Modification of the Core Repulsion Function

During the evolution of the current semi-empirical methods (AMI, PM3) a number of refinements were made to the core-repulsion function in order to improve, for example, the description of hydrogen-bonding [20, 21]. Such changes have in general led to increased flexibility within the modified semi-empirical Hamiltonians resulting in quite marked improvements in the accuracy of the parent methods. 

the current semi-empirical methods (MNDO, AMI and PM3) differ in the way in which core-repulsions are treated. Within the MNDO formalism the corerepulsion ( asmndo) is expressed in terms of two-centre, two-electron integrals (Eq. 5-4), where Za and Zb correspond to the core charges, Rab is the internuclear separation, and a a and aB are adjustable parameters in the exponential term [19]. 

When the core-repulsion function involves either hydrogen-oxygen or hydrogen-nitrogen interactions, a modified form of this function is used (A = H, B = O, N Eq. 5-5). 

Current AMI and PM3 methods use an alternative core repulsion function which differs from that used in MNDO in that an additional term involving one to four Gaussian functions is used (defined by parameters a-c, Eq. 5-6) [20, 21], These extra terms help to reduce the excessive core-core repulsions just outside bonding distances. 

Despite these modifications there remain a number of well-documented problems with the AM1/PM3 core-repulsion function [37] which has resulted in further refinements. For example, Jorgensen and co-workers have developed the PDDG (pair-wise distance directed Gaussian) PM3 and MNDO methods which display improved accuracy over standard NDDO parameterisations [38], However, for methods which include d-orbitals (e.g. MNDO/d [23,24], AMl/d [25] and AMI [39,40]) it has been found that to obtain the correct balance between attractive and repulsive Coulomb interactions requires an additional adjustable parameter p (previously evaluated using the one-centre two-electron integral Gss, Eq. 5-7), which is used in the evaluation of the two-centre two-electron integrals (Eq. 5-8). 

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AMI is currently one of the most commonly used of the Dewar-type methods. It was the next semiempirical method introduced by Dewar and coworkers in 1985 following MNDO. It is simply an extension, a modification to and also a reparameterization of the MNDO method. AMI differs from MNDO by mainly two ways. The first difference is the modification of the core repulsion function. The second one is the parameterization of the overlap terms (3s and (3p, and Slater-type orbital exponents (s and (p on the same atom independently, instead of setting them equal as in MNDO. MNDO had a very strong tendency to overestimate repulsions between atoms when they are at approximately their van der Waals distance apart. To overcome this hydrogen bond problem, the net electrostatic repulsion term of MNDO, J RAH) given by equation (8.2), was modified in MNDO/H to be... 

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