354 Computational Chemistry

6.2.5.6 SAM1

Semi ab initio method number 1 (SAM1) was the last SE method to be reported (1993, [50]) by Dewar’s group. SAM1 is essentially a modification of AM1 in which the two-electron integrals are calculated ab initio using contracted Gaussians (an STO3G basis set) as in standard ab initio calculations (section 5.3.2). This is in contrast to AM1, where the two-center two-electron integrals are calculated from the one-center two-electron integrals, which are estimated spectroscopically. As Holder and Evleth point out in a brief but lucid outline of the basis of AM1 and SAM1 [51], a key distinguishing feature of each SE method is how it calculates the two-electron repulsion integrals. Since the NDDO approximation discards all the threeand four-center two-electron integrals, the number of two-electron integrals to be calculated is greatly reduced. This, and the limitation to valence electrons, makes SAM1 only about twice as slow as AM1 [51].

One of the main reasons for developing SAM1 was to improve the treatment of hydrogen bonding (this was also a primary reason for developing AM1 from MNDO; evidently success there was only limited). SAM1 is indeed an improvement over AM1 in this respect, and “appears to be the first semiempirical parameterization to handle a wide variety of [hydrogen bonded] systems correctly”; in fact, it was said that “the results from SAM1 for virtually every system has improved over AM1 and PM3, fulfilling the criteria for SAM1 to be a reasonable successor to AM1 and PM3 for general purpose semiempirical calculations” [51]. An extensive list of experimental heats of formation compared with those calculated by SAM1, AM1, and PM3 has been published [49]. Actually, despite its apparent generally significant superiority over AM1, there have been relatively few publications using SAM1. This is probably because the program at present is available only in the commercial SE package AMPAC [52], which seems to be used mainly by chemists working in industry who cannot always publish freely, and because the parameterization of SAM1 has not yet been fully disclosed in the open literature (researchers are perhaps uncomfortable about using a black box, or even a gray one).

6.2.5.7Inclusion of d orbitals: MNDO/d and PM3t; explicit electron correlation: MNDOC

The original (and most widely-used) versions of MNDO, AM1, and PM3 do not use d orbitals. Hence they might be expected to show reduced accuracy for elements in the “second-row” (computational chemists’ lingo) and beyond like, P, S, Cl, Br, and I, and cannot be used for transition metals. Actually, because of appropriate parameterization AM1 and PM3 are able to treat monovalent Cl, Br and I as standard elements (C, H, O, N, F), and they handle divalent S reasonably well. To make them able to work better with elements in the second row and beyond, and/or to handle transition metals (note that in Zn, Cd, and Hg the d electrons are not normally involved in bonding), d orbitals have been incorporated into some SE methods. MNDO/d [53] uses d orbitals for some post-first row nonmetals and has been parameterized for several transition metals. Some versions of SPARTAN [54] have PM3 (tm), PM3 with d orbitals for many transition metals. PM3 (tm) geometries have been compared with experimental and ab initio ones;