Molecular eigenvalues

The molecular eigenvalues are obtained by looking for the LCAO solution... 

FIG. 6. The valence molecular eigenvalues,MSM, in the muffin-tin potential for FeCl4 calculated using different basis sets as discussed in the text [78]. 

We believe that much more efficient descriptors can be discovered and this is a focus of our work. Until recently QSAR analyses have used relatively simple molecular descriptors based on substituent constants (e.g., Hammett constants, n, or molar refractivities), physicochemical properties (e.g., partition coefficients), or topological indices (e.g., Randic, Weiner, or Kier and Hall indices). Recently we and others have developed several new information rich, computationally efficient representations. The most interesting of these are the molecular eigenvalue indices. 

The vibrational frequency shift arises from the perturbation of the molecular eigenvalues by adsorption. The interaction potential depends on the internal stretching coordinate =(r-re)/re. The vibrational potential of the adsorbed molecule V(0 is composed of the internal potential of the free molecule and the external potential... 

The electronic structure of polymers is different from that of discrete molecules. Molecular eigenvalues are quantized that is, they can only assume definite values. Polymers, on the other hand, do not have quantized eigenvalues instead, their eigenvalues form bands of energies. This is a consequence of the infinite nature of the system an infinite number of atoms would give rise to an infinite number of eigenvalues. 

A key issue in describing condensed matter systems is to account properly for the number of states. Unlike a molecular system, the eigenvalues of condensed matter systems are closely spaced and essentially mfmite in... 

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. 

These new wave functions are eigenfunctions of the z component of the angular momentum iij = —with eigenvalues = +2,0, —2 in units of h. Thus, Eqs. (D.l 1)-(D.13) represent states in which the vibrational angular momentum of the nuclei about the molecular axis has a definite value. When beating the vibrations as harmonic, there is no reason to prefer them to any other linear combinations that can be obtained from the original basis functions in... 

HUCKEL MOLECULAR ORBITAL THEORY I EIGENVALUES by the matrix... 

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