CNDO theory equations

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. 

Returning to the SCE formalism of HE theory, one can proceed in the spirit of an effective Hamiltonian method by developing a recipe for the replacement of matrix elements in the HE secular equation, Eq. (4.53). One of die first efforts along these lines was described by Pople and co-workers in 1965 (Pople, Santry, and Segal 1965 Pople and Segal 1965). The complete neglect of differential overlap (CNDO) mediod adopted the following conventions ... 

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. 

In semiempirical approaches, the standard Hartree-Fock SCF-MO equations are simplified by integral approximations which are designed to neglect all three-center and four-center two-electron integrals. The CNDO, INDO, and NDDO schemes have been introduced for this purpose [12,31]. They are rotationally invariant generahzations of the zero-dififerential-overlap approximation from ir-electron theory to valence-electron systems. The most refined of these schemes is NDDO which assumes... 

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... 

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