Dispersion semiempirical methods

A key advantage of semiempirical methods is that they give heats of formation directly. Small cyclic hydrocarbons are typically computed to be too stable, and sterically crowded structures are predicted to be too unstable. This is because semiempirical methods do not describe weak interactions well, e.g. those arising from London dispersion forces thus, they would not be suitable to describe, for instance, molecular structures that rely heavily on hydrogen bonding interactions. 

One such link between semiempirical theory and experiment that appeared about that time was the development of calculational methods for optical rotatory dispersion. Moffitt s theoretical work with Kronig—Kramers transforms coupled with Djerassi s experimental data on steroids gave rise to rules for the prediction of the sign of optical rotation. Computer calculations with semiempirical methods played a role. i Wavefunctions of at least an approximate sort were needed for the dipole and dipole velocity matrix elements of the theory. 

To conclude this section, we mention an article [68] that discusses desirable features for next-generation NDDO-based semiempirical methods. Apart from orthogonalization corrections and effective core potentials that are already included in some of the more recent developments (see above) it is proposed that an implicit dispersion term should be added to the Hamiltonian to capture intramolecular dispersion energies in large molecules. It is envisioned that dispersion interactions can be computed self-consistently from an additive polarizability model with some short-range scaling [68]. 

Tuttle, T, and Thiel, W. (2008], OMx-D semiempirical methods with orthogonalization and dispersion corrections. Implementation and biochemical application, Phys. Chem. Chem. Phys. 10,2125-2272. 

Dispersion corrections to DFT and HF (including semiempirical methods) have recently been reviewed [59, 60] and hence only a brief description is given. Asymptotically correct approaches are either atom-pair-based (e.g., DFT-D3 [42], XDM [61], or Tkatchenko-Scheffler (TS)-vdW [62]) or compute the dispersion energy from the electron density (called vdW-DF [25, 63]). For recent work on the... 

The Born model is only a rough approximation. Improvements of the method take into account a local permittivity e and effective ionic radii fl= a -I- 5 , where Si is the distance between an ion and an adjacent solvent dipole. More elaborate models include in the calculation the energy of formation of a spherical cavity in the pure solvent into which an ion and its solvation shells can be transferred from the vacuum. Further interactions that can be taken into account result from ion-quadrupole, ion-induced dipole, dipole-dipole, dispersion, and repulsion forces. For nonaqueous electrolyte solutions most of the molecular and structural data needed for this calculation of the solvation energy are unknown, and ab initio calculations have not so far been very successful. Actual information on ion solvation in nonaqueous solutions is based almost exclusively on semiempirical methods and/or the extrathermodynamic assumptions quoted in Section II.C. 

Finally, we should also briefly discuss the performance of semiempirical methods. These are methods that neglect some of the more expensive integrals in Hartree-Fock molecular orbital theory and replace others with empirical parameters. Because semiempirical methods are based on Hartree-Fock theory, and because Hartree-Fock theory does not capture dispersion effects, semiempirical methods are not suitable for computing dispersion-dominated noncovalent interactions. Semiempirical methods yield repulsive potentials for the sandwich benzene dimer, just as Hartree-Fock does. However, given that semiempirical methods already contain empirical parameters, there is no reason not to fix this deficiency by adding terms proportional to r, as is done in force-field methods and the empirical DFT-D methods. Such an approach has been tested for some base pairs and sulfur-7t model systems. 

An independent indication that frequency dispersion of DIIR and PIIR spectra is due to the CL distribution comes from the extensive calculations carried out by Mori and Kurihara [139,140] and Mori et al. [141]. These authors calculated by MNDO the infrared spectrum of (C H + 2) in = 17-37), which corresponds to a charged soliton embedded in a chain with increasing CL [139-141]. Even with such a semiempirical method of calculation, one of the modes, namely 1 3, shows strong frequency and intensity dispersion with chain length. On the other hand, frequency and intensity dispersion of 1/3 is confirmed by the use of ab initio calculations with large basis sets (6-31 G) on soliton-containing polyenes... 

In contrast with the EHF energy, which can generally be estimated by ab initio methods for many systems of practical interest (see ref. 140 for a semiempirical treatment), the interatomic correlation energy is most conveniently approximated from the dispersion energy by accounting semiempiri-cally for orbital overlap and electron exchange effects. Thus the following... 

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