CNDO theory applications

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. 

The widespread application of MO theory to systems containing a bonds was sparked in large part by the development of extended Hiickel (EH) theory by Hoffmann (I) in 1963. At that time, 7r MO theory was practiced widely by chemists, but only a few treatments of a bonding had been undertaken. Hoffmann s theory changed this because of its conceptual simplicity and ease of applicability to almost any system. It has been criticized on various theoretical grounds but remains in widespread use today. A second approximate MO theory with which we are concerned was developed by Pople and co-workers (2) in 1965 who simplified the exact Hartree-Fock equations for a molecule. It has a variety of names, such as complete neglect of differential overlap (CNDO) or intermediate neglect of differential overlap (INDO). This theory is also widely used today. 

Nowadays, the success of the methods proposed by Hoffmann 50> and by Pople and Segal 51> among the chemists tends to promote the use of pure atomic orbital bases for all-valence treatments. The first method is a straightforward application of the Wolfsberg-Helmholz treatment of complexes to organic compounds and is called the Extended Hiickel Theory (EHT), because its matrix elements are parametrized in the same way as the Hiickel method with overlap for n electrons. The other method, known under the abbreviation Complete Neglect of Differential Overlap (CNDO), includes electron repulsion terms by extending to a orbitals the successful approximation of zero-differential overlap postulated for n electrons. 

In the preceding examples on the application of quantum-mechanical methods to the study of conformational problems in biochemistry, we have centered our attention essentially on results obtained by the PCILO method. The reason for this situation resides in the first place in the fact that the results obtained by this procedure are by far the most abundant. A second reason is, however, that they appear also the most satisfactory, being in particular superior to those obtained by the Extended Huckel Theory, which comes next after PCILO in the amount of work carried out. (For practical reasons, very few calculations have been performed in this field using the CNDO/2 method.)... 

Besides these theories, which are applicable to general systems, some other theories of less general applicability have been proposed. These are outlined separately below. A group of empirical methods which has been omitted from the present review are the semi-empirical molecular orbital methods known by acronyms such as MINDO, INDO and CNDO. The reader is referred to a book by Murrell and Harget259 for a description of these methods and to articles by Chutjian and Segal260 and by MacGregor and Berry261 for examples of their use. 

See, for example, M, C. Bohm and R. Gleiter, Theor. Chim. Acta, 59, 127 (1981). A CNDO/INDO Molecular Orbital Formalism for the Elements H to Br. Theory. Theor. Chim. Acta, 59, 153 (1981). A CNDO/INDO Molecular Orbital Formalism for the Elements H to Br, Applications. 

Dynamic Response Functions. - The perturbation series formula or spectral representation of the response functions can be used only in connection with theories that incorporate experimental information relating to the excited states. Semi-empirical quantum chemical methods adapted for calculations of electronic excitation energies provide the basis for attempts at direct implementation of the sum over states (SOS) approach. There are numerous variants using the PPP,50,51 CNDO(S),52-55 INDO(S)56,57 and ZINDO58 levels of approximation. Extensive lists of publications will be found, for example, in references 5 and 34. The method has been much used in surveying the first hyperpolarizabilities of prospective optoelectronically applicable molecules, but is not a realistic starting point for quantitative calculation in un-parametrized calculations. 

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. 

Hybrid approaches combining ab-initio or DFT and semiempirical approaches have become popular. As an example, we can refer to LEDO (hmited expansion of differential overlap) densities application to the density-functional theory of molecules [262]. This LEDO-DFT method should be well suited to the electronic-structure calculations of large molecules and in the anthors opinion its extension to Bloch states for periodic structures is straightforward. In the next sections we discuss the extension of CNDO and INDO methods to periodic stmctures - models of an infinite crystal and a cyclic cluster. 

The next, short, chapter reviews different semiempirical crystal-orbital theories [tt-electron CO theories, namely Huckel and Pariser-Parr-Pople theory, as well as all valence electron CO theories with different degrees of neglect of the so-called differential overlap (CNDO, INDO, MINDO, etc.)]. Applications to highly conducting polymers and to periodic biopolymers are also presented. 

Semiempirical calculations (using EH and modified CNDO methods) had first shown that bonding must be due to 5s orbital interactions [7], see also later reports on application of MO theory to catalysis [8] and on catalysis by small metal clusters [9]. 

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