NDO methods

The complete neglect of differential overlap (CNDO) method is the simplest of the neglect of differential overlap (NDO) methods. This method models valence orbitals only using a minimal basis set of Slater type orbitals. The CNDO method has proven useful for some hydrocarbon results but little else. CNDO is still sometimes used to generate the initial guess for ah initio calculations on hydrocarbons. 

The Extended Hiickel method neglects all electron-electron interactions. More accurate calculations are possible with HyperChem by using methods that neglect some, but not all, of the electron-electron interactions. These methods are called Neglect of Differential Overlap or NDO methods. In some parts of the calculation they neglect the effects of any overlap density between atomic orbitals. This reduces the number of electron-electron interaction integrals to calculate, which would otherwise be too time-consuming for all but the smallest molecules. 

NDO calculations use the Hartree-Fock (HE) approximation to solve the Schrodinger equation. HE methods deal with several kinds of electron-electron interactions. By understanding these interactions, you can appreciate differences between the NDO methods and gain insight into why the NDO approximation works well or fails. 

The NDO methods in HyperChem are built on three different approxim ation s to th e treatm en t of electron -electron in teraction s. The NDO methods are discussed in the following sections. 

The five semi-empirical methods in HyperChem differ in many technical details. Treatment of electron-electron interactions is one major distinguishing feature. Another important distinguishing feature is the approach used to parameterize the methods. Based on the methods used for obtaining parameters, the NDO methods fall into two classes ... 

The choice of the NDO method depends on several factors including your previous experience and preferences. If you want to compare the results to other studies, you must use the same semi-empirical method. Since some methods can converge much more quickly than others, you might want to use a fast method to obtain an approximation of the final answer, and then a more accurate method for the final result. 

Although CNDO is less accurate than other NDO methods, there are two common reasons for using it ... 

Documentation on the reliability of the different NDO methods for various applications is scattered throughout the chemistry literature. Original papers describing the methods present relevant material. The CNDO and INDO methods are discussed in books by Pople and Beveridge and by Murrell and Harget. Compilations exist for MINDO/3 and MNDO in a book by Clark. For MNDO,... 

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.. 

In the case of simple stacked aromatics, we find that NDO methods overestimate p values (by about 20%) compared to ab initio methods using standard split-valence basis sets, presumably because of the overly rapid decay of through-space propagation [11]. If n-n separation distances are greater than 4 A, the use of diffuse functions in the basis set is required. Both semiempirical and ab initio methods indicated that r-stack interactions dominate coupling for intercalated donors and acceptors. The case is more complex for backbone-attached donors and acceptors, where either the r-stack or the backbone may dominate, depending upon distance and attachment mode [12-15]. 

In the discussion below, adapted from [22], one can see, for some of the NDO methods, how the core Hamiltonian matrix elements H/(/( (diagonal) and H (off-diagonal)] and electron-electron repulsion integrals /(v are given by several possible combinations of ... 

The results are typical of the methods Extended Hiickel overestimates ring strain and favors unbound structures i ). The semiempirical NDO methods usually underestimate ring strain and thus make small rings too stable i >. The ab initio results, which should be the best, are intermediate between the semiempirical ones. The ah initio geometries were not optimized, however, and therefore the absolute energies will not be correct. 

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