Population analysis electron density

Crystal can compute a number of properties, such as Mulliken population analysis, electron density, multipoles. X-ray structure factors, electrostatic potential, band structures, Fermi contact densities, hyperfine tensors, DOS, electron momentum distribution, and Compton profiles. 

The diagonal elements of P show (only qualitatively) how most of the electron density is in the vicinity of the He rather than the H nucleus. A better appreciation of this would be obtained by a population analysis. The density matrix of (3.271) is not that of HeH (it differs by a factor of 2) but that of two noninteracting electrons in the field of the nuclei. 

Journal of the American Chemical Society 112 114-118. iiai ii rach S M 1994. Population Analysis and Electron Densities from Quantum Mechanics. In Lipkowitz K B and D B Boyd (Editors). Reviews in Computational Chemistry Volume 5. New York, VCl 1 Publishers, pp 171-227. 

Chemists are able to do research much more efficiently if they have a model for understanding chemistry. Population analysis is a mathematical way of partitioning a wave function or electron density into charges on the nuclei, bond orders, and other related information. These are probably the most widely used results that are not experimentally observable. 

A much less basis set dependent method is to analyze the total electron density. This is called the atoms in molecules (AIM) method. It is designed to examine the small effects due to bonding in the primarily featureless electron density. This is done by examining the gradient and Laplacian of electron density. AIM analysis incorporates a number of graphic analysis techniques as well as population analysis. The population analysis will be discussed here and the graphic techniques in the next chapter. 

Vector quantities, such as a magnetic field or the gradient of electron density, can be plotted as a series of arrows. Another technique is to create an animation showing how the path is followed by a hypothetical test particle. A third technique is to show flow lines, which are the path of steepest descent starting from one point. The flow lines from the bond critical points are used to partition regions of the molecule in the AIM population analysis scheme. 

The subscripts i and j denote two nuclei one in the QM region and one in the MM region. The atomic charges for the MM atoms are obtained by any of the techniques commonly used in MM calculations. The atomic charges for the QM atoms can be obtained by a population analysis scheme. Alternatively, there might be a sum of interactions with the QM nuclear charges plus the interaction with the electron density, which is an integral over the electron density. 

The consistent total energy makes it possible to compute singlet-triplet gaps using RHF for the singlet and the half-electron calculation for the triplet. Koopman s theorem is not followed for half-electron calculations. Also, no spin densities can be obtained. The Mulliken population analysis is usually fairly reasonable. 

Optimize the structure of acetyl radical using the 6-31G(d) basis set at the HF, MP2, B3LYP and QCISD levels of theory. We chose to perform an Opt Freq calculation at the Flartree-Fock level in order to produce initial force constants for the later optimizations (retrieved from the checkpoint file via OptsReadFC). Compare the predicted spin polarizations (listed as part of the population analysis output) for the carbon and oxygen atoms for the various methods to one another and to the experimental values of 0.7 for the C2 carbon atom and 0.2 for the oxygen atom. Note that for the MP2 and QCISD calculations you will need to include the keyword Density=Current in the job s route section, which specifies that the population analysis be performed using the electron density computed by the current theoretical method (the default is to use the Hartree-Fock density). 

Compute the isotropic hyperfine coupling constant for each of the atoms in HNCN with the HF, MP2, MP4(SDQ) and QCISD methods, using the D95(d,p) basis set Make sure that the population analysis for each job uses the proper electron density by including the Density=Current keyword in the route section. Also, include the 5D keyword in each job s route sectionfas was done in the original study). 

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. 

In order to save computation time, set up the second and subsequent jobs to extract the electron density from the checkpoint file by using the Geom=Checlcpoint and Densiiy=(Checkpoint/AP2) keywords in the route section. You will also need to include Den iiy=MP2 for the first job, which specifies that the population analysis should be performed using the electron density computed at the MP2 level (the default is to use the Hartree-Fock density). 

Most users of population analysis seem to be concerned with the first meaning. Take the LCAO-MO treatment of dihydrogen as an example. We focus on the electron density... 

In Chapter 3, we studied the topic of population analysis. In population analysis, we attempt a rough-and-ready numerical division of the electron density into atom and bond regions. In Mulliken theory, the bond contributions are divided up equally between the contributing atoms, giving the net charges. The aim of the present section is to answer the questions Are there atoms in Molecules , and if so, How can they be defined . According to Bader and coworkers (Bader, 1990) the answers to both questions are affirmative, and the boundaries of these atoms are determined by a particular property of the electron density. 

An example of quantum mechanical schemes is the oldest and most widely used Mulliken population analysis [1], which simply divides the part of the electron density localized between two atoms, the overlap population that identifies a bond, equally between the two atoms of a bond. Alternatively, empirical methods to allocate atomic charges to directly bonded atoms in a reasonable way use appropriate rules which combine the atomic electronegativities with experimental structural information on the bonds linking the atoms of interest. A widely used approach included in many programs is the Gasteiger-Hiickel scheme [1]. 

Bachrach, S. M., 1995, Population Analysis and Electron Densities from Quantum Mechanics Rev. Comput. Chem., 5, 171. 

In the simple LCAO treatment in which the AO overlap is neglected, the density concept is rather clear-cut. An ambiguity arises in the case of inclusion of overlap. The extended Hiickel calculation is one of the cases. The electron density is usually called "population 70>. An analysis has been made with respect to the composition of population 71>. The population of the rth AO, qr is defined by... 

If population analysis is not synonymous with the concept of an AIM, it becomes necessary to introduce a proper set of requirements before one can speak of an AIM. An AIM is a quantum object and as such has an electron density of its own. This atomic electron density must obviously be positive definite and the sum of these atomic densities must equal the molecular density. Each atomic density pA(r) can be obtained from the molecular density p(r) in the following way ... 

It is well-known that a superposition of isolated atomic densities looks remarkably much like the total electron density. Such a superposition of atomic densities is best known as a promolecular density, like it has been used by Hirshfeld [30] (see also the chapter on atoms in molecules and population analysis). Carbo-Dorca and coworkers derived a special scheme to obtain approximate electron densities via the so-called atomic shell approximation (ASA) [31-35]. Generally, for a molecule A with atoms N, a promolecular density is defined as... 

Steven M. Bachrach, Population Analysis and Electron Densities from Quantum Mechanics. 

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