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# Mulliken population analysis

About: Mulliken population analysis is a research topic. Over the lifetime, 1958 publications have been published within this topic receiving 56436 citations.

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TL;DR: In this paper, an analysis in quantitative form is given in terms of breakdowns of the electronic population into partial and total ''gross atomic populations'' and ''overlap populations'' for molecules.

Abstract: With increasing availability of good all‐electron LCAO MO (LCAO molecular orbital) wave functions for molecules, a systematic procedure for obtaining maximum insight from such data has become desirable. An analysis in quantitative form is given here in terms of breakdowns of the electronic population into partial and total ``gross atomic populations,'' or into partial and total ``net atomic populations'' together with ``overlap populations.'' ``Gross atomic populations'' distribute the electrons almost perfectly among the various AOs (atomic orbitals) of the various atoms in the molecule. From these numbers, a definite figure is obtained for the amount of promotion (e.g., from 2s to 2p) in each atom; and also for the gross charge Q on each atom if the bonds are polar. The total overlap population for any pair of atoms in a molecule is in general made up of positive and negative contributions. If the total overlap population between two atoms is positive, they are bonded; if negative, they are antibonded. Tables of gross atomic populations and overlap populations, also gross atomic charges Q, computed from SCF (self‐consistent field) LCAO‐MO data on CO and H2O, are given. The amount of s‐p promotion is found to be nearly the same for the O atom in CO and in H2O (0.14 electron in CO and 0.15e in H2O). For the C atom in CO it is 0.50e. For the N atom in N2 it is 0.26e according to calculations by Scherr. In spite of very strong polarity in the π bonds in CO, the σ and π overlap populations are very similar to those in N2. In CO the total overlap population for the π electrons is about twice that for the σ electrons. The most easily ionized electrons of CO are in an MO such that its gross atomic population is 94% localized on the carbon atom; these electrons account for the (weak) electron donor properties of CO. A comparison between changes of bond lengths observed on removal of an electron from one or another MO of CO and H2, and corresponding changes in computed overlap populations, shows good correlation. Several other points of interest are discussed.

9,238 citations

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TL;DR: In this paper, a method of "natural population analysis" was developed to calculate atomic charges and orbital populations of molecular wave functions in general atomic orbital basis sets, which seems to exhibit improved numerical stability and to better describe the electron distribution in compounds of high ionic character.

Abstract: A method of ‘‘natural population analysis’’ has been developed to calculate atomic charges and orbital populations of molecular wave functions in general atomic orbital basis sets. The natural analysis is an alternative to conventional Mulliken population analysis, and seems to exhibit improved numerical stability and to better describe the electron distribution in compounds of high ionic character, such as those containing metal atoms. We calculated ab initio SCF‐MO wave functions for compounds of type CH3X and LiX (X=F, OH, NH2, CH3, BH2, BeH, Li, H) in a variety of basis sets to illustrate the generality of the method, and to compare the natural populations with results of Mulliken analysis, density integration, and empirical measures of ionic character. Natural populations are found to give a satisfactory description of these molecules, providing a unified treatment of covalent and extreme ionic limits at modest computational cost.

8,332 citations

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TL;DR: In this paper, an extension of the tight-binding (TB) approach to improve total energies, forces, and transferability is presented. The method is based on a second-order expansion of the Kohn-Sham total energy in density-functional theory (DFT) with respect to charge density fluctuations.

Abstract: We outline details about an extension of the tight-binding (TB) approach to improve total energies, forces, and transferability. The method is based on a second-order expansion of the Kohn-Sham total energy in density-functional theory (DFT) with respect to charge density fluctuations. The zeroth order approach is equivalent to a common standard non-self-consistent (TB) scheme, while at second order a transparent, parameter-free, and readily calculable expression for generalized Hamiltonian matrix elements may be derived. These are modified by a self-consistent redistribution of Mulliken charges (SCC). Besides the usual ``band structure'' and short-range repulsive terms the final approximate Kohn-Sham energy additionally includes a Coulomb interaction between charge fluctuations. At large distances this accounts for long-range electrostatic forces between two point charges and approximately includes self-interaction contributions of a given atom if the charges are located at one and the same atom. We apply the new SCC scheme to problems where deficiencies within the non-SCC standard TB approach become obvious. We thus considerably improve transferability.

3,448 citations

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TL;DR: In this paper, the authors proposed a modified Wolfsberg-Helmholz formula to reduce the effect of counterintuitive orbital mixing in extended Hiickel and limited basis set ab initio SCF calculations.

Abstract: In both extended Hiickel and limited basis set ab initio SCF molecular orbital calculations an intriguing phenomenon occurs, especially in calculations on transition metal complexes. Some of the lower orbitals, which are made up primarily of ligand 2s combinations, mix into themselves the metal virtual orbitals, 4s and 4p, in an out-of-phase manner, opposite to what one would have predicted from a simple perturbation analysis. We call this counterintuitive orbital mixing (COM). The conse- quences of COM are lowered metal to ligand overlap populations and negative Mulliken gross atomic populations of the virtual orbitals. We analyze the prerequisites for occurrence of COM in both semiempirical and SCF methods and propose a modified Wolfsberg-Helmholz formula for reducing the magnitude of the effect in EH calculations.

987 citations

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TL;DR: In this paper, a method of analysing molecular wavefunctions is described, which can be regarded as an extension of Mulliken population analysis, and can be used both to give a qualitative or quantitative picture of the molecular charge distribution, and in the accurate evaluation of molecular multipole moments of arbitrary order.

Abstract: A method of analysing molecular wavefunctions is described. It can be regarded as an extension of Mulliken population analysis, and can be used both to give a qualitative or quantitative picture of the molecular charge distribution, and in the accurate evaluation of molecular multipole moments of arbitrary order with negligible computational effort.

966 citations