摘要:

Chemical Society Reviews Editorial Board Professor H. W. Kroto FRS (Chairman)Professor M. J. Blandamer Dr. A. R. Butler Professor B. T. Golding Professor M. Green Professor D. M. P. Mingos Professor J. F. Stoddart Consulting Editors Dr. G. G. Balint-Kurti Professor S. A. Benner Dr. J. M. Brown Dr. J. BurgessDr. N. Cape Professor A. Hamnett Dr. T. M. Herrington Dr. R. Hillman Professor R. Keese Dr. T. H. Lilley Dr. H. Maskill Professor Dr. A. de Meijere Professor J. N. Miller Professor S. M. Roberts Professor 6. H. Robinson Dr. A. J. Stace Staff Editors Mr. K. J. Wilkinson Dr. J. A. Rhodes University of Sussex University of Leicester University of St. Andrews University of Newcastle upon Tyne University of Bath Imperial College London University of Birmingham University of Bristol Swiss Federal Institute of Technology, Zurich University of Oxford University of Leicester Institute of Terrestrial Ecology, Lothian University of Newcastle upon Tyne University of Reading University of Bristol University of Bern University of Sheffield University of Newcastle upon Tyne University of Gottingen Loughborough University of Technology University of Exeter University of East Anglia University of Sussex Royal Society of Chemistry, Cambridge Royal Society of Chemistry, Cambridge It is intended that Chemical Society Reviews will have the broad appeal necessary for researchers to benefit from an awareness of advances in areas outside their own specialities.Deliberate efforts will be made to solicit authors and articles from Europe and further afield, in order to present a truly international outlook on the major advances in a wide range of chemical areas. It is hoped that it will be of interest and help to students planning a career in research. In particular, it will be the place to find succinct and authoritative overviews of timely topics in modern chemistry. In line with the above, review articles will not be comprehensive, too detailed, or heavily referenced; they should act as a springboard to further reading. Interdisciplinary awareness should thereby be heightened and the student should be stimulated to take a more professional interest in the topic of the review. Although the majority of articles are intended to be specially commissioned, the Society is always prepared to consider offers of articles for publication. In such cases a short synopsis, rather than the completed article, should be submitted to the Senior Editor (Reviews), Books and Reviews Department, The Royal Society of Chemistry, Thomas Graham House, Science Park, Milton Road, Cambridge CB4 4WF. @ The Royal Society of Chemistry, 1992 All Rights Reserved No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form, or by any means, electronic or mechanical, photographic, recording, or otherwise, without the prior permission of the publishers. Typeset by Servis Filmsetting Ltd. Printed in Great Britain by Blackbear Press Ltd.

ISSN:0306-0012    

DOI:10.1039/CS99221FX001

出版商:RSC    

年代:1992

数据来源: RSC

摘要:

The Theory of Atomic and Molecular Collisions John N. Murrell School of Chemistry and Molecular Sciences, University of Sussex, Falmer, Brighton BN 1 9QJ S. Danko Bosanac Ruder Boskovic Institute, P.0. Box I016, 4 1001 Zagreb, Croatia 1 Interatomic and Intermolecular Potentials The interaction of atoms, either individually or as components of molecules, is determined by potentials which are functions of the relative positions of these atoms. The cohesion of liquids and solids, the sticking of molecules to surfaces, the transport of heat in gases, chemical reactivity; all of these can in principle be explained or predicted if these potentials are known. For some of these phenomena we only need to determine the dynamics of bimolecular collisions; others, such as the melting of a solid, are macroscopic properties and one needs to involve the statistical behaviour of -atoms or molecules.All observable properties such as those mentioned above can be used on a trial and error basis to determine features of the potential: take a potential, calculate the property, and compare with experimental observations. If the agreement is good then a certain range of the potential will be satisfactory. However, individual properties are not sufficiently sensitive to all features of the potential, so in general one will need to measure a potential against several different properties before one can be satisfied with it. The connection between atomic and molecular properties and interatomic or intermolecular potentials is a subject generally referred to as the theory of intermolecular forces, and this has been frequently reviewed.’ In this review we examine an important part of this subject, namely the dynamics of atomic and molecular bimolecular collisions in crossed-beam experiments.The reason for its importance is that this type of experiment can in principle provide a more sensitive test of potentials than any other. If one takes two beams of molecules with narrow ranges of velocities, and with the molecules all in the same quantum state (electronic, vibrational, and rotational state as appropriate), and after crossing these beams in a vacuum chamber measures the distribution of products as a function of angle relative to the incident beams, each product being separately identified not only for its molecular composition but also for its individual quantum state, then that is a great deal of information.If the experiment is performed for several collision velocities and for several initial quantum states then we have even more data, and all of this can in principle be explained by potential functions, perhaps even a single potential function. Let us first be a little more formal about the term potential. An Professor Murrell (B.Sc., Ph.D., F.R.S.C.) is a theoretical chemist ttyhose research interests have covered many branches of valence theorj’, spectroscopj?, and the states of matter. He has u)ritten seven books on these topics, the most recent ofwhich are on potential energj, functions and scattering theory; these are now the main topics of his research. He M’US elected a Fellobt, ojthe Royal Societjy in 1991.Professor Bosanac obtained his first degree in theoretical physics from the Universitj? ofZagreb in 1968 and his Ph.D.from Sussex Universitj. in 1972. He uws Ladjg Davis Fellow at the Hebrew Universitj?of Jerusalem in 1977178. His present research interests include the dynamics qf molecular collisions, interaction of radia- tion Mith matter, and the general aspects of the classical and yuan tum theories. important element of theories of molecular spectroscopy and reactivity is the Born-Oppenheimer approximation that the motion of electrons and nuclei can be treated as separate but linked problems.The basis for this is that nuclei have a much larger mass than the electron so that their motion is sluggish compared with the motion of electrons. We can conclude that electronic states (their wave functions and energies) adjust smoothly and instantaneously to movements of the nuclei. These energies, when added to the repulsion of the nuclei, provide a potential which governs the nuclear motion. There are certain features of spectroscopy that can only be explained by going beyond the Born-Oppenheimer approxima- tion. In these cases the quantum states cannot be identified with a unique electronic wave function. Likewise, there are chemical reactions in which the electronic state changes somewhere in the passage from reactants to products; these reactions are usually referred to as non-adiabatic but they will not be covered in this review. 2 The Theoretical Tools Three theoretical techniques are available for calculating the motion of nuclei on a potential energy surface; classical mecha- nics, quantum mechanics, and semi-classical mechanics.Our picture in classical mechanics is that of the snooker table; but the atoms are not hard spheres and the motion is in three dimensions not two. Our picture of collisions in quantum mechanics is of waves breaking around a lighthouse, and we interpret the calculations using the fundamental postulate of quantum mechanics that the probability of events is obtained by squaring the wave functions. Quantum mechanics has a well defined classical limit when the de Broglie wavelength of the particle, A = h/p,is small compared with the range of the potential.For example, a hydrogen atom, moving with a kinetic energy of 0.1 eV has a wavelength of approximately 1 8, which is comparable to interatomic dis- tances. One would therefore expect to see wavelike properties from the collision of such atoms with molecules or solids; such properties as diffraction and interference. Heavier atoms and higher energies will make these properties more difficult to see and in such cases the classical picture is appropriate. Quantum mechanics always operates, even for heavy particles. The question is whether the characteristic quantum phenomenon can be resolved in the experiment.The simplest formulation of classical mechanics when the interaction potential is complicated and the equations have to be solved numerically is that provided by Hamilton’s equations. These govern the time dependence of the coordinates q and momenta p of the particles; a set of variables q(t), p(t). For N atoms at a given time these variables are represented by a point in 6N dimensional space, and this point moves along a path which is called a trajectory that can be calculated by solving Hamilton’s equations. Hamilton’s equations are coupled first-order differential equations of the form 17 where H is the Hamiltonian, which is the sum of the algebraic expressions for the kinetic and potential energies H=T+V (3) If V is very simple, say a constant or a harmonic function, equations (I) and (2) can be solved analytically.In other cases they must be solved numerically by taking a step by step evolution of the trajectory [q(t),p(t)]using a Taylor expansion of the variables. There are two Schrodinger equations in quantum mechanics. The one most familiar to chemists is the time-independent equation which governs the so-called stationary states or eigen- states of the system. This is commonly written where His the quantum mechanical Hamiltonian and 4 is the wavefunction. Schrodinger's second equation, called the time-dependent equation, describes the time evolution of the wave function in a non-stationary state of the system and is At first sight it may appear that the time-dependent Schrodinger equation is more appropriate to the scattering experiment than the time-independent equation; molecules come from a source, collide with one another, and are scattered into a detector.If the experiment is to fire pulses of molecules into the scattering chamber and to measure not only the angular distribution of the products but also their time of arrival at the detector, then the time-dependent equation is needed. However, an alternative scattering experiment is to have a continuous stream of mole- cules coming from the source, and after scattering, arriving at the detector. This experiment has no time evolution; a snapshot at any time shows the same situation. In this case the observable properties can be obtained by solving the time-independent Schrodinger equation; both give the same scattering angles.Currently the time-independent approach is more favoured because normally it is computationally the simpler approach. Moreover, all the concepts of scattering theory except collision time emerge from this approach and for these reasons we only use the time-independent approach in this review. Scattering is always a multidimensional problem; even for atomic collisions one has both radial (distance between the atoms) and angular variables, and for molecular collisions one also has variables to describe vibrational and rotational states. The computational demands in scattering increase rapidly with the number of variables, so that atom-molecule scattering is much more difficult than atom-atom, and if atoms are exchanged in the scattering process, there is another increase in difficulty. Quantum mechanical probabilities show the characteristics of interference; these are oscillations in the probability which arise from cross terms when one squares a wave function.In classical mechanics one calculates probabilities directly from trajectories. To get interference from classical mechanics one would have to take the square root of the probability, but without further information this is undefined to within a phase factor 4, for we note Semi-classical mechanics provides a recipe for assigning a phase 4 to a classical trajectory. The origins of this lie in the old quantum theory of atoms developed by Bohr.His recipe for quantization can be written CHEMICAL SOCIETY REVIEWS. I992 $pdq = nh (7) where n is an integer and the integral, called the action integral, is taken over a complete orbit. In semi-classical mechanics we calculate the phase associated with a classical trajectory by the formula This result can be proved by taking the classical limit of quantum mechanics (h-0) and deriving what is called the JWKB approximation to the wave function. 3 Types of Collision The simplest type of scattering experiment to treat theoretically is the collision of two atoms when there is no transfer of charge and no change in the electronic states of the atoms. We call these collisions elastic, the term implying that there is no change in the internal energies of the colliding species.In a collision, atoms will change their individual translational energies; but if the positions of the two atoms are r1 and r2 (vectors referred to space fixed coordinates) then the positions of the centre of mass is and the vector of their relative separation is Using these variables, called a centre-of-mass or molecule-fixed system the translational energies associated with R and Y are separately conserved. 4 "1 Figure 1 Newton diagram for the transformation from laboratory (vl,v2) to centre-of-mass velocities ( V,v).The laboratory beams have been taken as perpendicular. Figure 1 shows the relationship between the velocity vectors; so-called Newton diagram. In the laboratory we measure the deflection angle OL of one of the beams (I, say).What we calculate from theory is the deflection angle Oc of the relative velocity vector; v does not change its length on collision as do v1 and v2. The relationship between the two is shown in Figure 2. To compare theory with experiment we always have to make this transformation from centre-of-mass to laboratory systems: it is a little more complicated if there is a change in internal energy on collision (for then the length of v changes) or if there is a change of mass (for then the ratio of the two components of v about the centre of mass point P will change). In an inelastic collision there is an exchange of energy between the translational motion of the colliding species and their internal states but no exchange of atoms.Rotational energy spacings are typically 10 ~ * eV, and vibrational energy spacings typically 10-eV. If there is sufficient energy in the collision to excite vibrations, then rotational energies will also change. In reactive scattering there is the added complication that the THE THEORY OF ATOMIC AND MOLECULAR COLLISIONS-J. \ \ Figure 2 Transformation from laboratory to centre-of-mass velocities for elastic scattering. When rn, < rn2 there is a unique Oc for each OL; if rn, > rn2 there are two possible values of Oc for each OL. coordinates describing rotations and vibrations will be different for reactants and products, and that complicates considerably the solution of the quantum mechanical problem.To summarize: we have three types of collision which in order of complexity are elastic, inelastic and reactive; we have three types of theory which in order of computational difficulty are classical, semi-classical, and quantum. For elastic scattering of atoms we can easily carry out all three types of calculation and make useful comparisons of the results. At the other extreme, for reactive scattering only classical calculations are easy, and it is only in recent years that full quantum mechanical calculations have become feasible. The formal proofs of mathematical relationships and descrip- tions of the numerical methods used to calculate scattering cross sections are not given in this review.Most are covered in our own book on the subject2 and there are many other valuable texts, mostly written at the postgraduate level. 4 Atom-Atom Elastic Scattering; Classical Mechanics Figure 3 shows a typical classical trajectory (cm coordinates) for two atoms interacting under a repulsive potential. A particle of 0 Figure 3 Parameters for central field scattering. N. MURRELL AND S. D. BOSANAC effective mass p = WZAWZB/(WZA+ ms)comes in along a line paral- lel to the z-axis in the xz plane, is scattered by V(r)centred at 0, and disappears to infinity along a line making an angle 8with the z-axis; 8 is called the deflection angle. The kinetic energy of relative motion is where i. = dr/dt, etc. It is easier to solve the problem in polar than in Cartesian coordinates, so writing x = rsinO, z = rcosO (12) and taking derivatives with respect to time we find The total energy is obtained by adding to this the potential, The angular momentum of the system is defined by the vector product which is directed along the y axis.Angular momentum like the energy is unchanged during the trajectory. In polar coordinates its magnitude is and if this is introduced into equation 14 we have 1 . L2E = -pr2 + -+ V(r) (17)2 2pr2 L2/2pr2 is the centrifugal potential; it acts as a repulsive compo- nent, which has to be added to the central force potential when we solve the dynamics as a one-dimensional problem in r. Figure 4 shows some effective potentials VL(r)for several values of L.V(r)generally decays faster than the centrifugal potential at large r; typically as rP6so that for non-zero L the centrifugal potential is always the dominant term at large r, the exception being potentials between ions. For small values of L there is a centrifugal barrier at large r and the centrifugal potential reduces the depth of the potential well (as in Figures 4b and 4c). At some critical value of L the centrifugal potential is just large enough to remove completely the well in the effective potential (as in Figure 4d) so for values of L above this, VL(r)is wholly repulsive. The dashed line in Figure 4 shows a possible collision energy and we can think of the atoms coming in along this line from r = 00 until they meet VL(r).This point, the smallest value of r in the trajectory, is called the classical turning point (r, in Figure 3), for after this r increases with time as the atoms depart from each other to infinity.At small values of L, r, occurs in the repulsive region of the potential well, but for large L the classical turning point occurs in the region of the centrifugal barrier. Whether or not a trajectory surmounts a centrifugal barrier or not depends on the collision energy. However, at large L the classical turning point is always determined by the centrifugal barriey. From equation 16 we obtain an expression for 8 and from equation 17 an expression for i. and dividing one by the other we obtain dO-8-f L_-_-dr i pr2{2(E-V,,(r)}: The positive sign applies to the inward part of the trajectory (r decreases as 8 decreases) and the negative sign to the outward CHEMICAL SOCIETY REVIEWS, 1992 b) "I I r Figure 4 Effective potentials for atom-atom scattering.(a) L = 0; (b), (c), (d) L f 0. (a) and (b) have one classical turning point, (c) has three turning points, and (d) shows an inflection point (L= 55). part. If we integrate from Y = co (6 = TT) to the classical turning point (Y = Y,) and then back to infinity the final value of 6 will be the deflection angle. Writing the total integral over Y as twice the integral from Y, to co,we have m It is useful to introduce an important quantity, labelled b in Figure 3, called the impact parameter. A head-on collision has b = 0, a completc miss is at such a large value of b that V(b)= 0.The angular momentum, energy, and impact parameter are related by so that the expression for the deflection angle can be written in terms of E and b as drB(E,b)= n -2b s r2{ 1 --[g] ?}+ 'C This integral can be solved analytically in only two cases of interest. One of these is for a hard-sphere collision V(r)= 0, r > d; V(r)= ac, r < d (22) where dis the sum of the radii of the two hard-sphere atoms. The result is Ob cos-= -(23)2d which we note is independent of E. The other case is the repulsive coulomb potential V(r)= -B (B > 0)r for which d)VI \ r O(E,b)= 2sin-For neutral atom scattering we must consider potentials of the type shown in Figure 4a.For large impact parameters the trajectory only experiences the long range part of the potential and in this case trajectories will be bent towards the scattering centre. To preserve continuity between b and 6, the deflection function is defined as a continuous function between 7~and -GO. The general form of O(E,b)for collisions in which E is large compared with the depth of the well is as shown in Figure 5. For atom-atom scattering there is no experimental way of distinguishing between the deflection angles 6 and -6; onlyI 6 I can be measured and this is called the scattering angle. Thus in Figure 5 the b values corresponding to the crosses contribute to the same scattering angle. 0 n \ Giory 0 yVxt Rainbow Figure 5 Typical deflection function for atom-atom potentials when the collision energy is large compared with the well depth.The crosses show the three impact parameters that scatter into 8 = 50". To calculate a quantity which can be related to experimental measurements we must consider a stream of particles coming in with cylindrical symmetry parallel to the :axis and being scattered into a cone by the scattering centre. Figure 6 illustrates an annulus of the incoming beam with impact parameter lying between b and b + db, being scattered into a conical section between 6 and 6 + do. Particles crossing the area THE THEORY OF ATOMIC AND MOLECULAR COLLISIONS-J. I Figure 6 Parameters for the derivation of the cross-section for central field scattering. are scattered into the solid angle Results are described by a quantity called the cross-section which is the notional area of the incident beam scattered into a given unit solid angle.As all of the trajectories crossing dA go into the solid angle dQ, the area that goes into unit solid angle is This can be rewritten where, by taking the modulus, we allow for the fact that each b value contributes positively to 8 whatever the sign of sin8 or do/ db. If there are several b values contributing to the same scattering angle 8, we add their individual terms such as equation 29. By integrating ~(8)over 8 we obtain a total cross-section If the cross-sections are calculated for the hard-sphere potential from equation 23, we find U(8) = d2/4and u = xd2; the latter agrees with our intuitive expectation.We note that ~(8)is infinite if either sin8 = 0 or (d8/db) = 0. The former is called a glory and the latter a rainbow. Both of these will occur if the potential has both attractive and repulsive branches. However, the classical picture of associating specific trajectories (bvalues) with each scattering angle is not the whole truth. In quantum mechanics such specificity is forbidden by the uncertainty principle; in a sense each impact parameter gives some contribution to scattering at all angles. Nevertheless, the classical picture is qualitatively correct. Although infinities do not occur in experiments, the presence of strong scattering at certain angles does, and these are associated with the classical glories and rainbows.N. MURRELL AND S. D. BOSANAC 5 Quantum Scattering by a Central Force We expect readers to be already familiar with the solution of one central force problem in quantum mechanics, which is the electronic energy levels of the hydrogen atom. The Schrodinger equation for this system is most easily solved by taking spherical polar coordinates as variables and separating the wave function into a product of angular functions and radial functions. Formally the Schrodinger equation for central force scatter- ing is very similar to that for the hydrogen atom, differing only in the replacement of the coulomb potential between an electron and a proton by the atom-atom potential. For bound-state problems the wave functions must approach zero when Y approaches infinity; this condition produces quantization of the energy levels.In the scattering problem the wave functions arc not zero at infinity, instead they must represent the atoms coming together initially along straight lines and departing from one another in some angular pattern. The wave function exp(ikz) represents a stream of particles moving with momentum kh in the direction of increasing z; it is called a plane wave. We can show this by noting that this function is an eigenfunction of the momentum operator -ih (d/dz) with eigenvalue kh. After the collision, when the atoms are well away from the collision region, we have particles still moving with momentum k but they are moving out in all directions. If the particles were moving isotropically they would be described by a wave function exp( ikr) r which is called a spherical wave.The r in the denominator is required to preserve probability within a given solid angle. To introduce anisotropy into the scattered wave, we use the function r wheref’(8) is called the scattering amplitude. Only one angular variable is needed for central force scattering as the scattering has cylindrical symmetry about the z axis. We can now establish the boundary conditions on the wave functions through the asymptotic expression where -indicates the limit as Y -+ co.What we do not know is the form of the wave function in the interaction region (where the interatomic potential is non-zero), and to find this we must solve the Schrodinger equation with this boundary condition.The Schrodinger equation for the system is and by introducing the variables (35) this takes the simpler form [V* + k2 -U(r)]+(r) = 0 (36) A general solution to this can be obtained as an expansion in Legendre functions (37) CHEMICAL SOCIETY REVIEWS, 1992 v I v VJ Figure 7 Radial wave-functions for an Ar-Ar potential. which is called the partial wave expansion. On substituting equation 37 into equation 36 we find that the radial wave functions $/(Y) are solutions of [-$+ kZ -Ul(r)$(r) = 01 (38) where 1(Z+ 1)U,(r)= U(r)+ r2 (39) is the effective potential. Notice its close similarity to the effective potential that occurs in classical theory (equation 17), the difference only being the replacement of L2by h2(1(1+ l)}, a familiar feature in quantum mechanics.There are two linearly independent solutions of equation 38 for each value of k2 and 1. However, only one of these is physically acceptable and that is the one which is zero at Y = 0; called the regular solution. Figure 7 shows typical functions. When r reaches a value such that U,(r)can be neglected, the wave functions have the form $(r)-sin(kr + (40) However, it can be shown that the centrifugal potential contri- butes -h/2to the phase q1so the effect of U(r)alone is measured by 6/ = 7,+ tT 2 which is called the phase shift. Broadly speaking, the repulsive regions of U(r)give negative contributions to and the attract- ive regions give positive contributions.Figure 8 shows the dependence of the phase shift on 1 for the same interatomic potential used for the classical calculation shown in Figure 5. To derive the relationship between the scattering amplitude f(6) and a1, we can equate the asymptotic form of equation 37 which is with the asymptotic form, which represents the physical situa- tion in the crossed-beam scattering experiment. To do this involves some standard but rather tedious algebra. The result is 1 20 0 -20 Figure 8 The variation in 6, for an Ar, potential. The collision energy is twice the well depth. function. In the incident beam the particles have a probability density and in the scattered beam the probability density across an area of the sphere which subtends the unit solid angle at the centre is The differential cross-section is the ratio of these two quantities, On replacingf(6) by the partial wave expansion (equation 43) we obtain the following expression for the cross-section x (eZrSI'-1)Pl(cos8)Pr(cos8) (47) in which we note that there are interference terms (cross terms) between 1and I' partial waves.The expression for the total cross- section is rather simpler because on integrating over 6, we can make use of the orthogonality of the Legendre polynomials so that only the terms with 1 = I' persist. The scattering cross-section can be deduced from the amplitudes of the incident and scattered waves in the asymptotic wave THE THEORY OF ATOMIC AND MOLECULAR COLLISIONS-J.For atomic collisions, at the energies normally encountered in laboratory conditions, one generally needs at least a hundred partial waves to obtain convergence of the cross-sections. An estimate of the maximum value of 1 which is needed can be obtained from the classical expression equation 20 by compar- ing the impact parameter with the range of the interatomic potential. ing associated with a deflection function of the type shown in Figure 8. The calculations were made for an Ar, potential and a collision energy equal to twice the well depth. for Ar-Ar scattering at a collision energy equal to twice the well depth (-0.04 eV). Approximately 200 partial waves were needed to obtain convergence.The fine oscillations arise from the cross terms (I + 1') in equation 47 and the broad oscillation with a peak at 0 z 7~/3is associated with the classical rainbow. When a large number of terms have to be included in the partial wave expansion, a number of approximations can be made to simplify the calculation. Moreover, if one makes use of the semi-classical approximation to the wave function, then one can show that for heavy atom scattering the quantum mechani- cal cross-section is consistent with the classical expression equation 29. IIICIdSLIL LUlIISIUII3 dlC IIIIpul LdllL 1J'ULCSSGS IWI LllC CSLdUIISIIIIICIIL of equilibrium populations of vibrational and rotational energy levels in gases and liquids. In crossed molecular beam experi- ments we can study the exchange of translational and rotational energies, so called T-R exchange, or translational and vibratio- nal energies (T-V exchange).Both of these depend mainly on collisions which probe the repulsive part of the inter-molecular potential, and a hard potential model can reproduce many of the important features. The main exception is if there is a strong long-range term in the interaction potential, e.g.for ion-dipolar molecule collisions. Although molecular collisions occur at all orientations, the strongest T-V exchange is expected when atoms collide along the direction of their attached bonds so the collinear atom- diatomic molecule collision is an interesting model.If the atoms are hard, the energy transferred in the collision depends on the phase of the diatomic oscillator at the moment of impact, the largest transfer occurring when the relative velocity of the colliding atoms is largest. Qualitatively, a similar result is obtained if the interaction potential is soft. N. MURRELL AND S. D. BOSANAC 23 5 4 4 m 0 3 3 I >* n2 z\2 2 4ul 1 1 I 0 I i7/2 I 5 Q, I 3V2 ioI 2iT Figure 10 Relationship between the energy transfer and the oscillator phase for a soft collinear collision with parameters chosen to model He + H,. The initial quantum number is n, = 1. Figure 10 shows the results of classical calculations with parameters chosen to model He + H,. The H, is represented as a harmonic oscillator whose energy can be represented by although in the classical model, the quantum number n is not restricted to integer values.The interaction potential was taken as an inverse exponential of the distance between the colliding atoms. The question now arises as to how one should interpret these classical calculations. We can easily deduce an average T-V energy transfer by averaging over the phase 4,but for state-to- state cross-sections we must go further. Two methods have been used; one called quasi-classical, the other semi-classical. In the quasi-classical method one assigns any trajectory that has a final value of n between k -f and k + + to the quantum state k. Thus if we run N trajectories, uniformly or randomly distributed over the initial phase 4,and Nk of these lead to state k, then the probability of the transition to k is Nk/N.In the semi-classical picture we pick out those trajectories that end with integer values of n. We see from Figure 10that there are only two values of the phase that lead from n = 1 to n = 2. If trajectories with phases between 4 and 4+ 84 lead to a final quantum number between n and n + an, then the contribution to the probability from this set of trajectories is Taking the limit (6-+0) and summing over all trajectories leading to the specified final n gives As we shall see later, this approach taken at the best semi- classical level gives state-to-state transition probabilities which agree quite well with the quantum results.7 The Classical Picture of T-R Exchange In the collinear collision model we can define transition probabi- lities but not cross-sections, either total or differential. For this we must have 3D collisions, and these will produce T-R energy transfer. The simplest model is the collision of an atom and a rigid rotor diatomic molecule, with the interaction potential between these being a 'hard' shape. Angular momentum is conserved in a collision and for atom- molecule collisions the angular momentum consists of two parts: the orbital angular momentum of the relative motion of the centres of mass (the equivalent of L in elastic scattering) and the rotational angular momentum of the moleculej. As both of these are vector quantities, the total angular momentum is J = L +j.This vector coupling leads to some standard but rather complicated algebra in the theory of rotational inelasti- city. In two dimensions (co-planar collisions), j and L are perpendicular to the plane of motion, and hence the magnitude of the total angular momentum is eitherj + L or I j -L 1 . 1 t Figure 11 Effective impact parameter for a two-dimensional hard potential. Figure 11 shows a 2D hard potential that might apply to the collision of an atom and a small polyatomic molecule. The molecule will have its rotational energy changed by a collision if the impact force (which is perpendicular to the perimeter curve) does not pass through its centre of mass. The torque is pro- portional to the perpendicular distance from the centre of mass to the line of force; we call this the effective impact parameter 6,1.Figure 12shows the function b,(8) for the shape shown in Figure 11. The most important feature is that b,(6) has maxima and minima. Collisions at these points on the perimeter give the largest changes in rotational energy; more important, they dominate the energy change because 6, changes slowly as the point of collision moves away from these points. If one has a mathematically defined hard shape potential, then from the equations conserving energy and angular momentum, Figure 12 Effective impact parameter as a function of orientation angle for the potential of Figure 11 CHEMICAL SOCIETY REVIEWS, 1992 the change in rotational angular momentum can be deduced for different scattering angles as a function of 6,1.Cross-sections can then be deduced for each pair of initial and final rotational states of the molecule (characterized byj, andjf).The relevant formula is a generalization of that given for elastic scattering (equation 29) (a is the initial angle of the molecule relative to the line of collision). As for elastic scattering this expression has the possibility of singularities when the two terms appearing in the square brack- ets are zero or cancel. These so-called rotational rainbows appear as dominant features of the differential cross-sections for each pair of initial and final states, although, as with elastic scattering, quantum mechanics will smooth out the classical infinities.8 Quantum Mechanics of Inelastic Scattering For molecular scattering the wave function depends on the vector r of relative motion of the two centres of mass and on a set of internal variables s which are associated with the vibrational and rotational states of the molecules. As r approaches infinity the interaction potential V(r,s)approaches zero and the wave functions can be written as products of continuum functions for the relative motion and the wave functions for the discrete internal states. It is not possible to obtain the asymptotic form of the scattering wave function by direct numerical integration of the many-dimensional Schrodinger equation with this boundary condition. The procedure normally followed is the one used to find the bound states of many-dimensional systems with non- separable potentials, namely to make an expansion of the wave function in a set of known functions, which is called the basis set (e.g.the well known LCAO expansion in molecular orbital theory). For scattering wave functions the basis covers only the internal variables s. Two types of basis are commonly used, one depending only on s and the other that depends on both Y and s.The former leads to what is called the diabatic representation of the wave function and the latter to an adiabatic representation. Adiabatic bases are more complicated functions and may be difficult to obtain, but to compensate for this one should need fewer of them to provide a specified computational accuracy.Both the diabatic and adiabatic sets must represent the eigenfunctions for the internal motion of the molecules in the asymptotic region. Thus if the diabatic set are the functions x,{s) the adiabatic set cl/{r,s)will satisfy the condition To derive the multi-channel equations we write the total Hamil- tonian as where the interaction potential V depends only on the scalar distance between the interacting species; it is of course depen- dent on the orientations of the molecules relative to r, but these angles are in the set of internal coordinates s. In the diabatic basis we expand the total wave function as where xxs), the eigenstates of. HO, are an orthonormal set satisfying THE THEORY OF ATOMIC AND MOLECULAR COLLISIONS-J.The Schrodinger equation then takes the form This can be converted to a set of coupled equations in Y by multiplying in turn by each of the basis functions and integrating over s. Making use of the orthogonality of the basis, a typical equation is where Equations 58 and 59 are called the multi-channel equations. They can be thought of as a set of elastic equations, one for each basis function, which are coupled together by off-diagonal elements of the interaction potential V,(Y);Viiand EP are called the channel potentials and channel energies respectively. Similar equations are obtained from an adiabatic basis. The basis functions are in this case defined by and if one substitutes into the Schrodinger equation and forms matrix elements with the basis functions, one gets a set of coupled equations in which the coupling arises from the kinetic energy operator V2(v).Both the diabatic and adiabatic expansions provide, in princi- ple, an exact description of the wave function; in quantum mechanical terms we say the bases are complete. However, in practice we must take a finite rather than an infinite number of terms in the expansions. The finite set of multi-channel equa- tions is called the close-coupling equations. To progress further with the coupled channel equations for full three-dimensional scattering we have to make a partial wave expansion of $(r). This leads to rather complicated equations which reflect the fact that the orbital angular momentum of one molecule around the other is coupled with the rotational angular momenta of the molecules, only the total of these being con- served. However, no such complications arise for the collinear collision model of vibrational inelasticity so we will briefly look at this example for the collinear collision A + BC discussed in Section 7.With the diabatic basis we must evaluate matrix elements such as where the xi(Rec)are harmonic oscillator eigenfunctions. In this expression Y is the distance between A and the centre of mass of BC. Taking the case where B and C have equal masses, for simplicity, we have so that when the integration over RBCis carried out the result is a function of Y. This is where the coupling arises from; if the interaction potential were an exponential in Y alone, there would be no T-V exchange.We will not give details of how the multi-channel equations are solved beyond the fact that one integrates numerically from Y = 0 out to a sufficiently large value that the scattering wave functions are strictly periodic, and this is done for each of the internal states in turn. As Y goes to m the wave function picks up N. MURRELL AND S. D. BOSANAC contributions from other internal states. This complete set of wave functions (one for each internal state) is then taken in linear combinations so as to match the asymptotic condition required of the scattering wave function. If we want a wave function that represents the system in an initial internal state i, emerging in final statesj, then we write thejth component of this wave function (i.e.the function $,-(r) in equation 55 as We have an incoming wave which is non-zero only for the ith component, and outgoing waves exp(ik,r) for all energetically accessible channels. Channels are characterized by their wave vectors k which, from equation 35, are defined by If the total energy E is greater than the channel energy E: the transition i jjis allowed in the collision; k, is real and we say the channel is open. If E is less than EP, i+j is energetically forbidden, k, is imaginary, and the channel is closed. Although closed channel functions may be included in the basis (in equation 56) to improve accuracy in the interaction region, they must have zero amplitudes in the asymptotic wave functions.S,, are elements of a matrix called the scattering or S matrix. The factor (k,/k,)his also included in the amplitude so that the square modulus of S gives directly fluxes of particles not just probability densities; note that the ratio of velocities appeared in equation 53 for the classical cross-section for the same reason. 2.5 4.5 6.5 Etotal 1 90 Figure 13 Quantum mechanical transition probabilities for the collinear collision of an atom and a harmonic oscillator with parameters modelled on He + H2(a = 0.314, m = 2i3). Figure 13 shows the transition probabilities calculated for He + H,, with the H, being initially in the quantum state n = 2, as a function of the collision energy.Channels 0 and 1 are open at all energies, but note that the probability for 2 -+ I is consider- ably greater than 2 -+ 0. Channel 3 becomes open at E = 3.5hv0 (hvo being the harmonic oscillator interval) and 2 -+ 4 at 4.5hvo. The transition probabilities increase slowly for energies in excess of the threshold, and the elastic component 2-+2 decreases accordingly to conserve total probability. Table 1 compares transition probabilities for several initial and final states as calculated by quantum, classical, and semi- classical methods. Of the two semi-classical methods the simpler is the one described earlier in this review and the uniform is a better approximation to the quantum mechanical results, as is evident from the results.Note particularly some cases where the Table 1 Transition probabilities for He-H, collisions at an energy of IOhv, (-4.5 eV) Transition Quantum Classical Semi-classical n1 n2 Simple Uniform 0 0 0.060 0 0 0.058 0 I 0.218 0.356 0.472 0.21 1 0 2 0.366 0.2 12 0.416 0.38 1 0 3 0.267 0.232 0.359 0.266 0 4 0.089 0 0 0.075 1 1 0.286 0.I58 0.290 0.287 1 2 0.009 0.130 0.009 0.01 1 1 3 0.170 0.128 0.168 0.174 1 4 0.240 0.159 0.285 0.240 1 5 0.077 0 0 0.062 2 2 0.366 0.2 12 0.416 0.38 1 2 3 0.018 0.105 0.020 0.017 2 4 0.169 0.114 0.165 0.I70 2 5 0.194 0.169 0.262 0. I94 2 6 0.037 0 0 0.045 The table is taken from reference 2 where a fuller description is given of the calculations and references to the original work.classical and simple semi-classical transition probabilities are zero; Figure 14 shows, for example, that I -+ 5 is forbidden. However, these channels are open by the criterion of equation 65 and we can attribute their transition probabilities to the tunnel effect (i.e. trajectories that are not classical because they must pass into regions where the potential energy is greater than the total energy. The uniform approximation of semi-classical theory allows for the effect of these non-classical trajectories. For the collinear collision problem one may typically need about ten basis functions to obtain convergence in the S matrix elements, but for rotational inelasticity a hundred or more would be typical. There are two reasons for this.First, at the collision energies normally met in experiment many rotational channels are likely to be open. Secondly, in a collision, particu- larly one with a hard intermolecular potential. the free rotor basis functions are individually poor representations of the motion at the point of impact; typically the motion here is libration rather than rotation. There has been a great deal of interest in finding approximate solutions to the multi-channel equations which are computatio- nally less demanding. The first method to be explored was an iterative solution suggested by Born. Unfortunately, in practice convergence is usually very slow for molecular collisions.The most commonly used approximations to the multi- channel equations come under the description ‘sudden’, the term implying that the inelastic processes occur in a time that is short compared with the periods of internal motion. Mathematically the situation is this: if one could find a linear combination of the basis functions such that the potential energy matrix VJr)was diagonal, we would have removed this source of coupling, but it would be at the expense of introducing off-diagonal coupling terms in EP -E. However, if the total energy is large compared with the internal energies of the states that are populated, then we can replace all the EY -E by some average (A@ and in that case after diagonalizing V, LIE will still only appear on the diagonal.Likewise, in 3D scattering one has a centrifugal term on the diagonal 1(1+ l)r2 and if this is replaced by an average l(1+ l)/r2, then after diagonalizing V one still has a diagonal centrifugal matrix. One can therefore derive approximations which are so-classed energy-sudden, or centrifugal-sudden, or with both approximations, infinite-order-sudden (10s).The latter is very commonly employed and, in some cases, has proved to be quite accurate. Finally, we should mention the fact that the quantum mecha- nics of collisions over hard potentials can be carried out without great computational difficulty. For atom-atom scattering the solution was found in the early 1930s, but for atom-molecule, CHEMICAL SOCIETY REVIEWS. 1992 rotational inelasticity, such calculations are much more re~ent.~ Although one does not avoid the use of multi-channel equations in this approximation, the calculations are easier because the coupling only occurs at the potential wall, and not over a wide range of r; it is in this sense properly described as sudden.9 Reactive Scattering Reactive scattering is a category of inelastic scattering in which the internal states depend on the manner in which the atoms are grouped together in the initial and final states. For example, in the simple atom-diatomic molecule exchange reaction repre- sented symbolically as A + BC+AB + C (67) the internal states will be both BC states and AB states, and if there is also the possibility of forming AC molecules or of having sufficient energy in the reaction to give A + B + C, then these must be added to the list of internal states.The quantum mechanical treatment of inelastic scattering relies for its success on finding good basis functions for the internal states. A prerequisite for this is that the coordinates can be separated into an internal set s and scattering coordinates Y. It is obviously much more difficult to make such a separation when the internal states encompass reaction than when they do not. Because of this the quantum mechanical treatment of reactive scattering is much more difficult than that of inelastic non- reactive scattering. There are two approaches to the coordinate problem. One of these is to use different coordinates for the reactants and product regions of s.In this case, the basis functions which describe the internal states must change with the coordinates and it will be necessary to maintain continuity of the wave functions at boundaries in the interaction region. The second method is to use coordinates which cover the whole space but which are not linear transformations of either the reactant or product coordi- nates. In this case the best coordinates may depend on the specific problem to be solved. The best known of these is the Marcus ‘natural coordinate system’ for collinear collisions which is illustrated in Figure 14. The reaction coordinate, pr, is a curve which follows the bottom of the reactant valley, passes over the saddle point and exits along the bottom of the product valley.The internal coordinate p.r is a vector perpendicular to pr at all points. In this figure the reactant and product valleys have been drawn in so-called skew coordinates with so that the classical expression for the kinetic energy contains no cross terms XY. Yl Figure 14 The Marcus natural reaction coordinates. THE THEORY OF ATOMIC AND MOLECULAR COLLISIONS-J. The Marcus system has the advantage that it can be tailored to the potential so that full use can be made of any separable approximations to the potential. However, there are disadvan- tages; particularly non-uniqueness in some regions. Other curvi- linear systems have been proposed based on transformations of rectilinear variables that are independent of the potential func- tion.One of these is that of Delves which was developed for use in nuclear physics. Starting from a system in which the kinetic energy is separable, a transformation is made to polar coordi- nates such that X = rcosa, Y = rsina (69) with u being defined in the range 0 to fl (the skew angle). Delves’ coordinates in polar form are particularly suitable for describing the heavy-light-heavy triatomics for which the skew angle p is small. They can also be generalized for higher dimensions and become what are known as hyperspherical coordinates. If there are n dimensions, a coordinate set can always be found in which there is only one distance variable, Y, and the other n -1 variables are all angles.The advantage of hyperspherical coordinates is that all the reaction and product channels are at Y= co and are dis-tinguished by different values of the angular variables. Thus Y can be taken as a scattering coordinate for all reactive or non- reactive processes. The disadvantage of hyperspherical coordi- nates is that the contours of the potential do not follow the lines of constant Y or constant angle, so there are very strong coupling terms in the potential energy for such a system. The choice of variables is a problem for quantum mechanics because the wave functions have to satisfy boundary conditions which are different for different variables. In classical mechanics the matter is much less important because the equations deter- mining the classical trajectories can be integrated numerically in any coordinate system, although there are advantages in having variables that change slowly with time.The classical treatment of reactive scattering is much the simpler and we therefore turn now to this technique. In the classical trajectory method one examines a batch of trajectories, with initial conditions chosen randomly and makes a statistical analysis of the outcome; this is called the Monte Carlo method. The number of trajectories that have to be examined depend on the questions being asked. For example, if one takes a batch of N trajectories, all conforming with equal weight to certain initial conditions, and if N, lead to reaction and N -N, to no reaction, then the probability of reaction is and the standard error of this result is which is roughly proportional to N-f if NJN is a reasonably large fraction.To double the accuracy of a result one needs to increase the number of trajectories by a factor of four. However, if N,/N is small, the error is proportional to N,-J; hence one needs more trajectories to obtain a given level of accuracy for improbable events, e.g.ifone is interested in knowing what is the probability of a product being in a particular vibrational and rotational energy state. If one considers the initial conditions for an A + BC trajec- tory, then in the centre-of-mass coordinate system we have twelve conditions to be specified. Some of these will be deter- mined by the initial state of the reactants, some will be arbitrary (arising from an arbitrary choice of axes) and others will be chosen randomly so as to simulate the whole range of collisions that can occur. For example, in an ideal state-selected crossed- beam experiment BC would be in a well-defined vibrational- N.MURRELL AND S. D. BOSANAC rotational state so the quantum numbers v andj will determine two of our twelve initial conditions. A third is given by the relative velocity of A to the centre of mass of BC. The initial value of the y relative position coordinate is the impact parameter b. In a real collision any value of b is possible but the probability of reaction will fall to zero as b goes to infinity. In general there is a sharp decrease in the probability of reaction beyond a certain value of b and by running a small number of trajectories one can establish a minimum value of b beyond which no reaction occurs; this is typically a few ang- stroms.This minimum value gives the upper limit of h, called bmax,which has to be sampled in a batch of trajectories in order to simulate all feasible reactive collisions. The usual procedure for selecting the b value for a trajectory is to generate a random number, 5, between zero and one and to take As the area of the cross-section between b and b + db is 2nbdb one must weight the result of each trajectory by its b value. Finally, one has initial conditions arising from the orientation of BC and the phase of the BC vibration at the start of the trajectory and these also must be chosen randomly with appro- priate weighting.When the trajectory is completed, the coordi- nates and momenta must be transformed to the appropriate products and analysed to give the distribution ofenergy between the relative translational motion and the vibrational and rota- tional motion of the diatomic species. The scattering angle in the centre-of-mass coordinate system will be given by the angle between the incoming vector v, and the equivalent outgoing vector for the relative translational motion. From the vibratio- nal and rotational energies we can determine semi-classical quantum numbers v‘ and j’, and these can be discretized by rounding then; to the nearest integer number, as discussed for inelastic scattering.The probability of reaction to particular products for specific values of v,, v,j, and b is called the opacity function, PR.The reaction cross-section is then Equation 73 is the cross-section for reactions that proceed over the particular potential energy surface on which the trajectories have been calculated. A further complication is that for most reactive systems there is more than one surface that emanates from the state of the reactants, and the total cross-section is the appropriate average for motion on all of these. For example, in the reaction the total electronic degeneracy of the reactants is six for C1 and three for O,, so that there are eighteen different electronic states that are asymptotic to these reactants.The ground-state surface of C10, is a doublet but has no orbital degeneracy, so that only one in nine collisions of the reactants will pass over the ground- state surface. If the reaction only proceeds over the ground-state surface, which would be the case if all the excited-state surfaces had high barriers to the formation of products, then to compare the calculated cross-section with experimental quantities one would have to multiply equation 73 by a degeneracy factor of 119. In any experiment, even in a molecular beam reaction, there will be some averaging over v,, v, andj. It follows that cross- sections such as equation 73 must be weighed by state popula- tions in order to compare calculated and experimental results. By applying Maxwell-Boltzmann statistics for the state popu- lations and velocity distributions in an equilibrium gas, one can determine thermally averaged rate constants from cross-sections.The quantum theory of reactive scattering is currently an area of intense research activity so we give only an outline of the most popular approach. We have already stressed the difficulty of defining coordinates and basis functions for reactive scattering. Another problem is that there are frequently a large number of open channels. This is particularly true for reactions which must surmount a potential energy barrier because this can entail a large energy release in the reaction channels with the product molecules produced in a wide range of rotational and vibrational states.The number of multichannel equations that have to be integrated is usually much higher than in a typical inelastic scattering problem. It is not surprising that the most intensely studied problem is the H + H, isotope exchange reaction. This system has the advantage of a small activation barrier and a large rotational spacing, so that close to the reaction threshold only a few rotational channels are open. We will pass over the early studies of the collinear model for this reaction, although they were in their time important. Wolken and Karplus4 were the first to solve the multi-channel equations for the reaction in 3D using a small rotational basis (j= 0 to 6) for reactants and products, only the ground vibrational states, and values of the total angular momentum up to 12.Different coordinates were used for each reaction channel and a transformation from one to the other made in the interaction region. The main conclusion from this work was that the threshold for reaction was considerably lower than that found from classical trajectory calculations due to tunnelling through the barrier. The simple view of tunnelling is that it is the passage of particles into regions where the potential energy is greater than the total energy; in consequence the momentum is imaginary in these regions. However, of equal importance is the zero-point vibrational energy of the system, because this changes as the system evolves on the potential energy surface.Calculations on 1D and 2D models of the H + H, reaction show that the threshold energy increases by about 0.06 eV with each additional dimension, and this is approximately equal to the zero-point energy for the bending mode of the H, transition-state structure. Many current quantum calculations on reactive systems use hyperspherical coordinates. These were first employed for H + H, by Kuppermann and co-workers5 on the collinear reaction. Schatz6 later used the method for 3D calculations on this system and on C1 + HCl collisions, systems with very different /3 values, and showed it worked well. However, the field is developing so rapidly that one cannot yet do it justice in a review. Zhang and Miller’ have given a valuable list of refer- ences to work carried out until 1989.10 References 1 M. Rigby, E. B. Smith, W. A. Wakeham, and G. C. Maitland, ‘The Forces between Molecules’, Clarendon Press, Oxford, 1968. 2 J. N. Murrell and S. D. Bosanac, ‘Introduction to the Theory of Atomic and Molecular Collisions’, John Wiley, Chichester, 1989. 3 S. D. Bosanac and J. N. Murrell, J. Chem. Phjs., 1991,94, 1 167. 4 G. Wolken and M. Karplus, J. Chem. Phys., 1974, 60, 351. 5 A. Kupperman, J. A. Kaye, and J. D. Dwyer, Chem. Phys. Lett., 1980, 74. 257. 6 G. C. Schatz, Chem. Phys. Lett., 1988,92, 150. 7 J. Z. H. Zhang and W. H. Miller, J. Chem. Phys., 1989,91, 1528. 11 Bibliography 1 M. S.Child, ‘Molecular Collision Theory’, Academic Press, London and New York, 1974.2 R. D. Levine and R. B. Bernstein, ‘Molecular Reaction Dynamics and Chemical Reactivity’, OUP, Oxford, 1987. CHEMlCAL SOCIETY REVIEWS, 1992 3 R. B. Bernstein, ‘Introduction to Atom-Molecule Collisions: The Interdependency of Theory and Experiment’, in ‘Atom-Molecule Collision Theory: A guide for the Experimentalist’, ed. R. B. Bernstein, Plenum Press, New York, 1979. 4 U. Buck, ‘Elastic Scattering’, Ah. Chem. Phys., 1975, 30, 313. 5 E. E. Nikitin, ‘Theory of Elementary Atomic and Molecular Pro- cesses in Gases’, Clarendon Press, Oxford, 1974. 6 J. P. Toennies, ‘Molecular Beam Scattering Experiments on Elastic, Inelastic, and Reactive Collisions’ in ‘Physical Chemistry’, Vol. 6, ed. H. Eyring, W. Jost and D. Henderson, Academic Press, New York, 1974-5.7 M. V. Berry and K. E. Mount, ‘Semi-classical Approximations in Wave Mechanics’, Rep. Prog. Phys., 1972,35,315. 8 R. E. Johnson, ‘Introduction to Atomic and Molecular Collisions’, Plenum Press, New York, 1982. 9 ‘Molecular Beam Scattering’, ed. K. P. Lawley, Adv. Chem. Phys.. 1975, 30, 1. 10 H. S. W. Massey, ‘Atomic and Molecular Collisions, Taylor and Francis, London, 1979. 11 N. F. Mott and H. S.W. Massey, ‘The Theory of Atomic Collisions’, Clarendon Press, Oxford, 1965. 12 H. Pauly, ‘Elastic Scattering Cross-sections’. in ‘Atom- Molecule Collision Theory: A Guide for the Experimentalist’, ed. R. B. Bernstein, Plenum Press, New York, 1979. 13 A. E. De Pristo and H. Rabitz, ‘Vibrational and Rotational Collision Processes’, Adv.Chem. Phys., 1985,42, 271. 4 A. S. Dickinson, “on-reactive Heavy Particle Collision Calcula- tions’, Comp. Phys. Commuri., 1979, 17, 51. 5 G. A. Fisk and F. F. Crim, ‘Single Collision Studies of Vibrational Energy Transfer Mechanics’, AN. Chem. Res., 1977, 10, 73. 6 W. R. Gentry, ‘Vibrational Excitation: Classical and Semi-classical Methods’, in ‘Atom-Molecule Collision Theory: A Guide for the Experimentalist’, ed. R. B. Bernstein, Plenum Press, New York, 1979. 7 D. Rapp and T. Kassal, ‘The Theory of Vibrational Energy Transfer between Simple Molecules in Non-reactive Collisions’, Chem. Rev., 1969, 69, 61. 18 D. Secrest, ‘Theory of Rotational and Vibrational Energy Transfer in Molecules’, Ann. Rev. Phys. Chem., 1973, 24, 379. 19 H. K. Shin, ‘Vibrational Energy Transfer’, in ‘Dynamics of Molecu- lar Collisions’, ed. W. H. Miller, Plenum Press, New York, 1976. 20 ‘Molecular Collision Dynamics’, ed. J. M. Bowman, Springer- Verlag, Berlin, 1983. 21 M. Faubel and .I. P. Toennies, ‘Scattering Studies of Rotational and Vibrational Excitation in Molecules’, Adv. At. Mol. Phjs.. 1977, 13, 229. 22 D. J. Kouri, ‘Rotational Excitation’. in ‘Atom-molecule collision theory: A Guide to the Experimentalist’, ed. R. B. Bernstein, Plenum Press, New York, 1979. 23 H. J. Loesch. ‘Scattering of Non-spherical Molecules’. Adv. Chem. Phys., 1989, 42,421. 24 J. P. Toennies, ‘The Calculation and Measurement of Cross-sections for Rotational and Vibrational Excitation‘, Ann. Rev. Phys. Chem.. 1976, 27, 225. 25 M. Baer, ‘The Theory of Chemical Reaction Dynamics’, CRC Press, Boca Raton, Fl., 1985. 26 ‘The Theory of Chemical Reaction Dynamics’, ed. D. C. Clary, Reidel, Boston, 1986. 27 W. H. Miller, ‘Reaction Path Models for Polyatomic Reaction Dynamics from Transition State Theory to Path Integrals’, in ‘The ~ Theory of Chemical Reaction Dynamics’, ed. D.C. Clary, Reidel. Boston, 1986. 28 J. T. Muckerman, ‘Applications of Classical Trajectory Techniques to Reactive Scattering’, in ‘Theoretical Chemistry’, ed. D. Hender- son, Academic Press, New York, 198 1. 29 R. N. Porter, ‘Molecular Trajectory Calculations’, Ann. Rev. Phj-s. Chem., 1974.25, 317. 30 L. M. Raff and D. L. Thompson, ‘Classical Trajectory Approach to Reactive Scattering’. in ‘The Theory of Chemical Reaction Dyna- mics’, ed M. Baer, CRC Press, Boca Raton, Fl., 1985. 3 1 G.C. Schatz, ‘Overview of Reactive Scattering’, in ‘Potential Energy Surfaces and Dynamics Calculations’, ed. D. G. Truhler, Plenum Press, New York, 198 1.

ISSN:0306-0012    

DOI:10.1039/CS9922100017

出版商:RSC    

年代:1992

数据来源: RSC

摘要:

Cyclopentadienyl Molybdenum and Tungsten Dihalides Malcolm L. H. Green and Philip Mountford Inorganic Chemistry Laboratory, South Parks Road, OxfordOX1 3QR 1 Introduction Mono-7-cyclopentadienyl transition metal halide complexes form an important class of precursor in the synthesis of other organometallic compounds. In this class, compounds of the general type [M(~-C,R,)X,]n (X = halogen) are now estab- lished for the majority of the transition metals. Until recently, however, reactivity had only been explored in substantial detail for the metal-metal non-bonded Group 9 complexes [M2(7- CSRs),X2(p-X),] (M = Rh or Ir).I In this article we review the synthesis, structures, and reactivity of the tungsten and molyb- denum members of this class. 2 Synthesis and Structures We shall begin by examining the synthesis and molecular structures of the compounds [M(7-CSR,)X,], (M = Mo or W, X = halide, n = 2 or uncertain).Two extreme geomctries (Figure 1; A and B) have been observed for the binuclear derivatives depending both upon the identity of the metal and the substituents on the 7-cyclopentadienyl ring. There is a third potential basic geometry (Figure 1; C) which possesses two terminal and two bridging halide ligands. The geometry C has not been observed for M = Mo or W, but in fact is the most common amongst the other [M(7-C,RS)X,], derivatives of the transition metals, including the first member of the triad, chromium., Table 1 lists the crystallographically characterized [M(T-C,R,)X,], derivatives of Mo and W along with their predicted M-M valence electronic configuration (vide infra -Bonding).Malcolm Green obtained his Ph.D. at Imperial College of Science and Technology in 1959. He moved to Cambridge as a Demon- strator in 1960 anda Fellow of Corpus Christi College (1961). He cvas appointed Fellow and Tutor in Inorganic Chemistry at Balliol College, Oxford in 1963, and became Professor of Inorganic Chemistrj, at Oxjord University in 1989. He has been an A. P. Sloan Visiting Professor at Harvard University (1973) and a Sherman Fairchild Visiting Scholar at the Calijornia Institute of Technology (1981). His work has been recognized by the award of a Corday-Morgan Medal, a Tilden Lectureship and Prize, the ACS Award for Inorganic Chemistry (1984) andhe was electedFellow of the Royal Society in 1985. He has published 2 books and over 350 articles in the jield of organotransition metal chemistrj9.Philip Mountford was educated at Hatjield Polytechnic [B.Sc. (Hons., Class I) and the Smith, Kline, and French prize in applied c*hemistrj>,19861 and Balliol College, Oxford (D. Phil, 1990) \t,here he carried out research bzyith Professor M. L. H. Green into the structures and reactivity of organoditungsten complexes. In 1989 he bi.as elected to a Junior Research Fellobvship at Wolfson College, und in 1990 took up the post of Departmental Demon- strator in the Inorganic Chemistry Laboratory, Oxford. He is co- author qf'over 20publications and his research interests include the synthesis, reactivity, and electronic and molecular structures of complexes containing metal-metal or metal-ligand multiple bonds.Figure 1 The three basic geometries for 7-cyclopentadienyl metal diha- lide dimers. No particular bond order is implied by the line between the metal atoms. The dimolybdenum dimers [Mo2(7-C,H,CHR,), (p-CI),] (R=Me or Ph) were first prepared by treatment of the corres- ponding 7-fulvene complexes [M0(ys ,yl-cs H,CR,)(r)-C,H 6)] with HCl gas.3 The molecular structure for R=Me is of the type A (Figure l), and is shown in Figure 2(a). The complexes [Mo,(~-C,H4CHR2),(p-C1),] were the first examples of dinuc- lear complexes with four bridging halide ligands, and their diamagnetic nature together with simple electron-counting pro- cedures and a Mo-Mo bond length of 2.607( 1) 8, (for R=Me) suggested that they possess a molybdenum-molybdenum single bond.Attempted preparation of the tungsten analogues by treatment of [W(~S,~1-C5H4CR,)(~-c6H6)]with HCI gas failed to afford any tractable pr~duct.~ R = Me or Ph (1) Recently, Alt and co-workers found that treatment of [W,(,- C,H,),(CO),(p-H),] with HCl gas at low temperature gave a blue, insoluble, carbonyl-free material formulated as [W(,- C,H,)Cl,], on the basis of analytical and infra-red data., Previously, Schrock had reported that reduction of [W(,-C,Me,)CI,] with two equivalents of sodium amalgam or 29 30 CHEMICAL SOCIETY REVIEWS, 1992 Table 1 Structure and bonding of crystallographically characterized [M(y-C, R,)Cl2I2 (M = Mo or W) complexes Compound Structural type M-M electronic configuration M-M bond length (A) Reference [Mo2(77-C5H4Pr'),(CL-C1)41 A a26*2 62 2.607(1) c [W2(77-C,H4Pr1)2C141 B U2T4 2.3678(8) d[w,(?-C5Me5)2 (CL-c1)41 A U26*262 2.626(1) e See Figure I.h J. C. Green, M. L. H. Green, P. Mountford, and M. J. Parkington, J. Chem. Soc., Dalton Trans., 1990, 3407. P. D. Grebenik, M. L. H. Green,11 A. ILquierdo, V. S. B. Mtetwa, and K. Prout, J. Chem. Soc., Dalton Trans., 1987, 9. M. L. H. Green, J. D. Hubert, and P. Mountford, J. Chem. Soc., Dalton Trans., 1990, 3793. C. J. Harlan, R. A. Jones, S. U. Koschmieder, and C. M. Nunn, Polyhedron, 1990,9, 669.p Reduction of the mono-ring-substituted tetrahalide com-plexes [W(y-C,H,R)X,] (R = Me or Pr', X = Br or C1) with two equivalents of sodium amalgam gave the corresponding green complexes [W,(y-C,H,R),X,] in 4&60% yield.* An X-ray crystal structure determination of [W2(+2,H4Pri),Cl4] [Figure 2(c)] revealed a dimer with an unsupported W=W triple bond, in striking contrast to the structure of its dimolybdenum congener [Figure 2(a)] and the pentamethylcyclopentadienyl analogue, [W,(y-C,Me,),(p-Cl),].An analogous reductive dimerization route may also be used to prepare the dimolybdenum com- pounds [Mo2(TCsMe5)2 (P-c1)41 or [MO~(~~-~SH,R>,(,-X>~I(R=Me, Pr', or But; X = Br or Cl) from the tetrahalides [Mo(q- C,R,)X4],s and is thus the best general route into these dimer systems.A (3) M = Mo or W; X = CI or Br; R = Me, Pr', or But Unfortunately, the analogous ring-unsubstituted homolo- gues [M(y-C, H ,)X2In cannot be prepared cleanly using sodium amalgam because of their insolubility and consequent contami- nation with the sodium halide by-product. However, Poli has shown that the use of zinc as a reducing agent with [M0(7- C,H,)Cl,] in thf solution affords an insoluble, golden-yellow, crystalline material formulated as [M(y-C,H,)CI,] and which is thought to be oligomeric in the solid ~tate.~ Very recently, the cationic p-iodo species [Mo,(v-C,Me,),(p-I),] +. has been prepared and shows reversible oxidation and reduction waves in its cyclic voltammogram. O LiBEt,H afforded an emerald green material for which no 3 Bonding characterizing data were presented, but which was described as The bonding in the two different geometries found for the [M(y- [W,(y.-C,Me,),(p-Cl>,] with a structure analogous to those of C,R,)X,], (M = Mo or W) dimers has been the subject of a the dimolybdenum complexes described above.6 This com- detailed study using gas-phase He-I and He-I1 photoelectron pound was later crystallographically characterized [Figure 2(b)] (PE) spectroscopy and extended-Huckel molecular orbital cal- as its [P,But4] co-crystallate (obtained from the reduction of culations.' l The model complexes studied were [Mo2(y-(type A) and [W2(t7-CsHs)2C141 (type B) idea- [W(T&,M~,)C~~]with LiPBu',) and has the type A tetrachlor- CSHS)~(P-C~)~] with no unusual lized to Czhsymmetry; the interaction diagrams are given in ide-bridged structure [W 2(y-C ,Me,), (P-C~)~] contacts between the [P2But4] and ditungsten molecules.' Figures 3 and 4 respectively. The type A structure possesses a ~~6*~i3~configuration for the Mo-Mo interaction amounting to a net metal-metal single bond which agrees with formal electron-counting procedures 4 BuiPLi (note that although the symmetry of these molecules is lower W-toluene than cyclindrical, the classification of metal-based orbitals according to the (T, T,and 6 notation is nevertheless a useful distinction based on predominant orbital type).The 0-bonding orbital (la,) arises from overlap of the metal valence dzz orbitals CYCLOPENTADIENYL MOLYBDENUM AND TUNGSTEN DIHALIDES-M.L. H. GREEN AND P. MOUNTFORD 8 a* X t Y Lz Figure 3 Interaction diagram for [Mo2(~-C,H,),(p-C1>41. (Reproduced by permission from reference I I .) and the 8 (2b,) and S* (la,) levels are the in- and out-of-phase combinations respectively of the dxy orbitals. The remaining 4d -12)orbitals of molybdenum (d,,, d,:, dT2 are involved in Mo-(p- C1) framework bonding and are thus raised high in energy. The apparently curious ordering of the S* and 8 metal-based orbitals (la, and 2b, respectively in Figure 3) has been attributed to the different extent of their interactions with the appropriate symmetry-adapted combinations of the bridging ligand orbitals. Similar reversals of 8* and 8 metal-based orbitals have been proposed for other dimetallic complexes. In contrast, the type B structure (Figure 4) possesses a W=W triple bond of valence electronic configuration (T~x,.In this case the metal-metal 0 bond (1ag)also arises from overlap of the & orbitals, but removal of the bridging ligands allows the d,, and d,; metal orbitals to come down in energy and form the two virtually isoenergetic components of the x system (la,,and 1bJ.At relatively low energy are vacant 8 (2ag, LUMO) and S* (2b,) molecular orbitals formed from the in- and out-of-phase combi- nations of the Sd,2 atomic orbitals. The green colour of the ~ 12 [W,(v-C,H,R),X,] complexes has been tentatively ascribed to u 8* and/or x 4 8 transitions.' The electronic structure of [W2(~-C,H,),C1,] is broadly similar to those of the related metal-metal triply-bonded &-A3 dimers [X,MrMX,] (M = Mo or W; X = NR,, OR, alky1).'3,14 The PE spectra of the type A complexes [Mo2(7-CsH4Me)2(p-Br)4]1 and [W,(~-C,Me,),(p-C1)4]1 are consis- tent with the molecular orbital description outlined above, showing ionizations assignable to excitations from three separ- ate metal-based orbitals.The first vertical ionization energy for the dimolybdenum complex (6.29 eV) is substantially higher than that of the pentamethylcyclopentadienyl ditungsten com- plex (5.74eV) indicating that the latter is more electron-rich. The relatively narrow band width of the 0-ionizations (approxima- tely equal to those of the 8 and 8* ionizations) in these complexes has been discussed in terms of the inflexibility of the M2(p-X)4 core.Thus the anticipated lengthening of the M-M bond in the 2A,ion state formed on removing an electron from the (T orbital may be countered by increased CI-Cl lone pair repulsions in the 3a 2a la la X Y /--' Figure 4 Interaction diagram for [W2(~-CsH5)2C14]. (Reproduced by permission from reference 1 1.) (p-Cl), bridge as the Mo2(p-Cl), unit elongates along the Mo-Mo vector." The He I and He I1 PE spectra for [W,(~-C,H,Prl),CI,] showed only one, symmetrical metal-based ionization at 6.48 eV, whereas two might have been expected both from the extended-Huckel calculations and from a general anticipation of a stronger 0-bonding than X-bonding interaction on valence orbital overlap criteria.' However, assuming Koopmans' theorem, the PE spectra suggest that the (T and x levels are isoenergetic. Similar phenomena have been noted in other metal-metal multiply-bonded dimers' and have been attri- buted to the relatively close approach of the two metal centres in such complexes.' This leads to a substantial unfavourable overlap between the valence ndZ2orbital of one metal atom with the outer core ns or np, orbital of the other, and to a destabiliza- tion of the metal-metal valence 0-interaction.The first ioniza- tion energy (6.48 eV) for [W,(~-C,H,Prl),Cl,] suggests that this complex is more electron-rich than the related metal-metal triply-bonded carbonyl complexes, [M,(7-CsH,),(CO),] (M = Cr, Mo, or W; 1st i.e.= 7.25-7.36 eV)17 and most of the [M,X,] complexes of Chisholm and Cotton.' 3,14 The different ground state molecular geometries of [Mo2(7- C,H,Pr'), (p-Cl),] and [W,(,-C H4Pr1),C14] has been rationa- lized in terms of the extent of metal-metal overlap afforded in the type B geometry for the two metals." The quadruply- bridged structure A clearly favours metal-ligand bonding whereas the type B geometry emphasizes metal-metal bonding. Extended-Huckel molecular orbital calculations predict a larger total metal-metal overlap population for M = W than for M = Mo in the type B complex [M,(7-C5H5),Cl4]. It was concluded that 'there exists a delicate balance between metal- metal and metal-ligand bonding' in these complexes. ] ] This statement is underscored by the structure of [W2(7-CSMes),(p- Cl),] for which a quadruply-bridged type A geometry presuma- bly minimizes 7-C,Me,-chloride ligand steric interactions at the expense of direct metal-metal bonding.However, the importance of metal-metal bonding in setting the basic geome- tries of Group 6 metal complexes is further emphasized by the 32 structures of the dichromium complexes [Cr,(q-C,R,),X,(p- X),] (R = H or Me; X = C1, Br, or I) which are paramagnetic, of the structural type C and contain no metal-metal bond., bu -\ \\ T 'ii1 %-/= A-2 -1 &-/ as -a5J Figure 5 Correlation diagram for the opening of a quadruply-bridgeddimer (type A) to a doubly-bridged dimer (type C).(Reproducedby permission from reference 1 1.) The possibility of a metal-metal bonded type C (doubly- bridged) geometry intermediate between the two extremes A and B for the molybdenum or tungsten complexes has been probed using extended-Huckel calculations which gave the correlation diagram reproduced in Figure 5.For a d3-d3 electron count, a quadruply-bridged (type A) structure is favoured over the doubly-bridged one both in terms of metal-based orbital energe- tics and an unfavourably small HOMO-LUMO gap in the type C geometry. 4 Reactivity The two very different alternative geometries (Le., either a quadruply-bridged or unsupported metal-metal bond) found for the [M(q-C,R,)X,], complexes, might, at first sight, lead one to anticipate that their reactions would be clearly partitioned according to individual ground-state structures. However, there appears to be relatively little energy difference between the two extreme geometries, which are sensitive to changes in metal or cyclopentadienyl ligand substituents, and a solution equilibrium situation [type A-type B] lying well to one side or the other could be envisaged.Moreover, a recent study of the symmetry- allowed 'opening-up' process, [M,(q-C,H,),(p-CI),] (type A) -,[M2(q-CsH~)2Cl,] (type B ) using extended-Huckel pro- cedures for M = Mo or W predicted no significant energy barrier (in the absence of steric effects) along the reaction coordinate for a d3-d3 dimer.'* It is found in fact that the reactions of the bridged and non- bridged [M(q-C,H,)X,], complexes have some features in common, but in other instances differ substantially according not only to the basic ground-state geometry of the dimer, but also to the nature of X.4.1 Lewis Base Addition Reactions The reactions of [M(q-C,R,)X,]n with Lewis bases are summar- ized in Scheme 1 and fall broadly into two categories depending on whether the products obtained are dinuclear or mononuc- lear. The formation of mononuclear compounds may be accom- panied by a change in formal oxidation state giving MI1 or MIv derivatives. Addition of chloride ions to the molybdenum or tungsten CHEMICAL SOCIETY REVIEWS, 1992 complexes [M(q-C5H4R)C12],, gives the binuclear, anionic deri- vatives [M,(q-C5H4R),Cl4(p-CI)]-(M = Mo, R = H or Me; M = W, R = Me or A crystal structure determination for M = Mo, R = H revealed a metal-metal bond length of 2.413(1) A, and Fenske-Hall molecular orbital calculations suggest that this molecule contains a Mo-Mo triple bond.9 The anions are labile at room temperature and the fluxional process can be interpreted as one involving effective rotation of the p-chloride ligand around the metal-metal vector.l9 The anion [Mo,(q-C,H4Me),Cl4(p-C1)]-reacts with HCl gas returning the quadruply-bridged precursor [Mo,(q-C,H,Me),(p-Cl,)] in quantitative yield, presumably via the intermediate Mo" dimer [Mo,(q-C,H,Me),Cl,(p-Cl)(p-H)] which might then reductively eliminate HC1.In support of this hypothesis the corresponding ditungsten anion is readily proto- nated to give the stable p-hydrido complex [W,(,-C~H4Pr1)2Cl,(p-Cl)(p-H)].The differing reactivities of Mo and W illustrate the accepted view that W has a greater ability than Mo to support higher oxidation states.Treatment of [Mo,(q-C,H,Pr'),(p-Cl),] or [Mo(q-C,H,)CI,] with monodentate or certain bidentate tertiary phosphines (Scheme 1) affords the paramagnetic, mononuclear Mo"' deri-vatives [Mo(q-C5 H, R)Cl,(PR;),]. 3.2 O The crystal structures for R = Prl, (PR;), = dppe,,O and for R = H, R' = Me23 have been reported and confirm the 'four-legged piano stool' geo- metry depicted in Scheme 1. The complexes [Mo(q-C,H,Pr')CI,(PR;),] are precursors to the Mo'" trihydrido derivatives [Mo(q-C,H,Prl)H,(PR;),l ,some of which are H-D exchange catalyst^.^ In contrast, [Mo,(~-C,H,Pr~),(p-CI),]reacts with dmpe to afford the Moll derivative [Mo(q-C,H,Pr')(drnpe),] which is + readily protonated to give the hydrido cation, [Mo(q-+C,H,Pr')(dmpe),H]Z .3 On treatment of [Mo(q-C,H,)Cl,] with dmpe, the first intermediate observed by ESR spectroscopy gives a quintet resonance indicative of a complex containing a Mo(dmpe), unit and again no evidence for a mono-dmpe adduct was reported.,, The differing reactivity of dmpe compared to that of the other mono- and bi-dentate phosphines described above has been discussed in terms of a smaller Tolman cone angle for the dmpe ligand.3 Addition of bipyridyl to [Mo2(q- C,H,Prl),(p-Cl),] gives mononuclear Mo"' complexes analo- gous to those described above for the reactions with phosphines.O In contrast to the behaviour of the dimolybdenum complexes, treatment of the WrW triply-bonded complex [W,(q-C,H,Me),Cl,] with dmpe gave the diamagnetic, dinuclear complex [W,(q-C,H,Me),CI,(p-Cl),(dmpe)] (Figure 6) for which a structure determination revealed a relatively long W-W bond [W-W = 3.196(1) A].,, The isolation of a dimeric com- plex for tungsten may reflect a greater strength of W-W verszis Mo-Mo bonds. The corresponding reaction of [W2(q-C,H,Me),Cl,] with PMe, afforded no tractable The nuclearity of the products obtained from treating [W,(q- C,H,R),X,] (R = Me or Pr', X = Br or C1) with carbon monox- ide (Scheme 1) depends critically on the identity of X and further highlights the delicate balance of factors at work in setting the reaction pathways of these complexes.For X = C1, the dinuclear species [W ,(?-C ,H, R),Cl, (p-Cl), (CO),] analogous to [W 2(q-C,H,Me),Cl,(p-Cl),(dmpe)] are obtained. The complexes[W,(~-C,H,R),Cl,(p-C1)2(CO)2]exist as a ai. 2: I mixture of isomers in solution. The major isomer has been crystallographi- cally characterized and possesses the C, geometry shown in Scheme 1. Its solution NMR spectra show one diastereotopic 7-C,H,R and CO ligand environment. The second isomer cannot be separated from the major one, and although it is known that it contains two types of diastereotopic q-C,H,R and CO ligands in its NMR spectra it is not possible unambiguously to assign a molecular structure.l9 For X = Br, only the mononuclear WtV derivativefac-[W(q- C,H,Prl)Br,(CO),] was isolated. This complex has also been crystallographically characterized. Presumably the longer W-W bond required in the W,(p-X), core for X = Br makes the 33CYCLOPENTADIENYL MOLYBDENUM AND TUNGSTEN DIHALIDES-M. L. H. GREEN AND P. MOUNTFORD C(16) C(23) I I\ Figure 6 Molecular structure of [W,(?-C,H,Me),Cl,(p-Cl),(dmpe)]. Hydrogen atoms are omitted for clarity. (Reproduced by permission from reference 24.) formation of a dinuclear derivative unfavourable. The quad- ruply-bridged, pentamethylcyclopentadienyl species [W,(,- C,Me,>,(p-Cl),] also reacts with CO and gives the correspond- ing dinuclear product [W,(~-C,Me,),CI,(p-Cl)~(CO)2].Treatment of [W2(~-C,H,R),Cl4) (R = Me or Pr') with Bu'NC does not give analogues of either of the carbonyl complexes described above. The reaction leads instead to com- plexes which contain both a terminal and bridging t-butylisocya- nide ligand on the basis of their IR and NMR ~pectra.'~ A structure consistent with the spectral data is [W,(,-C,H,R),C13(p-Cl)(Bu1NC){p-(~+ n)-Bu'NC)] (see Scheme 1). 4.2 Ligand Exchange Reactions Treatment of [Mo,(~-C,H4Pri),(p-C1),] with LiSR (R = Me, Ph, or adamantyl) affords in modest yields the corresponding tetra-p-t hiola to derivatives [Mo, (7-C ,H,Pr'), (p-SR),] which CI,$CIL* d RKWPWRoc..'j \".-.c, viii R CI co vii/ have been crystallographically characterized for R = Me and Ph.20 With LiSBu' the mixed p-sulphido-p-thiolato complexes cis,anti-and fvuns,s~yn-[M~,(~-C~H~Pr~)~(p-S)~(p-SBu~),]were formed.The reaction of [Mo,(~-C,H~P~~)~(~-C~)~]with EtSSiMe, gave a mixture of [Mo2(~-,C,H,Pr1),(p-SEt),land cis,unti-and tr~ns,syn-[Mo,(~-C~H~Pr')~(p-S)~(p-SEt),]. The yield of [Mo,(7-C,H4Pr'),(p-SMe),l from the reaction with LiSMe can be substantially increased by the addition of a four-fold excess of FeCI, to the tetrachloride dimer before addition of the LiSMe. This modified route may proceed viu an anionic intermediate such as [Fe(SMe),12- and we note that treatment of [Mo2(r)-C,H4Pri),(p-C1),] with [NEt,],[Fe(S-p- tol),] affords a small yield (< 2%) of the p-S-p-to1 species, [Mo2(7-C5H,P~-~),(p-S-p-tol),].~~ The electron-rich sulphur- or selenium-molybdenum cubane- like complexes [Mo2(~-C,H,R),(p3-Y),1 (R = Pr', Y = S or Se; R = Me, Y = S) may be prepared in reasonable yields from [Mo,(~-C,H,R),(p-Cl),] and LiYH.The X-ray structure for R = Pr', Y = S has been rep~rted.~~.'~ A second product of the reaction for R = Me, Y = S was [MO~(~-C,H,M~),(~-S)~(~-SH),]; it is not known if this is a side product of the reaction or an intermediate in the formation of the cubane itself.26 The mixed sulphur/selenium cubanes [MO,(~-C,H,P~~),(~,-S).~(~~-S~),-.] (x = 04) can be prepared as a mixture of compounds from [Mo,(~-C,H4Pri),(p-Cl),]and LiSHiLiSeH, but unfortunately they cannot be separated by column chromatography.'s R R h In contrast, treatment of the quadruply-bridged tungsten complex [W,(~-C,Me,),(p-CI),] with LiSH under reflux in t Reagents: i, Bu'NC, Et,O, ca.70% (R = Me or Pf); ii, dmpe, toluene, 30%; iii, dmpe, acetone/thf, > 33% (R = Prl) or dmpe, thf, observed by ESR only (R = H); iv, PR;, toluene, > 90% (R = Pr', R' = Me, PR; = PMe,Ph; R = H, R' = Me, Et, or Ph, PR; = PMe,Ph or PMePh,); v, L-L, toluene, > 75% (R = H or Prl; L-L = dppe, dippe, or bipyridyl); vi, [PPNICl, CH,Cl,, > 90% (R = H, Me, or Prl; M = Moor W); vii, CO( I atm.), toluene, 40%; viii. CO (1 atm.), toluene, > 90% Scheme 1 Reactions of [M(q-C,H,R)X,],, with Lewis bases. toluene gave a mixture of the previously-reported dimeric sulphido complexes [W,(~-C,Me,),S,(p-S),] and [W,(7-C5Me,),S,(p-S,)].1 In another ligand replacement reaction of [W,(~-C,Me,),(p-Cl),], Schrock has found that treatment with LiAlH, affords, on cold methanolysis work-up, the perhydro complex [W,(~-C,Me,),H,(p-H),] in 40-50% yield.6 (5) 4.3 Oxidative Addition Reactions The complexes [M(7-CSH4R)X2],, undergo a number of oxida- tive addition reactions, some of which are illustrated in Scheme 2.Poll has recently shown that [Mo(7-CsHs)Cl,] reacts with PhICI, to give [Mo(7-C,H,)C13] which is a useful precursor to other Mo'" complexes.29 The compound [Mo(7-CSH 5)C13] may also be prepared by valence comproportionation of [MO(V-C,H,)CI,] and [Mo(7-C,HS)C1,], or by reducing the latter with TiCl,.Treatment of the complexes [W,(~-C,H,Prl),X,] with dihyd- rogen (2-3 atm.) affords the corresponding p-dihydro deriva- tives [W,(,-C ,H,PT~),X,(~-H)~](Scheme 2). The bridging nature of the hydride ligands was inferred from the magnitude of the Ia3W satellites (ca26% by area of total signal; lS3W, 14.5% natural abundance, 1 = 3). A bridging molecular dihydrogen [W,(p-H,)] representation of the bonding was discounted by the low-temperature T, value for the hydride ligands (ca. 1.2 s at -9OOC) and by the magnitude of the one-bond hydrogen- tungsten coupling constant (1J11H-1*3W] = 112-1 16 Hz).~~ For X = CI the dihydrogen addition reaction is reversible, and warming a toluene solution of [W2(7-CsH4Pr1)2C14(p-H)Z] to 60 "C under reduced pressure, returned the precursor [W,(7- C,H,Prl),Cl,] in quantitative yield as the first example of the reversible addition of H, to a metal-metal multiple bond.In CHEMICAL SOCIETY REVIEWS. 1992 contrast, the bromide-supported analogue [W,(7-C,H,Pr'),Br,(p-H),] is stable up to cu. 100°C in toluene. Treatment of a toluene solution of the pentamethylcyclopenta- dienyl analogue, [W,(,-C,Me,),(p-Cl),], with dihydrogen (1 0 atm.) gave no reaction. * This latter observation contrasts with the behaviour of the ditantalum analogue, [Ta,(+, Me,),(p-Cl),], which reacts with H, (3 atm.) to give the p-hydrido derivative, [Ta,(q-C,Me,), Cl,(p-H ,)I. The W-W triply-bonded dimers readily insert into P-H, S-H, and CI-H bonds, but do not undergo insertion into N-H or O-H bonds, presumably due to the greater bond strengths of the latter.The primary and secondary phosphines PPhR'H (R' = H or Ph) react readily with the complexes [Wz(7- C,H,R),X,] to afford the corresponding p-phosphido deriva- tives [W,(7-CSH,R),X,(p-H)(p-PPhR')](R = Me or Pr'; R' = H or Ph; X = Br or Cl) in good yield.30 The metal-metal bond length of 2.6556(7) 8, found for [W,(7-C,H,Pr1),C1,(p- H)(p-PPh,)] is consistent with the W-W double bond expected from simple electron-counting procedures. A qualitative mole- cular orbital interpretation of the metal-metal bonding sug- gested a valence electronic configuration of ~~d.~~ Treatment of [W,(T-C,H,R),Cl,] with HCl gas in toluene gives the p-chloro-p-hydrido compounds [W,(y- C,H,R),CI,(p-Cl)(p-H)] in > 90% yield.30 These latter com- plexes may also be prepared by protonation of the p-chloride anions [W,(7-CSH4R),Cl4(p-C1)]-.The corresponding molybdenum species [Mo, (7-C H, R),Cl,(p-Cl)(p-H)] cannot be prepared by either route.'9.32 The compounds [WZ(7-C5H4R),C14(p-Cl)(p-H)]are fluxio- nal and at room temperature their 'H NMR spectra show an AA'BB' spin system for the 7-cyclopentadienyl ring protons, whereas at low temperature an ABCD spin system is observed. dG$valuesof12.5~0.15(at263K)and12.3~O0.15kcalmol~' (at 268 K) were measured for [W,(y-C,H,R),Cl,(p-Cl)(p-H)] (R = Pr' and Me rcspectively). The mechanism illustrated below, involving an equilibrium between edge-sharing square- based pyramidal slid trigonal bipyramidal structures, has been proposed to account for the fluxional behaviour of these com- plexes.,O Similar behaviour has been suggested for the p-phosphido carbonyl complexcs, [Mo,(~-C,H,),(CO),(p-H)(p-PPhR)] (R = H or Ph).,, vi 1iii I Reagents: i, H2(3 atm.), toluene, ca.100% (X = Br or Cl); ii, 50 "C,[2H,]toluene, cu. 100% (X = Cl); iii, HCl gas. toluene, > 90% (R = Me or Prl); iv. PHPhR', toluene > 80% (R = Me or Pr'; R' = H or Ph; X = Br or Cl); v. R'SH, toluene, > 70% (R = Me or Prl: R' = Me. Et. Pr', Bu', or Ph); vi excess of PMe,, toluene, > 45% Scheme 2 Oxidative addition reactions of [W2(+2,H,R),X,]. CYCLOPENTADIENYL MOLYBDENUM AND TUNGSTEN DIHALIDES-M. L. H. GREEN AND P. MOUNTFORD L R = Me of Pi A series of p-arene- and p-alkane-thiolato derivatives [W ,(?-C,H,R),CI,(p-SR’)(p-H)] (R = Pr’ or Me; R’ = Me, Et, Pr’, But, or Ph) have been prepared (Scheme 2) and are also fluxional Inon the NMR time~cale.~~ the high temperature (fast exchange) limit the 7-C,H,R ring protons appear as a single ABCD spin system, whereas in the low temperature (slow exchange) limit they appear as two inequivalent ABCD spin systems.For R‘ = Me or But the fast and slow ring exchange limits respectively could not be observed. A fluxional process analogous to that postulated above for [W,(q-C,H,R),Cl,(p- Cl)(p-H)] was rejected since the p-SPh complexes are fluxional at room temperature whilst the closely-related p-phosphido com- plexes [W,(q-C,H,R),CI,(p-PPhH)(p-H)] are static up to at least 90 “C in toluene-d,.The free energies of activation for the fluxional process in the complexes [W,(q-C,H,Pri),C1,(p-SR’)(p-H)] (R’ = Me, Et, Pr’, or Ph) [see Figure 7(a)] show that dGS clearly decreases with increasing steric demands of the p-SR‘ moiety. The mechanism shown in Figure 7(b) involves lone pair inversion at the p-S atom. dGS decreases with steric bulk because the two ground- state geometries [at left and right in Figure 7(b)] are more sensitive to the steric demands of the bridging ligand than is the postulated transition state (at centre) in which the R’ group is orientated directly away from the W,(q-C,H,R)2C1,(p-H) frag-ment. Therefore as R‘ increases in size the ground state geometry is destabilized relative to the transition state and so AGS decreases. O The oxidative addition products [W,(~-C,H,Pr’),X,(p-H)(p-Y)] (Y = H, SR‘, PPhR‘, or Cl) react with PMe, (Scheme 2).For Y = SR’ or C1 (X = Cl), only the mononuclear product [W(q- C,H,Pri)(PMe3),C1] could be isolated. For Y = H (X = C1 or Br) or PPh,(X = Cl), however, the dinuclear Lewis base adducts, [W,(q-C,H,Pri),X,(p-X)(p-H)(p-Y)(PMe,)lwere obtained and the solid state structure for Y = PPh, has been determined. 4.4 Alkyne Addition and Related Reactions The W=W triply bonded complexes [W,(q-C,H,R),X,] react with one or two equivalents of alkyne in a manner similar to that found for the related metal-metal triply-bonded complexes [M,(OR),(py),] (M = Mo or W; n = 0-2) and [M2(q-C,H,),(CO),] (M = Cr, Mo or W).34The pentamethylcyclo- pentadienyl analogue [W,(q-C,Me,),(p-Cl),] does not react with but-2-yne, and the dimolybdenum complex [Mo2(q- CsH4Pr1)2(p-Cl)4]gives intractable products.26 The alkyne addition and coupling reactions of [W,(q-C,H,R),X,] are shown in Scheme 3.Addition of one equivalent of C,R, to [W,(~-C,H,Pr’),X,] affords the corresponding mono-p-alkyne derivatives [W,(q- C,H,Prl),X,(p-C,R,)] (X = Br, R = Me or Ph; X = C1, R = Et or SiMe,) in 40-70°/0 yield.,,,, A preliminary crystal structure determination for X = Br, R = Ph revealed a distorted dimetal- latetrahedrdne geometry for the W,C, core (Figure 8) whereby the projection of the alkyne C-C vector is not mutually ortho- gonal with respect to the W-W vector (deviation ca.26 ”). The C-C and W-W bond lengths [1.41(4) and 2.795(3) respecti-vely] in [W,(q-C,H,Pr1),Br,(p-C2Ph2)] are consistent with sub- stantial back-donation of electron density from metal-metal bonding orbitals to the 7~*orbitals of the p-alkyne ligand. The dimers [W,(q-C,H,R),X,] react with but-2-yne to give the flyover bridge complexes cis-[W,(q-C,H,R),X,(p-C,Me,)] (Scheme 3), the NMR data for which show the q-C,H,R ligands to be equivalent (note that the NMR data alone do not allow discrimination between isomers with q-C,H,R ligands either cis or trans to the p-hydrocarbyl moiety and only the former is illustrated in Scheme 3). The cis complexes convert in solution (or, for X = C1, in the solid state at ca.200”C!) to the corres- ponding trans isomers (Scheme 3) which show two q-C,H,R ring environments in their NMR spectra, the resonances due to the p-C,Me, moiety remaining virtually indistinguishable from those of the cis isomers. The X-ray crystal structure of trans-[W2(~-C5H,Me),Cl,(p-C4Me4)] revealed a symmetrically-bridging p-C,Me, ligand perpendicular to the plane containing the W-W bond. The complexes [W,(q-C,H,R),Cl,(p-C4Me4)] are the second examples of flyover bridge complexes in which the p-C,R, moiety coordinates symmetrically to each metal centre in a q4-fashion. The energy of activation for the cis +trans isomerization for X = C1, R = Pr’ in solution is 23.6 f0.2 kcal I 13 Me Et Pr‘ R’ Figure 7 (a) Plot of AGS (320 K) against R’ group for the fluxional process in [W,(q-C,H4Pri),C14(p-H)(p-SR’)] (R’ = Me, Et, Pr’, or Ph).The value for R = Ph is indicated by the horizontal dashed line. The line joining the data points for R’ = Me, Et, and Pr’ was fitted by simple interpolation. (b) Proposed fluxional process for [W,(q-C,H,R),Cl,(p-H)(p~SR’)] (R = Me or Pr’; R’ = Me, Et, Pr’, But, or Ph). The molecule is viewed as a Newman projection along the W-W vector where Rcp represents q-C5H4R. (Reproduced by permission from reference 30.) CHEMICAL SOCIETY REVIEWS, 1992 ing that the alkyne linking mechanism in this instance involves simple insertion of the second equivalent of alkyne into the Brpr Figure 8 Molecular structure of [W,(~-C,H,Pr'),Br,(p-C2Phz)] viewed along the molecular C, axis.Hydrogen atoms are omitted for clarity.32 mol-l, and the rates at 336 K for this process increase in the order [W,(~-C,H,Pr~),X,(p-C,Me,)] (X = Br < Cl) < [W2(y-C,H,Pr1),Br,(p-C,Et2Me2)].32.3 Treatment of [W,(~-C,H,Pr'),Cl,] with an excess of EtC,Me affords the mixed-alkyne flyover bridge derivatives [W2(y- C,H,Prl),Cl,{p-( 1,3)-C,Et,Me,f] and [W,(y-C,H,Pr'),Cl,{p- (l,4)-C4Et,Me,}] where the numbering in the flyover bridge refers to the positions of the ethyl substituents. Derivatives with a p-(1,2)-or a (2,3)-C,Et,Me, linkage were not obscrved. However, addition of but-2-yne to the pre-formed mono-alkyne adduct [W,(~-C,H,Pr'),Cl,(p-C2Et2)] gave the [W2(y-C,H,Prl),Cl,{p-( 1,2)-C,Et,Me,)] isomer exclusively, suggest- W-C(a1kyne) bond of the mono-alkyne add~ct.~ The alkyne coupling reactions of [W,(y-C,H,R),X,] for X = Br do not appear to proceed in the same manner as for X = C1.The dinuclear monoalkyne adducts [W(y-C,H,Prl),Br,(p-C,R,)] (R = Me, Et, or Ph) do not undergo alkyne coupling reactions. However, poorly-understood lab- ile intermediates with the repeat formula [W,(q-C,H,Prl)Br,(CR)],, (x = 1 or 2) have been isolated from the reaction of [W2(~-C,H4Pr'),Br,] with C, R,. These complexes, which slowly convert to the corresponding dimers [W,(y- C,H,Pr'),Br,(p-C,R2)] in solution, react with added butyne to give the flyover bridge derivatives [W,(~-C5H,Pr1),Br4{p-( 1,2)-C,R,Me,)] (R = Me or Et).32 The flyover bridge complexes cis-and trans-[W,(y-C,H,R),Cl,(p-C,Me,)] react with aqueous acetone to give the red, pentane-soluble mono-0x0 derivatives [W,(,-C,H,R),Cl,(0)(p-C,Me4)].The X-ray crystal structure for R = Me shows that the strong trans influence of oxygen results in a 7"deviation of the p-C,Me, linkage from the ideal perpendi- cular geometry found for the otherwise identical tetrachloro species, trans-[W,(y-C, H,Me), Cl,(p-C,Me,)]. Some further reactions of the mono-alkyne adduct, [W,(y- C H,Prl),Cl,(p-C,Et,)] have been explored (Scheme 3) ., Addition of alkali metal thiolates or alkoxides allows replace- ment of one chloride ligand only, even in the presence of excess reagent, to give the complexes [W,(~-C,H,Prl),C1,(YR)(p-C,Et,)] (YR = SMe or OEt).Two chloride ligands in [W,(y- C,H,Pr1),CI,(p-C,Et2)] may be replaced by treatment with (Me,Si),NMe to give the structurally characterized p-imido derivative [W,(~-C,H,Pr'),Cl,(p-NMe)(p-C,Et2)], whereas reduction with two equivalents of sodium amalgam in the presence of PMe, forms the bis(phosphine) derivative [W,(y- iv -\ liii IvR' Reagents: i, C,Me,, toluene, > 60% (R = Me or Pr', R' = RZ= Me, X = Br or CI);ii, C,R:, toluene, 40-70%0 (R'= Me, Et, Ph, or SiMe,; X = Br orC1); iii, C,Me,, thf, 70% (R = Pr', R' = Et, R2 = Me, X = Cl); iv, thf, 1-2 d, ca. 100% (R = Me or Pr', R' = Me or Et, R2 = Me, X = Br or Cl); v, H,O/acetone, 80% (R = Me or Pr', R' = R2 = Me); vi, PMe,, 2 Na/Hg, thf, 40%; vii, M'YR, thf, 60% (M'YR = NaOEt or LiSMe); viii, PMe,R, thf, 70% (R = Me or Ph); ix, MeN(SiMe,),, thf, 60% Scheme 3 Alkyne addition and related reactions of [W,(v-C,H,R),X,].CYCLOPENTADIENYL MOLYBDENUM AND TUNGSTEN DIHALIDES-M. L. H. GREEN AND P. MOUNTFORD C H4Pri)2 C1, (PMe,),(p-C, Et,)]. Addition of tertiary phosphine PMe2R to [W2(rl-C5H4Pri)2C14(p-c2Et2)laffords the eighteen- electron COmPleXeS, [W2(rl-C5H4Pri)2C13(~-c2Et2)(~-c1) (PMe,R)](R = Me Or Ph). The crystal structure for R = Me has been determined.36 Included in this section is the reaction of[W,(rl-C5H4R),CI4] (R = Me Or Pr’) with nitriles R‘CN (R‘ = Me, Et, Of Ph) which give the highly moisture-sensitive, brown p-(~+ r)-nitrile deri- R = Me or Pr‘ R’= Me,Et, or CH2Ph vatives [W,(~-C,H4R),C1,(p-Cl){p-(~ A crystal + TT)-R’CN)].~~ structure determination for R = Me, R’ = Et confirmed the basic geometry illustrated below.This structure is reminiscent of that proposed for the isocyanide complexes [W2(7-C,H4R)2Cl,(p-CI)(ButNC){p-(~+ r)-Bu‘NC}] (vide supra), except that the latter have an additional terminal donor ligand. Treatment of the nitrile complexes with HCl in toluene affords the purple p-y2:q2-iminoacyl derivatives [W2(~-C,H,R),Cl,(p-R’CNH)]. The crystal structure for R = Pr’, R’ = Et (Figure 9) confirmed the p-q2:~2mode of coordination of the R’CNH ligand and showed it to be the first example of this type of ligation for the iminoacyl moiety. The N-H proton could not be located crystallographically, but its presence was indicated by IR and NMR deuterium labelling The iminoacyl derivatives are clearly related to the p-alkyne complexes [W,(~-C,H4R),CI,(p-C1)(p-C2Et2)(PMe2R)](see Scheme 3) with which they are valence isoelectronic.Figure 9 Molecular structure of [W,(~-C,H,Prl),CI,(p-Cl)(p-EtCNH)]. Hydrogen atoms bonded to carbon are omitted for ~larity.~’ An orange intermediate of identical empirical formula to that of the final, crystallographically characterized purple complex (Figure 9) may be isolated in the reaction of the p-nitrile complexes [W2 (y-C,H,R), C1, (p-Cl){p-( 0 + r)-R’CN)] with HCl. These intermediate species readily convert to the corres- ponding purple isomers in solution, and on the basis of their IR and NMR spectra, have tentatively been assigned analogous structures with a trans arrangement of the 7-C5H4R ligands.19 5 ConcIuding Remarks We have shown in this article that the molybdenum and tungsten complexes [M(+,R5)X2ln have a rich and diverse reaction chemistry which has obvious potential for further study and development.Complexes with apparently dramatically different ground state structures (viz h viz either terminal or bridging halide ligands) may sometimes give rise to parallel chemistry, R’ (7) while a seemingly minor change from CI to Br can sometimes lead to a quite different reaction pathway. Further studies of the chemistry of these dinuclear complexes are clearly required in order to evaluate the subtle factors which moderate the various structures and pathways of reactivity.6 References 1 R. Poli, Chem.Rev., 1991,91, 509. 2 F. H. Kohler, R. deCao, K. Ackermann, and J. Sedlmair, Z. Naturforsch., Teil. B, 1983,38, 1406; F. H. Kohler, J. Lachmann, G. Miiller, H. Zeh, H. Brunner, and J. Pfauntsch, J. Organomet. Chem., 1989,365, C15; D. B. Morse, T. B. Rauchfuss, and S. R. Wilson, J. Am. Chem. Soc., 1990,112,1860; D. B. Morse, T. B. Rauchfuss, and S. R. Wilson, J. Am. Chem. Soc., 1988, 110, 8234. 3 P. D. Grebenik, M. L. H. Green, A. Izquierdo, V. S. B. Mtetwa, and K. Prout, J. Chem. Soc., Dalton Trans., 1987, 9. 4 J. J. Martin-Polo, D. Phil. Thesis, Oxford, 1982. 5 H. G. Alt, T. Frister, E. E. Trapl, and H. E. Engelhardt, J. Organomet.Chem., 1989, 362, 125. 6 J. Okuda, R. C. Murray, J. C. Dewan, and R. R. Schrock, Orguno-metullics, 1986, 5, 1681. 7 C. J. Harlan, R. A. Jones, S. U. Koschmieder, and C. M. Nunn, Polyhedron, 1990, 9, 669. 8 M. L. H. Green, J. D. Hubert, and P. Mountford, J. Chem. Soc., Dalton Trans., 1990, 3793. 9 R. Poli and A. L. Rheingold, J. Chem. Soc., Chem. Commun., 1990, 552. 10 R. Poli, J. C. Gordon, J. U. Desai, and A. L. Rheingold, J. Chem. SOL..,Chem. Commun., 1991, 1518. 11 J. C. Green, M. L. H. Green, P. Mountford, and M. J. Parkington, J. Chem. Soc., Dalton Trans., 1990, 3407. 12 J. A. M. Canich, F. A. Cotton, L. M. Dainels, and D. B. Lewis, Inorg. Chem., 1987, 26,4046; F. A. Cotton, Polyhedron, 1987, 6, 667. 13 E. M. Kober and D. L.Lichtenberger, J. Am. Chem. Soc.. 1985,107, 7199. 4 F. A. Cotton, G. G. Stanley, B. J. Kalbacher, J. C. Green, E. A. Seddon, and M. H. Chisholm, Proc. Natl. Acad. Sci. U.S.A., 1977, 74, 3 109. 5 J. C. Green, N. Kaltsoyannis, and P. Mountford, unpublished results. 6 A. W. Coleman, J. C. Green, A. J. Hayes, E. A. Seddon, D. R. Lloyd, and Y. Niwa, J. Chem. Soc., Dalton Trans., 1979, 1057. 7 B. J. Morris-Sherwood, C. B. Powell, and M. B. Hall, J. Am. Chc>m. Soc., 1984, 106, 4079. 8 P. Mountford, unpublished results. 19 Q. Feng, M. Ferrer, M. L. H. Green, P. Mountford, and V. S. B. Mtetwa, J. Chem. Soc., Dalton Trans., submitted for publication. 20 D.P. S. Rodgers, D. Phil Thesis, Oxford, 1983. 21 B. E. Owens, R. Poli, S. T. Krueger, and A.L. Rheingold, submitted for publication; R. G. Linck, B. E. Owens, and R. Poli. Gazz. Chim. ftal., 1991, 121, 163; S. T. Krueger, B. E. Owens, and R. Poli, fnorg. Chem., 1990,29,2001. 22 B. E. Owen and R. Poli, Inorg. Chim. Acta, 1991, 179, 229. 23 S. T. Krueger, R. Poli, A. L. Rheingold, and D. L. Staley, Inorg. Chem., 1989, 28,4599. 24 M. L. H. Green and P. Mountford, J. Chem. Soc., Commun., 1989, 732. 25 P. Mountford, D. Phil Thesis, Oxford, 1990. 26 J. D. Hubert, Part I1 Thesis, Oxford, 1989. 27 J. A. Bandy, C. E. Davies, J. C.Green, M. L. H. Green, K. Prout, and D. P. S.Rodgers, J. Chem.Soc., Chem. Commun., 1983,1395; J. Qin, D. Phil. Thesis, Oxford, 1987. 28 M. D. Hobson, Part I1 Thesis, Oxford, 1988. 29 R. Poli and M. A. Kelland, J. Organomet. Chem., 1991,419, 127. 30 Q. Feng, M. Ferrer, M. L. H. Green, P. Mountford, V. S.B. Mtetwa, and K. Prout, J.Chem. SOC.,Dalton Trans., 1991, 1397. 31 C. Ting, N. C. Baezinger, and L. Messerle, J. Chem. SOC.,Chem. Commun., 1988, 1133. CHEMICAL SOCIETY REVIEWS, 1992 32 M. L. H. Green, Q. Feng, and P. Mountford, manuscript in preparation. 33 K. Henrick, M. McPartlin, A. D.Horton, and M. J. Mays, J. Chem. SOC.,Dalton Trans., 1988, 1083. 34 M. J. Winter, Adv. Organomet. Chem., 1989, 29, 101; W. E. Buhro and M. H. Chisholm, Adv. Organomet. Chem., 1987,27,311. 35 M. L. H. Green and P. Mountford, Organometallics, 1990,9, 886. 36 M. L. H. Green, P. C. McGowan, and P. Mountford, unpublished results. 37 Q. Feng, M. Ferrer, M. L. H. Green, P. C. McGowan, P. Mountford, and V. S. B. Mtetwa, J. Chem. Soc., Chem. Commun.. 1991,552.

ISSN:0306-0012    

DOI:10.1039/CS9922100029

出版商:RSC    

年代:1992

数据来源: RSC

摘要:

Lariat Ethers: From Simple Sidearms to Supramolecular Systems George W. Gokel Department of Chemistry, University of Miami, Coral Gables, Florida 33124, U.S.A. 1 Conceptual Development of the Lariat Ethers Until the 196Os, complexation of alkali and alkaline earth metal cations was problematic. Although such Ca2 + binders as ethyle- nediaminetetraacetic acid, EDTA, were well known, neutral compounds that bind these metals were not. This situation changed abruptly and dramatically when Pedersen reported the crown ethers. Shortly thereafter, Lehn reported the cryptands,2 and Cram began to study their use in selective c~mplexation.~ Pedersen, Cram, and Lehn shared the 1987 Nobel prize for their efforts. As the crowns and cryptands became more familiar, the relationship of these synthetic substances to naturally occurring molecules became apparent.One of the best known K+ com-plexing agents is the mitochondria1 ionophore valin~mycin.~ It is a cyclododecadepsipeptide, that is, a macrocyclic peptide that alternates amino and hydroxy acids. its structure contains repeating units of L-lactate (L-lac), L-valine (L-Val), D-hydroxy- isovalerate (D-hyv), and D-vahe (D-Val): (L-lac-L-Val-D-hyv-D- val),. The molecule thus contains six amide and six ester carbonyl donor groups and a hydrophobic surface composed of nine isopropyl and three methyl groups. The structural features of valinomycin are both interesting and revealing. The 36-membered ring, if planar (i.e.crown-like), is too large to accommodate K+, for which it is quite selective.Instead, the molecule folds over to create a three-dimensional cavity. In so doing, the backbone assumes a ‘tennis-ball-seam’ geometry. The resulting conformation has the hydrophobic alkyl residues turned outward and a cavity that is the appropri- ate size for K . The amide donor groups are more polar than are + the ester carbonyls but the latter bind the cation. This is for two reasons. First, the amides participate in transannular hydrogen bond formation that helps hold valinomycin in the binding conformation. Second, since the amides are involved in hydro- gen bonds, they cannot bind to the cation. This is important because the polar amides would favour more charge dense cations like Ca2 + rather than the K+ preferred by valinomycin.The three-dimensionality of valinomycin’s cavity is important for solvating the bound cation and excluding water. The isopro- pyl and methyl groups interact with the hydrophobic membrane during transport and their orientation outward may also play a conformational role in directing the carbonyl groups inward. The amide carbonyl groups play another role as well. Complexa- tion of a cation by valinomycin would likely be difficult if the large macro-ring had to fold, turn the alkyl groups outward, and bind the cation all at once. The intra-annular hydrogen bonds that form when valinomycin folds, stabilize the binding confor- George Gokel I.Z’USborn in NeM1 York City in I946 but moved as a child to Miami, k2here he was raised.He earned the B.S. in chemistry ut Tulane University in New Orleans in 1968 and the Ph.D. ut the University of Southern Cal[fornia in 1971 and then didpost-doctorul work \I’ith D. J. Cram at U.C.L.A. He has held positions ut Dupont ’sCentral Research Department, the Pennsyl- vania State University, the University of Maryland and is cur-rentlj. Professor of Chemistry at the University of Miami. He has published books and research papers in the areas of.ferrocene chemistrj,, phase transfer catalysis, crobtw and lariat ether chemis trj., and molecular recognition. mation so that a smaller energy price must be paid upon complexation. A recognition of some, but admittedly not all, of these properties of valinomycin led us to design the lariat ethers.2 Design and Syntheses of the Lariat Ethers The paradox of membrane transport is that a carrier should optimally have different properties in each of the three, chemi- cally-different regions (source phase, lipid membrane interior, receiving phase) encountered by the ionophore. At the mem- brane’s source phase, binding should be fast and strong. Chemi- cally speaking, this means that in the binding equation (1) both Ks and k, should be large. Inside the hydrophobic mem- brane, the cation should be strongly bound, i.e., KS should be large. Finally, at the receiving or exit side of the membrane, Ks should be small and k-, should be large. Obviously, these conflicting requirements cannot all be met.Thus, some com- promise is apparent in the binding strengths and dynamics of each successful carrier. When we decided to undertake an effort to study and mimic valinomycin, it was apparent that the cryptands had the required three-dimensionality but lacked dynamics. On the other hand, the crowns were dynamic but lacked both the capability to envelop a cation and the requisite binding strength, especially in water. Our solution to this problem was to explore crown ethers having sidearms. Each sidearm would contain one or more donor groups placed in a position appropriate to provide a third dimension of solvation to a ring-bound cation. The lariat ether idea is represented schematically in Figure 1. The schematic, the appearance of the molecular models, and the use of a lasso in the American west to ‘rope and tie’ an animal all suggested the name lariat.6 L ;\ Figure 1 Schematic of the lariat ether complexation process.2.1 Structural and Synthetic Considerations In an article as short as this one, the design considerations can, at best, only be adumbrated. We chose to study macrocycles having the traditional -CH,CH,O-subunits as the new properties of the lariat ethers would thus be more readily distinguished from those of the known crown ether relatives. Most of the design work was accomplished by a consideration of Corey-Pauling-Koltun (CPK) atomic models. It was apparent, for example, that if the sidearm was attached to the macro-ring at nitrogen, the best distance for interaction between a ring- bound cation and an apical donor group was three, rather than two, carbons.This required, however, a non-optimal conforma- tion in the sidearm. Further, direct attachment of the sidearm to 39 an all-ethyleneoxy macrocycle (a carbon-pivot lariat) was diffi- cult using a carbon<arbon bond and worse using a carbon- oxygen bond. In the latter case, an acetal would have been contained within the ring potentially leading to chemical instabi- lity. Thus, design plans were carefully made but compromises were required at an early stage. The first attachment point chosen was the -CH,-0- unit, based upon glycerol (HOCH,CHOHCH,OH]. This afforded the carbon-pivot (C-pivot) lariats. The N-pivot lariats were accessible from the known azacrowns by N-alkylation or by preparing the crowns from the appropriately substituted dietha- nolamine derivative, R-N(CH,CH,OH), .Because H(OCH,- CH,),OH is readily available and H(OCH,CH,),OH is not, the first C-pivots were 15-membered while both 15- and 18-mem- bered N-pivots could be prepared fairly easily. Typical struc- tures in each group are shown in Figure 2. 2.2 Syntheses of C- and N-pivot Compounds Two families of molecules were prepared. The first family to be completed was that of the C-pivot compounds [(I-5) Figure 31 discussed below.' The N-pivot compounds were undertaken as well but had a lower priority for completion.* As envisioned, the carbon-pivot lariat ethers proved to be more chemically stable but less dynamic than the N-pivot counterparts.The greater flexibility of the latter is due to the facile inversion of the nitrogen atom, a property not shared by carbon. A carbon-pivot lariat ether A nitrogen-pivot lariat ether R O*O R-N N-R A bibracchial lariat ether (BIBLE) A tribracchial lariat ether (TriBLE) Figure 2 Carbon-pivot and nitrogen-pivot lariat ethers. 3 Confirmation of Sidearm Participation Obviously, all research efforts in chemistry require imagination. When novel hosts are designed in the hope that they will bind to specific guests ('property-directed synthe~is'~)one often imagines specific modes of interaction. The NMR spectrum of the complex may be consistent with the interactions envisioned, but this is often permissive evidence rather than proof.A vast array of structural techniques is available to the modern chemist. More than one of these should be used to confirm the structure of a non-covalently linked complex or, as Lehn has termed it, a supermolecule.'O An arsenal of NMR techniques including relaxation time measurements and NOESY experi- ments are available to assess solution interactions. Solid state studies, if not directly applicable to the solution phase, are very important in this area as they involve the key molecules (host and guest). The structure may not correspond directly to solu- tion but it certainly represent at least a local energy minimum. We determined at the outset to use whatever physical techniques were available to confirm the participation of the sidearm in cation binding. We began with the preparation of a family of C-pivot lariats.The series of compounds obtained included examples that were expected to be good cation binders and those that were not. CHEMICAL SOCIETY REVIEWS. 1992 Once these compounds were in hand, it was important to assess whether or not the sidearm participated in the binding as designed. Several closely related structures were selected for study. All of the compounds studied were 15-crown. 5 deriva-tives. The derivatives included compounds having no donor groups in the sidearms or no sidearm, different lengths of donor-group-containing sidearms, and a special pair of structures having isomeric sidearms in which one was thought to be sterically capable of interaction with a ring bound cation and the isomer was not.The well-known picrate extraction technique (see below) was used for this purpose. The compounds studied are shown in Figure 3. (1) R=H (2) R = CH20CH3 (3) R = CH20CH2CH20CH3 CH20CH2 (4) R= a OCH, CH20CHZ I I OCH, Figure 3 Compounds (1)-(5). 3.1 The Picrate Extraction Technique A brief comment about the picrate extraction technique is in order here.' The method is straightforward and uses readily available UV-visible instrumentation. The principle is as follows. A two-phase mixture, usually of CHCl, and water is prepared. The ligand (crown, cryptand, lariat ether, etc.) is dissolved in CHCl, and a metal picrate salt is dissolved in H,O.In the absence of a ligand, the yellow picrate salt remains in the aqueous solution. When shaken, the ligand extracts the metal cation and the yellow picrate anion accompanies it into the chloroform phase, which turns yellow. By using Beer's law and the extinction coefficient of picrate, one can assess how much of the available cation (assuming I :1 M +picrate-) has been extracted. The extraction constant (YO)is (moles of picrate in CHCl,)/(moles of picrate corresponding to 100% extraction) x 100. The problem with this method lies in the details. Sometimes, M + picrate- is prepared by dissolving picric acid in an excess of M+OH-. In such a case, the ionic strength of the medium is quite different from an aqueous solution of M+picrate-.Other variables include solution temperature, relative solvent volumes, vigour of mixing, etc. Unless all variables are kept constant, results will not be comparable between studies. 3.2 Evidence for Sidearm Participation Extraction constant data for five of the new lariats were particu- larly revealing. In these 15-crown-5 derivatives, the sidearms and percents of Na+ extracted were: (l), H (7.6%); (2), CH,OCH, (5.1%); (3), CH,OCH,CH,OCH, (18%); (4), CH2-2-methoxyphenyl(15.7%); and (9,CH2-4-methoxyphe-nyl (6.4%). The most immediate conclusion drawn from these data is that the lariat ether concept was confirmed. Clearly, when the sidearm was too short to solvate a ring-bound cation [(2), CH,OCH,, 5.1YO],Na+ binding was low but when the sidearm was extended [(3),CH,OCH,CH,OCH,, 18%], extraction was much greater.Further, when the sidearm donor group was sterically inaccessible (5), binding was far lower (6.4%) than when it was appropriately placed [(4), 15.7%]. All of this seemed very satisfying. We then thought to compare our data with those obtained in other laboratories for somewhat related systems. Here the difficulties of the picrate extraction method became apparent. In some cases, the con- LARIAT ETHERS: FROM SIMPLE SIDEARMS TO SUPRAMOLECULAR SYSTEMS-G. W. GOKEL ditions used in other laboratories were similar to ours, but in others, not even the two solvents were identical. We thus made the strategic decision to measure the equilibrium cation binding constants12 (Ks for the equilibrium: Cr + M+*[Cr.M+]) in homogeneous solution so that our values could be compared with those obtained by others even if different techniques were used to obtain them.The change to a homogeneous system (anhydrous methanol) gave surprising and, frankly, distressing results. For compounds (1)-(4), the homogeneous binding constants, log,, Ks for compounds (1)-(5) are shown with the extraction values in parentheses: (I), 3.27 (7.6%); (2) 3.03 (5.1%); (3), 3.01 (18%); and (4), 3.24 (15.7%). Obviously one would draw different conclusions from these two sets of data but cation binding results obtained by these two distinctive methods are often considered to be interchangeable. Since none of the log Ks values for (2)-(4) exceeded that for (I), in which no sidearm was present, we felt the need to confirm ring-sidearm cooperation by other methods.Two things were encouraging, however. Dilution of solutions containing (3) or (4) did not alter log K, as would be expected if intermolecular interactions were involved. Second, although log Ks did not show dramatic binding enhancement when a sidearm was present, binding was improved by location of the methoxy group in the accessible ortho-position compared to the sterically inaccessible para-posi tion. 4 Complexation: The Solution Phase One difficulty with the conflicting data presented above is that none of the binding strengths shown is particularly large. This is primarily because compounds (2)-(5) are C-pivot lariat ethers.The CPK models of these derivatives seem relatively inflexible and we expected the C-pivots to have certain shortcomings as valinomycin models. We thus undertook our first detailed assessment of ring-sidearm cooperativity with the N-pivot structures. A study of CPK models and results obtained by othersI3 suggested that the tetrahedral ammonium (NHZ) cation would be well accommodated in an 18-membered macrocycle: it should form three EN-H 0 hydrogen bonds. The corresponding 15-membered ring could not, at least according to models, form more than two such bonds. When the sidearm was long enough [as in (6), n = 21, a fourth hydrogen bond could form which should stabilize the complex even further.We thus determined log K,(NH:) for the family of 15- and 18-membered ring, N- pivot lariat ethers having (CH,CH,O),CH, sidearms. The prediction for this experimental test of ring-sidearm interaction was that NH,+ binding for all of the 15-membered ring com- pounds would be poor to modest regardless of sidearm length and that 18-membered rings should fare better. In the latter case, peak binding was expected to occur when the sidearm was CH,CH,OCH,CH,OCH, (70 + 1N = 8 total donors, see Figure 5).14 (6) n = 1, R = (CH2CH20)3CH3 (7) n = 2, R = CH3 ANY (8) n = 2, R = CH2CH20CH3 (9) n = 2, R = (CH2CH20)2CH3 (10) n = 2, R = (CH2CH20)3CH3 (11) n =3, R= CH3(1 oJ (12) n = 3, R = CH2CH20CH3b-J (13) n = 3, R = (CH2CH20)2CH3 (14) n = 3, R = (CH2CH20)3CH3 Figure 4 Nitrogen-pivot lariat ethers.This experimental test was effective. The predictions made from molecular models were fully realized. Peak binding (log Ks = 4.8) occurred when eight total donors were present. Models suggested that four hydrogen bonds should be formed in the latter case. Thus, a value of = 1.2 log units per hydrogen Ammonium Ion Binding by Lariat Ethers -A-15-Crown-5 -+-18-Crown-6 h+ tIz Y rr,Y ' 3' I I I I I I I ' ' I 3 4 S 6 7 8 9 10 11 12 13 14 15 Number of Oxygen Atoms Figure 5 Ammonium ion binding. bond was established. In the 15-membered ring lariat ether cases expected to form a maximum of three hydrogen bonds, peak binding was nearly 3.6.A general study of cation binding was undertaken in order to see if the design goal of enhanced binding was actually realized. Cation binding constants for just a few compounds are shown in Table 1. All were determined in anhydrous methanol using ion selective electrode (ISE) methods. The ISE method is convenient and reliable but it has another advantage: Ks values can readily be determined at different temperatures. Determination of equi-librium constants at various temperatures permits application of the van't Hoff relationship and the calculation of thermodyna-mic parameters. 4.1 A Comment on the Hole-Size Relationship The fact that (9) and (12) showed identical log Ks(Na+) values surprised us.Indeed, we found that throughout the range of compounds prepared, when an identical number of donor groups were present, the binding was nearly the same, no matter whether the macro-ring was 15 or 18-membered. This seemed to contradict the so-called 'hole-size' relationship. When we exa- mined the literature to discover on what data the latter principle was based, we discovered that the idea has little more credibility than a rumour. Cation binding data for cryptands correlate well with a relationship between cation diameter and cryptand cavity size. Such three-dimensional, enveloping ligands might well be expected to exhibit selectivity. The crown ethers are another matter, however. We surveyed Na+, K+, Caz+, and NH,+ Table 1 Cation binding for selected lariat ethers log Ks Compound Ring +No. Size Sidearm Na K+ (6) 12 (CH C H O), CH, 3.64 3.85 (7) 15 CH, 3.39 3.07 (8) 15 CH,CH,OCH, 3.88 3.95 (9) 15 (C H C H 0)CH, 4.54 4.68 (10) 15 (CH ,C H ,0),CH, 4.32 4.91 (1 1) 18 CH.3 3.93 5.33 (12) I8 CH,CH,OCH, 4.58 5.67 (13) 18 (CH CH 0) CH , 4.3 3 6.07 (14) 18 (CH CH ,0) CH, 4.28 5.81 42 binding by 12-crown-4, 15-crown-5, 18-crown-6, 21 -crown-7, and 24-crown-8.' In short, 18-crown-6 bound all cations better than any of the other ligands and, in all cases, K+ was bound more strongly than any other cation.The latter result is expected based on a consideration of cation solvation enthalpies. 18- Crown-6 probably was superior in this regard because it had sufficient (six) donors for effective complexation but is neither strained nor constrained to an unfavourable geometry for binding.Indeed, the idea that flexible systems can be effective binders regardless of the complement of ring size and sidearm length is in accord with our observations on lariat ether binding. Cation Complexation Constants Data for 3n-Crown-n Compounds -++-Na+ -+--K+ -C-NH4+ -B-Ca++ I A/\ p5 C.-4 cn Y 2 1 9 12 15 18 21 24 27 Number of Atoms in Ring Figure 6 Graph: Hole-size relationship. 4.2 13C-NMR Relaxation Time Studies Although the Author favours predictive experiments designed to test a specific point, there is much to be said for the application of general analytical techniques.Indeed, use of any method, instrumental or otherwise, is far superior to simply presuming that the hoped-for complex has formed. We thus undertook a series of spectroscopic studies to determine the nature of the lariat ether complexes in solution. In collaboration with Echegoyen' we studied the molecular dynamics of several crown and lariat ethers and their cation complexes by measuring 3C-NMR relaxation times, This tech- nique permits a carbon-by-carbon (when resonances are resolved) assessment of host interactions with a bound cation. Such information permits inferences to be drawn concerning microstructural interactions in the complexes. Generally, the C- 13 relaxation time varies with atom mobility: the greater the motion of the atom, the longer the relaxation time.For 15-crown-5 and 18-crown-6, T, values were determined in both 90% CH,OD:D,O and in CDCI,. In the former solvent, T, values for 15C5 versus 18C6 were 2.14 and 1.28 s respectively. The smaller macrocycle thus appears more mobile. In chloro- form, both molecules should be less encumbered by viscosity and hydrogen bonding so the T,values should be longer. For 18- crown-6, T, increases from 1.28 to I .56 s. The same trend was observed for the lariat ethers. Relaxation time studies demonstrated that the macro-rings in carbon-pivot systems participated strongly in the binding. The most interesting confirmation of sidearm participation could again be demonstrated by comparing (4) and (5).When the methoxy was ortho and well-positioned for binding Na+, the CH, T,decreased 50% from 3.60 s for (4) to 1.80 s for (4) -Na+. In para-methoxy lariat (9,the methyl group T, increased slightly from 4.30 s to 4.60 s in the presence of Na . The N-pivot + CHEMICAL SOCIETY REVIEWS, 1992 compounds showed much less change in T, values on binding even though measured Ks values showed clearly that the sidearms were involved in binding. This suggested that binding was distributed more evenly over all donors in the N-pivots compared to the C-pivots in which the main interaction was the the ring. Indeed, when seven donors (60, IN) were present in the N-pivot system, log K,(Na+) was identical and equal to 4.56 f0.02 irrespective of whether the donors resulted from a 15-membered ring and a -CH,CH,OCH,CH,OCH, sidearm or an 18-membered ring and a -CH,CH,OCH, sidearm.4.3 Lanthanide Shift Reagents This important technique provided additional confirmation of sidearm participation for (4) but not for (5). Experimental difficulties such as severe line broadening proved problematic but the limited conclusions that could be drawn corresponded to the findings described above. l7 4.4 Complexation Kinetics An important presumption about the lariat ethers was that they would be more dynamic than cryptands if less dynamic than crowns. Because complexation kinetics are generally rapid, an appropriate method was required. We were fortunate to find collaborators who could undertake such studies.Using the T- jump method, Eyring and Petrucci showed that complexation takes place in two steps. First, the cation is bound by the macro- ring and then a conformational change takes place in which the sidearm presumably folds over the ring. The kinetic parameters they determined for (9) binding Na' in methanol solution were as follows. For complexation of the cation by the macro-ring, k, = 9.0 x 10'O M-' s-l, kk, = 2.1 x lo8 s-,, and K, = 429 M-l. For the second step, in which the sidearm moves into binding position, k, = 1.2 x lo'sp1, k-, = 1.5 x lo5 SKI,and K, = 80. Kz = 3.47 x lo4 M-' (log,, Ks = 4.54).18 Kinetic confirmation of the two-step mechanism along with the NMR data, binding data, and shift reagent studies placed the lariat ether concept on a firm footing.We still desired solid state structure data because details of interactions obtained from such a study are really not available using any other technique. 5 Complexation: The Solid State Although it is correctly argued that interactions apparent in solution do not always correspond to those observed in the solid state, judicious use of solid state data is critical to understanding three-dimensional interactions. Indeed, the correspondence of solution and solid structures often proves to be excellent when both are known. While it may be acceptable to argue that the solid state structure does not guarantee an identical organiza- tion of atoms in solution, it is foolish to ignore its implications.Moreover, the effort to obtain solid state structures should be made with all vigour, especially when the design of supermole- cules is the goal. We were fortunate enough to obtain crystals of complexes between various lariat ethers and several different cations. In such an endeavour, one often must accept the crystals that form since not all complexes give crystals and those that do may fail to yield useful X-ray data. In fact, we have never been able to obtain crystals of a carbon-pivot lariat ether complex. The nitrogen-pivot studies have been more rewarding, however. In collaboration with Atwood, Fronczek, and Gandour, we have obtained numerous solid state structures in which both macro- ring and sidearm interactions were obvious.Four structures are shown schematically in Figure 7. It is interesting to note that the solid state structure work confirmed all that had been learned from solution studies. Indeed, certain subtleties that were not imagined became appar- ent from the structures. For example, the potassium cation, when complexed by (1 2), remained slightly below the mean plane of the macro-ring suggesting why the complexes are so dynamic. LARIAT ETHERS: FROM SIMPLE SIDEARMS TO SUPRAMOLECULAR SYSTEMS-G. W. GOKEL Table 2 Complexation by one- and two-armed lariat ethers No. of log K, V CH3 CH3 II Na+co “7 -NOONYyy1 Figure 7 Solid state structures of lariat ethers. The solid state work also made clear that when two sidearms were present, cation complexation could involve neither sidearm, both from the same side, or both from opposite sides of the macro-ring.No example of single sidearm participation was found in the BiBLE series. The only examples of non-participa- tion were observed when the sidearms lacked heteroatom donors. When the cation was bound by both sidearms from the same side, the donor group array strongly resembled that of the corresponding cryptand. 6 Multi-Sidearmed Lariat Ethers When more than one sidearm was present on the macrocycle, we used the Latin word bracchium, which means arm, to designate them. Thus, two-armed lariat ethers were bibracchial lariat ethers, or BiBLEs. Three-armed structures were Tri BLEs, etc. The syntheses of two-armed, nitrogen-pivot structures were undertaken and eventually methods were developed that could provide 4,13-diaza- 18-crown-6 in a single step or other diaza- macrocycles in several steps.20 The only tribracchial systems we have studied thus far are based upon symmetrical triaza-18- crown-6, prepared originally by Lehn and co-workers.2 Two issues concerning the BiBLEs were of particular interest to us.We wondered whether cation binding would involve one or both sidearms and, if the latter, whether they would bind from the same or opposite sides of the macro-ring. Second, allowing our presumption that both sidearms are involved in cation binding, we wondered if we could find evidence for n-complexa- tion of a ring-bound alkali metal cation. The answer to the latter question has thus far been ‘no,’ but thereby hangs a tale which follows below.The addition of a second, potentially cation-binding sidearm should alter cation binding. A simple comparison of binding strengths for one- and two-armed lariat ethers might tell whether one or both sidearms participate in complexation. The question then becomes which two or more compounds should be com- pared. Addition of a second sidearm in the N-pivot series requires replacement of 0 by N in the process. Complexation of an alkali metal cation is usually weakened by the change from 0 to N, so this fact complicates the assessment. Sodium and potassium cation binding data (determined in methanol at 25 ”C)are shown in Table 2 for a small selection of lariat ethers.The problems are apparent. It appears, for example that an increase in ring size from 15 to 18 members, while keeping the sidearm constant improves potassium binding more than sodium binding. Alas, the number of donors has changed as well. A comparison of the second and fourth entries in the table suggests that Na A binding is enhanced but K binding is not, if+ ring-size and sidearm identity remain constant. Of course, the number of nitrogen atoms is unequal in these two cases. Solid state data permitted us to answer the question of sidearm participation (see Table 2). A survey of a broad range of Macrocycle N’s 0’s Na+ K+ Aza-15-crown-5-CH CH OCH 1 5 3.88 3.95 Aza-18-crown-6-CH2CH20CH3 1 6 4.58 5.67 Aza-18-crown-6-CH2CH20CH2CH20CH31 7 4.33 6.07 Diaza-I 8-crown-6-(CH,CH20CH,), 2 6 4.75 5.46 structures showed that when no donor group was present in the sidearm, complexation was accomplished exclusively by the macro-ring and counterion.’ 9c When donor groups were present in the macro-ring, they generally bound sodium from the same side (pseudo-crypt) and potassium from opposite sides (anti).9d In the absence of solution data, the solid state studies proved critical to understanding complexation in these systems. 6.1 n-Donor Sidearms and Thermodynamic Studies It is synthetically difficult to incorporate unsaturation into a cryptand so we felt that bibracchial lariat ethers presented an ideal vehicle to explore n-participation in cation binding. We prepared diaza- 18-crown-6 derivatives having n-propyl, ally1 (-CH,CH=CH,), and propargyl (-CH,C=CH) sidearms.Crystals of complexes involving crowns having allyl sidearms were obtained but no evidence of any T-electron donation to an alkali metal could be discerned. Cation binding studies sug- gested otherwise, however. The diaza- 18-crown-6 derivatives noted above had the following Na+ and K + binding constants (log Ks, MeOH): n-propyl, 2.86, 3.77; ally], 3.04, 4.04; and propargyl, 3.61,4.99. Thus, both Naf and K+ binding ascended with the potential for n-participation. An additional experiment altered the trend, however. The cyanomethyl group, -CH,C-N, is the isostere of and electronically similar to propargyl and was expected to act in a similar fashion to the latter.Log Ks values for this BiBLE were as follows: Na+, 2.69; K+, 3.91. We realized that we would need to determine AH and TAS for these systems in order to understand the binding. Although extensive calorimetric studies had been undertaken and reviewed by Izatt and co-workers,22 we did not have a calori- meter at our disposal. Since we could determine K,, an equili- brium constant, at different temperatures, we could apply the van’t Hoff relationship to these systems. We did so and found that AH for the Na+ binding reaction increased in the order propyl < allyl < propargyl (-2.82, -3.56, -4.97 kcal/mole). The enthalpic contribution to binding for cyanomethyl, -4.87 kcal/mole, was identical to that for propargyl. The cation binding constants reflected an unfavourable entropy (TAS)in the cyanomethyl case that diminished binding compared to the isostere. The thermodynamic information seemed to be in accord with n-participation.The corresponding enthalpies for K+ binding were: propyl, -6.28; allyl, -7.34; propargyl, -4.97; cyanomethyl, -9.54 kcal/mole. Clearly the latter data set cannot be explained in terms of T-participati~n.~ An equally important lesson is that complexation is, to coin a phrase, complex. Organic chemists tend to think structurally (enthalpically) and build upon such data as are obtained in cation binding studies. When major changes in solvation are involved, the enthalpic terms may be identical and the entropic component of AG may completely alter the binding profiles.It is therefore important to assess AH and AS as well as the equili- brium constant in any binding, complexation, or supermolecule- forming reaction. 6.2 Calcium Binding Ionophores The intriguing -(amide-ester),- structure of valinomycin sug- gested a special possibility to us. In valinomycin, the more polar amide donors are involved in hydrogen bonding to hold the 'tennis-ball-seam' conformation so that the less polar esters can bind K +.We reasoned that if the amide donors were free to bind a cation, a more charge-dense cation than K+, e.g. Na+ or Ca2+ ,would be favoured. We thus prepared diaza-18-crown-6 derivatives having -glycine-amino acid ester sidearms.Exam- ples included Gly-Gly-OMe, Gly-Ala-OMe, Gly-Val-OMe, and Gly-Leu-OMe. Binding and selectivity results were disappoint- ing when determined in methanol solution under our 'standard' conditions. Since calcium-selective electrodes cannot easily be used in methanol solution, we had developed a competitive method to determine Ca2+ binding in this solvent.'5 The method requires the determination of ligand binding to, for example, Na+, in the absence and then presence of Ca2+.The results proved inconclusive but suggested that Ca2 + complexa-tion might be significant. n R = H (Gly-Gly); R = CH,; (Gly-Ala); R = CH(CH,), (Gly-Val); R = CH2CH(CH,), (Gly-Leu) Figure 8 Dipeptide lariat ethers. If Ca2 + binding in methanol was so strong that it prohibited the competitive method from giving information, perhaps bind- ing in water could be measured.Cation binding strengths of crowns and cryptands generally increase with decreasing polar- ity so water is rarely the best choice for a complexation study. The advantage in this case was that calcium selective electrodes could be used directly in water. When we measured the binding constants, we were gratified to find that log Ksfor Ca2 + in water, for all four of the BiCLEs identified above were > 6 (i.e., Ks > lo6).In water, log Ks(Na+) is z 2. Thus, the selectivity in water for one cation over a similarly sized cation proved to be an unprecedented 104-105 .24 Why is the cation binding by the dipeptide BiBLEs so high? Several factors no doubt contribute.First, crown ethers gener- ally are characterized by a selectivity profile that correlates with the inverse of cation solvation enthalpy. When the ether donor groups are altered to more polar residues such as carbonyl, amide, or carboxylate, the binding assumes a Coulombic profile. The normal, non-Coulombic cation binding order (log Ks in CH,OH) is represented by either 15-crown-5 or 18-crown-6: K > Na+ > Ca2+.A rigid system such as [2.2.2]-cryptand will + favour K+ over Na+ because the cryptand's cavity and the cation are of a similar size. An ionizable system such as ethylenediaminetetraacetic acid (EDTA) will prefer Ca2 + over either Na+ or K+ because it is the most charge-dense of the three.The ester and particularly the amide donor groups of the dipeptide BiBLEs are quite polar. The amides exhibit resonance of the type NH-C=O++NH+=C-O-. The partially charged oxygen donor favours more charge dense cations just as EDTA's carboxylate groups do. A second factor is that these dipeptide BiBLEs may be able to fold into a solvent-excluded binding pocket that parallels the calcium binding loop arrangement in such peptides as lactalbu- mhZs Such proteins bin< Ca2+ with high selectivity in the aqueous cellular milieu. Zinik has recently shown that these same dipeptide BiBLEs can also selectively transport protected amino acids. Thus the versatility of these small molecular systems may be great indeed.23" CHEMICAL SOCIETY REVIEWS, 1992 6.3 Tribracchial Lariat Ethers The three-armed lariat ethers are little studied thus far because the preparation of triaza- 18-crown-6 has been difficult.We have recently solved the synthetic problems and prepared a few derivatives in the hope that the binding profiles would tell us whether the third sidearm enhances the binding2 * The difficul- ties associated with such comparisons are noted above but the data, shown in Table 3, deserve at least brief consideration. When the sidearm is CH2COOCH2CH, there is little difference in the Na +,K +,and Ca2 + binding strengths between the di- and triaza- 18-crown-6 derivatives. When the sidearm is CH2CH20CH, the triaza binding is generally weaker than that for the corresponding diaza- 18-crown-6 structures.This cvi- dence is far from conclusive but it suggests what is obvious from molecular models: there really is not enough room in the solvation sphere for more sidearms. To date, we have been unsuccessful in obtaining solid state data that could confirm this conclusion. Table 3 Comparison of two- and three-armed lariat ethers 1% Ks Crown Ether Sidearms Na+ K+ CaZ+ Diaza-18-c-6 CH,CH,OCH, 4.75 5.46 4.48 Triaza- 18-c-6 CH,CH,OCH, 4.19 4.93 4.07 Diaza-18-c-6 CH,COOCH,CH, 5.51 5.78 6.78 Triaza-18-c-6 CH,COOCH,CH, 5.13 5.87 6.70 7 Sidearms to Self-Assembly The earliest concept of lariat ether chemistry was primarily to develop flexible, three-dimensional cation binders. This was accomplished, the structures developed have been fully charac- terized, and the lariat ether concept has been validated by several methods.Beyond the basic preparation and characterization of these systems, however, lay broader prospects that are described below. 7.1 Redox-switched Cation Binding The paradox of membrane transport may be solved by com- promise as noted in Section 2 or by switching. In the latter approach, a poor cation binder is altered in some way to make it a strong binder. Thus altered (switched on), it conducts a cation from the source side across a membrane whereupon it is returned (switched off) to its original, weak binding state. The weak binder readily yields its cation at the receiving side phase. A number of switches have been developed including pH, thermal, and photochemical control.Our own approach, deve- loped in collaboration with Echegoyen and Kaifer, utilized redox control.26 In the systems studied, electrochemical reduc- tion switched a weak binder to a much stronger one. Ultimately, oxidation converted the radical anion back to its original, neutral state. Examples of lariat ether sidearms that exhibited this switching characteristic are nitrobenzenes and anthraqui- nones. In recent work, the concept has been extended to ferroceneZ7 which, as part of a cryptand structure, exhibits stronger binding when neutral but ejects the cation when oxidized. The nitrobenzene and anthraquinone lariats, and anthraquinone cryptand, and a ferrocenyl cryptand are shown in Figure 9.7.2 Steroidal Lariat Ethers and Membranes While the redox-switchable systems made possible controlled transport in membranes, the steroidal lariat ethers made poss- ible the formation of novel membranes themselves. Cholesterol is present in many bio-membranes and provides organization to the system. We reasoned that a steroidal lariat ether might have LARIAT ETHERS: FROM SIMPLE SIDEARMS TO SUPRAMOLECULAR SYSTEMS-G. W. GOKEL 0 Figure 9 Redox-switchable lariat ethers and cryptands. the appropriate balance of hydrophobicity and hydrophilicity, either in the neutral state or with a cation bound, to form a membrane. Indeed, nearly all of the systems examined showed a tendency to organize either into micelles or vesicles.Aza-15-crown-5-CH2COC1 was treated with cholesterol or cholestanol to form the lariat ester. In principle, the carbonyl could serve as a donor group for a ring-bound cation, but that was not the intent in this case. Rather, the steroidal units were expected to self-assemble into an organized array. Indeed, the vesicles formed from the neutral aza- 15-crown-5-CH2CO- -cholestanyl compound proved to be stable and similar in size to those formed from egg lecithin (phosphatidylcholine). An important difference between the lariat and pc vesicles was that the former were far more rigid. Indeed, using steroidal EPR probes, we found that the steroidal lariat niosomes were approx- imately 300-fold more rigid than the lecithin counterparts.This is not surprising in light of the steroid's natural tendency to aggregate and rigidify, but gratifying, nevertheless.,* W Figure 10 Cholesteryl lariat ether. 7.3 Nucleotide Bases as Sidearms No group of molecules is more important or ubiquitous than the purine and pyrimidine bases of RNA and DNA. Cumulated base pairs are the archetype of the supermolecule. Incorporation of either purines or pyrimidines in crown ethers should lead to systems that could use base-pairing interactions to organize monomers into supermolecules. We have explored this possibi- lity by preparing diaza- 18-crown-6 derivatives having adenine or thymine sidearms at the end of short hydrocarbon chains. We represent these derivatives using the shorthand A-0-A to represent diaza- 18-crown-6 having two adenine-terminated sidechains (CH,CH,CH, groups in this case).We have also prepared T-0-T, the complement of A-0-A. When A-0-A and T-0-T are dissolved together, evidence suggests that an aggregate, perhaps the dimer box shown in Figure 11, is formed.29 Another interesting structure is a compound that might be represented as A-0-T-A. Preliminary evidence suggests that adenine folds back on thymine, an interaction consistent with x-stacking in CDCl, (or CD,CN). The adenine in the stacked pair then forms a single hydrogen bond to the opposite adenine. Evidence for this is currently limited to an examination of CPK molecular models and detailed NOESY NMR experiments consistent with the structural possibility.Nevertheless, studies of such systems may lead to novel induccd- fit receptors and to a better understanding of nucleotide base interactions in the megamolecules RNA and DNA. 7.4 A Cation-conducting Channel Two main modes of cation transport exist in natural systems: cation carriers and cation channels. The former is exemplified in nature by valinomycins and the latter by grami~idin.~~ Synthetic cation carriers based upon podands, crown ethers, cryptands, etc. are too numerous to catalogue and discussion of them may be found in reference 11. Several attempts have been made to design and synthesize small molecular (non-peptidic) cation- conducting channels. Notable among the attempts3 is that of Fyle~.~l'>fIt is based upon a central crown ether framework similar to that of Lehn3'" but appears to be a more functional design.Our own effort32 to prepare cation-conducting channels was based upon our notion that Nature sets the structural stage for most biofunctional molecules with the primary amino acid sequence. Secondary and tertiary structure then afford the structural intricacies that lead to binding, catalysis, and other functions. The forces that accomplish this remarkable biological activity are, for the most part, feeble and include hydrogen bonding, r-stacking, conformational preferences, van der Waals interactions, and salt bridge formation. We felt that if we could construct a flexible framework having the appropriate elements for channel formation, biofunction would follow.We already knew that crowns could both bind cations and serve as polar head groups in micelle and bilayer formation. We therefore designed a system that had crowns as head groups held at a distance appropriate to be at opposite ends of a bilayer. A third crown ether served as the mechanical central point and perhaps as ion relay in residence near the bilayer's mid-plane. A stylized illustration of the concept is shown in Figure 12. Efficacy in cation transport was established in egg lecithin (phosphatidyl choline) vesicles by 23Na NMR. Using a dyspro- sium shift reagent, Na+ inside and Na+ outside the vesicles could be distinguished. The rate of transport could thus be assessed from the linewidths. By this method, it was shown that Na was transported through the synthetic channel about 100- + fold slower than through gramicidin but the kinetic order was interesting.The gramicidin channel is a dimer of two identical pentadecapeptides. Thus, transport is second order. A single molecule of our channel presumably spans the bilayer and, indeed, kinetics were found to be first order. Numerous other channel model compounds are under preparation in our group and we hope that much information concerning channels will soon be revealed as part of this effort. 8 Toward Supramolecular Assemblies Crown ethers, cryptands, lariat ethers, and other variations on this theme33 have proved to be the starting point for numerous, more complex molecular structures. The work has proved evolutionary and revolutionary as fairly simple structures have been adapted to remarkably complex tasks such as to mimic intricate biological functions.The work recorded here is just one thread of this multifarious fabric. It is hoped that the strand of development is apparent but perhaps more important is the lesson that structural analysis both in solution and in the solid state are required for all of the work to have a firm foundation. The field requires the efforts of designers, synthetic chemists, crystallographers, magnetic resonance experts, and many more. The author has benefited profoundly from interactions and collaborations with many talented individuals whose expertise was beyond his own in many areas. The author gratefully acknowledges these interactions and offers the following advice to any entering the field of supramolecular chemistry: Let your imagination go where it will but distinguish carefully between evidence that merely supports your conclusions and evidence that confirms it.CHEMICAL SOCIETY REVIEWS, 1992 + 0O1 A-0-A Figure 11 Nucleotide-based molecular box /A/wdG 0 LO Figure 12 Cation-conducting channel. Acknowledgments. The Author warmly thanks the NIH for support of this work by several grants, currently including GM 36262. The contributions of co-workers named on the cited references are gratefully acknowledged. In addition, collabor- ation with Professors J. L. Atwood, (the late) J. J.Christensen, L. A. Echegoyen, E. M. Eyring, F. R. Fronczek, R. D. Gandour, R. M. Izatt, A. E. Kaifer, (the late) M. Okahara, A. Nakano, S. Petrucci, and M. pinib has proved invaluable. 9 Notes and References 1 (a) C. J. Pedersen, J. Am. Chem. Soc., 1967, 89, 6017. (b) C. J. Pedersen, J. Inclusion Phenom., 1988, 6, 337. 2 J. M. Lehn, J. Inclusion Phenom., 1988, 6. 351. 3 D. J. Cram, J. Inclusion Phenom., 1988, 6, 397. 4 E. Grell, T. Funck, and F. Eggers, in 'Membranes', ed. G. Eisenman, Marcel Dekker, New York, 1975, Vol. 3, p. 1. 5 (a)W. L. Duax, H. Hauptmann, C. M. Weeks, and D. A. Norton, Science. 1972.176.91 1. (6)G. D. Smith, W. L. Duax, D. A. Langs,G. T. DeTritta, J. W. Edmonds, D. C. Rohrer, and C. M. Weeks, J. Am. Chem. SOC.,1975,97, 7242.6 G. W. Gokel. D. M. Dishong, and C. J. Diamond, J. Chem. Soc., Chem. Commun. 1980, 1053. 7 D. M. Dishong, C. J. Diamond, M. I. Cinoman, and G. W. Gokel, J. Am. Chem. Soc., 1983, 105,586. 8 R. A. Schultz, B. D. White, D. M. Dishong, K. A. Arnold, and G. W. Gokel, J. Am. Chem. Soc., 1985, 107,6659. 9 G. W. Gokel, J. C. Medina, and C. Li, Synlett., 1991, 677. 10 J. M. Lehn, Strucf. Bonding, 1973, 16, 1. 11 For additional discussion of this and other binding techniques, see 'Cation Binding by Macrocycles', ed. Y. Inoue and G. W. Gokel, Marcel Dekker, New York, 1990. 12 (a) H. K. Frensdorff, J. Am. Chem. Soc., 1971, 93, 600. (b)D. M. Dishong and G. W. Gokel, J. Org. Chem., 1982, 47, 147. (c) K. A. Arnold. and G. W. Gokel, J.Org. Chem., 1986, 51, 5015. 13 D. J. Cram, and K. N. Trueblood, Top. Curr. Chem., 198I, 98,43. 14 (a)R. A. Schultz, E. Schlegel, D. M. Dishong, and G. W. Gokel, J. Chem. Soc., Chem. Commun., 1982,242. (6)K. A. Arnold, J. Mallen, J. E. Trafton, B. D. White. F. R. Fronczek, L. M. Gehrig, R. D. Gandour, and G. W. Gokel, J. Org. Chem., 1988,53,5652. 15 G. W. Gokel, D. M. Goli, C. Minganti, and L. Echegoyen, J. Am. Chem. Soc., 1983, 105,6786. 16 (a)L. Echegoyen, A. Kaifer, H. D. Durst, and G. W. Gokel, J. Org. Chem., 1984,49, 688. (b)A. Kaifer, L. Echegoyen, H. Durst, R. A. Schultz, D. M. Dishong, D. M. Goli, and G. W. Gokel, J. Am. Chem. Soc., 1984, 106, 5100. 17 A. Kaifer, L. Echegoyen, and G. W. Gokel, J. Org. Chem., 1984,49, 3029. 18 (0)G.W. Gokel, L. Echegoyen, M. S. Kim, E. M. Eyring, and S. Petrucci, Biophys. Chem., 1987, 26, 225. (b)L. Echegoyen, G. W. Gokel, M. S. Kim, E. M. Eyring, S. Petrucci. J. Phps. Chem., 1987, 3854. 19 (a) F. R. Fronczek, V. J. Gatto, R. A. Schultz, S. J. Jungk, W. J. Colucci, R. D. Gandour, and G. W. Gokel, J. Am. Chem. SOC.,1983, 105, 6717. (6) F. R. Fronczek, V. J. Gatto, C. Minganti, R. A. Schultz, R. D. Gandour, and G. W. Gokel, J. Am. Chem. Soc., 1984, 106, 7244. (c) R. D. Gandour, F. R. Fronczek, V. J. Gatto, C. Minganti, R. A. Schultz, B. D. White, K. A. Arnold, D. Mazzocchi, S. R. Miller, and G. W. Gokel, J. Am. Chem. Soc., 1986, 108,4078. (d)K. A. Arnold, L. Echegoyen, F. R. Fronczek, R. D. Gandour, V. J. Gatto, B. D. White, and G.W. Gokel, J. Am. Chem. Soc., 1987, 109,3716. (e)B. D. White, F. R. Fronczek, R. D. Gandour, and G. W. Gokel, Tetrahedron Lett., 1987, 1753. 20 (u)V. J. Gatto and G. W. Gokel, J. Am. Chem. SOC.,1984, 1C5,8240. (b)V. J. Gatto, K. A. Arnold, A. M. Viscariello, S. R. Miller, C. R. Morgan, and G. W. Gokel. J. Org. Chem., 1986,51, 5373. 21 S. R. Miller, T. P. Cleary, J. E. Trafton, C. Smeraglia, F. R. Fronczek. and G. W. Gokel, J. Chern. Soc., Chem. Commun., 1989, 806. 22 (a)R. B. Davidson, R. M. Izatt, J. J. Christensen, R. A. Schultz, R. M. Dishong, and G. W. Gokel, J. Org. Chem., 1984,49,5080. (6) R. M. Izatt, J. S. Bradshaw, S.A. Nielsen, J. D. Lamb, J. J. Christensen, and D. Sen, Chem. Rev., 1985,85,271. 23 (a) K. A. Arnold, L.Echegoyen, and G. W. Gokel, J. Am. Chem. Soc., 1987, 109, 3713. (6) K. A. Arnold, A. M. Viscariello, M. Kim, R. D. Gandour, F. R. Fronczek, and G. W. Gokel, Tetrahedron Lett., 1988, 3025. 24 (u) B. D. White, J. Mallen, K. A. Arnold, F. R. Fronczek, R. D. Gandour, and L. M. B. Gehrig, J. Org. Chem., 1989,54,937.(b)J. E. Trafton, C. Li, J. Mallen, S. R. Miller, A. Nakano, 0.F. Schall, and G. W. Gokel, J. Chem. Soc., Chem. Commun., 1990, 1266. (c) M. Zinic, L. Frkanec, V. Skaric, J. Trafton, and G. W. Gokel, J. Chem. Soc., Chem. Commun., 1990, 1726. 25 A, C. R. daSilva and F. C. Reinach, Trends Biochem. Sci., 1991, 16, 53. 26 A. E. Kaifer and I. Echegoyen, in 'Cation Binding by Macrocycles', ed. Y. Inoue and G. W. Gokel, Marcel Dekker, New York, 1990, LARIAT ETHERS: FROM SIMPLE SIDEARMS TO SUPRAMOLECULAR SYSTEMS-G. W. GOKEL p. 363. 27 (a)J. C. Medina,T. T.Goodnow, S. Bott, J. L. Atwood, A. E. Kaifer, and G. W. Gokel,J. Chem. Soc., Chem. Commun., 1991,290.(h)J. C. Medina, I. Gay, Z. Chen, L. Echegoyen, and G. W. Gokel, J. Am. CJwm. Soc., 1991. 113, 365. 28 G. W. Gokel and L. Echegoyen, Bioorgunic Chemistry Frontiers, 1990, 1. 116. 29 M. Kim. and G. W. Gokel J. Chem. Soc., Chem. Commun., 1987, 16x6. 30 (N) D. W. Urry, T. L. Trapane, and C. M. Venkatachalam, J. Memhr. Biol.. 1986, 89, 107. (h)B. A. Wallace. and K. Ravikumar, Science, 1989. 241. 182. D. A. Langs, Science, 1989, 241, 188.((3) 31 (a)I. Tabushi, Y. Kuroda, and K. Yokoto, Tetrahedron Lett., 1982, 4601. (h)U. F. Kragton, M. F. M. Roks, and R. J. M. Nolte, J. Chem. Soc., Chem. Commun., 1985, 1275. (c)J.-H. Fuhrhop, U. Liman, and H. H. David, Angew. Chem., Int. Ed. Engl., 1985, 24, 339. (d)L. Julien, J.-M. Lehn, Tetrahedron Lett., 1988, 3803. (e)V. E. Carmi-chael, P. J. Dutton, T. M. Fyles, T. D. James, J. A. Swan, and M. Zojaji, J. Am. Chem. Soc., 1989,111,767.(f) T. M. Fyles, Bioorgunic Chemistry Frontiers, 1990, I, 7 1. 32 A. Nakano, Q. Xie, J. V. Mallen, L. Echegoyen, and G. W. Gokel, J. Am. Chem. Soc., 1990, 112, 1287. 33 G. W. Gokel, 'Crown Ethers and Cryptands', Royal Society of Chemistry, Cambridge, 199 1.

ISSN:0306-0012    

DOI:10.1039/CS9922100039

出版商:RSC    

年代:1992

数据来源: RSC

摘要:

LUDWIG MOND LECTURE* Taking Stock: The Astonishing Development of Boron Hydride Cluster Chemistry Norman N. Greenwood School of Chemistry, University of Leeds, Leeds, LS2 9JT 1 Introduction It is a great privilege to have been invited to give the Ludwig Mond Lectureship during this 150th Anniversary meeting of the Royal Society of Chemistry, and it is a particular personal pleasure to be able to deliver it, for the first time I believe, on a subject in main-group element chemistry: the boron hydrides. In my view this is one of the most exciting and significant areas of modern chemistry and, in choosing my title, I want to pay tribute to the seminal studies of Alfred Stock who started to work on the boranes in 1909, the year that Ludwig Mond died.Stock was born in 1876 when Mond was 37 years old, and he was 33 years old when Mond died. His first publication on the boron hydrides came 3 years later in 1912. Stock not only pioneered the chemistry of boron and silicon hydrides but he developed, from scratch, the chemical high- vacuum techniques which enabled him to study these extremely reactive, spontaneously flammable materials. He also made important contributions to chemical education and nomencla- ture, and to the pathology and detection of mercury poisoning from which he himself disastrously suffered. He therefore made major contributions to what we would still regard as the four main concerns of modern chemistry: (i) Health and safety at work in the laboratory. (ii) Chemical education at all levels.(iii) The development of new techniques for handling and measuring compounds. (iv) The synthesis and characterization of novel chemical corn bina tions. It is the last of these, Stock’s experimental studies on the extraordinary new class of compounds, the boranes, which I want to emphasize in this lecture. Stock’s first five papers on the boron hydrides appeared during 1912-1914 and in all he published just 16 papers on the boranes and their derivatives over a period of 20 years. The classic summary of his findings is in his George Fisher Baker Lectures given at Cornell University in 1932. He synthesized and characterized six boranes -B,H,, Norman Greenii’ood is Emeritus Professor of Chemistry in the Universitj.of‘ Leeds and lists among his present main interests the teaching of chemistrji and the public understanding oj science.He has received numerous honours and prizes both in this countrjt and overseas and as electeda Felloiz, of the Royal Society in 1987. He has been President ofthe Dalton Division (1979-84, Chairman of the Heads of Universitji Chemistrj> Departments (1985-87) and, most recentlj., Presideizt of the Chemistrj. Section of the British AssociatioiiJbr the Advancement of Science (1990-91). On the international scene he has been Chairman ofthe IUPAC Commission on Atomic Weights, President of the Inorganic Chemistrjs Divisioiz of IUPAC, and a visiting Professor at several universities in USA, Canada, Australia, Denmark, China, and Japan.He has made major research contributions to solid-state chemistrj?, Miisshauer spectroscopy, main-group element chemistrjv, and the chemistry of boron hydride clusters. B4H10, B,H,, B,H,,, BsHlo, and BioH14 -plus a seventh of uncertain composition, possibly B,H 2. Experimentation was made even more difficult by the fact that these compounds rapidly react and interconvert with one another. He also recog- nized that they formed two rudimentary classes distinguished by their formulae, viz. B,H,+ and B,H, + 6, which we now know as nido and arachno boranes. No other laboratory anywhere in the world undertook work on these fiendishly difficult compounds during this time but at the very end of the period, in 1931, H. I.Schlesinger and A. B. Burg in Chicago published their first paper on diborane and pentaborane., In fact, no additional boranes beyond Stock’s original six or seven were synthesized until 1958 when nonaborane, n-B,H, ,,was made by W. V. Kotlensky and R. Schaeffer, -a hiatus of 30 years -though the very stable anion BH, was made by H. I. Schlesinger and H. C. Brown in 1940.4 You will notice that BH, is isoelectronic with both methane, CH,, and the ammonium ion, NH;, but it differs notably from them in being able to form stable complexes as a monohapto, dihapto, or even trihapto ligand. Starting, then, from this baseline of a mere half-dozen com- pounds, I want to trace the astonishing developments which have occurred during the past three decades, as a result of which we now know over 50 neutral boron hydride molecules and a similar number of polyhedral borane anions -100 binary borane species in all, so far!, In addition there are literally thousands of derivatives incorporating elements from all areas of the periodic table.From the very beginning the boranes posed serious problems of both structure and bonding. Stock’s earliest publications predated the Lewis-Langmuir octet theory of electron-pair bonds by some five years and the boranes proved to be that theory’s most troublesome ‘exception’. Boron is in Group I11 (group 13) of the periodic table, so one would expect the simplest hydride to be BH,. Yet, despite extensive and diligent experi- mentation, no sign of BH, was ever encountered by Stock, and the simplest member of the series was diborane, B,H,.The stoicheiometry is clearly similar to that of ethane, C,H,, but as the boron atom has one electron less than carbon there are apparently insufficient electrons to form two-centre two-elec- tron bonds between each contiguous pair of atoms. The boranes were said to be ‘electron deficient’ but, as Robert Rundle correctly observed, it was really chemists who were ‘theory deficient’. The key to the dilemma was found by H. C. Longuet-Higgins in the late nineteen-forties with his seminal concept of the three- centre two-electron bond: if electrons are in short supply then a pair of electrons can bond three atoms in a triangular array, rather than just two atoms., He successfully established and interpreted the bridged dimeric structure of B,H, and then, generalizing from three-centre to multi-centre bonding, made the brilliant prediction of stable polyhedral dianions of unprece- dented structure, namely the octahedral cluster B,Hg -and the icosahedral cluster B,,H:;.This was five years before A. R. Pittochelli and M.F. Hawthorne serendipitously discovered such species in 1960., The structural and bonding systematics * Delivered at the 150th Anniversary Meetings of the RSC at Imperial College. London, on 11 April 1991 49 CHEMICAL SOCIETY REVIEWS, 1992 6 B2H6 B4H 10 n b d Figure 1 Molecular structures of some simple boranes: large circles represent boron atoms and small circles represent hydrogen atoms.Note the prevalence of triangles of boron atoms and the occurrence of 2-coordinate bridging hydrogen atoms. were developed into a topological theory by W. N. Lipscomb’ and the apotheosis of these ideas found expression in the elegant yet powerful simplicity of K. Wade’s rules (in 1971) relating electron counting to cluster geometry.8 The structurcs of some of the simplcr boranes are shown in Figure 1 from which it can be seen that the predominant structure motifs are fragments of triangulated polyhedral clus- ters. However, in viewing these and similar structures it is crucial always to remember that straight lines joining pairs of atoms no longer necessarily represent pairs of electrons, they merely indicate geometrical connectivities: three-centre and multi- centre bonding is the rule.As first shown by R. E. Williams in 1971 and elaborated by him in a later re vie^,^ the observed clusters fall into three geometrically distinct stoicheiometric series which he called closo-B,H,2 -, nido-B,H,+, and arachno-B,H,+ 6. The last two stoicheiometries clearly correspond with Stock’s two rudimen- tary series mentioned earlier. The structural relations between the three series are shown in Figure 2; with nido-boranes being formed by removing one highly connected vertex from the corresponding closo polyhedron, and arachno-boranes by removal of two normally adjacent vertices. The electron-count- ing systematics of Wade’s rules then indicate that clusters with (2n + 2) skeletal electrons adopt a closo structure, those with (2n + 4) skeletal electrons adopt a nido structure, and those with (2n + 6) an arachno.So much by way of general introduction. For the rest of the lecture I want to concentrate on what I believe are the two major intellectual puzzles and challenges of polyhedral borane chemistry: first, what are the mechanisms and reaction pathways by which these cluster molecules interconvert so facilely and build up into still larger clusters; and second, is this cluster behaviour unique to boron or can other elements be incorpor- ated into the cluster framework? As a result of work in our own laboratory and elsewhere important advances have been secured in both these areas and I shall attempt to summarize some of the more significant results obtained so far.B((lJ’B(3) v B10H14 2 Gas-Phase Thermolysis Reactions Stock observed in his earliest experiments that the simple boranes rapidly interconvert with each other at very moderate temperatures. However, without large-scale supplies of the purified boranes, and in the absence of rapid and reliable methods for product analysis, detailed kinetic and mechanistic studies were impossible. And yet the intriguing question remains: how does diborane manage to build up into larger clusters -what are the mechanisms of these facile interconver- sion and aufbau reactions which occur so readily at what are really very low temperatures, in the range 5O-15O0C? The problem is clearly one of some complexity and the answers are only now becoming clear. In fact, the reactions occurring in gaseous mixtures of boron hydrides probably comprise one of the most complex sequences of interconnccted reactions ever to be studied in any detail in the whole ofchemistry.Kinetic studies began in the USA in 1951. Where have we got to 40 years on? 2.1 Thermolysis of Diborane(6) Early work established that the gas phase thermolysis of dibor- ane at moderate temperatures and pressures was homogeneous with an order of reaction of 3/2, at least in the initial stages. The activation energy appeared to be in the range 92-1 35 kJ mol- I, the most recent value being 93 f5 kJ mol- I. The generally accepted mechanism (until two years ago) was a three-step process: PAS1 (BH,j + B,H, * {B,H,) In these and subsequent reactions, species in curly brackets are non-isolable reaction intermediates. The scheme clearly explained the 3/2 order in diborane since the rate-determining reaction 3 involved a triboron species.It was also consistent with the observation that the rate of thermolysis was repressed by the presence of an excess of dihydrogen, and with several other features of the reaction. However, recent very high level compu- tations were able to locate the transition state and led to the LUDWIG MOND LECTURE-N. N. GREENWOOD 11 13 s closo Figure2 The polyhedral shapes of closo, nido, and arachno boranes and related clusters; s = number of skeletal electron pairs.The one ex0 hydrogen atom attached to each skeletal atom in these species, and the endo hydrogen atoms of the nido and arachno species have been omitted for clarity. (Reproduced by permission from M. E. O'Neill and K. Wade, 'Compre- hensive Organometallic Chemistry', Vol. I, ed. G. Wilkinson, F. G. A. Stone, and E. W. Abel, Pergamon Press, Oxford 1982, Chapter 1). conclusion that it was reaction 2 that was rate-determining. O The calculations were also at variance with the literature value of about 5: 1 for the relative rates of thermolysis of B,H6 and B2D6, giving a value of only about 1.7 for this ratio if reaction 2 were rate-determining. To resolve these difficulties we undertook a careful experimental reinvestigation of the relative rates using a sophisticated mass spectrometric technique to monitor the initial stages of the reaction.' As a result of many runs at 147"C and an initial pressure of about 3.5 mm Hg we found the ratio to be 2.57 f0.65. We had previously found', that, under similar conditions, the initial rate of decomposition of B2H6 was ++ ',. ,v. I' ; ", I r S' w arachno decreased by a factor of about 3.4 in the presence of a 14-fold excess of H, and subsequent work showed that D, depressed the rate of thermolysis of B,D, by a similar amount.13 We can therefore now say that, taken as a whole, the experimental and computational results indicate that the rate-determining step following the symmetric dissociative equilibrium 1 is neither the ,formationof (B3H9)by reaction 2 nor its subsequent decompo-sition by reaction 3 but rather the concerted formation and decomposition of (B3H,) in a single step: This is an important result, but it is salutary to recall that it has taken so long to get an explanation of this reaction which Alfred Stock first observed and exploited 75 years ago.Moreover, this only takes us as far as (B3H,) which is itself an unstable, non- isolable reaction intermediate. There is no time to tell the rest of the story in any great detail but a few other highlights can be briefly mentioned. The first isolable intermediate was estab- by the elegant work of Riley Schaeffer. ,, B4Hlished as It is probably formed mainly by the reaction: However, B4H1, is itself unstable above about 45°C so we decided to study its decomposition and co-thermolysis with other small boranes.2.2 Thermolysis of Tetrab~rane(lO)~~J~ When we started, there was uncertainty about all aspects of B4H 10 thermolysis. By developing a novel, versatile, and rapid mass spectrometric method of product analysis we were able to establish that the initial gas-phase reaction was homogeneous and first order, with an activiation energy of 99.4 f3.4 kJ mol-l. A typical reaction profile is shown in Figure 3 from which it can be seen that, during the first 30 min at 78 "C, more than half of the B4H10is consumed, and there is a rapid formation of H, and B5H,, with lesser amounts of B6H12, B,H,, and B1oH14. Further work showed that added H, substantially retarded the rate of reaction but left the activation energy unchanged; there was likewise no change in the relative rate of B,Hll production but a marked increase in the rate of B2H6 production, almost complete inhibition of solid 'polymer' formation, and a complete absence of and B1OH14.10 \. 9 8 7 6 0I E5E \ Q L 3 2 1 I /min Figure 3 Reaction profile for the thermolysis of B4H,, (see text): (O)H,, (O)B,Hl0, (A)B5Hll. For clarity, only selected data points have been plotted for the minor species (.)B,H,, (A)B,Hl, and (U)B,,H,,. Furthermore, in the presence of D,, B4H,, rapidly underwent H/D exchange. These results can all be interpreted in terms of an initial rate-determining loss of H, from B4H10 to form {B4H,) followed by rapid reaction with a second molecule of B4H10: Thus, reaction 6 explains the ready exchange with D, and also the effect of an excess of H, in repressing the rate of decompo- sition without a change in activation energy, whilst reaction 7 CHEMICAL SOCIETY REVIEWS, 1992 ensures that the relative rate of B,Hl, production to B4H,, consumption remains unaltered in the presence of H,.The {B3H7)formed in reaction 7 would then react with an excess H, by the reverse of reactions 4and 1, thus ensuring the enhanced formation of B,H, and absence of other products. 2.3 Structure and Thermolysis of B,H,, arachno-Pentaborane is a mobile colourless liquid that boils at 65 "C.Its molecular structure is based on a B, skeleton formed by removing one apical and one equatorial vertex from a pentagonal bipyramidal CIOSO-B,cluster. However, an X-ray diffraction study led to a structure which lacked the expected mirror-plane symmetry (C,).To see whether this was a crystal packing distortion or whether the asymmetry persisted in the gas-phase molecule the structure was redetermined by gas electron-diffraction analysis;' there is indeed a definite distor- tion to C, symmetry which places the apical endo-hydrogen atom above the open face significantly closer to B(2) than to B(5) (see Figure 4).Subsequent ab initio calculations confirmed this distortion and gave values for B(2)-H,,d0 and B(5)-Hend0of 143.7 and 204.3 pm respectively, a difference of 60.6 pm; there were other smaller distortions in the molecule also.l8 endo endo endo Figure 4 Structure of urachno-B,H, as determined by gas-phase elec- tron diffraction. Note the C, symmetry resulting from the fact that the semi-bridging H(l),,,dc, atom is closer to B(2) than to B(5). Thermolysis studies of B5H1 in the temperature range 40- 150"C established first order kinetics with a rather low activa- tion energy of 72.6 f2.4 kJ mol- and the astonishingly small Arrhenius pre-exponential factor A = 1.3 x lo7 s-' (see later).l9 The main volatile products were H, and B,H,, the latter appearing at the rate of about 0.5 mol per mol of B,Hl consumed. B,H, is also produced, plus smaller amounts of the hexaboranes and B10H14, and traces of B4H10.Neither the activation energy nor the absolute rate of disappearance of B5Hl1 was affected by a 14-fold excess of H, but there was a dramatic change in product distribution, with B4H, being the main product, its rate of formation in the initial stages being almost equal to the rate of consumption of B5H1,; B2H6also appears but the formation of all other boranes is almost entirely suppressed. These results find ready interpretation if the initial rate- determining step is followed by the reverse of reaction 1 to give $B,H6. Alternati-vely, the {BH3Jcould react with a second molecule of B5HiI to generate a further molecule of { B,H,) plus B,H, in the correct mole ratio: The precise fate of the {B4H8)moiety was not rigorously established in the thermolysis of B,Hl alone, though several plausible reactions release appropriate amounts of H, (see reference 19 for details). In the presence of an added excess of H, this rapidly reacts with the {B,H,} via the reverse of reaction 6.LUDWIG MOND LECTURE-N. N. GREENWOOD Note that the absence of any effect of added H, on the rate and activation energy of the thermolysis of B,H,, stems from the fact that reaction 8 is the rate-determining initial step, and these observations also eliminate the possibility of the alternative initial reaction path to give B,H, + H, directly. The results also establish for the first time that the well-known (1 933) Burg-Schlesinger equilibrium (reaction 10),O does not occur as a bimolecular reaction but rather as the monomolecular dissociation (reaction 8) followed by the reverse of reactions 6 and I.2.4 The Structure and Thermolysis of B,H,, It has already been mentioned (see Figure 3) that the second most abundant borane product in the initial thermolysis of B4H, at moderate temperatures is the elusive B6H1,, Stock's possible seventh borane. Very little was known about this borane though viable preparative routes had been devised in the 1970s and its NMR spectrum had been studied in the preceding decade. It is the one simple borane whose structure has not yet been determined by X-ray diffraction analysis since it tends to form a non-crystalline glassy solid when cooled. However, its structure has now been determined by gas-phase electron dif- fraction.20 It turns out to be a chiral molecule of C, symmetry as shown in Figure 5 (see also reference 186).Note the incipient BH, units in the structure; it is like a B4HI0butterfly with two extra BH, groups replacing bridging H, atoms on opposite sides of the butterfly. This turned out to be crucial to its chemistry. H V )endo m Figure 5 The chiral C2 structure of arachno-B,H ?. There is a more subtle structural point. The C, molecule has been described as an 'icosahedral belt' (i.e.B, = +Bl,) but such a description implies that the dihedral angles between successive B, triangular planes should be close to the internal dihedral angle of an icosahedron, 138.2' (i.e.x -sin-2/3).However the observed dihedral angles in B,H,, are 167 f22" between the inner faces joined by B(2)-B(5), and 128 f 12" between the outer pairs of faces joined by B(2)-B(6) and B(3)-B(5). This is just what one would expect on the basis of Wade's rules since L-UY~C~~O-B,H,should be geometrically related to the dodeca- hedral cluster of closo-B,H; by removal of two adjacent five- connected vertices (see Figure 2).The characteristic internal dihedral angles of a regular triangular dodecahedron are 157" and two of 120",close to the observed angles. This suggests that the structure of arachno-B6H1,retains some information of its putative parent, closo-B,Hi -, and that the magnitude of dihed- ral angles is a useful supplementary criterion for distinguishing between alternative geometrical descriptions of open clusters.We also found that, when highly purified, B,H,, was rather more stable than earlier workers had found but it does thermo- lyse at a convenient rate in the range 90-100 "C.,I Typical data are shown in Figure 6 from which is can be seen that the predominant products are B,H, and B,H, (formed in a 2:l cnI E .E 2 0)u) 2 a 10 20 30 f /min Figure 6 Concentration-time profile for the thermolysis of arachno-B6H,, at 100°C.Only every fifth datum point on each curve has been plotted. for clarity: ( O)HZ, ( .)B2H6, (O)B,H,, ( +)B,H, o, and )B6H12. molar ratio) with a rather smaller amount of B,Hl0 and H, (formed in equimolar amounts). There were virtually no other volatile products or solid 'polymer' formation, thus making the thermolysis of B,H ,,the cleanest and simplest of all boranes yet studied.Further analysis showed that the thermolysis was first order with an activation energy of 81.3 f2.6 kJ mol~ and an unusually low Arrhenius pre-exponential factor of 3.1 x 1O8 s-I similar to those found for B5H1 ,(precedingsection). These facts find ready interpretation in terms of an initial unimolecular rate- determining loss of {BH,) to give B,H,, as in reaction 11 rollowed by dimerizalion of {BH,) by the reverse of reaction I. The alternative possibility that {BH,} reacted with a second molecule of B6H ,was eliminated by co-thermolysis of B,H , with {BH,}-radical generators such as BH,.CO, and with CO.,, + {BH,) -+++B,H, + B,H6 (12) Reactions 11 and -1 explain the major reaction-product stoi- cheiometry and the minor products appear to result from the alternative reaction path 13: Reactions 11 and 13 could well proceed via the same reaction intermediate (see Figure 7) since the breaking of the three-centre bond between B(3)B(4)B(5) leads to a pendant BH, group, H,BH,, which could then either eliminate with cluster closure at B(l)-B(3) to form B,H, and (BH,}, or swing round to insert at this position, thereby forming B6HlOwith elimination of H,.The close structural relationship between the three arachno-boranes B4H10, B,Hl 1, and is emphasized in Figure 8, which also shows the close similarities between the Arrhenius parameters of the latter two: the very similar activation energies and extremely low pre-exponential factors are particularly notable features of both B,H,, and B6H12 thermolyses, both these boranes having structural features which are absent in B4H 10-There are many other systems that have been studied, includ- ing numerous co-thermolysis reactions and also the thermolysis CHEMICAL SOCIETY REVIEWS, 1992 P P I h 0 /I P + H, Figure 7 Suggested mechanisms for the elimination of either {BH,) or H, from B,H,, via a common intermediate to form B,H, or B,H,, respectively .EA 99.4* 3.4kJ mor' 78.5_+ 2.5kJ mot-' 81.3k 2.6 kJ mot-' A 6.0~lO"s-' 9.8x lo7 S-' Figure 8 Structural relationship between the three arachno boranes B,H,,, B,H,,, and B,H,,, together with a comparison of their Arrhenius parameters, showing the great similarity of the last two.of nido-B,H,, which turns out to be second ~rder.~~,~~ Unfortu-nately there is not the space to discuss these in detail here. However, one final point should be made: the ease with which these various thermolysis reactions occur does not derive from the weakness of BBB or BHB three-centre bonds but from the availability of unfilled orbitals and alternative structures at thermally accessible energies. Indeed, the cluster bonds in the borane molecules are amongst the strongest two-electron cova- lent bonds known, as indicated by the data in Table 1. Thus the average bond dissociation energy of boron is greater than that of either dihydrogen or carbon (diamond) as determined by the heats of atomization of the elements (column 1); likewise intercomparison of the values in columns 2 and 3 shows that the bond enthalpy of B-B is almost identical to that of C-C, whilst the three-centre bond enthalpies of BBB and BHB probably exceed these of the two-centre B-C and H-H bonds respectively.24 To summarize this first half of the lecture we can say that, as a result of our work in Leeds and that of several other laboratories particularly in the USA and Czechoslovakia, Stock's original six or seven boranes have now expanded to over 50 neutral boranes and a further 50 or more anions, making about 100 binary borane species in all.Perhaps even more significantly we are now finally solving the mysterious details of the complex but extre- 3.1x 108s-' Table 1 Enthalpies of atomization (d,-If298)and bond enthalpy contributions, E(X-Y) A,-H",,,/kJ mol-' E(X-Y)/kJ - mol-I E(X-Y)/kJ - mol-' H(g) B(g) C(g) ix436 566 356 B-B(2c,2e) BBB(3c,2e) B-H(2c,2e) BHB(3c,2e) 332 380 381 441 C-C B-C C-H H-H 331 372 416 436 mely facile thermal interconversions and aufbau reactions by which diborane and its homologues can grow into larger clusters.3 Metallaboranes and Other Heteroatom Boranes Let me now introduce the second major theme of the lecture by asking the question: is boron unique in this ability to form molecular clusters? Are there any other elements that have, like boron, fewer electrons than orbitals available for bonding? The answer is, of course, yes; there are many such elements: we call them metals.And so we asked ourselves the question (over 25 years ago now): is it possible to incorporate one, two, or even more metal centres within polyhedral borane clusters? It turned out to be an amazingly fruitful idea and the field of boron cluster chemistry has expanded enormously as a result. So far, over 45 LUDWIG MOND LECTURE-N. N. GREENWOOD elements have been included as cluster vertices, some 40 of them being metals or metalloids. Metals could therefore be regarded as ‘honorary boron atoms’ in these polyhedral clusters. More- over, because many metals can contribute differing numbers of electrons and orbitals to the cluster bonding, instead of the invariable two electrons and three orbitals of a BH vertex, such elements can be regarded as ‘flexi-boron atoms’.Examples are now known of elements which can contribute 0, 1, 2, 3, or 4 cluster-bonding electrons and 1, 2, 3, or 4 frontier orbitals. In this way novel cluster geometries can be constructed which are unknown among the binary boranes themselves. Much of this work has been reviewed already in my Liversidge Lecturez5 and elsewherez6 30 and I want to recall here only the salient overall themes before mentioning some exciting new developments which have occurred during the last two or three years. 3.1 Metallaboranes We found that, far from being ‘electron deficient’, many boranes and particularly their anions are very effective polyhapto ligands to appropriate metal centres.The resulting metallaboranes are often much more stable than the parent borane ligands, and this concept of ‘boranes as ligands’ can be used to systematize a huge body of new information by means of isolobal sequences and the general rules of coordination chemistry. But there were surprises too, as indicated at the end of the preceding paragraph, and novel iso-doso, iso-nido, and iso-arachno cluster geometries emerged,z5 30 different from those illustrated in Figure 2. Clusters of clusters are also possible in which boranes or metallaboranes are conjoined in various ways, for example (a) via a direct B-B or B-H-B bond, (b) via a commo B or M atom, (c) by sharing a common edge of two atoms, (d) by sharing a common triangular fxe, or (e) by more complex conjunctions. Thus two nido-decaboranyl units, -B10H13, can be joined via a B-B bond to give 11 distinct geometrical isomers of conjuncto- BzOHz,, four of which exist as enantiomeric pairs making 15 isomers in all, most of which have been isolated and ~haracterized.~ 5 Figure 9 Crystallographically determined molecular structure of the double cluster compound [((r16-C6Me,),Ru,H,IRuB, ,H,(OEt),].An intriguing example of a commo structure is provided by [((q6-C6Me6)zRu, H,)RuB ,H, (OEt),] which comprises an Ru, cluster and an RUB,, cluster conjoined at a common ruthenium atom Ru(1) as shown in Figure 9.32This dark red triruthenium-decaboron double cluster compound was obtained in 32% yield by reacting the yellow arachno four-vertex species [Ru(q*-B, H8)(q6-C6 Me6)C1] with closo-[B ,H ,I2 -in refluxing ethanol.It is the first (and so far only) example of a ruthenium cluster compound that does not contain carbonyl ligands, and has several other interesting features such as a triply 55 bridging H atom and three doubly bridging H atoms. Note also that, as each (Ru(q6-C6Me6)) vertex is isolobal with a {BH) unit, the ((q6-C,Me6),Ru,H,) moiety is equivalent to a polyhapto B2H6 group. Many examples of the other concatenating modes (c)-(e) are now also known in the numerous conjuncto and macropolyhedral metallaboranes previously reviewed. 30 Heterobimetallic clusters can also readily be constructed starting with a given metallaborane substrate and adding a second, different metal vertex.This procedure sometimes gener- ates novel cluster geometries as, for example, when the nido-decaborane analogue [6-(q5-C,Me,)IrB,H, 3] reacts with the rhodium dimer [((~5-C,Me,)RhC1,)z] in the presence of ‘proton sponge’ (i.e. N,N,N’,N‘-tetramethylnapthalene-1,8-diarnine) in dichloromethane solution at room temperat~re:,~ the dimetalla product has the structure shown in Figure 10. n Figure 10 Molecular structure of [(~5-C,Me,),RhIrB,H, I] showing the quadrilateral open face (1,3,7,4); due to crystallographic disorder the two metal positions are not assignable between Rh and Ir and there is a 5050 occupancy factor between B(2) and its equivalent position above the (1,3,7,4) face.For clarity the methyl H atoms and the nine terminal bordne H atoms are omitted; the two bridging H, atoms between Ir( 1)Rh(4) and B(3)B(7) respectively were located by NMR spectroscopy. The Rh-H-Ir and B-H-B hydrogen bridges in the quadri- lateral open face were detected by NMR spectroscopy. It will be noted that, since both {Rh(q5-C,Me,)) and {Ir(qs-CsMes)~ are isolobal with (BH) and all are expected to provide two electrons to the cluster bonding, the dimetalla product is a 24-electron (2n + 2) 1 1 -vertex species. One might therefore have expected a closo configuration. However, the product has neither a closo nor a regular nido structure (with a 5-vertex open face) but adopts an isonido configuration with a quadrilateral open face.Several other 1 1-vertex (2n + 2) heteroborane clusters which in the past have reasonably been assumed to have a ckoso octadeca-hedral structure similar to that long postulated for cfoso-[B, ,HI -(see Figure 2) have recently been shown to have the quadrilateral open-faced isonido structure,2 and this has important implications for cluster-bonding theories. 3.2 Incorporation of Very Electronegative Atoms as Cluster Vertices Most transition metals and post-transition metals have an electronegativity that is very similar to that of boron (2.0 on the Pauling scale). Their incorporation into polyhedral borane clusters therefore poses no great electrovalent distortion on the predominantly covalent cluster bonding.Carbaboranes, thia- boranes, and their metalla derivatives are also well known (electronegativity of C and of S is 2.5). However, with the even more electronegative elements nitrogen (3.0) and oxygen (3.5) it is more difficult to devise successful synthetic strategies and few azaboranes, oxaboranes, and the corresponding metallaboranes were known until very recently. Related constraints are the ease with which Lewis-base adducts can be formed, and the great 56 affinity of boron for oxygen which makes it difficult to prevent hydrolysis or complete oxidation of the poly(metal1a)borane cluster to B(OH),, B(OR),, B203, or similar species. The first fully contiguous azametallaborane to be reported was the air-stable, orange-red eleven-vertex closo-type ruthe- nium compound [(y6-MeC6H4-4Pr1)RuNB,H0] shown in Figure I 1.34 n 2-S Figure 11 Crystallographically determined molecular structure of the 1 1 -vertex doso-azaruthenaborane [(T~-M~C,H,-~-P~’)RUNB,H,J.The arachno ten-vertex azaplatinaborane [6,9-{(PPh,),Pt}NB,H, 1] is also known.35 A subsequent example of a contiguous metallaheteroborane, containing both nitrogen and carbon cluster vertices, is the extraordinary arachno-type twelve vertex (RuNCB,} cluster compound [{(y6-C6Me6)Ru) N(Me)C(H)B,H, I(OMe)] which was made by reacting the nido ten-vertex ruthenaborane [((y6-C6Me6)RU}B,H, ,] with MeNC in the presence of methanol.36 The unprecedented structure is in Figure 12, which clearly shows the presence of four-membered (BBCN), five-membered (BBBBN), and six-membered (RuBBCNB) open faces.The elements of MeNC are also clearly discernible, the isonitrile group itself being intimately involved as a bridging unit in all three open-faces. A differing structural motif is displayed in the Me,N-bridged arachno cluster ~-6,9-(NMe,)-5-{(y6-C6Me6)Ru)B,H,o-10-(PMe,Ph)] which is formed during the stepwise reduction of MeNC to Me,NH by [{(y6-C6Me6)RU)B9Hl 3] in the presence of PMe,Ph.,’ An even more remarkable dialkylamino derivative of a metallaborane is the purple air-stable compound isocloso-[l-{(~5-CsMe,)Ru)B,oH9-4-(NEt2)]which is readily obtained in 66% yield by the reaction of Et,NH with the orange-yellow isocloso eleven-vertex parent metallaborane [{(y5-C,Me,)Rh)B,oH,o].38 The compound is so far unique in being the only known example of a multiply-bonded N-substituted metallaborane involving N 3B 7~ bonding into the cluster; the multiple bonding is manifest by (a) the unusually short N-B distance of 142.7(8) pm (compared with the usual ‘single-bond’ N-B distance of about 158 pm), (b) the planar arrangement of 0 n CHEMICAL SOCIETY REVIEWS, 1992 nA Figure 12 Molecular structure of the 12-vertex arachno-azacarbaruthe- naborane [(~6-C6Me6)RuN(Me)C(H)B9Hll(OMe)]; the six-mem- bered open face Ru(S)B( IO)B(S)C(SS)N(67)B(6) carries the three bridging H atoms.The four-membered open face B(7)B(S)C(89)N(67) and the five-membered open face B(6)B(2)B(3)B(7)N(67) can also be seen.bonds about the N atom, and (c) the pronounced barrier to 180” rotation about the B-N linkage of 53.8(5) kJ mol- at 272 K. A recent review of various routes to non-metal-containing azabor- ane clusters should also be mentioned.,, Oxametallaborane clusters are even less numerous, and fewer than half a dozen species have so far been synthesized and characterized. The first to be reported40 was the oxaferra nido ten-vertex compound [((y5-C,Me,)Fe}OB,H, 0] which has the skeletal structure I shown in Figure 13. A second example, from our own laboratory the following year,4 was the red crystalline nido cluster compound [((y5-CsMes)Rh)OBloH9Cl(PMe2Ph)]which has the skeletal struc- ture I1 in Figure 13; it is of particular interest in being the first example of a cluster that incorporates a contiguous oxygen atom vertex bound solely to boron atoms, and the first open-faced twelve-vertex metallaborane cluster that does not also contain carbon atoms as cluster vertices.Other examples of oxametalla boranes are now beginning to emerge as a result of mild air- oxidation of rhodaboranes, for example the nido twelve-vertex cluster compound [{(y5-C,MeS)Rh}OB, ,H ,(NEt,)] and the 0x0-bridged bis-nido compound [{(~S-C,Me,)RhB9H,2),0] which have been shown by detailed X-ray diffraction analysis to have the skeletal structures 111 and IV in Figure 13.42 Clearly the range of structural possibilities for metallahetero- atomborane clusters is far from exhausted, and exciting possibi- lities for the synthesis and characterization of such aesthetically pleasing and potentially useful compounds abound.Stock’s elegant and perceptive studies on the six original boron hydrides have certainly stimulated some astonishing and deeply signifi- cant developments. I I1 111 IV Figure 13 Skeletal structure types of various oxametallaboranes (see text). LUDWIG MOND LECTURE-N. N. GREENWOOD 4 References 1 A. Stock, ‘The Hydrides of Boron and Silicon’, Cornell University Press, Ithaca, N.Y., 1933, 250 pp. 2 H. J. Schlesinger and A. B. Burg, J. Am. Chem. Soc., 1931,53,4321. 3 W. V. Kotlensky and R. Schaeffer, J. Am. Chem. Soc., 1958,80,4517. 4 H. I. Schlesinger and H. C. Brown, J. Am. Chem. Soc., 1940, 62, 3429.5 N. N. Greenwood in ‘Rings, Clusters and Polymers of Main Group and Transition Elements’, ed. H. W. Roesky, Elsevier, Amsterdam, 1989, pp. 49-105. 6 N. N. Greenwood and A. Earnshaw, ‘Chemistry of the Elements’, Pergamon Press, Oxford, 1984, pp. 179-185, and references cited therein. 7 W. N. Lipscomb, ‘Boron Hydrides’, Benjamin, New York, 1963,275 PP. 8 K. Wade, Adv. Inorg. Chem. Radiochem., 1976, 18, 1. 9 R. E. Williams, Adv. Znorg. Chem. Radiochem., 1976, 18,67. 10 J. F. Stanton, W. N. Lipscomb, and R. J. Bartlett, J. Am. Chem. Soc., 1989, 111, 5165. 1 1 R. Greatrex, N. N. Greenwood, and S. M. Lucas, J. Am. Chem. Soc., 1989,111,8721. 12 M. D. Attwood, Ph.D. Thesis, University of Leeds, 1987. 13 S. M. Lucas, Ph.D. Thesis, University of Leeds, 1990. 14 R.Schaeffer, J. Inorg. Nucl. Chem., 1960, 15, 190. 15 R. Greatrex, N. N. Greenwood, and C. D. Potter, J. Chem. Soc., Dalton Trans., 1984, 2435; 1986, 8 1. 16 M. D. Attwood, R. Greatrex, and N. N. Greenwood, J. Chem. Soc., Dalton Trans., 1989, 391. 17 R. Greatrex, N. N. Greenwood, D. W. H. Rankin, and H. E. Robertson, Pol.vhedron, 1987,6, 1849. 18 (a)P. von R. Schleyer, M. Buhl, U. Fleischer, and W. Koch, Znorg. Chem., 1990, 29, 153; (b) M. Buehl and P. von R. Schleyer in ‘Electron Deficient Boron and Carbon Clusters’, ed. G. A. Olah, K. Wade, and R. E. Williams, Wiley, New York, 1991, 113. 19 M. D. Attwood, R. Greatrex, and N. N. Greenwood, J. Chem. Soc., Dalton Trans., 1989, 385. 20 R. Greatrex, N.N. Greenwood, M. B. Milliken, D. W. H. Rankin, and H. E. Robertson, J. Chem. Soc., Dalton Trans., 1988,2335. 21 R. Greatrex, N. N. Greenwood, and S. D. Waterworth, J. Chem. Soc., Chem. Commun., 1988, 925. 22 R. Greatrex, N. N. Greenwood, and S. D. Waterworth, J. Chem. Soc., Dalton Trans., 1991, 643. 23 P. Davies, Ph.D. Thesis, University of Leeds, 1988. 24 N. N. Greenwood and R. Greatrex, Pure Appl. Chem., 1987,59,857. 25 N. N. Greenwood, Chem. Soc. Rev., 1984, 13,353. 26 N. N. Greenwood, Pure Appl. Chem., 1983,55,77 and 1415. 27 ‘Metal Interactions with Boron Clusters’, ed. R. N. Grimes, Plenum, New York, 1983,327 pp. 28 J. D. Kennedy, Prog. Inorg. Chem., 1984,32,519; 1986,34,211. 29 J. D. Kennedy in ‘Boron Chemistry’, ed. S. Heimanek, World Scientific, Singapore, 1987, 207.30 N. N. Greenwood and J. D. Kennedy, Pure Appl. Chem., 1991,63, 317. 31 S. A. Barrett, N. N. Greenwood, J. D. Kennedy, and M. Thornton- Pett, Polyhedron, 1985, 4, 1981, and references cited therein. 32 M. Bown, X. L. R. Fontaine, N. N. Greenwood, J. D. Kennedy, P. MacKinnon, and M. Thornton-Pett, J. Chem. Soc., Chem. Com- mun., 1987,442; J. Chem. Soc., Dalton Trans., 1987, 2781. 33 K. Nestor, X. L. R. Fontaine, N. N. Greenwood, J. D. Kennedy, and M. Thornton-Pett, J. Chem. Soc., Chem. Commun., 1989,455. 34 K. BaSe, M. Bown, X. L. R. Fontaine, N. N. Greenwood, J. D. Kennedy, B. Stibr, and M. Thornton-Pett, J. Chem. Soc., Chem. Commun., 1988,j 240. 35 K. BaSe, A. Petrina, V. PetriCek, K. Maly, A. Linek, and I. A. Zakharova, Chem. Znd., 1979, 212; K. BaSe, B. Stibr, and I. A. Zakharova, Synth. React. Inorg. Metal-Org. Chem., 1980, 10, 509. 36 E. J. Ditzel, X. L. R. Fontaine, N. N. Greenwood, J. D. Kennedy, Zhu Sisan, B. Stibr, and M. Thornton-Pett, J. Chem. Soc., Chem. Commun., 1990, 1741. 37 E. J. Ditzel, X. L. R. Fontaine, N. N. Greenwood, J. D. Kennedy, Zhu Sisan, and M. Thornton-Pett, J. Chem. Soc., Chem. Commun., 1989, 1762. 38 E. J. Ditzel, X. L. R. Fontaine, N. N. Greenwood, J. D. Kennedy, and M. Thornton-Pett, J. Chem. Soc., Chem. Commun., 1989, I1 15. 39 P. Paetzold, Pure Appl. Chem., 1991,63, 345. 40 R. P. Micciche, J. J. Briguglio, and L. G. Sneddon, Inorg. Chem., 1984,23, 3992. 41 X. L. R. Fontaine, H. Fowkes, N. N. Greenwood, J. D. Kennedy, and M. Thornton-Pett, J. Chem. Soc., Chem. Commun., 1985, 1722; J. Chem. Soc., Dalton Trans., 1987, 2417. 42 E. J. Ditzel, X. L. R. Fontaine, H. Fowkes, N. N. Greenwood, J. D. Kennedy, P. MacKinnon, Zhu Sisan, and M. Thornton-Pett, J. Chem. Soc., Chem. Commun., 1990, 1692.

ISSN:0306-0012    

DOI:10.1039/CS9922100049

出版商:RSC    

年代:1992

数据来源: RSC

摘要:

The VSEPR Model Revisited Ronald J. Gillespie Department of Chemistry, McMaster University, Hamilton, Ontario L8S 4M 1, Canada 1 Introduction It is now over thirty years since the basic ideas of the VSEPR model were first proposed in a review entitled ‘Inorganic Stereo- chemistry’.’ The name Valence Shell Electron Pair Repulsion (VSEPR) model was proposed in 19632 and a comprehensive survey of the use of the model for the prediction and rationaliza- tion of molecular geometry was first published in 1972.3 In the subsequent years the model has continued to be very useful as a basis for the discussion and understanding of molecular geo- metry while at the same time its basic ideas have been reformu- lated to some extent, and considerable progress has been made in understanding its physical basis.4 A new detailed account of the model and its many applications has recently been published.’ The purpose of this review is to give a brief up-to- date account of the model, with emphasis on an improved reformulation of some of the basic ideas, together with some examples of new applications.2 The Points-on-a-Sphere Model The VSEPR model is based on the Lewis diagram for a molecule in which electrons are considered to be arranged in pairs that are either bonding (shared) pairs or non-bonding (lone or unshared) or pairs. The basic postulate of the VSEPR model is that the arrangement of the electron pairs in a valence shell is that which places them as far apart as possible or, more precisely, that maximizes the least distance between any two pairs.A simple model is to consider each electron pair as a point on the surface of a sphere surrounding the core of the atom. The arrangement of the points that maximizes the least distance between any pair of points gives the expected arrangement of the same number of electron pairs. For two electron pairs the arrangement is linear, for three it is triangular, for four it is tetrahedral, and for six it is octahedral (Figure 1). For five pairs of electrons both a square pyramid and a trigonal bipyramid, and any arrangement between, maximizes the least distance between any pair. But if we also make the reasonable assumption that the number of least distances is minimized the trigonal bipyramid is the pre- ferred arrangement.It is assumed that the core of the atom is spherical and therefore has no effect on the arrangement of the valence shell electron pairs. This assumption is usually, but not always, valid for main group elements but not for the transition metals as discussed later. Ronald J. Gillespie is a citizen of Canada. He was born in London, England in 1924. He obtained his BSc. (194.5), Ph.D. (1949), and D.Sc. (19-57) degrees from University College, London. He was an Assistant Lecturer in the Department of Chemistry at University College from 1948 until 1950 and then a Lecturer until 19-58 when he moved to McMaster University, Canada as Associ- ate Professor in the Department of Chemistry. He was appointed Professor in 1960 (Chairman, Department of Chemistry, 1962- 1965).Since 1988he has been Emeritus Professor of Chemistry at McMaster University. He is an inorganic chemist with particular interests in non- aqueous solvents, superacid chemistry, main-group chemistry, structural chemistry and molecular geometry, and chemical education. He has published 3 books and over 330 journal articles in thesefields. He was elected Fellow of the Royal Society in 1977. 59 Figure 1 The-points-on-a-sphere model. Arrangements of points that maximize their distance apart: (a) linear arrangement of two points; (b) equilateral triangular arrangement of three points; (c) tetrahedral arrangement of four points; (d) trigonal bipyramidal arrangement of five points; (e) octahedral arrangement of six points.X I 0 X-A-X X I 0 0,-/A,lX x/A,lx ,xp X X X xx X X X X x x X x X X x Figure 2 Predicted shapes for all molecules with a central atom A having up to six electron-pairs in its valence shell and a spherical core. Each of the arrangements of three to six electron pairs can give rise to two or more molecular shapes, depending on how many of the electron pairs are non-bonding pairs. All the possible molecular geometries that can be derived in this way are summarized in Figure 2. 3 The Electron-pair Domain Model Although the points-on-a-sphere model is useful for predicting the arrangements of a given number of electron pairs, it is more CHEMICAL SOCIETY REVIEWS, 1992 elastic band toothpick or nail Styrofoam sphere Figure 3 Styrofoam sphere models of electron-pair domain arrange- ments.Two or three Styrofoam spheres are joined by elastic bands held in place by small nails or toothpicks. Each sphere represents an electron-pair domain. The elastic band models the electrostatic attrac- tion of the positive core situated at the mid-point of the elastic band and the electron pairs. The spheres naturally adopt the arrangement shown. If they are forced into some other arrangement, such as the square planar arrangement of four spheres, they immediately adopt the preferred tetrahedral arrangement when the restraining force is removed. realistic to consider an electron pair as a charge cloud that occupies a certain region of space and excludes other electrons from this space.That electrons behave in this way is a result of the operation of the Pauli exclusion principle, according to which electrons of the same spin have a high probability of being far apart and a low probability of being close together. As a consequence the electrons in the valence shell of an atom in a molecule tend to form pairs of opposite spin. To a first approxi- mation, each pair may be considered to occupy its own region of space in the valence shell such that its average distance from other pairs is as large as p~ssible.~ We will call the space occupied by a pair of electrons in the valence shell of an atom an electron-pair domain. In its simplest form this model assumes that all electron-pair domains have a spherical shape, are the same size, and do not overlap with other domains.This model was first proposed by Kimball and by Bents,9who called it the tangent-sphere model but we will call it the spherical domain model. These spherical domains (tangent-spheres) are attracted to the central positive core and adopt the arrangement that enables them to get as close as possible to the core, or, alternati- vely, that keeps them as far apart as possible if they are all at a given distance from the core. These arrangements can be demon- strated very simply. A Styrofoam sphere is used to approxima- tely represent the domain of an electron pair.l0 These spheres are then joined into pairs and triples by elastic bands (Figure 3).By twisting together the appropriate number of pairs and triples, arrangements offour, five, and six spheres can also be made. The elastic band represents the force of attraction between the nucleus imagined to be at the midpoint between the spheres. In each case, two to six spherical electron-pair domains adopt the same arrangements as predicted by the points-on-a-sphere model (Figure 3). If a model is distorted from its preferred arrangement a gentle shake will cause it to return to that arrangement. Later we show that it is sometimes useful to use a better approximation for the shape of a domain such as an ellipsoid or a ‘pear’ or ‘egg’ shape. The electron-pair domain version of the VSEPR model emphasizes the different sizes and shapes of the electron-pair domains rather than the relative magnitudes of lone-pair-lone- ~pair, lone-pair bond-pair, and bond-pair -bond-pair repul- sions.’ The two versions of the model are equivalent and lead to the same predictions, but in general the domain version is THE VSEPR MODEL REVISITED-R.J. GILLESPIE simpler and easier to use. There would therefore be some advantage in replacing the acronym VSEPR with VSEPD standing for Valence Shell Electron Pair Domain. 4 Deviations from Regular Shapes An important feature of the VSEPR model is that qualitative predictions about deviations from the bond angles and bond lengths corresponding to the regular geometries in Figure 2 can be made very easily. Deviations from the ideal bond angles and bond lengths may be attributed to differences in the sizes and shapes of electron-pair domains.For the valence shell of the central atom A in a molecule AX,E,, where X is a ligand and E is a lone pair, there are three important factors that influence the size and shape of an electron-pair domain: (i) A bonding domain is subjected to the attraction of two positive cores and is shared between the valence shells of A and X whereas a non-bonding domain is entirely in the valence shell of A and spreads out around the core as much as it can. Thus a non-bonding domain is larger and occupies more space in the valence shell of A than a bonding-pair domain and is closer to the core than a bonding-pair domain. (ii) Double- and triple-bond domains are composed of two and three electron-pairs, respectively, and are therefore larger than single-bond domains.(iii) An increasing amount of electron density is drawn away from the valence shell of A and into the valence shell of the ligand X with increasing electronegativity of X. Thus the space occupied by a bonding domain in the valence shell of A decreases, and in the valence shell of X, increases with increasing electronegativity of X. Figure 4 Lone pairs and bond angles: (a) equilateral triangular arrange- ment of three equivalent bonding domains with a bond angle of 120"; (b) triangular arrangement of two bonding domains and a lone-pair domain giving a bond angle of less than 120". Table 1 Bond angles (") in AX,E and AX,E, molecules AX,E AXzEz NH, 107.2 H2O 104.5 NF, 102.3 F*O 103.1 PF, PCI, 97.7 100.3 SF,sc12 98.0 102.0 PBr, 101.0 S(CH,)2 99.0 AsCI, AsF, 98.9 95.8 TeBr, Se(CH,), 104 96 5 Non-bonding or Lone Pairs To a first approximation we may represent a lone-pair domain as a sphere that is larger than a bonding domain and which, because it is attracted only by one atomic core, tends to surround this core, and is therefore on average closer to the core than a bonding pair (Figure 4).As a consequence the bond angles in AX,E molecules and AX,E, molecules are smaller than the Figure 5 Lone pairs and bond lengths.A section passing through the lone pair and three ligands in an AX,E molecule. The bonding domains adjacent to the lone-pair domain are pushed away from the central core more than the bonding domain trans to the lone pair.Thus the basal bonds are longer than the apical bond. Table 2 Bond lengths (pm) and bond angles (") in AX,E square pyramidal molecules Bond lengths Bond angle apical basal apical-basal ClF, 157 I67 86 BrF, 168.9 177.4 85.1 IF5 184.4 186.9 83.0 XeF:(PtF,) 181.0 184.3 79 (Rb + )SF; 155.9 171.8 88 (Na +)TeF; 186.2 195.7 79 (K+),SbF: - 181.6 207.8 82 (NHz)2SbCI: 236 258 269 85 tetrahedral angle (Figure 4).Some examples are given in Table Because it occupies more space and tends to surround the core a lone-pair domain tends to push adjacent bonding-pair domains away from the core thus increasing the bond lengths.This effect cannot be detected in AX,E and AX,E, molecules because all the bond lengths are affected equally. However, in AX,E molecules the four bonds in the base of the square pyramid are closer to the lone pair than is the apical bond, consequently the four bonds in the base are longer than the apical bond (Figure 5). Some examples are given in Table 2. In a trigonal bipyramidal AX, molecule the equatorial positions have only two close neighbours at 90"whereas an axial position has three close neighbours at 90".Thus an axial position is more crowded than an equatorial position. Consequently larger non-bonding domains are expected to occupy preferen- tially the equatorial positions. In all known AX,E, AX,E,, and AX,E, molecules the lone pairs do indeed occupy the equatorial positions. Some examples are given in Figure 6.The prediction of the shapes ofAX,E, AX,E,, and AX,E, molecules in the first paper on the VSEPR model' involved counting the numbers of each kind of repulsion between electron pairs at 90". ignoring the repulsions between electron pairs at 120°,and assuming that the relative magnitudes of electron-pair repulsions are: lone-pair-lone-pair > lone-pair bond-pair > bond-pair bond-pair This method also leads to the conclusion that the lone pairs occupy the equatorial positions. However, the electron-pair domain version of the VSEPR model in which a lone-pair domain is assumed to be larger than a bond-pair domain is simpler and leads directly to an unambiguous prediction of the structures of AX,E, AX,E,, and AX,E, molecules.6 Multiple Bonds A model of the ethene molecule that predicts its planar shape can be based on the tetrahedral arrangement of four electron-pair domains around each carbon atom with two bonding domains CHEMICAL SOCIETY REVIEWS, 1992 F F F I l+ I F F F F Figure 6 In molecules with five electron-pair domains in the valence shell of the central atom lone pairs always occupy the equatorial positions and never occupy the axial positions. nH-Cwc-H nH8c@3:H Figure 7 Geometry of ethene and ethyne: (a) bent-bond models; (b) electron-pair domain models. 0”H(&H c@H Figure 8 Multiple bond domains: (a) a double-bond domain and a model of ethene; (b) a triple-bond domain and a model of ethyne.S, single-bond domain; D, double-bond domain; T, triple-bond domain. forming the double bond (Figure 7). This model corresponds to the classical bent-bond model for the double bond that is sometimes criticized because it appears to show that there is no electron density along the CC axis (Figure 7). But a bond diagram is only a very approximate representation of the electron distribution. The electron-pair domain model gives a better and less misleading, although still very approximate, representation of the electron distribution in ethene. The linear structure of ethyne is also predicted by the domain model in which both carbon atoms have a tetrahedral arrangement of four bonding domains in their valence shell (Figure 7).The electron-pair domain model can be improved and also simplified by considering that the two electron-pair domains of a double bond are merged into one larger domain and that the three electron-pair domains of a triple bond are merged into one still larger domain (Figure 8). In ethene each of the two carbon atoms then has three domains in its valence shell, two single H-CEC-H bond domains, and a double bond domain. These three domains adopt a triangular AX, arrangement giving a planar geometry around each carbon atom (Figure 8). In ethyne each carbon atom has only two domains in its valence shell, a single-bond domain and a triple-bond domain. These two domains adopt a linear AX, arrangement so that each carbon atom has a linear geometry (Figure 8).The shapes of some other related molecules containing double and triple bonds can be predicted in a similar manner as shown in Figure 9.The otherwise very useful (J -T model of the double bond cannot be used to predict the planar shape of the ethene molecule. The description of the bonds around each carbon atom in terms of sp2 hybrid orbitals forming (T bonds plus a p orbital forming a T bond is based on the known geometry of the ethene molecule and so this description of the bonding cannot be used to predict the molecular geometry. The VSEPR model is the only simple model that predicts the planar geometry of the ethene molecule. The above model of double- and triple-bond domains is particularly useful for discussing the structures of molecules in which there are more than four electron pairs in the valence shell of the central atom A. For example, according to this model SO, THE VSEPR MODEL REVISITED-R. J.GILLESPIE H\ ,c H H 0" Figure 9 Electron-pair domain models of H,CO, HCN, and CO,. L, lone-pair domain. Figure 10 Electron-pair domain model of SO, in which the sulfur atom has an AX,E geometry. is an AX,E molecule in which there is one lone-pair domain and two double-bond domains in the valence shell of sulfur (Figure 10). Other examples of molecules containing double and triple bonds are given in Table 3. Because a double-bond domain is larger than a single-bond domain and a triple-bond domain is larger still, we expect that there will be deviations from the ideal bond angles in molecules containing double and triple bonds.In ethene we expect the angles between the double bond and the two CH bonds to be larger than 120" and the angle between the two CH bonds to be smaller than 120". Experimental data for ethene, some substi- tuted ethenes, and other molecules with an AX, geometry are given in Table 4.In each case the angle between the single bonds is less than 120" and the angle between a single bond and a double bond is greater than 120". The experimentally deter- mined bond angles for some AX, molecules containing multiple bonds are given in Table 5. In each case the db:db and db:sb angles are larger than the sb:sb angle.In a trigonal bipyramidal molecule we expect a large double- bond domain preferentially to occupy one of the equatorial sites. All known trigonal bipyramidal molecules with a double-bonded ligand do indeed have the double-bonded ligand in an equatorial position. Some examples are given in Figure 1 1. The bond angles in these molecules are consistent with the larger size of the double-bond domain. In the molecule H,C=SF, the CH, group is perpendicular to the equatorial plane through the sulfur atom. This geometry is most easily accounted for in terms of the octahedral arrange- ment of six single electron-pair domains around the sulfur atom, two of which are used to form the S=C double bond (Figure 12).The tetrahedral arrangement of the four electron-pair domains in the valence shell of carbon then leads to the observed geometry. The domain model of double and triple bonds can be improved by replacing the spherical shape with the more realistic prolate ellipsoidal 'egg' shape for a double bond and an oblate ellipsoidal 'doughnut' shape for a triple bond (Figure 13). In .. =0.. :.o =c =0.: AX2 ethene the ellipsoidal double-bond domain minimizes its inter- actions with the other domains by having its long axis perpendi- cular to the plane of each CH, group so that the molecule has an overall planar shape (Figure 13). A cross-section through the calculated electron density of the ethene molecule perpendicular to the CC axis and through the mid-point of this axis has the expected ellipsoidal shape (Figure 13).An alternative model of the molecule H,C=SF, can be based on a trigonal bipyramidal arrangement of five domains, one of which is an ellipsoidal double-bond domain. This double-bond domain will minimize its interactions with the other domains in the valence shell of sulfur by having its long axis in the equatorial plane, thus giving the observed molecular shape (Figure 14). 7 Ligand Electronegativity A bonding domain can be conveniently represented by a non- spherical 'pear' or 'egg' shape when the electronegativity of X is not equal to that of A (Figure 15). In this figure also we represent the lone-pair domain as having an oblate ellipsoidal or 'dough- nut' shape. The space occupied in the valence shell of A by the domain of a bonding pair decreases with increasing electronega- tivity of X.Thus in molecules with one or more lone pairs in the valence shell of A the bonding pairs are pushed closer together by the lone pair(s) as the electronegativity of X increases and so the angle between an AX bond and its neighbours decreases correspondingly. Some examples of the effect of the electronega- tivity of X on the bond angles in some AX,E and AX,E, molecules are give in Tablz 6. In a trigonal bipyramidal molecule the larger domains of the bonds to less electronegative ligands will preferentially occupy the less crowded equatorial sites. Some examples are given in Figure 16. 8 Seven Electron-pair Domains The prediction of the geometry of molecules in which there are more than six electron-pairs in the valence shell of the central atom A is less reliable than for molecules in which there are six or fewer electron-pairs in the valence shell.There may be several arrangements of points on a sphere that have similar least distances. In other words there may be alternative arrangements of the electron-pair domains that have similar energies. Differ- ences in the sizes and shapes of the electron-pair domains may then cause an arrangement other than that predicted for equiva- lent domains to be favoured. Moreover, only small movements of the ligands through low energy barriers are required to convert one geometry into another when there are seven or more electron-pair domains in the valence shell, so that such mole- cules are often fluxional.Despite the difficulty of making completely reliable predic- tions of geometry for molecules with more than six electron-pair 64 Table 3 Shapes of molecules containing multiple bonds Bonding Lone-pair Domains Arrangement domains domains 2 Linear 2 0 3 Triangular 3 0 2 I 4 Tetrahedral 4 0 1 2 5 Trigonal 5 Bipyramid 4 1 6 Octahedron 6 0 Table 4 Bond angles in some molecules containing C=C and C=O double bonds X2C=CY2 xcx YCY xcc YCC H,C=CH, 116.2 116.2 121.9 121.9 F2C=CH, 110.6 119.3 124.7 120.3 F,C=CF, 112.4 112.4 123.8 123.8 Cl,C=CCl, 115.6 115.6 122.2 122.2 (CH,),C=CH, 115.6 116.2 122.2 121.9 xcx xco H,CO 116.5 121.7 C1,CO 111.8 124.1 F2C0 107.7 124.1 HFCO 110 123 ~~ domains in the valence shell of the central atom A, the VSEPR model can nevertheless make an important contribution to our understanding of the geometry of such molecules.Moreover, there is no other simple model that allows one to make compar- able predictions. We discuss here some molecules with seven domains in the valence shell of A. The arrangement of seven points on the surface of a sphere CHEMICAL SOCIETY REVIEWS. 1992 Molecular shape Linear CI -0 0 Triangular >CEO >A=, o>s=o CI -0 V-Shape Tetrahedral Trigonal pyramid V-Shape F Trigonal bipyramid F F F I Disphenoid OYe: 0" { F F 0 0 F\ It/F HO, ll,OH Octahedron F/i\F HOI~~OH F OH ~~ Table 5 Bond angles in AX, molecules containing multiple bonds sbsb sbdb (tb) sbsb dub POF, 101.3 117.7 F,SO, 96.1 124.0 POCl, 103.3 115.7 Cl,SO, 100.3 123.5 POBr, 104.1 115.0 ClFSO, 99 123.7 PSF, 99.6 122.7 (NH,),S02 112.1 119.4 PSCl, 101.8 117.2 (CH,),SO, 102.6 119.7 PSBr, 101.9 117.1 NSF, 94.0 125.0 that maximizes the least distance between any pair of points is the monocapped octahedron (Figure 17a).But the monocapped trigonal prism and the pentagonal bipyramid have only slightly larger least distances and therefore have only slightly greater energies (Figure 17b, c). Among the compounds of the main group elements and transition metals with spherical cores AX, molecules are known with each of these geometries. For example NbOFg- has the 1:3:3 structure, NbF:- and TaF$- have the 1 :4:2structure, and IF, has the 1:5:1 structure.The pentagonal bipyramidal structure of iodine heptafluoride appears to be THE VSEPR MODEL REVISITED-R. J. GILLESPIE F F F F Figure 11 In trigonal bipyramidal AX, molecules a large double-bond domain always occupies an equatorial position. F F Figure 12 The bent-bond model of H2C=SF, showing why the CH, group is perpendicular to the equatorial plane through sulfur. B Figure 13 Multiple bond domains: (a) a prolate ellipsoidal double-bond domain and the corresponding model of ethene in which each carbon atom has a triangular AX, geometry; (b) an oblate ellipsoidal triple- bond domain and the corresponding model of ethyne in which each carbon atom has a linear AX, geometry; (c) a cross-section of the total electron density through the midpoint of the CC bond and perpendi- cular to this bond in the ethene molecule, showing contours of equal electron density.slightly distorted by some buckling of the equatorial plane and the molecule is fluxional. If there are one or more lone-pair domains we expect these domains to occupy the least crowded positions. The mono- capped octahedron or 1:3:3 arrangement has three non-equiva- lent sets of sites. The unique capping site has only three nearest neighbours and is therefore the least crowded site.So the lone pair in an AX6E molecule is expected to occupy this site giving a distorted octahedral geometry for the molecule. Xenon hexa- fluoride is an AX6E type molecule and it does indeed have a fluxional distorted octahedral geometry. We expect an AX,E, molecule to have a structure in which both lone-pairs occupy sites that are less crowded than the remaining five. In the pentagonal bipyramid arrangement the two axial sites are less crowded than the five equatorial sites. The two axial sites have all their neighbours at 90" whereas each equatorial site has two close neighbours at 72". So we expect the F I F Figure 14 Model of the CH,=SF, molecule with a prolate ellipsoidal double bond domain. (a1 (b) Figure 15 Electronegativity and bonding domain size.The space occu- pied by a bonding domain in the valence shell of the central atom A decreases with increasing electronegativity of the ligand X. (a) lone pair on A; (b) x(X) < x(A); (c) x(X) = x(A); (d) x(X) > x(A). Table 6 Effect of ligand electronegativity on bond angles H,O 104.5 F,O 103.1 SF, 98.0 SC1, 102.7 NH, 107.2 NF, 102.3 PI, 102 PBr, 101.0 PCl, 100.3 PF, 97.7 AsI, 100.2 AsBr, 99.8 AsC1, 98.9 AsF, 95.8 two lone-pairs to occupy the axial sites giving a planar pentago- nal molecule. The XeF; ion is an AX,E, molecule and a recent structure determinationI4 shows that it has a planar pentagonal geometry (Figure 18). We similarly expect a double-bond domain to occupy an axial position in a pentagonal bipyramid.The 19F NMR spectrum of a solution of IOF; is consistent with five equatorial fluorines and an axial fluorine with a double-bonded oxygen presumably occupying the second axial position of a pentagonal bipyramid.' 6.1 A valence shell containing seven or more electron-pair domains is very crowded and appears only to be found for main group elements under two conditions: (a) The ligands are very electronegative, for example fluorine, so that the bonding domains in the valence shell of the central atom are small. (b) The central atom has a large valence shell and, in particular, is a fifth period element such as xenon. Some molecules in which the central atom is from periods 3 and 4 and in which the ligands are less electronegative than fluorine do not, therefore, have sufficient space in their valence shell to accommodate six bonding domains and a large lone-pair CHEMICAL SOCIETY REVIEWS, 1992 F F F F ILFF-P F-P I I Lc' F F Figure 16 In molecules with five electron-pair domains in the valence shell of the central atom the smallest bonding domains and therefore the most electronegative ligands always occupy the axial positions.Figure 17 Arrangements of seven points on a sphere: (a) the mono- capped octahedral or 1:3:3 arrangement; (b) the monocapped trigonal prism or 1 :4:2 arrangement; (c) the pentagonal bipyramidal or 1 :5:1 arrangement. F5, /-F5 w-F Figure 18 The pentagonal planar geometry of the XeF; ion and the (idealized) pentagonal bipyramidal geometry of the IF, molecule. domain.In such molecules the lone pair is squeezed into a spherical domain surrounding the core and inside the bonding domains which therefore have an octahedral arrangement. Thus some AX,E molecules such as SeCl: and BrF; have a regular octahedral shape, but with longer than normal bonds. These and F F therefore has no influence on the geometry. There are, however, two cases in which this may not be the case: (a) When the core is very polarizable. (b) When the central atom A is a transition metal. In this section we consider an example of the effect of a polarizable core on the shape of some main-group element molecules. Molecules of the transition metals are discussed in the following section.There is good evidence that some dihalides of the group 2 metals are bent whereas they would be expected to have linear AX, structures. Experimental values for the bond angles in these molecules from gas-phase measurements at high temperature are given in Table 7. Although these molecules are rather flexible and the bond angles have not been determined with great accuracy it seems clear that the bent form is favoured for the heavier central atoms and lighter halogens. Table 7 Bond angles (") for the gaseous alkaline earth dihalides MX, M X F c1 Br I Be 180 180 180 I80 Mg Ca 180 133-1 55 180 I80 180 173-1 80 I80 180 Sr 108-135 120-143 133-180 161--180 Ba 100-1 15 100-127 95-1 35 103-105 If the outer shell of the core is completely filled, as it is for second and third period elements (ls2and 2s22p6,respectively), we expect that the core will have a low polarizability and will be difficult to deform.However, for fourth and subsequent period elements, and in particular for Ca, Sr, and Ba, the spherical ns2np6core has vacant dorbitals so it is much more polarizable than the core of a second or third period element such as Be or Mg and may be deformed by interaction with the bonding electron-pairs. It seems reasonable to suppose that in a dihalide of Ca, Sr, or Ba the repulsion between the two bonding electron- pairs and the eight electrons of the outer shell of the core causes these eight electrons to localize to some extent into four tetra- hedrally arranged pairs.The two bonding pairs would tend to avoid these domains so that in the limit of a very strong interaction they would be located opposite two of the faces of the tetrahedron thus giving a bond angle of 109"(Figure 19). If the interaction with the core is weak then repulsion between the bond pairs will increase the bond angle which in the limiting case of a negligible interaction with the core will be 180". The polarizability of the core increases from Be to Ba so there is an increasing tendency for the bond angle of the dihalides to decrease from Be to Ba. For the halide ligands the polarizability decreases and the charge density increases from the iodide to the fluoride, so we expect the interaction with the core electrons to increase from the iodide to the fluoride and the bond angle to decrease correspondingly.related molecules have been discussed in detail else~here.~.~~~ 9 Non-spherical Cores As it is usually presented in textbooks the VSEPR model is based, explicitly or implicity, on the assumption that the core beneath the valence shell of the central atom A is spherical and 10 Transition Metal Molecules In most discussions of the VSEPR model it is assumed that it is not applicable to molecules of the transition metals unless they have do,d5,or d10 configurations, because, for other configu- THE VSEPR MODEL REVISITED-R. J. GILLESPIE Figure 19 A bent AX, molecule such as CaF,.The eight electrons of the outer shell of the ns2np6 core are to some extent localized into four tetrahedrally arranged pair domains. Interaction between the two bonding domains and the four core domains causes the molecule to be bent rather than linear. rations, the assumption that the core is spherical is not valid. However, the VSEPR model can be used to predict the geometry of a transition metal molecule if it is assumed that for these d configurations the core has an ellipsoidal shape rather than a spherical shape. An important feature of molecules of the transition metals that distinguishes them from molecules of the main-group elements is that there are no lone pairs in their valence shells. Any non-bonding electrons are delectrons from the penultimate shell.These d electrons may be considered to constitute a subshell that forms the outer layer of the core. Therefore the basic shapes of transition metal molecules are simply the AX,, AX,, AX,, AX,, and AX, shapes. These basic shapes are not distorted by spherical do, AS (five unpaired electrons) and d'O subshells as shown by the examples in Table 8. Table 8 Shapes of transition metal molecules with do,ds,and d1O spherical subshells Number of Shape d electrons Example AX2 AX3 AX4 Linear Equilateral Triangle Tetrahedron 10 5 10 0 Ag(NHd2 FeCl3(g)Cu(CN): -TiCl, 5 FeCl, 10 ZnC1:- AX5 Trigonal Bipyramid 0 5 NbCl, FeC1: - 10 CdCl: - Octahedron 0 WF6 5 CoFg - 10 Zn(NH& + If the core is non-spherical the simplest assumption that we can make about its shape is that it is ellipsoidal, either prolate or oblate. The core may have a more complex shape in some cases but an ellipsoidal shape appears to be a reasonable approxima- tion in most cases and it allows us correctly to predict the shapes of many molecules.An ellipsoidal shape is expected, for exam- ple, for a d9 configuration. Removing an electron from a dx2-c'2 orbital or a dz2 orbital in a spherical d*O subshell gives a prolate or an oblate ellipsoidal core respectively (Figure 20). It cannot be predicted whether a non-spherical d subshell will have an oblate or a prolate ellipsoidal shape but this same problem arises in a more conventional treatment in which the direction of a Jahn-Teller distortion cannot be predicted. 10.1 AX4 Molecules Figure 21 shows how an ellipsoidal core distorts the tetrahedral AX, geometry.An oblate ellipsoid will cause an elongation of the tetrahedral geometry but this type of distortion has not been observed. A prolate ellipsoid distorts the tetrahedral geometry to a disphenoid and in the limit to a square planar geometry. The d" oblate el I ipsoidal d subshell 0W dlo dX2_y2 prolate el Ii psoid d subshell Figure 20 (a) Removing a dzzelectron from a spherical d1° subshell gives an oblate ellipsoidal d subshell; (b) removing a d.yz,,z electron from a ~ spherical d10 subshell gives a prolate ellipsoidal d subshell. Figure 21 Distortion of the tetrahedral AX, geometry by an ellipsoidal d subshell.(a) A prolate ellipsoid produces a disphenoid that may be described as a 'flattened' tetrahedron and in the limit a square plane; (b) an oblate ellipsoid produces a disphenoid that may be described as an 'elongated' tetrahedron. disphenoidal geometry is rare but an example is provided by the CuCli- ion in Cs,CuCl, that has bond angles of 104" and 120" compared with 109.5' for the tetrahedral geometry and 90" and 180" for the square planar geometry. There are many examples of square planar molecules in which the transition metal has a d8 subshell, such as Ni(CN)i-, PdCli-, Pd(NH,):-, Pt(CN):-, PtCli-, and AuCl, . 10.2 AX, Molecules Figure 22 shows how an ellipsoidal core distorts the octahedral AX, geometry.An oblate ellipsoid causes a flattening of the octahedron while a prolate ellipsoid causes the more commonly observed elongation of the octahedron, which in the limit gives a square planar AX, geometry with the loss of two ligands. Some examples of tetragonally distorted octahedral geometry in some d9 copper compounds are given in Table 9. Many other exam- ples are 10.3 AX, Molecules Transition metal molecules of this type exhibit a number of interesting and instructive features as do AX, molecules of the main group elements. Figure 23 shows how the trigonal bipyra- midal AX, geometry is distorted by an ellipsoidal core. In all trigonal bipyramidal molecules with a spherical core the axial bonds are longer than the equatorial bonds because of the greater crowding in the axial sites compared to the equatorial sites.An oblate ellipsoidal core repels the axial bond domains less than the equatorial domains thus reducing the normal difference in the axial and equatorial bond lengths. This differ- ence may be reduced to zero, or even reversed to give longer equatorial than axial bonds (Table 10). CHEMICAL SOCIETY REVIEWS, 1992 Figure 22 Distortion of the octahedral AX, geometry by an ellipsoidal d subshell. (a) A prolate ellipsoid produces a square bipyramid that may be described as an elongated octahedron; (b) An oblate ellipsoid produces a square bipyramid that may be described as a ‘flattened’ octahedron. Table 9 Bond lengths (pm) in some tetragonal d9 copper compounds Elongated octahedron Flattened octahedron (prolate ellipsoidal d-shell) (oblate ellipsoidal d-shell) CuF, 193 227 KCuF, 196 207 Na,CuF, 191 237 K,CuF, 195 208 (NH,),CI, 231 279 cuc1, 230 295 KCuC1, 229 303 I Figure 23 Distortion of the AX, trigonal bipyramidal geometry by an ellipsoidal d subshell.(a) A prolate ellipsoid stabilizes the square pyramidal geometry with respect to the trigonal bipyramid; (b) an oblate ellipsoid decreases the axial bond lengths and increases the equatorial bond lengths of the trigonal bipyramid. A prolate ellipsoidal core will destabilize the trigonal bipyra- mid with respect to the square pyramid which even for spherical cores has only a slightly higher energy. Therefore we expect some AX, molecules of the transition metals to have a square pyramidal geometry as is observed (Table 10).The geometry of these molecules differs in an important way from AX,E square pyramidal molecules of the main-group elements. In the latter the four bonds in the base of the square pyramid are longer than the apical bond (Figure 5) but in the AX, square pyramidal molecules of the transition metals interaction with a prolate ellipsoidal core causes the apical bond to be longer than the equatorial bonds (Table 10). Thus although we cannot predict which AX, molecules of the transition metals will have a trigonal bipyramidal shape and which will have a square pyramidal shape we can make some useful predictions about the deviations from these ideal shapes that show interesting differences from main group molecules with the same basic shape.In general the basic shapes of the molecules of the transition metals follow directly from the VSEPR model and distortions of these shapes by a non-spherical core can be readily predicted on the basis of the assumption that the core (or d subshell) is not spherical but has either a prolate or an oblate ellipsoidal shape. Table 10 Bond lengths (pm) in AX, molecules of the transition metals Trigonal Bipyramid Molecules Axial Equatorial WCO), 181 183 Co(CNCH,): 184 188 Pt(SnC1,): -2 54 254 Ni(CN): -184 I90 cuc1: -230 239 Square Pyramid Molecules Apical Basal MnC1: -258 230 Ni(CN): -217 I86 RuCI,(PPh,), RU-P 239 223 Pd B r,(PPh,),, Pd-Br 293 252 TriarsNiBr,, Ni-Br 269 237 11 Postscript The VSEPR model remains the simplest and most reliable qualitative method for predicting molecular geometry. It is not based on any orbital model, and in general for the qualitative discussion of molecular geometry it is superior to such models.The VSEPR model may be expressed in orbital terms by representing each electron-pair domain by an appropriate loca- lized (hybrid) orbital, such as an sp3 orbital. However, it is not necessary to express the VSEPR model in orbital terms and indeed there is little advantage in doing so. The VSEPR domain model gives a very approximate description of the electron distribution in a molecule that is based on the role of the Pauli exclusion principle in determining the electron density distribu- tion.This very approximate description of the electron density of a molecule is, moreover, consistent with accurate electron density distributions calculated by ab initio methods and, in particular, with the analysis of such distributions in terms of the Laplacian of the electron den~ity.~ -’Although theoretical calculations’ show that, in general, electrons are not as loca- lized into discrete pairs as the VSEPR model assumes, the Laplacian shows that there are local concentrations of electron density that have all the properties of relative size and location that are ascribed to the electron-pair domains of the VSEPR m0de1.~-~ 12 References 1 R. J. Gillespie and R.S. Nyholm, Quart. Rev.Chem. Soc., 1957, 11, 339. 2 R. J. Gillespie, J. Chem. Educ., 1963,40, 295. 3 R. J. Gillespie, ‘Molecular Geometry’, Van Nostrand Reinhold, London, 1972. 4 R. F. W. Bader, P. J. MacDougall, and C. D. H. Lau, J. Am. Chem. Soc., 1984, 106, 1594. THE VSEPR MODEL REVISITED-R. J. GILLESPIE 5 R. F. W. Bader, R. J. Gillespie, and P. J., MacDougall, J. Am. Chem. Soc., 1988, 110, 7320. 6 R. F. W. Bader, R. J. Gillespie, and P. J. MacDougall, in ‘From Atoms to Polymers: Isoelectronic Analogies’ in Vol. 11 of ‘Molecu- lar Structure and Energetics’, ed. J. F. Liebman, and A. Greenberg, VCH, 1989. 7 R. J. Gillespie, and I. Hargittai, ‘The VSEPR Model of Molecular Geometry’, Allyn and Bacon, Boston, 1991; Prentice Hall Inter- national, London, 199 1. 8 G. E. Kimball, References to unpublished work by Kimball and his students are given by H. A. Bent (reference 9). 9 H. A. Bent, J. Chem. Educ., 1963 40, 446, 523; 1965, 42, 302, 348; 1967,44, 512, 1968.45, 768. 10 R. J. Gillespie, D. A. Humphreys, N. C. Baird, and E. A. Robinson, ‘Chemistry’, 2nd Edn., Allyn and Bacon, Boston, 1989; Prentice Hall International, London, 1989. 11 R. F. W. Bader, T. S. Slee, D. Cremer, and E. Kraka, J. Am. Chem. Soc., 1983, 105, 5061. 12 J. W. Adams, H. B. Thompson and L. S. Bartell, J. Chem. Phys., 1970,53,4040. 13 L. S. Bartell, R. M. Gavin, and H. B. Thompson, J. Chem. Phys., 1965,42,2547; L. S. Bartell and K. M. Gavin, J. Chem. Phys., 1968, 46,2466. 14 K. 0.Christe, E. C. Curtis, D. A. Dixon, H. P. Mercier, J. C. P. Sanders, and G. J. Schrobilgen, J. Am. Chem. Soc., 1991,113,3351. 15 K. 0.Christe, J. C. P. Sanders, G. J. Schrobilgen, and W. W. Wilson, J. Chem. Soc., Chem. Commun., 1991,837. 16 A. R. Mahjoub, A. Hoser, J. Fuchs, and K. Seppelt, Angew. Chem., int. Ed. Engl., 1989, 28, 1526. 17 R. F. W. Bader, and M. E. Stephens, J. Am. Chem. Soc., 1975,97, 7391. R. F. W. Bader, ‘Atoms in Molecules: A Quantum Theory’, Oxford University Press, Oxford, 1990.

ISSN:0306-0012    

DOI:10.1039/CS9922100059

出版商:RSC    

年代:1992

数据来源: RSC

摘要:

The Nature of the Hydrogen Bond to Water in the Gas Phase A. C. Legon Department of Chemistry, University of Exeter, Stocker Road, Exeter EX4 400 D. J. Millen Christopher lngold Laboratories, Department of Chemistry, University College London, 20 Gordon Street, London WCI H OAJ 1 Introduction One of the reasons for investigating the hydrogen bond is the central r6le played by this weak interaction in biological struc- tures and processes, in the chemistry of aqueous solutions and, of course, in determining the properties of water. It is necessary in pure water that the water molecule acts both as a proton donor and a proton acceptor in forming a hydrogen-bond interaction. The same is true, for example, of hydrogen fluoride molecules in liquid hydrogen fluoride or of ammonia molecules in liquid ammonia.But what happens in aqueous solutions of these substances? Do the water molecules then act as the proton acceptor or the proton donor? Many other important questions about such mixtures also arise but are difficult to answer because of the complications associated with the liquid phase. A simpler approach is to consider, for example, the interaction of a water molecule and a hydrogen fluoride molecule in the gas phase at low pressure and therefore in the isolated heterodimer. In fact, the particular heterodimer of H,O and HF has been investi- gated' 'in great detail via its rotational spectrum and conse- quently more is known of its properties in isolation than any other dimer.In parallel, a number of other gas-phase dimers involving water either as the proton acceptor or the proton donor have been examined. Examples in which water is the proton acceptor H,O*--HX include:' l2 H,O--*HF, H20-..HCl, H20-.*HBr, H,O*..HCN. H,O***HCCH, H20*.. H20 while among those in which water is the donor are' 3.14 It is timely to review the conclusions reached about hydrogen bonding by the water molecule in this range of dimers in a A. C. Legon is Professor of Physical Chemistr-v in the Universit<v of' E-yeter. He was educated at the Coopers ' Company School in Bol.t., London and at University College London. His recent research interests include systematic investigations of hydrogen- bonded (and other N-eakly bound) complexes by microwave and infrured spectroscopy qf pulsed, supersonic jets.He was Tilden Lecturer and Medallist qf the Royal Society of Chemistry for 1989-90. D.J. Millen began research at University College London under the supervision of Dr. H. G.Poole and Sir Christopher Ingold. In 1950 he 1.1'~s a Conirnom-ealth Fund Fellow at Harvard working with Professor Bright Wilson. He returned to UCL and was uppointed Reader in 1959 and Professor in 1964. In 1967 he was Nyholm Lecturer and Medallist of the Royal Society of Chemistry and President of its Education Division for 1979-81. He has had u long-standing research interest in hydrogen bonding, first in Raman spectroscopy of some solid hydrates, then in infrared ypectroscopji qfgas-phase dimers, and more recently in microwave spectroscopy of' such dimers.general way and in the archetypal dimer H,O...HF in detail. We consider first which questions about the hydrogen-bond interaction are important to answer. The first of these is: can we predict under which circumstances H,O will act as a proton donor and under which circumstances it will act as an acceptor. We shall show later that it is possible to assign to a molecule numbers E and N, called the gas-phase electrophilicity and nucleophilicity, respectively, that measure the propensity for that molecule to act as a donor or an acceptor. The product of E and N then provides a criterion for deciding, for example, whether H20 * * * HF or HF * -HOH is the favoured isomer of the dimer of H,O and HF.Thus, if EH,ONHF < EHFNH,O the lower energy form will be H,O.-.HF. In this case, the inequality is large and the conclusion is in accord with chemical intuition. For the dimer of H20 and HCN, on the other hand, the favoured isomer is not self-evident and this is reflected in a near-equality of the two terms. Given that the form H20-..HF of the water-hydrogen fluoride dimer in which H20 is the proton acceptor is favoured, the second question concerns the configuration at the oxygen atom: is it planar or pyramidal, i.e. does H20*.. HF have C,,, or C, symmetry? This question, which does not have a simple answer, will be discussed in detail. We shall show that the angular geometry of a dimer B--.HX is determined, in good approximation, by the variation of the electrostatic potential around B.Hence, in so far as angular geometries are concerned, interest will centre on dimers H20***HX rather than dimers B-*.H,O since only in the former does H20 control the geo- metry. The third question is simply: is the description H,O..*HX or H30f -.*X- appropriate? We shall show from simple arguments that in isolation H20 HX is overwhelm- ingly favoured for X = F, C1, Br, CN, and we can therefore expect to observe this form spectroscopically in the vapour phase. Only under extreme conditions, such as exist in an electrical discharge, can the ion H30+ be observed in the gas phase but, of course, the concept of ions H30+ and X-is familiar in discussions of aqueous solutions of mineral acids where solvation plays a controlling rble.Hydrogen-bonded ion pairs do exist in the gas-phase, however. When H,O in H20..-HX is replaced by the stronger nucleophile (CH,),N, the description (CH3),N +H --.X-can become more appropri- ate, as in the case X = Br. Other important questions about H20 -* HX are concerned with the distance r(O..*X)and its dependence on H/D substitu-tion, the exact position of the hydrogen-bond proton (i.e. how much does HX extend on dimer formation), the energy required to extend the hydrogen bond infinitesimally and infinitely, and the energy required to bend the hydrogen bond. Finally, we shall address the question of what electrical perturbations of the subunits accompany formation of H20*.*HX.2 When Does Water Act as a Proton Acceptor and When Does it Act as a Proton Donor? The intermolecular stretching force constant k, for a weakly bound dimer is available on the basis of a very simple model' from the centrifugal distortion constant D,(or A,) which is in 71 72 turn straightforwardly determined from the rotational spectrum of the dimer. The model assumes that each of the subunits in B-**HX is itself rigid and in the quadratic approximation DJ depends only on the hydrogen-bond stretching force constant. As a result, k, is available for a wide range of hydrogen-bonded dimers and by systematically varying first B and then HX it has been possible to recognizeI6 a simple pattern among the k, values, namely that a number N, called the limiting gas-phase nucleophilicity, can be assigned to B and that a number E, correspondingly, the electrophilicity can be assigned to HX such that for a given B HX, k, is related to N and E by-9 k, = cNE (1) Table I Nucleophilicities N and electrophilicities E for selected molecules Molecule N E H2O 10.0 5.0 HF 4.8 10.0 HCl 3.1 5.0 HCN 7.3 4.25 HCCH 5.1 2.4 where c = 0.25 Nm-’.Table 1 shows a selection of N and E values so assigned. We now consider the relative stability of the two isomers H20...HX and HX..*HOH that can be formed by water and a molecule HX. It is assumed that if the product NH,OEHX > NHxEH,o,the isomer H,O*-.HX will be more stable than the isomer HX***HOH, and vice versa.For dimers B.**HF where both k, and dissociation energy Do are known, there is a good correlation between these quantities, suggesting that the order of k, values may well parallel the order of Do. In Table 2, we compare the products NH,OEHX and NHXEH,O for a series of dimers H,O.*.HX and HX.*.H,O, where HX = HF, HCI, HCN, HCCH, and H20. We note that for the first two members of thc series the form H,O-** HX is strongly favoured. Although the isomer H,O**.HX is slightly favoured for X = CN, the two isomers H,O.*.HCCH and HCCH*.-HOH appear to be of similar stability. In fact, in experiments using supersonically expanded mixtures of H,O and HX in argon only the isomers H,O * * HX have so far been observed for all groups X mentioned above.Of course, in these experiments the effective temperature of the expanded gas is very low and only the lowest energy isomer will be observed even when the energy difference is very small. We conclude that, because the N value for water is significantly larger than its E value, dimers of the type H,O.*.HX predominate in the observations made so far. Nevertheless if NHxis large enough compared with EHx(eg.as in NH,) the form HX-.-HOH will be observed in supersonic expansions (e.g. H,N-*.HOH’3). Table 2 Values of NH20 EHx and NHx EH20for dimers H,O...HX and HX.*.HOH HX HF HCl HCN HCCH H,O NH20 EHx 100.0 50.0 42.4 24.0 50.0 NH XEH o 24.0 15.6 36.4 25.6 50.0 3 The Configuration at Oxygen in H,O ---HF: Planar or Pyramidal? Traditionally, rotational spectroscopy has been a powerful method of determining the geometry of a molecule in isolation and relies on the fact that the observed transition frequencies lead to moments of inertia and these depend on the distribution CHEMICAL SOCIETY REVIEWS.1992 of mass within the molecule i.e. on the positions of the atoms. The detailed examination of the rotational spectra obtained from numerous isotopomers of H,O.-*HF shows that the order of the nuclei is unambiguously as indicated.’ The contribution from the hydrogen atoms to the moments of inertia is however necessarily small in this case, and it proves not to be possible on the basis of moments of inertia to distinguish between a geo- metry having a pyramidal configuration at oxygen (i.e.one of C, symmetry) and one having a planar arrangement at oxygen (i.e. with C,, symmetry). The difficulty arises because the observed moments of inertia are not equilibrium values and are signifi- cantly modified by the zero-point motion of the molecule. If the three principal equilibrium moments of inertia ZZ;, Zg, and Z;, were available the conditions ZF < 1; + Zx, would provide a criterion of planarity (=) or otherwise (<). When zero-point moments of inertia are used, however, the equality does not strictly hold, even for a molecule with a planar equilibrium geometry. To make further progress with zero-point quantities, we must examine the variation of the moments of inertia with vibrational excitation of the mode vIS(,,)that takes the planar molecule out of the plane or, if the equilibrium geometry is non-planar, that takes the molecule towards the plane. A schematic diagram of this motion is included in Figure 1, where for convenience a planar arrangement is assumed.The motion can in fact be defined in terms of a single vibrational coordinate 8 (see Figure 2) which under the above assumption is zero in the planar form. w.....< Figure 1 Schematic representation of the three lowest energy hydrogen bond modes in H,O.-.HF. Figure 2 Definition of the angle 0 in H,O.**HF Depending on the equilibrium conformation of H,O **-HF, we can envisage three general forms for the variation of the potential energy of the molecule as 8 is changed from zero. These are shown in Figure 3.When the equilibrium geometry is planar (8, = 0) the vibrational energy levels [v~(~)]associated with the mode are well behaved (Figure 3a) and the vibrational probabili- ties are as shown. Of course, states with even v have a maximum probability at 8 = 0 while those of odd v have zero probability there. If a small barrier is now introduced at 8 = 0, its effect is to perturb even states disproportionately so that the I’ = 0 and v = 1 levels move closer together while v = 1 and t’ = 2 diverge. The result for a barrier that is lower than the ti = 2 level is shown in Figure 3b. As the barrier height is increased these effects increase very rapidly and the v = 0 and 1 levels soon become effectively degenerate, as illustrated in Figure 3c where the barrier is so high that the v = 2 and 3 levels are also degenerate.Molecules in the v = 0,l pair of degenerate levels are then THE NATURE OF THE HYDROGEN BOND TO WATER IN THE GAS PHASE-A. C. LEGON AND D. J. MILLEN 0 X XX Figure 3 (a) Potential energy function, vibrational energy levels, and probability distributions of a harmonic oscillator. (b) As a barrier is introduced at .Y = 0, the vibrational energy levels begin to draw together in pairs. (c) In the limit of a high barrier, the pairs have become degenerate. permanently pyramidal. For a molecule with a potential energy function V(6)like that in Figure 3b, the zero-point state can be described as eflectively planar because the vibrational wavefunc- tion has C,,, symmetry but the equilibrium geometry of the molecule nevertheless has C, symmetry, i.e.is pyramidal. It is possible to assign H,O.-*HF to one of the types in Figure 3 by examining the rotational spectrum in several of the vibrational states vB(o)= 0,1,2. . . . In the case of H,O**-HF, it is possible to show that the potential energy function V(6)is not of the type shown in Figure 3c by arguments based on a nuclear spin statistical weight effect in the rotational spectrum.' Briefly, the effect in H,O.**HF is just as observed in the dihydrogen molecule, where some rotational energy levels have a weight of 3 (ortho-H,) and the others have a weight of 1 (para-H,). This establishes that, as for the dihydrogen molecule, a twofold rotation exchanges a pair of equivalent protons in H,O..* HF.Thus, a rigidly pyramidal molecule of the type in which the lowest pair of vibrational energy levels are degenerate, as in the example of Figure 3c, is excluded because it has no C, axis and no equivalent hydrogen atoms under a twofold rotation. It remains to decide whether H,O * -* HF is governed by a function of the type in Figure 3a or 3b, both of which would lead to the observed nuclear spin statistical weight effects. This can be achieved by considering the variation of the observed moments of inertia with the vibratio- nal quantum number v~(~)-.The observed quantity is an average over the vibrational state in question and will thus reflect even a small perturbation of the wavefunction arising from a small potential energy barrier at the planar molecule.When the barrier is zero, the effective moments of inertia I, will vary smoothly with v, but when V(6)has a double minimum the relatively larger perturbation of v even states leads to a zig-zag behaviour of I,,when plotted against v. H,O*-*HF does indeed exhibit this effect2 and therefore the barrier at 6 = 0 cannot be zero. It has already been shown, however, that the barrier cannot be large. Hence H,O-.*HF corresponds to the case shown in Figure 3b. Relative intensity measurements of a given rotational transition in the vB(o)= 0,1, and 2 states lead2 to the vibrational spacings of 64( 10)and 203(35) cm- for vpB(o)= 1 + 0 and 2 + 1 respectively, thus confirming the irregular vibrational spacing and the qualitative form of the potential energy func- tion.In fact, the quantitative form of V(6) has also been determined,, essentially by fitting the variation of I, with vBco) and the observed vibrational separations. The result is shown in Figure 4 where it is seen that the barrier is indeed low at 1.5 kJ mol-, which should be compared with the dissociation energy Do (34 kJ mol-') of the complex. 4 The Configuration at Oxygen in H.O... HF: Can it be Predicted by a Simple Model? The experimental result that V(6)for H,O.*.HF is a double- minimum potential energy function (see Figure 4) with the equilibrium angle 6, = 46(8)" has important consequences for A B -80 -40 0 40 80 0 Ideg Figure 4 The experimentally determined one-dimensional potential energy function V(0) versus 0 for the hydrogen-bonded dimer H,O.-.HF.See Figure 2 for the definition of the angle 0. Figure 5 A simple model that accounts qualitatively for the form of the observed potential energy function V(0)in H,O**.HF. In each of the two equivalent equilibrium conformations, the HF molecule lies along the axis of a non-bonding electron pair (drawn schematically) on the oxygen atom. modelling the hydrogen bond. First, it strongly suggests a very simple electrostatic model1' in which the HF molecule lies at equilibrium along the axis of a non-bonding electron pair on the oxygen atom, as illustrated in Figure 5. The assumption is that the electric charge distribution of H,O is not greatly perturbed by the proximity of the HF molecule.The variation of the 6, along the series B... HF, where B = 2,5-dihydrofuran7 oxetane, and oxirane, from 48.5" through 57.9" to 71.8" strongly supports the simple n-pair model because such an increase is consistent with opening of the inter-lone-pair angle as the angle COC decreases along with the series of molecules B.18 Secondly, the quantitative form of V(6)for H,O-*. HF provides a critical test for theoretical modelling of the angular dependence of the hydrogen-bond interaction, especially because of the small number of electrons in this entirely first-row dimer. In fact, it is interesting to record that the variation with 6 of the electrostatic potential energy of a test point-charge at a fixed distance from the oxygen atom leads to a curve of shape closely similar to that in Figure 4.The result when the point charge is + 0.54 e and the distance is the experimental r(O*.*H) is shown in Figure 6.19 The potential energy barrier of z0.5 kJ mol- is in reasonable agreement with the observed value. The reason for choosing a charge of + 0.54 e is that the electric charge distribution of HF can be represented in good approximation simply by 0.54 e on H and -0.54 e on F. Consequently, if the F end is ignored in making a zeroth approximation to the HF molecule, the interac- tion energy of H,O and HF is just the electrostatic potential energy shown in Figure 6. At the next level of approximation, the charge on F can be included and HF considered as an extended electric dipole.When such a charge distribution is rolled around water, the variation of V(6)is as shown in Figure 6, where the component electrostatic energies of the charges on H and F are also given. We note that Be is now very close to one half of the tetrahedral angle, further reinforcing the non-bonding pair interpretation, while the barrier height is 3.5 kJ mol-'. I 1 -80 -40 0 40 80 0Ideg Figure 6 Variation of the electrostatic potential energy with angle B for a point charge + 0.54 e at the experimental O.-*Hdistance from 0 in H,O-*-HF[VH(O)], for a point charge -0.54 e at the experimental distance O.*.F from 0 in H,O--*HF [vF(d)], and the sum VH(0)+ VF(d).See text fordiscussion and Figure 2 for the definition of the angle 19. An even better description of the interaction between the H,O and HF molecules uses a complete description of the electric charge distribution of each and was developed by Buckingham and Fowler.20 In fact the curves referred to in Figure 6 rely on the more complete description of the electrostatic charge distri- bution for water given by these authors. Their method is to represent accurately a good ab initio SCF charge distribution of the molecule by the so-called Distributed Multipole Analysis (DMA) which places point charges, dipoles, and quadrupoles on each atom. The global minimum found in the electrostatic energy of interaction as a function of the relative angular orientation of the two component molecules at an appropriate van der Waals distance has been found to give excellent agree- ment with the experimental angular geometry for a wide range of dimers, whether hydrogen-bonded or other weakly bound systems.In fact, the reason for choosing in the above discussion HF as an extended electric dipole having charges f0.54 e stems from the Buckingham-Fowler DMA of HF in which the point charges dominate the description. Of course, a point-charge model for both H,O and HF would have advantages from the view point of simplicity and physical insight. Such a model has in fact been developed for a small number of molecules B, includ- ing H,O. In this simplified model,2 a point-charge representation of the electric charge distribution of B is used together with the above-mentioned extended point dipole model of HF.In parti- cular it has been shown that to obtain agreement with experi- ment (where available) and with calculations based on the full Buckingham-Fowler model, it is necessary to place only small fractional electronic charges at physically reasonable distances along the directions usually associated with non-bonding elec- tron pairs. The definition of the fractional electronic charges 6, and their distances rfrom oxygen at the required angle of a = 54" are shown in Figure 7. The point charges on H and 0are 0.401 e and -0.724e, as in the published DMA for H,O but with 2 x 8 i 0 i 6 Figure 7 Definition of the fractional charge 6, its distance r from the 0 atom and the angle a for a simple point-charge model of H,O.See text for discussion. CHEMICAL SOCIETY REVIEWS, 1992 (= 2 x -0.039 e)removed from the charge on 0.Such a model of H,O gives the correct dependence of V(0)on 0 with a potential energy barrier of magnitude % 3.5 kJ mol-' and 8, = 45". Parallels with the valence-shell-electron-pair repulsion model of Gillespie and Nyholm22 and with the partial localization of electron density along non-bonding pair directions discussed by Bader et uL.~~are obvious. Thus this model accounts for the pyramidal configuration at oxygen in H20 -* * HF by placing small fractional electron charges in the positions usually attri- buted to non-bonding pairs while the Buckingham-Fowler model achieves the same result with the aid of a point electric quadrupole on oxygen.5 How Does the Configuration at Oxygen Change Along the Series H,O.-*HX, Where X = F, CI, Br, or CN? It is clear from the discussion in Section 4 that the angular geometry of a hydrogen-bonded dimer like H,O..- HF is deter- mined largely by the variation of the electrostatic potential with angle at a given distance in the vicinity of B (i.e. H,O).Presumably, as the distance from H,O increases the double minimum apparent in the potential function V(8) (see, for example, Figure 6) begins to disappear. This is shown clearly in Figure 8 where the electrostatic potential energy of the HF molecule described as an extended dipole + 0.54 e and -0.54 e is plotted as a function of angle 8 for various distances r(0.a.H).Even for distances as small as 2.0-2.5a the function has only a single minimum and therefore a dimer H,O * -HX in which the r(O-**H) distance is of this magnitude would have a planar equilibrium geometry of C,,, symmetry. Distances r(0-a-H) in this range have been observeds lo in H,O.--HCI, H,O***HBr, and H,O**. HCN. Consequently, it seems possible that some of these dimers have the C,, equilibrium arrangement. The experi- mental investigationss- O made on this series certainly indicate a low barrier to the planar form in each case, but have so far been unable to distinguish between the effectively planar C,molecule with a low barrier and the strictly planar CIVequilibrium geometry. 6 What is the Length of the Hydrogen Bond and Where is the Proton in H,O --HX? The questions of most interest about the length of the hydrogen bond in H,O.-*HX are: (i) What is the distance between the heavy atoms 0 and X? (ii) Has the HX bond lengthened significantly on formation of H,O * * HX? (iii) Are the 0,H, X nuclei collinear at equilibrium? The first of these questions is the easiest to answer from the observed ground-state moments of inertia of H20 * * -HX.This is achieved simply by assuming unchanged H,O and HX geome- tries (see below) and an effectively planar arrangement in the zero-point state. In fact, small changes in the OH and HX distances contribute negligibly to the dimer moments of inertia.The distance r(O**.X) is then varied until the ground-state rotational constants are reproduced. The results for X = F, CI, Br, and CN are given in Table 3.l.*--lo Another point of interest is the effect on r(B*.*X) of a change from a hydrogen to a deuterium bond in B***HX. A wide range of B-.-H(D)X has been investigated (including B = H,O), a generalization identi- fied, and a model proposed to account for the observed effects.24 A concomitant of the insensitivity of the calculated rotational constants to the distance rHXis that the latter quantity is not available from the former. But, in the dimers B...HF, the H,F nuclear spin-nuclear spin coupling constant, which is pro- portional to the zero-point average of rfi8 carries the required information.Unfortunately, this information is convoluted in the coupling constant with the effects of the angular motion of the HF subunit in the dimer which makes the predominant THE NATURE OF THE HYDROGEN BOND TO WATER IN THE GAS PHASE-A. C. LEGON AND D. J. MILLEN 20 16 12V(0) / kJmol'I 8 4 0 -120 -80 -40 0 40 80 120 0 /drg Figure 8 Calculated variation of the electrostatic potential energy V(0) of the HF molecule with the angle 8 in the H,O---HF.The HF molecule, treated as a simple extended electric dipole with charges +0.54 e and -0.54 e on the H and F atoms, makes an angle 8 with the bisector of the HOH angle and lies in the plane of the non-bonding electron pairs on 0.Each curve refers to a different distance r of the H atom of HF from 0.Table 3 Observed r(O*.-X) in H20.*.HX, where X = F, C1, Br, or CN H,O * --HX r(O -..X)/A F 2.662"c1 3.219 Br 3.41 1" CN 3.1 39d "Ref. 1. hRef.8. (Ref.9. dRef. 10. contribution to the zero-point average. However, a deconvolu- tion is possible if the isotopomer B*..DF is examined and the deuterium nuclear quadrupole coupling constant is available. Details of the approach are given elsewhere25 for a series of dimers B...H(D)F . The result for H20...HF is a lengthening 6r = 0.017 8, of the HF bond which is in excellent agreement with the value from a sophisticated ab initio SCF calculation that includes electron correlation via second and third order Mdler- Plesset perturbation theory.26 A very simple electrostatic put forward recently for the HF bond lengthening leads to a value of 0.020A which is in satisfactory agreement with both experiment and the ab initio value.We conclude, therefore, that the contribution of the valence-bond structure H20 *.. HF to the description of the dimer is preponderant while that of H,O+ .*.F-is very small. The small contribution of H,O+ *.*F-is in agreement with some conclusions based on simple thermodynamic arguments applied to the process If it assumed that r(O-..X)is unchanged, dE2can be estimated from energy changes for the following reactions: H,O--*HX= H,O + HX (3) H,O + H+ = H30+ (4) HX=H++X-(5) H,O+ + X-= H,O+ ..-X- (6) 6 since LIE, = C dEi and the LIEi are readily estimated.Thus, i= 3 dE, M Do, the zero-point dissociation energy, which has been measured7 for H,O***HF and whose value for other X can be estimated by assuming that the Do values scale according to the known k,. LIE, can be approximated as minus the proton affinity Table 4 Estimates of the energy change LIE, for the reaction H,O--*HX= H30+ ***X-, where X = F, C1, Br, or CN AEi/kJ mol-'" Med H,O..*HX i=3 4 5 6 2" F 34.3d -691.6 1554 -521.9 374.8 c1 17.1' -691.6 1394 -432.1 287.4 Br 14.4' -691.6 1354 -407.3 269.5 CN 14.6' -691.6 1461 -440.7 343.3 %ee text and ref. 28 for the origin of the various AE, values. The subscript refers to equations 3-6. hMeRis the effective Madelung constant. It is the number by which AE, must be multiplied to make AE, zero.The smallest 1.718 1.665 1.662 1.779 i possible value for a Madelung constant is 1.748 for a face-centred cubic lattice. Hence, the solid H,O + HX where X = F, CI, and Br will be ionic but H,O + HCN is unlikely to be. CAE,= AE, (see text). dExperimenta1 value of ,=3 0, from ref. 7. 'Estimated values assuming k:/kr = 0:/0: holds for the series H,O-*-HX. of H20. LIE, is well known and LIE, is just the Coulombic energy gained when the ions are brought to the appropriate distance apart. The small repulsive contribution to dE6 can be ignored for present purposes. The results of this procedure are summar- ized in Table 4. For each X, it is clear that LIE, is large and positive and we can conclude that the form H20**.HX is predominant in each case in the gas phase.But the situation is quite different in condensed phases. For the solid phase, the calculation of dE, would require the use of dE6 but multiplied by the appropriate Madelung constant. It is convenient there- fore to calculate an effective value of the Madelung constant MeE which makes LIE, zero. These values are shown in the final column of Table 4. We note that for X = C1 and Br MeR is considerably less than the typical value 1.748 for the rock salt lattice and so it can be understood why these mineral acid monohydrates have ionic crystal structures. On the other hand, for H,6...CN, MeE is larger than the typical value and suggests that, in the solid state, hydrogen cyanide monohydrate would not be ionic.In aqueous solution, solvation energies replace lattice energies in these considerations but, if it can be assumed that the solvation energy of H36 is similar to that of an alkali metal cation for which the solvation enthalpies are closely similar to the appropriate lattice energy, it is not unexpected that HCl and HBr are strong acids. It is worth noting at this point that the ion-pair from 6H Xcan have lower energy than the simple hydrogen bonded dimer B***HX even in the gas phase if the acceptor molecule B has a sufficiently large proton affinity and the donor molecular HX has a suitably small energy for dissociation in the manner of equation 5.Thus it has been demonstrated2 by investigation of its rotational spectrum that trimethylammonium bromide is, better described in the gas phase as the ion pair (CH,),NH...Br than as the simple hydrogen-bonded dimer (CH,),N -..HBr. The third question posed above, which concerns the collinear- ity of the 0,H, and X nuclei at equilibrium, is difficult to answer through rotational spectroscopy because of the insensitivity of rotational constants to the exact position of the H atom.On the other hand, the electrostatic model of Buckingham and Fowler20 finds a small deviation from linearity in H20 HF, as illustrated in Figure 9, in the direction that would result from a 0" /' Figure 9 The angular geometry of the H,O * -* HF dimer predicted by the Buckingham-Fowler electrostatic model. Note that the hydrogen bond is predicted to be slightly bent in the direction that would favour a secondary H---Finteraction and that the angle 0-.-H-F is 172".secondary hydrogen bond interaction. In fact, recently some experimental evidence for a similar degree of bending has been presented for the vinyl fluoride-hydrogen chloride dimer. 29 Reasons why only small deviations from linearity are found in isolated hydrogen-bonded dimers have been discussed in the light of the hydrogen-bond bending force constants5 and the electrostatic mode119 of H,O.-.HF. 7 How Strong is the Hydrogen Bond in H,O .* -HF? There are, of course, several ways to measure the strength of a hydrogen bond. We might first ask how easily is the hydrogen bond stretched (radial deformation), either infinitesimally or infinitely, and then how easily is the bond bent (angular deformation). 7.1 How Difficult is it to Deform H20-HF Radially? The ease of radial deformation of H20...HF can be measured in two ways.First, the quadratic force constant k, associated with the hydrogen-bond stretching mode V, gives, via the usual expression +k,8r2, the energy required for a unit infinitesimal extension 8r along the dissociation coordinate from equilibrium. Second, the dissociation energy Do defines the energy necessary for an infinite extension along the same coordinate to give the separate components H20 and HF. Both of these quantities can in fact be obtained from measurements of the rotational spec- trum in the case of H,0***HF.7316 Table 5 Intermolecular stretching force constants k, for dimers H,O * * * HX Dimer k,/Nm-H,O .-* HF 24.9* H,O --* HCl 12.5" H,O --* HCN 11.10 H,O.**H,O 11.7h H,O..*HCCH 6.5" BFor a convenient compilation, see ref.16. ORef. 12. The determination of k, from the centrifugal distortion constants DJ (or dJ)has already been mentioned in Section 2. Values of k, determined for H,O.-*HX, where X = F, C1, CN, and Br, are recorded in Table 5. The quantity Docan be obtained by measuring the integrated intensity of a ground-state rotatio- nal transition in each of H,O, HF, and H,O..*HF in an equilibrium mixture containing the three components at a single temperature T (indirectly in the case of HF, as it turns out).The integrated intensities lead, via the known rotational partition functions, to the number densities n0,,(H20), n,,,(HF), and n,,,(H,O-*.HF) of the components in their v = 0 and J= 0 states and thence, through the simple expression to Do.If sufficient is known about the vibrational frequencies of the dimer (as is the case for H,O -HF), Docan be corrected for the zero-point motion to give D,. The values found7 for H,O--.HF are Do = 34.3(3) kJ mol-l and D,= 42.9(8) kJ mol-I. As expected, the hydrogen bond in H20..-HF is relatively strong according to this measure. Although such values of Do have not been determined for other members of the series H20***HX, where X = CI, CN, or Br, the values of k, in Table 5 lead us to expect a decrease in Do along the series also.Likewise, if H,O is replaced by the poorer proton acceptor HCN, we expect the strength of binding to decrease. This is indeed reflected in the smaller value^^^,*^ Do = 18.45(11) kJ mol-' and k, = 18.2Nm-' for HCN**.HF. CHEMICAL SOCIETY REVIEWS, 1992 7.2 How Difficult is it to Deform H20* * HF Angularly? The ease with which the hydrogen bond in H,O...HF can be bent is measured by the bending force constants which are available from three main sources: vibrational wavenumbers from infrared spectra, vibrational wavenumbers from satellites in microwave spectra, and vibrational amplitudes from hyper- fine structure in microwave spectra. Two coordinate systems have been used in the analysis of results from these experimental methods.The first consists of the angular internal coordinates, as conventionally used in vibrational spectroscopy and defined for the present purpose by 8 and 4 in Figure 10. The second set, the oscillation coordinates as defined by a and ,f3 in Figure 10, are conveniently used in the treatment of amplitudes from nuclear quadrupole or nuclear spin-spin hyperfine constants. Transfor- mation between the two coordinate systems allows the com- bined use of all three types of information when these are a~ailable.~ (b) Figure 10 Definition of the oscillation coordinates a and /3 and the angular internal coordinates 0 and + used in the determination of the hydrogen-bond bending force constants of a dimer CB... HA (e.g. H,O...HF) from spectroscopic data.For H20*..HF all three types of information are in fact a~ailable~~2~Jand this dimer has been treated in more detail than any other member of the series H,O...HX where there is information only from hyperfine structure at present. The out- of-plane bending potential for H,O*.*HF has a double mini- mum, as already discussed. For in-plane bending the reported force constants5 are fo(i)o(,) ;2.52 x J Tad-, and j&i),+(i)= 19.70 x J rad- . It is seen that bending at hydrogen is much more strongly resisted than bending at oxygen. The implication is that distortion of hydrogen bonds at the demand of the environment in condensed phases is energeti- cally more likely to be met by bending at oxygen than at hydrogen. Finally, it is of interest to compare the relative resistance to in-plane bending and out-of-plane bending at oxygen.The former has a single minimum potential while the latter has a double minimum, and not surprisingly it has been shown that the zero-point amplitude of out-of-plane bending is much larger than that for in-plane bending, and correspondingly in-plane distortion is more strongly resisted than out-of-plane distortion. It has been pointed out that if this is generally true for hydrogen bonding to oxygen then it allows an interpretation5 of an observation from statistical analyses of large numbers of diffraction investigations for hydrogen bonds of the type O.*.H-O in the solid state. The analyses show that, while there is some preference for hydrogen bonding in the plane containing the axes of the non-bonding pairs on oxygen, there is no favoured angle for hydrogen-bond formation in that plane.For the remaining members of the series H, 0* * HX that have been investigated, information about bending force constants is derived solely from amplitudes of the HX oscillation in the di~ller.~~Values of kSBthat have been obtained are as follows: H20..*HF23.8 x J rad-,; H,O...HCl 10.0 x J radF2; H,O...HCN 5.9 x J rad-2. As might be expected they are found to decrease along the series with k,. 8 What Electric Charge Redistribution Occurs on Formation of H,O . . HX? When a dimer H20*.*HX is formed by bringing the infinitely separated components together there is inevitably some electric charge rearrangement.This will of course include polarization THE NATURE OF THE HYDROGEN BOND TO WATER IN THE GAS PHASE-A. C. LEGON AND D. J. MILLEN of one molecule by the other and vice versa. There is also, however, the possibility of transfer of charge, either electronic or protonic, between the two components. The measureable quan- tities so far available that carry information about charge redistribution are the electric dipole moment enhancement and the various nuclear hyperfine coupling constants of the HX subunit. Arguments based on the H,F nuclear spin -nuclear spin coupling constant in H20..-HF (see Section 6) indicate that the extention 6r of the HF bond within the dimer is small and that proton transfer can be ignored. It is difficult to separate the contributions of electron transfer and polarization to the above-mentioned observable but for Xe...HC1 Flygare and co- worker~~~concluded that less than 5 x e is transferred from Xe to HCI. Hence, polarization is likely to be the predomi- nant contributor. The observable quantity that is most directly related to electric charge redistribution on hydrogen bond formation is the electric dipole moment of the dimer. For H20**.HF more detailed studies have been made than for any other dimer while no information is yet available for any other member of the series H,O * * * HX. Stark effect measurements in the rotational spectrum of H20 --HF have led to values of the dipole moment of the dimer, not only in its vibrational ground state but also in excited vibrational states associated with the low-lying intermo- lecular modes.3 The results are collected in Table 6 where the nomenclature [v~(~), v,] denotes the vibrational quantum vB(+ numbers of the three modes illustrated in Figure 1, namely the out-of-plane bending mode v~(~),the in-plane bending mode vB(i) and the stretching mode v,, respectively.The value p = 4.073 D for the ground state implies an effective enhancement of 0.39 D over the sum of the monomer moments. This enhancement is low by comparison with that of 0.80 D obtained for HCN.**HF but it has to be remembered that enhancement reflects not only electronic changes but is also determined in part by zero-point effects.The main contribution to such effects arises from the large amplitude out-of-plane bending mode and when allowance for this is made the enhance- ment increases to 0.68 D. A correction for the smaller zero-point effects of the other intramolecular modes can also be estimated. Table 6 Dependence of the electric dipole moment of H20* HF on vibrational state Vibrational state (VB(O,,”B(I,JJ PID (0, 0, 0) 4.073 (7) (1, 0, 0) 3.802(7) (0, 1, 0) 4.074( 16) (1,1, 0) 3.76(4) (0, 0, 1) 3.9 l(4) For v~(~)and V, the effect of one half quantum of zero-point motion is available from Table 6. The only remaining intermole- cular modes to consider are the high frequency bending modes, denoted v~(~)and vB(i), in which essentially the HF molecule oscillates through the angle ,f3 defined in Figure 10.Assuming that, for the purpose of calculating this small correction, the two modes may be considered isotropic and degenerate we can write the reduction as 2pHF (1 -cos Pav) in which cos pa, is available from amplitude studies described in Section 7. By taking all the intermolecular modes into account, we find the dipole enhance- ment to be 0.89 D. If we assume that the zero-point effects of all the monomer modes remain unchanged on dimer formation then this enhancement is the value appropriate to planar H,O***HF,i.e. to a geometry with 0 = 0, by comparison with non-interacting monomers with the same geometric rela tionship. More indirect evidence about charge redistribution comes from an interpretation of the C1-nuclear quadrupole coupling constants in the series of dimers B...HCl (including B = H20).3s This interpretation considers the response of the electronic distribution in HCI to the electric charge distribution of B and provides a goal for ab initio calculations of charge rearrangement and in particular the consequences close to quadrupolar nuclei.9 How Much H.O-.-HF is Formed in Gas Mixtures of H,O and HF? It was indicated in Section 7.1 how spectroscopic measurements on H20*..HF in an equilibrium mixture with H20 and HF can give the dissociation energy, Do,as well as the rotational and vibrational partition functions of the dimer. By taking all this information together it becomes possible to calculate changes in thermodynamic properties for the formation of the dimer from the monomer^.^^ This, for T= 298.15K, AH: = -39.1kJmol-], AS; = -94.2J K-I mol-’, and AG; = -11.0kJ mol-’.Hence we can estimate that for this temperature with initial partial pres- sures PHFzPH~OZ 1 Torr there is a 10% conversion to H,O **-HF, while for initial pressures of 100mTorr (as typically used in microwave spectroscopy) there is still a 1 % conversion. This is much higher than for any other dimer so far investigated. For example, the conversion for HCN.-.HF under the same spectroscopic conditions is 5 x No other dimer H20..*HX has so far been observed spectroscopically in an equilibrium mixture. Evidently, even for H20 HCl AH; has too small a magnitude to allow detection with present sensitivity.10 References 1 J. W. Bevan, A. C. Legon, D. J. Millen, and S. C. Rogers, J. Chem. SOC., Chem. Comrnun., 1975,341;J. W. Bevan, Z. Kisiel, A. C. Legon, D. J. Millen, and S. C. Rogers, Proc. R. Soc. London, Ser. A, 1980,372,441. 2 Z.Kisiel, A. C. Legon, and D. J. Millen, Proc. R. SOC. London, Ser A, 1982,381,419. 3 Z. Kisiel, A. C. Legon, and D. J. Millen, J. Chem. Phys., 1983, 78, 29 10. 4 A. C. Legon and L. C. Willoughby, Chem. Phys. Lett., 1982,92,333. 5 Z.Kisiel, A. C. Legon, and D. J. Millen, J. Mol. Struct., 1984,112,1. 6 Z. Kisiel, A. C. Legon, and D. J. Millen, J. Mol. Struct., 1985, 131, 201. 7 A. C.Legon, D. J. Millen, and H. M. North, Chem. Phys. Lett., 1987, 135,303.8 A. C.Legon and L. C. Willoughby, Chem. Phys. Lett., 1983,95,449. 9 A.C.Legon and A. P. Suckley, Chem. Phys. Lett., 1988,150,153. 10 A.J. Fillery-Travis, A. C. Legon, and L. C. Willoughby, Proc. R. Suc. London, Ser. A, 1984,396,405. 11 G.T. Fraser, K. R. Leopold, and W. Klemperer, J. Chem. Phys., 1983,80, 1423. 12 T. R. Dyke, K. M. Mack, and J. S. Muenter, J. Chem. Phys., 1977, 66, 498. 13 P.Herbine and T. R. Dyke, J. Chem. Phys., 1985,83, 3768. 14 H.0.Leung, M. D. Marshall, R. D. Suenram, and F. J. Lovas, J. Chem. Phys., 1989,90, 700. 15 D. J. Millen, Can. J. Chem., 1985, 63, 1477. 16 A. C.Legon and D. J. Millen, J. Am. Chem. SOC., 1987, 109,356. 17 A. C.Legon and D. J. Millen, Discuss. Faraday Soc., 1982,73,71. 18 R. A. Collins, A. C. Legon, and D. J. Millen, J. Mol. Struct., 1987, 162,31. 19 A. C.Legon and D. J. Millen, Chem. Soc. Rev., 1987,16,467. 20 A. D. Buckingham and P. W. Fowler, Can.J. Chem., 1985,63,2018. 21 A. C.Legon and D. J. Millen, Can. J. Chem., 1989,67, 1683. 22 R. J. Gillespie and R. S. Nyholm, Quart. Rev. Chem. SOC., 1957,11, 339. 23 R. F. W. Bader, R. J. Gillespie, and P. J. MacDougall, J. Am. Chem. Suc., 1988, 110, 7329. 24 A. C.Legon and D. J. Millen, Chem. Phys. Lett., 1988, 147,484. 25 A. C.Legon and D. J. Millen, Proc. R. Soc. London, Ser. A, 1986, 404, 89. 26 M. M.Szczesniak, S. Scheiner, and Y. Bouteiller, J. Chem. Phys., 1984,81, 5024. 27 A. C.Legon and D. J. Millen, J. Mol. Struct., 1989, 193, 303. 28 A. C.Legon, C. A. Rego, and A. L. Wallwork, J. Chem. Phys. 1990, 92, 6397. 29 Z. Kisiel, P. W. Fowler, and A. C. Legon, J. Chem. Phys., 1990,93, 3054. 30 A. C. Legon, D. J. Millen, P. J. Mjoberg, and S. C. Rogers, Chem. Phys. Lett., 1978, 55, 157. 31 P. Cope, D. J. Millen, and A. C. Legon, J. Chem. Soc., Faraday Trans. 2, 1986, 82, 1 189. 32 R. K. Thomas, Proc. R. Soc. London, Ser. A, 1975,344, 579. 33 P. Cope, D. J. Millen, and A. C. Legon, J. Chem. Soc., Faraday CHEMICAL SOCIETY REVIEWS, 1992 Trans. 2, 1987,83, 2163. 34 M. R. Keenan, L. W. Buxton, E. J. Campbell, T. J. Balle, and W. H. Flygare, J. Chem. Phys., 1980, 73, 3523. 35 A. C. Legon and D. J. Millen, Proc. R. Soc. London, Ser. A, 1988, 417, 21. 36 S. L. A. Adebayo, A. C. Legon, and D. J. Millen, J. Chem. Soc., Faraday Trans., 1991,87,443,

ISSN:0306-0012    

DOI:10.1039/CS9922100071

出版商:RSC    

年代:1992

数据来源: RSC

摘要:

The Structure and Mechanism of Formation of Ozonides Robert L. Kuczkowski Department of Chemistry, University of Michigan, Ann Arbor, Michigan, 48109-1055, U.S.A. The cleavage of the alkene double bond by ozone to give aldehydes, ketones, and acids is a well known and widely utilized reaction. It is also known that cyclic intermediates called ozonides precede the formation of these products during the course of the reaction (Scheme 1). However, few synthetic chemists have ever isolated an ozonide. It is an unnecessary diversion if the carbonyl containing compounds are the desired products. Moreover, ozonides have a reputation of being un- stable and even explosive, although this latter characteristic varies markedly with alkene substrate. Nevertheless, investi- gators who are interested in the mechanism of ozonolysis isolate and characterize ozonides since they provide key information on the reaction process.This article will review the mechanism that describes the formation of these ozonides. The identification of ozonides and the rationalization for their formation during ozonolysis was first described nearly 35 years ago. Using classical structure-proof methodology and trapping experiments, Rudolf Criegee and his co-workers isolated many ozonides and determined their structures.2 This led Criegee to describe their formation with a three step mechanism, shown in Scheme 2. This proposal is so attractively simple that it is often included in undergraduate lectures. In its simplest form, the mechanism is usually explained using 1,3-dipolar cycloaddition ~oncepts.~A more sophisticated description incorporates con- cepts from frontier molecular orbital the~ry.~ In terms of these paradigms, reaction 1 in Scheme 2 is a cycloaddition between the ozone 1,3-dipole and the alkene dipolarophile leading to (l), which is called a molozonide or primary ozonide.This is a symmetry allowed 277 + 477 cycloaddi-'c=c/ +03 ,-e RCHO, R2C0, RCOOH /\ t,n o'"'0 0-0 \c/\I \I ___t-c-c-/\ \ primary secondary ozon ide ozonide (molozonide) Scheme I Robert L. KucTkowski was born in Buflalo, N.Y. where he attended Canisius College. The Ph.D. degree w*asreceived from Harvard Universitj! in 1964 under the mentorship of E.Bright Wilson, Jr. A NAS-NRC postdoctoral-fellowship was held at the National Bureau of Standards (Washington, D.C.) in the Mic- r~iwwve and Injiared Spectroscopy Section. He joined the Chemistry Department at the University of Michigan in 1966 where he presentljt is Professor and Chair. His research interests include the heterogeneous catalysed oxidation of alkenes, the mechUniS'm Of OZOnO/~SLS, and StrUctUrd studies by conventional and Fourier transjbrm microume spectroscopy. 79 OR0'O J\ -c-c-/\ 1 (3) 3 2 Scheme 2 tion. The orbital description of the reaction for ethylene and ozone is shown in Figure la; the strongest interaction involves the HOMO of the alkene and the LUMO of ozone. Figure 1b illustrates the idealized envelope transition state consistent with this orbital picture.The molozonide is very unstable and cleaves via a cycloreversion in reaction 2 to a stable carbonyl compound and an elusive carbonyl oxide (2), sometimes called the Criegee intermediate. The carbonyl oxide is isoelectronic with ozone and can be considered another 1,3-dipole. It quickly combines in reaction 3 with the internally generated carbonyl compound to produce (3) via a cycloaddition reaction which is formally analogous to the first step in the mechanism. Species (3) has several names in the literature: final ozonide, secondary ozonide or, as in this paper, simply ozonide. Ozonides can often be isolated and thoroughly characterized. This article will explore several questions of current interest about the basic three step Criegee mechanism.These range from evidence for the elusive intermediates (1) and (2), to fundamen- tal tests of the cycloaddition process. For example, can it be ascertained whether the cycloadditions and cycloreversion are concerted reactions? What is the stereochemistry of the process and how is this incorporated into the mechanism? What role Figure I (a) HOMO-LUMO interaction diagram for the cycloaddit,on of ozone and ethylene. (b) Orbital overlaps in the idealized cycloaddi- tion transition state. does the solvent and the solvent cage play in the reaction? Investigations which provide insight on these questions are the focus of this review. Several examples originate from the auth- or's laboratory, where isotopic tracer experiments have been used extensively as a probe of the mechanism.1 4 5 The primary ozonide (1) produced in the first step of the Criegee mechanism has been observed by NMR and IR at low temperatures for a variety of alkene~.~ From these data, as well as the conversion of primary ozonides into 1,2-diols,, the cyclic 1,2,3-trioxolane structure has been inferred, although other forms such as (4) or (5) are not completely eliminated by such data. It is therefore satisfying that a definitive characterization of a primary ozonide by microwave spectroscopy has very recently been reported for the product between ozone and ethylene.6 This primary ozonide was observed in the gas phase after the co-condensed reactants were allowed to warm.The structure of the primary ozonide is illustrated on the right side of the postulated reaction diagram in Figure 2. It is interesting that the envelope structure closely conforms to the postulated transi- tion state for a concerted cycloaddition. Even more remarkably, the van der Waals complex between ozone and ethylene has also recently been observed by micro- wave spectroscopy (Figure 2, left species).' The complex also resembles the postulated transition state in Figure 1b, strongly suggesting that it lies along the reaction coordinate for the cycloaddition. The structure of the transition state itself has been estimated using ab initio methods* (Figure 2, centre species); the 0, and ethylene are separated by a distance of about 2 8, which is intcrmcdiatc to those found in the weak van der Waals adduct and the primary ozonide.The stereochemical test for a concerted cy~loaddition,~ viz. retention of configuration about the double bond, was also explored in the microwave study by ozonizing trans-or cis-ethylene-1,2-d2. The trans species gave exclusively the trans-d, primary ozonide (reaction 4). The cis isomer gave an equimolar I E . I CHEMICAL SOCIETY REVIEWS, 1992 0-0 H ;c =c,' D \n \ D' 'H (4) mixture of the endo and exo d,-forms with no evidence for stereo randomization about the carbon-carbon double bond (reaction 5). This extensive set of structural data from experiment and theory is consistent with the many previous studies which inferred a concerted cycloaddition between ozone and the alkene.Evidence for a concerted cycloreversion as the primary ozo- nide cleaves in the second step of the Criegee mechanism is considerably less direct.*,5 One of the products of the cyclorever- sion, viz. the carbonyl oxide, is highly reactive which has impeded a study of this question. The carbonyl oxide had not been detected spectroscopically until recently when it was observed by IR in low temperature matricesg>' O and by transient species UV techniques in solution. 1-1 Subsequent spectro- scopic studies and electronic structure calculations of the sim- plest carbonyl oxide and substituted analogues have appeared,' 3-1 as well as for the cyclic dioxirane isomer and the energetics of interconversion between the isomers.' How-ever, during normal ozonolysis conditions, the carbonyl oxide concentration apparently never rises high enough to allow its detection and direct study.The principal evidence for its exis- tence arises from trapping experiments. The carbonyl oxide is readily trapped17l4 by carbonyl compounds, alcohols or, as shown recently, by an activated alkene containing an alkoxy group (Scheme 3).,O Because of the transitory nature of the carbonyl oxide, the evidence that the cycloreversion is concerted is much more inferential in nature. A rationale is constructed from the stereo- selectivity which is usually evident in the ozonide product. This stereoselectivity can be summarized by the observation: the ozonolysis of cis(trans)-1,2-alkenes with bulky substituents yields more cis(trans)-ozonides respectively (reaction 6).Since the first step of the Criegee mechanism is stereospecific (Figure 1b), the stereoselectivity must arise in the second or third steps, or both. In the second step, stereo effects are readily incorpor- ated by postulating syn-anti isomerism in the carbonyl oxide Figure 2 Structures of the van der Waals complex between ozone and ethylene (left),6 the reaction transition state (middle),8 and the primary ozone product (right)' plotted along a hypothetical cycloaddition reaction coordinate. THE STRUCTURE AND MECHANISM OF FORMATION OF OZONIDES-R. L. KUCZKOWSKI \c/ 0-0 \,/ORI ,R-C-OOH I / \c' I \ 0/"' 0-0 OR0\O I\I -c-c-2i/\ J Scheme 3 R R'c=c' /\ / \I -C-C-R"\ /O-P-0 = '0 I II C' C R/ 'H R/ 'H anti (reaction 7).2 This is consistent with the electronic properties of a carbonyl oxide which has a three-centre 7~ orbital perpendicu- lar to the molecular plane similar to isoelectronic ozone, result- ing in a high barrier to syn-anti equilibration.A cycloreversion from the envelope transition state, which is preferred on orbital alignment grounds for a concerted process, could readily lead to a preference for either the syn or anti conformer (Figure 3). The isomer preference and extent of stereoselectivity depends on substituent steric effects, secondary orbital interactions, ano-meric interactions etc.In the case of trans alkenes with bulky substituents, it has been postulated that the cycloreversion yields syn carbonyl oxides.22 This was based on steric arguments which orient the substituents diaxial in the envelope transition state, an orientation favourable to formation of the syn carbonyl oxide upon decomposition. By a similar rationale, cis alkenes would produce anti carbonyl oxides. However, it has so far proven to be impossible to devise a straightforward test of the stereochemi- cal properties of the carbonyl oxide in order to examine this hypo thesis. The cycloaddition between the carbonyl oxide and the carbo- nyl compound resulting in the ozonide in the third step of the Criegee mechanism should also occur via a putative envelope transition state according to orbital overlap arguments.Thus a syn (or anti)carbonyl oxide will react with an aldehyde in either an endo or exo transition state to give cis or trans ozonide (Figure 4). This third step, like the second, can also occur with varying degrees of stereoselectivity dependent on substituent interac- tions, electronic effects etc. In this manner, the stereoselectivity in the overall ozonolysis process can be rationalized in a manner consistent with simple orbital overlap arguments for a 3+2 cycloaddition reaction. Although this general outline lays the basis for a rationale to incorporate stereochemistry in the ozonolysis reaction, the detailed argumentation for a particular system is often ad hoc and specific to the problem at hand.A set of rules have been devised as a guide to stereochemical predic- tions;s>22 they are more the nature of a working hypothesis rather than well tested hard and fast laws. The concerted nature of the third step of the Criegee reaction has been explored using a phenomenon called kinetic secondary isotope effects. Secondary isotope effects are observed when deuterium is substituted at a site at which other new bonds are being formed or broken in the reaction transition state. Basi- cally, the zero point vibrational energies of the reactants and transition states are affected differently when deuterium substi- U anti Figure 3 Envelope transition states for the cleavage of the primary ozonide leading to carbonyl oxide isomers.SY" trans R SYn cis R anti trans anti cis Figure 4 Envelope transition states for the cycloaddition of the carbonyl oxide and carbonyl compound producing the final ozonide isomers. tution occurs at the reaction site, leading to a change in the kinetics of the reaction of approximately 10-20% per deuterium atom substitution. It was observed using HDCO or D2C0 as the aldehyde trap and HDCOO as the dipolar~phile~~.~~ (reactions 8 and 9) that secondary isotope effects occur due to deuterium substitution in both the aldehyde and the carbonyl oxide during the third step. This is consistent with the carbon atoms in both species being involved in the transition state, which implies a concerted cycloaddition.(9)c+ H/c\(D)H/ ‘H H Recently, the stereochemical test for a concerted cycloaddi- tion has also been investigated for the reaction of the carbonyl oxide with a dipolarophile. This became possible with the discovery that carbonyl oxides will trap an activated alkene containing an alkoxy substituent.20 The product was a 1,2-alkoxy dioxolane along with the expected ozonide (reaction 10, relative yields). It was apparent when the alkene was stereo labelled with deuterium, that retention of stereochemistry about the double bond occurred when the alkene was trapped by the carbonyl oxide (reaction 1 1, relative yields).2 This was the first example where stereospecificity, implying concertedness, was directly observed for a reaction of a carbonyl oxide with a substrate.At the same time, the deuterium substitution at C-5 (the end carbon sans OR substituent) occurred stereoselectively. This latter result can be explained by stereoselective production of syn and anti-HDCOO in step 2 of the Criegee mechanism. 78% 12% J\\ H H 25% 75% Similar results have been obtained with the ozonolysis of (a-or (Z)-CH,CH=CHOEt.26 These results, along with the kinetic secondary isotope effect data, the stereoselectivity discussed above, and thermochemical reasoning2’ are the principal experi- mental evidence for concertedness in the third step of the Criegee mechanism. It should be noted that there is evidence that a non- concerted or stepwise cycloaddition probably also occurs when conditions are propitious as in the case of more substituted and complex alkenes or in certain solvents.This body of data has been discussed recently. l4 CHEMICAL SOCIETY REVIEWS, 1992 Additional insights on the third step can also be garnered with cross ozonide formation and aldehyde insertion experiments. The former technique examines the ozonide product distribu- tion when an unsymmetrical alkene (reaction 12) or mixtures of alkenes are ozonized (reaction 13). Insertion experiments involve the ozonolysis of a mixture of an alkene and foreign aldehyde (i.e. one not generated in the reaction itself, reaction 14). Such experiments can explore steric effects, electronic effects, and solvent cage effects.An example of each of these applications will be given. A body of data from the ozonolysis of unsymmetrical cis-alkenes (reaction 12) reveals that when the bulk of the substi- tuents are different (R > R’), the heavy molecular weight ozo- nide cross product (RR) will contain more cis isomer while the low molecular weight ozonide (R’R’) will contain more trans The cisltrans product ratio for the normal ozonide (RR’) will usually fall in between the two cross ozonides. The explanation for this behaviour is complex. It assumes the production of different synlanti ratios for the two carbonyl oxides, RHCOO and R’HCOO, which are produced in the cycloreversion decomposition of the primary ozonide. Steric effects in the envelope transition state leading to the carbonyl oxides are the basis for the differential carbonyl oxide isomer production.The literature should be considered for a more detailed discussion. 5,2 1,22.27h R=x X=P-NO, XEH 62.8% 93.3 22.3% 1.5 14.8% 5.2 x = CH3 95.1 0.6 4.4 A striking difference in the normal and cross ozonide product distribution (relative amounts) is observed when para-substi- tuted styrene substrates are ozonized as exemplified in reaction 15.28 This is probably the result of electronic effects which influence the cleavage direction of the primary ozonide (i.~. the relative amounts of H2CO0 and RHCOO which are produced) and the recombination kinetics of the carbonyl oxides with the two aldehydes which are present (H,CO,RHCO).The results can be accounted for by a kinetic scheme in which the rate constants in the primary ozonide cleavage step and the recombi- nation step vary systematically with change in electronic proper- ties of the substituents. For example, the increase in the amounts of styrene ozonide and decrease in cross ozonides with increase in the electron withdrawing character of the substituents corre- late with a Hammett 0of 1.4. This indicates that accentuation of positive charge at the reactive carbon centre of the carbonyl oxide and the benzaldehyde involved in bond formation assist the formation of the styrene ozonide. This observation also THE STRUCTURE AND MECHANISM OF FORMATION OF OZONIDES-R. L. KUCZKOWSKI 80% 2% 10% holds for the reaction of the diphenyl substituted carbonyl oxide with a series of para-substituted ben~aldehydes.,~ Another interesting observation involves the yields of ozo- nides (relative amounts) when propylene is o~onized.~* Reac-tion 16 describes a typical result.The relative amounts of the products are fairly insensitive to temperature and solvent polar- ity. On the other hand, using C,H,/C,D, mixtures, the amounts of the cross ozonide. ethylene- 1,l-d2 ozonide, varied from about 3% in non-polar solvent to almost 40% in a polar The explanation for these results must take into account several factors including cleavage direction competition (to CH,CHOO and CH20 ver.ms H,COO and CH3CH0 in reaction I6), kinetic effects in the recombination steps, and kinetic secondary isotope effects in the reactions involving CD,O and CD,OO.Neverthe- less, a difference in the cross ozonide formation with solvent polarity is readily apparent between the propylene and ethylene substrates. Kinetic modelling indicated that ozonide formation in the propylene system occurred almost entirely outside the original solvent cage while this was the case only in polar solvents for the ethylene ozonolysis. Thus, substitution of H with a methyl group in the simplest carbonyl oxide significantly affects the reaction kinetics in the original solvent cage. An increased stability for CH,COO compared to H,COO is one possible explanation for the results. These examples underscore the subtle complexities that affect ozonide yields when alkenes are cleaved by ozone.Basically, the ozonolysis mechanism is a network of competing reactions and processes for which the kinetics at each step must be considered. When one reflects that small differences in reaction energetics for competing kinetic processes can lead to marked effects on yields, then much of the reaction diversity with change in conditions, substituents. and solvent can be appreciated. For example, the ratio of the yields of propylene ozonide to ethylene ozonide in reaction 16 might be explained by activation energy differences of about 0.5 kcal/mol in the third step of the mechanism while the energy difference resulting in unequal cis-trans ozonide stereo ratios in reaction 12 can be even smaller. Consequently, very modest energy changes will markedly affect competitive processes resulting in complex and often puzzling results.This is a sobering realization since solvent interactions, zero point energy effects in competing transition states, and other hard-to- identify factors (because they are small) may enter into a complete microscopic understanding of the details of the ozono- lysis reaction. In spite of such obfuscations, great progress has been made in elucidating the bare bones Criegee mechanism and in under- standing puzzling aspects of the ozonolysis reaction using traditional physical organic techniques and reasoning. Aided by such work and the ever advancing sophistication in chemical analysis techniques, including theoretical approaches which include solvent effects in reaction simulations, we expect that our understanding of this fascinating reaction will continue to grow. Perhaps some day ultrafast laser techniques will allow the study of incipient carbon-oxygen bond formation when ozone reacts with ethylene! Acknowledgements. The work carried out in the author’s labora- tory was supported by grants from the American Chemical Society-Petroleum Research Fund and the National Science Foundation.The author is pleased to acknowledge the contribu- tions of his co-workers mentioned in the references and particu- larly Professor C. W. Gillies who first initiated the study of the ozonolysis mechanism at Michigan and has recently observed spectroscopically the primary ozonide of ethylene and the pre- reaction complex between ethlylene and ozone. References 1 P.S. Bailey, ‘Ozonation in Organic Chemistry’, Academic Press, N.Y. Vol. 1, 1978; Vol. 2, 1982. 2 R. Criegee, Angeur. Chem., 1975,87,765;Int. Ed. Engl., 1975,14,745. 3 R. Huisgen, in ‘1,3-Dipolar Cycloaddition Chemistry’, ed. A. Padwa, Wiley, New York, 1984, Vol. 1, Chapter 1. 4 K. N. Houk, J. Sims, R. E. Duke, Jr., R. W. Strozier, and J. E;, George, J. Am. Chem. SOC.,1973,95,7287. 5 R. L. Kuczkowski. in ‘1.3-Dipolar Cvcloaddition Chemistry’, ed. A. Padwa, Wiley, New York, 1984, Vol. 2, Ch. 11. 6 J. Z. Gillies, C. W. Gillies, R. D. Suenram, and F. J. Lovas, J. Am. Chem. Soc., 1988, 110,7991. 7 C. W. Gillies, J. Z. Gillies, R.D. Suenram, F.J. Lovas, E. Kraka, and D. Cremer, J. Am. Chem. Soc., 1991, 113,2412. 8 M. L. McKee and C. M. Rohlfing, J. Am. Chem. Soc., 1989, I 11, 2497. 9 0.L. Chapman and T. C. Hess, J. Am. Chem. Soc., 1984,106. 1842. 10 G. A. Bell and I. R. Dunkin, J. Chem. Soc., Chem. Commun., 1983, 1213. 11 H. L. Casal, S. E. Sugamori, and J. C. Scaiano, J. Am. Chem. Soc., 1984,106, 7623. 12 H. L. Casal, M. Tanner, N. H. Werstiuk, and J. C. Scaiano, J. Am. Chem. Soc., 1985,107,4616. 13 W. Sander, Angew. Chem., 1990, 102, 362; Int. Ed. Engl., 1990, 29, 344. 14 W. H. Bunnelle, Chem. Rev., 1991,91,335. 15 D. Cremer, T. Schmidt, W. Stander, and P. Bischof, J. Org. Chem.. 1989,54,2515. 16 R. D. Suenram and F. J. Lovas. J. Am. Chem. Soc., 1978,100,5117.17 W. Adam, Y.-Y.Chan, D. Cremer, J. Gauss, D. Scheutzow, and M. Schindler, J. Org. Chem., 1987, 52, 2800. 18 J. Gauss and D. Cremer, Chem. Phys. Lett., 1987, 133,420. 19 D. Cremer, T. Schmidt, J. Gauss, and T. P. Radhakrishnan, Angew. Chem., 1988, 100,431; Int. Ed. Engl., 1988,27,427. 20 H. Keul, H. S. Choi, and R. L. Kuczkowski, J. Org. Chem., 1985,50, 3365. 21 (u)N. C. Bailey, J. A. Thompson, C. E. Hudson, and P. S. Bailey, J. Am. Chem. Soc., 1968,90, 1822; (h)P. S. Bailey and T. M. Ferrell. J. Am. Chem. Soc., 1978, 100,899. 22 R. P. Lattimer. R. L. Kuczkowski, and C. W. Gillies, J. Am. Chem. Soc., 1974, 96, 348. 23 G. D. Fong and R. L. Kuczkowski, J. Am. Chem. Soc., 1980, 102, 4763. 24 J.-I. Choe, M. K. Painter, and R. L. Kuczkowski, J. Am. Chem. Soc., 1984,106,2891. 25 H. Keul and R. L. Kuczkowski, J. Org. Chem., 1985,50, 3371. 26 B. J. Wojciechowski, W. H. Pearson, and R. L. Kuczkowski, J. Org. Chem., 1989,54, 115. 27 (a) P. S. Nangia and S. W. Benson, J. Am. Chem. Sue., 1980, 102, 3105; (6) D. Cremer, J. Am. Chem. Soc., 1981, 103, 3619. 28 M. K. Painter, H. S. Choi, K. W. Hillig 11, and R. L. Kuczkowski, J. Chem. Soc., Perkin Trans. 2, 1986, 1025. 29 R. W. Murray and M. M. Morgan, J. Org. Chem., 1991,56,684. 30 J.-I. Choe, M. Srinivasan, and R. L. Kuczkowski, J. Am. Chem. Soc., 1983, 105,4703.

ISSN:0306-0012    

DOI:10.1039/CS9922100079

出版商:RSC    

年代:1992

数据来源: RSC