Nuclear molecules

We now consider planar molecules. The electronic wave function is expressed with respect to molecule-fixed axes, which we can take to be the abc principal axes of ineitia, namely, by taking the coordinates (x,y,z) in Figure 1 coincided with the principal axes a,b,c). In order to detemiine the parity of the molecule through inversions in SF, we first rotate all the electrons and nuclei by 180° about the c axis (which is peipendicular to the molecular plane) and then reflect all the electrons in the molecular ab plane. The net effect is the inversion of all particles in SF. The first step has no effect on both the electronic and nuclear molecule-fixed coordinates, and has no effect on the electronic wave functions. The second step is a reflection of electronic spatial coordinates in the molecular plane. Note that such a plane is a symmetry plane and the eigenvalues of the corresponding operator then detemiine the parity of the electronic wave function. 

The Concept of the Magnetic Orbital and of Overlap Density in an A-B Bi-nuclear Molecule... 

A. Thiel, The Landau-Zener effect in nuclear molecules, J. Phys. G 16 867 (1990). 

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 ... 

Our perception on hardness equalization during the chemical event of the formation of hetero nuclear molecules is as follows ... 

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 ... 

Another structural motif was exhibited by the structure of the mixed ligand hexa-nuclear molecule [Mo6(0)6(Ai3-0)2(Ai-OEt)6(M-Cl)2Cl6] with a cyclic array of six Mo(v) atoms in a chair conformation. The six valence electrons are paired off in three Mo-Mo bonds (2.665 A, 2.672 A, 2,741 A) alternating around the ring. The /x -oxo ligands are in planar three-coordination (T-shaped). 

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,... 

On the other hand, in recent decades a wealth of experimental and theoretical evidence has been accumulated demonstrating molecular-like structure for systems not traditionally considered as molecular systems. One may include in this list the nuclear molecules in nuclear physics [18, 19], various exotic molecules composed of fundamental particles other than electron, protons and neutrons [20-31], artificial molecules in condensed-matter physics [32-35], and the molecular Bose-Einstein condensates [36-39]. In considering such molecular-like systems the question emerges whether any underlying AIM structure is derivable from the wavefunctions of these systems. To answer this question one must apply the AIM analysis to these systems however, all such systems are intrinsically non-Coulombic in their nature and the formalism of the orthodox QTAIM must be modified to be... 

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