Physical Chemistry Third Edition

826 20 The Electronic States of Diatomic Molecules

First excited state

Ground state


 4

 2

0

2

4

6

2

R/10
^10 m

EBO

/eV

1

Figure 20.3 The Born–Oppenheimer Energy of the Ground State and First Excited

State of the Hydrogen Molecule Ion as a Function of Internuclear Distance.

1

2

(a)

(^) g *u
(b)
Figure 20.4 The Orbital Regions for the Hydrogen Molecule Ion (Schematic).(a) The
ground state. (b) The first excited state.
symmetricabout the bond axis. The orbital region ofψ 1 has no nodal surfaces except
atr→∞. The orbital region ofψ 2 has a nodal plane halfway between the nuclei. If
the mathematical limit is taken asrABapproaches zero, a hypothetical atom called the
united atomis obtained. The united atom for H+ 2 is the He+ion. In this limitψ 1 turns
into the united-atom 1sorbital, andψ 2 turns into the united-atom 2pzorbital.
A molecular orbital without a nodal surface between the nuclei generally corre-
sponds to an orbital energy with a minimum value as a function ofrABand is called
abonding molecular orbital. An orbital with a nodal surface between the nuclei
generally corresponds to an orbital energy that decreases asrABincreases and is
called anantibonding molecular orbital. A bonding orbital corresponds to a significant
probability that the electron will be found between the two nuclei, attracting both nuclei
and stabilizing the bond. An antibonding orbital corresponds to a small probability that
the electron will be found between the nuclei, allowing the nuclei to repel each other
more strongly. A bonding orbital also corresponds to a de Broglie wave with a longer
wavelength, which means a smaller speed and a smaller kinetic energy than with an