Potential Energy Function
The Morse potential energy function is of the form
Here is the distance between the atoms, is the equilibrium bond distance, is the well depth (defined relative to the dissociated atoms), and controls the 'width' of the potential (the smaller is, the larger the well). The dissociation energy of the bond can be calculated by subtracting the zero point energy from the depth of the well. The force constant of the bond can be found by Taylor expansion of around to the second derivative of the potential energy function, from which it can be shown that the parameter, is
- ,
where is the force constant at the minimum of the well.
Since the zero of potential energy is arbitrary, the equation for the Morse potential can be rewritten any number of ways by adding or subtracting a constant value. When it is used to model the atom-surface interaction, the Morse potential is usually written in the form
where is now the coordinate perpendicular to the surface. This form approaches zero at infinite and equals at its minimum. It clearly shows that the Morse potential is the combination of a short-range repulsion and a longer-range attractive tail.
Read more about this topic: Morse Potential
Famous quotes containing the words potential, energy and/or function:
“Humanity has passed through a long history of one-sidedness and of a social condition that has always contained the potential of destruction, despite its creative achievements in technology. The great project of our time must be to open the other eye: to see all-sidedly and wholly, to heal and transcend the cleavage between humanity and nature that came with early wisdom.”
—Murray Bookchin (b. 1941)
“Since the beginning of time, three-quarters of the mental energy and of the lies inspired by vanity have been expended for their inferiors by people who are only abased by such expenditure. And Swann, who was easygoing and unaffected with a duchess, trembled at the thought of being scorned and put on airs when he was with a housemaid.”
—Marcel Proust (1871–1922)
“Philosophical questions are not by their nature insoluble. They are, indeed, radically different from scientific questions, because they concern the implications and other interrelations of ideas, not the order of physical events; their answers are interpretations instead of factual reports, and their function is to increase not our knowledge of nature, but our understanding of what we know.”
—Susanne K. Langer (1895–1985)