Semi-empirical implementations

A yet more realistic cavity shape is that obtained from the van der Waals radii of the atoms of the solute. This is the approach taken in the polarisable continuum method (PCM) [Miertus et al. 1981], which has been implemented in a variety of ab initio and semi-empirical quantu/rt mechanical programs. Due to the non-analytical nature of the cavity shapes in the PCM approach, it is necessary to calculate numerically. The cavity surface is divided... 

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. 

There are two types of Cl calculations implemented in Hyper-Chem — singly excited Cl and microstate CL The singly excited Cl which is available for both ab initio and semi-empirical calculations may be used to generate UV spectra and the microstate Cl available only for the semi-empirical methods in HyperChem is used to improve the wave function and energies including the electronic correlation. Only single point calculations can be performed in HyperChem using CL... 

As with the other semi-empirical methods, HyperChem s implementation of ZINDO/1 is restricted to spin multiplicities up to a quartet state. ZINDO/1 lets you calculate the energy states in molecules containing transition metals. 

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. 

Semi-empirical methods, such as AMI, MINDO/3 and PM3, implemented in programs like MOPAC, AMPAC, HyperChem, and Gaussian, use parameters derived from experimental data to simplify the computation. They solve an approximate form of the Schrodinger equation that depends on having appropriate parameters available for the type of chemical system under investigation. Different semi-emipirical methods are largely characterized by their differing parameter sets. 

To make matters worse, the use of a uniform gas model for electron density does not enable one to carry out good calculations. Instead a density gradient must be introduced into the uniform electron gas distribution. The way in which this has been implemented has typically been in a semi-empirical manner by working backwards from the known results on a particular atom, usually the helium atom (Gill, 1998). It has thus been possible to obtain an approximate set of functions which often serve to give successful approximations in other atoms and molecules. As far as I know, there is no known way of yet calculating, in an ab initio manner, the required density gradient which must be introduced into the calculations. 

Semi-empirical methods, such as those implemented in the MOPAC [9] program, simplify the equations considerably by neglecting many terms, but then compensate for this by parameterising some of them so that the calculations reproduce experimental information on, for example, the heat of formation. Once the various approximations are made, the molecular properties to which the parameters are fitted, and the molecules used in the fitting, define a model Hamiltonian, of which the most commonly used are the AMI and the PM3 Hamiltonians found in MOPAC. A major advantage of semi-empirical methods is... 

Computational procedures following a classical mechanical picture, as it was outlined in section 2.3, can be and have been implemented by a number of people. The quantum/classical schemes belong to this family [6,123], At a semi empirical level of electronic theory, Warshel and coworkers approach is the most complete from the statistical mechanical viewpoint. For early references and recent developments see ref.[31, 124], Simplified schemes have been used to study chemical events in enzymes and solution [16, 60, 109, 125, 126],... 

The numerical model is implemented for the three current collector configurations previously mentioned. Since the model uses semi-empirical parameters, this is first calibrated and then validated, through a comparison with experimental data. For collecting the current, a silver wire is wrapped around the cathode, while a nickel spring is placed in contact with the anode (case 3 previously defined). The tests are performed using pure hydrogen at a constant flow rate. Voltage is varied by the use of a load bank, and the relative current is measured. The temperature of 800°C is... 

These immediate and simple findings motivated me to accept Gerrit Schuiirmann s request and to implement COSMO as a new kind of SCRF model in the semi-empirical quantum chemistry package MOPAC [39]. Shortly afterwards, I met Jimmy Stewart, the author of the MOPAC package, in a European Computational Chemistry Workshop in Oxford, where he was available as a supervisor for a entire workshop. I gave a short presentation of my COSMO ideas and he was interested to get COSMO as the first solvation model in MOPAC. Therefore, he introduced me to some extend to the MOPAC program code, and we identified the places where COSMO would have to link in. 

Non-Lorentzian dielectric functions discussed in Section 1.6.7 cannot be directly applied to treat solvation energies. The poles of e(k) promote numerical instabilities in calculations. They have deep physical roots originating from the interference between polarization and density fluctuations in the vicinity of the solute [37], Attempts to suppress this complication in terms of unusually sophisticated methods have been reported [51,52], However, simple traditional solutions look more expedient and efficient. Restricting the treatment by purely Lorentzian functions s(k) resolves the problem and provide a consistent and satisfactory semi-empirical theory for ordinary practical implementations. 

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