Davidson correction

It is possible to make a method approximately size-extensive by adding a correction to the final energy. This has been most widely used for correcting CISD energies. This is a valuable technique because a simple energy correction formula is easier to work with than full Cl calculations, which require an immense amount of computational resources. The most widely used correction is the Davidson correction ... 

A slightly improved form of this equation is the renormalized Davidson correction, which is also called the Brueckner correction ... 

This generally gives a slight improvement over the Davidson correction, although it does not reach the full Cl limit. 

Another method for making a method size-extensive is called the self-consistent dressing of the determinant energies. This is a technique for modifying the Cl superdeterminant in order to make a size-extensive limited Cl. The accuracy of this technique is generally comparable to the Davidson correction. It performs better than the Davidson correction for calculations in which the HF wave function has a low weight in the Cl expansion. 

The principal deficiency of CISD is the lack of the TI term, which is the main reason for CISD not being size extensive. Furthermore, this term becomes more and more important as the number of electrons increases, and CISD therefore recovers a smaller and smaller percentage of the correlation energy as the system increases. There are various approximate corrections for this lack of size extensivity which can be added to standard CISD. The most widely known of these is the Davidson correction, sometimes denoted CISD - - Q(Davidson), where the quadruples contribution is approximated as... 

Estimates of the energy contributions from higher than double excitations out of the reference space were obtained by means of one form of the "Davidson correction" [11,7]. More details can be found in references [7,8]. 

MR SD-CI potential curves including the Davidson corrections are presented in Figure 1. 

Fig.l. Poiential energy curves including the Davidson correction of the X ll, A Ifl and 1a states of PN... 

Several spectroseopie constants derived with and without the Davidson correction (Table 6) show little differences except for ke, tte and tOeXe, the overall agreement with experiment being satisfactory. As for the X state, the Davidson correction tends to reflect experiment sometimes better, e.g. for cOeXe.Be. whereas the discrepancy with respect to experiment is sizeably reduced for Oe-... 

Note 0 The CISD energies, which include Davidson correction for unlinked quadruple excitations, where obtained ot the MCSCF/6-31 G(d)optimized geometries and used a TC-SCF reference for closed-shell singlet states and a single configuration reference for triplet and open-shell singlet states. The SCF/6-31G(d) geometry was employed for the A state. See Ref. 55. 

DABCO, see l,4-Diazabicyclo[2.2.2]octane Dative bond, 49, 262 Dauben-Turro-Salem analysis, 212-213 Norrish type I, 215-217 Norrish type II, 213-215 orbital interaction diagram, 213 Davidson correction, 240 Density, 22... 

The simplest schemes for correcting the behaviour of the Cl correlation energy with particle number are of a type first suggested by Langhoff and Davidson [19] and usually termed a Davidson correction. Fbr the CISD case we have... 

A number of workers have developed similar corrections to Eq. 2.8 but modifying the behaviour in both limits [21, 22]. These modified Davidson corrections have found little favour, although extensive series of comparisons suggest they axe superior to the original [23]. 

The Davidson correction is often applied to multireference Cl results as well as the CISD case. Two formulas can be envisaged for the multireference case ... 

---