Modified NDDO approximations

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 ... 

The philosophy in the Semi-ab initio Method 1 (SAMI and SAMID) modelis slightly different from the other modified methods. It is again based on the NDDO approximation, but instead of f lacmg all integrals by parameters, Uie one- and two-... 

NDDO [20] goes beyond INDO in that the ZDO approximation (section 6.2.1, point (3)) is not applied to orbitals on the same atom, i.e. ZDO is used only for atomic orbitals on different atoms. NDDO is the basis of the currently popular semiempirical methods developed by Dewar and coworkers modified NDDO (MNDO), Austin method 1 (AMI) and parametric method (PM3). 

In 1993, Dewar and co-workers modified AMI to give the SAMI (semi-ab initio model 1) method [M. J. S. Dewar, C. lie, and G. Yu, Tetrahedron, 23,5003 (1993) A. J. Holder and E. M. Evleth in D. A. Smith (ed.). Modeling the Hydrogen Bond, American Chemical Society, 1994, p. 113]. A major difference between SAMI and AMI is that SAMI evaluates the two-center ERIs as (/ii Acr)sAMi = s( ab)(m Ko-)stc)-3g> where ( v Ao-)sto-3g is the accurate value of the ERI calculated using a STO-3G basis set, and the function (Rab) is a certain function of the intemuclear distance that reduces the magnitudes of the ERIs so as to allow for electron correlation and use of a minimal basis set. The function (Rab) contains parameters whose values have been adjusted to maximize the performance of the method. Because of the need to calculate two-center ERIs accurately, SAMI is slower than AMI, but is still far faster than ab initio methods, due to the NDDO approximation. 

As we have seen, MINDO/3 was based on the INDO approximation, which could not represent lone-pair lone-pair interactions therefore, as expected, MINDO/3 had difficulty with systems which contained lone pairs. To rectify this, Dewar embarked on developing and parameterizing a wholly new method based on the NDDO approximation. This was completed by Dewar and Thiel only two years after MINDO/3 was published. They called the new method, which was published in 1977, modified neglect of diatomic overlap or MNDO. ... 

Meta- Position in the Substituted Benzene Ring Minimum Energy Coordinates Modified Neglect of Differential Overlap [NDDO (Neglect of Diatomic Differential Overlap) Approximation, Method]... 

Semiempirical SCF calculations were done using the approximations NDDO (neglect of diatomic differential overlap) [18], MNDO (modified neglect of diatomic overlap) [19], INDO (intermediate neglect of differential overlap) [20], SINDO (symmetrically orthogonalized INDO [21]) [22], and CNDO (complete neglect of differential overlap) [20, 23]. Another type of approximation [24] to the ab initio method was also applied to OF2 [16]. 

H = Hiickel, EH = extended Hiickel, PPP = Pariser-Pople-Parr, CNDO = complete neglect of differential overlap, INDO = intermediate neglect of differential overlap, NDDO = neglect of diatomic differential overlap, MNDO = modified neglect of differential overlap, MINDO = modified intermediate neglect of differential overlap. Note AMI and PM3 are MNDO methods that differ only in the way constants are chosen to approximate various integrals. 

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],... 

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