Semiempirical DFT

One such model that has promise is density functional tight-binding (DFTB) theory. In DFTB, we begin by expressing the energy associated with a reference density po(r) as 

A quick comparison of tliis equation witli Eqs. (8.15) and (8.18) should make clear that this expression is indeed valid its form is reminiscent of Eq. (4.39) insofar as the energy is expressed as a sum of orbital energies (tlie hist tenn on the r.h.s.) corrected for doublecounting of electron-electron interactions (tlie next three terms on the r.h.s.). In addition the nuclear repulsion term, which is constant for a given geometry, is explicitly written here for reasons that will become clear shortly. 

To speed this process up further for very large systems, one can make some further assumptions entirely analogous to those found in semiempirical MO theory. In particular, one may assume 

This same restriction of consideration to no more than pairwise interactions can be adopted for the remaining terms on the r.h.s. of Eq. (8.36), which are usually grouped together and referred to collectively as the repulsive energy frep, so tliat this energy component is computed as 

With these further simplifications, enonnously large systems may be handled fairly easily to include geometry optimization. This non-self-consistent protocol defines DFTB. 

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Semiempirical, DFT, and ah initio methods also work well. Correlation effects are sometimes included for the sake of increased accuracy, but are not always necessary. One particular case for which correlation is often necessary is fluorine compounds. 

Density functional calculations are usually faster than ab initio, but slower than semiempirical. DFT is relatively new (serious DFT computational chemistry goes back to the 1980s, while computational chemistry with the ab initio and semiempirical approaches was being done in the 1960s). 

Table 7.10 Calculated (ab initio, semiempirical, DFT) and experimental [111] UV spectra of methylenecyclopropene, wavelength, nm (relative intensity). The recommended ab initio basis set [111] and DFT functional and basis set [110] are used. The ab initio results are from Table 5.16, and the semiempirical results are from Table 6.5...

Useful source of information on the calculation of energy quantities heats of formation, reaction energies, bond energies, activation energies, etc. Methods group additivity, molecular mechanics, semiempirical, DFT, and high-accuracy ab initio (G2, CBS, etc.) energies of solvation. 

Another perspective is offered by considering the size dependence of the self interaction (ii ii). This integral displays Ksize-dependence according to Eq. (2-25) and hence it vanishes for a completely delocalized orbital of an infinitely periodic insulator. For a spatially localized orbital, the same self interaction is nonzero. This is a consequence of the lack of orbital invariance of this integral. In HF theory, the self interaction is cancelled between Coulomb and exchange terms and does not spoil the orbital invariance of the total energy and wave function. In semiempirical DFT and TDDFT, since the cancellation is not exact, the remnant, positive self interaction (ii ii) is usually minimal for a delocalized orbital. This renders semiempirical DFT and TDDFT a universal tendency to favor delocalized wave functions irrespective of the true nature of chemical systems. 

Another well-known example of the same problem of semiempirical DFT is electronic structures of /ran.v-polacetylene [99-105], This is a one-dimensional system subject to a Pierels distortion. Therefore, it is an insulator with a bond-alternated structure at a sufficiently low temperature. However, semiempirical DFT fails to reproduce a large band gap or bond-alternated structure, predicting incorrectly that frans-polyacetylene is (nearly) metallic at zero temperature. This is another manifestation of DFT s nonphysical tendency to favor delocalized wave functions. The HF or HF-based correlated theories do not exhibit this problem. 

Although usual diagrammatic argument does not apply, for these reasons, semiempirical DFT and TDDFT may be said to lack size correctness. 

Among the possible types of available quantum chemical technologies (e.g. semiempirical, DFT and ab initio, see Scheme 12.2 for a rough classification in terms of computational cost—vertical—and accuracy— horizontal) one could use to compute... 

Derosa, P. A. (2009). A combined semiempirical-DFT study of oligomers within the finite-chain approximation, evolution from ohgomers to polymers. J Compu. Chem. 30,... 

The preceding methods discussed in this section are semiempirical MO methods. The SCC-DFTB method (self-consistent-charge density-functional tight-binding method) is a semiempirical DFT method [M. Elstner et al., Phys. Rev. B, 58, 7260 (1998) M. Elstner, Theor. Chem. Acc., 116, 316 (2006)], somewhat similar to the semiempirical MO methods. The exchange-correlation energy functional used in SCC-DFTB is usually the PBE functional (Section 16.5). The SCC-DFTB method treats only the valence electrons... 

The development of quantum chemistry and the growth of computing power have led to the fact that modem semiempirical, DFT and ab initio methods of the quantum chemistry can significantly improve the speed and accuracy of calculations of various physical and chemical characteristics of the objects or processes and in many cases allow to achieve precise agreement with the experimental data [5]. This makes it possible to predict the molecular force constants and frequencies of normal vibrations. The second derivative of the total energy of the molecule on the internal... 

See also this earlier study in which the structures of cyclohep tatriene and some methoxy derivatives were optimized using semiempirical, DFT, and ab initio methods Donovan, W. H. White, W. E. J. Org. Chew. 1996, 61, 969. 

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