md2011-04-note_Part_5

md2011-04-note_Part_5 - Morse Potential Pair potentials...

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Morse Potential I Pair potentials work reasonably for simple metals (e.g., Na, Mg, Al and fcc/hcp metals). Another often used one is the Morse potential [Phys. Rev. 34 (1930) 57] . I Also used in the mdmorse code. I Functional form is U ( r ) = X ij De - 2 α ( r ij - r 0 ) - 2 De - α ( r ij - r 0 ) . (16) -3 -2 -1 0 1 2 3 4 2 2.5 3 3.5 4 4.5 5 Energy (eV) r (Å) R A U I Developed for solving the Schrödinger equation since it has an analytical solution with this functional form. I Efficient to evaluate and decays faster than LJ less problems with cutoff. I Many parametrizations exist (see, e.g., [Phys. Rev. 114 (1959) 687] ). Notes
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O P P I The “good” ones work for those materials which have a close-packed structure as the ground state (usually fcc or hcp). I However, people have tried some tricks with pair potentials to extend their usage to covalent materials. I Note, many of these trick introduce pathological problems to the potentials. Extreme care is adviced if one ever needs to use any of such potentials.
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