Helium molecular orbital model

We will now apply the molecular orbital model to the helium molecule (He2). Does this model predict that this molecule will be stable Since the He atom has a configuration, s orbitals are used to construct the molecular orbitals, and the molecule will have four electrons. From the diagram shown in Fig. 9.30 it is apparent that two electrons are raised in energy and two are lowered in energy. Thus the bond order is zero ... 

It is straightforward to write down and solve the many-electron Schrodinger equation if it is assumed that the electrons do not interact, or interact only to a very small extent. Indeed, it is on this premise that the fabric of modem qualitative molecular orbital theory is based. For the two electrons in a helium atom [Z = 2] for example, this independent particle model Schrodinger equation is simply... 

Unfortunately there is as yet no known way to obtain the repulsion energy from properties of the separate molecules. An attempt has been made to characterise the repulsive surface of a molecule by performing IMPT calculations between the molecule and a suitable test particle, such as a helium atom. Because the helium atom has only one molecular orbital and is spherically symmetrical, such calculations can be done much more easily than calculations involving two ordinary molecules. From the data for the repulsion between molecule A and the test particle, and between B and the test particle, it may be possible to construct a repulsive potential between A and B. Some limited progress has been made with this idea. An alternative approach has been based on the suggestion that the repulsion energy is closely correlated with the overlap between the molecular wavefunctions, but this seems likely to be more useful as a guide to the form of analytic models than as a direct route to accurate potential functions. 

State, decreases dramatically from its known values 0.99 in helium and 0.93 in neon. An (admittedly rather crude) second-order perturbation argument suggests the squamp to decrease from 0.7 to 0.3 for Z increasing from 30 to 70. If we insist to express molecular orbitals (M.O.) in the model of linear combinations of atomic orbitals (L.C.A.O.) we may have many reasons to worry with a squamp around a-half. Quantum chemistry adds new complications to those present in monatomic entities, but it takes over the whole burden of the many-electron atoms supplying fascinating difficulties . It is noted that the typical heats of atomization of compounds (per atom) are 30 to only 2 or 3 percent of—go g from Z = 11 to 99, once more implying that quantum chemistry (in the deductive, not the classificatory, sense) is hazardous for two-digit Z values. 

In the standard models of quantum chemistry of Chapter 5, the A -electron wave function is expanded in products of the one-electron basis functions introduced in Chapter 6. In the present chapter, we shall examine the orbital expansion of the many-electron systems by considering a simple two-electron system the ground-state helium wave function. In this manner, we shall obtain a clearer picture of the possibilities and limitations offered by the orbital expansion for many-electron systems. The information obtained by studying the helium system will later prove useful when we go on to construct molecular basis sets from AOs in Chapter 8. 

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