Soft harmonic oscillators

Hurd and soft cliromuphorc. 164-68 Harmonic oscill.iior eigenfunction, 36 Hariree-Fock approximation, 52 Heavy atom effect. 28. 22.3-24. 255. 264. 269-70. 306. 412. 419 external and internal. 270 Heitier-London. 237 Helicene. 151, 441 Hemaloporphyrin. 295 Keptucycicnc, t46 Keptalene. 169... 

The confinement model has been extensively used to analyze the hydrogen atom enclosed by hard and soft spherical boxes [1-98], with confining boxes of diverse geometrical shapes [31,88-98], and it has also been applied to studies of the helium atom [99-122], many-electron atoms [50, 52,55,123-131], molecules [132-142] and the harmonic oscillator [143-171], among others. 

We first generate the matrix elements of G as a function of co in a harmonic-oscillator basis, using the Reid soft-core potential [26] and the Barrett-Hewitt-McCarthy technique [27] as modified by Vary and Yang [28]. We repeat this calculation of G as the size of the 02p = 0 space... 

Use of this potential can then provide a quantitative measure of cohesion in these solids. One measure of the strength of these potentials is the vibrational frequency that would correspond to a harmonic oscillator potential with the same curvature at the minimum this is indicative of the stiffness of the bond between atoms. In Table 1.1 we present the frequencies corresponding to the Lennard-Jones potentials of the common noble gas elements (see following discussion and Table 1.2 for the relation between this frequency and the Lennard-Jones potential parameters). For comparison, the vibrational frequency of the H2 molecule, the simplest type of covalent bond between two atoms, is about 500 meV, more than two orders of magnitude larger the Lennard-Jones potentials for the noble gases correspond to very soft bonds indeed ... 

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