Atoms in Molecules.

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Paul L Popelier

An Introduction

gradient…..

It is clear from the previous chapter that the molecular electron density is dominated by huge values near the nuclei. In order to eliminate these nuclear peaks, crystallographers have introduced the deformation density. In many cases this density reveals chemical features such as bonding regions and lone pairs. Still the main question remains:

can we disclose chemistry in the molecular electron density without subtracting from it a reference electron density?

The answer is yes. In fact we do not need to introduce an external reference density at all: we can use the original molecular electron density itself. In other words, we eliminate the need for an extra arbitrary reference density to compare with our original molecular electron density.

A mathematical tool called the gradient vector or simply the gradient makes it possible to invoke the molecular density as its own reference. The gradient is defined via partial derivatives usually in the context of a mathematical branch called vector calculus (see Box 2.1 ). The following rather exotic but simplified illustration of the gradient will help to understand the physical meaning behind its mathematical definition. Suppose a scientist is aboard a small submarine somewhere in the middle of the Atlantic Ocean.

She is exploring the bottom of the sea near the midAtlantic fault where ocean water is expected to be in contact with slowly emerging lava. Suppose that the submarine’s spotlights do not reach further than a few metres in the pitch-dark water but that it is equipped with thermometers all around. At a distance of several tens of metres the scientist is still able to detect the place where lava emerges from the ocean floor simply by reading the water temperature in various directions around the submarine. This is possible because the temperature decreases away from this hot spot. Put more formally, we know that the fault is surrounded by a nested set of envelopes or surfaces of constant temperature………..DOWNLOAD

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