Molecular orbital theory CNDO method

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). 

Hiickel and extended Huckel methods are termed semi-empirical because they rely on experimental data for the quantification of parameters. There are other semi-empirical methods, such as CNDO, MINDO, INDO, in which experimental data are still used, but more care is taken in evaluating the Htj. These methods are self-consistent field procedures based on 3 SCF. They are discussed in various works on molecular orbital theory.4... 

More recently, an all valence electron, semiempirical molecular orbital theory known as the Complete Neglect of Differential Overlap (CNDO) has been proposed by Pople based on self-consistent field (SCF) formalism (5). Although this method uses a more sophisticated approximation of the wavefunction, it neglects differential overlap. 

A wide range of theoretical methods has been applied to the study of the structure of small metal clusters. The extremes are represented on the one hand by semi-empirical molecular orbital (Extended Huckel) (8 ) and valence bond methods (Diatomics-In-Molecules) ( ) and on the other hand by rigorous initio calculations with large basis sets and extensive configuration interaction (Cl) (10). A number of approaches lying between these two extremes have been employed Including the X-a method (11), approximate molecular orbital methods such as CNDO (12) and PRDDO (13) and Hartree-Fock initio molecular orbital theory with moderate Cl. 

According to the frontier molecular orbital theory (FMO theory), the reactivity of a 1,3-dipole is inversely proportional to the energy difference between the frontier orbitals of a 1,3-dipole and a dipolarophile. The frontier orbital energies of the parent azomethine ylide 110 are calculated by a CNDO/2 method to be highest occupied molecular orbital (HOMO) =... 

Since the first quantum mechanical calculation of phenol performed in 1967 using the CNDO/2 method" , the phenol geometry was considered at a variety of computational levels "" ranging from the HE to the MP2 method of molecular orbital theory and density functional theory (DFT) employed with several basis sets, mainly of the split valence type as, e.g. 6-31G(d,p) and 6-31- -G(d,p). These computational results are summarized in Tables 1-3 and Figure 4. It seems noteworthy that the semi-empirical geometries listed in Table 1 are rather close to the experimental observations. Also, to complete the theoretical picture of the phenol molecule, its theoretical inertia moments calculated at the B3LYP/6-31- -G(d,p) level are equal to 320.14639, 692.63671 and 1012.78307 a.u. 

Many approximate molecular orbital theories have been devised. Most of these methods are not in widespread use today in their original form. Nevertheless, the more widely used methods of today are derived from earlier formalisms, which we will therefore consider where appropriate. We will concentrate on the semi-empirical methods developed in the research groups of Pople and Dewar. The former pioneered the CNDO, INDO and NDDO methods, which are now relatively little used in their original form but provided the basis for subsequent work by the Dewar group, whose research resulted in the popular MINDO/3, MNDO and AMI methods. Our aim will be to show how the theory can be applied in a practical way, not only to highlight their successes but also to show where problems were encountered and how these problems were overcome. We will also consider the Hiickel molecular orbital approach and the extended Hiickel method Our discussion of the underlying theoretical background of the approximate molecular orbital methods will be based on the Roothaan-Hall framework we have already developed. This will help us to establish the similarities and the differences with the ab initio approach. 

Hiickel theory separates the tt system from the underlying a framework and constructs molecular orbitals into which the tt electrons are then fed in the usual way according to the Aufbau principle. The tt electrons are thus considered to be moving in a field created by the nuclei and the core of a electrons. The molecular orbitals are constructed from linear combinations of atomic orbitals and so the theory is an LCAO method. For our purposes it is most appropriate to consider Hiickel theory in terms of the CNDO approximation (in fact, Hiickel theory was the first ZDO molecular orbital theory to be developed). Let us examine the three types of Fock matrix element in Equations (2.252)-(2.254). First, In... 

Another example of the application of molecular orbital theory to drug design has been given by Andrews. Molecular orbital calculations by the EHT and CNDO/2 methods were made on a number of anticonvulsant drugs and related compounds. 

These methods are parameterized to reproduce ab initio results. As such, they are approximate molecular orbital theories—they approximate a well-defined theoretical model. They were very important in the early development of computational MO theory, but they are not extensively used now, except for certain specialized versions for particular applications, such as CNDO/S for spectroscopy. 

Let us now look at die approximations used in CNDO. Although not the forum for a detailed explanation of the theoretical background, we will focus on the differences between the various methods. For a detailed description of approximate molecular orbital theory, interested readers are referred to the excellent book by Pople and Beveridge. ... 

HyperChem currently supports one first-principle method ab initio theory), one independent-electron method (extended Hiickel theory), and eight semi-empirical SCFmethods (CNDO, INDO, MINDO/3, MNDO, AMI, PM3, ZINDO/1, and ZINDO/S). This section gives sufficient details on each method to serve as an introduction to approximate molecular orbital calculations. For further details, the original papers on each method should be consulted, as well as other research literature. References appear in the following sections. 

The molecular orbital methods which have been employed for such studies include extended Hiickel theory (EHT), CNDO, and ab initio LCAO-SCF. 

The theoretical interpretation of the results was made (334) in terms of the molecular orbital perturbation theory, in particular, of the FMO theory (CNDO-2 method), using the model of the concerted formation of both new bonds through the cyclic transition state. In this study, the authors provided an explanation for the regioselectivity of the process and obtained a series of comparative reactivities of dipolarophiles (methyl acrylate > styrene), which is in agreement with the experimental data. However, in spite of similar tendencies, the experimental series of comparative reactivities of nitronates (249) toward methyl acrylate (250a) and styrene (250b) are not consistent with the calculated series (see Chart 3.17). This is attributed to the fact that calculation methods are insufficiently correct and the... 

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