Results Obtained with Semiempirical Procedures

This restriction rules out all discrete models exclusively based on semiempirical force fields, leaving among the discrete models the MC/QM and the MD/QM procedures, in which the second part of the acronyms indicates that the solute is described at the quantum mechanical (QM) level, as well as the full ab initio MD description, and some mixed procedures that derive the position of some solvent molecules from semiclassical simulations, replace the semiclassical description with the QM one, and repeat the calculation on these small supermolecular clusters. The final stage is to perform an average on the results obtained with these clusters. These methods can be used also to describe electronic excitation processes, but at present, their use is limited to simple cases, such as vertical excitations of organic molecules of small or moderate size. This limitation is due to the cost of computations, and there is a progressive trend toward calculations for larger systems. 

The combined QM/MM model described so far is a general procedure that can be used in various quantum mechanical schemes, although some of the energy expressions have been given in the formalism of molecular orbital theory. Because a majority of the computational results reviewed in this chapter are obtained with the use of MO theory, especially semiempirical methods, some key features of these calculations are summarized here. The combined QM/MM approach has recently been applied with the use of density functional theory in molecular dynamics simulations °2,io3. a summary of the latter method is also given in this section. 

Table 2.5 presents the positions and widths of the valence and conduction bands of poly(TNCQ) and poly(TTF) obtained with the help of the above-described procedure. The most striking result in the table, as in the case of the previous semiempirical band-structure calculations,< > is that the valence band of poly(TTF) [from which the charge transfer (CT) occurs] is comparatively broad ( 0.3 eV) and the conduction band of poly(TCNQ) (to which the charge is transferred) is broad ( 1.2 eV), while both the valence band of poly(TCNQ) and the conduction band of poly(TTF) (which do not take part in the Cl process) have widths less than 0.1 eV. One should also note that the positions of the conduction band of poly(TCNQ) and the valence band of poly(TTF), respectively. 

Another semiempirical PCM formulation has been presented by Rauhut et al. (1993). They use a marching-cube algorithm to define tesserae (Lorensen and Cline, 1987). The flat mesh thus obtained is then projected on a van der Waals surface (factor Z =1.15). These authors point out that the full NDDO (Neglect of Diatomic Differential Overlap) expression of the (xm VBf xJ elements is convenient in order to have good results, when combined with the original PCM procedure for the surface charge renormalization. 

Semiempirical methods, for example, MNDO. AMI, and PM3. are simplifications of ab initio molecular orbital theory and employ empirically determined parameters in essence, they only differ in the approximations being made. These methods involve adjustable parameters associated with molecular properties that are calibrated against experimental data. The chief advantage of semiempirical calculations over ab initio calculations is that they are several orders of magnitude faster. Thus, calculations for systems of up to c. 200 atoms are currently possible, whereby with ab initio methods, the limit is a moderately sized molecule (about 50 atoms at the time of writing), if rational results are to be obtained. Frequently, semieinpirical methods have proved to be the computational procedures of choice for studying relatively large molecules. 

From the correlations (13) or (14), dipole moments of allenes with axially symmetric substituents may be predicted. Furthermore, it has been shown (9) that dipole moments obtained from the preceding regressions agree well with dipole moments i(CNDO/S) of allenes calculated with the semiempirical CNDO/S procedure. (Dipole moments calculated with the ab initio STO-3G MO method give inferior results.)... 

PBT has been synthesized according to well known standard procedures [77,78]. The resulting polymer is characterized by a crystallinity degree of about 40%, with a melting point of 225°C and a Tg of 5FC. The number average molecular weight, as obtained by viscosimetric analysis using a semiempirical relation between the intrinsic viscosity and [79], was 24,000. 

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