MEDLA

Walker, P.D. and Mezey, P.G. (1993) Program MEDLA 93, Mathematical Chemistry Research Unit, University of Saskatchewan, Saskatoon, Canada. 

Borman, S. (1995) MEDLA Technique Calculates Electron Densities, Chem. Eng. News, 73, 29. 

The main purpose of the method is to define molecular shapes through isodensity surfaces. Tests on a number of small molecules show that this aim is achieved with a great efficiency in computer time. Discrepancies between MEDLA densities and theoretical distributions, averaged over the grid points, are typically below 10% of the total density. While this does not correspond to an adequate accuracy for an X-ray scattering model, the results do provide important information on the shapes of macromolecules. 

Fig. 4. Block diagram showing possible sampling sites of GTN sampling medla (modifled strahler 1969)...

An Application of the MEDLA Method for the Direct Computation of Electron Densities of Functional Groups... 

MEDLA Fragment Selection Based on Density Domains... 

The additive fuzzy electron density fragmentation scheme of Mezey is the basis of the Molecular Electron Density Lego Assembler (MEDLA) method [67,70-72], reviewed in section 4. of this report, where additional details and applications in local shape analysis are discussed. The MEDLA method was used for the generation of the first ab initio quality electron densities for macromolecules such as proteins [71,72] and other natural products such as taxol [66],... 

There is no longer any inherent difficulty in computing reasonably accurate electron densities for small molecules by either of the two main computational approaches wavefunction methods [85,86] and density functional methodologies [87-89]. With the introduction of the MEDLA technique [67,70], ab initio quality electron densities can be computed for virtually any macromolecule, including... 

The application of the additive fuzzy electron density fragments for the building of electron densities of large molecules is called the Molecular Electron Density Lego Assembler method, or MEDLA method [5,37,66,67,70-72],... 

Both of the natural requirements of additivity and fuzziness are fulfilled by Mezey s fragmentation scheme that has served as the basis of the MEDLA method. 

Several numerical tests and detailed comparisons of MEDLA electron densities to electron densities computed by traditional ab initio SCF technique using 3-21G and 6-31G basis sets have shown [67,71] that the MEDLA results are invariably of better quality than the standard 3-21G ab initio results, and the MEDLA results are virtually indistinguishable from the standard ab initio 6-31G basis set results obtained with the traditional Hartree-Fock method. 

In all tests, the MEDLA method performed consistently better than standard ab initio SCF 3-21G basis computations, consequently, the claim of "ab initio quality" appears justified. 

By combining the results of two of these tests, one may conclude that the MEDLA method does not appear to show a bias concerning the joining of various density domains. This is an important concern for the analysis of functional groups. 

The MEDLA method does not impose any size limitation on the fragments only the feasibilty of traditional ab initio calculations limits the actual size of the fragments and the size of the "coordination shell" around them in the small molecule imitating the actual surroundings within the target molecule. Electron densities of satisfactory accuracy have been obtained in all the test calculations. 

The properly positioned electron density contribution PabcdM to each point r of the ABCD fragment in the target molecule from the A B C D MEDLA fragment of the database is obtained as follows ... 

If high accuracy is required, then the option of generating a new fragment density with the exact required nuclear geometry is always available, and the new density fragment can be added to the database. All distortions due to the TS transformations can be avoided by using the new fragment from the MEDLA database. 

A similar n-dimensional column vector b( ) is defined for each nucleus Bj of the fuzzy fragment stored in the MEDLA database. The components of this vector are the lexicographically ordered unique products of the nuclear position vector components x j, y j, and z , where for simplicity we assume that nucleus Bq is located at the origin of the local coordinate system. For example, for dimension n=9, the components of the column vector b( ) of nucleus Bj are listed below ... 

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