MNDO/d method

With only s- and p-functions present, the two-centre two-electron integrals can be modelled by multipoles up to order 2 (quadrupoles), however, with d-functions present multipoles up to order 4 must be included. In MNDO/d all multipoles beyond order 2 are neglected. The resulting MNDO/d method typically employs 15 parameters per atom, and it currently contains parameters for the following elements (beyond those already present in MNDO) Na, Mg, Al, Si, P, S, Cl, Br, 1, Zn, Cd and Hg. 

Considering that the parameters for the MNDO/d method for all first row elements (which are present in most of the training set of compounds) are identical to MNDO, the improvement by addition of d-functions is quite impressive. It should also be noted that MNDO/d only contains 15 parameters, compared to 18 for PM3, and that some of the 15 parameters are taken from atomic data (analogously to the MNDO/AMl parameterization), and not used in the molecular data fitting as in PM3. 

Modified Neglect of Diatomic Overlap Parametric Method Number 3 (MNDO-PM3) 3.10.6 The MNDO/d Method 88 89 5.5 5.6 5.4.5 Correlation Consistent Basis Sets Extrapolation Procedures Isogyric and Isodesmic Reactions 162 164 169... 

INDO, and INDO/S methods. MOPAC (J. J. P. Stewart,/. Comp.-Aided Mol. Design, 4, 1 (1990) home.att.net/ mrmopac/) has the MINDO/3, MNDO, AMI, and PM3 methods and is available in workstation and IBM-PC-compatible versions. MND094 (www.oxmol.co.uk/prods/unichem/cap/) has the AMI, PM3, MNDO, MINDO/3, and MNDO/d methods. AMPAC 6.0 (www.semichem.com/) has the SAMI, AMI, PM3, MNDO, and MNDO/d methods. 

Thiel and Voityuk [W. Thiel and A. A. Voityuk, J. Am. Chem. Soc., 100, 616 (1996)] extended MNDO to include d orbitals for many second-row and later elements, giving the MNDO/d method. MNDO/d does not add d orbitals for first-row elements, so for a compound containing only C, H, 0, and N, MNDO/d is precisely the same as MNDO. Also, it was found that for Na, Mg, Zn, Cd, and Hg, inclusion of d orbitals made little difference. 

Semiempirical methods are widely available in many programs. Gaussian 09 (Section 15.14) includes the MNDO, AMI, PM3, PPDG, PM6, MINDO/3, INDO, and CNDO methods. Spartan includes the MNDO, MNDO/d, AMI, PM3, PM6, and RMl methods. HyperChem has the MNDO, MNDO/d, AMI, PM3, RMl, MINDO/3, CNDO, INDO, INDO/S and extended Hiickel methods. MOPAC2012 (openmopac.net/homeJitml) has the MNDO, AMI, PM3, PM6, PM6-DH2, PM6-DH-H, PM7, and RMl methods. It is available in Linux, Macintosh, and Windows versions and is free to academic researchers. An older version is MOPAC2009 (openmopac.net/MOPAC2009.htmI). AMPAC 9 (www. semichem.com) has the SAMI, AMI, PM3, RMl, PM6, MNDO, and MNDO/d methods and a molecule builder, and is available for Windows, Linux, and Macintosh operating systems. 

The MNDO/d method extends the original MNDO formalism to include d orbitals. It differs from MNDO in the underlying model (a) due to the use of a laiger basis, in the integral evaluation (c) with regard to generalizations required for d orbitals, and in the actual parameters (d). A separate article in this encyclopedia describes MNDO/d in more detail (see MNDO/d). 

The established MNDO-type methods, i.e., MNDO, AMl, and PM3 (see AMI MNDO and PM3) employ an sp basis without d orbitals in their original implementation. Therefore, they cannot be applied to most transition metal compounds, and difficulties are expected for hypervalent compounds of main-group elements where the importance of d orbitals for quantitative accuracy is well documented at the ab initio level. To allow for an improved semiempirical description of such compounds, the MNDO formalism has been extended to d orbitals. This extension forms the basis of the MNDO/d method " and the independent PM3/tm parametrization. ... 

The MNDO/d method from Walter Thiel et al. was also introduced in 1992. This method still utilizes a modified point-charge model (multipole expansion as in AMI and PM3) for computing the two-center two-electron integrals (TERIs). MNDO/d is essentially layered onto the older (1977) MNDO model for the elements where Z < 11, Heavier elements were then re-parameterized utilizing an expanded version of... 

Mixed basis sets, 154 MM2, MM3, MM4 force fields, 40 MMFF force field, 40 MMP2, MMP3 method, 27 MNDO/d method, 89 MNDOC method, 87... 

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