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Book Review Chemical Bonding and Molecular Geometry From Lewis to Electron Densities. By Ronald J. Gillespie and Paul L. A. Popelier

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Angewandte
Chemie
Chemical Bonding and Molecular
Geometry
From Lewis to Electron Densities. By
Ronald J. Gillespie
and Paul L. A. Popelier. Oxford University Press, New York
2001. 268 pp., softcover $ 39.50.–
ISBN 0-19-510496-X
The explanation of molecular geometries in terms of theoretical models is
one of the most fundamental concepts in
chemistry. Nearly every chemistry textbook devotes an introductory chapter to
the question of how the geometrical
arrangement of the atoms in a molecule
can be rationalized by means of an
ordering scheme, the rules of which
should be as simple and comprehensive
as possible. The search for an explanation of the shape of molecules has a
long history, which has involved a large
number of ad hoc models and other
rules and models based on quantum
chemistry. The well-known dilemma for
students, particularly in the first semester, comes from the fact that, depending
on the preference of the professor,
several models for explaining molecular
geometries may be discussed without
explaining the connections and the frequent contradictions. It often happens
that the MO and VB models, frontier
orbitals and the HSAB concept, the
octet rule and hybridization, the
VSEPR model, and the H¸ckel rule
are introduced without giving a deeper
insight into their basic principles, which
can easily lead to a state of resigned
Angew. Chem. Int. Ed. 2003, 42, 143 ± 147
confusion. The situation becomes aggra- physical observable and it cannot be
vated by the strong tendency of chemists measured by an experiment. They rathto judge the value of a model more by its er side with the electron density as the
simplicity and ease of visualization than elementary basis for their models, beby how well it agrees with physical laws cause the analysis of the density is based
and quantum-theoretical insights. Al- on a physically observable property of
though MO models have become im- the molecule. At this point the authors
portant for understanding aromaticity must be reminded of the ground-breakand for the interpretation and predic- ing publication by Heitler and London
tion of pericyclic reactions, it cannot be in 1927, which showed that the fundasaid that the wavefunction has received mental basis of the chemical bond is the
much affection from chemists, despite resonance of the wavefunction, and it
its fundamental importance for chem- cannot be explained simply by the
ical phenomena. The mathematical con- electron density. The latter is the prodcept y is too abstract and too elusive for uct but not the driving force of the
the human imagination to grasp to allow chemical bonding. That this finding can
it to become the focus of orthodox be ignored, while still obtaining a widely
chemistry, which instead strives for pic- valid ordering scheme based on the
tures that are accessible for the human electron density, is on the one hand a
pleasing result when one seeks models
senses.
The aim of this prologue is to try to based on considering simple analogies.
characterize the intention of the book On the other hand, however, it supports
Chemical Bonding and Molecular Ge- the deceptive idea that the origin of the
ometry by Ron Gillespie and Paul chemical bond lies in the change of the
Popelier. The authors describe their electron density distribution. The third
attempt to explain in a consistent way pillar of the models is the more recent
the geometry of molecules using three LCP (ligand close packing) model which
complementary models or theories. The was introduced in 1997 and 1998 by
authors restrict their endeavor to mole- Gillespie and Robinson.
The book is divided into nine chapcules of the Main Group elements,
because (p. 257) ™the study of the shape ters. Chapter 1, ™The Chemical Bond:
of transition metal molecules in terms of Classical Concepts and Theories∫, gives
the electron density distribution is still a short overview of the historical develthe subject of research and it has not opment of models of the chemical bond.
reached a sufficient stage of develop- It begins with the evolution of the
Periodic System of the
ment to enable us to
elements and the introdiscuss it in this book.∫
The first of the three
™...the strong tendency duction of drawing a
line as a symbol for a
models is the VSEPR
bond, and it ends with a
(valence shell electron of chemists to judge
critical discussion of the
pair repulsion) model, the value of a model
limitations of the Lewis
which in its original ver- more by its simplicitiy
model and the octet
sion was introduced in and ease of visualizarule. It is noticeable
1957 by Gillespie and
tion than by how well that models which refer
Nyholm. The heuristic
VSEPR model has be- it agrees with physical to the wavefunction are
not mentioned at all.
come an important stan- laws and quantumThe 4n þ 2 rule, which
dard model for under- theoretical insights.∫
is based on the work of
standing the structure of
H¸ckel, is not even
inorganic
molecular
even mentioned, alcompounds. In this book
it receives a quantum-chemical justifi- though the geometry and stability of
cation and interpretation that is based aromatic compounds cannot be underon the AIM (atoms in molecules) theory stood without considering the special
of Richard Bader, which is the second role of p orbitals. Although one may
pillar of the models in this volume. Like concede that Gillespie as an inorganic
Bader, the authors reject the wavefunc- chemist might have a biased viewpoint,
tion as a basis for the explanation of there are several places in the book
molecular geometries because it is not a where the geometries of organic com-
¹ 2003 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
1433-7851/03/4202-0143 $ 20.00+.50/0
143
Books
pounds are discussed in great detail. rectangular geometry with two long and
However, in those cases the authors two short bonds.
Chapter 3, ™Some Basic Concepts of
carefully avoid bonding models that are
Quantum Mechanics∫, is devoted to
based on orbitals.
Chapter 2, ™Bond Properties∫, con- elementary concepts and ideas of quantains a critical discussion of elementary tum theory and to basic foundations of
terms which are often used when the quantum-chemical methods such as MO
chemical bond is considered. These are and VB theory. The authors do not
bond distance, bond order, bond disso- devote much attention to mathematical
ciation energy, force constant, dipole details but instead focus on the descripmoment, etc. Especially noteworthy is tion of the most important principles
the discussion about the connection and the understanding of the physical
between dipole moment and charge quantities. Particularly well done is the
distribution. The authors show nicely discussion about the importance of the
that it is not possible to use the dipole Pauli exclusion principle, the relevance
moment, which is a vector, as an indica- of which for the electronic structure of
tor for the molecular charge distribu- molecules is often neglected. Except for
tion, although this is often wrongly the final section, ™Postscript∫, this chapclaimed. The electronic charge distribu- ter gives a concise and successful description of the elemention in a molecule is
tary concepts of quanhighly anisotropic, and
tum chemistry. But then
therefore it is also not ™At this point the
one reads (pp. 81 ± 82):
possible to use atomic authors must be rewave function ...
partial charges to estiminded of the ground- ™The
does not directly give us
mate the ionic characany understanding of
ter of a bond. This part breaking publication
the bonding or geomeis well done and worth ... which showed that
reading, but then on the fundamental basis try of a molecule. To
page 39 one finds some of the chemical bond is attempt to obtain such
an understanding we
statements about the
the resonance of the
need to interpret the
bonding situations in
wave function.∫ This is
BF3 and SiF4 which in- wavefunction, and it
followed (p. 82) by: ™Alvolve contradictory and cannot be explaned
ternatively, we can base
selective
arguments. simply by the electron
our analysis on the elecThe authors say that
density.∫
tron density, which as we
the explanation of the
have seen, is readily obshortness of the bonds
tained from the wave
in terms of resonance
structures which have boron ± fluorine function ... Because this analysis is
and silicon ± fluorine double bonds due based on a real physically observable
to p backdonation would be inconsistent property of a molecule, this approach
because this would lead to positive appears to be more fundamental.∫ It
partial charges at the fluorine atom. remains the secret of the authors why
The positive charges of the resonance the electron density r should be more
structures would not agree with the fundamental than the wavefunction y,
calculated large negative values. Every even though r is determined by y and
relevant textbook, including the present not vice versa. Since the publication by
work, explicitly points out that the Heitler and London in 1927 we know
partial charges of Lewis structures have that it is only the wavefunction that
only a formal meaning. ™Formal charges gives an explanation for the chemical
may even be of opposite sign to the real bond, whereas all attempts to explain
charge∫ (p. 17). On page 39 the authors the chemical bond in terms of the
ignore what they say on page 17! In the electron density have failed. It is hard
second part of this chapter, under the for human beings to accept that the
heading ™Resonance Structures∫, the fundamental principles of elementary
authors introduce among others ben- quantities of science are not accessible
zene, without addressing the question of to their sensory perception. It is at this
why cyclobutadiene, which also has two point that the preference for ™solid∫
equivalent resonance structures, has a observable quantities which is often
144
¹ 2003 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
1433-7851/03/4202-0144 $ 20.00+.50/0
found in chemistry becomes connected
with the false statement that the latter
has a higher status than a mathematical
quantity. This part should be read with
great caution! It is also appropriate at
this point to mention that the electron
density distribution is the result of
chemical interactions but not their driving force.
Chapter 4 introduces the VSEPR
model which is probably known to most
readers. There have been some modifications since the time when the original
version was published in 1957. The term
™electron domain∫, which is the spatial
region of a bonding or lone electron
pair, has been introduced more recently.
It becomes important in the context of
the AIM theory which is discussed later.
The authors make it clear that the
repulsion of two electron domains
comes mainly from Pauli repulsion and
not from electrostatic forces. The other
parts of this chapter are mainly concerned with comparing experimental
bond angles with the predictions of the
VSEPR model. The interpretation of
the bonding situation and geometry of
ethylene and substituted ethylenes is not
convincing and ignores some facts. The
construction of C2H4 from two CH2
fragments in the triplet state, yielding
two banana bonds (™bent bonds∫), is
comprehensible. However, the discussion of the bond angles of haloethylenes
fails to mention that CX2 (X ¼ halogen)
has a singlet ground state, and therefore
X2C ¼ CX2 should not be planar. When,
finally, one even reads the statement (p.
106) that orbital models with s and p
bonds would not predict that ethylene is
planar, it becomes clear that the viewpoint of the authors is very biased. This
also becomes obvious from the discussion about the influence of electronegativity on the bond angle of AX3 molecules (pp. 98 ± 99). The decrease of the
bond angle with higher electronegativity
is explained by using the VSEPR model.
There is only a discussion of those
examples from Table 4.3 which agree
with the VSEPR model, although the
data show that on going from AH3 to
AF3 the bond angle increases in the case
where A is P, whereas it decreases where
A is N or Sb. At the end of the chapter it
is finally admitted that the VSEPR
model may fail in two cases. These are
molecules with ligand ± ligand interacAngew. Chem. Int. Ed. 2003, 42, No. 2
Angewandte
Chemie
tions and transition metal compounds. compared with the VSEPR model: ™... marize the most important definitions
The second case is not discussed in the the LCP model can be regarded as an and results of the AIM theory.
The two concluding chapters, 8 and
book. For the first case the authors extension and a refinement of the
recommend the LCP model, which is VSEPR model in which bond pair ± 9, attempt to explain the geometries of
bond pair repulsions are replaced by compounds of Main Group elements on
introduced in Chapter 5.
the basis of the above three models. It is
The LCP model (Chapter 5) is based ligand ± ligand repulsions∫ (p. 132).
The AIM theory and the topological reasonable that the molecules of the first
on the observation that the ligand ± ligand distances X ± X in compounds analysis of the electron density after octal row elements, whose coordination
Bader are introduced in number is rarely larger than 4, are
AXn , where A is an
Chapter 6. The second discussed separately in Chapter 8, while
element of the first octal
derivative of the elec- compounds of the heavier Main Group
row and X is an electro- ™It remains the secret
negative element, have of the authors why the tron density, the so- elements are discussed in Chapter 9.
a remarkably constant electron density should called Laplace distribu- Chapter 8, after some introductory retion, is discussed sepa- marks, focuses on fluorides, chlorides,
value which is independ- be more fundamental
rately in Chapter 7. The and hydrides of the elements lithium to
ent of the type of molethan the wavefunctopological analysis of carbon. The calculated atomic charges
cule. For example, the
the electron density dis- are then used as a basis for a superficial
F ± F distances in BF3 tion, even though the
tribution which was de- and biased presentation of the topic,
und BF4- have the same electron density is devalue, 226 pm, and the termined by the wave- veloped by Richard with the headline ™Polar Bonds and
F ± F distance in CF3þ
function and not vice Bader is, from the view- Ionic ± Covalent Character∫ (p. 185),
point of chemical mod- which also contains wrong statements.
(216 pm) has nearly the
els, perhaps the most There is, for example, the assertion on
same value as in CF4 versa.∫
attractive discipline of page 187 that ™... the attraction between
(215 pm). Also, the A ± X
quantum theory, be- the two atoms ... in a pure covalent bond
bonds become longer
when the coordination number is in- cause many heuristic models of the ... is due only to the electron density
creased. From this the authors conclude prequantum time can be obtained by a accumulated between their nuclei∫. Althat the ligands X are close-packed mathematical treatment of the electron though this explanation is frequently
around the central atom A, and that density in a quasi-natural way. Atoms in given, it is completely wrong! Here the
the longer A ± X distance in higher a molecule are derived as subdomains of dislike of the authors against considercoordinated compounds is caused by the functional space of the electron ing the wavefunction goes so far that
ligand ± ligand repulsion. It is suggested density of molecules, and, more impor- fundamental knowledge gained by
that the A ± X distance of linear mole- tantly, the bonding line between bonded quantum theory is simply ignored. This
cules AX2 should be considered as the atoms is revealed without making more is followed by the attempt to prove the
™natural∫ bond distance, which becomes or less arbitrary assumptions. The differ- weakness of the concept of ionic and
longer in AX3 because of steric repul- ences in the type of bonding, i.e., the covalent bond using LiF and BF3 as
sion. Accordingly, the longer C ± F dis- difference between covalent and ionic examples which, following the argutance in CF4 (131.9 pm) compared to interactions, can also be verified with ments of the authors, can only be solved
with the AIM model.
CF3þ (124.4 pm) is not explained by the this theory. The AIM
Because the atomic
change from sp3 to sp2 hybridization but theory has therefore bepartial charges in BF3
rather in terms of fluorine ± fluorine come an important tool ™It is hard for human
repulsion. Considering the large number among other methods
(fluorine: -0.81; boron:
beings to accept that þ 2.43) suggest a stronof quantum-chemical investigations for analyzing the bondwhich clearly show that the bond dis- ing situation in mole- the fundamental prin- ger interatomic charge
tance between two bonded atoms is cules. Proponents of the ciples of elementary
attraction than in LiF
determined primarily by their direct AIM theory prefer to quantities of science
(fluorine: -0.92; lithielectronic interactions, the LCP model see the results of the
um: þ 0.92), while at
are not accessible to
appears rather odd. The authors also topologial analysis of
the same time the elechave great difficulty in explaining why the electron density not their sensory perceptron density at the bond
this model fails for heavier Main Group as complementary to tion.∫
critical point, in agreeelements. For example, the A ± X dis- chemical models and in
ment with the electrotances for A ¼ Al, Si, P, S and X ¼ F, Cl, particular to MO modnegativities, indicates
O become shorter and not longer when els, but rather as a substronger covalent bondthe coordination number increases from stitute for them. However, this attempt ing in BF3 than in LiF, the authors
four to six, and the P ± F distance in PF4þ has not been successful so far. Because conclude that there is a contradiction
(145.7 pm) is significantly shorter than the domains of electron concentration within the accepted bonding model,
in PF3 (157.0 pm) although the F ± F are very important for the AIM theory because the ionic and covalent contridistances are nearly the same. Although as well as for the VSEPR model, it is butions cannot both increase at the same
the LCP model is not very convincing understandable that the two disciplines time. This argument is nothing but a con,
here, the authors hail it as a step forward are connected. Chapters 6 and 7 sum- because it should be clear to every
Angew. Chem. Int. Ed. 2003, 42, 143 ± 147
¹ 2003 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
1433-7851/03/4202-0145 $ 20.00+.50/0
145
Books
chemist that the absolute strengths of culations for such complexes. This paper
the ionic and covalent contributions shows that the energy difference bemay both increase whereas the ionic/ tween the planar equilibrium geometry
covalent character is determined by the and a pyramidal structure with a given
ratio of the two values. And the state- tilt angle is higher for BF3 than for BCl3 .
ment of the authors that the ionic and However, the model calculations are
covalent character of a bond cannot be totally irrelevant for the real molecules
clearly defined is also not correct. There F3B ± NH3 and Cl3B ± NH3 and for the
have been many theoretical studies in deformation energies of BF3 and BCl3 in
recent years in which the absolute values the complexes! If one calculates the
and the ratio of electrostatic and cova- energies of the Lewis acids with the
lent bonding, based on a clearly defined frozen geometries of the complexes and
quantum-chemical partitioning of the compares them with the energies of the
bonding energy, have been given quan- equilibrium structures, it turns out that
titatively.
BF3 actually has a smaller deformation
The calculated partial charges are energy than BCl3 . Thus, BCl3 is also an
frequently used in the following discus- intrinsically stronger Lewis acid than
sions for explaining the geometries and BF3 !
other properties of molecules in terms of
There are further absurdities in this
the above three models. Although the and in the following chapter. On page
number of molecules discussed is not 192, Table 8.3, the AIM partial charges
very large, it is not difficult for the which are praised as a basis for the
careful reader to find several exceptions nature of the chemical bond have a
in the tables which are either not problem, because the calculated values
mentioned or are explained with ques- for CH4 give a small negative charge for
tionable arguments, or are commented the hydrogen atoms. Everybody who
on laconically as on page 212: ™The knows about the fundamental difference
reasons for the large bond angles in between the chemical behavior of protic
N(CF3)3 and N(SCF3)3 are not clear∫. and hydridic hydrogen will be startled
Particularly noteworthy is the highlight- by this. In Section 8.6.1 (pp. 204 ± 205)
ed discussion in a special section on page there is a discussion of the geometry of
191. It is devoted to the question of why the CF3O- anion using the LCP model,
BCl3 is a stronger Lewis acid than BF3 , in which the authors fail to justify why
even though the partial charge of the they are using the radius of carbonyl
boron atom in BF3 (þ 2.43) is higher oxygen for the O atom, even though the
calculated partial charge
than in BCl3 (þ 1.93).
of CF3O- (-1.26) is nearThis finding can therefore not be explained
ly the same as that of
by the electron density ™This gives a fundaCH3OH (-1.24). Why is
distribution. Because
the C ± O distance of the
mentally false unterthe generally accepted
former molecule typical
model suggests stron- standing of the
of a double bond whereger p(p)-backdonation chemical bond.∫
as that of the latter molof fluorine compared
ecule is typical of a sinwith chlorine, thus ingle bond? Here the auvolving the wavefuncthors use the observed
tion, which is against the chemical view- fact as a starting point for a deceptive
point of the authors, they offer an explanation which seemingly supports
alternative explanation. The authors the LCP model. The power of the latter
say that BF3 is intrinsically a stronger is grotesquely exaggerated by the stateLewis acid than BCl3 . Then, however, ment (p. 206) that the shorter bond
they claim that the energy which is length of CO compared with CO2 is in
necessary to deform planar BF3 into a agreement with the LCP model. The use
pyramidal geometry in complexes with of Lewis structures, on the other hand, is
strong bases such as NH3 is greater than criticized at several points using faulty
that for BCl3 . As a proof for the state- arguments. For example, on page 203 in
ment they cite a publication by Gillespie the discussion of the three Lewis strucet al. (Inorg. Chem. 1999, 38, 4659) tures of the carbonyl group, there is the
which reports on quantum-chemical cal- statement that the bonding line of a
146
C ± O single bond would suggest a nonpolar covalent bond. No chemist would
agree with this.
The extremely biased presentation
continues in the final chapter, where the
geometries of selected molecules of the
heavier Main Group elements are discussed. First there is the introduction of
well-known bonding models for hypervalent compounds, such as hybridization
with inclusion of d-orbitals and threecenter four-electron bonds. Then there
is the rejection of writing Lewis structures because, among other reasons, the
15 equivalent resonance structures of
SF6 which can be written in accordance
with the octet rule would give a formal
charge of þ 2 for sulfur, whereas the
partial charge calculated by the AIM
method is þ 3.55 (p. 230). Here again the
authors ignore their explicit statement
given on page 17 that the charges of
Lewis structures are only formal. The
following sections discuss geometries of
molecules with increasingly higher coordination numbers. Conspiciously, the
authors discuss only cases where there is
good agreement with the VSEPR and
LCP models, although one soon finds
contradictions in the tabulated values.
For example, the equatorial S ± F distance in SF4 (154.5 pm) is significantly
shorter than in SF2 (162.5 pm), although
the LCP model predicts a longer bond.
It becomes clear that the explanations
for the observed geometries become
more and more difficult for the authors.
This becomes perfectly clear from the
discussion of the C3v geometries of SeF62-,
IF6-, and XeF6 (p. 254). The reason why
the lone electron pair of the central
atom is suddenly without stereochemical significance, although it was suggested to play an important role for the C4v
geometry of IF5 , remains unclear. Enlightenment could be found in the nearly
20-year-old review by Kutzelnigg about
the chemical bonding of heavier Main
Group elements (Angew. Chem. 1984,
96, 262; Angew. Chem. Int. Ed. Engl.
1984, 23, 272), but that would mean that
the wavefunction has to be considered.
To sum up: the book by Gillespie
and Popelier is entertaining reading for
every chemist who wants to review his
or her ideas about models for molecular
geometries by comparing them with the
arguments of the authors. If one reads it
with scepticism, it may even enrich one×s
Angew. Chem. Int. Ed. 2003, 42, 143 ± 147
Angewandte
Chemie
knowledge about the subject, because it
clearly shows the limitations of the
correlation between electron density
distribution and molecular geometries.
However, the greatest caution is advised, because the authors make the
statement that the electron density is
more fundamental than the wavefunc-
Angew. Chem. Int. Ed. 2003, 42, 143 ± 147
tion and that the electron density distribution would be an explanation for
molecular structures. This gives a fundamentally false understanding of the
chemical bond. Therefore, a strong
warning must be made with regard to
the explicit goal of the authors (preface,
page xi) ™to provide undergraduate
students with an introduction to models
and theories of chemical bonding and
geometry∫.
Gernot Frenking
Fachbereich Chemie
Universit‰t Marburg (Germany)
147
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