General Semiempirical MO Methods

The FE MO, HMO, and PPP methods apply only to planar conjugated molecules and treat only the 77 electrons. The semiempirical MO methods discussed in this section apply to all molecules and treat all the valence electrons. 

Semiempirical MO theories fall into two categories those using a Hamiltonian that is the sum of one-electron terms, and those using a Hamiltonian that includes two-electron repulsion terms, as well as one-electron terms. The Hiickel method is a one-electron theory, whereas the Pariser-Parr-Pople method is a two-electron theory. 

The Extended Hiickel Method. The most important one-electron semiempirical MO method for nonplanar molecules is the extended Hiickel theory. An early version was used by Wolfsberg and Helmholz in treating inorganic complex ions. The method was further developed and widely applied by Hoffinann [R. Hoffinann, J. Chem. Phys., 39, 1397 (1963) 40, 2745, 2474, 2480 (1964) Tetrahedron, 22, 521, 539 (1966) M. Wolfsberg and L. Helmholz,/. Chem. Phys., 20,837 (1952)]. 

The extended Hiickel (EH) method begins with the approximation of treating the valence electrons separately from the rest (Section 13.20). The valence-electron Hamiltonian is taken as the sum of one-electron Hamiltonians  

In the simple Hiickel theory of planar hydrocarbons, each tt MO contains contributions from one Ipir AO on each carbon atom. In the extended Hiickel treatment of nonplanar hydrocarbons, each valence MO contains contributions from four AOs on each carbon atom (one 2s and three 2p s) and one Is AO on each hydrogen atom. The AOs used are usually Slater-type orbitals with fixed orbital exponents determined from Slater s rules (Problem 15.79). For the simplified Hamiltonian (16.76), the problem separates into several one-electron problems  

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This chapter is devoted to SCF calculations which represent the overwhelming majority of the reported ab initio calculations. We are not going here to treat general problems of SCF theory which are also inherent in popular semiempirical methods such as PPP and CNDO, These features will be intentionally suppressed. Instead, emphasis will be laid on specific problems of the ab initio SCF approach that are not encountered in semiempirical MO methods and on the progress achieved in solution of these problems in last years. 

AMI AMBER A Program for Simulation of Biological and Organic Molecules CHARMM The Energy Function and Its Parameterization Combined Quantum Mechanics and Molecular Mechanics Approaches to Chemical and Biochemical Reactivity Density Functional Theory (DFT), Hartree-Fock (HF), and the Self-consistent Field Divide and Conquer for Semiempirical MO Methods Electrostatic Catalysis Force Fields A General Discussion Force Fields CFF GROMOS Force Field Hybrid Methods Hybrid Quantum Mechanical/Molecular Mechanical (QM/MM) Methods Mixed Quantum-Classical Methods MNDO MNDO/d Molecular Dynamics Techniques and Applications to Proteins OPLS Force Fields Parameterization of Semiempirical MO Methods PM3 Protein Force Fields Quantum Mechanical/Molecular Mechanical (QM/MM) Coupled Potentials Quantum Mecha-nics/Molecular Mechanics (QM/MM) SINDOI Parameterization and Application. 

Divide and Conquer for Semiempirical MO Methods Force Fields A Brief Introduction Force Fields A General Discussion Hyperconjugation MNDO Molecular Mechanics Conjugated Systems Monte Carlo Quantum Methods for Electronic Structure PM3 PRDDO SINDOl Parameterization and Application. 

The relative merits of various MO methods have been discussed in die literature. In general, the ab initio type of calculations will be more reliable, but the semiempirical calculations are faster in terms of computer time. The complexity of calculation also increases rapidly as the number of atoms in the molecule increases. The choice of a method is normally made on the basis of evidence that the method is adequate for the problem at hand and the availability of appropriate computer programs and equipment. Results should be subjected to critical evaluation by comparison widi experimental data or checked by representative calculations using higher-level mediods. Table 1.12 lists some reported deviations from experimental AHf for some small hydrocarbons. The extent of deviation gives an indication of the accuracy of the various types of MO calculations in this application. 

Molecular orbital calculations, whether by ab initio or semiempirical methods, can be used to obtain structures (bond distances and angles), energies (such as heats of formation), dipole moments, ionization energies, and other properties of molecules, ions, and radicals—not only of stable ones, but also of those so unstable that these properties cannot be obtained from experimental measurements." Many of these calculations have been performed on transition states (p. 279) this is the only way to get this information, since transition states are not, in general, directly observable. Of course, it is not possible to check data obtained for unstable molecules and transition states against any experimental values, so that the reliability of the various MO methods for these cases is always a question. However, our confidence in them does increase when (1) different MO methods give similar results, and (2) a particular MO method works well for cases that can be checked against experimental methods. ... 

In principle, methods that can be used to calculate dipole moments are the various MO methods, which can be divided into three large groups emipirical, semiempirical, and ai initio. In contrast, VB methods are generally not suited for calculations of dipole moments because here the motion of electrons is completely synchronized. If, however, one uses additional ionic,... 

This review concerns the analysis of electronic spectra of radicals by quantum chemical methods. Both semiempirical and ab initio MO methods have been examined, the former in greater detail. The radicals treated are of various structural types, e.g. diatomic systems as well as large conjugated molecules. The papers cited do not represent a complete coverage of the literature on this topic, in particular with ab initio calculations. This was dictated by the length of the article and by our desire to present typical applications and representative results of available MO methods. Therefore we have favoured more recent papers and studies whose results appear to be of general importance. Moreover, we are aware that some interesting papers may have escaped our attention. 

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