Semi-empirical methods molecular orbitals

Eor transition metals the splitting of the d orbitals in a ligand field is most readily done using EHT. In all other semi-empirical methods, the orbital energies depend on the electron occupation. HyperChem s molecular orbital calculations give orbital energy spacings that differ from simple crystal field theory predictions. The total molecular wavefunction is an antisymmetrized product of the occupied molecular orbitals. The virtual set of orbitals are the residue of SCE calculations, in that they are deemed least suitable to describe the molecular wavefunction. 

Several older theoretical studies are included in the review by Knowles <1996CHEC-II(7)489>, and little has been reported since. Nagy et al. carried out quantum calculations on several [l,2,3]triazolo[4,5-t/ pyridazines to reveal electron distributions in the ground and the excited state using the semi-empirical Hiickel molecular orbital (MO) method to explain the fluorescence of such compounds (see Section 10.13.3.2) <2002JPH83>. 

Thiel W 1996 Perspectives on semiempirical molecular orbital theory New Methods in Computationai Quantum Meohanios (Adv. Chem. Phys. XCiti) ed I Prigogine I and S A Rice (New York Wiley) pp 703-57 Earlier texts dealing with semi-empirical methods include ... 

The first point to remark is that methods that are to be incorporated in MD, and thus require frequent updates, must be both accurate and efficient. It is likely that only semi-empirical and density functional (DFT) methods are suitable for embedding. Semi-empirical methods include MO (molecular orbital) [90] and valence-bond methods [89], both being dependent on suitable parametrizations that can be validated by high-level ab initio QM. The quality of DFT has improved recently by refinements of the exchange density functional to such an extent that its accuracy rivals that of the best ab initio calculations [91]. DFT is quite suitable for embedding into a classical environment [92]. Therefore DFT is expected to have the best potential for future incorporation in embedded QM/MD. 

In this section, the conceptual framework of molecular orbital theory is developed. Applications are presented and problems are given and solved within qualitative and semi-empirical models of electronic structure. Ab Initio approaches to these same matters, whose solutions require the use of digital computers, are treated later in Section 6. Semi-empirical methods, most of which also require access to a computer, are treated in this section and in Appendix F. 

HyperChem uses the Linear Combination of Atomic Orbitals-Molecular Orbital (LCAO-MO) approximation for all ofitsnl) initio semi-empirical methods. If /j represents a molecular orbital and... 

J. N. Murrell and A. J. Harget, Semi-empirical Self-consistent Molecular Orbital Theory of Molecules, Wiley-Interscience, London, 1972 G. H. Wagniere, Introduction to Elementary Molecular Orbital Theory and to Semiempirical Methods, Springer-Verlag, Berlin, 1976 J. Sadleij, Semi-empirical Methods of Quantum Chemistry, Wiley, New York, 1985. 

Molecular orbital theory is a semi-empirical method devoted to interpreting the energy-level structure of optical centers where the valence electron cannot be considered as belonging to a specific ion. In our ABe reference center, this would mean that the valence electrons are shared by A and B ions. The approach is based on the calculation of molecular orbitals (MO) of the ABe pseudo-molecule, V mo, from various trial combinations of the individual atomic orbitals, V a and of the A and B ions, respectively. The molecular orbitals V mo of the center ABe are conveniently written in the form... 

In the decade between 1985 and 1995, molecular orbital calculations using semi-empirical methods for 1,2,3-triazoles and benzotriazoles have received increasing interest. In particular, the semi-empirical methods AMI, PM3, and MNDO, have been widely used in theoretical calculations for... 

As presented, semi-empirical methods are based on a single-configuration picture of electronic structure. Extensions of such approaches to permit consideration of more than a single important configuration have been made (for excellent overviews, see Approximate Molecular Orbital Theory by J. A. Pople and D. L. Beveridge, McGraw-Hill, New York... 

Various theoretical methods and approaches have been used to model properties and reactivities of metalloporphyrins. They range from the early use of qualitative molecular orbital diagrams (24,25), linear combination of atomic orbitals to yield molecular orbitals (LCAO-MO) calculations (26-30), molecular mechanics (31,32) and semi-empirical methods (33-35), and self-consistent field method (SCF) calculations (36-43) to the methods commonly used nowadays (molecular dynamic simulations (31,44,45), density functional theory (DFT) (35,46-49), Moller-Plesset perturbation theory ( ) (50-53), configuration interaction (Cl) (35,42,54-56), coupled cluster (CC) (57,58), and CASSCF/CASPT2 (59-63)). 

Molecular orbital calculations, whether by ab initio or semi-empirical 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.21 Many of these calculations have been performed on transition states (p. 210) 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. 

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... 

The molecular electron density function needed for EP calculation can be obtained through ab initio as well as various semi-empirical methods. Since ab initio calculations are not economical for large molecules (several hundred atoms), the use of well-parameterized semi-empirical methods are still justified. When semi-empirical methods are used the three-center potential integrals usually disappear, and therefore the electronic contribution can be easily calculated by Slater-type orbitals. In ab initio methods (primitive or contracted) Gaussian-type orbitals are used for calculating the three-center integrals because their calculations are clumsy with Slater-type orbitals. 

Boron Tetrahalides, BjX,. Although these molecules have been extensively investigated by semi-empirical methods, only recently have ab initio calculations been performed. Using minimal basis sets for the core and s-orbitals, but DZ for the valence p-orbitals, SCF calculations on B2CI4 and B2F4 (as well as on B4CI4 and B4F4) were carried out, and the results analysed in terms of localized molecular orbitals. 

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