SAMIS approach

The MNDO/d formalism for the two-electron integrals has several advantages Conceptually, it employs the same approach as the established MNDO-type methods [19-22], including an effective reduction of the Coulomb interactions to allow for dynamic electron correlation. Moreover, it is rotationally invariant and computationally efficient, and analytical first and second derivatives of the integrals are available [121]. An alternative formalism has been implemented more recently in the SAMI approach [23,122], which apparently involves the analytical evaluation of the two-electron integrals in an spd basis and subsequent scaling (details still unpublished). 

The documented successes of MNDO/d (see above) suggest an extension to transition metals. The MNDO/d parametrization has been completed for several transition metals [123] and is in progress for others, but a systematic assessment of the results is not yet feasible. Elsewhere the published MNDO/d formalism for the two-electron integrals [33] has been implemented independently [124] and combined with PM3 in another parametrization attempt for transition metals [125]. Moreover, the SAMI approach is also being parametrized for transition metals [122,126]. Given these complementary activities it seems likely that the performance of MNDO-type methods with an spd basis for transition metal compounds will be established in the near future. 

The term "semi-empirical" has been reserved commonly for electronic-based calculations which also starts with the Schrodinger equation.9-31 Due to the mathematical complexity, which involve the calculation of many integrals, certain families of integrals have been eliminated or approximated. Unlike ab initio methods, the semi-empirical approach adds terms and parameters to fit experimental data (e.g., heats of formation). The level of approximations define the different semi-empirical methods. The original semi-empirical methods can be traced back to the CNDO,12 13 NDDO, and INDO.15 The success of the MINDO,16 MINDO/3,17-21 and MNDO22-27 level of theory ultimately led to the development of AMI28 and a reparameterized variant known as PM3.29 30 In 1993, Dewar et al. introduced SAMI.31 Semi-empirical calculations have provided a wealth of information for practical applications. 

The semiempirical molecular orbital (MO) methods of quantum chemistry [1-12] are widely used in computational studies of large molecules. A number of such methods are available for calculating thermochemical properties of ground state molecules in the gas phase, including MNDO [13], MNDOC [14], MNDO/d [15-18], AMI [19], PM3 [20], SAMI [21,22], OM1 [23], OM2 [24,25] MINDO/3 [26], SINDOl [27,28], and MSINDO [29-31]. MNDO, AMI, and PM3 are widely distributed in a number of software packages, and they are probably the most popular semiempirical methods for thermochemical calculations. We shall therefore concentrate on these methods, but shall also address other NDDO-based approaches with orthogonalization corrections [23-25],... 

The first (1967) of the Dewar-type methods was PNDDO [35], partial NDDO), but because further development of the NDDO approach turned out to be unexpectedly formidable [33], Dewar s group temporarily turned to INDO, creating MINDO/1 [36] (modified INDO, version 1). The third version of this method, MINDO/3, was said [33] [to have] so far survived every test without serious failure , and it became the first widely-used Dewar-type method. Keeping their promise to return to NDDO the group soon came up with MNDO (modified NDDO). MINDO/3 was made essentially obsolete by MNDO, except perhaps for the study of carbocations (Clark has summarized the strengths and weaknesses of MINDO/3, and the early work on MNDO [37]). MNDO (and MNDOC and MNDO/d) and its descendants, the very popular AMI and PM3, are discussed below. Briefly mentioned are a modification of AMI called SAMI and an... 

AMI and PM3 perform similarly and usually give quite good geometries, but less satisfactory heats of formation and relative energies. A modification of AMI called SAMI (semi-ab initio method 1), relatively little-used, is said to be an improvement over AMI. AMI and SAMI represent work by the group of M. J. S. Dewar. PM3 is a version of AMI, by J. J. P. Stewart, differing mainly in a more automatic approach to parameterization. Recent extensions of AMI (RM1) and PM3 (PM6) seem to represent substantial improvements and are likely to be the standard general-purpose semiempirical methods in the near future. 

This completes the general overview over choices (a)-(d) in a semiempirical framework. We shall now briefly characterize some current treatments MNDO [19], MNDOC [20], AMI [21], PM3 [22], SAMI [23,24], SINDOl [25,26], and INDO/S [27,28]. These methods are widely available in distributed software packages and have generally replaced older methods in practical applications (e.g., CNDO/2 [29], CNDO/S [30], INDO [31], and MINDO/3 [32]). Recent developments from our group, such as MNDO/d [33-36] and approaches with ortho-gonalization corrections [37,38] are discussed later (see Section III.B). 

The reason for this explanation is not to promote SAMIS for supply chain accounting. The purpose is to show that the issues faced in supply chain accounting are not new, and creative approaches have been developed. What is needed is irmovation in addressing the issues. Any supply chain partnership should consider SAMIS-type solutions in the design or operation of their own extended enterprises. 

In SINDOl and MSINDO, the TERIs are evaluated analytically over -functions with different exponents for s-, p-, and <7-type AOs. SAMI uses an at initio-style approach, which involves the analytical evaluation of the TERIs and subsequent scaling. 

SAMI represents somewhat of a new theoretical approach, with a different theoretical basis than previous models. The basic direction of development chosen for SAMI (discussed in more detail in SAMI) was to improve certain components of the general model from AMI, MNDO, and PM3. The two chosen were the two-electron repulsion integrals and the one-center two-electron terms. SAMI has been parameterized for a number of main group elements (C, H, O, N, F, Cl, Br, I, Si, S, P) as well as the transition metals Fe and Cu. 

In summary, several methods exist for treatment of transition metals using semiempirical approaches. INDO/S, SINDOl, and NDDO/MC are best applied to the computation of specific properties. The other methods (SAMI, MNDO/d, and PM3(tm)) are still largely untested in variety of situations and a clearly preferred approach has not emerged. 

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