Semiempirical computational effort

In an overall assessment, the established semiempirical methods perform reasonably for the molecules in the G2 neutral test set. With an almost negligible computational effort, they provide heats of formation with typical errors around 7 kcal/mol. The semiempirical OM1 and OM2 approaches that go beyond the MNDO model and are still under development promise an improved accuracy (see Table 8.1). 

We now turn to the problem of simplifying the recovery of the dynamic correlation energy. We consider the simplest situation, viz., where the zeroth-order wavefunction can be chosen as the SCF approximation. A challenging disparity exists between the energetic smallness of these refinements and the complexity and magnitude of the computational efforts required for their variational determination. In order to reduce this disproportion, various semiempirical approaches have been proposed (56-61), notably in particular the introduction of semiempirical elements into MP2 theory which has led to the successful Gn methods (62-64). 

Computational efforts to describe the conformational preferences of (R,R)-tartaric acid and its derivatives - mainly for isolated molecules - were made recently [18-25]. The conformations of these molecules also attracted attention from experimental chemists [22-40]. (/ ,/ [-tartaric acid and its dimethyl diester were observed in crystals, in conformations with extended carbon chain and planar a-hydroxy-carboxylic moieties (T.v.v and Tas for the acid and the ester, respectively) [25-28] (see Figure 2). The predominance ofthe T-structure was also shown by studies of optical rotation [31], vibrational circular dichroism (VCD) [23], Raman optical activity [32, 35], and nuclear magnetic resonance (NMR) [22, 33, 34]. The results of ab-initio and semiempirical calculations indicated that for the isolated molecules the Tsv and T as conformers were those of lowest energy [22, 21, 23, 25]. It should be noted, however, that early interpretations of NMR and VCD studies indicated that for the dimethyl diester of (/ ,/ [-tartaric acid the G+ conformation is favored [36-38]. 

In the benzo-fused series, synthetic efforts have given rise not only to new quinazolines, but also to new methods of preparing them. Quinazoline 34 has been obtained via deprotonation of A-phenyldiethylketenimine with excess strong base (LTMP/KOrBu) in rert-BuOMe followed by addition of another equivalent of the ketenimine and subsequent introduction of rBuCOCl [95T9031]. Semiempirical computational analyses were conducted to provide support for the... 

With any type of molecular modeling, there is generally a tradeoff between cost and reliability, and one typically shuns models that cost more without increasing reliability. In practice, this cost is usually expressed as computational effort, or computer time. In gas phase modeling, one typically finds molecular mechanics and semiempirical molecular orbital theory at the low-cost end and multireference configuration interaction or coupled-cluster theory at the other, with the choice dictated by the size of the system. System size also influences the choice of solvation model. We consider first the least expensive models, those that take no account of the quantum mechanical nature of the solute. 

The CNDO method is used to a lesser extent than EHT or less approximate semiempirical methods (see Sec. 6). The accuracy of energetic and electronic properties obtained with CNDO is, in general, inferior to that of the methods described in the next sections, while the computational effort of the SCF calculation is comparable. 

In ground-state reactions, the PESs of all states involved in a photochemical reaction are usually quite useful as a first step in establishing the reaction mechanism the location of minima and barriers will give hints as to which states are involved in the photoreaction and where conical intersections are likely to be found. Because of the low computational efforts, semiempirical methods are particularly suited for such preliminary investigations. 

Semiempirical quantum mechanics. The computational effort in ab initio calculations increases as the fonrth power of the size of the basis set, and, therefore, its appfication to large molecnles is expensive in terms of time and computer resources. Consequently, semiempirical methods treating only the valence electrons, in which some integrals are ignored or replaced by empirically based parameters, have been developed. The various semiempirical parameterizations now in nse (MNDO, AM 1, PM3, etc.) have greatly increased the molecnlar size that is accessible to quantitative modeling methods and also the accnracy of the resnlts. 

At present, ab initio methods, density functional methods, and semiempirical methods serve as the major computational tools of quantum chemistry. There is an obvious trade-off between accuracy and computational effort in these methods. The most accurate results are obtained from high-level correlated ab initio calculations (e.g., multireference Cl or coupled cluster calculations with large basis sets) which also require the highest computational effort. On the other end of the spectrum, semiempirical MO calculations are very fast, and it is therefore realistic to... 

In summary, semiempirical and ab initio or DFT calculations differ in their computational effort by at least three orders of magnitude. Hence for any given hardware, there will be certain applications that are feasible only with a semiempirical approach, and others where a combined use of semiempirical and ab initio or DFT methods would seem attractive. In such cases, the essential question is whether the available semiempirical methods provide the accuracy desired. 

The two-electron integrals require the main computational effort in a HF calculation and their number is significantly reduced in semiempirical methods by the zero differential overlap (ZDO) approximation. This basic semiempirical assumption sets products of functions for one electron but located at different atoms equal to zero (i.e. /xa(1)vb(1) = 0, where and vb are two different orbitals loeated on centers A and B, respectively). The overlap matrix, S, is set equal to the unit matrix, S v = and the two-electron integrals (/xv Act) are zero, unless fx = v and k = a, that is,... 

Later, he was instrumental in the development and use of semiempirical quantum chemistry methods, like MINDO, MNDO, and AMI, for analysis of organic reactions [24]. Semiempirical methods are generally based on the Hartree-Fock formalism, but the computational effort is reduced by various approximations to the two-electron and overlap integrals that appear in Hartree-Fock... 

---