Journal of Molecular Structure (Theochem), 169 (1988) 289-330 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands
THE ELECTRONIC STRUCTURE OF METHANE AND ITS DERIVATIVES: APPARENT VERSUS EFFECTIVE SYMMETRY CONTROL OF SIGMA BONDING*
N.D. EPIOTIS Department of Chemistry, University of Washington, Seattle, WA 98195-9550 (U.S.A.) (Received 21 October 1987; in final form 24 November 1987)
ABSTRACT Resonance theory is one major conceptual basis of chemistry. However, it has been shown that resonance theory is “VB theory without symmetry control”. Hence, many qualitative concepts of chemistry must either be incorrect or accidentally correct. Molecular orbital valence bond (MOVB ) theory is “VB theory over canonical fragment MOs” or “VI3 theory with symmetry control made clear” and it is ideally suited for explaining old facts and for designing new chemistry. In this paper, a systematic presentation is given of central problems which are now recognized to have no satisfactory solution. The MOVB solution is put forward, and the problems with current interpretations are explained. The electronic structures of methane and fluoromethane are discussed in order to illustrate the following general MOVB concept: the nature of the AOs of an atom creates a distinction between apparent and effective molecular symmetry. When the constituent atoms are all first-row non-metal atoms the former is different from the latter. For example, the apparent symmetry of fluoromethane is C,,, but the effective symmetry is Td, i.e., the o bonds are made as if the true molecular symmetry were Td (methane-type bonds). By contrast, the apparent and effective symmetries of, for example, chlorostannane are the same, C3”. This difference between C and Sn is a result of the different absolute and relative radial extensions of the valence AOs of the central atom.
In the 1950s the experimental frontier of organic chemistry was what today is referred to as Physical Organic Chemistry. At the same time, accurate quantum mechanical calculations of organic molecules were not possible. In the 1980s ab initio computations of portions of organic reaction hypersurfaces have become routine. However, the experimental frontier of organic chemistry has moved: organic metals, organic superconductors, organic ferromagnets, etc. are now at the focus of interest. Accurate ab initio computations of such systems are not feasible at present. It is this simple realization, namely that the * Dedicated to Professor Linus Pauling.
0 1988 Eleevier Science Publishers B.V.
frontier of computational quantum chemistry lags significantly behind the frontier of experimental chemistry that focused my own interest on what one may call “conceptual quantum chemistry”. That is to say, my strategy has been to extract out of fundamental equations and computations chemical concepts which could then be projected to the frontier of experimental research or, even better, define a new frontier of experimental endeavor. That “concepts are more important than numbers” is an opinion which has been voiced by many pioneers of theoretical physics and chemistry and I speculate that this credo might have been shaped by the recognition stated above, at least in so far as chemistry is concerned. In my list of relevant quotations, I find a remark by Schriidinger that, “Suppression of details may yield results more interesting than a full treatment. More importantly, it may suggest new concepts. Pure quantum mechanics alone, in all its detail, cannot supply a definition of, for example, an acid or a base or a double bond”. Wigner suggests how computational power may be constructively used in a remark that is more pertinent today than ever before: “If one had a great calculating machine, one might apply it to the problem of solving Schradinger’s equation ... It would be preferable instead to have a vivid picture of the wavefunctions, a simple description of the essence of the factors ... The principal purpose of accurate calculations ... is to assure us that nothing truly significant has been overlooked”. Finally, Coulson aptly describes the taste of a minority of theorists today, “It is futile to obtain accurate numbers, whether by computation or experiment, unless these numbers can provide us with simple and useful chemical concepts; otherwise one might as well be interested in a telephone directory”. With this preamble, it is obvious why it is a special pleasure for me to contribute to an issue dedicated to Professor Pauling, the first and by far the most influential purveyor of the philosophy I spoke of above to chemistry, a philosophy which influenced in a very direct way my thinking and led to what I will briefly describe and illustrate in this paper. To be specific, Pauling used approximate VB theory and often its simplified version, resonance theory, to explain and predict chemical trends. What I have done is to recognize that symmetry control of chemical bonding is not made clear by VB theory (rigorous or otherwise). I replace VB by MOVB theory, the result of a fusion of MO and VB concepts, which can be thought of as “VB theory with symmetry control made clear” because of the usage of canonical fragment MOs rather than symmetry non-adapted AOs. This development has revolutionalized my own way of viewing chemical bonding and I wish to illustrate this by reference to a problem which still needs to be solved. Why is the reaction, 2CH2 FP-+CF4+CH4, exothermic and why is the CF bond shorter in CF, than in CH2F2? It will be argued that these phenomena are the result of symmetry control of bond making, and that although it appears that there are an equal number of polar bonds on the reactant and product side (and such polar bonds are very strong as Pauling taught us) this is not actually so. The interaction of
H and F in CH2F2 causes the hydrogens to acquire fluorine character and the fluorines to acquire hydrogen character so that polar bond formation is negated. One credo of this author is that “computing does not mean understanding”. The thermochemistry of the reaction above can be predicted correctly (at least qualitatively) by a variety of computational schemes ranging from extended Hiickel to good quality ab initio SCF MO theory. Indeed, this equation defines a trivial calculational problem nowadays. However, why is the enthalpy negative? No clear answer has been given to this question. The answer I will present is not the result of more computing but the result of the application of a new theory which is tailored for generating concepts rather than mere numbers. INTRODUCTION
In an age when computational accuracy can compete with experimental accuracy in the regime of small molecule chemistry [ 11, at a time when reliable calculations of organometallic complexes and even metal clusters are feasible [ 21, and in an era which has seen the proliferation of computer programs capable of performing accurate computations of organic ground states and transition states [ 31, the question still remains, do such computations lead to a true understanding of molecular electronic structure? In attempting to provide an answer, we must come to grips with the stark reality that questions such as the following remain unanswered. Question (a). Why does the C-F bond length, rcF, decrease  and the corresponding bond energy, D cF, increase  along the series CH3F, CH2F2, CHFB and CF4 ? Question (b). Why is the reaction shown below exothermic ? 2HzCF2-
CFI + CH,
AH, = - 24.9 kcal mol-’
Question (c). Why is it that replacement of C by Cz changes the above reaction from exothermic to endothermic [ 7]? 2Hz C2F2--
C,F, + C, H,
AH, = + 15.6 kcal mol-’
Question (d). Why is it that replacement of C and F by “heavier” isoelectronic atoms, such as Sn and Cl, renders reaction ( 1) endergonic [ 8]? 2R, SnC12-
SnCl, + SnR,
AH, = 7.0 kcal mol- ’
Questions (a) to (c ) define the so-called perfluoro effect problem. Questions (a) to (d) define what I will call a general methane problem. If we really understand the electronic structure of methane, then we must be able to provide clear and succinct answers to the above questions. That this is not possible with present-day concepts with regards to the first two questions has been
recognized independently by various workers. For example, in connection with question (a), Chambers [ 61 concludes that “the very range of explanations that have been offered is some indication in itself of the uncertainty which exists in explaining this very fundamental and interesting aspect of fluorine chemistry”. Smart [91 and Liebman and Greenberg [lo] have reviewed the various conflicting models for bond contraction and bond strengthening in fluoromethanes and conclude that the matter remains unresolved. To question (a), three more questions have been added for which simple and self-consistent answers are required. If a confident understanding of methane is still lacking, i.e. if we still cannot answer questions (a) to (d), how can we claim to understand a conformational equilibrium, a transition state, a metal cluster, etc.? About ten years ago, considerations of the type outlined above forced us to abandon MO theory [ 111 and to seek to develop another formalism through which we could understand methane and ferrocene, a ground and a transition state, a ground and an excited state, tetrahedrane (highly “strained”) and P4 or Be, (highly stable), and so on, by using one and the same set of qualitative concepts based on rigorous polydeterminant theory, rather than intuitive, approximate one-determinant MO theory. The product of these efforts has been MOVB theory [ 12-141, a compromise between MO and VB formalism which combines the most desirable conceptual aspects of the two methods. On this basis, some general comments are made and then specific answers to each of the questions posed above are given. First, some general points are outlined which are necessary for placing the contents of the paper in proper perspective. (a) Computational chemistry is important nowadays because of the ingenious efforts of theoreticians to adapt quantum mechanics to the computer. By contrast, MOVB theory represents an attempt to adapt quantum mechanics to the chemist’s mind and it was constructed with total disregard for its computer implementation potentiality. (b) Because of the diametrically opposed views identified above, computeradapted formalisms can compute but cannot interpret, and MOVB theory can interpret but not directly compute. This is why the four questions posed above remain unanswered, whereas even low level monodeterminant SCF MO computations can easily duplicate the experimental trends defined above, at least in a qualitative sense. In other words, methane is trivial to compute but hard to understand. Now, the two different philosophies generate tools which are complementary rather than antagonistic, as perceived unjustly by certain ab initio computational workers. For example, in practicing MOVB theory, we make extensive use of computations carried out in different frames (e.g., SCF MO [ 31, GVB [ 151, CASSCF [ 161, etc.) through translation. The recent work of Bernardi, Robb and coworkers [ 17,181 will make explicit MOVB computations possible in the future. (c ) No self-consistent quantum mechanical interpretation of chemistry ex-
ists. All that exist are intuitive rationalizations which make use of quantum mechanical terminology. The reason for this is that the models which have been employed are simply too primitive, even in a qualitative sense. A justification of this statement lies in the findings of MOVB theory. Specifically, three different types of chemical bonding have been identified [ 191. (1) Overlap bonding when a system is made up exclusively of first row atoms from B to F, and hydrogen. Here, symmetry controls the situation entirely. However, recognizing how symmetry orchestrates bonding is hard to “see” via available methodologies and the answers to the questions posed above will fully explain what is meant by this. (2) Overlap dispersion and overlap induction in systems made up of “metallic” atoms. These two mechanisms of bonding cannot be formally described by EHMO theory [ 201. Now, the important point is that, unless one adopts a “state viewpoint” or, equivalently, a “configuration interaction viewpoint”, rather than an “orbital viewpoint”, one cannot interpret with confidence a hydrogen molecule, methane, an organic transition state, an organometallic complex, a cluster or a van der Waals molecule. Because of the “orbital viewpoint”, chemists nowadays are under the false impression that molecular electronics is an exercise in constructing symmetry adapted orbitals and discussing them by using familiar overlap notions. MOVB theory shows us that bonding is much more diversified and intriguing, e.g. carbon obeys completely different bonding rules than lead, rhombic H, and Lil have the same “orbital structure” but widely different properties, and so on [ 211. The four problems defined by questions (a) to (d) are used in order to illustrate the MOVB approach and, in the process, to expose the inadequacy (logical and theoretical) of the currently used models which have been repeatedly employed to “explain” chemistry despite glaring inconsistencies and contradictions. However, before continuing with the main task, a brief description of MOVB theory is given along with some necessary background information. WHAT IS M0V.R THEORY?
It is well known that the fundamental contribution of Heitler and London in the late 1920s [ 22 ] was developed soon after into what can be loosely termed Eyring-Pauling VB theory [ 23,241. This eventually paved the way to resonance theory [ 251. Because of the approximations which were made in these VB approaches, certain problems remained outside their range, e.g., the problem of chemical stereoselection or relative (not absolute) aromaticity and antiaromaticity [ 261. As an example, one can write three equivalent low energy VB structures for both cyclopropenyl cation and cyclopropenyl anion, yet experimental evidence indicates that the former (aromatic) entity is much more stable than the latter (antiaromatic). Since it has now been shown that VB theory, in which the signs of matrix elements which are odd powers of overlap
integrals are explicitly considered, leads to the proper prediction of aromatic and antiaromatic behavior [ 12,13,27], we can say that the resonance theory is “VB theory without symmetry”, i.e. the so-called orbital symmetry consequences were accidentally omitted [ 12,283. It is tempting to speculate that it was primarily this deficiency of resonance theory that turned the attention of chemists (especially organic chemists) to Htickel MO (HMO) theory [ 291, a theory with many limitations owing to the neglect of interelectronic repulsion [ 271. MOVB theory is “VB theory with symmetry”. Since no approximations are made, it can stand side by side with any “perfect” ab initio polydeterminant theory. Finally, it can be presented in pictorial format so that non-theorists can understand it and learn how to use it. The recipe for formally implementing MOVB theory is as follows. (a) A molecule in a given geometry is dissected into two fragments. The most convenient dissection choice is the one for which the local symmetry of the fragments is highest. (b) The symmetry-adapted fragment orbitals (MOs or AOs) are written from first principles or computed by using an effective one-electron Hamiltonian of the extended HMO (EHMO) variety [ 201. (c) The electrons are distributed so as to generate the MOVB configuration wavefunctions (CWs), fI+. (d) The MOVB CWs are partitioned into sets, T, and each set is diagonalized separately to generate the diabatic states, S,+ (e) The diabatic states are, finally, diagonalized to produce the final adiabatic states, v/i. At this point, it is clear that MOVB theory differs from the conventional methods to the extent that the total wavefunction is not obtained as a linear combination of Qj but as a linear combination of Smi. It turns out that choices of partitioning the 0, into sets Z’, exist so that each emi, called a bond diagram, has explicit chemical meaning and it can be represented pictorially in a simple way. Thus, one arrives at a total wavefunction, v/i,which is a resonance hybrid not of CWs (as in the traditional polydeterminant theories), but a resonance hybrid of bond diagrams. In this way, we can follow how symmetry dictates bonding changes as the geometry of a molecule changes, in an explicit fashion, taking into consideration all electrons, all orbitals and all “effects” (i.e. all integrals which correspond to chemical bonding mechanisms). We are now ready to state the fundamental postulate of MOVB theory by which mere formalism is transformed into chemical sense: the partitioning of CWs into sets is carried out in such a manner so that each 8mi, the ground state resulting from diagonalizing the Qi of T,, represents just one way of making interfragmental bonds or antibonds. With this convention, the approximate form of the ground total wavefunction becomes CY,= [email protected]
m +’ M
/ / ,
““t-, \ +
I Y Y
'1 /' ' '1
is to say, higher diabatic states of appropriate symmetry (e.g. Smi with i> 1) are deemed to be relatively unimportant. Two different bond diagrammatic
representations of the reaction 2MAD -+MA2 + MD2 (vide infra ) illustrate our approach in Scheme 1. Some important aspects of the “mechanics” of MOVB theory and the associated terminology are now emphasized. (a) With respect to the two fragments which make up the molecule, each individual configuration may contain any one or all of the following elements: (1) non-bonding electron pairs (or odd electrons); (2) two-electron DET bonds (each results from in-phase double electron transfer (DET) and is completely analogous to the classical single bond of singlet ground Hz (Fig. la); (3) twoelectron DET antibonds (each results from out-of-phase DET and is completely analogous to the antibond of triplet Hz (Fig. la); (4) four electron (or (a) SINGLET DET BOND
TRIPLET DET ANTIBOND
DELOCALIZED DET BOND
- - -
_ __+ +t-
3-e BOND (?I
Fig. 1. (a) Illustration of DET bonds and antibonds. (b) Bonding implications of individual configurations and of configuration interaction indicated by dashed lines. A 3-e antibond may end up as a 3-e bond because of configuration interaction.
three electron) antibonds (each is due to repulsion arising from the overlap of filled orbitals ). (b ) To construct the principal bond diagram, one generates the parent configuration by placing electrons in orbitals so as to form the maximum number of bonds and the minimum number of antibonds by occupying as many orbitals having as low energy as possible. Then, dashed lines connecting orbitals which belong to the same irreducible representation are added and these now represent how electrons can be shifted in order to generate configurations which will interact with each other, i.e. the dashed lines tell one how “symmetryallowed” delocalization will take place. (c ) A dashed line connecting a doubly occupied with a vacant orbital is said to define a coordinate bond (for lack of a more evocative term). Dashed lines connecting two orbitals with a total of one and three electrons define one- and three-electron bonds, respectively. Finally, a dashed line connecting two orbitals with two electrons defining a DET bond defines a delocalized DET bond. These considerations are illustrated in Fig. lb. (d) Higher energy bond diagrams are constructed in an analogous fashion. (e) When referring to the excitation which is needed for connecting two fragments with bonds specified by the corresponding bond diagram, we always refer to the parent configuration of the bond diagram and we inquire as to whether a delocalization mechanism exists which can act to lower the excitation one would calculate by assuming that only the parent configuration exists. (f) Configuration interaction within each diagram is completely specified by the dashed lines and it represents electron delocalization. This can occur by two different types of electron transfer mechanism which are of crucial importance: single electron transfer (SET) and correlated electron transfer (CET) as illustrated below.
A brief illustration is now given of the approach used here by showing the bond diagrammatic representation of two different species A=B and C=D. The two systems differ only in the way the four orbitals match in symmetry and this is indicated by the double arrows below. p2-
Each system is a four-orbital-four-electron system and each represents an important class of chemical compounds. For example, putting A=Ni and B = Hz, we have C,, NiH2 and by putting A = Be and D = Hz we have DcvhBeH,. The MOVB representations of the ground states of A=B and C=D are shown in Fig. 2. Henceforth, our approach is illustrated by reference to the A-B system. According to the “drawing convention” of MOVB theory, dashed lines connecting orbitals belonging to the same irreducible representation imply the set of configurations which can be generated by shifting electrons along them starting from the parent configuration “projected” by the diagram itself. Thus, in our example, 69, represents two interfragmental bonds created by the interaction of @I to aI0 shown in Fig. 3, & represents one interfragmental antibond with 0, = &, and 49,represents one x interfragmental antibond with e3 = o12. (a)
A = Ni, a = Jd
AB = NiH2
2 C = Be, c = Zs, c* = 2p Hz, d=
CD = BeH2
a* = 4s xy' ,b*=c*
Fig. 2. Bond diagrammatic wavefunctions of A=B and C-D.
!i w" zi
E + Q +I--
+ aJ 8
-+ 01 9
Fig. 3. The MOW3 configurations needed for the description of A-B. Configurations 1 to 10 are “cont.&ml” in 8,. The principal configuration of 8, is @. 8, end 6 are made up of one configuration ( GII and Q12, respectively~ each.
The parent of e1 is C& and the bond diagram 63, as written “projects” this lowest-energy configuration. The approximate total wavefunction is simply a linear combination of these three “bonding schemes”, i.e. these three bond diagrams.
v/‘AIt!i$ [email protected]
,+A,@, In fact, for ground state A=B, v- 9,. This is so because 0, and @, being antibonds, lie much higher in energy than two bonds. In general, either the “best” or the two leading bond diagrams will be sufficient for most qualitative analyses attempted here. There are two classes of problems. (a) Problems in which the mere construction of the principal bond diagram(s) is sufficient for obtaining insights. In such cases, symmetry alone controls the situation and determining whether delocalization occurs by SET or CET mechanism is not crucial for the argument. (b ) Problems in which the mere construction of the principal bond diagram is insufficient. In such cases, explanations and predictions hinge upon the determination of the mechanism of electron delocalization. We say that such problems need considerations beyond simple symmetry arguments. Problems of the first type are, in principle, treatable at the level of EHMO theory which “contains” symmetry control. However, the conceptual difficulties that plague MO theory preclude a clear understanding of how symmetry influences the way in which bonding occurs. Examples of this type can be found in our published work [ 141. Problems of the second type lie beyond EHMO and, in fact, monodeterminant MO theory, and can be dealt with only by a theory that explicitly accounts for correlated electron motion. The treatment of such problems by the MOVB method has been described in previous papers. In the following, a brief summary of conclusions relevant to this paper is given. What is the conceptual advantage of the MOVB bond diagrammatic representation of the wavefunction of a molecule? The principal bond diagram makes possible an immediate visualization of the energy cost necessary for promoting a fragment to a “valence state” from which it can make a countable number of interfragmental bonds. Excitation is an investment, bond making is the capital one generates from the investment, and stability is the net profit associated with the investment. Now, high excitation is justified if the resulting bonds formed by orbital overlap are strong, and vice versa. Hence, the electronic properties of a molecule must be controlled by the intrinsic ability of the constituent atoms to enter into strong or weak overlap interaction. This leads to the following idea: the Periodic Table is a systematic classification of elements which have gradually changing electronic properties, and the index of their characteristic properties must then be some measure of the ability of their AOs to sustain overlap interaction. The index of choice is the resonance integral PAZconnecting an A0 of atom A with a fixed A0 of atom Z at the equilibrium bond distance rAz.According to the Wolfsberg-Helmholz approximation [ 301, PAZ is proportional not only to the overlap integral SAz, but also to the valence orbital ionization energies I_&and Iz
This means that if SAz remains constant, PAZwill decrease as A becomes increasingly electropositive. In actual fact, SAZalso varies in such a way so as to reinforce this prediction in main group elements. Specifically, there is an abrupt decrease in SAZin going from a 2sA (first row) to a 3sA (second row) AO. In contrast, SAz remains relatively constant in going from a 2pA to a 3pAA0. Accordingly, the atoms from boron to fluorine must have substantially greater overlap binding ability than the much more electropositive atoms Li and Be of
THE OVERLAP BINDING ABILITIES OF ATOMS BLACK
OVERALL OVERLAP BINDING
Fig. 4. Color classification of atoms according to their overlap binding abilities.
the same row as well as their second row relatives, namely aluminum to chlorine. These considerations are more fully developed in Chapter 1 of ref. 13. They naturally lead to a subdivision of the Periodic Table in three colored areas as follows: black (first row non-metallic), green (heavier semi-metallic), and red (metallics). This subdivision is shown in Fig. 4. Henceforth, rather than introducing new language, we shall use the terms black, green and red. Black are strong and green and red are weak overlap binders. At this point, it is emphasized that the relative overlap binding ability of two AOs of the same n but different quantum numbers, e.g. no and np, measured by the corresponding ratio of PAZvalues (hence termed the overlap binding ratio) exhibits a variation across the Periodic Table that is a manifestation of fundamental properties. Thus, a number of workers, namely Mulliken and Jorgensen (cited in refs. 31 and 32), Pyykkij [31,32] and Kutzelnigg  (see also ref. 13) have clearly recognized the fact that the first nodeless orbital without precursors (e.g. Is, 2p, etc.) has a special position among valence orbitals with the same quantum number. That is to say, 1s causes an expansion of 2s so that 2s ends up having an R,, comparable with that of 2p, etc. The expansion of 4d caused by the 3d precursor has been termed “primogenic repulsion” by Pyykkij [ 321. This effect is not relativistic in origin and it is primarily responsible for the decrease in the n&p ratio in going from the first to the second row in the Periodic Table and the decrease in the ns/(n- 1)d ratio in going from the first to the second transition series. The trend continues down a column as a result of three relativistic effects [ 341: (a) the relativistic contraction; (b ) the spin-orbit splitting; (c ) the relativistic self-consistent expansion. The atomic radius at which the density of a given ns or np valence A0 has its maximum value is designated R,,. The quantity AR,,, = R&,,(np) R&(m) is a measure of the relative overlap binding abilities of the np and ns AOs. In going from a black to a green or red atom of the same column, a reduction of overlap binding ability goes hand in hand with (and, in fact, is a result of) increasing AR, [ 351, or, in more familiar language, a decreasing s/p overlap binding ratio. What this means is that a black atom will tend to bind by adopting a configuration in which the 2s A0 is singly occupied, i.e. the black atom will be excited so that it can take advantage of the great overlap binding ability of the 2s AO. The opposite will be true in the case of green and red atoms in which the its A0 does not offer any great binding advantage relative to the np AO. Therefore a mismatch of the valence AOs in terms of R,, means that optimum overlap of one valence A0 of A implies impaired overlap of a second valence A0 of A with the AOs of some fixed fragment Z. In addition, high electropositivity means reduced capacity to promote overlap bonding. Black atoms differ from green and red atoms to the extent that only the latter have the properties just mentioned. We are now prepared to continue with our main task. However, at the outset,
the mere fact that we have recognizedthat “resonance theory” is “VB theory without symmetry control” gives us an important clue. We cannot expect the answers to the four questions to sound or be familiar in any sense. The reason for this is that all previous explanations of organic chemistry, i.e. the chemistry of the “overlap bond” are either “resonance theory” explanations, EHMO versions of the “resonance theory” explanations, or “classical” Coulomb explanations. The final conclusion of the MOVB analysis is that the four trends defined within questions (a)-(d) are manifestations of how symmetry in conjunction with individual atomic properties, such as A0 structure, determines hybridization (i.e. bonding) within a given system. The failure of the previous approaches is a result of their failure to perceive symmetry control.
THE ELECTRONIC STRUCTURES OF THE FLUOROMETHANES
We begin by comparing the MO, VI3 and MOVB descriptions of methane which are shown in Fig. 5. At the simplest MO level, we have four occupied bonding and four unoccupied antibonding MOs. At the simplest VB level, we have four sp3 hybrid carbon AOs forming four bonds with the four hydrogens within the perfect-pairing VB configuration (corresponding to the Lewis structure of methane). These are familiar representations which need no further comment. Now, the steps one must take for the purpose of constructing the principal bond diagram of methane are as follows: (a) Methane is viewed as a composite made up of two fragments: a core, C, fragment plus a ligand, H4, fragment. In other words, methane is viewed as “C plus H4”. (b) The symmetry-adapted orbitals of the two fragments are drawn and are classified according to the irreducible representation to which they belong. The appropriate group theoretical symmetry label is placed next to each orbital. (c ) The eight valence electrons are placed in the eight valence orbitals so as to generate the maximum number of multicenter bonds. (d) The four bonds obtained in this way are the result of spin pairing within individual configurations, plus delocalization brought about by the mixing of the configurations “contained” within the principal bond diagram shown in Fig. 5c. (e) A key thing to note is the large splitting of the ligand a, and t2 orbitals which is a consequence of strong non-bonded Hls---Hls overlap. It is because of this that both core and ligand orbitals separate into a high energy tz set and a low energy a, orbital. The role of non-bonded A0 overlap in determining how direct bonds are formed [ 131 is one unappreciated element of molecular stereoelectronics.
H H _--
d) FICTITIOUS "ALLOWED" METHANE
,+a1 '\ \ '\\ \\\I t \/\
\ q\ 1 ' /
\'\ \--+ ' ,‘+
Fig. 5. The MO, classical VB and MOVB descriptions of methane (note the “parallel” (“forbidden”) and “diagonal” (“allowed”) overlap of the orbitale of the two fragments ) .
(f) The MOVB formula of methane is H=M This brings us to the first important point. The advantage of the MOVB theoretical description is that it explicitly reveals that tetrahedral methane is less than perfect. The four multicenter bonds are connecting an excited tetravalent carbon to an excited H, fragment so that the two lowest energy a, orbitals of the two fragments can never be simultaneously occupied by two electron pairs. That is to say, the configuration shown below is not contained within the principal bond diagram of methane.
We then realize that real tetrahedral methane is a “forbidden” molecule relative to a hypothetical (non-existing) “allowed” methane, in which the four multicenter bonds are made as indicated by the principal bond diagram of Fig. 5d. Configuration 0, is now contained within the principal bond diagram of “allowed” methane. The hallmarks of “forbidden” and “allowed” molecules should be noted. In the former, the dashed lines run parallel in designating the bonds connecting the two fragments, whereas in the latter, at least a pair of dashed lines cross. These are the fingerprints of “forbidden” and “allowed” transition states in so far as orbital overlap is concerned and, hence, our terminology [ 361. Tetrahedral methane belongs to the Tdpoint group. Replacement of one H by F yields CH,F which belongs to the C,, point group. What is the effective symmetry of the four bonds connecting carbon to H3F? We will argue that the effective symmetry is not CBvbut Td,that is to say, the four bond orbitals of the H,F fragment in CH3F resemble the four bond orbitals of the H4 fragment in CH4. The two principal bond diagrams of CH3F necessary for correctly describing hybridization are shown in Fig. 6. It is immediately obvious that &, represents four interfragmental bonds much like those of Tdmethane (Fig. 5~). By contrast, @,, represents four bonds made in a completely different fashion. We say that the four bonds within S, are “Tdbonds” while those within Sn are “C3v bonds”. If it turns out that there are compelling reasons for declaring Qu the dominant bond diagram, then we will be forced to conclude that bonding in CHP resembles that within CH4, i.e. although CHBF has lower symmetry than CH4, nonetheless, both molecules are “forbidden” because the effective symmetry of both is Td.Now,t& will be the dominant bond diagram if the H3F
"PARALLBL" OVERIAP PATTERN "FORBIDDEN" BONDING
__t -DIAGONAL" QVRRIAP PAll'ERR"ALLLHRD" BONDING
+, \ \ \ \ \
Fig. 6. Bond diagrammatic representation of CH,F (note how one contributor involves “parallel” a1 overlap (as in methane itself) and the second contributor “diagonal” a, overlap). Which contributor dominates is determined by the detailed structure of the a1 ligand (HP) MOs. The q1 MO haaprincipal F2p and the qz MO principal Hlr, cherncW (symbola in perentheses).
fragment orbit& have the shapes shown in Fig. 7a rather than the shapes shown in Fig. 7b. Is there any reason to expect that q1 and q2 wil1 look as shown in Fig. 7a rather than as in Fig. 7b, given that q3 and q4 are invariant? It may now be appropriate to slow down and go over, step by step, the construction of the principal bond diagrams of CHBF shown in Fig. 6. First, we subdivided the molecule into two fragments, namely C plus H,F. Then we wrote the AOs of C and we constructed the MOs of H3F starting from the A0 basis shown below.
A. Black Atoms Effective Td Symmetry
Effective C3" Symmetry
Fig. 7. Ligand MOs of CH3F generated under two different constraints: zero H---F overlap interaction (set B) and strong H- - -F overIap interaction (set A). The two different assumptions affect only the structures of the a1 MOs (note that the a, MOs contain both H and F AOs, while theeMOearepureHMOe).
Specifically, F is assigned one valence sp A0 and two lone pair 2p AOs, while neglecting the lone pair sp A0 which points away from the carbon center. H is assigned one valence 1s A0 as usual. As a result, we obtain four valence MOs ( ql-q4) and two lone pair MOs (n, and &. Next, symmetry lab& are affixed on the individual orbit&, the electrons are fed therein, and bonds are made subject to the orbital symmetry restrictions (i.e. only orbitals carrying the same symmetry label can overlap and define a bond). Now, E+, represents one way
of making four bonds and &, a second way for accomplishing the same. The only difference between S, and On comes about because the four a, singly occupied orbitals can be coupled either in parallel (6) or in diagonal (SD) fashion simply because there are two spin independent ways of coupling four electrons into two bonds and delocalizing them accordingly. Remembering what each dashed line signifies, we can redraw the two original bond diagrams as shown in Fig. 8 so that the“‘parent configuration” of each one is the dominant configuration of the set of configurations contained within each bond diagram. This makes clear that 63” represents “forbidden” and @, “allowed” bond for.+----+______+
Fig. 8. Equivalent bond diagrammatic representation of CH,F where the dominant contributor configuration of @,, is the one which places two electron pairs in the two lowest energy a1 orbitals of the two fragments.
mation. The rest of the bonds, i.e. the two e bonds, remain invariant in a oneelectron sense. The following trends are now evident. (a) In CH4, the H4 ligand fragment MOs all span atoms of the same type. As a result, there is an analogy between VB electron pair C-H bonds and MOVB multi-center C-H bonds (Fig. 5). This analogy ceases to exist in CH3F where two of the H3F ligand MOs ( q1 and q2) span two different types of atoms. As a result, q1 is really a mixture of VB electron pair C-F and C-H bonds, with the former making a dominant contribution, and q2 is the same mixture with the latter making a major contribution. Thus, in general, MOVB bonds do not have the same meaning as VB bonds. (b) Reduction of symmetry from Tdin methane to Csv in fluoromethane is signaled by the fact that we can now superpose @, on S, (Fig. 8) for a proper description. The physical meaning of this additional bond diagram is that symmetry reduction causes fragment de-excitation through charge transfer from q2 to q1 and electron demotion from C2p to C2s. This fact is portrayed in the principal configuration projected by &, in Fig. 8. However, a price must be paid. In this principal configuration, the electron pair used for making an MOVB bond of principal C-F character now resides in q1 and the electron pair used for making an MOVB bond of principal C-H character now resides in C2s. As a result, one CF-type and one CH-type MOVB bond have partly ceased to exist. Furthermore, because of the engendered overlap repulsion of the C2s and q1 pairs, the two aforementioned MOVB bonds are antagonistic. Thus we expect the CH and CF bond lengths of CH3F to be longer than those in CH4 and CFI, respectively, where this antagonism no longer exists. These ideas are described in Section III, Chapter 4 of ref. 13. MOVB theory shows, in an explicit fashion, how symmetry controls fragment excitation for the purpose of bond making and it projects the interplay of the last two opposing factors. CH3F is more deexcited than CH4, but it has impaired bonding. (c) CH3F has two pure C-H MOVB bonds of e symmetry, one impure C-H MOVB bond of a, symmetry and one impure C-F MOVB bond also of a, symmetry. The last two are antagonistic regardless of how small or large the contribution of 6+, is, i.e. this statement is based exclusively on symmetry considerations. Henceforth, the term C-H bond will be taken to mean pure MOVB bond, the term “C-H” bond to mean impure C-H bond and the term VB C-H bond to mean the usual VB description with which the chemist is familiar. Let us return to the original question. Will the symmetry a, MOs of the H3F fragment look like q1 and q2 or like ql* and q2*? The approximate explicit expressions of these orbitals are
q: =Q1 (A, =small) q2 =Q2 (~2=larg4
qz =Q2 (A, =small) &I=Nf+b Q2 =M
(~1+sz +ss) 1 +s, +s,) -A,fl
where si are hydrogen and f fluorine valence AOs. What will be the value of the mixing coefficient jzi? If it is large, & is dominant and we have effective Td symmetry. If it is small, we have effective equals real C,, symmetry. Two important factors exist which cause di to be large. (a) The geminal non-bonded overlap of the H and F valence AOs is very large, much like the geminal overlap of AOs of atoms attached on a central first row atom [ 371. Replacement of C by Si will reduce non-bonded overlap and the value of Ii. (b) The central atom controls the value of Ii to the extent that a large Li means that the delocalized q1and q2 can yield large overlap integrals with the C2s and C2p, AOs, respectively, provided that these AOs have radii of maximum electron density which are very similar (i.e. provided that the central atom is a strong overlap binder). Because q1 and q2 span the same AOs (by virtue of being delocalized), a mismatch of the radial extensions of C2s and C2p would create a situation in which optimal C2s-q, overlap would necessitate poor C2p,-q, overlap, or vice versa. In such a case, q1and qzwould become localized qf and q$ so as to engender fragment de-excitation, since now only one (rather than two) strong interfragmental bond could be formed. Hence, we say that even in the absence of direct H---F interaction, the q1and q2MOs will be delocalized as a consequence of the fact that C2s and C2p are both strong overlap binders. In other words, the nature of the AOs of the central atom alone can control the effective symmetry of the molecule. When C is replaced by Si, the unequal radial extensions of 3s and 3p causes increased localization of q1 and q2 and SiH3F tends to have effective Csv symmetry. The MOVB theoretical analysis is over. Now the principal bond diagrams, 6, of the fluoromethanes are constructed. The “effective Td symmetry” bond diagrams of CH3F, CH2F2, CHF, and CF, are shown in Figs. 9 and 10. All we have to do is to count the ligand valence MOs of exclusive F character which make bonds in conjunction with the upper 2p AOs of the core fragment. The count is zero for CH3F, one for CH2F2 (b, bond), two for CHF, (the two e bonds) and three for CF, (the three t2 bonds). This means that the percentages of C-F polar bonds, i.e. the percentages of C-F bonds formed via utilization of the more electropositive C2p AO, are 0.0, 50.0,66.6 and 75 in CH3F, CH2F2,
~ ob2+---_$fb2 -
+ 9 . . . ..
Fig. 9. Principal bond diagrams of CH3F and CHZF, inciudiig the fluorine 2p lone pairs.
CHF3 and CF4, respectively. Had &, been dominant (see Fig. 6)) the percentages of C-F bonds made through utilization of C2p would have been 100,100, 100 and 75 for CH3F, CH2F2, CHF, and CF,, which is a quite different trend. Furthermore, we see that the percentages of “C-F” bonds, each of which is antagonized by a “C-H” bond of a, symmetry, are 100,50,33.3 and zero within the same series of molecules. This is because “C4”‘-“C-H” bond antagonism exists only in CH3F, CHzFz and CHF3 which have symmetry lower than T+ Since the bond of diatomic H-F is the prototype of an optimal polar bond resulting from the coupling of the relatively electropositive Hls and the relatively electronegative F2p A0 and, at the same time, it is not antagonized by any other bond, we say that “H-F-type bonding” becomes increasingly prevalent in moving from CH3F to CF4. Since only total energy arguments are valid in any qualitative discussion of molecular electronic structure and since the problems that were defined in the introduction call for some kind of comparison of non-isomeric and normally non-comparable molecular species, we can now see a simple way of attaining
‘I ‘\\ II ‘\\
Fig. 10. Principal
bond diagrams of CHFB and CF,.
TABLE I Ligand interchange
AE (kJ mol-‘)
Reaction HgMez + HgCl* HgMe, + HgI,
- 28.5 - 17.2
SnMe, + SnCI,
Data taken from ref. 8. HMB = hexamethylbenzene.
this last goal. Recognizing that ideally electropositive ligands prefer to bind to electronegative AOs of a core fragment and vice versa (e.g. H prefers to bind to C2s and F to C2p thus generating polar bonds), we can see that the total number of optimal C-H and C-F bonds are three, two, one and zero in CF4, CF3, CHpFz and CHBF, respectively. That is to say, the number of optimal bonds equals the number of optimal C-F bonds (remembering that the term “optimal” means that the bond is polar plus there is no antagonistic interaction between this bond with some other existing bond on symmetry grounds alone). Hence, total energy arguments can be made by reference to C-F bonds only in the case of fluorocarbons. With this background, the direct and specific answers to questions (a), (b) and (d) can be given. Firstly, the CF bond length decreases steadily in going from CH3F to CF., paralleling the percentage of optimal C-F bonds. Secondly, reaction ( 1) is exothermic because the number of optimal bonds in the product exceeds that in the reactant, i.e. CH2F2 has one, CH, one and CF, three optimal bonds and one plus one is less than one plus three. Thirdly, in reaction (1 ), the effective symmetry of each reactant is the same as the effective symmetry of each product, namely Td, despite the fact that the reactants belong to lower symmetry point groups than the products. As a result, there is no “forbiddenness” reduction as we go from products to reactants, the products have more optimal C-F bonds and, hence, more favorable overall bonding, and the reaction is exothermic. By contrast, in reaction (3)) the effective symmetry of each species is identical to the actual symmetry which is attested by the point group, the reactants are less “forbidden” than the products, and the reaction becomes endothermic. In Table 1, data are shown which clearly indicate that when the components are red “metallic” atoms, there is ligand antisymbiosis, i.e. changing the central atom from black to red changes the trend defined by eqn. (1). This can be explained in alternative language. When the constituent atoms are green or red, as in reaction (3)) the best placement of ligands is the one in which a o donor and a u acceptor group are placed on the same atom so that charge donation from the donor to the acceptor has the concomitant effect of converting the central atom from tetravalent to divalent (central atom deexcitation). This is precisely what the bond diagrams of Fig. 8 tell us when 6&, becomes dominant (green and red component atoms). The key conclusions of our analysis are now translated into a language familiar to the chemist by reference to the prototypical reaction shown below in which each species is bent with constant angle and D and A stand for “cr donor” and “CJacceptor”, respectively. 2MAD -
MA, + MD2
Each molecule-is viewed as an M core plus an AD, A, or D2 ligand fragment, with M having an upper m* and a lower m orbital and D and A having an a and a d valence orbital, respectively. Our contribution has been to point out that
this Lewis representation is misleading and that the appropriate molecular formulae depend on the nature of all three species M, D and A. Specifically, a gradation exists between two limits. (a) When M is a strong overlap binder, d mixes with a in MAD so that each of D and A ends up having properties intermediate between D and A. The benefit of this contamination (delocalization) is that the lower ligand MO, z, can overlap strongly with the lower m orbital of M and the same is true of the upper ligand MOs z* and m*. This permits the formation of two good semipolar interfragmental bonds which tend to be shielded from each other because z cannot overlap effectively with m* and z* cannot overlap effectively with m* and z* cannot overlap effectively with m (prevention of interbond overlap repulsion). At the same time, maximization of the overlap of M with AD requires that the acceptor/donor aspect of the ligands is lost. This state of affairs does not exist on the product side where each species has one non-polar and one polar interfragmental bond. Hence, the correct Lewis formulae are the ones shown below, with the asterisks indicating that D and A are acting as groups with properties intermediate between a donor and an acceptor in MAD only.
The approximate bond diagrammatic description of the reaction is shown in Scheme la where we have assumed zero non-bonded interaction. Firstly, it should be noted that M is divalent and each ligand (D and A) is univalent in the parent configurations of the reactant and product bond diagrams. The ligand hybridization that takes place in MAD produces z and z* ligand MOs which approach degeneracy half way between the one-electron energies of the d and a orbitals. This is called indirect ligand hybridization in MAD and it is energetically beneficial, i.e. it represents the best MAD can do to maximize its stability. In actual fact, it is reinforced by strong non-bonded interaction which splits the x/x* and y/y* degeneracy and the z/z” near-degeneracy. This is called direct ligand hybridization in MAD and it is energetically deleterious because it tends to change the two semipolar bonds to two non-polar bonds in MAD, whereas it has less impact on MA2 and MDz. In previous papers, we emphasized the latter component as the two effects cannot be easily separated. In any event, the important factor is that, at the limit when M is a very strong overlap binder, the mixing of the ligand orbitals d and a is very strong, the principal bond diagram is &, the ratio of the coefficients of 6+, and 6&, u: d, is large and the effective symmetry of MAD is not C, but rather CZvlike that of MA, and MD2. The reaction is exothermic because one polar bond plus one non-polar bond is better than two semipolar covalent MOVB bonds. In other words, the
products are more stable than the reactants because the reactants have more asterisks. The pattern of orbital overlap in all three molecules (when the ligand fragment MOs are non-degenerate) is characteristic of a Woodward-Hoffmann “forbidden” system. (b) When M, A and D become weak overlap binders, the wavefunctions representing the three molecules change. The approximate bond diagrammatic representation is shown in Scheme lb. The dehybridization of the ligand AD orbitals (z = a and z* = d) and the fact that an electron pair occupies the m core orbital (which we assume is contracted relative to m* and incapable of strong overlap binding, by definition) in the parent configurations of the reactant and product bond diagrams should be noted. Furthermore, a pair is now placed within an antibonding ligand MO in MA2 and MD2 and this, in VB theory, implies partial charge transfer from one ligand to the other as does the placement of an electron pair in the lower ligand MO of MAD. At this limit, the mixing of the ligand orbitals tends to zero (directly and indirectly), the principal bond diagram is 6, the u : d ratio tends to zero and the effective symmetry of MAD is C,. In direct contrast to the situation in (a), &, describes weaker bonds (no “spin-pairing” in the parent configurations) formed with overcompensating M fragment relaxation ( = de-excitation). The key idea is that generation of zerovalent M effectively triggers charge transfer from one ligand to the other. As a result, the reactants are now more stable than the products because a donor-acceptor relationship of the ligands exists only in the former. The chemical formulae which express the critical difference between reactants and products are M *.
+ A +
+ :A -
z D +
It is obvious that the situation described in (b) is intermediate to the limiting case of two-bond exchange represented by the following formulae.
It should be noted that it is only at this limit that any bond contraction effect goes to zero because the M-D and M-A “bonds” in the reactants and the products have equal length: infinity. Our analysis makes the following connection obvious. As M tends to divalency and as the M-A and M-D overlap bonding become stronger, reaction (4) will tend to be exothermic. As M tends to zero valency and the overlap components of the M-A and M-D bonds become weak, the reverse will occur. This leads to the following partial rule: for constant A and D ligands, the exotherm-
icity of reaction (4) will be a function of the effective promotional energy that takes zero valent M with electronic configuration m2 to divalent M with electronic configuration m ’ m *l. As discussed in the original work (see pp. 249251 of ref. 12), this effective promotional energy is not equal to the spectroscopic promotional energy since it additionally reflects the differential overlap binding ability of the m and m* orbitals. So, for example, the 3s-3p gap in Si is smaller than the Bs-2p gap in C, in a one-electron orbital sense, but the effective promotional energy of Si is much larger than that of C reflecting the inability of the contracted 3s (relative to 3~) to sustain overlap bonding. Hence, spectroscopic promotional data can be used for row but not for column comparisons. Recalling that progressive fluorination stabilizes the singlet m2 relative to the triplet m’m*’ state of a carbene, and that SiH, is predicted to have a much higher effective promotional energy than CH2, but that the reverse is true in the NH/PH and O/S comparisons, the ab initio computational results [ 381 which stimulated this work and which are cited below, leave little doubt about the validity of our proposal. These data refer to reaction (4) (varying M, A=F and D = H) with negative promotional energy implying that triplet M has lower energy than singlet M (energy units, kcal mol-‘). The large
CHF CFZ SiH, SiHF SiF2 NH PH 0 S
sp”-2p sp”-2p sp”-2p sp”-3p sp”-3p sp”-3p sp”-2p 3PY- 3PZ sp”-2p 3PY- 3PZ
Effective promotional energy m2+m1m*1 Negative 1 Positive Positive 1 More positive Negative More negative Negative More negative
AE - 14.0 -8.5 +1.1 -8.3 -2.1 +4.2 - 10.0 - 16.4 -3.2 - 16.1
preference for symbiosis when M is PH or S should be noted, in which case m and m* are degenerate (because the P or S o lone pair is accommodated in the inert 3s AO). Pairing two electrons in the same A0 has zero de-excitation benefit and causes severe interelectronic repulsion. The huge enthalpy change in going from reaction ( 1) to (2 ) can now be explained, recognizing that M = C and M = C2, respectively, and realizing that each reaction is a double redistribution of the ligands (i.e. four DA are rearranged to two D2 plus two A2 units). We say that the enthalpy switches from negative to positive by about 40 kcal mol-’ because C is ground divalent with an accessible tetravalent state, while C, is ground singlet (in which essentially two ground divalent carbons are
linked by two bonds) with a very high lying tetravalent state appropriate for ethylene formation. In addition, the two sets of ljgands ( F2 and H,) become segregated in CzHzFz but they are forced to close proximity in CHzFz and this works in the same direction. The logical consistency of our analysis can be further illustrated. In moving from entry (a) to (b) to (c) , and from entry (d) to (e) to (f), we go from the limit of reaction (5a) to that of reaction (5b). In each series, the negative hyperconjugation model predicts constant enthalpy, because each of the three reactions involves replacement of two nr-&r by two n,-o& interactions. Therefore it fails. The MOVB model predicts that symbiosis will give way to antisymbiosis because progressive fluorination stabilizes the singlet relative to the triplet state of a carbene or silene. Furthermore, realizing that, owing to the indirect effect of non-bonded overlap repulsion of lone pairs, bond strength varies in the order C-F > N-F > O-F, we see that, in moving from entry (a) to (g) to (i), we move from reaction (5a) to reaction (5b) and symbiotic tendency is progressively diminished. IMPLICATIONS OF THE “FORBIDDEN METHANE” CONCEPT
We now move beyond the topics defined by the four initial questions to further demonstrate the consistency of this approach [ 431. Specifically, we can now account for the following additional experimental and calculational facts. (a) Because the H AOs overlap with the geminally disposed F AOs, cis CHF=CHF (which is more stable than truns CHF=CHF) has effective Dzh symmetry. Small
F\ c=c /” F/
Hence, F,C=CH2 is “allowed” (C,, effective symmetry) and cis CFH-CFH is “forbidden” (Dzh effective symmetry) and this is why the former is so much more stable than the latter (Table 2 ). The principal bond diagrams of the two molecules and of tetrafluoroethylene are contrasted in Figs. 11 and 12. (b) The C=C bond of F&=CH2 is shorter than that of cis CHF=CHF because the former is “allowed”; the core and ligand fragments are partly de-excited, i.e. w7 is vacant and w4 is doubly occupied most of the,time (Fig. 12). (c) Induction is an implied bonding mechanism of the “allowed” F2C=CH2. That is to say, the fact that we have concomitant fragment de-excitation ( w7+ w4 and 44442) in going from CFH=CFH (Fig. 12) to F2C=CH2 (Fig. 12) means that C, will be polarized by Hz and F; only in the latter species. Induction is brought about by the interaction of the “extrinsic” configurations
~ b 2 g w6
q4 al I
--[-a19~:>--O~a, [ w4 ,
q2 b2~ I I / / ql al' I
- - ~ b2u q3 I
. . . . . . ,.
,...%...~-4--4- a u
a21 1 hi11 b21!
I I b1~
-t+ al @ - - - @ . g @
I I b1~ II b2u
Fig. 11. Principal bond diagranm of F2CffiCH2 and F2CffiCF~.
which describe one-electron intrafragmental promotion or demotion, with the configurations contained within the principal bond diagram. By definition, these polarization configurations are added separately as they are not included in the bond diagrams [12,13]. Induction of C2 within F2CffiCH2 is mostly a result of w 4 ~ w 7 one-electron excitation where the two C2 b2 MOs, w4 and w7, which are the origin and terminus of the one-electron promotion, span the same AOs. A second mechanism of induction involves ws-~ w2 demotion. Had c/s CHFffiCHF been an "allowed" molecule, induction would be inferior because it would involve two (al or bl) MOs which span different AOs, [39a]. Therefore, it is the fact that F2C--CH2 is "allowed" and that the C2 MOs are
319 TABLE 2 Structural data of fluoroolefins Molecule
Rel. energiesb (kcal mol-*)
“K.-H. Hellwege and A.M. Hellwege (Eds.), Structure data of free polyatomic molecules, in Landolt-Biirnstein - Numerical Data and Functional Relationships in Science and Technology, Vol. 7, Springer-Verlag, Berlin and New York, 1976. bN.D. Epiotis, J.R. Larson, R.L. Yates, W.R. Cherry, S. Shaik and F. Bemardi, J. Am. Chem. Sot., 99 (1977) 7460.
optimally “paired” for induction that makes F&=CH2 look like A while cis CFH=CFH looks like B.
+ c= +
Induction is expected to he a weak binding mechanism in molecules made up of black atoms where overlap is dominant [ 39b]. Nonetheless, it will make a definite contribution which will tend to lengthen the C=C bond [ 40,411. (d) The cause of the exothermicity of reaction (1) and the endothermicity of reaction (2) is overlap. Hence, replacing F by X = OR, N&, CR, is expected to diminish but not change the sign of the effect. This is precisely what happens
[71. LIE(kcal 2(CH3)&=CHz
0 I ;----4-
wl H F
Fig. 12. Principal bond diagrams of c/s CHF=CHF and CF2ffiCH2contrasting a bonding in the two molecules: the former has effective D2h (rather than C2v) symmetry, while the latter has effective C2v symmetry in so far as a bond tasking is concerned. The bond diagrams of CF2ffiCH~in this and in Fig. 11 are equivalent but they portray different generator configurations. (e) E q u a t i o n (6) s h o w n below is exothermic. C o m p u t a t i o n a l work [42 ] shows t h a t r e p l a c e m e n t o f b l a c k F b y g r e e n C1 a n d black C b y green Si e l i m i n a t e s or reduces t h e e x o t h e r m i c i t y . , zlE (kcal tool - 1 ) 2CHsF , H2CF2 + CH4 - 14 (6) 2CH3C1
H2SiF2 + Sill4
H2SiC12 + Sill4
We expect that better computations
will render eqn. (9) endothermic.
cl))c2 I NO "LONE PAIR" EFFECT
c ec 12
: "LONE PAIR" EFFECT
Fig. 13. Bond pair-lone pair hybridization according to MOVB theory and the necessity for conceptual invariance of the definitions of “bonding AO” and “lone pair AO”.
THE CONCEPTUAL TRAPS OF MO THEORETICAL MODELS
The MOVB interpretation of chemical trends defined within the initial as well as of additional trends which have long been regarded as puzzling has been outlined. What remains to be done is to use MOVB theory to show clearly what exactly is wrong with previously attempted rationaliza-
tions of these phenomena. Firstly, we show why we have totally neglected the lone pairs in the bond diagrams of Figs. 9 and 10 and why the correct explanation has nothing to do with lone pairs. Secondly, we show why the preoccupation with lone pairs in seeking answers to the stated questions is the result of logical as well as theoretical misunderstanding. Consider a carbon 2p A0 which is making a bond with a valence fluorine AO, Q,which is oriented favorably towards 2p. A lone pair is contained within a fluorine AO, n, which overlaps minimally with 2p.
The way in which the C-F bond is formed is described in MOVB theory by a’ linear combination of two bond diagrams as shown in Fig. 13. Now, suppose that we carry out two calculations, one by eliminating the doubly occupied n A0 and a second in which the entire system is properly treated. The change in energy in going from the first to the second calculation reflects an improvement of overall bonding. This improvement will be either small or colossal depending on how efficiently 4 and n overlap with 2p in the coordinate system of choice. That is to say, if we orientate q and n as above, the improvement will be small and vice versa. Hence, the “lone pair effect” will depend upon some arbitrary choice of the initial set of AOs. The important thing to understand is that regardless of what we called “valence AO” and “lone pair AO” in the beginning, we will always end up with a resonance hybrid of 8, and S, which will represent one bond formed via some optimal valence AO, q' , and one lone pair housed within an optimal lone pair AO, n' . Whatever physical interpretation we advance should always be definition invariant. The way in which lone pairs enter into play can be understood by examining the principal diagrams of the four fluoromethanes. These are shown in Figs. 9 and 10 under the assumption that the principal bond diagram of CH,F, CHzFz and CHFB is 6. These diagrams show explicitly the “observer” symmetryadapted lone pair MOs (constructed from the 2p fluorine AOs) which will hybridize with the cr symmetry-adapted interfragmental bonds as decreed by symmetry. This hybridization is represented by writing additional bond diagrams in the fashion illustrated in Fig. 13. Now, assuming that ;1I =& = k and symbolizing by u and d the coefficients off& and en, we re-define an optimal C-F MOVB bond as one which fulfills three (rather than two) conditions.
(a) The ligand group orbital spanning F atoms responsible for the bond has either unique symmetry, or it has the same symmetry as another ligand group orbital spanning X atoms, but with the mixing coefficient k equal to zero. An example of the first type is q2 of CH2F2 and an example of the second type is q1 when it is totally uncontaminated by hydrogen AOs (k = 0). (b) The ligand orbital identified in (a) couples with an upper core A0 or MO to make the bond. An example is the C2pq2 coupling in CH,F,. (c) An associated “observer” MOVB lone pair orbital (henceforth called F lone pair) exists spanning F atoms with the same symmetry as the ligand identified in (a). The result is C-F bond -F lone pair hybridization. An example is the hybridization of the C2pq2 bond with the n, lone pair, (both having b, symmetry) in CH2F2. Finally, an optimal C-H bond is defined as that which involves an uncontaminated ligand orbital spanning the H atoms which couples with a lower core A0 or MO in making a multicenter MOVB bond. An example is the a, symmetry bond of methane viewed as “C plus H4”. With the conditions just specified, let us count the optimal bonds in the four fluoromethanes assuming that &, ‘is the dominant contributor. From Figs. 9 and 10, the count is simply zero, one, two and three for CH3F, CH2F2, CHF, and CF4, respectively. Now, let us count again assuming that k and the u: d ratio are zero and that &-, is the dominant contributor. The results are now entirely different: two, three, four and three for the same series. It is now clear that our prediction of the enthalpy sign of reaction (1) will depend on the “method” of counting. Assuming 6& dominance, reaction (1) is predicted to be exothermic because the products have more optimal bonds. However, the same reaction is predicted to be endothermic by assuming &, dominance. Therefore, the operationally important factor in making predictions about symbiosis is our ability to count correctly. That is to say, should we count by reference to 6& or by reference to E&? We count by reference to the former when k and u:d are large, in which case the effective symmetry of a molecule is higher than the apparent symmetry. We count by reference to @n when k and u: d tend to zero, in which case effective equals apparent symmetry. By doing so, any emerging argument automatically contains the effect of r~bonding plus the effect of any symmetry-allowed hybridization. Realizing that the bond pair-lone pair hybridization described in Fig. 13 contains nF-o& negative hyperconjugation, we conclude that by explaining bond contraction in fluoromethanes and fluorine symbiosis on carbon by negative hyperconjugation is accidentally correct, because the latter effect is simply an inseparable part of optimal bond formation. However, the distinction between non-optimal and optimal r~bonding exists even in the absence of lone pairs, i.e. it still exists after eliminating criterion (c) above. Hence, we conclude that the celebrated trends discussed before are principally due to ~7bonding [ 441.
Finally, we argue that whatever legitimate lone pair effects exist beyond hybridization are caused by differential symmetry constraints. To see this point, the reader is referred to Figs. 9 and 10 and it is recalled that up until now, we counted optimal bonds by assuming constancy of the non-optimal “C-F” and “C-H” bonds. Obviously, this is not the case. For example, such non-optimal bonds exist in CH3F, CH2F2 and CHF3 and they are observed by zero, one, and two optimal bonds, respectively, as well as by zero, one and one (more delocalized) lone pairs of a, symmetry, respectively. Recognizing that more optimal bonds means more charge withdrawal from carbon and that a lone pair can coordinate with a proton, it can be seen that in going from CH3F to CHF3, there will be a pronounced tendency to convert the non-optimal to optimal bonds by setting K equal to zero and increasing the contribution of 6$,. So, for example, the H of CHFB acts as an electron donor with respect to the C2s A0 to counteract the electron density depletion and, at the same time, the lone pair of a, symmetry coordinates with the vacant Hls AO. To put it simply, in going from CHBF to CHF3, the optimal bonds and the existing lone pairs act to “protonize” the hydrogen and to change the “C-H” (and concomitantly the “C-F”) bond into an optimal bond. In other words, CH3F and CHF3 are both CsVbut the former approaches effective Td symmetry (i.e. it is “forbidden”) more than the latter partly because of a lone pair effect. What is wrong with the “no bond-double bond resonance” concept and hyperconjugation [ 45-47]? The idea that we can interact bond MOs and hope to understand stereoselection is false because all bond orbitals within a molecule interact even if they are orthogonal. Put in different language, the use of hyperconjugation is implicitly based upon the false assumption that orthogonal hybrids do not interact. Let us take a closer look at the fallacy, “Hybrid orbitals, which are orthogonal to each other do not interact”. This mistake occurs because chemists. believe that interaction is synonymous with overlap. The truth of the matter is that hybrid AOs interact. The magnitude of the interaction represents the driving force of a system to place two electrons in that A0 of the set which makes up the hybrid A0 with the lower energy. For example, the overlap integral of two sp hybrid AOs, Si2, is zero, but the interaction matrix element, H12, is non-zero. The interaction is proportional to the sp energy gap and it tends to store two electrons in the s A0 rather than letting them occupy separately the s and p AOs for the purpose of making bonds. n1 -->
The mere fact that hybrid AOs interact with each other and with whatever is attached on them virtually eliminates any possibility of understanding what goes on, even in a system as simple as methane. Somebody who understands the difference between canonical and local MOs will have no problem accepting this [ 481. Interpretation is feasible only over canonical MOs because this is the simplest choice for “seeing” symmetry control. Is the concept of hyperconjugation useless? It can be labeled either as “nominal fallacy” or as “poor algorithm”. Saying that reaction is more exothermic because there is hyperconjugation on the product side implied by the “picture” shown in Fig. 14a is nominal fallacy because what one is really saying is that reaction is exothermic because the products have better bonds. This is not explanation but, rather, restatement. The reader who doubts that all that hyperconjugation means is “covalent bond formation without regard of symmeARGUMENT!THE REACTION CH F + CHgF +CHq 3 OF 'WYE'ERCONJUGATION** IN cHZF2.
+ CH2FZ IS EXOTHERMXC BECAUSE
INTUITIVE RESONANCE THEORY VERSION OF HYPERCONJUGATION IN CH2F2.
INTUITIVE MO THEORETICAL VERSION OF HYPERCONJUGATION IN CH2F2.
(b) F \ -Hj4 "F F \ C-F Fig. 14. Resonance theory and perturbation MO formulations of hyperconjugation.
try control” is directed to the interaction diagram of Fig. 14b. Because of the polarization of the C-F antibond n-o cF* interaction roughly describes covalent C-F bond formation. What is omitted is how the rest of the molecule controls this process, i.e. how molecular symmetry, real or effective, enters the problem. A second interpretation of hyperconjugation is that it is an algorithm which sometimes succeeds and sometimes fails. This algorithm says, “prefer structures in which you can place a lone pair or a high lying o bond MO coplanar and preferably truns to a low lying o antibond” [ 111. Whenever a correct prediction is arrived at via this algorithm, the theoretical basis remains immutable: the favored system is one in which symmetry permits a high lying core MO to define a polar multicenter bond with a low lying ligand MO, i.e. the algorithm frequently identifies correctly the geometries which contain strong polar bonds [ 491. The reader should construct the @n bond diagrams of the four species shown below and ascertain that C is more stable than D and E more stable than F because more polar bonds can form in C and E than in D and F, respectively. The principal bond diagrams, &, of each isomer are identical.
What does the “fluoromethane adventure” teach us? We cannot understand why cyclobutadiene is antiaromatic and benzene aromatic by disregarding symmetry control. By the same token, we cannot answer any of the stated questions without respecting symmetry. Symmetry control within methane is a tougher problem than symmetry control in pericyclic transition states and previous explanations have uniformly failed to incorporate this pivotal aspect, i.e. they have failed to perceive that effective symmetry is what orchestrates bonding. Are there examples of MO theoretical applications where the conceptual traps have been avoided? Yes, and a good example are two papers by Hall [ 501 in which the author clearly perceives the importance of intra-atomic excitation in “preparation” for bonding. Bond ionicity is a de-excitation mechanism since an electron hops from a higher to a lower (in a one-electron sense) orbital, much like 2p+2s demotion is a de-excitation mechanism accompanying the Da,,-+C,, transformation of NH3. PROSPECTS
Imagine that today is the year 1960, we possess the great computational power that theoreticians have at their disposal in 1988, and we are asked to
give an answer to the following question. Why does cyclobutene open stereospecifically via conrotation to 1,3-butadiene? What we may do is start with available concepts, which in the 1960s included steric effects , hyperconjugation [ 521 and others [ 531, choose one as the best rationalization, and “dress it up” with computed indices. A better alternative would be to say that, in organic molecules, the covalent bond reigns supreme, recognize that it is orbital symmetry that controls overlap binding, and construct a symmetry argument to answer the question. In 1988, we know that this last mode of operation would be best because we are aware of the Woodward-Hoffmann rules [ 541 and we fully appreciate the importance of symmetry in bonding. To put it crudely, people do not resort to steric effects, hyperconjugation, etc., to answer the question stated above because they understand how symmetry determines the properties of a systems, e.g. cyclobutadiene versus benzene, and they can extrapolate from that knowledge to four-orbital-four-electron transition state complexes [ 55 1. What I would like to suggest is that the methane problem I defined in the introduction is the reincarnation of the problem of stereoselectivity of a pericyclic reaction (actually, its 0 analogue). People understand K but not rs symmetry control and, furthermore, they remain unappreciative of the difference between apparent and effective symmetry because of the lack of conceptual explicitness of MO theory. As a result, researchers keep on putting their computational and experimental power behind heuristic concepts such as dipole effects, hyperconjugation, Qaromaticity [ 561, etc. in a hopeless struggle to enforce upon nature their own preconceptions concerning bonding. The result is testimony that something is amiss. Cyclobutene conrotation has nothing to do with steric effects, and the perfluoro effect has nothing to do with lone pairs. Both problems have to do with bonds and symmetry. The contribution of this paper lies in going one step further in declaring that it is not the point group label that is important, but rather it is the effective symmetry of the molecule which is responsible for how bonds are made. This effective symmetry cannot be recognized if geminal non-bonded interaction is neglected. All these conclusions have been thrust upon us by the MOVB bond diagrams. To quote Pople, “Point group specification is an unduly coarse method of conveying symmetry information” [ 571. Things become progressively worse when we tackle transition states, organometallic ground states, metal clusters, etc. Here, the existing concepts not only lack conceptual power, but they are formally incorrect. The bonds offerrocene are not made like the bonds of methane, etc. How can we progress when we still do not understand methane? MOVB theory has done its part. We have provided in monograph and paper form a theoretical approach that has been applied to diverse problems across the Periodic Table, offering interpretations and predictions which differ in sound and substance from those with which the reader is familiar. We now understand methane and, as a result, we understand why cyclopropane is “strained”, why hydrazine is gauche, how ferrocene
differs from methane, why tetrahedrane is a very different problem compared with isoelectronic P4, why rhombic H4 and Li4 have the same symmetry MOs but very different stability properties, etc. [ 58]. The reader must now decide whether a shift to “CI thinking” in place of “orbital thinking” is warranted on both conceptual and formal grounds.
8 9 10 11 12 13 14
15 16 17
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330 (d) J.N.‘Murrell, in N.H. March (Ed.), Orbital Theories of Molecules and Solids, Clarendon, Oxford, 1974, Chapter 7. (e) K. Morokuma, Act. Chem. Res., 10 (1977) 294. (f) P. Hobza and R. Zahradnik, Top. Curr. Chem., 93 (1989) 53. (g) P.C. Schmidt, M.C. Bohm and A. Weiss, Ber. Bunsenges. Phys. Chem., 89 ( 1985) 1330. 41 x delocahzation also contributes to the greater stability of the 1,l isomers relative to the 1,2 C2H2F2 isomers. However, replacement of F by a pseudoatom H’ having the same electronegativity as F but no lone pairs does not alter the energetic preference for the former at the level of EHMO theory (J.R. Larson, Ph.D. Thesis, University of Washington, 1986). n lone pair delocalization is expected to be very small in the fluoroethylenes. R delocalization plays a key role in CZH2X2molecules, where X is an unsaturated group, e.g. vinyl, where the 1,2 isomers are more stable than the 1,l isomers. 42 P. v. R. Schleyer, E.D. Jemmis and G.W. Spitznagel, J. Am. Chem. Sot., 107 (1985) 6393. (b) H.B. Schlegel, J. Phys. Chem., 88 (1984) 6254. (c)P. Ho, M.E. Coltrain, J.S. Binkley and C.F. Mehius, J. Phys. Chem., 89 (1985) 4647. 43 N.D. Epiotis, Nouv. J. Chim., 11 (1987) 303. 44 Of course, lone pair-lone pair overlap repulsion does depend on the lone pairs and it may cause problems with larger halogens (e.g. I) when two or more are bound on the same carbon. 45 L. Pauhng, The Nature of the Chemical Bond, 3rd edn., Cornell University Press, Ithaca, N.Y., p. 314. 46 An example: the charge-ahernant structures which one may write in representing cyclobutadiene cannot contribute to the cyclobutadiene hybrid by symmetry. 41 (a) E.A.C. Lucken, J. Chem. Sot., (1959) 2954. (b) J.F.A. Wiiiams, Tetrahedron, 18 (1962) 1477. 48 An example of early recognition of this problem: 0. Eisenstein, N.T. Anh, Y. Jean, A. Devaquet, J. Cantacuzene and L. Salem, Tetrahedron, 30 (1974) 1717. 49 For successful predictions of the hyperconjugation algorithm for the reason stated in the text see: (a) P. v. R. Schleyer and A.J. Kos, Tetrahedron, 39 (1983) 1141. (b) C. Romers, C. Altona, H.R. Buys andE. Havinga, Top. Stereochem., 4 (1969) 39. (c) S. David, 0. Eisenstein, W.J. Hehre, L. Salem and R. Hoffmann, J. Am. Chem. Sot., 95 (1973) 3896. 50 (a) M.B. Hall, Inorg. Chem., 17 (1978) 2261. (b) K.L. Kunze and M.B. Hall, J. Am. Chem. Sot., 108 (1986) 5122. 51 M.S. Newman, Steric Effects in Organic Chemistry, Wiley, New York, 1956. 52 M.J.S. Dewar, Hyperconjugation, Ronald Press, New York, 1962. 53 (a) E.L. Eliel, N.L. Allinger, S.J. Angyai and G.A. Morrison, Conformational Analysis, American Chemical Society, Washington, 1981. (b) C.B. Anderson and D.T. Sepp, J. Org. Chem., 32 (1967) 607. 54 R.B. Woodward and R. Hoffmann, The Conservation of Orbital Symmetry, Verlag Chemie, Weinheim, 1970. 55 (a) M.J.S. Dewar, The Molecular Orbital Theory of Organic Chemistry, McGraw-Hill, New York, 1969. (b) H.E. Zimmerman, Act. Chem. Res., 5 (1972) 393. 56 M.J.S. Dewar, J. Am. Chem. Sot., 196 (1984) 669. In this paper it is argued that the carbon crframe of cyclopropane (a 4N+ 2 electron system) is similar electronically to the carbon 0 frame of benzene (a 4N electron system)! For a correct theoretical description of rings and clusters, see N.D. Epiotis, J. Mol. Struct. (Theochem), in press. 51 J.A. Pople, J. Am. Chem. Sot., 102 (1980) 4615. 58 N.D. Epiotis, in press.