Neglect of Diatomic Differential Overlap Approximation NDDO

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. 

PM3 is a reparameterization of AMI, which is based on the neglect of diatomic differential overlap (NDDO) approximation. NDDO... 

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. 

One way to keep the cost of the calculations low but improve the accuracy is to use semiempirical molecular orbital calculations in which some of the parameters are fit to data for the specific reaction of interest or for a limited range of reactions. We call this approach SRP for specific reaction parameters or specific range parameters. In several applications we have combined the SRP approach with semiempirical molecular orbital theory employing the neglect of diatomic differential overlap (NDDO) approximation. This is called the NDDO-SRP approach [49]. 

The method Neglect of Diatomic Differential Overlap (NDDO) was originally developed by Pople and Beveridge [8] and Pople et al. [37]. The ZDO approximation [Eq. (26)] is only applied for orbital pairs centered at different atoms. Consequently, new types of two-center integrals appear compared to the INDO method, (pv pX) and (/t Fb v). This means that not only monopole-monopole interactions are taken into account, but also dipole and quadrupole terms. Thus, in principle, NDDO-based methods should give an improved description of long-range intra- and interm olecular... 

The semiempirical methods are based on the simplification of the HF LCAO Hamiltonian and require the iterative (self-consistent) density matrix calculations complete and intermediate neglect of differential overlap (CNDO and INDO - approximations), neglect of diatomic differential overlap (NDDO) and others, using the neglect of differential overlap (NDO) approximation. 

The neglect of diatomic differential overlap (NDDO) method [236] is an improvement over the INDO approximation, since the ZDO approximation is applied only for orbital pairs centered at different atoms. Thus, all integrals pv Xa) are retained provided p and v are on the same atomic center and A and a are on the same atomic center, but not necessarily the center hosting p and v. In principle, the NDDO approximation should describe long-range electrostatic interactions more accurately than INDO. Most modern semiempirical models (MNDO, AMI, PM3) are NDDO models. 

Various NDO schemes differ from CNDO in that they do not utilize fully the ZDO approximation. These schemes are discussed in the book by Pople and Beveridge (1970). In the intermediate neglect of differential overlap (INDO) model the differential overlaps between orbitals on the same atom are kept in one-center two-electron integrals, while the neglect of diatomic differential overlap (NDDO) model neglects only diatomic differential overlaps in any two-electron integral. 

Model calculations were performed on the VAMP [24], DMOL [25, 26], and CASTEP [27] modules of the Materials Studio program package from Accelrys. Full geometry optimizations and vibrational frequency analyses were carried out in all electron approximation using in DMOL the BLYP [28, 29] functional in conjunction with the double-numeric-basis set with polarization functions (DNP) and the IR models were calculated from the Hessians [30], In CASTEP the gradient-corrected (GGA) PBE [31] functional was selected for the density functional theory (DFT) computations with norm conserving and not spin polarized approach [32], In the semi-empirical VAMP method we used the PM3 parameterization [33] from the modified neglect of diatomic differential overlap (NDDO) model to obtain the Hessians for vibrational spectrum models [30],... 

I lie next level of approximation is the neglect of diatomic differential overlap model (NDDO [Pople et al. 1965]) this theory only neglects differential overlap between atomic orbitals on... 

The NDDO (Neglect of Diatomic Differential Overlap) approximation is the basis for the MNDO, AMI, and PM3 methods. In addition to the integralsused in the INDO methods, they have an additional class of electron repulsion integrals. This class includes the overlap density between two orbitals centered on the same atom interacting with the overlap density between two orbitals also centered on a single (but possibly different) atom. This is a significant step toward calculatin g th e effects of electron -electron in teraction s on different atoms. 

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... 

---