Dipole-bound anions and relations
In most chemistry textbooks you will find that the electron acceptor
properties of a molecule are determined by its empty valence
orbitals. Yet, many molecules can bind electrons through long-range interactions
such as a dipole or polarization potential. The prototypical example is the
acetonitrile molecule H3C-CN; it has a dipole moment of 3.9 Debye,
and it can bind an electron in an extended orbital off the methyl group:
This Figure shows the dipole-bound molecular orbital of CH3CN. The molecule itself
is dwarfed by the diffuse cloud of the excess electron. The inner iso-contour
encloses 20%, the outer iso-contour encloses 80% of the excess electron density.
Electron correlation is crucial
Whereas for many neutral ground states electron correlation is not
of particular importance (depending quite a lot on whom you ask), it
is absolutely crucial for weakly attached electrons. This seems
counterintuitive as electrons occupying the relative compact valence region
should be (and are) more strongly correlated with each other than with a diffuse
electron off the nuclear framework. However, correlation is the difference
between a one-particle and a many-particle description, and "correlation is
crucial" simply implies that a one-particle description of the excess electron
This Figure shows the excess electron orbital of CH3CN computed
with and without electron correlation. The outer iso-contour
encloses 50% of the excess electron density computed at the Hartree-Fock level,
the inner iso-contour encloses 50% of the natural orbital describing the excess
electron computed at the equation-of-motion coupled-cluster level of theory.
With electron correlation the density of the excess electron is far more
compact, and the computed electron binding energy is increased from 6 to 18 meV.
Excess electrons bound to real molecules
There is a lot of work done on electrons bound to dipole, quadrupole, and
polarization model potentials represented by point-multipoles, point-charge
distributions, and point-polarizable sites.
I am interested in electrons bound by molecules, and to what
extent the binding to a molecule can be characterized (and modeled)
as dipole-bound or polarization-bound.
Here is an example, the anti conformer of succinonitrile
(NC-CH2-CH2-CN). This conformer binds an electron with
roughly 10 meV binding energy, and it has been called a quadrupole-bound
state. Yet, the quadrupole moment is too small to do the job, and only
when, in addition to the electrostatic potential, electron correlation is
included, the electron becomes bound.
| 12% contour
|| 30% contour
|| 50% contour
In the picture the natural orbital from an equation-of-motion coupled-cluster
calculation is shown. Close to the molecule the orbital is roughly donut shaped
and wraps around the four H atoms, but it is so diffuse that this shape can only be seen when
contours containing a small portion of the total density are plotted. About 2%
of the excess electron's density resides within the van der Waals volume of the molecule.
Coupling between dipole-bound and valence states
If a molecule has both, a diffuse dipole-bound state and a compact valence
anion state, the two states will couple and an the excess electron can be
transferred from the molecular periphery on to the nuclear framework (or vice versa).
The diffuse state can be though of as a doorway allowing a
molecule to capture a near zero-energy electron even though its unoccupied valence
orbitals does have a much higher energy.
|| Nitromethane is a prototypical system that has both: A dipole-bound state
(lhs) and a valence anion (rhs). Note the different scales of the figures.