Other density-based methods

In addition, one may distinguish between density- and wavefunction-based methods. With the wavefunction-based methods one attempts to solve the electronic Schrodinger equation as accurately as possible, in some cases at high computational costs. The density-based methods are based on the density-functional theory and have, in practical applications, to invoke some more or less controllable approximations. On the other hand, in most cases they lead to accurate results at less computational costs as the wavefunction-based methods. In some of the earlier reports by the present author in this series, the performance of density-based methods has been studied and also compared with that of wavefunction-based methods. ... 

Chrastil s correlation, the empirical basis for which had previously been noted by Stahl [74], is discussed alongside other density-based correlation methods in [73]. Ziger and Eckert s correlation [75] which is based on solubility parameters, is also discussed. 

Density functional theory (DFT) has become very popular in recent years. This is justified based on the pragmatic observation that it is less computationally intensive than other methods with similar accuracy. This theory has been developed more recently than other ah initio methods. Because of this, there are classes of problems not yet explored with this theory, making it all the more crucial to test the accuracy of the method before applying it to unknown systems. 

To date the majority of QM-MM applications have employed density functional methods ab initio or semiempirical methods in the quantum region. The energy tenns evaluated in these methods are generally similar, but there are specific differences. The relevant equations for the density functional based methods are described first, and this is followed by a description of the specific differences associated with the other methods. 

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