Variations on the basic MNDO are MNDO/d and MNDOC, both developed by
the research group of Thiel. MNDO/d has d functions added to the minimal-basis
valence s and p functions, in an attempt to solve one of the most persistent problems
of semiempirical methods, that of obtaining good results for compounds tradition-
ally believed to utilized orbitals, including “hypervalent” compounds [ 43 ].
Although the term hypervalent is not unambiguous,hypercoordinatebeing perhaps
preferable, and the role of d orbitals here is controversial [ 44 ], parameterization
with d functions is a pragmatic approach to finding a semiempirical method that
works. MNDO/d was applied to “normal” molecules and, more to the point,
compounds of metals like magnesium, zinc, cadmium and mercury, and some
hypercoordinate molecules. MNDO/d was said to give “significant improvements”
over established semiempirical methods, especially for hypervalent compounds
[ 43 ]. The particularly difficult task of parameterizing MNDO for transition metal
compounds does not appear to have been satisfactorily solved. The application of
MNDO and related methods to such compounds has been reviewed [ 45 ]. See too
Chapter 8, Section 8.3.4.
MNDOC denotes MNDO with configuration interaction (CI; Section 5.4.3) [ 46 ].
This may seem odd, since MNDO (and the related AM1 and PM3,..., PM6) are
parameterized to match experiment, and should therefore “automatically” include
electron correlation (Section 5.4.1), which CI is designed to handle. However, the
parameterization uses compounds (ground-electronic state species), not transition
states and excited states, and electron correlation changes on going from a ground
state to a transition or excited state. In a transition state this is because of a
loosening of bonds, akin to the effect discussed in connection with homolytic
bond cleavage (Section5.4.1), and in an excited state there is of course a dramatic
altering of the electron arrangement. A perfect parameterization would therefore
give perfect properties, such as heats of formation and geometries, for ground-state
molecules only. Specific inclusion of CI in MNDO is designed to improve the
modeling of transition states and excited states, and MNDOC was said, compared to
MNDO, to be “superior for [transition states]” [46(b)] and to warrant “cautious
applications...to photochemical problems” [46(c)]. In other studies involving
transition states, MNDOC was said to outperform MNDO and compare reasonably
well with ab initio calculations [ 47 ]. Augmenting an experimental study in which
matrix-isolated dimethyloxirene was said to be have been observed, Bachmann
et al. performed MNDOC calculations to estimate the barriers for the ring-opening
of some oxirenes to the oxo carbenes (“ketocarbenes”) [ 48 ]:
OR R..OR RThey obtained these barriers (kJ mol"^1 / kcal mol"^1 ): oxirene (R¼H, 24/5.8);
dimethyloxirene (R¼CH 3 , 31/7.3); di-t-butyloxirene (R¼t-C 4 H 9 , 56/13.5); cyclo-
hexyne oxide (R, R¼CH 2 CH 2 CH 2 CH 2 , 0/0); benzyne oxide (R, R¼CHCHCHCH,
67/16). The ordering of energies may well be correct, but MNDOC seems to
6.2 The Basic Principles of SCF Semiempirical Methods 407