Higher semiempirical methods

A long period elapsed before significant extensions were made to Huckel s 1931 molecular orbital theory. In the 1950s mutual repulsion energies were taken into account by Pariser, Parr, (1953) and Pople (1953) in calculating matrix elements. Hoffmann (1963) devised a scheme whereby the important off diagonal matrix elements for a bonds as well as n bonds were calculated as the arithmetic mean of the adjacent diagonal elements 

In our simple test case for Ahydf/298 (ethene), MNDO calculations yield A H29S = 15.4 and -19.7 kcal mol 1 respectively for ethene and ethane. This gives Ahydi/29g (ethene) = -36.1 kcal mol 1 as contrasted to the experimental value of-32.6 0.05 kcal mol 1. PM3 calculations yield A H29S = 16.6 and -18.1 kcal mol 1 for ethene and ethane respectively. This gives Ahyd/f29g (ethene) = -34.7 kcal mol 1 as contrasted to the experimental value of-32.6 0.05 kcal mol 1. 

Thiel (1998) lists mean absolute deviations between calculated AfH29S and experimental AfH29S for two ab initio methods, a density functional variant of the ab inito method and three semi-empirical methods. They are G2 1.58, G2(MP2) 2.04, B3LYP 3.11, MNDO 9.32, AMI 7.81, and PM3 7.01 kcal mol 1 respectively. See below for comments on ab initio calculations. 

One condition we impose on the set of functions % that we choose as a basis set is that they be as nearly complete as possible, that is, we hope that the set will span the vector space. In practice, this is never quite achieved. Another condition we would like to build into our basis set is that of easy computation so as to be as economical of computer resources as possible. 

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As can be seen in the studies mentioned above, prior to the massive usage of semiempirical methods in the production runs, a thorough validation against experiment or higher level ab initio method is necessary. The choice in our studies for validation purposes is the application of the well-established MP2 method for ground state structures and properties, and the usage of ADC(2) for excitation... 

The preference for the 1,2,3-thiadiazoline structure in more polar solvents is explained by the higher dipole moment (ca 5 D as compared to ca 2 D) of the transition structure452. Extensive ab initio calculations on the reaction of diazomethane with thioformaldehyde concluded that both regioisomers should be formed via concerted pathways452, but some semiempirical methods (AMI, MNDO-PM3) suggest that the reaction takes place in a stepwise manner. 

A major weakness of semiempirical methods is that they must be assumed to be unreliable outside molecules of the kind used for their training set (the set of molecules used to parameterize them), until shown otherwise by comparison of their predictions with experiment or with high-level ab initio (or probably DFT) calculations. Although, as Dewar and Storch pointed out [125], the reliability of ab initio calculations, too, should be checked against experiment, the situation is somewhat different for these latter, at least at the higher levels studies of exotic species, in particular, are certainly more trustworthy when done ab initio than semiempirically. Semiempirical heats of formation are subject to errors of tens of kJ mol-1, and thus heats (enthalpies) of reaction and activation could be in error by scores of kJ mol-1. AMI and PM3 underestimate steric repulsions, overestimate basicity and underestimate nucleophilicity, and can give unreasonable charges and... 

Calculations on MDA with semiempirical methods (INDO and CNDO/2) for C2v and Q conformers gave almost coincidental potential wells whereas STO-3 G shows the c2v to have a single minimum but of higher energy than Cs by 44.5 kJ mol-1 (6-31G basis set)109). 

The most recent calculations seem to indicate some improvements in the theoretical evaluation of relative tautomer energies. At the 3-21G level the structures are accurate enough for higher-level calculations, which in turn clearly give better relative energies. Here the 6-310 basis set shows the most promise. Another fact to consider is the almost uniform neglect to calculate ASa,b and 8 a 0) even though the vibrational frequencies can be obtained with semiempirical methods. This makes the comparison of the calculated and experimental equilibrium constants even more difficult. 

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