Mulliken charge partitioning method

The Mulliken and Ldwdin methods give different atomic charges, but mathematically there is nothing to indicate which of these partitionings gives the best result. There are some common problems with all population analyses based on partitioning the wave function in terms of basis functions. 

The atomic parameters xt qf are usually calibrated to represent atomic charges calculated with ab initio QM methods. Mulliken charges are generally used, although charges calculated with other partitioning schemes... 

This exercise will examine other ways of computing charges other than Mulliken population analysis. Since atomic charge is not a quantum mechanical observable, all methods for computing it are necessarily arbitrary. We ll explore the relative merits of various schemes for partitioning the electron density among the atoms in a molecular system. 

The values are called the net atomic populations and the overlap population. Chemists speak of the charges on atoms in molecules, and Mulliken s second contribution was to propose a method of partitioning the overlap population between contributing atoms. He proposed that the overlap populations be divided equally between participating atoms, so giving the gross atomic populations of... 

The relationship between the herbicidal activity of 1,2,5-oxadiazole iV-oxides and some physicochemical properties potentially related to this bioactivity, such as polarity, molecular volume, proton acceptor ability, lipophilicity, and reduction potential, were studied. The semi-empirical MO method AMI was used to calculate theoretical descriptors such as dipolar moment, molecular volume, Mulliken s charge, and the octanol/water partition coefficients (log Po/w) <2005MOL1197>. 

Two general techniques are used to extract charges from wave functions - the Mulliken population analysis, based on partitioning the electron distribution, and the ESP method, based on fitting properties which depend on the electron distribution to a model which replaces this distribution by a set of atomic... 

The Mulliken procedure for subdivision of the electron density is not unique, and numerous other recipes have been proposed. Most of these make use of the overlap between atomic functions to partition the charge, and are identical to the Mulliken method for semi-empirical procedures (where atomic functions do not overlap see Chapter 2). All such procedures contain an element of arbitrariness. 

Assigning atom charges and bond orders involves calculating the number of electrons belonging to an atom or shared between two atoms, i.e. the population of electrons on or between atoms hence such calculations are said to involve population analysis. Earlier schemes for population analysis bypassed the problem of defining the space occupied by atoms in molecules, and the space occupied by bonding electrons, by partitioning electron density in a somewhat arbitrary way. The earliest such schemes were utilized in the simple Hiickel or similar methods [256], and related these quantities to the basis functions (which in these methods are essentially valence, or even just p, atomic orbitals see Section 4.3.4). The simplest scheme used in ab initio calculations is Mulliken population analysis [257]. 

The NBO method can be used for ab initio calculations at the HE and any correlated levels as well as for DFT methods. The results do not strongly depend on the size of the basis set, which is one reason that the NBO method has replaced the outdated Mulliken population analysis, for example, for the calculation of atomic partial charges. But there is a price that has to be paid for the advantages. Like any orbital-based method for partitioning the electronic charge into atomic and bonding domains, the choice of the selection procedure has some arbitrary character that needs to be known in order to judge the quality of the results. 

Related with the chemieal bonding description, there is for first interest also a method for determining the atomic partition function in molecule here the Mulliken picture of the population analysis, a., will be presented yet modified, in the way of assuming the overlapping of charge unequally distributed between the atoms involved in the bond. Considering the linear combination of atomic orbitals (LCAO) expansion of the molecular function, the density assoeiated to the atomic orbitals F. is written (Rychlewski Parr, 1986 Li Parr, 1986) ... 

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