Mulliken analysis

Mulliken analysis is most often used with semiempirical wave functions. 

During this process the atomic charges for the adsorbed molecules were taken from a Mulliken analysis of a DZP basis set Hartree Fock calculation (using CADPAC on the MOPAC (PM3) optimized molecular structure. Table 3 gives the cation charges for the sulfoxide group and C2 for each cation. In both cases the sulfur and transferred proton are positively charged but at sulfur the... 

Hiickel s application of this approach to the aromatic compounds gave new confidence to those physicists and chemists following up on the Hund-Mulliken analysis. It was regarded by many people as the simplest of the quantum mechanical valence-bond methods based on the Schrodinger equation. 66 Hiickel s was part of a series of applications of the method of linear combination of atom wave functions (atomic orbitals), a method that Felix Bloch had extended from H2+ to metals in 1928 and that Fowler s student, Lennard-Jones, had further developed for diatomic molecules in 1929. Now Hiickel extended the method to polyatomic molecules.67... 

Mulliken analysis shows there is some charge back-donation from the occupied orbitals of the ligand to the metal. On the basis of these data the preferred coordination mode arises from a delicate balance between these contributions. Two methods used attribute different weights to the ionic and covalent factors and thus result in a different absolute minimum. 

The Mulliken analysis [122] of the valence orbital populations has shown the bonding in the 6d-elements to be dominated by a large contribution of both... 

The Mulliken analysis data of Table 9 show Bh03Cl to be more covalent (a larger OP) than Tc03Cl and Re03Cl. Such an increase in covalence is typical of halides and oxyhalides of the elements at the beginning of the transactinide series (Rf, Db and Sg) and this is a relativistic effect as discussed earlier. The dipole moments increase from the Tc to the Bh compound... 

Here we note that only a single polarizability or susceptibility exists for any system. The reconstruction from local contributions is in fact an abstraction, the result of which depends on the detail wanted macroscopic with local susceptibilities or microscopic with local polarizabilities and—more importantly—on the partitioning of such properties. However, experimental chemists are used to such procedures from well-chosen series of compounds they derive bond energies as local contributions to heats of formation and ionic radii from crystal structures. Theoretical chemists obtain atomic charges from, e.g., a Mulliken analysis of their wave functions. We are able, following similar reasoning, to construct molecular polarizabilities from atomic ones [38,60], although there is formally no connection between them. In an opposite direction we can decompose a molecular polarizability into a many-center... 

Mulliken analysis is a quick and relatively simple way to break down the charge density into atomic contributions but it is dependent on the basis set used. In particular, if the number of basis functions is unevenly distributed between atoms, those with rich basis sets will tend to have too much charge assigned through the Mulliken procedure. To attempt to rectify this, methods based on the charge density alone have also been developed. For example, Bader analysis uses the minima in the density to define a region around each atom over which the density can be integrated numerically [41]. 

The approach of the substrate towards the active site of SP was studied with electrostatic field potentials (ESP) by Lamotte-Brasseur et al. (1990). They examined the force exerted by the active sites of the serine proteinases alpha-chymotrypsin and subtilisin on an approaching substrate. About 20 residues from each of these enzymes were employed to construct electrostatic potential maps, using point charges derived from CNDO calculations (Pople and Beveridge, 1970) with e =l.Net charges were obtained from a mulliken analysis... 

Mulliken-type populations are a useful tool when it comes to analysing the charge and spin distribution in a molecule or solid. However, one must bear in mind that there is rigorously no such thing as an atom in a molecule or in a crystal, and thus such analysis must be viewed somewhat critically. Especially when atomic orbitals are very diffuse, their Mulliken-type populations may not be very realistic. On the other hand, the Mulliken analysis has the advantage that individual atomic orbital occupations may be obtained. 

Nevertheless, numerous papers detailing the difficulties, problems, and inconsistencies in the Mulliken analysis abound in the literature. We discuss most of these in the third section, but a few points need to be immediately addressed. 

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