Energy-correcting methods

There is also a local MP2 (LMP2) method. LMP2 calculations require less CPU time than MP2 calculations. LMP2 is also less susceptible to basis set superposition error. The price of these improvements is that about 98% of the MP2 energy correction is recovered by LMP2. 

The more recently developed methods define an energy expression for the combined calculation and then use that expression to compute gradients for a geometry optimization. Some of the earlier methods would use a simpler level of theory for the geometry optimization and then add additional energy corrections to a final single point calculation. The current generation is considered to be the superior technique. 

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 ... 

There are many more error correction methods, which are reviewed in detail by Duch and Diercksen. They also discuss the correction of other wave functions, such as multireference methods. In their tests with various numbers of Be atoms, the correction most closely reproducing the full Cl energy is... 

Frequencies computed with methods other than Hartree-Fock are also scaled to similarly eliminate known systematic errors in calculated frequencies. The followng table lists the recommended scale factors for frequencies and for zero-point energies and for use in computing thermal energy corrections (the latter two items are discussed later in this chapter), for several important calculation types ... 

Compute the frequencies at each optimized geometry using the same method to obtain the zero point energy corrections. 

The introduction of various empirical corrections, such as scale factors for frequencies and energy corrections based on the number of electrons and degree of spin contamination, blurs the distinction between whether they should be considered ab initio, or as belonging to the semi-empirical class of methods, such as AMI and PM3. Nevertheless, the accuracy tiiat tiiese methods are capable of delivering makes it possible to calculate absolute stabilities (heat of formation) for small and medium sized systems which rival (or surpass) experimental data, often at a substantial lower cost than for actually performing the experiments. 

Methods that compensate for nonequilibrium effects in the situation of E-parametrized coefficients are very complicated, and are sometimes not firmly grounded. Because the electron temperature also gives reasonable results without correction methods, the rate and transport coefficients were implemented as a function of the electron energy, as obtained from the PIC calculations presented in Figure 25. 

The results of the simple DHH theory outlined here are shown compared with DH results and corresponding Monte Carlo results in Figs. 10-12. Clearly, the major error of the DH theory has been accounted for. The OCP model is greatly idealized but the same hole correction method can be applied to more realistic electrolyte models. In a series of articles the DHH theory has been applied to a one-component plasma composed of charged hard spheres [23], to local correlation correction of the screening of macroions by counterions [24], and to the generation of correlated free energy density functionals for electrolyte solutions [25,26]. The extensive results obtained bear out the hopeful view of the DHH approximation provided by the OCP results shown here. It is noteworthy that in... 

The results of the various semi-empirical calculations on the reference structures contained within the JSCH-2005 database (134 complexes 31 hydrogen-bonded base-pairs, 32 interstrand base pairs, 54 stacked base pairs and 17 amino acid base pairs) are summarised in Table 5-10. The deviations of the various interaction energies from the reference values are displayed in Figure 5-5. As with the S22 training set, the AMI and PM3 methods generally underestimate the interactions whereas the dispersion corrected method (PM3-D) mostly over-estimates the interactions a little. Overall the PM3-D results are particularly impressive given that the method has only... 

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