Helium atomic interactions

Figure 2. The minimum potential energy, tm, of a helium atom interacting with the 100 face of an argon crystal is plotted as a function of the position of the helium atom relative to the surface lattice...

The special case of liquid helium allows us to present one aspect of direct geometry spectroscopy in particular. Since helium atoms interact so weakly, there are almost no restoring forces in the liquid and only the conservation of momentum plays a significant role in its INS spectrum. The spectrum of a mixture of liquids He and He is shown in Fig. 5.9 [21], as can be seen from the figure it consists of two continuous traces. The first response, with a slope of 5.6, is from the light isotope of helium, He. The second response, of slope 4.2, is from the common isotope of helium, mass four. (The ratio of the slopes is 4.2/5.6 = 3/4.) There are no excitations in the spectrum and the observed response is the result of atomic recoil. 

When two helium atoms interact there are four electrons to place in the orbitals and so both the filled antibonding orbital completely negates the effect of the filled bonding orbital. No energy is gained by the system and so He2 does not form. 

Rare-gas clusters can be produced easily using supersonic expansion. They are attractive to study theoretically because the interaction potentials are relatively simple and dominated by the van der Waals interactions. The Lennard-Jones pair potential describes the stmctures of the rare-gas clusters well and predicts magic clusters with icosahedral stmctures [139, 140]. The first five icosahedral clusters occur at 13, 55, 147, 309 and 561 atoms and are observed in experiments of Ar, Kr and Xe clusters [1411. Small helium clusters are difficult to produce because of the extremely weak interactions between helium atoms. Due to the large zero-point energy, bulk helium is a quantum fluid and does not solidify under standard pressure. Large helium clusters, which are liquid-like, have been produced and studied by Toennies and coworkers [142]. Recent experiments have provided evidence of... 

The tliird part is tire interaction between tire tenninal functionality, which in tire case of simple alkane chains is a metliyl group (-CH ), and tire ambient. These surface groups are disordered at room temperature as was experimentally shown by helium atom diffraction and infrared studies in tire case of metliyl-tenninated monolayers [122]. The energy connected witli tliis confonnational disorder is of tire order of some kT. 

The first ab initio smdy of an interaction polarizability was that of O Brien et al. (1973) on a pair of helium atoms. They obtained /0(r) for the range r = 3.5ao through lOao- The experimentally determined value of is negative, which suggests that the incremental mean pair polarizability must be negative around the minimum in the potential curve. 

A measurement of the density of helium gas shows that it is a monatomic gas. Molecules of He2 do not form. What difference between hydrogen atoms and helium atoms accounts for the absence of bonding for helium The answer to this question also must lie in the attractive and repulsive electrical interactions between two helium atoms when they approach each other. Figure 16-4A shows the attractive forces in one of our hypothetical instantaneous snapshots. There are, of course, four electrons and each is attracted to each nucleus. In Figure 16-4B we see the repulsive forces. Taking score, we find in Figure 16-4A eight attractive interactions, four... 

Figure 16-3D shows the simplified representation of the interaction of two helium atoms. This time each helium atom is crosshatched before the two atoms approach. This is to indicate there are already two electrons in the Is orbital. Our rule of orbital occupancy tells us that the Is orbital can contain only two electrons. Consequently, when the second helium atom approaches, its valence orbitals cannot overlap significantly. The helium atom valence electrons fill its valence orbitals, preventing it from approaching a second atom close enough to share electrons. The helium atom forms no chemical bonds. ... 

Each helium atom does have, of course, vacant 2s and 2p orbitals which extend farther out than the filled Is orbital. The electrons of the second helium atom can "overlap with these vacant orbitals. Since this overlap is at great distance, the resulting attractions are extremely small. This type of interaction presumably accounts for the attractions that cause helium to condense at very low temperatures. 

Note that the other electrons do not block the influence of the nucleus they simply provide additional repulsive coulombic interactions that partly counteract the pull of the nucleus. For example, the pull of the nucleus on an electron in the helium atom is less than its charge of +2e would exert but greater than the net charge of +e that we would expect if each electron balanced one positive charge exactly. 

As an example we may calculate the energy of the helium atom in its normal state (24). Neglecting the interaction of the two electrons, each electron is in a hydrogen-like orbit, represented by equation 6 the eigenfunction of the whole atom is then lt, (1) (2), where (1) and (2) signify the first and the second electron. 

VIII. THE PAULI EXCLUSION PRINCIPLE. THE INTERACTION OF TWO HELIUM ATOMS... 

But if the system contains more than two electrons explicit consideration must be given the spins. This is particularly evident in the problem of the interaction of two helium atoms. There are four individual eigenfunctions pa, pfi, four electrons. The only eigenfunction allowed by Pauli s principle for the system is... 

In an atom of the second column of the periodic system, such as mercury, the two valence electrons are in the normal state s-electroiis, and form a completed sub-group. Two such atoms would hence interact in a way similar to two helium atoms the attractive forces would be at most very small. This is the case for Hg2, which in the normal state has an energy of dissociation of only 0.05 v.e. But if one or both of the atoms is excited strong attractive forces can arise and indeed the excited states of Hg2 are found to have energies of dissociation of about 1 v.e. 

Evidence has been advanced8 that the neutral helium molecule which gives rise to the helium bands is formed from one normal and one excited helium atom. Excitation of one atom leaves an unpaired Is electron which can then interact with the pair of Is electrons of the other atom to form a three-electron bond. The outer electron will not contribute very much to the bond forces, and will occupy any one of a large number of approximately hydrogen-like states, giving rise to a roughly hydrogenlike spectrum. The small influence of the outer electron is shown by the variation of the equilibrium intemuclear distance within only the narrow limits 1.05-1.13 A. for all of the more than 25 known states of the helium molecule. 

To understand how electrons with spin interact, it is useful to examine a system consisting of two electrons, such as the helium atom. Let this two-electron system be described by the wave function, in space coordinates, (r), If the electrons are interchanged the wave function will in general be different, ( ), but since the electrons are identical (ignoring spin) the energy of the system will not be affected. The wave functions therefore belong to degenerate levels. 

The peculiar behavior of H might be relevant to understand the hydrogen bond, which deforms the electronic cloud of the proton. On the other hand, it is surprising to discover an anomalous behavior for a closed-shell atom like He. However, it has been demonstrated in helium-atom-scattering that interactions between He atoms... 

K. The mass of the 4He atom is low and the intermolecular interactions are very weak. This means that the motion of the helium atoms is unusually large, too large in fact for a solid-like structure to persist... 

Fig. 13.4 Logarithm of error(Eh) in the configuration interaction energy for the ground state of the helium atom as a function of maximum orbital quantum number, L, of the one-electron basis functions. The data were obtained in an...

Takada, Y., and Kohn, W. (1985). Interaction potential between a helium atom and metal surfaces. Phys. Rev. Lett. 54, 470-472. 

In order to appreciate the size of the basis sets required for fully converged calculations, consider the interaction of the simplest radical, a molecule in a electronic state, with He. The helium atom, being structureless, does not contribute any angular momentum states to the coupled channel basis. If the molecule is treated as a rigid rotor and the hyperfine structure of the molecule is ignored, the uncoupled basis for the collision problem is comprised of the direct products NMf ) SMg) lnii), where N = is the quantum number... 

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