Now consider the London interaction between the phenyl groups of two Phe residues (see Problem P14B.5). (a) Estimate the potential energy of interaction between two such rings (treated as benzene molecules) separated by 0.4 nm. For the ionization energy, use I = 5.0 eV. (b) Given that force is the negative slope of the potential, calculate the distance-dependence of the force acting between two non-bonded groups of atoms, such as the phenyl groups of Phe, in a polypeptide chain that can have a London dispersion interaction with each other. What is the separation at which the force between the phenyl groups (treated as benzene molecules) of two Phe residues is zero? Hint: Calculate the slope by considering the potential energy at r and r + δr, with δr << r, and evaluating {V(r + δr) − V(r)}/δr. At the end of the calculation, let δr become vanishingly small.
Now consider the London interaction between the phenyl groups of two Phe residues (see Problem P14B.5). (a) Estimate the potential energy of interaction between two such rings (treated as benzene molecules) separated by 0.4 nm. For the ionization energy, use I = 5.0 eV. (b) Given that force is the negative slope of the potential, calculate the distance-dependence of the force acting between two non-bonded groups of atoms, such as the phenyl groups of Phe, in a polypeptide chain that can have a London dispersion interaction with each other. What is the separation at which the force between the phenyl groups (treated as benzene molecules) of two Phe residues is zero? Hint: Calculate the slope by considering the potential energy at r and r + δr, with δr << r, and evaluating {V(r + δr) − V(r)}/δr. At the end of the calculation, let δr become vanishingly small.
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