Applications of Semiempirical Methods

A good, brief overview of the performance of MNDO, AMI and PM3 as of ca. 1999 is given by Levine [87]. Hehre has compiled a very useful book comparing AMI with molecular mechanics (Chapter 3), ab initio (Chapter 5) and DFT (Chapter 7) methods for calculating geometries and other properties [88], and an extensive collection of AMI and PM3 geometries is to be found in Stewart s second PM3 paper [70]. 

Many of the general remarks on molecular geometries in Section 5.5.1, preceding the discussion of results of specifically ab initio calculations, apply also to semiempirical calculations. Geometry optimizations of large biomolecules like proteins 

Both AMI and PM3 consistently underestimate C-C bond lengths (by about 0.02 A). 

C-X (X=0, N, F, Cl, S) bond lengths appear to be consistently neither over- nor underestimated by AMI, while PM3 tends to underestimate them as stated above, the PM3 lengths seem to be the more accurate (mean errors 0.013 versus 0.028 A for AMI). Both AMI and PM3 give quite good bond angles (largest error ca. 4°, except for HOF for which the AMI error is 7.1°). 

AMI tends to overestimate dihedrals (10+, 0—), while PM3 may do so to a lesser extent (7+, 3—). PM3 breaks down for HOOH (calculated 180°, experimental 119.1°, and does poorly for FCH2CH2F (calculated 57°, experimental 73°). Omitting the case of HOOH, the mean dihedral angle errors for AMI and PM3 are 5° and 4.5° however, the variation here is from 1° to 11° for AMI and from —1° to —16° for PM3 (although not wildly out of line with the AMI, PM3 or MP2 calculations, the reported experimental ClCH2CH2OH HOCC dihedral of 58.4° is suspect see Section 5.5.1). 

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The authors, not being familiar with carbohydrate chemistry, have limited this to a general discussion of two potential applications of semiempirical methods to the study of carbohydrate chemistry. 

At the present time, it appears that the applicability of semiempirical methods to the study of carbohydrate chemistry has been neglected. Methods are now available for the non—theoretician to investigate molecular systems, reaction mechanisms, and fundamental physical properties, without the need for any extensive knowledge of theoretical methods. Despite this, most computational studies appear to be limited to the use of molecular mechanics techniques. 

The established semiempirical methods developed until 1990 have been applied extensively in chemical research. There are thousands of publications with applications of semiempirical methods to solve chemical problems, as indicated by the Science Citation Index where the number of citations for the original papers on CNDO/2 [13], MINDO/3 [15], MNDO [16], AMI [18], PM3 [19], and INDO/S [23] currently (June 2004) exceeds 2500, 2100, 5800, 9800, 4500, and 1200, respectively. This is further illustrated in Fig. 21.1 which shows the corresponding citations per year between 1966 and 2003. Assuming that the number of citations reflects the actual use of these methods, it is obvious that AMI and PM3 are presently the most popular semiempirical tools in computational work. 

As the combined analysis of the PE and SOC surfaces is particularly suited for determining the triplet state reactivity, this approach extends the applicability of semiempirical methods to discuss triplet photoreactions as well. 

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