CNDO theory

And what if the basis functions are centred on different atoms The CNDO solution to the problem is to take all possible integrals such as those above to be equal, and to assume that they depend only on the atoms A and B on which the basis functions are centred. This satisfies the rotational invariance requirement. In CNDO theory, we write the two-electron integrals as pab and they are taken to have the same value irrespective of the basis functions on atom A and/or atom B. They are usually calculated exactly, but assuming that the orbital in question is a Is orbital (for hydrogen) or a 2s orbital (for a first row atom). 

In the case of transition metal complexes, the CNDO theory was first applied by Dahl and Ballhausen [24] to MnO,. Their scheme was later extended to INDO by Ziegler [25] and implemented into the general package ODIN [26], Better known is the INDO program ZINDO [27] by M. Zemer and the NDDO implementation due to D.S. Marynick [28]. Both have been applied with some success in transition metal chemistry for structure determination and studies of excited states. Attempts have also been made to extend AMI, PM3 and MNDO to transition metals. All in all it must be said that the methods based on integral approximations have been more prolific in studies of main group compounds than transition metal complexes. The reason for that is likely the considerable extra complexity added by the -orbitals combined with the fact that other attractive schemes are available for d-block compounds. 

If a zero differential overlap (ZDO) approximation (47) is invoked, as in semiempirical CNDO theories, the gross atomic population reduces to the electron density Paa (24). 

Invariant Procedures. Journal of Chemical Physics 43 S129-S135. pie J A and G A Segal 1965. Approximate Self-Consistent Molecular Orbital Theory. II. Calculations with Complete Neglect of Differential Overlap. The Journal of Chemical Physics 43 S136-S149. iple J A and G A Segal 1966. Approximate Self-Consistent Molecular Orbital Theory. III. CNDO Results for AB2 and AB3 systems. Journal of Chemical Physics 44 3289-3296. 

Molecular mechanics and semiempirical calculations are all relativistic to the extent that they are parameterized from experimental data, which of course include relativistic effects. There have been some relativistic versions of PM3, CNDO, INDO, and extended Huckel theory. These relativistic semiempirical calculations are usually parameterized from relativistic ah initio results. 

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. 

Th ere are sim ilar expression s for sym m etry related in tegrals (sslyy), etc. For direct comparison with CNDO, F is computed as in CNDO. The other INDO parameters, and F, are generally obtained [J. I. Slater, Quantum Theory of Atomic Structure, McGraw-Hill Book Company, Vol. 1, New York, I960.] from fits to experimental atomic energy levels, although other sources for these Slater-Con don parameters are available. The parameter file CINDO.ABP contains the values of G and F (columns 9 and 10) in addition to the CNDO parameters. 

The Huckel methods perform the parameterization on the Fock matrix elements (eqs. (3.50) and (3.51)), and not at the integral level as do NDDO/INDO/CNDO. This means that Huckel methods are non-iterative, they only require a single diagonalization of the Fock (Huckel) matrix. The Extended Huckel Theory (EHT) or Method (EHM), developed primarily by Hoffmann again only considers the valence electrons. It makes use of Koopmans theorem (eq. (3.46)) and assigns the diagonal elements in the F... 

Before 1980, force field and semiempircal methods (such as CNDO, MNDO, AMI, etc.) [1] were used exclusively to study sulfur-containing compounds due to the lack of computer resources and due to inefficient quantum-chemical programs. Unfortunately, these computational methods are rather hmit-ed in their reliability. The majority of the theoretical studies under this review utilized ab initio MO methods [2]. Not only ab initio MO theory is more reliable, but also it has the desirable feature of not relying on experimental parameters. As a consequence, ab initio MO methods are apphcable to any systems of interest, particularly for novel species and transition states. 

Hermann RB. Structure-activity correlations in the cephalosporin C series using extended Htickel theory and CNDO/2.1 Antibiot 1973 26 223-7. 

These compounds have been the subject of several theoretical [7,11,13,20)] and experimental[21] studies. Ward and Elliott [20] measured the dynamic y hyperpolarizability of butadiene and hexatriene in the vapour phase by means of the dc-SHG technique. Waite and Papadopoulos[7,ll] computed static y values, using a Mac Weeny type Coupled Hartree-Fock Perturbation Theory (CHFPT) in the CNDO approximation, and an extended basis set. Kurtz [15] evaluated by means of a finite perturbation technique at the MNDO level [17] and using the AMI [22] and PM3[23] parametrizations, the mean y values of a series of polyenes containing from 2 to 11 unit cells. At the ab initio level, Hurst et al. [13] and Chopra et al. [20] studied basis sets effects on and y. It appeared that diffuse orbitals must be included in the basis set in order to describe correctly the external part of the molecules which is the most sensitive to the electrical perturbation and to ensure the obtention of accurate values of the calculated properties. 

The simplest theory that is consistent with these requirements employs the complete neglect of differential overlap (CNDO)29. This semi-empirical approach will be discussed in some detail, albeit without extensive mathematical justification, as it illustrates the type of approximations that are made in more advanced theories. In addition to the assumptions outlined above, the remaining Coulomb-type integrals are reduced to a single value -yAB that depends only on the nature of atoms A and B with which < > and t are associated, respectively, and not on the actual type of orbitals that overlap. This is equivalent to stating ... 

Two philosophies have emerged in connection with the various semi-empirical methods (for a review, see Klopman and Evans, 1976). In both cases certain matrix elements are assumed to be negligible, others are computed, and others are chosen according to some criteria. According to one philosophy, the chosen parameters should lead to agreement with exact Hartree-Fock theory. Then, if desired, correlation can be added in some form. Methods called CNDO and INDO are examples of this. A more recent development is the partial retention of diatomic differential overlap (PRDDO) method (see Estreicher et al., 1989). 

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

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. 

J. A. Pople and G.A. Segal, Approximate self-consistent molecular orbital theory. III. CNDO results for AB2 and AB3 systems, J. Chem. Phys. 44 3289 (1966). 

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... 

Before we tarn to MO theory of molecular interactions a short discussion on the reliability of semiempirical calculations of the CNDO type by means of perturbation theory would be useful. For a better understanding of the possibilities and limitations of semiempirical MO approaches to intermolecular forces we calculated first-order perturbation energies for very simple complexes with and... 

The exchange contribution in an ab initio perturbation theory is the only repulsive term ) around the energy minimum in most of the stable complexes and consequently we would expect no net repulsion between two closed shell molecules in semiempirical calculations. On the other hand it is known from actual calculations that intermolecular interactions are described more or less correctly by the CNDO/2 procedure. Indeed, strong repulsion is obtained between closed shell molecules. Evidently there must be another approximation which compensates for the neglect of exchange energy. With regard to the simplifications of the CNDO/2 method we find that this is in fact the case. The approximation shown in Eq. (17) is responsible for the repulsive term. 

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