Binding energy/position of maximum energy value

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SUMMARY

The binding energy of the ion H2+ is calculated to be -16.3 eV at an equilibrium separation of 0.106 nm. Utilizing the Hellman-Feynman theorem, the force between the nuclei is derived from the electrostatic repulsion and attraction to the electron distribution. The repulsion energy is determined to be 13 eV, while the attraction energy is calculated as -2.7 eV, indicating that the system is unbound when the total energy is positive. The squared modulus of the electron wave function in H2+ must be maximized at the position where the attractive force balances the repulsive force.

PREREQUISITES
  • Understanding of quantum mechanics and wave functions
  • Familiarity with the Hellman-Feynman theorem
  • Knowledge of electrostatic forces and potential energy calculations
  • Basic concepts of molecular binding energy
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  • Study the application of the Hellman-Feynman theorem in molecular systems
  • Explore the mathematical derivation of binding energy in diatomic ions
  • Learn about the implications of wave function normalization in quantum mechanics
  • Investigate the relationship between electron distribution and molecular stability
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Students and researchers in quantum chemistry, physicists studying molecular interactions, and anyone interested in the principles of binding energy in molecular systems.

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Homework Statement


The binding energy of the ion H2+ is -16.3 eV at the equilibrium separation 0.106 nm. The Hellman-Feynman theorem states taht the force between the nuclei in a molecule can be calculated from the electrostatic repulsion between the nuclei and the electrostatic attraction of the nuclei to the electron distribution. According to this theorem, where must the squared modulus of the electron wave function in H2+ have its maximum value?

Homework Equations


P(x) = abs(psi(x))^2=1

The Attempt at a Solution


Urepulsion = 1/(4*pi*epsilonnaught)*q^2/r= 13 eV
Uattraction = Ebinding + Urepulsion = -2.7 eV
 
Physics news on Phys.org
The sum of attraction plus repulsion is the binding energy. -2.7 eV + 13 eV is positive, so the whole system would be unbound.

How do you find the attraction as function of the electron position?
 

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