All the methods are similar enough to describe simultaneously. In the following discussion, applications specific to each method will be indicated in the text. This will allow easy comparison among the methods, a comparison that is not obvious from their names.
MNDO stands for Modified Neglect of Diatomic Overlap.
AM1 is Austin Model 1: these are the first two of the MNDO-type methods.
PM3 is the Modified Neglect of Diatomic Overlap, Parametric Method Number 3
RM1 is Recife Model 1, developed by the group of A. M. Simas, Recife, Brazil
MNDO-d, is MNDO with d orbitals.
CNDO (Complete Neglect of Differential Overlap) ignored all terms involving two different atomic orbitals
on one atom.
CNDO is an example of a ZDO (Zero Differential Overlap) method. (For a good introduction to CNDO, see "Approximate Molecular Orbital Theory", J. A. Pople, D. L. Beveridge, McGraw-Hill, New York, 1970. CNDO was first described in: J. A. Pople, D. P. Santry, and G. A. Segal, "Approximate Self-Consistent Molecular Orbital Theory I. Invariant Procedures", J. Chem. Phys., 1965, 43, S129-S135 (1965); J. A. Pople and G. A. Segal, "Approximate Self-Consistent Molecular Orbital Theory II. Calculations with Complete Neglect of Differential Overlap", J. Chem. Phys., 1965, 43, S136-S149 (1965); and J. A. Pople and G. A. Segal, "Approximate Self-Consistent Molecular Orbital Theory. III CNDO Results for AB2 and AB3 Systems", J. Chem. Phys., 1966, 44, 3289-3296 (1966).),
MNDO, AM1, etc belong to the family of NDDO (Neglect of Diatomic Differential Overlap) methods. In these methods all terms arising from the overlap of two atomic orbitals which are on different centers or atoms are set to zero. As this is not the forum for developing the ideas of Hartree-Fock theory, the derivation of the Roothaan-Hall equations will be assumed, and our description of the methods will start with the final Roothaan [52]-Hall [53] equations.