Molecular Anions
Henry Eyring Center for Theoretical Chemistry
Opening remarks:
This
web-based text book offers many web links to researchers who have contributed
much to the study of molecular anions. It also offers many literature
references pertaining to the examples I use to illustrate the families of
molecular anions discussed. It is my hope that the reader will find this text
to be a useful resource for learning why the experimental and theoretical study
of anions is such an exciting endeavor for so many chemists. I also hope it
contains some surprises that offer even the most knowledgeable reader new
insight into the behavior of negative molecular ions. If I have been
successful, I am confident that wonderful new knowledge about molecular anions
will be produced by readers of this text and that new workers will be drawn to
this exciting field of study.
If you wish
to download a .pdf version of this text, please click here. I am
still working out the bugs encountered in posting the html version on the web
(e.g., the Greek and math symbols). If you wish to access the most recent
version, click here (I
found that Internet Explorer does a better job than other browsers at
displaying the symbols). If you want to offer input for future improvements or
additions, please click here to send
me email. I hope you enjoy browing through this text and connecting to its many
web links.
Table of Contents (click on a Chapter or Section header label to go to
it)
Chapter 1. Introduction to Molecular Anions
I. Anions Have Very Different
Valence-Region Electronic Potential Energies Than Neutrals and Cations
II.
Anions Are Difficult to Prepare and Study as Isolated Species
A. Making
Anions
B.
Selecting Specific Anions
C.
How Fields Are Used to Focus and Select Anions
D.
Problems That Can Occur
III.
Anions Experience Strong Environmental Effects
IV. Spectroscopic Probes
V. Reaction Dynamics Probes
Chapter 2.
Anions Also Present Special Challenges to Theoretical Study
I.
Special Atomic Basis Sets Must be Used
II.
The Hartree-Fock SCF Process is Usually the Starting Point
III.
KoopmansÕ Theorem Gives the First Approximation to the Electron Affinity
IV.
Electron Correlation Involving the Excess Electron Usually Must be Treated
V.
Various Methods Can be Used to Treat Correlation
A. The
multiconfigurational self-consistent field (MCSCF) method
B. The configuration interaction (CI) method
C. The M¿ller-Plesset perturbation (MPPT) method
D. The Coupled-Cluster (CC) method
E. Density
Functional Theory (DFT)
VI. Computational
Requirements, Strengths, and Weaknesses of Various Methods
VII. Direct Calculation of Intensive Energy Methods
VIII. Complete Basis Extrapolations
IX. Why is Electron Correlation So Important for EAs?
X. Reaction Paths
XI. Summary
Chapter 3. Chemically Conventional Anions
I. What Makes these Anions Conventional?
II. They May be Conventional, but They Involve Complexities
III. Common Multiply Charged Anions are Not Conventional
Chapter 4. Multipole-Bound Anions
I. Electrostatic Attractions
A. The Point and Fixed Finite Dipole Models
B. Binding to Real Molecules
C. Summary
II. Binding an Electron to Quadrupolar Molecules
A. Is
There a Critical Value for the Quadrupole Moment?
B. Real Molecules that Quadrupole Bind
III. Binding Through Higher Moments
IV. Double-Rydberg Anions
V. Zwitterion-Bound Anions
Chapter 5. Multiply Charged Anions
I. Binding to Polar
Molecules
A. What the PD and FFD
Models Suggest
B. Real Cases
II. Binding to Two Distant Sites in a Single Molecule
III. Binding to
Proximate Sites
IV. Special Techniques are Needed to Handle Metastable Anions
Chapter 6. Cluster Anions
I. Anions that are Solvated
II. Clusters With an Electron Attached
III. Clusters Can be Used to Probe Chemical Reactions
IV. Sometimes the Isomers are New Anions
V. Covalent and Metallic Cluster Anions
Chapter 7.
Anions of Biological Molecules
I. Dipole-bound and Valence Anions
II. Virtual Orbitals May Not be Electronically Stable
III. Electrons Attached to DNA
IV. Electrons Fragmenting Peptides
Within
the pages of this book, my personal perspectives are offered on the chemical
study of negative molecular ions. Not much emphasis will be placed on
discussing atomic anions as isolated species because it is my view that
chemistry deals primarily with molecules and materials and with their reactions
and properties, and I think the world of molecules begins with two or more
atoms held together by chemical bonds.
Therefore, I view the study of isolated atomic anions as primarily the
domain of the atomic physics community although, of course, I do think it
useful to discuss atoms as building blocks that form molecules. A recent review by Professor David J. Pegg
from the point of view of a physicist with emphasis on atomic anions can be found
at this online
link.
For
insight into the experimental study of negative molecular ions from a chemistÕs
point of view beyond what is presented in this text, I refer the reader to the
web sites of Professor
W. C. Lineberger and Professor John
I. Brauman.
Carl Lineberger,
University of Colorado John Brauman,
Stanford University
These
two scholars have done as much if not more than anyone else over the past forty
years to contribute to chemistsÕ knowledge about electron affinities and the
chemical structures, reactions, and spectroscopy of molecular anions. Their
groups have also pioneered many of the most useful experimental tools for
studying molecular anions and have generated many scientific offspring who
became major figures in this field. Of course, even they stood on the shoulders
of earlier masters such as Louis Branscomb (Atomic and Molecular Processes, edited by D. R. Bates, Academic Press, New York,
N.Y. (1962)), George Schulz (Rev. Mod. Phys. 45, 373, 423 (1973)), and Sir H. S. W. Massey (Negative Ions, Cambridge Univ. Press (1976), Cambridge, England).
I will make use of many examples of chemical studies
carried out by Professors Brauman and Lineberger as well as results from the
laboratories of many others I mention throughout this text. In so doing, I do
not mean to suggest that only the groups I mention in each example have
contributed to such studies; in fact, most of the groups I highlight pursue
work on many if not most of the molecular anions treated in this book. However,
for brevity, I have had to select but a few examples for each of the classes of
anions treated from among the many studies these workers have undertaken.
Many other senior scholars have contributed much to
the advancement of experimental studies of molecular anions in recent decades
and continue to do so. Several of them are shown below. They and many of their
scientific offspring continue to expand the horizons of this field of study.
Kit Bowen,
Johns Hopkins Jim Coe,
Ohio State Dan Neumark,
Berkeley
Bob
Compton, Tennessee Mark Johnson, Yale Torkild
Andersen, Aarhus
Lars Andersen,
Aarhus Paul Burrow,
Nebraska
Lai-Sheng Wang,
Washington State
Jack Beauchamp,
Caltech Kent Ervin, Nevada, Reno
Michael Allan,
Fribourg
Veronica
Bierbaum, Colorado; Barney Ellison,
Colorado; Eugen
Illenberger, Berlin
Leon Sanche,
Sherbrooke Ron Naaman,
Weizmann Tilmann
Mrk, Innsbruck
Paul Kebarle,
Alberta Will Castleman, Penn State
The University of
ColoradoÕs Joint Institute for Laboratory Astrophysics (JILA) has a very long
tradition of experimental advances and studies of molecular anions. Below we
see several JILA scientists whose scientific careers are linked strongly to
this field of study; can you identify them?
The University of Colorado, JILA, Ion Gang in 1980.
Throughout this text, I
will show many examples from labs of the people shown in the above figures of
experimental data on a wide range of molecular anions.
Of course, there have been theoretical chemists who
have also advanced our knowledge of molecular anions during the same
timeframe. Professor R. S. Berry
was among the earliest pioneers (R. S. Berry, Chem. Rev. 69, 533 (1969)) of such studies.
Steve Berry, Chicago
Several other senior
chemistry scholars who have contributed much to the advancement of the
theoretical study of molecular ions are shown below. They and their scientific
offspring continue to advance this field of study.
Lenz Cederbaum,
Heidelberg Alex
Boldyrev, Utah State Ken Jordan,
Pittsburgh
Josef Kalcher, Gratz Piotr Skurski,
Gdansk Maciej
Gutowski, Edinburgh
Vince
Ortiz, Auburn Ludwik Adamowicz, Arizona Howard Taylor, USC
Fritz Schaefer,
Georgia Ernest
Davidson, Washington
Kwang Kim,
Pohang
Peter Rossky,
Texas Pavel Rosmus, de Marne la Valle
I will also show results
from these scientistsÕ research efforts throughout this text, but again only a
small fraction of what they have contributed can be covered.
Prior
to the time most of the people shown above began to study molecular anion
chemistry, the electron affinities of most atoms were not known and very little
was known about the electron affinities of molecules and radicals. It was
largely because of experimental advances in ion sources and spectroscopic
probes that the determination of molecular electron affinities and the study of
molecular anions began to advance rapidly in the 1960s and 1970s. Once
experimental chemists began to be able to make and study negative molecular
ions, it was natural for theoretical chemists to become involved in this field.
However, they too faced significant challenges and had to develop new models
and new computational tools to study anions as I will show later in this text.
My
own history in the field dates to 1973, when our first paper (Theory of
Electron Affinities of Small Molecules, J. Simons, and W. D. Smith, J. Chem.
Phys., 50, 4899-4907 (1973)) dealing
with the ab initio calculation of electron affinities (EAs) using what we
termed the equations of motion (EOM) method was published. At about this same
time, Professor Lenz
Cederbaum was developing what turned out to be an equivalent method [[1]]
for directly calculating ion-molecule energy differences, as were other groups
[[2]].
Prior to this time, quantum chemical calculations of molecular EAs [[3]],
including many from Professors Enrico
Clementi, Ernest
Davidson and Fritz Schaefer were most
commonly carried out using approximate solutions to the Schrdinger equations
to obtain the total electronic energies of the neutral (Eneu) and anionic (Ean) species and subtracting these two quantities to
compute the EA as
EA = Eneu
– Ean.
However, because the EA
is a very small fraction of the total electronic energies of the neutral or the
anion, this process is fraught with danger because one must obtain each of the
two total energies to very high percent accuracies to obtain the EA to a
chemically useful accuracy. To illustrate, we note that EAs typically lie in
the 0.01-5 eV range, but the total electronic energy of even a small molecule
is usually several orders of magnitude larger. For example, the EA of the 4S3/2
state of the carbon atom is [[4]]
1.262119 ± 0.000020 eV, whereas the total electronic energy of this state of C
is
–1030.080 eV (this total energy is defined relative to a C6+ nucleus and six electrons infinitely distant and not moving). Since the EA is ca. 0.1 % of the total energy of C, one needs to compute the C and C- electronic energies to accuracies of 0.01 % or better to calculate the EA to within 10%.
Moreover,
because the EA is an intensive quantity but the total energy is an extensive
quantity, the difficulty in evaluating EAs to within a fixed specified (e.g., ±
0.1 eV) accuracy based on subtracting total energies becomes more and more
difficult as the size and number of electrons in the molecule grows. For
example, the EA of C2 in its X 
ground
electronic state [4] is 3.269 ± 0.006 eV near the equilibrium bond length
Re but only 1.2621 eV at R 
Ž (i.e., the same as the EA of a carbon atom). However,
the total electronic energy of C2 is –2060.160 eV at R 
Ž and lower by ca. 3.6 eV (the dissociation energy [[5]]
of C2) at Re, so again the EA is a very small fraction of
the total energies. For buckyball C60, the EA is [[6]]
2.683 ± 0.008 eV, but the total electronic energy is sixty times
–1030.080 eV minus the atomization energy (i.e., the energy change for C60
60 C) of
this compound. This situation becomes
especially problematic when studying extended systems such as solids, polymers,
or surfaces for which the EA is an infinitesimal fraction of the total energy.
I should note that this same difficulty plagues the theoretical evaluation of
other intensive properties such as ionization potentials, electronic excitation
energies, bond energies, heats of formation, etc.
These
examples show that computing the EA of a molecule by using the total energies
of its neutral and anion may not be a wise approach. How do most experiments
determine molecular EAs? The most direct technique involves using a tunable
light source of frequency n to photodetach an electron
from a molecular anion A-. By
determining the minimum photon energy hn needed to detach an electron to form the neutral molecule A, one determines the EA. This offers an example of how
the EA is determined directly. Nowhere in this experiment is the extensive
total energy of either the anion or the neutral measured. So, it would appear
natural to seek a theoretical approach to determining EAs that follows the
experimental example.
In
the 1973 paper mentioned above, we did so by developing the equations of motion
(EOM) method as a route to calculating the intensive EAs directly as
eigenvalues of a set of working equations. In this theoretical development, one avoids (approximately) solving the
Schrdinger equation for the extensive energies of the neutral and anion and
then subtracting the two extensive energies to obtain the desired intensive EA.
In numerous of our subsequent publications, the EOM method was refined and
applied to a variety of molecular anions. In the intervening years, our group
and others [[7]] have greatly extended the EOM
method beyond the M¿ller-Plesset framework that we initially used to allow more
powerful coupled-cluster, multi-configurational, and other wave function
classes to be employed. Most of the subsequent developments of these
theoretical tools have been cast within the language of so-called Greens
function or propagators, but they could just as well have been written in our
EOM language. As a result of such advances by many different groups, several
direct-calculation techniques are now routinely used to compute EAs; that of
Professor Vince
Ortiz [7] is even contained within the widely used Gaussian suite of programs [[8]]
that many chemists use routinely.
In
the early studies of anions carried out in the 1970s and 80, emphasis was
placed on simply determining electron affinities (EAs) rather than on probing
the potential energy surfaces of chemical reactions involving anions,
determining their spectrocsopic and structural properties, or attempting to
design anions with novel structural or bonding characters. This was true both
of the theoretical and experimental investigation of anions primarily because
a. prior to 1970, even
these most fundamental thermodynamic data (i.e., EAs) had not been directly
(i.e., by laser photodetachment) determined for most atoms, molecules, and
radicals, and
b. the experimental and
theoretical tools available to determine EAs were in their formative stages and
needed to be tested on species whose EAs were reasonably well known from other
sources.
In the subsequent thirty
years, the field has broadened considerably to where the study of molecular anions
is now motivated by a variety of reasons including designing new anions having
specific bonding behavior or energy content and probing the influence of
electrons attached to biological molecules, water clusters, interfaces, and
within nanoscopic materials. Over
this same period, the number of research groups focusing on anion chemistry has
grown tremendously. In the 1970s, issues of J. Chem. Phys. or J. Phys. Chem.
contained very few papers on anions, but now essentially any issue of either of
these journals contains more than one anion paper and the number and range of
such papers in increasing rapidly.
Because
our knowledge of molecular anions has reached a stage in which the field has
very broad interest and impact, I felt it was time to offer a source from which
one could gain perspective about these species. By no means does this book
intend to thoroughly review the vast body of knowledge that has been
established on molecular anionsÕ properties or to tabulate molecular EAs.
Rather, it focuses on providing references to many practicing scientists and
other valuable sources of information and on introducing the reader to
a. the fundamental
properties that make anions qualitatively different from neutrals and cations,
b. introducing several
classes of anions whose study has substantially expanded in recent years but
which still offer promise of many more discoveries.
c. illustrating the
special challenges that the study of molecular anions present.
In my mind, this book is
a text from which one can learn rather than a reference book where one can look
up all that is known.
If
one is searching for tabulated values of atomic or molecular electron
affinities (EAs), the best places to search for such information are:
1. For atoms, the early
reviews of Hotop and Lineberger [[9]], and the more recent review by
Andersen, Haugen, and Hotop [[10]]
remain excellent sources.
2. For molecules, there
are several sources [[11],
[12],
[13],
[14],
[15]] that span many years, some of which
are accessible on the web.
The
primary focus of the present work is to first (Chapters 1 and 2) give an
introduction to some of the special challenges that negative molecular ions
present both in terms of experimental study and theoretical investigation. I
begin by considering some of the characteristics of negative ions that make
them qualitatively different from neutrals or cations. Also, I offer a brief
introduction to some of the challenges that one must face when studying anions
in the laboratory. Although I am a theoretical chemist and is not familiar with
all of the details involved in carrying out experiments on anions, I believe it
is essential for me to discuss such matters so readers will appreciate how
difficult it is to make anions in appreciable numbers and to confine them so
they can be probed, and how their low electron binding energies further
complicate matters.
Subsequent
focus (in Chapters 3-7) is aimed at introducing the reader to the wide variety
of negative ions that one encounters in chemical science and giving a few
examples of several such classes. As a result, these Chapters provide an
introduction to various kinds of molecular anions and the special
characteristics that they possess, but by no means do they offer exhaustive
reviews of the extensive literature on these anions.
Now,
let us begin the journey through the world of negative molecular ions by
examining in Chapters 1 and 2 what makes anions significantly different from
neutrals and cations, why these differences are important, and what makes their
experimental and theoretical study challenging.
Chapter 1.
Introduction to Molecular Anions
I. The Valence Electrons in Anions Experience Very
Different Potential Energies Than in Neutrals and Cations
The physical and chemical properties of anions are very different from those of neutral molecules or of cations. Obviously, their negative charge causes them to interact with surrounding molecules and ions differently than do cations or neutrals. For example, when hydrated, anions are surrounded by H2O molecules whose dipoles tend to have their positive ends directed toward the anion. For cations, the dipoles are directed oppositely and for neutrals, the local solventÕs orientation depends upon the polarity of the functional group on the solute nearest the solvent. Moreover, anions polarize the electron clouds of nearby molecules in the opposite sense that cations do. Because of their weakly bound valence electron densities, anions have large polarizabilities and thus tend to have stronger van der Waals interactions with surrounding molecules than do more compact, less polarizable neutrals and cations. The valence electron binding energies in anions tend to be smaller than in neutrals or cations, and anions seldom have bound excited electronic states whereas neutrals and cations have many bound excited states including Rydberg progressions. The source of all of these differences lies in the potentials that govern the movements of the valence electrons of the anions, cations, and neutrals.
As chemists know well, it is an atom or moleculeÕs outermost (i.e., valence) orbitals that govern the size, electron binding energy, and much of the chemical reactivity of that species. When an anionÕs electrons move to the regions of space occupied by its valence orbitals, they experience an attractive potential that is qualitatively different from in neutrals and cations. It is these differences that we need to now spend time discussing because these differences are of fundamental importance in determining many of the physical and chemical properties of anions that make them different.
Specifically, an
electron in the valence regions of an anion experiences no net Coulomb
attraction in its asymptotic (i.e., large-r) regions, but corresponding
electrons in neutrals and cations do experience such –Ze2/r
attractions (e.g., Z = 1 for a neutral and 2 for a singly-charged cation,
etc.). In fact, the longest-range attractive potentials appropriate to an
electron in singly charged anions are the charge-dipole (-m
r e/r3),
the charge-quadrupole (-Q
(3rr –r21) e/3r5), and the charge-induced-dipole
(-a
rre2/2r6)
potentials. Here, m, Q,
and a are the corresponding
neutral moleculeÕs dipole moment vector, quadrupole moment tensor, and
polarizability tensor, respectively; and r
is the position vector of the electron. The 
symbols
indicate dot products with the vectors or tensors, and 1 is the unit tensor. The most important thing to
note is that for cations and neutrals, the large-r attractive potential falls
of as –Ze2/r, whereas for anions, it falls off as a higher
power of 1/r.
These differences
are what produce major differences in the radial size, electron binding energy,
and pattern of bound electronic states of anions compared to neutrals and
cations. For example, recall that it is the 1/r dependence of the Coulomb
attraction combined with the 1/r2 scaling of the radial kinetic energy
operator (-h2/(2mr2)
/
r(r