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Just to add to the discussion: Mulliken charges are flawed in many aspects, but we know how and why, and therefore we accept its use, since it is simple and easily computed. But very dependent on the size of the basis set. Mulliken charges do not reproduce the dipole (or higher) moment, but can be made to do so easily: Thole, van Duijnen, "A general ...


17

Bader charge analysis In Bader's theory of Atoms in Molecules, we partition a molecule into "atoms" which are separated from each other by surfaces of minimum charge density:                                           You can then calculate the partial charges of the "atoms" in the molecule, e.g. H$_2$O might yield: \begin{array}{cc} \rm{...


16

To give a example of the "random number generator" behavior of Mulliken charge analysis pointed by @SusiLehtola, below I'm showing the results of some test runs I did before on the CO2 molecule using Psi4 version 1:1.1-5 (default version on Ubuntu 18.04 repository as of july 2020). For reproducibility purposes, first my input files: user@machine:~/...


16

Hirshfeld / CM5 (Charge Model 5) My main interest is in explaining CM5 charges, but to do that it's necessary to briefly explain what Hirshfeld charges are. Hirshfeld charges are obtained as: $$q_X=Z_X-\int\frac{\rho^0_X(\mathbf{r})}{\sum_Y\rho^0_Y(\mathbf{r})}\rho(r)d\mathbf{r}$$ where $Z_X$ is the atomic number of element $\ce{X}$, $\rho$ is the molecular ...


16

Electrostatic potential (ESP) derived charges Note that ESP1 derived charges include ChelpG (CHarges from ELectrostatic Potentials using a Grid-based method), the Merz–Kollman (MK) 2, and the RESP (restrained electrostatic potential) [3] scheme. While there are differences between the approaches the general idea is similar between the different methods. The ...


14

Mulliken population analysis The Mulliken charge scheme is based on the Linear Combination of Atomic Orbitals (LCAO), so, it is based on the system wave function and was described in a series of papers by R. S. Mulliken1,2,3,4. The idea is that the normalized Molecular Orbital (MO), $\phi_i$, of a diatomic molecule is written as a linear combination of ...


13

Mulliken and Löwdin population analysis In the atomic orbital basis set (enumerated in Greek indices), one finds that the number of electrons $N$ is equal to the trace of the product $\mathbf{PS}$ $$ N = \sum_\mu \left(\mathbf{PS}\right)_{\mu\mu} = \mathrm{Tr} \ \mathbf{PS} $$ where $\mathbf{P}$ is the density matrix, $\mathbf{S}$ is the AO overlap matrix, ...


10

Time-evolution of conceptual DFT quantities has been considered starting, I think, with Chattaraj ~2000. (I imagine there is some earlier work by Ghosh and/or Harbola, but I do not know a reference.) Example references: IJQC v91 633 (2003); J. Phys. Chem. A (Feature article) v21, 4513 (2019); Chapter 13 in "Theoretical Aspects of Chemical Reactivity&...


9

Voronoi charges Voronoi charges (here called VC) are based on the partition of the real space in a system into Voronoi polyhedra.$^1$ A given point in space belongs to the polyhedron of some atom if the point is closer to that atom than to any other atom. This allows to partition the space and thus assign the point charge expectation value of a given point ...


9

Wiberg (1968) Let's start with the "classic" bond order paper by Ken Wiberg (born in 1927 and still alive!). The Wiberg Bond Index (WBI) between fragments A and B of AB is calculated as follows: \begin{equation} \tag{1} W_{AB} \equiv \sum_{\mu \in A}\sum_{\nu \in B}D_{\mu \nu}^2~ , \end{equation} where $D$ is the following density matrix: \begin{...


8

It depends on what you want from it. If you're an organic chemist, you'd be mostly interested in the type of bond (single, double, triple, aromatic), and for that the bond order is most relevant (but tricky to compute). I sent a paper away earlier this year which deals with the choice of bond order analysis, and will post a link to it when it will be online. ...


8

Don't use Mulliken for charge analysis. It is basically a random number generator, since it lacks a basis set limit. By choosing a different basis set representation, you can basically freely move the electrons around; e.g. in a one-center expansion all the electrons are counted for the expansion center whereas all the other nuclei in the system become bare. ...


7

Only a partial answer: some setups are surely better suited than others for a given property. Some developers recognize this and thus do not bother implementing properties for which their setup will be bad, other developers simply lack the time. One example that I am familiar with are NMR/ESR properties. The ADF package (using Slater basis functions) can ...


7

Why Bond Order? Bond order isn't terribly useful to a computationalist directly; however, it can be invaluable for translating Quantum Mechanical results into a framework thats readily understood by experimentalists. Experimental chemists tend to make predictions about material properties, reaction feasibility, molecular structure, etc. based on a ...


7

Density-Derived Electrostatic and Chemical approaches Net atomic charges have two primary applications (dual use): (1) to quantify charge transfer between atoms in materials; this identifies cations and anions and (2) to provide an electrostatic model in classical force fields using atomistic simulations (e.g., classical molecular dynamics or Monte Carlo ...


7

How to test bond order methods for chemical consistency Some of the bond order methods that claim to work do not give consistent results across different SZ values of a spin multiplet or different levels of theory (i.e., basis sets and exchange-correlation functionals). Consequently, there have been several published methods claimed to compute bond orders ...


7

Laplacian Bond Order This method is an extension of the QTAIM (Quantum Theory of Atoms In Molecules) concept of using the Laplacian of the electron density $\nabla^2\rho$ to characterize bonding. Standard QTAIM just uses the value of $\nabla^2\rho$ at bond critical points (minimum electron density along the bond, max along orthogonal directions), but these ...


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