Modified NDDO Models

The MNDO, AMI and PM3 methods are parameterizations of the NDDO model, where the parameterization is in terms of atomic variables, i.e. referring only to the nature of a single atom. MNDO, AMI and PM3 are derived from the same basic approximations (NDDO), and differ only in the way the core-core repulsion is treated, and how the parameters are assigned. Each method considers only the valence s- and p-functions, which are taken as Slater type orbitals with corresponding exponents, (s and 

The two-center one-electron integrals given by the second equation in (3.74) are written as a product of the corresponding overlap integral times the average of two atomic resonance parameters, (3. 

Here /r and v again indicate either s- or p-type functions and the overlap is calculated 

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

The G-type parameters are Coulomb terms, while the H parameter is an exchange integral. The Gp2 integral involves two different types of p-functions (i.e., Py or pj. 

ELECTRONIC STRUCTURE METHODS INDEPENDENT-PARTICLE MODELS 

The overlap element is calculated explicitly (note that this is not consistent with the ZDO approximation, and the inclusion is the origin of the Modified label). 

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Modified NDDO Models 85 r 5.4.2 Dunning-Huzinaga Basis Sets 160... 

The semi ab initio model 1 (SAMI) is another modified NDDO method, but it does not replace integrals by parameters. The one- and two-center electron repulsion integrals are explicitly calculated from the basis functions [employing a standard STO-3G (Slater-type orbital from three Gaussian functions) Gaussian basis set] and scaled by a function which has to be parametrized. SAM 1 calculations take about twice as long as AMI or PM3 calculations do. 

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],... 

Dewar and Thiel (1977) reported a modified neglect of differential overlap (MNDO) method based on the NDDO formalism for the elements C, H, O, and N. With the conventions specified by NDDO for which integrals to keep, which to discard, and how to model one-electron integrals, it is possible to write the NDDO Fock matrix elements individually for... 

Various parameterizations of NDDO have been proposed. Among these are modified neglect of diatomic overlap (MNDO),152 Austin Model 1 (AMI),153 and parametric method number 3 (PM3),154 all of which often perform better than those based on INDO. The parameterizations in these methods are based on atomic and molecular data. All three methods include only valence s and p functions, which are taken as Slater-type orbitals. The difference in the methods is in how the core-core repulsions are treated. These methods involve at least 12 parameters per atom, of which some are obtained from experimental data and others by fitting to experimental data. The AMI, MNDO, and PM3 methods have been focused on ground state properties such as enthalpies of formation and geometries. One of the limitations of these methods is that they can be used only with molecules that have s and p valence electrons, although MNDO has been extended to d electrons, as mentioned below. 

Generalized Reaction Fields from Surface Charge Densities Ab initio formulations of the PCM model discussed earlier, undertaken primarily by Tomasi and co-workers (see, e.g.. Refs. 72, 73, 266, 267), have very recently been implemented into four different semiempirical packagcs.- - Available codes include MOPAC,30o,325 a locally modified s version of MOPAC, oo and VAMP.302 While the model used by Negre et al. o NDDO Hamiltonians follows exactly the derivation of Equations [23] and [27], those of Wang and... 

The first practical NDDO method was introduced by Dewar and Thiel in 1977.90 Called modified neglect of diatomic overlap (MNDO), the model was again parameterized on experimental molecular geometries, heats of formation, dipole moments, and ionization potentials. 

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. 

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