lecturenotes_oct282010

lecturenotes_oct282010 - Lecture notes for Lecture #6,...

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Lecture notes for Lecture #6, October28th, 2010 Definitions Pair-wise potential: The potential energy between two atomic sized, neutral, non- interacting, symmetric particles is very well described by the pair-wise potential. The parameters listed below are important features of the pair-wise potential r 0 : This defines the equilibrium distance between the two atomic sized, neutral, symmetric particles. r min : this is the minimum separation that will ever occur between the two particles r max : this is the maximum separation that will occur between the two particles σ : This defines the distance between the centers of the two particles. When the two particles are just touching, the distance between their centers is σ . ε : Often, 1 ε used to define the depth of the well. Nearest Neighbors: When investigating the structure of molecules, we can identify those atoms that are equidistant to one reference atom. These are called nearest neighbors. Next Nearest neighbors: As above, when investigating molecular structure, we can identify those atoms that are equidistant to one reference atom, further away than the nearest neighbor atoms, yet closer than the Next-next Nearest neighbor atoms. Atoms that satisfy this requirement area called Next-Nearest Neighbors. Modes This is new terminology for specifying the way a substance has energy The Pair-wise Potential Curve as a Tool The pair wise potential curve, shown below, graphically specifies the potential energy between two particles as a function of the changing separation between those two particles. An application of the information in the pair wise potential curve provides us a way to 1) determine if a particle is bound, and 2) surmise the energy required to completely disassociate that molecule. Let us see how this works. First, let us more clearly label and discuss all the parameters above. r 0 When these two particles are separated by a distance r 0 the force of attraction equals the force of repulsion, giving a net force of zero. The point or location where the net force is zero is, by definition, the location of the equilibrium position. On the graph below, r 0 corresponds to the r-coordinate of the location where the potential energy is a minimum. The energy coordinate (in units of ε ) is just the corresponding depth of the well ε .
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σ : We have seen that the equilibrium position, the distance at which the net force between the particles is zero, occurs not when they are touching, but a little bit apart from that, where the net force is zero. Remember that the force always points in the direction that will minimize the potential energy. If the potential energy is already a minimum, no additional force is required, as the natural state of affairs, the state of lowest potential energy or equilibrium, is already achieved.
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lecturenotes_oct282010 - Lecture notes for Lecture #6,...

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