Homo-nuclear molecules

There has been considerable interest in the possibility of bound excited states arising from the interaction of unMe noble gas atoms. Jortner and co-workers have searched for second continue in radiolysis studies of noble gas mixtures in the solid and liquid phase and at pressures of the order of 1000 mmHg (1 mm Hg = 133 Nm" ) in the gas phase. In general, emission from the homo-nuclear molecules is favoured even for the minor component, but weak continua have been ascribed to ArKr and KrXe. These states are postulated to correlate with the excited state of the heavier atom and their weaker bonding relative to homonuclear molecules is clear from comparison of the wavelengths corresponding to peak intensity of the continua ... 

We thus see that for analyzing macroscopic properties of the molecular Bose gas, one should first solve the problem of elastic interaction (scattering) between two molecules. In this section we present the exact solution of this problem for homo-nuclear molecules formed by fermionic atoms of different components (different internal states) in a two-component Fermi gas. The case of Af m will be discussed in Section 10.3. The solution for M = m was obtained in Refs. [49] and [50] assuming that the atom-atom scattering length a greatly exceeds the characteristic radius of interatomic potential ... 

Since the energy levels of the harmonic oscillator are equidistant only one IR vibrational line (-lO/xm) is obtained. If the potential deviates from the harmonic oscillator, transitions with Av = 2, Av = 3, etc. can also occur. These transitions, which are generally weak, are called overtones (harmonics). As for rotational motion, molecules of the type O2, Ng (i.e., homo-nuclear molecules), do not exhibit electric-dipole vibrational lines. However, quadrupole- and pressure-induced transitions of homonuclear molecules can be observed faintly. 

The strength and type of bonding between two atoms depend on the tendency of the participating atoms to donate, attract and share electrons. The variation of the electronic energy with the bond length r between the nuclei is schematically shown in Fig. 3.4 for the OH (hetero-nuclear) and O2 (homo-nuclear) molecules. The curve with the lowest energy corresponds to the ground state while the other curves represent different electronic states,... 

The simulations to investigate electro-osmosis were carried out using the molecular dynamics method of Murad and Powles [22] described earher. For nonionic polar fluids the solvent molecule was modeled as a rigid homo-nuclear diatomic with charges q and —q on the two active LJ sites. The solute molecules were modeled as spherical LJ particles [26], as were the molecules that constituted the single molecular layer membrane. The effect of uniform external fields with directions either perpendicular to the membrane or along the diagonal direction (i.e. Ex = Ey = E ) was monitored. The simulation system is shown in Fig. 2. The density profiles, mean squared displacement, and movement of the solvent molecules across the membrane were examined, with and without an external held, to establish whether electro-osmosis can take place in polar systems. The results clearly estab-hshed that electro-osmosis can indeed take place in such solutions. 

In fact, the measured dissociation energies of appropriate examples of homo-nuclear diatomic molecules and molecular ions are H, 2.648 e.v. H2, 4.476 e.v. He, 3.1 e.v. He2, only slight attraction in the ground electronic state (binding of van der Waals type, at internuclear separations large compared with typical chemical binding energies.)... 

There are several variations of correlation spectroscopy, all giving rise to different, complementary data. We have already met HH (homo-nuclear) COSY earlier in this chapter (Section 4.5). An obvious extension to the COSY experiment is to use it for heteronuclear correlation, e.g. correlation of all the H and C signals in a molecule... 

For real metals this value is close to 1. This value shows qualitatively if the association to homo-nuclear two-atomic molecules (AH°diss) (non metallic character) is energetically preferred over the formation of a coordination lattice (metallic character) and vice versa. According to this relation a metallic character can also be expected for the elements 112 and 114 [28]. Element 117, for example, can be assumed to have a semi-metallic character. 

The homonuclear diatomic molecules are the simplest closed set of molecules. Many of the electron affinities of the main group diatomic molecules have been measured by anion photoelectron spectroscopy (PES), but only a few have been confirmed. These Ea can be examined by their systematic variation in the Periodic Table. Calculating Morse potential energy curves for the anions and comparing them with curves for isoelectronic species confirm experimental values. The homo-nuclear diatomic anions of Group IA, IB, VI, VII, and 3d elements and NO are examined first. 

Parity labels only apply to MOs in molecules that possess a centre of inversion centrosymmetric molecules), e.g. homo-nuclear X2, octahedral EX and square planar EX4 molecules. Heteronuclear XY, or tetrahedral EX4 molecules, for example, do not possess a centre of inversion and are called non-centrasymmetric species... 

Figure 11.17 Bonding in s-block homo-nuclear diatomic molecules. Only outer (valence) AOs interact enough to form MOs. A, Li2- The two valence electrons from two Li atoms fill the bonding (ct2s) MO, and the antibonding remains empty. With a bond order of 1, U2 does form. B, Be2. The four valence electrons from two Be atoms fill both MOs to give no net stabilization. Ground-state Be2 has a zero bond order and has never been observed.

We shall now consider the electron configurations of each of the homo-nuclear diatomic molecules of the elements in the first short Period on the basis of the LCAO-MO theory outlined above. 

In summary, for a homo nuclear diatomic molecule there are generally (27 +1) (7+1) symmetric and (27+1)7 antisymmetric nuclear spin functions. For example, from Eqs. (50) and (51), the statistical weights of the symmetric and antisymmetric nuclear spin functions of Li2 will be and, respectively. This is also true when one considers Li2 Li and Li2 Li. For the former, the statistical weights of the symmetric and antisymmetric nuclear spin functions are and, respectively for the latter, they are and in the same order. 

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