Why do Bonds Form

It is now time to analyze our first chemical bond. Why does a bond form A typical answer is that the energy decreases because the electrons primarily reside in between the 

Kinetic energy is lowest for a diffuse wavefunction. A. Lowest energy wavefunction, B. Intermediate energy, and C. Highest energy wavefunction. 

To understand the changes in kinetic energy and potential energy that occur when a bond forms, let s analyze the simplest of bonds, that in H2. The Hamiltonian for H2 is given in Eq. 14.12, where A and B represent the individual nuclei. Here we leave out the internuclear repulsion term, drawing on a simplification known as the Born-Oppenheimer approximation (discussed more in Section 14.2.1). 

The Schrodinger equation for H2 can be solved in an alternative coordinate system called confocal elliptical coordinates. Just as with the hydrogen atom, certain wavefunctions result, each of which has a distinct energy. 

Cross-sections along the x axis showing amplitude versus distance for A. Is orbital, and for the two lowest energy wavefunctions B. i/fg and C. i// for H2 relative to the center of the bond. The x axis is internuclear distance (Bohr radii). A represents H positions. Adapted from course notes by W. A. Goddard III, Nature of the Chemical Bond.  

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