Mulliken’s population analysis

In this chapter, we use the definitions of bond order and valence indices provided by Mayer [4-6] (for a historical account, see Ref. [6a] and for other types of bond indices, see Ref. [6b]). In terms of electronic structure theory, they represent an extension to Mulliken s population analysis. The bond order is defined as... 

As it is, it should be remembered that Fig. 5.2 has become a sort of Rosetta stone whose deciphering paves the way toward a better understanding of what falsely seems to be an inherent intricacy of Mulliken s population analysis. 

Mulliken s population analysis is rooted in the LCAO (linear combination of atomic orbitals) formulation it is not directly applicable to other types of wavefunctions. With Cr i representing the coefficient of the rth type of atomic orbital (li, 2s, etc.) of atom k in the ith molecular orbital, we describe the latter by... 

We have learned about the unique ordering of the carbon net charges relative to one another. All methods using Mulliken s population analysis, both ab initio and semiempirical, no matter what basis sets are used to construct the wavefunctions, reproduce the following sequence of inductive effects ... 

Mulliken s population analysis has been thoroughly conducted to examine the net charge as well as the magnitude of covalent bondings. The author found that Mulliken s charge of Li in Li2.1V0.9O2 and Li1.1V0.9O2 and the BOP value for Li-O and V-O are different in their structure. It is contrary to the widely accepted picture of Li-intercalated compounds, and should be a very important consideration for the determination of battery properties such as OCV. The information should be helpful to investigate possibility of new electrode active materials. 

Although more advanced AFDF methods have also been intro-duced, in most applications to date " the simplest, Mulliken-Mezey AFDF scheme has been used. This scheme can be regarded as analogous to Mulliken s population analysis techniquewithout integration. This AFDF technique (described in the following text) is suitable for the generation of ab initio quality electron densities for virtually any macromolecule, protein, and supramolecular structure. 

Each VSIE is a function (empirically established) of charge and electronic configuration the latter is obtained by Mulliken s population analysis ° conducted on the molecular orbitals. Therefore an iterative method is required. Each secular determinant is solved in cycles until self-consistent charge distribution is obtained. Some relation between the output from one iteration and the input from the next is often necessary to ensure convergence... 

The author would like to thank Dr. Jun Yasui of Toyobo co., ltd. for his helpful discussion especially on Mulliken s population analysis. He is grateful to Mr. Fumihito Mohri of Institute for Fundamental Chemistry (now of Kaneka corporation) for his kind introduction of Okada s works(4,5) and Lowdin s work(7). He is also grateful to Dr. Shigeto Nishitani of Kyoto Univ. for his kind introduction of works of Pettifor and his coauthors(12-14). 

Mulliken, R. S. Unpublished comments. Topic of the discussions held at the crater of the volcano Teide, Tenerife, Canary Islands, June 20, 1976, between Prof. Mulliken and the author, on the fundamentals of local components of molecular wavefunctions, Mulliken s population analysis, and various atomic charge models based on overlap integrals. These discussions had a motivating role in the later development of the AFDF methods MEDLA and AOMA, both based on the realization by the author that Mulliken s population analysis without integration provides a simple, additive fiizzy electron density fragmentation (AFDF) scheme. 

A simple, additive fragmentation approach to the molecular electronic density, proposed by the author, can be used for the construction of electronic densities and density-based shape representations for macromolecules. The simplest of these approaches is motivated by Mulliken s population analysis technique,and can be regarded as a natural generalization of Mulliken s approach a formal population analysis without integration. This method, the Mulliken-Mezey approach, is the simplest realization of a more general, additive fuzzy density fragmentation (AFDF) principle. ... 

The cluster model of HAp/methyl acetate interface was shown in Fig.2 overlap population analysis was applied to this model. Using Monte Carlo method, 300 sampling points were put around each atom in the cluster. Molecular orbitals in the cluster were constructed by a linear combination of atomic orbitals (LCAO). Atomic orbitals used in this model were ls-2p for C, ls-2p for O, Is for H, ls-3d for P and ls-4p for Ca, which were numerically calculated for atomic Hartree-Fock method. Overlap population was evaluated by Mulliken s population analysis. 

The earliest definition of atomic charges is related to Mulliken s population analysis [24] and assumes equipartition of overlap populations between the relevant atoms, yielding the gross atomic populations ... 

The above arguments form the core of Mulliken s population analysis [83], and it is customary to call the atom-centered electrons the (atomic) net populations (NP) which, together with the overlap populations (OP), add up to the total electron number in the above example, this is 2 = NPi + NP2 + OP = 0.61 + 0.61 + 0.78. We might also cut the overlap population s)nnmetrically and add each half to the net populations, thereby defining (atomic) gross populations (GP) in the H2 example, this makes 2 = NPi + j x OP + NP2 + x OP = GPi + GP2 = 1.00 + 1.00 = 2, which is very simple. Within this scheme, the atomic charge Cj is the difference between the atomic number Z and the gross population cj = Z — GP = 1.00 - 1.00 = 0) such that the H atom is neutral in the H2 molecule, as expected. 

With the help of Mulliken s population analysis, the amount of charge shifted from the sugar-phosphate chain to the adenine or thymine chain has been computed using the results of the poly(ASP) and poly(TSP) chain calculations given in Table 2.7. The amounts of 0.212... 

The changes in charge distribution in the infinite chain introduced by the impurity and calculated by using Mulliken s population analysis are compared in Table 4.5. In the pure Li chain each Li atom has a charge of 3.0000. If one Li atom is replaced by a H atom, a strong ionic charge... 

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