Morse constant

In the following BOC-MP interrelations, the basic energetic parameter is the Morse constant Q0 [cf. Eq. (2)], which corresponds to the maximum M-A two-center bond energy Q0A. The value of Q0A, although not directly observable, can be easily scaled from the experimental heat of atomic chemisorption QA (atomic binding energy) identified with the M -A bond energy Q(n), namely,... 

The practical difference of using Eq. (8a) versus Eq. (8b) is that these BOC conditions introduce different Morse constants to describe the effective interaction of an atom A (or B) in a molecule AB with a metal surface, namely, the two-center A-M energy Q0A for Eq. (8a) and the polycenter A-M energy QA for Eq. (8b). Because the resulting approximate formulas for Qab w M be different, we should also make a decision about which molecules AB can be best described by each approximation. 

Now let us turn to the BOC condition of Eq. (8b). Although Eq. (8b) does not explicitly depend on n, it assumes the best possible coordination within the M -AB unit mesh, which reflects in the use of the experimental heats of atomic chemisorption, QA and QB, as the Morse constants in energy calculations. For the monocoordination rilpn in M -AB, the variational procedure now leads to an expression... 

With the quadratic force constant ke in units of mdyneA-1 and De in eV, the Morse constant in atomic units (a x) is calculated as... 

If this Morse function is used to represent any single bond, not necessarily of a diatomic molecule, the constant a calculated from the harmonic force constant may not be entirely appropriate, and especially not over the entire range of r. Before deriving multiple-bond properties from the single-bond curve it is therefore useful to optimize the Morse constant empirically to improve the match between calculated and observed single-bond values of De and re. 

The difference between the last two equations is that different Morse constants are used to describe the interaction of an atom A in a molecule AB with a metal surface, i.e., the two-center M-A energy Qoa for equation 6.39 and the polycenter M - AB energy Qa for equation 6.40. Consequently, a choice must be made about which molecules are best described by each representation, and this essentially depends on whether chemisorption is weak or strong . 

Strong chemisorption would be assumed to occur for surface species such as molecular radicals in which unpaired electrons retain most of their atomic character, and the adsorption pattern would resemble that for atoms, which includes a distinct preference for n-fold hollow sites. Examples would include radicals like CH, CH2, NH, OH and OCH3. In this case for monocoordination (Tri p,n,), such as M — AB, the Morse constants are better represented by the experimental heats of atomic chemisorption, Qa and Qb, and the use of equation 6.40 provides the following respective analogues for equations 6.41 and 6.52 ... 

The Morse constant a can be expressed through force constant and anharmonici-ty constant x of the oscillator formed by the bond atoms. The Morse function yields the energy eigenvalues of an anharmonic oscillator which are correct within a sizeable range of amplitudes (in the case of H2 for 0.4 < r/ro < 1.6). For large r, however, V becomes progressively too small [8b]. 

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