DOI: 10.1002/chem.200900239
A Bonding Quandary—or—A Demonstration of the Fact That Scientists Are
Not Born With Logic
Santiago Alvarez,[a]
Roald Hoffmann,[b]
and Carlo Mealli[c]
Dedicated to Professor Yitzhak Apeloig on the occasion of his 65th birthday
Introduction
The chemical bond is at the heart of our enterprise, yet its
nature continues to be debated. Into the idea of a chemical
bond enter experimental measures—distances, energies,
force constants, spectroscopic and magnetic criteria—and
theoretical ones: bond orders, overlap populations, quantum
theory of atoms in molecules (QTAIM) bond paths, electron
localization function (ELF) plots, and energy decompositions.
If one allows oneself to use a multiplicity of criteria,
bonds may exist by one measure, not by another. This is not
a reason to wring our hands, nor complain how unscientific
chemistry is (or how obstinate chemists are). Chemistry has
done more than well in creating a universe of structure and
function on the molecular level with just this “imperfectly
defined” concept of a chemical bond. Or maybe it has done
so well precisely because the concept is flexible and fuzzy.
We want to share with the community how a discussion
on bonding played out around a specific group of compounds:
small, sulfur-containing clusters of copper with associated
ligands. Its a real story, with some fierce debate
among friends, who questioned each others bonding assignment
both in print and in private conversations. We believe
our discussion has something of value to other chemists, for
several reasons:
1) There is in our exchange an underlying question of the
existence or absence of a chemical bond (in this case, an
SÀS bond), a matter, as we have said, debated across the
community and not just for these compounds.
2) The reaction in question—making or breaking a bond—
is formally an oxidative addition or reductive elimination,
a fundamental and widely useful organometallic reaction.
So are redox reactions in general.
3) Polynuclear metal complexes of oxygen and sulfur are
used by nature in a wide variety of biological redox reac-
tions.
Abstract: We document here a spirited debate among
three colleagues and friends who have strong opinions
on a specific bonding problem, the presence or absence
of a cross-ring sulfur–sulfur bond in a trinuclear Cu3S2
cluster. The example may seem esoteric, but through
their struggles with this specific bond (and with each
other) the authors approach the more general problematic
of chemistry, the chemical bond. The discussion focuses
on bond lengths and the population of bonding
and antibonding orbitals, and on oxidation states, electron
counting, and associated geometries. It expands to
encompass other bonding criteria, and introduces examples
ranging far across organic and inorganic chemistry.
The authors suggest molecules that might test their
ideas. An Appendix to the paper discusses a matter
rarely broached in the chemical literature—should one
review for publication a paper which criticizes one of
your own contributions.
Keywords: bond lengths · chemical bonding · cluster
compounds · SÀS bonding · sulfides
[a] Prof. S. Alvarez
Departament de Química Inorgànica and
Institut de Química Teòrica i Computacional (IQTC-UB)
Universitat de Barcelona
Martí i Franqu›s 1-11, 08028 Barcelona (Spain)
Fax: (+34)93-4907725
[b] Prof. R. Hoffmann
Department of Chemistry and Chemical Biology
Cornell University
Ithaca, NY 14853-1301 (USA)
Fax: (+1)6072555707
[c] Dr. C. Mealli
Istituto di Chimica dei Composti Organometallici
ICCOM-CNR
Via Madonna del Piano 10,
50019 Sesto Fiorentino, Firenze (Italy)
Fax: (+39)055225203
 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim Chem. Eur. J. 2009, 15, 8358 – 83738358
4) Much of what transpired in our exchange finds no place
in the scientific literature, or is dealt out of it. And yet it
is an essential part of the way science is done.
The participants in the debate are Santiago Alvarez (University
of Barcelona), Roald Hoffmann (Cornell University),
and Carlo Mealli (Istituto di Chimica dei Composti Organometallici,
Firenze). They will use their first names
throughout the debate. Each had important collaborators:
Anne Poduska for Roald, Gabriel Aullón and Rosa CarrasACHTUNGTRENNUNGco
for Santiago, Andrea Ienco for Carlo. And the discussion
centers on a compound made by William Tolman and coworkers
(University of Minnesota). The text of the correspondence,
as it evolved in real time, is available from the
authors.1
What we have here is a mutually agreed-on reconstruction
of the debates essential features.
How the Troubles Began
Roald: In 2007 in Ithaca, Anne Poduska was wending her
way toward her Ph.D. One of her projects involved a theoretical
analysis of the Isobe and Nishioka compounds:[1]
In these molecules, two S2
2À
complexes are reductively
linked, forming two single SÀS bonds and two “half” SÀS
bonds; we analyzed the composite system as a complex of a
Jahn–Teller distorted S4
2À
ring. With my failing memory, I
remembered vaguely that both Santiago and Carlo had
done work on S···S bond formation across a metal-containing
ring. So I wrote to both, asking for references.
Santiago: I replied to Roalds June 2007 E-mail, mentioning
a number of cases where we had studied the “trading off” of
MÀM for SÀS bonding. Among the papers I listed, there
was one emerging from my collaboration with Tolmans
group on a trigonal-bipyramidal Cu3 complex without an
SÀS bond: [(L2Cu)3ACHTUNGTRENNUNG(m3-S)2]3+
, L2 =Me2NCH2CH2NMe2
(called A throughout this paper).[2]
Its structure, shown
below, is also found in similar compounds with L2 =cyclo-
hexyldiamine.[2,3]
Little did I know what mentioning this
work would get me into.
Carlo: I also supplied Roald and Anne with some references,
for our interest in main group element–main group element
(XÀX) and MÀM bonds is one of long standing.[4]
I
was fascinated by the Isobe and Nishioka compounds, and
in the attempt of gaining a clearer picture of the bonding in
these compounds, I carried out with Andrea additional calculations
and qualitative molecular orbital (MO) analyses.
We wondered whether there could be other structures
thought to possess parallel S2
2À
units that in fact are being
reductively coupled. And we found some.
I started to see more generally some analogy between the
coupling of two disulfide bridges and the coupling of simpler
sulfide ligands, S2À
, which can potentially undergo reductive
coupling to S2
2À
. Excitedly, we corresponded with Roald
about this.
Roald: Building off Carlos and Andreas enthusiasm, an
Ithaca–Firenze collaboration took shape, examining the
presence and absence of SÀS coupling in a variety of organometallic
systems. I brought up the Tolman/Alvarez article
on the trinuclear cluster A, and upon reading it, Carlo started
wondering whether such a compound might actually
have an SÀS bond, especially since the SÀS separation of
about 2.7 Š is similar (or even shorter) than those in the S4
systems for which I and Anne proposed SÀS coupling.
I could sense a good debate on the horizon.
Roald and Carlo: Eventually, we wrote a paper about SÀS
coupling—including a discussion about A—which we submitted
to Angewandte Chemie on November 18, 2007.
Through a MO and Mulliken population analysis, we reassigned
the bonding in the molecule, saying that it was best
seen as possessing a CuII
2CuI
configuration of the metals,
with a coupled S2
2À
central unit. Being aware that our viewpoint
was opposite to that of Santiago, who envisaged discrete
sulfido ligands and CuII
2CuIII
oxidation states in A, we
sent him the manuscript we submitted for publication,
saying, “We would appreciate your comments, of course.
But you may want to save them for the review!”
Roald, Carlo, and Santiago: Indeed, shortly after receiving
Roalds E-mail, Santiago got the manuscript for review.
And he decided not to review it, writing to Roald and
Carlo: “I hope you understand that I might tell Peter Gçlitz1
At the price of three cases of good wine.
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ESSAY
that there is a conflict of interest because of your opposing
view to our description of Bill Tolmans compound A”.
Roald found this interesting: Santiagos decision here, he
thought, was not necessarily one that everyone in the community
would make when faced with a similar problem. So
Roald asked Santiago why he took this action, and he also
asked Carlo what he would have done in a similar situation.
Their opinions, as well as Roalds, we think are of interest
to the community. They provide a glimpse, a small one, of
the decisions people make in the reviewing process, a
human dimension of our microsociety that generally remains
obscure both to outsiders and to our own students when
they begin. We present the three opinions as Appendix A to
this paper.2
Our Differences, On the Record
That Santiago did not review our paper did not mean he
agreed with it. Far from it. A spirited debate followed, both
before the Mealli, Ienco, Poduska, and Hoffmann paper was
published in early 2008 and after, up to the day this paper is
written. To orient the reader, we begin by summarizing the
different interpretations of the electronic structure of A.
The viewpoint of Santiago, expressed in his original JACS
paper,[2]
is outlined first. Then, the related part of the manuscript
produced by Roald, Carlo, and co-workers is faithfully
reported as it eventually appeared in Angewandte Chemie.[5]
Santiago: The molecular ion A has interesting similarities
with the Cuz catalytic site of nitrous oxide reductase, a tetracopper
cluster with a tetrahedral m4-sulfido bridge.[6]
The
Cu3S portion of Cuz resembles half of A, with almost identical
CuÀS and CuÀN bond lengths. It is precisely what we
perceived as two uncoupled sulfide ions that made Tolman
propose it as a model for the Cuz site.
Another aspect that seemed to us consistent with the absence
of an SÀS bond in A and the resulting assignment of
the CuII
2CuIII
oxidation states was the apparent “switching
off” of SÀS bonding on going from a related dinuclear Cu2S2
compound to the trinuclear A. When a parent mononuclear
complex [L2CuACHTUNGTRENNUNG(NCMe)] is allowed to react with sulfur, two
different products are obtained, depending on the charge
and steric bulk of L. With neutral and less bulky ligands, A
is produced, having a long SÀS distance of 2.70 Š. However,
if an anionic and relatively sterically congested bidentate
ligand is present, a dinuclear compound B forms by the
same reaction, giving an SÀS bond (1.97–2.30 Š). Thus, it
seems that trimerization triggers an internal electron transfer
to the S2
2À
unit of the dimer B (which is assumed to
form first), reducing it to two S2À
ions.
The {Cu3S2}3+
group in A presents two unpaired electrons
and is highly symmetric (D3h), with the three copper atoms
appearing as equivalent both in the crystal structure and
from the hyperfine coupling with the copper nuclear spin
seen in the EPR spectrum. Consistently, our calculations
showed the two unpaired electrons to occupy two degenerate
molecular orbitals composed of the three x2
–y2
type orbitals
with admixture of the p* orbitals of the S2 unit delocalized
over the three copper atoms (2e’’ in Figure 1). A related
{Cu3O2}3+
core[7]
shown in C,3
also with a triplet
ground state, is asymmetric with localized CuII
2CuIII
oxidation
states. We could explain such a difference as due to a
reversal of the 2e’’ and 3a2’’ orbitals and the ensuing Jahn–
Teller effect (Figure 1). Therefore, to us both A and C
should be ascribed the formal oxidation state CuII
2CuIII
, and
they differ in the localized or delocalized character of the
mixed valence Cu3 core, as well as in the presence or absence
of a Jahn–Teller effect, both associated with the difference
in electronic structures shown in Figure 1. It must be
stressed that for the oxygen derivative C, with OÀO at
2.36 Š, no one would claim a bond.
Carlo and Roald: We think there is SÀS bonding in A. Here
is the reasoning in our paper as published. Nothing is linear
in the real world, and it must be admitted that the original
version of the paper, sent to both the journal and Santiago,
has been somewhat modified in this final product, following
the intervening exchange of ideas that we had with Santia-
go:
It has been proposed that the trigonal-bipyramidal Cu3S2
core of A contains uncoupled S2À
ions and consequently a
CuII
2CuIII
configuration of the metals. Our previous consider-
2
The reader less interested in chemistry than in struggles among chemists
and ethical questions in the refereeing process might at this point
just skip to the two Appendices of this paper.
3
Interestingly, the deformation manifests itself in the CuÀO distances,
given in C; this view emphasizes how similar the structures are other-
wise.
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S. Alvarez, R. Hoffmann, C. Mealli
ations [earlier in this paper] on the S2
2À
/2S2À
dichotomy lead
us to reexamine this assignment, and suggest that, on balance,
the sulfur atoms are coupled in A.
The diagram in Figure 2 shows that the levels 2a2’’ (populated)
and 3a2’’ (empty) are the bonding and antibonding
combinations between in-phase metal dp orbitals and the S2
s* level, respectively. The e’’ set in-between with two unpaired
electrons is CuÀS antibonding, as reflected by the
weakened CuÀS bonds.
We think there is SÀS bonding in this molecule. To establish
this point, we focus on the population of the s* FMO
(fragment molecular orbital) of the diatomic fragment (see
Figure 2). As a calibration, we looked at dimers of the type
[(PR3)2PtACHTUNGTRENNUNG(m-S)2PtACHTUNGTRENNUNG(PR3)2], which unequivocally combine
single sulfide bridges, not bonded to each other, and d8
ions.
In these compounds, the s* population is large (about 65%)
even when the SÀS distance is fixed as short as 2.7 Š. Similar
trends were found for selected trinuclear clusters such as
[{(PR3)2Co}3ACHTUNGTRENNUNG(m3-S)2ACHTUNGTRENNUNG(m2-SH)2ACHTUNGTRENNUNG(m2-PR2)]2+
which clearly contains
uncoupled sulfide-capping ligands.
In A, at the equilibrium S···S separation of 2.7 Š, the population
of s* is 33% and the value drops to <10% for S···S
2.3 Š. Only for S···S> 3.0 Š does the population of s*
reach 60%, a level at which reduction of S2
2À
to 2S2À
makes
sense as an idealized interpretation. Further support for S2
coupling comes from the computational result that for simpler
ligands on each Cu center (two ammonia molecules),
the SÀS distance falls to 2.2 Š.[5]
Terms for Making It a Fair Fight
Roald, Santiago, Carlo: Dozens of e-mails wended their way
between Firenze, Barcelona, Ithaca, and the many places
the protagonists found themselves traveling to, both before
and after the paper was published. We do not give the
actual historical account of the debate, which was fraught,
as any human action is, with many digressions. Instead we
proceed as follows: we describe the essential points that we
agree upon, and then argue out our disagreements (and oh,
do they still remain!). And no, not immediately in the heat
of the exchanges did we identify our common ground: this
only occurred after much correspondence and also when we
literally met on common ground in Barcelona.
Here are the things that we agree on: First, and most importantly,
we concur that nobody can win this debate simply
by performing the most powerful, state-of-the-art density
functional theory (DFT) calculation possible for this specific
system. Even as we do rely heavily on this useful quantummechanical
computational method. We want more than
numbers; we want understanding of chemically meaningful
trends, which is essential for suggesting geometries and electronic
states of as-yet-unmade molecules.
To get this qualitative understanding, we see the following
factors as important in this Cu3S2 system (and for many organometallic
molecules as well):
a) The nature of the metal M, the ligands L, and the capping
atoms X.
b) The symmetry of the system (D3h or distorted).
c) The geometries at L2MX2—locally “square planar” or
“tetrahedral” are the possible extremes (implying torsion
of the L2M rotor with respect to MX2). Also, the L-M-L
angle turns out to be important.
d) The X···X and MÀX separations. With only two geometrical
parameters free in the trigonal-bipyramid geometry
of the Cu3S2 core, there are implicit relationships between
MÀX, X···X or M···M separations and X-M-X or
M-X-M angles.
e) The total charge on the system, or the electron count.
An oxidation state or d-electron count assignment at
each metal may follow, subject to assumptions on how
ligand electrons are counted (a matter on which reasonable
people differ).
We can also play with these factors computationally, testing
the “limits” of the simplistic categories of bond/no-bond,
as well as to propose new molecules that could further support
or deny our hypotheses about the presence or absence
of an SÀS bond.
Out of the factors specified above, we agree that one is
particularly important in our discussion: oxidation states.
One group views the copper cluster A as having no bond
between two formal S2À
, which indicates a CuII
2CuIII
oxidation
state of the metals. The other group views the very
same molecule as having an SÀS bond (i.e. 2S2À
have been
Figure 2. Frontier MOs in complex A with a D3h Cu3S2 core.
Figure 1. Comparison of the energy ordering and occupation of the molecular
orbitals built up from x2
Ày2
copper atomic orbitals in the
{Cu3O2}3+
(C, left) and {Cu3S2}3+
(A, right) clusters.
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ESSAY
Chemical Bonding
oxidized to S2
2À
) and having a CuII
2CuI
oxidation state of
the metals.
Although we may disagree about the copper oxidation
states, we do agree that oxidation states are a convenient
way to keep track of electrons in a chemistry that is often
tunable and tuned by redox processes. We concur that oxidation
states certainly do not describe real charges on a
metal/ion, however those “real” charges are measured or
theoretically estimated.[8]
Moreover, we also think that the
oxidation state formalism is an extreme which could serve
as a valence-bond starting point for a good calculation. So
the best description of the ground state of A is no doubt a
mixture of the two configurations cited. We are really arguing
about which is the dominant configuration, realizing the
truth will fall in-between.
Another point of agreement is about a general orbital diagram,
given in Figure 3, which summarizes much information
that we need for our discussion on [(ML2)3ACHTUNGTRENNUNG(m-X)2] molecules.
It draws out schematically the six molecular orbitals
that carry MÀX bonding character, together with their antibonding
counterparts, and the occupation shown corresponds
to the case of the Tolman complex [(CuL2)3ACHTUNGTRENNUNG(m-S)2]3+
.
We show only one of the two e-type orbitals in the interest
of conserving space: the combinations not shown involve
the sulfur p orbitals perpendicular to the plane of the page.
The energies of these orbitals will vary with M and L in
predictable ways; for instance the levels will be lower in
energy for M=Cu than for M=Ni, two cases of interest to
us, but also for a higher oxidation state of the same metal.
The L-M-L angle and the X···X distance will affect especially
the energy of the crucial a2’’ orbitals, as well as their composition.
In particular, the relative weight of the metal d
and bridging atom pz orbitals in 2a2’’ and 3a2’’ varies in-between
the two extremes shown in Figure 4, depending on
the factors just commented on.
Let the Jousting Begin
In spite of the common ground that we eventually reached,
there remain major conceptual differences among us. In this
section, Santiago presents arguments in support of his case;
a rebuttal from Carlo and Roald, speaking separately,
ensues. There is always the question in any debate as to who
gets the last word. But, since we’re friends here, and Roald
and Carlo are too verbose in stating their positions,4
it
seems fair to give Santiago the last (well, maybe) word.
Santiago: Here are the essential points of my disagreement
with Roald and Carlos conclusions.
During the discussion with Roald and Carlo on the submitted
version of their paper, I admitted that the bonding in
the Cu3S2 core is highly covalent and probably neither the
CuII
2CuIII
configuration proposed by us nor the CuII
2CuI
alternative
is an accurate definition of its electronic structure.
However, I pointed out two structural aspects that seemed
to me inconsistent with their model with an SÀS bond and
the corresponding CuII
2CuI
formal oxidation states. I will
number my points so as to make it easier for Carlo and
Roald to respond:
[1] I did not think that the CuI
formulation is in keeping
with the square planar environment of the three copper
atoms in Tolmans compound. We would expect a four-coordinate
copper(I) atom to have a tetrahedral coordination
sphere. My concern somehow permeated into the final version
of their manuscript, reproduced as follows:
Figure 3. Qualitative diagram for the MOs in a M3X2 complex that enter
the discussion. The occupation shown corresponds to compound A.
Figure 4. Factors that may favor localization or delocalization of the
M3X2 MOs of a2’’ symmetry.
4
and Roald gets the last word too much anyway.
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S. Alvarez, R. Hoffmann, C. Mealli
As always, the metal oxidation state and configuration assignments
are an idealization of the actual delocalized bonding
situation. Our view, that the sulfurs in A are coupled and
the Cu oxidation states are closer to CuII
2CuI
than to
CuII
2CuIII
, does face an apparent problem—the square-planar
coordination at the coppers is maintained, and that is certainly
more typical of CuIII
than CuII
or CuI
. A suggestion of how
this may be rationalized is given in the Supporting Informa-
tion.
The real situation also may be less dichotomous. An extended
Hückel Walsh diagram for A (see SI), constructed by
varying the S···S separation from 2.2 to 3.1 Š, shows signs of
an avoided crossing between the levels 3a2’’ and 2a2’’ at about
2.7–2.8 Š. The corresponding orbital mixing is likely the
mechanism by which the electrons in 2a2’’ are transferred
from the metals to the sulfur atoms. That avoided crossing is
also an indication that a multiconfigurational computation
(which we have not yet attempted) might yield a description
that melds both metal configurational assignments.[5]
[2] The sulfur–sulfur distance was to me too long to be
considered a bonding distance. I went to the Cambridge
Structural Database (CSD)[9]
for an overview and found that
the distance between two sulfur atoms supported by two or
three transition metals presented the bimodal distribution
shown in Figure 5. To me, the experimental distribution of
over one thousand sulfur–sulfur distances clearly distinguishes
those compounds with SÀS bond and distances
shorter than 2.30 Š from those with non-bonded S···S distances
larger than 2.58 Š. The distance in compound A (2.7 Š
experimentally, 2.6 Š in our DFT calculations) clearly belongs
to the second group. Such a bimodal distribution with
a gap between the two maxima, I argued, is the signature of
two distinct minima in the potential energy surface separated
by an energy barrier, according to the structural correlation
principle postulated by Dunitz and Bürgi.[10]
A comparison
of calculated potential energy surfaces and the stereochemistry
of metal atoms in four-coordinate complexes recently
carried out in our group[11]
nicely shows the correspondence
between potential energy minima and structural
distribution maxima.
At some point during our exchange of E-mails, my friends
claimed that I was getting “into two positions which don’t
seem to be ultimately very chemical—one is not allowing
the community partial bonding; the other is on focusing on
bond lengths only”. Their argument was that carbon–carbon
bonds in p-bonded olefin complexes do present a wide variety
of bond distances, even very long ones. Similarly, they
said, the dihydrogen complexes show a continuous variation
between bonds and non bonds. I provided them with more
structural statistics, showing that in those two cases there is
a single peak in the distribution of the distances (the histogram
for dihydrido/dihydrogen complexes is shown in
Figure 5), in contrast with the two distinct peaks found for
sulfur–sulfur distances suported by metal atoms.
Besides the two points of disagreement associated with
geometrical bonding parameters, I also had conceptual reasons
for viewing their assignment of a formal sulfur–sulfur
bond as objectionable.
[3] Considering the population of the s* orbital of the S2
fragment as a criterion for the existence or not of an XÀX
bond is a quantitative approach that establishes a sharp
border between bond and non bond and will always be
questionable: one can ask why a population of, say, 0.45
electrons means no bond and 0.35 means bond? Adopting
such a criterion would leave us without arguments to predict
beforehand the existence of a bond from qualitative criteria
such as Lewis structures or electron counting. Moreover,
what we admit as a criterion for the existence of a s bond is
the difference in population between the bonding and antibonding
orbitals, not just the population of s*.
[4] From my previous studies on the slightly simpler M2X2
cores I was convinced that for a particular M3X2 compound
there are two neatly different geometries possible, one with
a long and one with a short X···X distance, and that they
can be switched by appropriate tuning of the electron count
(i.e., by a redox reaction). To illustrate this concept, Rosa
and Gabriel calculated two hypothetical
nickel compounds
analogous to the Tolman
copper cluster, but with two and
four less electrons, [(L2Ni)3S2]2+
and [(L2Ni)3S2]4+
.[12]
According to our qualitative
reasoning based on the orbital
diagram of Figure 3, we predicted
them to represent the
long/short distance dichotomy,
and calculations confirmed
that the S2 unit is stretched in
the first case to 2.87 Š, but
squeezed to a short 2.26 Š
upon two-electron oxidation.
[5] The coordination geometry
of the S atoms in A presents
four bonds in the same
Figure 5. Distribution of the sulfur–sulfur distances in M2S2 and M3S2 cores (left) and of the hydrogen–hydrogen
distances between two neighboring hydrogen atoms bonded to a transition metal (right), retrieved from
the CSD
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Chemical Bonding
region of space and none in the opposite direction. I tend to
think, maybe in a simple minded way, that sulfur makes use
of sp3
hybrid orbitals for bonding and therefore there
cannot be four two-electron bonds stemming from each S
atom in A, but one should rather invoke delocalized bonding
involving simultaneously the three metals and the opposing
sulfur atom. During the discussion Roald pointed out
that there is nothing wrong with having such a bonding pattern
and referred to the topologically analogous
[1.1.1]propellane, D.[13,14]
I argue that the four short carbon distances from an
apical carbon are not two-electron bonds, but a delocalized
description of the bonding in that molecule is required, that
includes occupation of an outward-pointing lone pair at the
apical atoms and only three sp3
hybrids of each bridgehead
carbon atom can be used to form its four CÀC “bonds”. The
presence of those lone pairs has been substantiated recently
through an analysis of the electron localization function.[15]
Carlo: I respond here to points [1], [2], and [4] raised by
Santiago and leave it to Roald to comment on the other ob-
jections.
[1] Your expectation of a tetrahedral geometry for a d10
ML4 molecule makes sense in our usual way of thinking in
inorganic chemistry. But there are situations (I believe the
present L6Cu3S2
3+
system is one such) where the metal–
ligand bonding is different, allowing a square-planar, fourcoordinate
d10
complex.5
This situation occurs when the sdonor
function of a ligand lies much higher in energy than
any d metal orbital. It then makes sense—in a bonding picture
based on perturbation theory—to assign one bonding
electron pair (a high-lying one, originally viewed as belonging
to the ligand) to x2
Ày2
. In this case, the ligand is such a
strong base that it is better seen as an acid. The M!L donation
does not change the coordination geometry, but the
metal can be formulated as d10
rather than d8
.
This is an old question in organometallic chemistry—
should one describe all ligands as Lewis bases, even if the
obvious acidity of some ligand molecules such as BR3 or
SnR3 clearly disfavors the anionic formulation?[18]
The relative
energies and overlaps of the interacting M and L orbitals
help to frame viewpoints bridging the “this ligand is a
base” and “this ligand is an acid” dichotomy. This is what
we attempted to do with the Tolmans compound A.
The proposal for such an “inverted” assignment of electrons
is not novel, especially for copper. An admittedly controversial
instance is Snyders suggestion[19,20]
that, in planar
[CuACHTUNGTRENNUNG(CF3)4]À
, a CuI
metal is bound to one CF3
+
and three
CF3
À
ions, in an averaged VB picture with four equivalent
resonance structures. In MO terms (see E), in this molecule
a ligand combination of four carbon s hybrids (antibonding
b1g) lies about 35 kcalmolÀ1
higher than x2
Ày2
(in an extended
Hückel (eH) calculation). Thus, the electron assignment
depends both on the particular set of ligands and metal
nature, copper being almost unique for combining low
energy and highly contracted d orbitals.
In contrast to Snyders view, common chemical intuition
favors CuIII
in square-planar [CuACHTUNGTRENNUNG(CF3)4]À
; in fact, the CuI
proposal was fiercely criticized by Kaupp and von Schner-
ing.[20]
The direction of the Cu–C electron flow is to some
degree a semantic problem, but to me a d10
(rather than d8
)
metal seems reasonable as a starting point. Analogously, in
compounds of type A there is a similar relationship between
the a2’’ metal combination of the x2
Ày2
-type orbitals and the
S2 s* combination of the same symmetry (see Figure 4).
Due to the diffuseness of the sulfur orbitals, s* is very sensitive
to the SÀS distance and, for values of about 2.65–
2.70 Š, it lies again (a coincidence) ca. 35 kcalmolÀ1
higher
than the Cu orbital (eH). For this reason, the proposed assignment
of the bonding electrons to copper has its own
logic. Also, I saw an analogy with the MÀh2
H2 interaction
involving H2 s*; that in turn led to a disagreement between
me and Roald (see Appendix B).
To help us understand the subtle role played by the a2’’ orbitals
in A (see Figure 4), the eH Walsh diagram of Figure 6
shows the frontier orbital variations on elongating SÀS, and
suggests a mechanism for inner electron transfer. Irrespective
of the intermediate energy of the singly populated e’’
frontier orbitals (refer to Figure 2), there is evidence for an
“avoided crossing” between the MOs 2a2’’ and 3a2’’, which
both carry SÀS antibonding but CuÀS bonding and antibonding
characters, respectively. The bonding character is
gradually switched between the two levels in question.
5
There are some known examples of square-planar, 18-electron, d10
metal
complexes (e.g. the AgI
complexes such as [AgACHTUNGTRENNUNG(olefin)4]+
,[16]
and
the compounds referenced in a review.[17]
In these the bonding and antibonding
combinations of the metal x2
Ày2
and the b1g ligand MO are
likely to be both filled, a net repulsive interaction on top of three
metal–ligand bonding ones. The metal pz, an alternative place for the
last electrons, is high in energy.
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S. Alvarez, R. Hoffmann, C. Mealli
Around 2.7 Š, the metal and sulfur weights are similar, but
over 3 Š the sulfide character prevails in 2a2’’. At this point,
the geometry is already far from any experimental and/or
optimized one.
[2] Your CSD histogram of Figure 5 is illuminating, showing
that no SÀS bond of 2.30–2.58 Š has been experimentally
found in the M3X2 and M2X2 families. I feel that the absence
of such examples is not definitive proof of only two
possibilities: S2
2À
or 2S2À
. I would like to propose one way
that this SÀS distance gap could be closed: computationally,
for now, and perhaps experimentally in the future. Andrea
and I have noticed that differently tailored nitrogen ligands
affect the opening of the N-M-N angles and in turn the SÀS
distance in [L6Cu3S2]3+
compounds. First, we carried out a
series of full and partial DFT optimizations (all triplets) for
the model compound [(NH3)6Cu3S2]3+
, with single amine
donors. This fully optimized all ammonia model has a short
SÀS distance of 2.21 Š and larger N-Cu-N angles of 1018.
We had a hunch that the N-Cu-N angle might have a governing
role in SÀS coupling, so we systematically optimized
the structures at different fixed N-Cu-N angles. The results
are shown graphically in Figure 7. As the angle gradually
changes, so does the SÀS distance. Also, the PES is rather
flat; the largest energy difference with respect to the fully
optimized structure is at most 6.5 kcalmolÀ1
as the N-Cu-N
angles vary between 858 and 1108. The corresponding s* S2
population ranges smoothly
between 25% (at 858) and 2%
(at 1108).
We have actually designed
other, more realistic chelates
(the results to be fully reported
elsewhere) that create, within
the [(L2)3Cu3S2]3+
system, compounds
falling in both the
shorter and larger SÀS range
but also in the “SÀS empty
zone” of the histogram in
Figure 5. As an example, the
structure of [(NH=CHÀCH2À
CH2ÀCH=NH)3Cu3S2]3+
(see
Figure 8) optimizes as a minimum
with the N-Cu-N angles
of 978 and the “intermediate”
SÀS distance of 2.52 Š (s*
population=19%).
If we believe the DFT calculations,
the 2d9
d10
configuration
and a disulfide ligand are appropriate
for free ammonias
(at large N-Cu-N angles), or
other chelates allowing an
even larger bite than that
shown in Figure 8. Far from
being tetrahedral, the reduced
metal structure is most close to
a trigonal planar one, as in d10
[L2MACHTUNGTRENNUNG(h2
-H2)] complexes.
Also for this reason, I continue to imagine an SÀS bond persisting
up to distances around 2.7 Š as in A, while a major
discontinuity would occur with an actual 2eÀ
oxidation of
the metals and the definite separation of the capping sulfide
anions (this is never observed, either experimentally and/or
computationally). Obviously, a planar d10
metal would be indefensible
in presence of discrete sulfido capping ligands.
[4] I find thought-provoking your optimization of a stable
[L6Ni3ACHTUNGTRENNUNG(m-S2)]4+
upon 2eÀ
oxidation of its dicationic precurFigure
6. Walsh Diagram (constructed with the eH package Cacao[21]
) for elongating the SÀS distance while
keeping fixed the CuÀS ones (2.23 Š). The eH total energy (dashed line) minimizes close to the experimental
structure and its full scale range is 70 meV.
Figure 7. The SÀS distance (optimized) as a function of N-Cu-N angle
(fixed) in the model complex [(NH3)6Cu3S2]3+
.
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ESSAY
Chemical Bonding
sor.6
The dramatic shortening of the S-S distance to 2.26 Š
confirms how prone these TBP frameworks are to various
internal or external redox processes involving coupling (or
decoupling) between all the vertices. We construct elsewhere
a general relation between equatorial, apical and interaxial
bonding in TBP compounds formed by main group
elements alone, or containing three equatorial metals, over
a wide range of skeletal electron counts.[22]
Here, I only wish
to remark how interaxial and skeletal bonding may correlate
for a given electronic structure of the M3X2 skeleton. In the
context of Figure 3 and 6, we see that in Ni3S2 compounds
the 2e’’ level is invariably depopulated. The SÀS s* 2a2’’
level is the HOMO of [L6Ni3ACHTUNGTRENNUNG(m-S2)]2+
but the LUMO of
[L6Ni3ACHTUNGTRENNUNG(m-S2)]4+
(and there is a significantly large HOMO–
LUMO gap also in this latter compound). The gap increases
with the amount of SÀS s* character in 2a2’’ when SÀS is
shortened. At the same time, this 2a2’’ level is also M3ÀS2
bonding and its depopulation causes a generalized elongation
of the NiÀS bonds.
An essential aspect of the Ni tetracation (highlighted by
an eH FMO analysis) is that, after the two-electron oxidation,
the NiÀS bonding which arises from a2’’ symmetry interactions
is not totally cancelled. In fact, the low lying S2
lone pair (1a2’’ MO in Figure 4) does not remain inert but
donates to the metals. Therefore, the donor capabilities of
S2
2À
are not limited to only four lone pairs, as it might be assumed
in a first approximation. A similar feature is also
found in the C5H6 propellane[13]
(already mentioned by you,
D) with one axial and six peripheral CÀC bonds. Here
again, a low-lying a2’’ level, externally hybridized with the
carbon 2s orbitals, must contribute to the six peripheral
CÀC bonds.
An additional point: I wish to make a final comment on one
of your initial statements, Santiago, in which you proposed
very similar electronic structures for the known Cu3O2
[7]
and
Cu3S2 compounds and their equal CuII
2CuIII
configuration.
In the Cu3O2 complex C, with no three-fold symmetry as a
consequence of a Jahn–Teller distortion, one metal is more
strongly bound to the two apical atoms (the corresponding
CuÀO distances are about 0.2 Š shorter than the others).
Moreover, the O···O separation is only 0.34 Š shorter than
the sum of the dianionic oxo radii. In contrast, the corresponding
difference in Cu3S2 is as large as 1 Š, and, as discussed,
the relatively stronger S···S interaction has implications
for potentially different oxidation states of the elements.
Also significantly, the sulfur system does not show
any pair of stronger MÀX bonds at a single metal atom that
would mark its d8
square-planar coordination. The MÀX
and XÀX distance are mutually dependent, so I infer that
the electronic structure of Cu3S2 is rather different from the
generalized 2X2
2À
and CuII
2CuIII
formulation. This is instead
the only possibility for Cu3O2.
Roald: [1]: I personally think Santiago has a point when one
looks at the totality of transition-metal chemistry. Molecule
A is a special, high-symmetry situation, and I could do some
hand-waving around that, but in the end, the absence of tetrahedral
distortion or twisting toward it troubles me. Not
that there aren’t a number of square-planar d10
complexes,
for instance of AgI
, which Carlo mentioned. I think it would
be fun to design some ligands that sterically allow, or even
favor, tetrahedral geometries at Cu.
[2] Santiagos CSD-based histogram is impressive. My
outlook is based on a nose for the unusual (looking too
much for perversion?): I think the distances that are in-between—neither
a full bond, nor no bond—are the interesting
ones. I also believe deeply in a continuity of chemistry—
SÀS bonding is there (or is not there, or is partially there)
whether one is looking at organic, main-group inorganic, or
transition-metal or solid-state chemistry. I also have to confess
to an antipathy to either-or attitudes or dichotomiza-
tions.
Early on I encountered partial SÀS bonding in thiothiophthenes
(trithiapentalenes), understandable as electron-rich
three-center bonding systems. Compound F[23]
is a representative
structure of this class, showing asymmetric SÀS bond
distances of 2.18 and 2.52 Š, which differ from the typical
SÀS distances in the symmetrical thiothiophthenes (2.31–
2.36 Š). The whole range of Santiagos gap is covered by a
goodly number of these compounds traversing a classical
Bürgi–Dunitz hyperbola.
Figure 8. The optimized structure of the model trication [(NH=CHÀ
CH2ÀCH2ÀCH=NH)3Cu3S2]3+
with an SÀS distance about 0.13–0.20 Š
shorter than in the experimental analogues known to date.[2,3]
6
In about ten structures of the type [L6Ni3S2]2+
, which are present in the
CSD files,[12]
the SÀS distance varies as much as 2.67–2.95 Š, the smaller
values being similar to those of the known [L6Cu3S2]3+
complexes.
Nonetheless, no comparable SÀS bonding can be invoked in this case,
since the SÀS s* population remains at least twice as large as we cited
for the Cu case, due to the higher energies of the Ni orbitals.
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S. Alvarez, R. Hoffmann, C. Mealli
Another example of partial SÀS bonding, falling on the
border of that gap in Santiagos diagram, is found in S4N4
and related compounds, shown in G.[24]
Santiago looks at his histogram (Figure 5), sees a dearth
of compounds with S···S contacts between 2.15 and 2.85 Š,
and a real gap between 2.30 and 2.58 Š, a gap that he interprets
as a region that separates bond from no-bond. I look
at the overall picture and focus on the few structures in the
2.15–2.85 Š interval. I remember (vaguely at first, then led
to the work by J. K. Bashkin) a discussion I had once with
Ed Stiefel around two of these, 2.73–2.8 Š.[25]
Stiefel noticed
the anomalous distances, agonized over them, came to a
conclusion of partial disulfide bond formation, I had and
have no troubles conceiving of a partial SÀS bond for two
sulfurs separated by 2.6 Š.
Let me put it another way, as provocatively as I can. Had
Santiago in hand that CSD histogram when he calculated
the S···S separation in compound A, he might have sat up
and said, “Hey, thats a very untypical SÀS separation, right
on the border of the gap in my histogram. Is the structure
wrong? Can’t the sulfurs get further apart, while remaining
bonded to the coppers? Or, maybe, just maybe, the structure
is giving us a big clue to something interesting going
on?”
[3] I think to establish bonding between a pair of atoms
one should look in principle at the population of all the orbitals
of the underlying coordinated diatomic. This is because
bonding can be weakened by depopulation of bonding
orbitals or population of antibonding ones—and even the
so-called lone pairs are weakly bonding or antibonding. But
as we have learned for coordinated H2 or C2H4 or CO, it appears
that population of s* (p* in the case of C2H4 and CO)
does the most damage to bonding.
My experience, rooted in my respect for chemical tradition
and the rudiments of political psychology (learned
mainly by teaching introductory chemistry), is that if you
propose something seemingly weird (an S2 threading a Cu3
ring?), tread gently. Try to validate your criterion (and so
get people to accept it) by looking first at cases where there
is general community agreement.
Heres something everyone will agree on: when two S2À
ions interact, there is no bond. When two neutral S atoms or
two SÀ
ions interact, there will be a bond. Thats for isolated
atoms—when two S atoms/ions are incorporated into a molecule,
the occupation numbers of s and s* FMOs will not
be 2 or 0; there will be some donation out of s and acceptance
of electrons into s*.
How much? Lets take a molecule where everyone agrees
(because of the history of inorganic chemistry, and its consistent
with so much else) that there is no effective S···S
bond. These would be the locally square-planar d8
–d8
[L2MACHTUNGTRENNUNG(m2-S)2ML2]
complexes. They are a major contributor to Santiagos
CSD graph. Heres a typical one: [(PPh2Pyr)2PtACHTUNGTRENNUNG(mS)]2,
with a S···S separation of 3.01 Š.[26]
In an eH calculation
with PH3 ligands, s* is populated at 75% (1.5 elec-
trons).7
We now have an operational definition of “large”
population of s* in a real molecule without an SÀS bond.
Now lets take a simple amine (L=NH3) model of compound
A, whose DFT-optimized structure turns out to have
SÀS short, 2.21 Š. Its not (yet) a real molecule, but no one
would question the SÀS bond at that distance. Here s* is
only 7% occupied.
If we do a calculation on the Cu3S2 compound A, at its experimental
distance of 2.72 Š, the S···S s* occupation is
39%.8
Its intermediate between 0 and 100%, but we think
that this is closer to the bonded model cited above. The s
orbitals remain largely occupied.9
[5] Propellane is a strange molecule for sure—I continue
to be amazed that it exists.
There are other examples of all four bonds to a main
group element atom lying in one hemisphere: SF4 is one,
but it is hypervalent, and the deformation different from the
one in A. There are square-pyramidal, four-coordinate bromide
complexes, and pentagonal pyramidal iodides of
CuI
.[29]
There is a horde of CaAl2Si2 structures[30]
(H) these
have Al2Si2
2À
two-dimensional layers, “electron-precise” in
the sense of each atom in the layer having four electrons
formally, and being four-coordinate. But one of the atoms is
quasi-tetrahedral, while the other is umbrella-shaped.
Closer to A and {Ni3S2}2+
compounds cited are the remarkable
Huttner complexes, [E2{W(CO)5}3], E=As, Bi,
Sb,[31]
structure I. Each retains short multiple EÀE bonds
while having the E2 dumbbell coordinated to three organometallic
fragments.
Another point: Quantum theory of atoms in molecules
(QTAIM) analyses of bonding are quite popular these days.
Santiago carried out such an analysis on compound A, find-
7
In our published paper, reproduced above, we used a [(Ph3P)4Pt2S2]
model,[27]
and reported 65% for the s* population. Subsequently, we realized
that there are serious problems with the correctness of this reported
structure[28]
which is why we switched here to a different model.
8
In our published paper, we wrote 33%. This number came from an calculation
on a [(NH3)6Cu3S2]3+
model with an imposed SÀS distance of
2.70 Š. A calculation on the A geometry as reported gives 39% occupation
of s*; a calculation on a theoretically optimized geometry
(CuÀS and CuÀN both elongated about 4% relative to the crystal structure)
gives 27% occupation of s*.
9
The “lone pairs” are not very well-developed at this separation—so the
SÀS s bonding is distributed among 1sg, mainly S 3s, and 2sg, mainly S
3p. The population of 1sg in A is 84%, of 2sg 97%. The antibonding
1su combination is 94% occupied. These are all eH results.
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ESSAY
Chemical Bonding
ing a bond critical point between the sulfurs. It might seem
that this would support Carlos and my point of view, that
there is an SÀS bond. Carlo tries to believe it, but as far as I
am concerned, “Thanks, but no, thanks.” Bond critical
points are a consequence of the topology of electron density—there
is a bond critical point between two S atoms in S2
for sure, but I bet there is also one between two S2À
ions approaching.
There are 60 bond critical points[32]
between He
and the 60 carbons of He@C60.10
In my opinion, the existence
of a bond critical point is not a criterion for bonding.
Santiagos Final Rebuttal: [1] Roald mentioned the possibility
of designing ligands that would favor the tetrahedral geometries
at Cu. Han et al.[34]
had actually prepared one such
compound with three tetrahedral copper(I) ions linked by
peripheral bridging bis(diphenyl-phosphino)amine ligands
with two triple bridging hydrosulfide ions at a very long
S···S distance (3.48 Š). This compound, however, has four
more valence electrons in the Cu3S2 skeleton than Tolmans
complex A. But we have now two variables to play with, the
electron count and the orientation of the ligands. I wouldn’t
be surprised if somebody comes up with a compound with
tetrahedrally coordinated copper atoms and a short S-S distance.
According to our framework electron counting
rules[33]
we would expect this to happen for a Cu3S2
+
core.
I don’t think the [AgACHTUNGTRENNUNG(olefin)4]+
complex you mention[16]
makes a good case for a d10
square planar stereochemistry in
general, because there the four olefin groups are rigidly
held in the same plane by four cyclohexyl bridges, making
the tetrahedral geometry impossible.11
If that constraint is
removed, as in [AgACHTUNGTRENNUNG(cod)2]+
, the coordination around the
silver atom is tetrahedral.[35]
But yes, one can find several
square planar structures of CuI
and AgI
complexes in the
Cambridge database. Many of those are special in several
respects: some have tetradentate ligands with a planar topology,
some others are in fact two coordinate with two
donor atoms held at longer distances in multidentate ligands,
while nearly half of them could be considered as sixcoordinated
because of the presence of short metal-counterion
distances. Nevertheless, there are still some whose
square-planar geometry is not easy to explain and may be
worthy of a deeper theoretical study.
We have intensely debated in private conversations Snyders
proposal of a CuI
oxidation state in [CuACHTUNGTRENNUNG(CF3)4]À
, but I
will not reproduce my arguments here because it represents
a different problem. In this mononuclear complex, what
Snyder proposed and Carlo supports is that it should be formulated
as composed of a CuI
ion and a {(CF3)4}2À
set of ligands,
at difference with the “classical” formulation as CuIII
and {(CF3)4}4À
. But no matter how you look at it, the total
number of valence electrons for the central ion is sixteen.
What we generally predict is that a four-coordinate, sixteenelectron
complex should be square planar, while an eighteen-electron
one should be tetrahedral. As a sequel of this
debate, we have considered [CuACHTUNGTRENNUNG(CF3)4]À
in the wider context
of families of complexes with different oxidation states and
donor atoms of varying electronegativities, and published a
more detailed discussion elsewhere.[36]
The case of A is quite different in two respects. First, we
cannot apply electron counting rules to each individual
copper atom because of the strong delocalization of the
x2
Ày2
electrons (1e’’ and 2a2’’ MOs in Figure 3), except for
the two extreme oxidation states, Cu3S2
À
with all CuI
and
two sulfido bridges (equivalent to Hans compound), and
Cu3S2
7+
with all CuIII
and a disulfido bridge (isoelectronic
with the Ni3S2
4+
complex calculated by us[33]
). Between
these two extremes, one can conceive eight one-electron oxidation
steps, in most of which the formal occupation of the
copper d orbitals would be fractional. What stereochemistry
should we expect when the three copper atoms have an
average electron configuration such as d9.33
or d8.66
, as would
correspond to your and my proposals for compound A?
Honestly, I do not think we have a clear answer to this question.
The second peculiarity of A, as compared with [Cu-
ACHTUNGTRENNUNG(CF3)4]À
, is that the S2 group in the former acts as a non-innocent
ligand, and therefore alternative assignments of oxidation
states and consequent dn
configurations ensue, a
problem that is at the basis of the present debate.
[2] The effect of external bond angles on the S···S distance
found by Carlo does not surprise me, since we had previously
done similar calculations for dinuclear M2X2 cores.[37]
For
those, we found a correlation between the peripheral L-M-L
bond angle and the XÀX distance: “other things being
equal, a larger L-M-L bond angle should appear for the
molecule with an XÀX bond than for that with isolated S2À
ions”.[38]
I agree that your Figure 7 shows a continuous variation in
the SÀS distance with the L-Cu-L angles. However, when I
look at this plot, I see three regions with different slopes:
two plateaus corresponding to long and short distances, respectively,
separated by a transition zone in which the distance
changes sharply with the bond angle. That graph has
then two alternative interpretations, depending on what you
focus on, continuity or dichotomy in SÀS bonding. But you
may agree that the N-Cu-N bond angles in A, mostly imposed
by the chelating nature of the external ligands (888,
both experimentally and computationally), clearly correspond
to the region of long distances in Figure 7.
[4] One of my research goals in the past years has been to
provide a delocalized version of bonding in rhombic
[(MLn)2ACHTUNGTRENNUNG(XRy)2] systems, because in those systems the same
orbitals of the MLn and XRy fragments (n=2–4 and y=0–3)
participate simultaneously in MÀX, MÀM, and XÀX bonding.
It is therefore sensible to discuss the structural details
of the M2X2 core as a whole, based on the occupation and
10
One can move beyond the existence or absence of a bond critical
point. Santiago finds that the electron density at the SÀS and MÀS
bond critical points changes with the number of electrons. To quote
him:[33]
“This, combined with the changes in the corresponding bond
distance in Cu3S2
3+
, Ni3S2
2+
and Ni3S2
4+
, clearly shows that the SÀS
bond is weakest and MÀS strongest for Ni3S2
2+
, while SÀS is strongest
and MÀS weakest for Ni3S2
4+
, with the values for Cu3S2
3+
being inter-
mediate.”
11
The atomic coordinates of that structure were not published.
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S. Alvarez, R. Hoffmann, C. Mealli
bonding characteristics of its framework molecular orbitals.
Taking into account their bonding characteristics with respect
to those three types of interatomic interactions as well
as their occupations, we came out with simple rules that
allow us to predict the existence or not of short through-ring
MÀM or XÀX interactions.[38]
In the process of writing a report of Rosas results on A,
the present debate prompted us to extend our framework
electron counting scheme to the M3X2 cages.[33]
Accepting,
at least in part, your view point that there is some residual
SÀS bonding in A, I would stress that this is a quantitative
issue, different from what occurs when one removes four
electrons, as in the {Ni3S2}4+
complex that we have calculated.
In that case there is a qualitative change in the bonding
situation that results in a really short SÀS distance.
Some concluding thoughts: While Roald declares having an
antipathy to either-or attitudes, I believe that there are
times for dichotomy and times for continuity. I find interesting,
for instance, that the negative charge at the S2 group in
mono-, di-, and trinuclear complexes shows a monotonous
increase with the number of CuÀS bonds, whereas the SÀS
distance changes only—in an abrupt way—upon formation
of the second and sixth CuÀS bonds.[33]
I think also on spin
crossover complexes. Sometimes they change their magnetic
behavior and associated properties (such as color or metal–
ligand bond lengths) gradually as the temperature is decreased,
but some complexes undergo an abrupt change
from high spin to low spin, within a temperature interval of
only a few degrees.
Then, why have we taken so much pains to discuss whether
there is or not a sulfur–sulfur bond, to use metal oxidation
states that correspond to particular ways of localizing
the electrons, or to debate on the population of S2
xÀ
units as
if they were independent entities? I think this is the result
of our psychological need for simple naming conventions to
address complex realities, such as the bonding in the Cu3X2
molecule A. We distinguish night from day, even if there is
no discontinuity in the intensity of the light that we receive
from the sun. That does not prevent us from enjoying the
beautiful atmosphere and nuances of dawn or dusk, no
matter how hard it may be to tell day from night.
In the end, maybe this is what we are debating here. At
the sunset of the sulfur–sulfur bonding, you are pointing to
the sky, where we can still see the precise colors and shapes
of the clouds on a dark blue background. On my side, I am
looking at the valley and the western face of the moun-
tains,12
where only black silhouettes remind us of the trees
and small towns in front of us. I hope that with this debate I
made you look also at the shaded zones as much as I had to
raise my eyes to the open sky. May we all enjoy the full palette
of differently illuminated areas at twilight.
Carlo, Roald, Santiago: Basta! As the reader can see, this
spirited debate is not over. OK, what have learned?
1. The obvious—that reasonable human beings, even
people from “the same school” can differ on such a
seemingly simple question as “Is there a bond between
the two sulfurs in A?” Perhaps the lesson is not that
people disagree (for it is in our nature to do so, and that
is how science progresses) but that the concept of the
chemical bond is not simple. This would have been nothing
new to Robert Mulliken, who has a well-known
quote to that effect.13
As we said at the outset, the presence
or absence of a bond may be judged by several experimental
and theoretical criteria. What was interesting
in our discussion is how we moved from simple distance
criteria to other gauges of bonding.
2. As inorganic chemists (OK, theoreticians, we’re smiling)
we always knew that oxidation states and d-electron configurations
were a convenient fiction, even as they are of
tremendous utility in chemistry. Our initial stances in this
debate made us (all) somehow stiffen, pushing us to the
categorical “Its CuIII
ACHTUNGTRENNUNG(CuII
)2”; or “No, its CuI
ACHTUNGTRENNUNG(CuII
)2.”
Thats not where we would normally like to be, so to
speak. With time, we relaxed and saw these were extremes—and
still remained insistent that the situation
was closer to one or the other!
3. The special strength of molecular orbital thinking—composed
in our day in doses of reliable DFT and correlated
Hartree–Fock computations, in part of qualitative orbital
pictures and arguments vouched in the friendly language
of perturbation theory—is that it can bridge extremes
and allow people to talk to each other.14
This is why the
Walsh diagram of Figure 6 is important: it allows one to
see in a single graphic a continuous transition between
having almost no SÀS bonding and having much of it.
The challenge to todays DFT-inclined quantum chemistry
community is to devise a language of Walsh and interaction
diagrams that is as easy and as chemical as the eH
FMO way of thinking, but still retains the reliable aspects
of DFT.
4. The debate was productive in many ways. It made us
think through and rethink the distance criterion for
bonding. It brought together organic and inorganic
chemistry. It made us comb the literature for examples in
support of our views. It made us think about the tetrahedral–square-planar
distinction for d10
complexes in more
detail than any of us had ever done before. We thought,
we learned.
Most productive are the real, tangible, chemical suggestions
arising from this work. Some are conceptual advan-
12
I wrote this paragraph in Prullans, on June 7, 2008, facing the valley of
La Cerdanya and the impressive walls of the Cadí mountains, after a
three-day meeting on “Not Strictly Inorganic Chemistry”.
13
“I believe the chemical bond is not so simple as some people seem to
think.”
14
A reviewer remarked “I could not avoid feeling that the question
could have been resolved nicely by valence bond theory.” Were not
sure about “resolved,” but certainly VB theory can also provide the
bridging function between two extreme descriptions.
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ESSAY
Chemical Bonding
ces—we think we understand much better now the factors
that influence internal oxidative and reductive processes,
such as what one needs in ligands, metals, and geometries to
effect oxidative coupling. The work was productive in suggesting
molecules that illustrate the bonding considerations,
from [(L2Ni)3S2]4+
to the ligands designed by Carlo and
Andrea to hold a certain L-Cu-L angle. Still other experiments
that come to mind are of probing the metal oxidation
state in A by comparing its X-ray absorption spectra with
those of the non-controversial mono- and dinuclear complexes
having copper in +1 and +2 oxidation states. And it
would be interesting to test the endurance of the M3X2 skeleton
to the attack of the sulfur lone pairs by a Lewis acid.
Fundamental disagreements are frustrating. But in the
end, even as each of us seemed occasionally bereft of logic
to the other(s) (in all permutations!), the underlying feeling
was that it was important to keep arguing, because at stake
was nothing less than our understanding. That the discussion,
frustrating as it sometimes was, would teach us something
about chemical bonding (and collectively we have
been at it for decades!): this kept us writing.
We think there is something in this story for you too. And
don’t miss the Appendices; you will be amused.
Appendix A: On Reviewing or Not Reviewing Papers
Where You Have a Vital Interest
As we mentioned, when Carlo and Roalds work essentially
reassigning the formal oxidation states in the paper of
Santiago and Bill Tolman was submitted for publication, it
was quite naturally (from the editors perspective) sent to
Santiago for review. He recused him, to use a legal term.
But not everyone would have done that. Thinking that the
reasons for reviewing or not reviewing a paper might be of
interest, Roald wrote the following to both:
“Santiago, there is something interesting here, and it may
be a question that some people, young and old, would ask:
“Why not review the paper, and criticize it as strongly as you
can?” If there is a strong difference of opinion, some would
fight to prevent it being published. Others (few, I think)
would do what you did. Did you do it because it is a general
conviction of yours in such cases? Or because of some perceived
respect and an accompanying desire to avoid conflict
with me? Or something else?
What would you have done in a similar situation, Carlo?”
Here are the responses:
Santiago: Why did I have doubts about making a negative
report?
One reason is that I try to avoid being dogmatic (probably
because I have a natural tendency to dogmatize) and
admit that another colleague may have an opposing view
that is just as respectable as mine.
Second, given the special relationship I have with Roald
and the friendship with Carlo, I found it more appropriate
to give my point of view in a friendly way and leave it up to
them to decide whether to take it into account or not.
Third, it seemed to me that the discussion on the Cu3S2
system was lateral to the main topic of your paper, which
dealt with Isobes compounds. Therefore, I felt that making
a negative report would in part have been unfair, because
the Isobe story was elegantly explained.
Fourth, I felt really uncomfortable in the double role of
holding a friendly, yet uncompromising, discussion with both
Roald and Carlo and trying to make an objective report.
Finally, from my readings on the history of science, I have
come to the conclusion that important issues are sooner or
later dealt with by other researchers, and debates, such as
the one we were having, are rarely settled once and forever.
So, why should I prevent someone from publishing a view
that differs from mine, when we are dealing more with concepts
than with facts (the facts supporting my ideas were
structural data, those supporting your opposing view were
some computational results)?
Is it a general conviction of mine in such cases?
It is hard to tell, this was a very special case. Trying not to
be too indulgent with myself, maybe the best thing to do is
to recall the closest case in which I was involved. It was also
an interesting story. We (Gabriel and myself) had been
studying a complex—a polynuclear palladium molecule reported
by Chen, Shimada and Tanaka—which they proposed
as showcasing the unusual PdVI
oxidation state,[39]
because
several aspects of its molecular structure and physical properties
seemed to us inconsistent with that oxidation state.
We had concluded that the authors had overlooked the presence
of SiÀSi s-bonded ligands, which would take the
formal oxidation state to PdII
.
We were at the stage of starting to write an article with
our results when I received from Peter Gçlitz a paper on
the same compound by Chris Cramer and co-workers in
Minnesota,15
so I explained the situation to Gçlitz, telling
him that there was a potential conflict of interest and that I
better refuse to make a report on Cramers paper. But he
replied asking me to submit my paper to Angewandte
Chemie and still make the report; in correspondence, our
paper would go to Minnesota for review. Although I knew
Chris (he had been on sabbatical in Barcelona), I did not
have a close relationship with him, and I did not feel like I
could not make a negative report if I felt it appropriate.
The story ended with both papers being accepted, with
positive reports from each other and from additional referees,
and they were published side by side.[40]
In those papers,
we disproved the existence of a PdVI
oxidation state, but
demonstrated that the Japanese group had discovered instead
the first example of a Si2 group s-bonded to a transition
metal!
Was there some perceived respect and an accompanying
desire to avoid conflict with Roald?
Certainly, there is respect for someone who has been so
influential in my scientific and intellectual endeavors. But
there is also a long-standing friendship and the perception
15
Notice the coincidences with the present case: Gabriel, Peter Gçlitz, a
Japanese compound, a colleague from Minnesota.
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S. Alvarez, R. Hoffmann, C. Mealli
that I could argue with Roald without eroding our relationship.
How could I forget the topic Roald chose for his honorary
degree at our University, “The Disputation at Barcelona“?
I was sure that Roald would not feel angry if I tried to
refute some of his assertions.[41]
Carlo: I think that I would have behaved very similarly to
Santiago.
It is true that by accepting a paper to referee one should
behave as a priest in the confessional and keep the secret.
This is professional deontology and one is left alone with his
own responsibilities. But we are all humans and cannot
ignore the identity of the person(s) we are supposed to
judge. In this case, Roald must be for Santiago as he is for
me: namely the one who has greatly influenced my way of
thinking and my scientific career. Why confront the person
who is most respectful in my eyes, especially if there is an
unexpected disagreement? Maybe I am the one who is
wrong.
At that time, I felt a little unhappy with Santiago because
he seemed to reject our viewpoint. Also, I realized how unhappy
he might have been. Nobody likes contradiction of an
analysis already considered as properly done. I imagine that
these were Santiagos feelings and for this, I found Santiagos
behavior even more worthy of appreciation. While he
could feel safe as a secret referee, he proposed giving up
any judgment and let other people do it.
Another point to consider is that, in this case, the decision
to be made by Santiago was not directly harmful to a third
party. The matter is more serious in a committee that decides
on who is hired or promoted. Or in the allocation of
research funds. The judgment at hand only concerned the
quality of science to be published. The more discussed, the
better it is. Usually, when I referee papers I am critical. I
write down my viewpoint but also I explicitly leave to the
authors the option of taking my perspective into account in
their revision or not. Obviously, this applies only if something
appears controversial but not definitely wrong.
In conclusion, it has been good that eventually we have
had the possibility of publishing the ideas which later have
stimulated the present debate. After all, I am convinced that
our viewpoints are not so much divergent. There is a great
range in-between bond formation and bond breaking (especially
for a soft element as sulfur) and this is the message
that we have all learned and want to transmit.
Roald: As my initial question revealed, I was aware of the
special factor that might affect a decision on reviewing or
recusal in this case—the relationship that emerged from
working with both Santiago and Carlo, of initial mentorship
that grew into friendship with the years. In that situation, to
deal with scientific disagreements is difficult. To have the
human bond and my teaching reaffirmed by you in the way
you did is…deeply touching.
I am torn in responding to my own question. Both Santiago
and Carlo have brought up the important issue of letting
into the literature contrary views. I very much agree. Parenthetically,
for this reason I never question the decision of an
editor to publish a paper for which I have given a negative
review. I may mumble (in Russian, so few understand)
“idioty”, thats about it. The world will sort things out. This
is also why sometimes I wonder about refereeing in general,
all that effort by the community to keep out indifferent
work (not a little of that) and crank papers (a smattering),
when we are teaching our students anyway to distinguish
junk from routine from good science.
To get back to the “review or not review” quandary, one
could argue that no one can make a stronger argument
against a paper than the person whose work is in some way
being questioned in that paper. The reviewers critical intelligence
is at its sharpest then. There may also be factors in
the original thinking that were omitted or not verbalized—
here is a chance for them to surface. Having the original authors
admittedly partisan argument is good for science.
And an editor needs all the help he or she can get to form
an informed judgment.
A counterargument is that in a balance of judgments,
when some reports on a paper are likely to be critical
anyway, a fault-finding review may easily tip the balance
against acceptance. Especially if the editor is not expert in
the field. Responding to that in turn is Carlos good point
that a negative publication review is hardly as critical as one
on funding or promotion—the work will get published
somewhere.
The refereeing process often raises significant questions,
not on facts (mute as they are) but on interpretations. Conceptual
issues bother the community, but are rarely the subject
of public discussion. Sometimes I wish reviews were
published. Not all, but some. Or be accessible on-line to all.
The ideal editor, a perceptive and reflective person, might
keep a list of the conceptual issues that arise in the course
of spirited yet reasoned (rather than merely vituperative) reviews.
I bet certain questions have a way of rearing their
head again and again. Our ideal editor (I know one) might
collect such issues, cull the list from time to time, maybe
proactively solicit an essay, or organize a conference on the
ideas that bother the community.
Let me not evade answering my own question. Agonizing
about voicing a disagreement with a respected mentor, I
would have reviewed the paper. In a note to the editor I
would have said, “You should know that I have a special interest
here, my work is being questioned. I will tell you what
I think, but I’m prejudiced; you might get a balanced opinion
from x, y, or z.” I would have written a review and identified
myself as a reviewer.
There are no easy choices here, for human and scientific
considerations cannot be separated. And not only in this refereeing
process.
Appendix B: A Christmas Exchange
The reader should not get the idea that it just came naturally
for Roald and Carlo to sing a duetto in unison. To give
a flavor of their interaction, some exchanges in the period
around Christmas 2007 are shown here:
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Chemical Bonding
Carlo: Christmas was approaching, I was about to go on a
long-awaited vacation (in Spain!) with my wife and friends.
But the revision had to be done. I spent many hours working
with Andrea Ienco on further calculations and on drawings,
in support of ideas I had had around the special bonding
situation of the S2
2À
unit.
I saw a relationship between the present bonding situation
and the d10
L2M (m2
-H2) complexes (or olefin analogues). In
all of these systems, the oxidative addition of the metal
seems to adapt to a continuum of situations, subtly governed
by the nature of the metals and the coligands.[42]
Also, in the
Cu3S2 case, metal-backdonation controls the extent of SÀS
coupling. I wrote to Roald:
“I hope that my arguments are convincing enough and
close the debate over the Cu2
II
CuI
or CuII
2CuIII
configuration
problem…It is Christmas Eve, I have worked too much and
Elisabetta is getting nervous.”
Roald: I answered:
“This doesn’t make sense, Carlo. Its time to stop deluding
yourself that S2
2À
is like H2 or ethylene.”
I also said to myself, sotto voce,
“Maybe those guys are thinking—this Jewish slavedriver in
Ithaca has no respect for Christmas. Nor the great Italian and
Catalan traditions of taking off for the holidays. And he
doesn’t have a life (like a wife…), he just works all the time.”
But I didn’t think too hard. They were friends, and they
were just as addicted to the science as I was.
Carlo: I didn’t give up. I sent some further cogent arguments
on Christmas day, ending:
Again, I wish to make my point clear. The idea was not to
compare d10
ACHTUNGTRENNUNG[L2MACHTUNGTRENNUNG(h2
-H2)] or [L2MACHTUNGTRENNUNG(h2
-C2H4)] complexes
with mononuclear d10
ACHTUNGTRENNUNG[L2MACHTUNGTRENNUNG(h2
-S2)] compounds (if any) in
general. The relation that I propose is limited to the key a2’’
interaction in the D3h symmetry. The two electrons involved
(those which make the difference between Cu2
II
CuI
and
Cu2
II
CuIII
configurations) are delocalized over three dp metal
orbitals. Together the latter have cylindrical symmetry and act
as a single metal dp orbital does in [L2MACHTUNGTRENNUNG(h2
-H2)] species.
To be more convincing, I drew for Roald Scheme J,
adding:
The interaction M3–dp + s* is analogous to the M–dp +
s* one in the classic dihapto coordination and its associated
dichotomy (i.e., hydrogen vs. dihydride or olefin addition vs.
metallocyclopropane). As far as the M3–S2 interaction of a2’’
type remains a back-donation, I don’t see anything wrong
with the local planar geometry of the metals and an indicative
2d9
d10
configuration for them.
Probably you are realizing now how stubborn I am.
Roald: How could I disagree?
After reading Carlos “reasonable” response, I found
myself flushed, pulse racing, measured my blood pressure,
and found it over 200. Answering Carlo, with clearly superior
arguments, brought it down.
Now I had two stubborn guys on my hands.
Carlo: As the messages flew back and forth on Christmas,
we thought to assign a comparable solemnity to our responses
in the following days by writing in the e-mail subject line
the corresponding Saints Name. So Roalds letter to me of
December 26th had as its subject line “St. Stephan”. On December
27, I headed my message, “Saints Roald and Carlo,
Martyres.”
Roald: On December 28, I tried to get us out of the combat
zone:
“I feel good that we can talk and argue, but also for the
things behind it, that these questions of understanding still
matter to both of us. And, facing realities of aging, especially
that I retain the desire to learn what and why those little molecules
are up to.”
Acknowledgement
Though we would have argued anyway—its in our blood, as they say—
there is no way we could have gotten whatever support we could muster
for our arguments without the help of our collaborators, Gabriel Aullón,
Rosa Carrasco, and Andrea Ienco. Anne Poduska played a special role
by suggesting we might have a debate, and by a careful reading of drafts
and good suggestions at two stages in our debate.
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Received: January 29, 2009
Published online: July 23, 2009
Chem. Eur. J. 2009, 15, 8358 – 8373  2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim www.chemeurj.org 8373
ESSAY
Chemical Bonding