NDDO approximation

PM3 is a reparam eteri/ation of AM I, wdi ich is based on the n eglect of diatomic differential overlap (NDDO) approximation. XDDO... 

PM3, developed by James J.P. Stewart, is a reparameterization of AMI, which is based on the neglect of diatomic differential overlap (NDDO) approximation. NDDO retains all one-center differential overlap terms when Coulomb and exchange integrals are computed. PM3 differs from AMI only in the values of the parameters. The parameters for PM3 were derived by comparing a much larger number and wider variety of experimental versus computed molecular properties. Typically, non-bonded interactions are less repulsive in PM3 than in AMI. PM3 is primarily used for organic molecules, but is also parameterized for many main group elements. 

A new parametric quantum mechanical model AMI (Austin model 1), based on the NDDO approximations, is described. In it the major weakness of MNDO, in particular the failure to reproduce hydrogen bonds, have been overcome without any increase in eoraputer time. Results for 167 molecules are reported. Parameters are currently available for C, H, O and N. 

In the Neglect of Diatomic Differential Overlap (NDDO) approximation there are no further approximations than those mentioned above. Using p and n to denote either an s-or p-type (pj, p or p ) orbital, the NDDO approximation is defined by the following equations. 

The main difference between CNDO, INDO and NDDO is the treatment of the two-electron integrals. While CNDO and INDO reduce these to just two parameters (7AA 7ab), all the one- and two-center integrals are kept in the NDDO approximation. Within an sp-basis, however, there are only 27 different types of one- and two-center integrals, while the number rises to over 500 for a basis containing s-, p- and d-functions. 

There are only five types of one-centre two-electron integral surviving the NDDO approximation within an sp-basis (eq. (3.76)). 

MNDO. Despite its success, Dewar recognized certain weaknesses (6) in MINDO/3 due to the INDO approximation, such as the inability to model lone pair - lone pair interactions. Additionally, due to the use of diatomic parameters in MINDO/3, it was increasingly difficult to extend MINDO/3 to additional elements. Because of this, Dewar began working on a new model based on the better NDDO approximation. 

This is referred to as the Neglect of Diatomic Differential Overlap or NDDO approximation. It reduces the number of electron-electron interaction terms from 0(N ) in the Roothaan-Hall equations to 0(N ), where N is the total number of basis functions. 

NDDO Approximation. Neglect of Diatomic Differential Overlap approximation. The approximation underlying all present generation Semi-Empirical Models. It says that two Atomic Orbitals on... 

The simple, or Hiickel based, molecular orbital theory (HMO and PPP methods) frequently provides useful qualitative insights but cannot be used reliably in a quantitative manner. For this purpose it is necessary to use a method which takes account of all the electrons as well as their mutual repulsions. A major bottleneck in such calculations is in the computation and storage of the enormous number of electron-repulsion integrals involved. Early efforts to reduce this problem led Hoffmann to the EH approximation (I.N. Levine, Quantum Chemistry, 4-th ed., 1991, Prentice-Hall, Inc., Ch. 16, 17), and Pople and co-workers to the CNDO, INDO and NDDO-approximations (B-70MI40100). 

Numerous other semiempirical methods have been proposed. The MNDO method has been extended to d functions by Theil and coworkers and is referred to as MNDO/d.155>156 For second-row and heavier elements, this method does significantly better than other methods. The semi-ab initio method 1 (SAM1)157>158 is based on the NDDO approximation and calculates some one- and two-center two-electron integrals directly from atomic orbitals. 

Recently, the MNDO type methods (MNDO [32], AMI [33] and PM3 [34]) have been tested for their ability to produce reliable MEP maps. These semi-empirical methods, just as the CNDO and INDO methods, are ZDO methods, and are based on the more sophisticated NDDO approximation [35]. 

In several works the NDDO approximation was maintained, i.e. the original ZDO MNDO type wavefunction was used without deorthogoanlization for calculating MEP maps [40-44]. Within the NDDO approximation Eq. (3) is modified as follows ... 

Rauhut and Clark used the AMI method within the NDDO approximation for calculating atomic charges [84], The point charges corresponding to the... 

J.J.P. Stewart, Optimization of parameters for semiempirical methods V Modification of NDDO approximations and application to 70 elements. J. Mol. Model. 13, 1173-1213 (2007)... 

Analysis of the general energy expression eq. (3.69) shows that for the MINDO/3 Hamiltonian the only HO orientation dependent contribution to the energy is the resonance energy of the two center bonds. In the NDDO approximation there are the orientation-dependent Coulomb contributions, but they are much less important and we consider them separately later. 

The popular semiempirical methods, MNDO (Dewar and Thiel, 1977), Austin Model 1 AMI Dewar et al., 1985), Parameterized Model 3 (PM3 Stewart 1989a 1989b), and Parameterized Model 5 (PM5 Stewart, 2002), are all confined to treating only valence electrons explicitly, and employ a minimum basis set (one 5 orbital for hydrogen, and one 5 and three p orbitals for all heavy atoms). Most importantly, they are based on the NDDO approximation (Stewart, 1990a, 1990b Thiel, 1988, 1996 Zemer, 1991) ... 

In Equation 6.31, A and B indicate atomic centers, and SAB is the Kronecker function, yielding 1 for A = B, and 0 for A 15. The NDDO approximation implies that (with orthonormal AOs) the overlap matrix S l v reduces to the unit matrix, and that all two-electron integrals with charge clouds arising from the overlap of AOs from two different atomic centers are ignored ... 

In the NDDO approximation, the second sum in Equation 6.51 vanishes (zero diatomic overlap between AOs from different atomic centers and orthogonality of different AOs at the same site), and thus the total number of electrons in a closed-shell system with n/2 doubly occupied MOs is... 

Because Equation 6.53, which is sometimes called the Coulson scheme for net atomic charges, is based on the NDDO approximation, it cannot be applied properly for ab initio methods. Here, a standard scheme to quantify net atomic charges is Mulliken population analysis (Mulliken, 1955 1962), despite some well-known deflciences such as its strong dependence on the basis set and its apparent lack of convergence with increasing basis set size. Nonetheless, Mulliken charges may... 

When the NDDO approximation is not applied, Equation 6.51 remains as it stands. The total number of electrons, n, is then obtained as ... 

In addition to the NDDO approximations, the Intermediate Neglect of Differential... 

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