Semi-empirical parameterization

The procedure of developing a semi-empirical parameterization can be generally formalized in terms of Eq. (2) as follows. A set of experimental energies 5(C QF5) corresponding to different chemical compositions C, molecular geometries Q, and electronic states with specific values of S and T is given. In the case when a response to an external field is to be reproduced the latter can be included into the coordinate set Q. Developing a parameterization means to find certain (sub)set of parameters w which minimizes the norm of the deviation vector with the components... 

In the present paper we demonstrated the feasibility of a semiempirical description of electronic structure and properties of the Werner TMCs on a series of examples. The main feature of the proposed approach was the careful following to the structural aspects of the theory in order to preclude the loss of its elements responsible for description of qualitative physical behavior of the objects under study, in our case of TMCs. If it is done the subsequent parameterization becomes sensible and successful solutions of two long lasting problems semi-empirical parameterization of transition metals complexes and of extending the MM description to these objects can be suggested. 

Molecular dipole moments are often used as descriptors in QPSR models. They are calculated reliably by most quantum mechanical techniques, not least because they are part of the parameterization data for semi-empirical MO techniques. Higher multipole moments are especially easily available from semi-empirical calculations using the natural atomic orbital-point charge (NAO-PC) technique [40], but can also be calculated rehably using ab-initio or DFT methods. They have been used for some QSPR models. 

This quantity is found to be related to the local polarization energy and is complementary to the MEP at the same point in space, making it a potentially very useful descriptor. Reported studies on local ionization potentials have been based on HF ab-initio calculations. However, they could equally well use semi-empirical methods, especially because these are parameterized to give accurate Koopmans theorem ionization potentials. 

The five semi-empirical methods in TlyperChem differ in many technical details. Treatm eii i of electron-electron in leraction s is one ma or dislin gnish m g featnre. Anoth er imporlaii 1 dislingnish-ing feature is the approach used to parameterize the methods. Based on the methods used for obtaining parameters, the XDO methods fall into two classes ... 

Nearly every technical difficulty known is routinely encountered in transition metal calculations. Calculations on open-shell compounds encounter problems due to spin contamination and experience more problems with SCF convergence. For the heavier transition metals, relativistic effects are significant. Many transition metals compounds require correlation even to obtain results that are qualitatively correct. Compounds with low-lying excited states are difficult to converge and require additional work to ensure that the desired states are being computed. Metals also present additional problems in parameterizing semi-empirical and molecular mechanics methods. 

HyperChem uses two types of methods in calculations molecular mechanics and quantum mechanics. The quantum mechanics methods implemented in HyperChem include semi-empirical quantum mechanics method and ab initio quantum mechanics method. The molecular mechanics and semi-empirical quantum mechanics methods have several advantages over ab initio methods. Most importantly, these methods are fast. While this may not be important for small molecules, it is certainly important for biomolecules. Another advantage is that for specific and well-parameterized molecular systems, these methods can calculate values that are closer to experiment than lower level ab initio techniques. 

The accuracy of a molecular mechanics or semi-empirical quantum mechanics method depends on the database used to parameterize the method. This is true for the type of molecules and the physical and chemical data in the database. Frequently, these methods give the best results for a limited class of molecules or phenomena. A disadvantage of these methods is that you must have parameters available before running a calculation. Developing parameters is time-consuming. 

The algorithms of the mixed classical-quantum model used in HyperChem are different for semi-empirical and ab mi/io methods. The semi-empirical methods in HyperChem treat boundary atoms (atoms that are used to terminate a subset quantum mechanical region inside a single molecule) as specially parameterized pseudofluorine atoms. However, HyperChem will not carry on mixed model calculations, using ab initio quantum mechanical methods, if there are any boundary atoms in the molecular system. Thus, if you would like to compute a wavefunction for only a portion of a molecular system using ab initio methods, you must select single or multiple isolated molecules as your selected quantum mechanical region, without any boundary atoms. 

Extended Huckel is the simplest and fastest semi-empirical method included in HyperChem, but it is also the least accurate. It is particularly simple in its treatment of electron-electron interactions it has no explicit treatment of these interactions, although it may include some of their effects by parameterization. 

ZINDO/S is an modified INDO method parameterized to reproduce UV visible spectroscopic transitions when used with the Cl singles methods. It was developed in the research group of Michael Zerner of the Quantum Theory Project at the University of Florida. As with the other semi-empirical methods, HyperChem s implementation of ZINDO/S is restricted to spin multiplicities of up to a quartet state. Higher spin systems may not be done using HyperChem. 

More sophisticated procedures involve taking the start MO coefficients from a semi-empirical calculation, such as Extended HUckel Theory (EHT) or Intermediate Neglect of Differential Overlap (INDO) (Sections 3.12 and 3.9). The EHT method has the advantage that it is readily parameterized for all elements, and it can provide start orbitals for systems involving elements from essentially the whole periodic table. An INDO calculation normally provides better start orbitals, but at a price. The INDO... 

To compensate for these approximations, the remaining integrals are made into parameters, and their values are assigned on the basis of calculations or experimental data. Exactly how many integrals are neglected, and how the parameterization is done, defines the various semi-empirical methods. 

An series of alternative, generally parameterized methods for introducing the effects of solvent into semi-empirical calculations are termed SMr, where the value of x represents the type and quality of parameterization27-76 81. These methods have potential value in studying solvation effects on the structure, electronic spectra, and reactivity of biologically... 

Although continuum solvation models do appear to reproduce the structural and spectroscopic properties of many molecules in solution, parameterization remains an issue in studies involving solvents other than water. In addition, the extension of these approaches to study proteins embedded in anisotropic environments, such as cell membranes, is clearly a difficult undertaking96. As a result, several theoretical studies have been undertaken to develop semi-empirical methods that can calculate the electronic properties of very large systems, such as proteins28,97 98. The principal problem in describing systems comprised of many basis functions is the method for solving the semi-empirical SCF equations ... 

Co2(CO)q system, reveals that the reactions proceed through mononuclear transition states and intermediates, many of which have established precedents. The major pathway requires neither radical intermediates nor free formaldehyde. The observed rate laws, product distributions, kinetic isotope effects, solvent effects, and thermochemical parameters are accounted for by the proposed mechanistic scheme. Significant support of the proposed scheme at every crucial step is provided by a new type of semi-empirical molecular-orbital calculation which is parameterized via known bond-dissociation energies. The results may serve as a starting point for more detailed calculations. Generalization to other transition-metal catalyzed systems is not yet possible. 

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