NDDO-based methods

NDDO-Based Methods from the Dewar Group MNDO, AMI, PM3 and SAMI, and Related Methods - Preliminaries... 

G. Rauhut, T. Clark, and T. Steinke,/. Am. Chem. Soc., 115, 9174 (1993). A Numerical Self-Consistent Reaction Field (SCRF) Model for Ground and Excited States in NDDO-Based Methods. 

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... 

NDDO-based methods from the Dewar group MNDO,... 

Currently the INDO- and NDDO-based methods are most frequently used for examining TM species. The CNDO-based methods, which were popular in the 1970s and 1980s to study molecular systems containing TM elements, are rarely used nowadays. More accurate INDO and NDDO methods have replaced CNDO methods at small cost in computing time. 

This NDDO-based method is available for prediction of binding energies and molecular geom-... 

PM3 or MNDO hamiltonians for calculations on organic molecules. The MOPAC and AMPAC packages are the usual sourees for these programs. The exeited state spectrum calculated in the NDDO based methods is usually inferior to that obtained in CNDO(S) or ZINDO/INDO, but sealing is sometimes used to overcome this diffieulty. It is essential to use SDCI or better if any reasonable treatment of the y-hyperpolarizabiUty is to be achieved. 

Tokmachev AM, Tchougreeff AL (2005) Efficient multipole model and linear scaling of NDDO-based methods. J Phys Chem A 109 7613-7620... 

This strategy has been found to be more efficient than using Gaussian functions and has now been used to extend the NDDO-based family of methods to the remaining main group elements [22], the AMI parameterisation of second row elements [39] and the transition metals titanium and zirconium [40] as well as our work extending the PM3 method to iron [26, 32],... 

The semiempirical molecular orbital (MO) methods of quantum chemistry [1-12] are widely used in computational studies of large molecules. A number of such methods are available for calculating thermochemical properties of ground state molecules in the gas phase, including MNDO [13], MNDOC [14], MNDO/d [15-18], AMI [19], PM3 [20], SAMI [21,22], OM1 [23], OM2 [24,25] MINDO/3 [26], SINDOl [27,28], and MSINDO [29-31]. MNDO, AMI, and PM3 are widely distributed in a number of software packages, and they are probably the most popular semiempirical methods for thermochemical calculations. We shall therefore concentrate on these methods, but shall also address other NDDO-based approaches with orthogonalization corrections [23-25],... 

Due to the integral approximations used in the MNDO model, closed-shell Pauli exchange repulsions are not represented in the Hamiltonian, but are only included indirectly, e.g., through the effective atom-pair correction terms to the core-core repulsions [12], To account for Pauli repulsions more properly, the NDDO-based OM1 and OM2 methods [23-25] incorporate orthogonalization terms into the one-center or the one- and two-center one-electron matrix elements, respectively. Similar correction terms have also been used at the INDO level [27-31] and probably contribute to the success of methods such as MSINDO [29-31],... 

To conclude this section, we mention an article [68] that discusses desirable features for next-generation NDDO-based semiempirical methods. Apart from orthogonalization corrections and effective core potentials that are already included in some of the more recent developments (see above) it is proposed that an implicit dispersion term should be added to the Hamiltonian to capture intramolecular dispersion energies in large molecules. It is envisioned that dispersion interactions can be computed self-consistently from an additive polarizability model with some short-range scaling [68]. 

SattehneyCT KW, Tirado-Rives J, Jorgensen WL (2006) Comparison of SCC-DFTB and NDDO-based semiempirical molecular orbital methods for organic molecules. J Phys Chem A 110 13551-13559... 

It was shown previously in a series of papers " that the OVGF method, developed by the Cederbaum group,can be coupled to NDDO-based semiempirical molecular orbital... 

The mixed models used in MNDO, AMI, and PM3, are identical, because all of these three methods are derived based on NDDO. The core Hamiltonian correction due to the interaction of the charges between the quantum mechanical region and the classical region is... 

The term "semi-empirical" has been reserved commonly for electronic-based calculations which also starts with the Schrodinger equation.9-31 Due to the mathematical complexity, which involve the calculation of many integrals, certain families of integrals have been eliminated or approximated. Unlike ab initio methods, the semi-empirical approach adds terms and parameters to fit experimental data (e.g., heats of formation). The level of approximations define the different semi-empirical methods. The original semi-empirical methods can be traced back to the CNDO,12 13 NDDO, and INDO.15 The success of the MINDO,16 MINDO/3,17-21 and MNDO22-27 level of theory ultimately led to the development of AMI28 and a reparameterized variant known as PM3.29 30 In 1993, Dewar et al. introduced SAMI.31 Semi-empirical calculations have provided a wealth of information for practical applications. 

With the intermediate NDO method ZDO is not assumed between a.o. s on the same atom in one-centre electron repulsion integrals. Various other schemes based on different ZDO assumptions together with different schemes of semi-empirical parametrization have been developed. These have become known by their acronyms such as CNDO/1, CNDO/2, INDO, MINDO/3 (m - modified), NDDO (d - diatomic), MNDO etc.. 

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... 

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). 

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