The Charge-Cloud Interpretation of Wave Function

 Earlier we have seen the probability interpretation of the wavefunction, according towhichJ2dsis the probability that it is found in the volumeds. However, an alternativeand more pictorial (though less strictly accurate) interpretation ofJhas been providedin terms of the charge cloud. If we are dealing with a moving electron then we supposethat this electron is spread out in the form of a cloud, called the charge cloud, whose density at any point being proportional to J2. Larger the value ofJ 2, denser the chargecloud, and hence greater the negative charge that shall be found. Hence, the essential difference between the two interpretations is that instead of speaking of the probabilitydensity or the chance of finding the electron in any given region we now speak of theactual particle density. This charge-cloud picture, though very useful, is not strictlycorrect because if a single electron is a particle, it cannot possibly be distributed overregions of the size of atom or molecule.

 

 As Coulson (1961) explained, a link between the two viewpoints may be found by asimple experiment: Perform a large number of measurements to exactly determine theposition of an electron and each time represents this position by a minute dot in a three-dimensional space. If the dots are so small that we cannot distinguish them from eachother then the general effect of this diagram will be exactly the same as that of a cloud. Inthis case, the densest parts of the cloud will be those where there are more dots andobviously these are the places where there is greater likelihood or probability ofdiscovering the electron. Hence the density of the charge cloud is a direct measure of theprobability function. Although the concept of charge cloud lacks validity it is very useful.The wavefunctions of an electron are not strictly confined but stretched to infinitedistance from the nucleus. Obviously, there is a finite chance of finding the electron evenat large distances. Using the charge-cloud picture we may say that there is a certaincontour for eachJsuch that most of the charge, say 90–95%, lies within this contour. The concept of charge cloud presents a mental picture for the charge distribution inspace and the shapes of contours largely determine the stereochemical disposition of theatoms in a polyatomic system. This concept shall be used to understand the ground stateof the hydrogen atom.

 

Principles and Applications of Quantum Chemistry 

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