Cylindrical harmonic potential

Due to the superior performance of the H-73 basis set in the Cl calculations of structures and energies for the excited states of hydrogen molecule, it was used in the subsequent studies of H2 enclosed in a cylindrical harmonic potential. The PECs of the ground and eight low-lying excited states of H2 encapsulated... 

Two forms of the cell model (CM) are then developed harmonic oscillator approximation and square-well approximation. Both forms assnme hexagonal closed packing (HCP) lattice structure for the cell geometry. The model developed by Paul and Di Benedetto [13] assumes that the chain segments interact with a cylindrical symmetric square-well potential. The FOV model discnssed in the earlier section uses a hard-sphere type repulsive potential along with a simple cubic (SC) lattice structure. The square-well cell model by Prigogine was modified by Dee and Walsh [14]. They introduced a numerical factor to decouple the potential from the choice of lattice strncture. A universal constant for several polymers was added and the modified cell model (MCM) was a three-parameter model. The Prigogine cell EOS model can be written as follows. 

We will illustrate the development of the even part of the crystal-field potential for the symmetries C4 and D3, First of all we determine which tesseral harmonics have the same symmetry elements as the point group C4. In C4, only a fourfold rotation axis is present. This axis can generate the symmetry operations C, C (= C2), C and the identity. The tesseral harmonics Z q, and Zgf, have cylindrical symmetry and are present in the even part of every crystal-field potential. The C4 axis is a symmetry element for the harmonics Z44, Z44, Zg4 and Zg4. We have thus the following coefficients in the even part of the crystal-field potential for C4 Bl, Bq, B, B l, 5 and B. The potential can be written as... 

---