Molecules normal state

The sample is burned in oxygen at 1000°C. Nitrogen oxide, NO, is formed and transformed into NO2 by ozone, the NO2 thus formed being in an excited state NO. The return to the normal state of the molecule is accompanied by the emission of photons which are detected by photometry. This type of apparatus is very common today and is capable of reaching detectable limits of about 0.5 ppm. 

The physical interpretation of the quantum mechanics and its generalization to include aperiodic phenomena have been the subject of papers by Dirac, Jordan, Heisenberg, and other authors. For our purpose, the calculation of the properties of molecules in stationary states and particularly in the normal state, the consideration of the Schrodinger wave equation alone suffices, and it will not be necessary to discuss the extended theory. 

Fig. 2. The Oscillational Frequency fob the Normal State of the Hydrogen Molecule as a Function of the Oscillational Quantum Number...

The best experimental value of the heat of dissociation of H2 is that obtained by Witmer (9) by extrapolating the oscillational levels of the normal state of the molecule to dissociation. The restoring force acting on the two nuclei becomes smaller as the nuclei get farther apart, and as a result the oscillational frequency in successive oscillational states becomes smaller and smaller. For H2 in the normal state this oscillational frequency... 

The problem has already been solved for the normal state of the hydrogen molecule-ion (ZA = ZB = 1) by the use of numerical methods. A rather complete account of these calculations of Burrau (30) will be given here, since the journal in which they were published is often not available. 

Fia. 4. The Electronic Energy of the Hydrogen Molecule-ion in the Normal State as a Function of the Distance Between the Two Nuclei (Burrau)... 

Curve 1 shows the total energy for the normal state of the hydrogen molecule as given by the first-order perturbation theory curve 2, the naive potential function obtained by neglecting the resonance phenomenon and curve 3, the potential function for the antisymmetric eigenfunction, corresponding to elastic collision. 

By bringing the nuclei into coincidence a helium atom in the normal state is formed and a value for its energy can be obtained from the expression for the hydrogen molecule by neglecting the internuclear energy and by putting p = 0. It is found that Wb. 19... 

The interaction of two alkali metal atoms is to be expected to be similar to that of two hydrogen atoms, for the completed shells of the ions will produce forces similar to the van der Waals forces of a rare gas. The two valence electrons, combined symmetrically, will then be shared between the two ions, the resonance phenomenon producing a molecule-forming attractive force. This is, in fact, observed in band spectra. The normal state of the Na2 molecule, for example, has an energy of dissociation of 1 v.e. (44). The first two excited states are similar, as is to be expected they have dissociation energies of 1.25 and 0.6 v.e. respectively. 

In other cases, discussed below, the lowest electron-pair-bond structure and the lowest ionic-bond structure do not have the same multiplicity, so that (when the interaction of electron spin and orbital motion is neglected) these two states cannot be combined, and a knowledge of the multiplicity of the normal state of the molecule or complex ion permits a definite statement as to the bond type to be made. 

The normal states of these ions are similar to certain excited states of ammonia, which also show doubling. The frequency of inversion of the normal ammonia molecule is negligibly small. 

Here symbols in parentheses represent unshared electrons attached to C and O, respectively, and those in braces represent shared electrons. An excited carbon atom 6S lies about 1.6 v. e. above the normal state, but can still form only a double bond with oxygen, so that the resultant molecule should be excited. We write... 

The first excited state of the molecule, c N , is built from normal atoms, and has the term symbol 2n. It lies 1.78 v. e. above the normal state. 

Fig. 1. The five canonical structures contributing to the normal state of the benzene molecule.

This quintic equation is easily reduced to three linear factors and one quadratic factor, the roots being -2a, -2a, 0, (-(13) -l)a, and ((13) -l)a. Since a is negative, the last of these roots, ((13) —l)a = 2.6055a, represents the normal state of the molecule. The eigenfunction corresponding to this is (before normalizing)... 

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