. The shape of the potential curve for nitrogen in a correlation-consistent polarized double-zeta basis set is presented for the variational 2-RDM method as well as (a) single-reference coupled cluster, (b) multireference second-order perturbation theory (MRPT) and single-double configuration interaction (MRCl), and full configuration interaction (FCl) wavefunction methods. The symbol 2-RDM indicates that the potential curve was shifted by the difference between the 2-RDM and CCSD(T) energies at equilibrium.

Correlation effects have already been mentioned a number of times. Let us discuss them here in more detail. In the Hartree-Fock approach (to be more exact, in its single-configuration version, which we have been considering so far) it is assumed that each electron in an atom is orbiting independently in the central field of the nucleus and of the remaining electrons (one-particle approach). However, this is not exactly so. There exist effects, usually fairly small, of their correlated, consistent movement, causing the so-called correlation energy. 

The concomitant advances in theoretical methodologies and algorithms have also played a vital role in increasing computational capabilities for theoretical thermochemistry. These advances include (1) new methods for accurate treatment of electron correlation in molecules and atoms such as coupled cluster and quadratic configuration interaction methods, (2) new basis sets such as the correlation consistent basis sets, and (3) development of model chemistry ... 

This effect originates in the various f electron configurations of lanthanides and actinides. This effect is based on the correlation observed between the full pattern of the effect and the sequence of values of the L quantum number [52]. The correlation consists of the occurrence of the same double symmetry in (a) the series of L quantum number values of the ground terms of f element ions and (b) the sequence of relatively stabilized or destabilized f electron configurations (i.e.) the double-double effect. Accordingly... 

This is equal to the measured experimental value. Let us note that the Pauling s evaluation is a first approximation, as it treats all 0-atoms as being independent and neglects correlations of configuration between neighbour 0-atoms. This correlation enters for a small part only in the value of the residual entropy, but it has up to now not been calculated. The existence of such a residual entropy has no important consequences, except that if it is not properly taken into account, thermodynamical values may differ when measured from different experiments, thus lacking consistency. 

Tab. 3.1 Selected vibrational energies (cm ) of H5OJ calculated by a variety of methods and experiment for the OH-monomer stretches. 2d+2d are the adiabatic 4d calculations of Ref [56], 4d are the fully coupled 4d calculations of Ref [27], CC-VSCF are the correlation-consistent vibrational self-consistent field calculations of Ref [58] and VCI are the virtual configuration interaction calculations of Ref [27]. The potential used in these calculations is indicated after the back-slash.

The ab initio HF treatment with correlation of large molecules is by no means a simple problem. On the other hand, without taking into account correlation effects only the ground state properties of a molecule in its equilibrium geometry can be calculated in a more or less reliable way. Further the standard method for the treatment of correlation, the configuration interaction (Cl) method, cannot be used well even for medium size systems, because it is not size consistent. Therefore, one has to apply either some form of many body perturbation theory (MBPT) or the coupled cluster (CC) approach, both in a certain approximation (both methods are size consistent). 

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