摘要:

HIGH RESOLUTION OF PROTON MAGNETIC RESONANCE SPECTRA BY W. A. ANDERSON* AND J. T. ARNOLD* Stanford University, Stanford, California, U.S.A. Received 10th March, 955 1. INTRODUCTION This paper reports briefly some findings in highly resolved spectra of proton magnetic resonances. A more detailed discussion will be published later.1 For nuclei having spin 1/2, the resonances in liquid samples are generally very sharp. For example, the protons in water can be expected to have a single resonance with a half-width of approximately 0.06 c/s. In a typical experiment in a magnetic field of 7000 oersted, protons have a resonance frequency of about 30Mc/s, giving a relative natural line width corresponding to two parts in 109. It is the extreme sharpness of the lines, corresponding to long lifetimes of energy states, which permits the study of delicate features of proton magnetic resonance spectra.It has been known for some time that the magnetic resonance frequency of a nucleus depends upon the chemical environment which surrounds it.2 For protons, this so-called " chemical shift " was first observed by Gutowsky and McClure,3 and has values of a few parts in 106. Nuclei which are in the same molecule but have different chemical environments show also a shift of their magnetic resonances. To distinguish it from the shift between nuclei in different compounds, we refer to this shift as " internal chemical shift ". Along with another intra-molecular interaction it was first observed indirectly by Hahn4 with the spin echo technique. Actual resolution of the chemically-shifted resonances in some of the alcohols was observed shortly afterwards.5 The development of apparatus with resolving power approaching one part in 108 has made possible the resolution of finer details of proton magnetic reson- ance spectra, and the confirmation of a rather simple Hamiltonian which was proposed by Hahn and Maxwell 6 to describe the energy of the protons.This Hamiltonian consists of two parts, one being dependent on the large magnetic field at the nucleus, and a second which is independent of the field and consists of a simple rotationally invariant interaction between nuclei. It may be written in the form + Here y is the gyromagnetic ratio of the nuclei. Hs is the magnetic field at the site of the nucleus S, and Is is its spin operator.EJRS measures the energy of interaction between the nuclei R and S. It is convenient to introduce the total spin of a group T by FT = Is,, where all the nuclei S' shall be exposed to the same local field HT, and all shall have the same interaction with other nuclei in --+ + + S' --* the molecule. F'T can take all magnitudes TI,-,-, (&!) - 1, ( ~ Z S # ) - 2, . . ., * now with CEKN, Geneva, Switzerland. 226W. A . ANDERSON AND J . T . ARNOLD 227 and it can be shown that it is a constant of the motion 6 described by (1). Except for an additive constant, the Hamiltonian may then be written in the form : where JTU is the common coupling JRS between any proton R in group T and any other protons S i n group U. 2. CALCULATED SPECTRA A simple form of the energy levels of the system may be obtained7 from (2) for two groups of nuclei with one group having a maximum value F = 1/2.However, it is possible, and in many cases more instructive, to treat the terms in the second summation as a small perturbation. This method is particularly fruitful in cases where the perturbation parameter I JTU/y(HT - Hu) 1 < 1. To simplify the discussion, we shall consider a case in which there are only two groups of nuclei A and B. The fields HA and HB shall be in the 2 direction. The first term of (2) is then for both groups diagonal in the F' representation, and the eigenvalues of (2) are given in terms of the eigenvalues m of Fz by With I JAB I < I HA - HB) I, the first-order corrections to (3) are given simply by Transitions are allowed when either mA or mB changes by 1, while FA and FB do not change, leading in first order to two groups of resonance lines : ---> +- w(0) = - [HAmA + HBmBl.(3) (4) w(1) = - f i J AB mA mB- The number of lines in one group is thus determined by (2Fm,, + l), where Fmax is the maximum total spin of the other group. The relative intensities of the components of one group may in zero order be inferred from the number of ways in which the corresponding value for the quantum number rn of the other group may be formed. The intensities of lines with frequency VA, when calculated in first order differ from this simple rule of statistical weights by a factor with the corresponding expression for those of frequency VB. Thc significance of this factor is manifested in that the line intensities in one group whose frequencies are farthest from the frequencies in the other group are diminished, whereas the intensities of the lines whose frequencies are nearest to those of the other group are augmented.It is interesting to note that the expression for the energy, given by (3) and (4) is linear both in m~ and nzg, and is independent of FA and FB. This simplicity, which is a i'eature of the first-order calculation only, results in a coincidence of frequencies of some lines, and in particular, the fact, seen in (3, that V A , B is independent of ~ Z A , B and is equally spaced for different values of m ~ , A . We have extended these calculations to second and third order. In contrast to their simple form in first order, the energy levels found in higher-order cal- culations depend not only on the quantum numbers m, but also on the total spins, F, of each group.Moreover, the correction terms contain the quantum numbers in multilinear combinations. Both these facts lead in most cases to a splitting 1 - ( U A B mB)/y(HA - Hd228 HIGH RESOLUTION of the energy levels found in first order, and when the transition frequencies are formed, to a removal of the coincidences mentioned above. 3. COMPARISON WITH BXPERIMENT The perturbation parameter JTu/y(HT - Hu) has, for many molecules studied, a magnitude of only about 0.1. This fact has facilitated not only the calculations but, more importantly, the understanding of successively revealed details. A typical molecule containing three groups of non-equivalcnt protons will have a spectrum with three major groups of lines.These major groups of lines embrace frequency intervals of a few c/s, but are separated by the internal chemical shift which in a field of 7000 oersteds will be several tens of cycles per second. Even though field inhomogeneities may be sufficiently large as to broaden all lines to as much as 10 c/s, the unresolved groups will form three separate peaks in the experimental spectra. Since there is no confusing multiplicity of the lines with this resolution, the association of these chemically shifted peaks with the chemical groups in the molecule is obvious. Fields having the degree of homogeneity required to resolve internal chemical shifts of protons have in recent years been available in carefully made electromagnets. Such an electromagnet was elaborately shimmed with very thin pieces of iron and nickel in an attempt to improve the resolution of early experimental spectra. In the course of this work, evidence of more detailed structure stimulated the development of a more flexible shimming technique using a distribution of very small currents on the faces of the magnet poles.With the aid of these " current shims " it was possible to resolve the first-order multiplicity of the chemically shifted peaks.* The field was still sufficiently inhomogeneous as to broaden all lines to about 3 c/s, so that structural details arising from second-order effects were obscured. However, the comparison of the observed spectra with thepre- diction of first-order calculations, and with the spin echo data of Hahn and Maxwell 6 was gratifying.A major difficulty in obtaining traces of spectra is the instability of the apparatus. As observed line widths become smaller, they must be traversed more and more slowly in order to avoid transient effects. To help overcome this difficulty which was becoming intolerable, when line widths wcre less than a few c/s, we decided to build a permanent magnet. This magnet was designed and built with special care directed toward good geomctry at the poles and adjustability of parallelism in the gap. With this magnet, the stability was much improved, and with current shims to increase the resolving power, the spectra gave evidence of unsuspected higher order structure in their components.We attempted to improve further the effective resolving power by means of a macroscopic motion within the sample.% 16 This method proved to be successful. Its potentialities were not realiscd, however, until a nuclear magnetic resonance probe was designed to minimize the field gradients introduced by the diamagnetic susceptibilities of the parts near to the sample. When this probe was uscd in conjunction with current shims and niacroswpic motion within the sample, a resolving power of about 1/3 c/s was realized, permitting the resolution of the higher-order effccts in the spectra. For the spectra which we have observed under this high resolution, the frequency intervals and line intensities confirm remarkably well the predictions found with the aid of thc Hamiltonian (2).4. LINE WIDTHS Under the highest resolution, we have found evidence which leads us to believe that the individual lines do not all have the same width. In particular this has been seen in the case of a molecule containing one proton in one group (A), and two in a second group (B). The frequency of lines associated with transitions in group A depend on FB as well as mB, and in this molecule FB can be eitherW. A . ANDERSON A N D J. T. ARNOLD 229 1 or 0. The line in group A associated with the singlet state of group B(F’ = 0) is demonstrably narrower than the lines associated with the triplet states. This fact finds its explanation in terms of the lifetimes of the states of the system. Randomly fluctuating fields found in the liquid can cause random transitions between the energy states.If such fields induce transitions in which the quantum number m changes but the quantum number F remains constant, then the states for which FB =-. 0 will have lifetimes which are longer than those of the states for which FB = 1. This difference in lifetime occurs because random transitions can take place between the triplet of sub-levels mB = 0, f 1 when Fn = 1, but cannot take place when FB = 0, there being only one Ievel ~ T Z B = 0 in this case. The fact that this difference in line widths is observed helps to justify an assumption that F is indeed a good quantum number. We hope that greater resolution can be achieved in the near future, permitting better determination of natural line widths. 5. HYDROXYL PROTON EXCHANGE The early spectra of the ethyl alcohol molecule showed always a single sharp line for the resonance of the hydoxyl proton.This observation led at the time to a belief that the coupling constant of the hydroxyl proton to other protons in the molecule was abnormally small. However, more recent observations show that the hydroxyl group of lines is coupled to the methylene group with a normal value of the coupling constant. This coupling results under certain conditions in a splitting of the hydroxyl group into a triplet of lines. Spectra for which the hydroxyl group has three components are obtained only when exceptional care is taken in the preparation of samples. It has been found that concentrations of more than about 10-5 N excess of either )I+ or OH- ions destroy the multiplicity of the group, collapsing the triplet into a single sharp line.At intermediate concentrations below this level, transition cases occur showing either a broadened single line or three broadened components. This behaviour is now understood in terms of a chemical exchange of hydroxyl protons between molecules of alcohol. In an exchange event, the hydroxyl proton is coupled first to one molecule having a specific set of spin quantum numbers and then subsequently to another for which the set of quantum numbers are not necessarily the same. If this exchange takes place with sufficient rapidity, the perturbation of the energy of the hydroxyl proton by the other protons within the molecule will effectively be averaged. The criterion for this averaging requires that the mean time T between exchange events be short when compared to the inverse of the interaction frequency and leads to a single sharp line. Tf T is comparable to the interaction frequency the averaging will be incomplete, and the lines will be broadened to a width characterized by the effective lifetime T. As T becomes still longer, the individual components of the multiplet are separated and become finally sharp. Since the interaction frequency is approximately 4 c/s, we find that mean times between exchange T may be determined in the range of from about 1 sec down to about 0.01 sec. 1 to be published in the Physic. Rev. This subject is also treated in thc unpublished 2 Proctor and Yu, Physic. Rev., 1950, 77, 717. 3 Gutowsky and MClure, Physic. Rev., 1951, $1, 276. 4 Hahn, Physic. Rev., 1950, 80, 580. 5 Arnold, Dharmatti and Packard, J. Chem. Physics, 1951, 19, 507. 7 Banerjee, Das and Saha, Proc. Roy. SOC. A , 1954,226,490. 8 Arnold, Physic. Rev., 1952, 85, 763. 9 Bloch, Physic. Rev., 1954, 94, 496. 10 Anderson and Arnold, Physic. Rev., 1954, 94,498. theses of the authors under the direction of Prof. Bloch. Hahn and Maxwell, Physic. Rev., 1952, $8, 1070.

ISSN:0366-9033    

DOI:10.1039/DF9551900226

出版商:RSC    

年代:1955

数据来源: RSC

摘要:

PROTON MAGNETIC RESONANCE SPECTRA OF CRYSTALLINE BOROHYDRIDES OF SODIUM, POTASSIUM AND RUBIDIUM BY P. T. FORD AND R. E. RICHARDS Physical Chemistry Laboratory, South Parks Road, Oxford Received 17th January, 1 955 Proton resonancc spectra have been recorded for crystalline samples of sodium, potas- sium and rubidium borohydrides at temperatures in the range 20" K to 293" K. The second moments of the resonance spectra arc used to deduce a value for the B-H distance in the BH4- ion. Evidence is presented in favour of values in the range 250 to 500 cm-1 for the torsional oscillation frequency of the BH4- ion in the crystal lattice. Assuming this to be correct, the B-H distance is found to be 1-255 f 0.02A. The variation of second moment with temperature in the region of the line width transitions has been measured, and shown to be consistent with potential barriers to reorientation of the BH4- ion of 2.4, 3.8 and 3.9 kcal/mole for the sodium, potassium and rubidium salts.The borohydrides of sodium, potassium rind rubidium havc been shown to contain the BH4- ion.L2 The broadening of the proton rcsonance spectrum of these salts in the crystallinc state theieforc depends primarily on the length of the B-H bond in the borohydride ion, and the purpose of these measurements was to determine this quantity. From mcasurcments of the variation in absorption linc width with temperature, information can also be obtained about the molecular motion of the borohydride ion in the solid statc. The principles of the method have been discussed elsewhcre.3~ 4.5 EXPERIMENTAL Sodium borohydride was obtaincd from L.Light & Co. Ltd. The salt was purified 6 first by recrystallization from water below 5" C and drying in zlacuo at 100" C for several hours. It was then placed in one arm of an inverted U-tube and dissolved in isopropyl- amine which had bccn previously dried over lithium hydridc. After some hours, the clear liquid was decanted into the other arm of the U-tube and the solvent pumped off. The salt was then heated to 160" C in vucuo for several hours. The sample was analysed by acid hydrolysis,6 and the theoretical volume of hydrogen was evolved. Potassium borohydride was obtained from May and Baker, and purified in a similar manner. The second solvent in this case was liquid ammonia which had been dried over sodium, and the recrystallization was therefore carried out in a high pressurc apparatus at room temperature.Analysis by measurement of the hydrogen liberated by acid gave 98.2 %. The sample of rubidium borohydride which had been prepared by Metal Hydrides Inc.,' was kindly loaned to us by Prof. L. V. Coulter. The purity is believed to be better than 98 %. The salts were compressed into pellets, and packed into thin walled Pyrex tubes which fitted closely into a silver r.f. coil wound internally in a soapstone former. All trans- ferences were carried out in a dry-box, except for the sealing of the sample tubes, which were drawn off rapidly in the atmosphere. The nuclear resonance spectrometer has been described previously.* The lowest tempcratures were obtained by the use of liquid hydrogcn.Other temperaturcs were obtained by using liquid nitrogen, oxygen, or mixtures of thesc two liquids of various compositions. These mixtures were in contact with the atmosphere and their composi- tion changed continuously thus producing a slow drift of temperature towards the boiling point of oxygen. The rate of drift was about 1 dcg. per hour. Some measurements on the rubidium salt were madc at tempcratures obtained by using boiling liquid oxygen at reduced pressures. The temperaturcs were measured by a thermocouple immersed in 230P . T . FORD A N D R . E . RICHARDS 23 1 the refrigerant and in contact with the copper can surrounding the sample. The thermal e.m.f. was measured by means of a Cambridge potentiometer and the temperature could be measured to better than 0*05", although the absolute accuracy is considerably less than this.Thc thermocouple was calibrated at liquid-nitrogen and liquid-oxygen tem- peratures. Above 90°K a cryostat, similar to the one described by Gutowsky and Meyer 9 was used. Radio frequency voltages of the order of a few millivolts input to the bridge were used, and a fivefold reduction of r.f. power produced no change in the observed line width, so that it can be assumed that no saturation was occurring. Magnetic field modulation amplitudes of 1.4 gauss peak to peak were used at the lowest temperatures, but this was decreased as the line width became smaller and the signal strength increased. RESULTS SODIUM BOROHY DRIDE Nineteen measurements were made of the second moment at 20" K, which was found to be 42.3 gauss2 with a standard deviation of 1.96 gauss2. The line width, defined as the separation of the maxima in the derivative curves, was 16.56 gauss at 20°K.The above second moment has been corrected for the small effects of field modulation 10 and of field homogeneity. The shape of the derivative curve is shown in fig. 1. There is a line width tran- sition near 85"K, and fig. 1 also shows how the shapes of the derivative curves change with temperature. Fig. 2 shows the variation of the square root of the second moment with temperature. The circles are experimental points, and the continuous curves are theoretical ones referred to in the discussion. Thecorrected second moments and line widths above the transition are 5.1 gauss2 and 6 gauss respectively, and at room temperature the corre- sponding values are 5.12 & 0.38 gauss2 and 5.46 gauss.POTASSIUM BOROHYDRIDE The corrected second moment and line widths from 32 traces at 20°K are 36.23 rt 1.59 gauss2 and 15.5 gauss respectively. The line-width transition at about 85" K is closely similar to that observed for the sodium salt, though its 1 ' I Gauss FIG. 1.-Derivative curves for NaBH4 at various temperatures . shape differs slightly. Fig. 3 shows typical derivative curves obtained, and fig. 4 illus- trates thc variation of the square root of the second moment with temperature. The corrected second moments and line widths above the transition are 3.05 gauss2 and 4.5 gauss respectively, and at room temperature the corresponding valuesare 2.68 f 0.26 gauss2 and 3-12 gauss.RUBIDIUM BOROHYDRIDE The corrected second moment and line widths from ten measurements at 20°K are 34.95 f 1-50 gauss2 and 15.6 gauss respectively. The line-width transition occurs at232 CRYSTALLINE BOROHYDRIDES about 74" K, and fig. 5 shows the variation of the square root of the second moment with temperature. The derivatives were closely similar in shape to those observed for the r NaBH4 7- L 3 0 I FIG. 2.-Sodium borohydride; variation of square root of second moment with temperature ; continuous line calculated for Y = 2.42 kcal/mole. Gauss FIG. 3.-Derivative curves for KBH4 at various temperatures. potassium salt, and are shown in fig. 6. The second moment and line width just above the transition are 3-39 f 0.22 gauss2 and 3.88 gauss and at room temperature they are 3.13 f 052 gauss2 and 3.95 gauss.P .T. FORD A N D R . E . RICHARDS 233 In the potassium and rubidium salts at temperatures very close to the top bend of the second moment transition which were obtained by using liquid air, a few anomalous runs were obtained for which the second moments were considerably larger than the majority of the runs and of the values obtained at 20" K. The anomalous results have not been included in the calculations. FIG. 4.-Potassium borohydride ; variation of square root of second moment with temperature ; continuous line calculated for V = 3-76 kcal/mole. Temp. K FIG. 5.-Rubidium borohydride ; variation of square root of second moment with temperature ; continuous line calculated for V = 3.9 kcal/mole.DISCUSSION The broadening of the proton resonance spectrum arises mainly from inter- actions between hydrogen atoms and between boron and hydrogen atoms. These interactions are conveniently considered as intra-ionic interactions and interionic interactions. The second moment 11 of the absorption line is therefore the sum of the second moment contribution of the intra-ionic effects and of the contribution of the interionic effects. The contribution of the intra-ionic broadening to the total second moment is the most important, and demnds on the inverse sixth234 CRYSTALLINE BOROHYDRIDES powers of the internuclear distances. In order to calculate the interionic con- tribution to the second moment it is necessary to know not only the positions of the B b - ions, but also their orientation in the crystal lattice.f '(H G a u s s FIG. 6.-Derivative curves for RbBH4 at various temperatures. SODIUM BOROHYDRIDE At room temperature, this compound adopts the facc-centrcd cubic structure of dimension. a = 6.161 f 0.009 A (Soldate 2), = 6.1635 & 0.0005 A (Abraham and Kalnajs 12), = 6.157A (Ford and Powell 13). At temperatures below its lambda point 14 transition (180" K) it conforms to a body-centred tetragonal lattice with a = 4.354 f OW5A a = 4.353 c = 5.907 f 0.005 c = 5.909.13 This tetragonal lattice can be considered as a slightly distorted face-centred cubic lattice. From thermodynamic considerations, Stockmayer and Stephenson 15 suggest that the BH4- ions are arranged so that the B-H links point along the cube diagonals, and that in alternate layers the BH4- ions are arranged on the alternate cube diagonals.This arrangement is to be contrasted with the bodycentred arrangement adopted by the ammonium halides in which the N-H bonds point towards the anions.16 In this case, since the hydrogen atoms bear an appreciable fraction of the positive charge of the ion, electrostatic attraction between the hydrogen and the anions is important. In the BH4- ion the hydrogen atoms carry very little charge,l' so that the electrostatic forces are much less important. Indeed this structure is not the most favourable one, if electrostatic interactions alone are taken into account, but masons are given below for believing that the orientations of the borohydride ions is not determined by coulombic interactions alone, although these forces seem to play an important part in determining the structure of the ammonium haIides.*8.19P.T. FORD AND R E . RICHARDS 23 5 Orientations of the BH4- ion which lead to smaller electrostatic potential energies than the above are (a) the ordered arrangement with the B-H bonds pointing along the cube face diagonals, and (b) the " single approach " model 20 in which one B-H bond points along the cube edge towards the positive ion. Arrangement (a) seems to be excluded by the thermodynamic data,ls which require an order-disorder change at the lambda point with an entropy of transition of R In 2 cal/deg. mole. Disordered arrangements of (a) involve very close approach of hydrogen atoms of adjacent ions.The single approach orientation is adopted by the face-centred cubic modification of ammonium iodide, and this leads to free rotation of the ammonium ion about the axis along the fixed N-H bond.21 Free rotation of the BH4- ion about one axis in this way would lead to a second moment of about 12 gauss2 even at low temperatures.22 The observed second moment at 20" K is 42-3 gauss2 and this is clearly inconsistent with one- dimensional rotation, whereas above the line width transition the second moment is 5.1 gauss2, and this is too small. For the calculation of the interionic broadening the model suggested by Stockmayer and Stephenson 15 has therefore been adopted ; the assumptions made are as follows : (i) the B&- ion is a perfect tetrahedron, (ii) the tetrahedra are disposed along the cube diagonals in alternate directions, (iii) the B-H distance is 1-25A (suggested from a preliminary examination of the results), (iv) at 20" K the crystal structure of the saIt is as given by Abraham and Kalnajs 12 with the lattice dimensions reduced by thermal contraction.In face-centred co-ordinates at 77" K, a and b are 6.156 A and c is 5.907 A. Thus a and b are not significantly different from their values at room temperature, although c is smallcr. Presumably the a and b axes show no thermal contraction because it is along these directions that the closest approach of hydrogen atoms (2.31 A) occurs. For our purposes the a and b dimensions at 20" K have therefore been taken to be 6.156 and the c dimension as 5-824A, the latter being obtained by extrapolation from room temperature through 77" K.In calculating the second moments from the equation of Van Vlcck11 the interactions of the individual hydrogen atoms were considered up to 86 nearest BH4- ions. For greater distances the four hydrogens of the borohydride ion were assigned to a lattice point and the interactions extrapolated to infinity. The broadenings obtained were interionic broadening due to : H-H interactions 8.65 gauss2, B-H 7 9 0.25 ,, Na-H ,, 0-77 ,, total interionic broadening 9.67 ,, Thus the intra-ionic broadening is 42.3 - 9-7 gauss2 or 32.6 gauss2. Before this result can be used to obtain the B-H distance, two types of ionic motion which rcduce the intra-ionic broadening must be considered.These are (a) the zero-point vibrations of the tetrahedral ion, and (b) the zero-point torsional oscillation of the ion in the crystal lattice. The first correction is a small one, amounting in this case to less than 1 % of the distance, and is discussed by Deeley and Richards.23 To evaluate the correction, the vibrational amplitudes of the hydrogen atoms in the borohydride ion were estimated to be 0.09A for the stretching vibration, and 0.1 35 8, for the bending vibrations, from a considcration of the values calculated by Morino et al. for CI-I,1 and SiHq.24 The narrowing effect on the absorption line of the zero-point torsional oscilla- tion of the ion in the crystal depends on the oscillation frequency according to an expression given by Gutowsky, Pake and Bersohn.19 The spectroscopic measurements on NaBH4 at prcesent available do not permit an evaluation of236 CRYSTALLINE BOROHYDRIDES this lattice frequency, but Stockmayer and Stephenson 15 state that the accurate specific heat measurement of Johnston and Hallett 14 can be fitted to a six-degree Debye and a three-degree Einstein function, and the latter leads to a torsional frequency of 350 cm-1.Using the intra-ionic broadening of 32.6 gauss2 and applying these two correc- tions, we find that the B-H distance is 1.25A. The standard deviation of the second moment measurements leads to an error of 0.015A for the distance, but this takes no account of systematic errors which may be present in the estimate of the second correction described above. Since the derived B-H distance is rather sensitive to thc value taken for the torsional oscillation frequency of the borohydride ion the calculated values for this distance are given in fig.7 for various other values of the torsional frequency, V, c m-' FIG. 7.-Variation of derived B-H distance with value of lattice torsional frequency (V6) assumed for sodium, potassium and rubidium borohydride. A = Nay X = K, 0 = Rb. POTASSIUM BOROHYDRIDE The crystal has a face-centred cubic form at temperatures above 90" K and a = 6.636 f 0.002 A at 90" K.13 There is an anomaly in the cooling curve near 76" K (private communication) which may indicate a phase change at this temperature, but it has not becii possible to study the X-ray diffraction patterns at temperatures bclow 90°K.The second moment of the proton resonance spectrum shows no significant change between 77" and 20" K, so that if there is a phase change it must be such as not to alter the interionic broadening appreciably. In view of the close similarity bctween the sodiuni and potassium salts, the samc arrangements of the BH4- ions have been assumed as for the sodium salt. The interionic broadening was evaluated as before. The lattice dimemions at 20" K (6.606A) were obtained from those at 90" K by extrapolating from room temperature through 90°K. Although this procedure cannot be accurate, the total correction is very small. In this case the closest approach of hydrogen atoms is greater (2.63 A) than 2.31 A, and it has thereforc been assumed that the thermal contraction continues to be isotropic.Interionic broadening due to : H-H interations = 4-355 gauss2, B-H 7 , = 0.139 ,, K-€3 7 9 == 0.013 ,, total interionic broadening == 4.51 ), Therefore the intra-ionic broadening is 36.2 - 4.5, or 31.7 gauss2.P. T. FORD AND R . E. RICHARDS 237 The correction for vibrational motion of the borohydride ion is applied as before. No data are yet available from which to compute the torsional oscilla- tion frequency of the BH4- ion in the KBH4 crystal, but in fig. 7 the derived valucs of the B-H distance for various values of this frequency are shown. The intra-molecular broadening of the proton resonance spectrum in potassium boro- hydride is not significantly different from that of sodium borohydride. RUBIDIUM BOROHYDRIDE At room temperature the crystal is facecentred cubic 12 with lattice constants 7.029 f 0,001 A.No other X-ray measurements are available. The lattice con- traction on cooling to 20" K has been assumed to be the same as for the potassium salt, and the lattice dimensions taken to be 6.906 A at 20" K. The total correction is extremely small and this estimate is not likely to introduce a significant error. from The interionic broadening was calculated as for the other salts to be : H-H in tcr ac t i ons B-H 9 9 = 0.11 ,, Rb-H ,, = 0.19 ,, = 3.08 gauss2, total interionic broadening = 3.38 ,, Thus the intra-ionic broadening is 31-57 gauss2, and this is the same within experi- mental error as that obtained for the sodium and potassium salts. The fact that the three derived values of the intra-ionic broadening of the BH4- ion in the sodium potassium and rubidium salts are closely similar implies either that the tor3ional oscillation frequencies of the BQ- ion are almost identical in the three salts (which seems very unlikely), or that the torsional frequencies are larger than 250 cm-1 so that their effect on the derived B-H distance is not sensitive to their value (sce fig.7). This conclusion is consistent with the estimate by Stock- mayer and Stephcnson of 350cm-1 in the sodium salt. Since the values for the potential barriers (see below) restricting the torsional motion derived from the line-width transitions are larger in the potassium and rubidium salts than in the sodium salt, we expect the torsional frequency of oscillation of the B&- ion to be greater than 350 cm-1 in the potassium and rubidium salts.From fig. 7, assuming that the torsional frequencies of the BH4- ion lie in the region of 300 to 5OOcm-1, we find that the B-H distance is 1.255& and the uncertainty of oscillation frequency would lead to an error of 0.005A. The standard deviation of the second moment measurements leads to a further possible error of about 0*015A. The B-H distance is therefore concluded to be 1.255 f 0.02A. THE LINE WIDTH TRANSITIONS The continuous curves in fig. 2, 4 and 5 were calculated by means of the expression given by Gutowsky and Pake,22 using potential barriers to the re- orientation of the B&- ion of 2.42, 3.76, 3.9 kcal/mole for the sodium, potassium and rubidium salts respectively. These values cannot be considered to be accurate without the additional measurement of the variation of the spin lattice relaxation timcs with temperature.However, the variation of the potential barrier is in accordance with the assumption made above that the orientation of the boro- hydride ions in the crystal is determined primarily by repulsion between the hydrogen atoms and the cation. The differences between the ionic radii of the metals and the boron-metal distances are 2.13 and 1-96A for the sodium salt, and 1-97A for the potassium and rubidium salts. The two distances for the sodium salt arise from the tetragonal symmetry of its crystal lattice. Reorienta- tion of the borohydride ions in the potassium and rubidium salts is therefore likcly to involve a somewhat higher potential barrier than in the sodium salt, if it is the repulsion between the hydrogen and the metal ions which is important.The second moments of the absorption lincs at room temperature are approxim- ately equal to the intermolecular broadenings. This implies that the BH4- ions238 CRYSTALLINE BOROHYDRIDES are undergoing reorientation about random axes as is found for the ammonium ions in ammonium chloride.lga25 The dotted lines in fig. 2, 4 and 5 indicate the position of the h-points of the salts, and there is no correlation between these temperatures and the line-width transition temperatures. The B-H distance in the BH4- ion is markedly greater than the corresponding value for the boron hydrides, where the distances are about 1-20 A,26, 27.28 or than borine carbonyl.29 Increases in bond length are also observed between BeF2 and BeF42-, wherc the Be-F distances are 1-52 A and 1.57 A respectively.30 The B-F distance increases from 1.30 8, in BF3,31 to 1-43 A in BF4-.32133 There appears to be an increase in bond length in the formation of some positive ions as well as in the above negative ones.For example, the N-H bond length in NH3 is 1.014 &34 and in N&+ is 1.035 A.19 The O-H distance also probably 35.4 increases in going from H20 to H3O-f. These facts suggest that the effect of the charge on the bond distances is less important than the effect of the change of hybridization of the central atom when the ion is formed. The bond lengths of the isoelectronic series, BH4- (1.255 A), CH4 (1.0924 A) 36 and NH4+ (1.035 &)I9 do not vary linearly with the atomic number of the central atom.We are pleased to acknowledge heIpful discussions with Prof. C. A. Coulson on the torsional motion of the BH4- ion in the crystals. We are also grateful to Prof. Coulter for lending us the sample of rubidium borohydride and for the interest he has taken in the work. These measurements were made during the tenure by one of us (P. T. F.) of a Maintenance Allowance from the D.S.I.R. 1 Price, J. Chem. Physics, 1949, 17, 1044. 2 Soldate, J. Amer. Chem. SOC., 1947, 69, 987. 3 Pake, Amer. J . Physics, 1950, 18, 438, 473. Smith, Quart. Rev., 1953, 7, 279. 4 Richards and Smith, Trans. Faraday SOC., 1951,47, 1261. 5 Richards, J . Inst. Petroleum (in press). 6 Davis, Mason and Stegeman, J.Amer. Chem. SOC., 1949, 71, 2775. 7 Banus, Bragdon and Hinckley, J. Amer. Chem. SOC., 1954, 76, 3848. 8 Pratt and Richards, Trans. Faraday SOC., 1953,49,744. 9 Gutowsky, Mcyer and McClure, Rev. Sci. Zmtr., 1953,24,644. 10 Andrew, Physic. Rev., 1953, 91,425. 12 Abraham and Kalnajs, J. Chem. Physics, 1954, 22,434. 13 Ford and Powell, Acta Cryst., 1954, 7, 604. 14 Johnston and Hallett, J. Amer. Chem. SOC., 1953, 75, 1467. 15 Stockmayer and Stephenson, J. Chem. Physics, 1953,21, 1311. 16 Levy and Peterson, Physic. Rev., 1952,86,766 ; J . Amer. Chem. SOC., 1953,75, 1536. 17 Pauling, Nature of the Chemical Bond (Cornell University Press, 1945), chap. 2. 18 Nagamiya, Proc. Physic. Math. SOC. Japan, 1942, 24, 148. 19 Gutowsky, Pake and Bersohn, J. Chem. Physics, 1954,22, 643. 20 Plumb and Hornig, J. Chem. Physics, 1953, 21, 366. 21 Hornig, private communication. 22 Gutowsky and Pake, J. Chem. Physics, 1950, 18, 162. 23 Deeley and Richards, Trans. Faraday SOC., 1954,50,560. 24 Morino, Kuchitsu, Takahashi and Maeda, J. Chem. Physics, 1953, 21, 1927. 25 Bersohn and Gutowsky, J. Chem. Physics, 1954, 22, 651. 26 Hedbcrg and Schomaker, J. Amer. Chem. SOC., 1951,73, 1482. 27 Dulmage and Lipscomb, Acta Cryst., 1952, 5,260. 28 Nordman and Lipscomb, J. Chem. Physics, 1953, 21, 1856. 29 Gordy, Ring and Burg, Physic. Rev., 1950,78, 512. 30 Gutowsky, McClure and Hoffman, Physic. Rev., 1951, 81, 635. 31 Levy and Brockway, J . Amer. Chem. SOC., 1937,59,2085. 32 Hoard and Blair, J. Amer. Chem. Soc., 1935, 57, 1985. 33 Pendred and Richards, Trans. Faraday SOC., in press. 34 Herzberg, Molecular Spectra and Molecular Structure, (Van Nostrand, 1951), vol. 2, 35 Herzberg, Molecular Spectra and Molecular Structure (Van Nostrand, 1951), vol. 2, 11 Van Vleck, Physic. Rev., 1948, 74, 1168. p. 439. p. 489. 36Boyd and Thompson, Proc. Roy. SOC. A, 1953,216,143.

ISSN:0366-9033    

DOI:10.1039/DF9551900230

出版商:RSC    

年代:1955

数据来源: RSC

摘要:

NUCLEAR MAGNETIC RESONANCE SPECTRUM AND MOLECULAR STRUCTURE OF ALUMINIUM BOROHYDRIDE BY RICHARD A. OGG, Jr. AND JAMES D. RAY Dept. of Chemistry, Stanford University, California, U.S.A. Received 3rd February, 1955 High resolution HI and B11 magnetic resonance spectra are presented for liquid ALB3H12 and highly deuterium-substituted derivatives. In the case of H1 spectra the technique of double resonance is also employed, with saturation of either the B11 or A127 resonance. It has been found, using such spectra for identification, that at moderate temperatures AlB3H12 undergoes reversible dissociation into B2H6 and a hitherto unrecognized com- pound, described as A12B4H18. The equilibrium is characterized by an extraordinarily large standard entropy change. The nuclear magnetic resonance spectra of the new substance have also been studied.It is concluded that AlB3H12 is characterized by a bridge bond structure, analogous to that of B2H6, but that a dynamic process renders bridge and terminal protons in- distinguishable. Evidence is offered in support of the view that a quantum-mechanical tunnel effect is involved. The structure assigned to A12B4H18 has similar features, but it is concluded that proton tunnelling and actual rotation of borohydride groups are in operation. In the course of an extensive programme of study of high resolution nuclear magnetic resonance spectra of boranes, the fist results of which have appeared,l the occasion arose to examine the remarkable compound aluminium borohydride, AlB3H12.2 The molecular structure of this undoubtedly covalent substance has been the subjcct of investigations of its vapour by electron diffraction 3 and by infra-red spectroscopy.4 These have established certain structural features, notably the location of the aluminium nucleus at the centre of an equilateral triangle formed by the three boron nuclei.The most probable arrangement of the protons 4 would appear to involve approximately tetrahedral configuration in groups of four about the respectivc boron nuclei, with two protons in terminal position and two in bridge position between boron and aluminium nuclei. This structure would lead one to expect nuclear magnetic resonance spectra somewhat similar to thosc observed 1 for diborane, B2fhj. In particular, the proton reson- ance spectrum should present the overlap of a sharply defined multiplet due to boron spin-spin interaction with terminal protons and of a probably ill-defined broad multiplet due to the bridge protons.(The A127 nucleus has spin quantum number 5/2. Since the predominant isotope B11 has spin quantum number 3/2, twenty-four lines are cxpected, with only accidental coincidences.) The first, and in many respects still the most remarkable result of the nuclear magnetic resonance studies, was the observation of a completely structureless proton resonance spectrum for liquid AIB3H12 in the entire temperature range practically available (melting point - 64" C to normal boiling point 4- 44" C). The brcadth and absolute position of this spectrum on the magnetic scale coincided roughly with those of borohydride on and diborane,l and were independent of temperature.In the course of experiments designed to elucidate the above phenomenon, it was observed that samples of AIB3H12 vapour heated in sealed glass vessels at -I- 80" C for periods of the order of 10 h, and then rapidly liquefied by cooling, displayed a strongly modified proton magnetic resonance spectrum. Such modified samples when allowed to remain at room temperature were observed 239 - -240 ALUMINIUM BOROHYDRIDE to revert slowly to the “normal” state (in the sense of the nuclear mabmetic resonance spectrum). The further observations that diborane was always present in the vcssels containing the “ abnormal ” aluminium borohydridc, and that artificial introduction of diboraxic suppressed the appearance of the “ abnormal ” form, led ultimately to the conclusion that AlB3H12 undergoes a reversible chemical changc into diborane and a hitherto unrecognized compound of aluminium, boron and hydrogen, whose formula would appear to be most probably A12B4H18.The programme of high rcsolution nuclear magnctic resonance studies whosc results are presented hcre is designed to elucidate the structural features of this ncw substance as well as those of AlB3H12, and to correlatc thcse withthe thermodynamic aspects of thc equilibrium involving the two substanccs. EXPERIMENTAL Several different samples of AIB3H12, synthesized by different methods, were used. There is no cause to believe that possible trace impurities are significantly responsible for the results obtained.Samples which had been stored in the liquid state at - 80” C or in the vapour state at room temperature yielded indistinguishable results. The conventional vacuum-line techniques were used for all transfers, and for preparing mixtures of B2H6 and AIB3H12. Partially deuterium-substituted samples, up to com- positions approximating AIB3H3D9, wcre prepared by heating mixtures of AIB3H12, .B2H6 and D2 in sealed glass vesscls provided with slender side arms for condensation of liquid. The deuterium gas was synthesized in the vacuum system by reaction of D2O and metallic sodium, and was dried by slow passage through liquid nitrogen cooled traps. The bulbs were heated at -I- 80” C for periods from 10 to 30 h. In the earlier studies the AIB3H12 samples were contained in sealed Pyrex vessels some 4 mm in diameter, with relatively small vapour space.The samples used for the observa- tion of the reversible chemical change were contained in vessels similar to those previously used for B2H6. In these the sample was largely in the vapour state at room temperature. Cooling of the slender tip caused condensation of the liquid for nuclear magnetic resonance study. Studies of nuclear magnetic resonance spectra were performed with the high resolution spectrometers of the research and development laboratories of Varian Associates, Palo Alto, California. Proton resonance was studied at 30.0013 Mc/s, and B11 resonance at 12.3 Mc/s. A vcry important aspect of the proton studies was the use of the double resonance technique, described in the paper by Dr.J. Shoolery. For B11 saturation a crystal controlled oscillator at 9.6257 Mc/s was used, final slight retuning being used for precise matching of resonance. A variable frequency oscillator with frequency counter was used for A127 saturation. The approximate frequency at which the best match was obtained was 7.8177 Mc/s. In most cases the shape of the containers made impractical the use of ‘‘ spinning ” of the sample to improve resolution, and hence great care was taken to search for the region of magnetic field giving maximum resolution. It is felt that no structural details of the spectra have been overlooked because of possible inferior adjustment of resolution. Calibrations were performed by the usual technique of modulation with an audio-frequency oscillator.RESULTS In fig. 1 are presented representative spectra selected from a very large number obtained for various samples of AlB3H12. For the proton spectra the calibration is with reference to protons in liquid water selected as the arbitrary zero on the magnetic scale. The numbers along the top of the record indicate displacements in parts per million, one part per million corresponding to 30c/s. For the boron spectra the zero was arbitrarily selected as the centre of the indicated band, the displacements again being in parts pcr million. At this frequency one part per million corresponds to 12-3 c/s. It is to be emphasized that the spectral details displayed in fig. 1 are practically inde- pendent of the temperature of the samples. Only with the proton resonance scanned whilc saturating the B11 resonance was there a noticeable change, in the sense that the ‘’ flat top ” appearance of the spectrum tended to round off as the temperature was raised. That presented corresponds to about - 60” C.Even for this the breadth at half maximum did not vary greatly.R . A. OGG, JR. AND J . D. RAY 241 For spectrum 1A the breadth at half maximum is about 300 CIS, while in 1B this has decreased to some 220 c/s. The separation of neighbouring peaks in spectrum 1C is some 87 c/s, a figurc in excellent agreement with that for the multiplet separation in fig. 1D. In fig. 2 arc presented spectra exactly comparable with those in fig. 1, but obtained with the most highly deuterium-substituted samplc obtained.Several samples of inter- mediate deuterium substitution, whose spectra are not presented here, showed intermediate spectra. Temperature effects are practically negligible, as in fig. 1. The relatively low fraction of protons leads to a rather unsatisfactory signal to noise ratio in A and 13, but as far as can be judgcd, the characteristic features are indistinguishable from those in the corresponding spectra in fig. 1. The definitely greater line breadth in fig. 2C, as compared to fig. lC, is a matter whose significance will be dealt with in the discussion. The highly complex appearance of fig. 2D is expected, since the sample is a mixture of several species, in most of which the 1311 resonance is split both by protons and deuterons. The small spacing compared to that in fig.1D is in satisfactory agreement with the ratio of gyromagnetic ratios for dcuterons and protons. In fig. 3 and 4 are presented spectra obtained for the ‘‘ abnormal ” substance obtained by heating the vapour of AlB3H12 (at a few hundred millimetres partial prcssure) at + 80” C for periods of the order of 10 h, and then condensing as rapidly as possible by cooling the vessel in liquid nitrogen. The details displayed here are observed to alter slowly as the sample is allowed to stand at room temperature, so that in most cases after a day or so the spectra are identical with those prcsented in fig. 1. In cases in which the sample was condensed with dry-ice in the side tip, and then sealed off, this ‘‘ reversion ” did not take place. It was also observed that a dark film (elementary boron) formed at the seal, and that the remaining relatively large bulb contained diborane, whose normal boiling point is considerably below dry-ice tempcrature.Samples to which diborane had been initially added before the above heating and condensation treatment showed a spectrum intermediate between those in fig. 1 and in fig. 3 and 4, i s . repression of the “ abnormal ” form. The samples which displayed most strongly the “ abnormal ” spectra were also obviously different in physical properties. Crude vapour pressure measurements were made by observing the fraction of liquid volatilized from the small side arm when main- tained at a known temperature, and without question the “abnormal” substance is less volatile than AlB3H12. The various observations are best explained by proposing the reversible reaction the equilibrium being slowly attained, with a value of the mass law constant very strongly temperature dependent, so that at 20” C the proportion of A12B4H18 is negligible, while at 80” C it is the dominant species.The above reaction would not cause any pressure change, and this is in accord with such observations as have been madc at clevated temperatures.5 For the purpose of subsequent discussion this intcrpretation is adopted, and the spectra in fig. 3 and 4 are hence presented as those of “A12B4H18”. (It is planned to subject this system to other physical chemical tcsts designed to test this hypothesis.) The most striking featurc of the simple proton resonance spectrum of A12B4H18 is its extraordinary sensitivity to temperature, as shown in fig.3A, 3B and 3C. At sufficiently low temperature its spectrum approaches that of AlB3H12. At these low temperatures simultaneous saturation of the A127 resonance is seen to have an effect very similar to that on the spectrum of AlB3H12. The absolute positions of the spectra on the magnetic scale are very similar to those for AlB3H12, any apparent displacement being probably within the calibration uncertainty. However, the multiplet separation in fig. 3D would appear to be 83 c/s (as compared with 87 in fig. 1C) and this difference is probably real. The proton rcsonance of A12B4H18 under B11 saturation is strikingly different from that of AlB3H12, as comparison of fig. 4A and 4B with fig. 1B demonstrates.This reson- ance is also temperature sensitive in the same scnse as the simple proton resonance, thc breadth at half maximum increasing from some 50c/s at room temperature to about 120 cycles at - 60” C. The B11 resonance of A12B4Hl8, fig. 4C, is strikingly similar to that of AIB3H12. fig. lD, except for a small decrease of multiplct separation (agreeing with the 83 c/s from fig. 3D). Unlike the proton resonance spectra of A12B4H18, the B11 resonance spectrum shows no marked alteration with temperature. Numerous experiments were performed with partially deuterium-substituted samples of AlzB4His. In fig. 4D is presented a representative spectrum, that of B11 in a specimen 2AlB3H12 A12B4H18 + B2H6,242 ALUMINIUM BOROHYDRIDE approximating A I ~ B ~ H I ~ D ~ .It appears to be the superposition of a spectrum like fig. 4C, and of a 1,3,3, 1 quartet, each meniber of which is a small triplet, due to deuteron splitting. The small spacings are similar to those in fig. 1D. DISCUSSION Interpretation of the nuclear magnetic resonance spectra of AlB3H12 leads unambiguously to the following conclusions regarding molecular structures. (i) All protons in a given molecule have identical electronic environment, i.e. are " chemically equivalent ". This is most simply shown by the spectrum in fig. lC, where the saturation of the A127 resonance has removed the spin-spin perturbing effect of this species. The resultant spectrum is virtually identical with that of simple borohydride,l the details resulting solely from spin-spin coupling with boron nuclei.Even the weak satellites due to the BlO species are partly resolved. (ii) All protons are spin-spin coupled to both aluminium and boron nuclei. This is shown by the spectrum in fig, lC, discussed above, and by that in fig. lB, where saturation of the B11 resonance has removed the spin-spin perturbing effect of this spccies. The spin-spin intcraction with A127 nuclei should produce a six- fold multiplct of equal intensities. The " flat-topped" spectrum in fig. 1B is interpretcd as this multiplet, the individual lines being sufficiently broadened by electric field gradient interactions with the large electric quadrupole moment of the A127 nucleus to give an apparent continuum. The separation of adjacent lines would appcar to be about 44 c/s.The appearance of thc simple proton spectrum in fig. 1A is rationally explained as the result of broadening each line in fig. 1C by the amount indicated in fig. 1B. (iii) All boron nuclei are spin-spin coupled, i.e. " chemically bonded " to four equivalent protons. This is demonstrated by the extraordinarily well-defined 1,4, 6,4, 1 quintet for B11 resonance displayed in fig. lD, again remarkably similar to that of free borohydride ion. Following the argumcnt given before,l the extreme sharpness of the resonanccs strongly suggests the tetrahedral configuration of the four protons. The reconciliation of the above conclusions with any strictly static model appears impossible. The model discussed in the introduction, in which half of the protons are bridge bonded and half are terminal, would appear to require some dynamic feature leading to exchange and hence time-average equivalence of the two typcs of protons.A conceivable mechanism of such exchange would involve bodily transfer of borohydride ion from one molecule to another, achieved eithcr by spontancous ionization, or by a displacement reaction catalyzed by adventitious impurity. Demonstration of such effects in quenching of multiplet structure has already been given.6 7 To explain the spectra presently observed, such chemical transfers would ncccssarily fall within a narrow frequency domain centred about the abovc given A127 multiplct separation of 44 c/s. An exchange much slower than this would lead to the observation of two types of protons, as discussed in the introduction.An exchange of much highcr frequency would lead to complctc quenching of the A127 spin-spin coupling, leaving only that due to boron spin-spin interaction. The invariance of the spectra over a very wide temperature range, and their independence of the source of the AlB3H12, would appear to exclude any such chemical transfer as a reasonable explanation. A mcchanisrn requiring internal rotation of borohydride groups, resulting in the breaking and reformation of the bridge bonds to the aluminium nucleus, would formally lead to interchange of bridge and terminal protons. Such an internal process is subject to the samc frequency restrictions discussed above. With any rcasonable assignment of the temperature independent factor, a first- order rate constant of some 44 sec-1 at, say, 300" K is associated with an activation energy of the order of 14 kcal/mole.The obscrved invariance over a 100-deg.R. A . OGG, JR. AND J . D . RAY 243 temperature range seems definitely to exclude such a process. It would appear that the potential barrier hindering internal rotation of the borohydride groups must be considerably higher than 14 kcal/mole. The only tenable remaining hypothesis would appear to call for a non-classical penetration of the proton system through the hindering potential barriers, i.e. the quantum-mechanical “tunnel effect”. The important feature of such a process is that it would leave the bonding electron system essentially invariant, i.e. it would not break the spin-spin coupling with the aluminium nucleus.Again a frequency criterion is involved, the essential quantity for comparison being the magnitude of the “chemical shift” between the bridge and terminal protons. In diborane 1 this chemical shift at 30 Mc/s amounts to some 130 c/s, and a rather smaller value might be expected for ALB3H12. Were the frequency of the “ tunnelling exchange ” small in comparison with such a figure, the observation of spectral detail resulting from distinguishable bridge and terminal protons would be expected. If the “ tunnelling ” frequency is sufficiently high, spectral identity of the protons results, with an electronic environment equivalent to the average of the values characteristic of bridge and terminal positions. The practical spectral identity of the protons is independent of the exact value of the “ tunnelling” frequency, provided only that the latter exceed a figure large in comparison with the chemical shift of bridge and terminal protons.A value in excess of some 103 c/s would certainly suffice to explain the present observations. Such a frequency restriction is in sharp contrast to the narrow range requirement for any process leading to rupture of the bridge bonds. The frequency of the proposed “ tunnelling ” process would depend in an inverse exponential fashion upon the total mass of the system of hydrogen nuclei undergoing concerted motion. It is to be expected that with a sufficiently extensive replacement of protons by deuterons (a minimum of two per borohydride group is indicated), the frequency could be sharply reduced. Such considerations dictated the experiments leading to the spectra displayed in fig.2. While in overall aspects these are very similar to those of ordinary AlB3H12, there appears to be a striking difference in ’the breadth of the proton resonance lines scanned while saturating the A127 resonance. Separate experiments (whose spectra are not presented here) suggest that in deuterium-substituted borohydridc ion any spin-spin interaction of protons and deuterons is too small to account for the observed broadening in deuterium-substituted AlB3H12. Thc broadening discussed above is in accord with the proposed “ tunnelling ” mechanism. Were the frequency of such a process to be negligibly small, the simple proton resonance spectrum corresponding to the bridge model would be the superposition of four narrow lines on a broad band, with some relative “ chemical shift ” of the respective centres of gravity.Saturation of A127 reson- ance should reduce the band to four narrow lines, not incident with the original four. If, now, conceptually the exchange frequency of bridge and terminal protons be monotonically increased, the eight lines must correspondingly broaden and merge pair-wise into a pattern of four lines which at the optimum exchange frequency havc a breadth of the magnitude of the chemical shift. Further fre- quency increase leads to progressive narrowing of each of these four lines. (Comparablc effects have been demonstrated7 for exchange due to a chemical mechanism.) It is suggested that in the highly deuterium-substituted AlB3H12 the exchange frequency is still higher than that of the chemical shift, but suf- ficiently reduced in comparison with ordinary AlB3H12 so that some residual broadcning is still to be observed.That even for the deuterium-substituted species the exchange fi-equcncy is so great as to lead to near environmental identity of the protons is in rational accord with the failure of the othcr spectra in fig. 2 to differ significantly from those in fig. 1. In short, the spectrum with saturation of the A127 resonance provides the most sensitive test of the expectcd effect.244 ALUMINIUM BOROHYDRIDE Rough quantum-mechanical calculations indicate that the appropriate " tunnelling " frequencies required to explain the above effects are compatible with a potential barrier structure of sinusoidal character with spacings determined by the known geometry of borohydride ion, and barrier heights in considerablc excess of 14 kcal/molc.The above evidence is suggested as strongly indicative of the essential correctness of the bridge model discussed in the introduction. From the standpoint of thermodynamic properties, at ordinary temperatures the possible internal rotation of borohydride groups is to be regarded as frozen out. The proposed " tunnel " effect does not of course result in any net angular momentum of the borohydride groups. With the magnitude of tunnclling frequencies indicated the splitting of torsional levels makes no significant differencc in the standard entropy. Before considering the structure of A12B4H18, it appears appropriate to discuss the thermodynamic aspects of the proposed equilibrium The nuclear magnetic resonance spectra may serve an analytical function, indicating the composition of a mixture, without regard to the detailed interpretation in terms of molecular structure.The spectrum in fig. 3A is interpreted as that of a mixture of AlB3H12 (responsible for the underlying continuum) and of A12B4H18. which in pure state would give four lincs going nearly down to the base. A graphical resolution of the observed superposition spectrum, and the comparison of the respective areas, allows in principle the estimation of the ratio of the two substances in the mixture. For the present it suffices to point out that clearly A12B4H18 is the more abundant, the ratio being at least three to one.Since this rcsult was obtained for several samples heated for different fairly long periods at 80" C, this rough ratio is taken to represent the composition of the equilibrium mixture, with a mass law constant of at least 10. Samples of AlB3H12 which have stood for weeks at 20" C show proton spectra with no trace of the four-fold structure, indicating a negligible contamination with &B4H18. However, the possibility of a trace of excess B2H6 (formed in the synthesis) must always be borne in mind. Weighing these facts, it would appear that the mass law constant at 20" C is almost certainly less than 10-1. These crude estimates make it highly probable that the equilibrium constant for the reaction in question increases at least a hundred-fold between 20" C and 80" C.This would indicate the reaction (left to right) to be endothermic by at least 16 kcal/mole &&&f18, with a standard entropy increase of at least 50 cal/deg. mole A12B4H18 at 80" C. It is to be emphasized that this rough estimate would appear to constitute a conservative lower limit. The accurate determination of the equilibrium constants at various temperatures may well yield a value of the standard entropy increase substantially larger than this figure. Such a magnitude of standard entropy increase for a gas-phase reaction in which the number of molecules remains constant appears to be without precedent. It should be noted that the change in translational entropy is relatively insignificant, and that such an effect must result from changes in rotational and vibrational entropy.The crudity of the data does not warrant a detailed discussion, but it would appear that only a marked increase of entropy of internal rotation could account for a figure of such a magnitude. The known thermodynamic properties of B2H6 force the conclusion that it is the species Al2B4H18 which is characterized by large entropy of internal rotation, and that AlB3H12 is normal. The above discussion is seen to lead independently to the conclusion that at moderate temperatures any internal rotation of borohydride groups in AlB3H12 molecules is frozen out. This is in gratifying agreement with the structural conclusions arrived at from the nuclear magnetic resonance studies. Conversely, the con- clusion that A12B4H18 is characterized by relatively free rotation of borohydride 2AlB3H12 + M2B4H18 3- B2H6.R.A . OGG, JR. AND J. D . RAY 245 groups should find confirmation from its nuclear magnetic resonance spectra. It will appear below that this is in fact the case. The structure suggested for A12B4H1g involves two hydrogen bridges between A1 centres, which are each bridge-bonded to two borohydride groups. The proton resonance of the AP-H-Al27 bridge structures in principle should exhibit 36 lines, expected to appear as a broad and relatively weak continuum. Super- imposed upon this should appear the borohydride structure. As was discussed previously, true rotation of the borohydride groups, leading to continuous rupture and reformation of their bridge bonds to aluminium, would at sufficiently high frequency result in practically complete quenching of any multiplet structure caused by spin-spin coupling with the A127 nucleus.This is seen to be the case in the spectrum displayed in fig. 3A. Saturating the B11 resonance under thcse conditions is seen to result in a single relatively narrow line, displayed in fig. 4A. Particularly interesting is the effect of lowering the temperature as seen in fig. 3B and 3C. A progressive broadening and ultimate nearly complete merging of the lines is seen to occur. This corresponds to a sharp decrease in the frequency of internal rotation, so that at the lowest temperature the spin-spin coupling with the A127 is scarcely disturbed. That it is this coupling which is responsible for the broad structure is shown clearly by the spectrum in fig.3D, where saturation of the A127 resonance has restored the four-fold structure. The temperature effects on the proton spectrum scanned while saturating B11 resonance (fig. 4A and 4B) arc in agreement. The broadening at low temperatures corresponds in sense to the broadening of the respective lines in fig. 3A, 3B and 3C. That the borohydride group protons in A12B4H18 are identical in environment as in AlB3H12, and are arranged tetrahedrally in groups of four around respective boron nuclei, is suggested by all of the nuclear magnetic resonance spectra. The clearest demonstration is offered by the B11 spectrum in fig. 4C, seen to be a well- defined 1,4, 6,4, 1 quintet, similar to that given by AlB3H12. Additional evidence is offered by the B11 resonance of partly deuterium-substituted A12B4H18, fig.4D. The maintenance of thesc details over a very wide temperature range, in contrast to the marked changes suffered by the proton spcctra, indicates that the identity of protons is achieved by a mechanism separate from the internal rotation of borohydride groups. This would logically appear to be the same type of " tunnelling " as that proposed for AIB3H12. As will appear below, an experi- mental test should be even more difficult with A12B4H1g. The models proposed for AlB3H12 and A12B4H18 are seen to have great structural similarities. In each case the rotations of borohydride groups leading to interchange of terminal and bridge protons are to be regarded as true chemical reactions, actually breaking the aluminium-hydrogen bridge bonds.The necessary energy requiremcnt corresponds to a potential barrier hindering rotation. The essential difference of the two species would appear to lie in the height of this barrier. In AIB3H12 this would appear to be so high that at ordinary temperatures practically all molecules occupy the lowest torsional level. It is from this level that the proposed tunnel exchange of protons occurs. In A12B4H1g the barrier would appear to be much lower, perhaps of the order of 10 kcal/mole, as the striking temperature coefficient of the proton spectra sho us. The relatively large internal entropy, above termed " rotational ", is more accurately to be regarded as associated with the relatively low frequency torsional oscillations. The frequency of tunnel effect exchange of protons through the relatively low barrier is expected to be extremely high. It is felt that the original objective of the investigation has been satisfactorily achieved. A strong case can be made for the bridge model for ALB3H12, with associated tunnel exchange of protons. It is of interest that the alternative behaviour of internal chemical reaction, rejected on logical grounds for AlB3H12, is apparently actually displaycd by the new compound discovered in the course of the work.246 GENERAL DISCUSSION The authors wish to acknowledge the generosity of Prof. A. B. Burg, who supplied the samples of aluminium borohydride and of diborane. The invaluable experimental assistance and stimulating suggestions of Dr. J. N. Shoolery of Varian Associates are gratefully acknowledged. Ogg, J. Chem. Physics, 1954,22, 1933. Schlesinger, Sanderson and Burg, J. Amer. Chem. Soc., 1940, 62, 3421. J. Amer. Chem. SOC., 1946, 68, 312. price, J. Chem. Physics, 1949, 17, 1044. egg, J. Chem. Physics, 1954,22, 560. 3Beach and Bauer, J. Amer. C/lem. SOC., 1940, 62, 3440. Silbiger and Bauer 5 Brokaw and Pease, J. Amer. Chem. SOC., 1952,74, 1590. 7 Ogg, Farady SOC. Discussions, 1954, 215.

ISSN:0366-9033    

DOI:10.1039/DF9551900239

出版商:RSC    

年代:1955

数据来源: RSC

摘要:

246 GENERAL DISCUSSION GENERAL DISCUSSION prof. H. S. Gutowsky (University of Illinois) said : The Chairman has raised the question of the relative merits of electromagnets versus permanent magnets for magnetic resonance experiments. This is a difficult question to answer because the range in quality and characteristics of magnets of both types exceeds any intrinsic differences. But there are some intrinsic differences which, all other features being equal, recommend electromagnets for some applications and per- manent magnets for others. The characteristics of a magnet include: (i) maximum field obtainable, (ii) adjustable range in field, (iii) stability, (iv) field homogeneity, (v) gap dimensions, (Vi) cost of magnet and accessories, (vii) reliability, ease, and cost of operation, (Viii) commercial availability.The nature of available permanent magnet materials limits the fields economically obtainable in gaps of the dimensions required to about 7,000 to 8,000 gauss. Electromagnets do not suffer as great a limitation. Moreover, an electromagnet can provide a continuously adjustable field from zero to its rated maximum value, while the field of a permanent magnet can be adjusted only over a small range, say up to + 50 gauss from the usual value, by using direct current coils at the gap or about the poles.' However, in terms of stability a permanent magnet has a definite advantage. Electromagnets can be electrcnically regulated to a truly remarkable extent, to fluctuations no greater than 1 part in 107 per min and this will no doubt be improved.But considerable elcctronics are required in the power supply, at a cost com- parable to the cost of the magnet itself. Permanent magnets have a reversible change in magnetization with temperature, -0.02 %/deg. for Alnico V. But simple thermoregulation combines with the large heat capacity of the permanent magnets to give easily field stability an order of magnitude or more better than that cited for electromagnets. As to field homogeneity, this is determined more by the pole cap material and its shape and mechanical alignment than by the source of the magnetic field. So there is little here in favour of either type of magnet. The field contours for an electromagnet do show hysteresis effects, being different on the demagnetization compared to the magnetizing cycle, and also are different at high fields where the pole cap material becomes saturated.On the other hand, if a permanent mamet is not kept at constant temperature, small changes occur in the field homogeneity, presumably becaure of changes in domain structures with temperature. The gap dimensions of a permanent magnet are somewhat more critical than for electro- magnets, if the permanent magnet material is to be utilized efficient1y.l If stability and homogeneity are important, then the cost of a permanent magnet, for fields up to 6000 gauss, will generally be less by a factor of 1/2 to 2/3 1 Gutowsky, Meyer and McClure, Rev. Sci. Instr., 1953, 24, 644.GENERAL DISCUSSION 247 than a comparable electromagnet. And this is mainly because of the current supply and control.A permanent magnet is undoubtedly simpler and more reliable in operation than even the best electromagnet. You do not have to turn a permanent magnet on or off. But some applications such as electronic para- magnetic resonance require that the field be adjustable over a wide range, from zero to as high as 6,000 or 10,000 gauss depending on whether you are working at 3 cm or 1 cm wavelengths. And in nuclear magnetic resonance, sensitivities are increased by working at the higher fields of large electromagnets. And it is sometimes desirable to have a wide enough range of fields available to check the field dependence of a phenomenon. In America electromagnets probably are at present more prcvalent than permanent magnets. This is partially because electromagnets of guaranteed stability and homogeneity are available commercially.Excellent permanent magnets can also be contracted for but gap design is still your own problem and the homogeneity is not specifiable. In summary, it is usually a qucstion of personal prcjudice or availablility which determines whether a permanent or electromagnet is used for nuclear magnetic resonance. Insofar as I know good versions of both types of magnets have been used successfully in practically every variety of nuclear magnctic reson- ance experiment. Dr. N . Sheppard (Cambridge University) (communicated) : Prof. Gutowsky discussed the high resolution n.m.r. spectrum of dimethyl formamide and deduced from thc nonequivalence of the two methyl groups that a barrier of at lcast 10 kcal per molecule restricted rotation about the C-N bond.Would he mind outlining how this calculation was madc? The more general question of whether or not n.m.r. methods can distinguish between the different stable configurations (rotational isomers) corresponding to minima in the potential energy curve associated with less highly restricted internal rotation is also of interest. For molecules such as 1 : 2-dichloroethane certain of the barriers may be as low as 3-4 kcal. Whereas the rotational isomers can be separately distinguished by infra-red and Raman spectroscopy, is it probable that thc rate of transition from one minimum to another will be too rapid for observation of other than average effects by the n.m.r. method? Prof. H. S . Gutowsky (University of Illinois) (communicated) : The high resolution proton magnetic resonance spectrum of liquid dimethyl formamide, (CH&NCHO, was observed in our laboratory 1 to consist of a close doublet and a third line, with relative intensities of 3 : 3 : 1.The doublet was at a &value of - 0.24 which is in the range of -- 0.20 to - 0.30 found2 for methyl groups attached to nitrogen. And the + 0.34 for the weaker line agrees in position with other compounds2 having structures of the sort N-CHO and 0-CHO. A doublet structure of the CH3 group resonance might in principle arise either from a chemical shift due to nonequivalence of the two CH3 groups or from an indirect spin-spin coupling 3 with the proton of the CHO group. However, the latter possibility is eliminated by the absence of any corresponding splitting of the resonance line for the proton in the CHO group.So it is concluded that the two CH3 groups are nonequivalent. The nonequivalence of the methyl groups is explained most readily by assuming a barrier to internal reorientations about the N - C bond, because of a double bonded contribution to the structure : CH3 H 0- 1 Meyer, unpublished results. 2 Meyer, Saika and Gutowsky, J. Amer. Chem. SOC., 1953,75,4567. 3 Gutowsky, McCall and Slichter, J. Chem. Physics, 1953, 21, 279.248 GENERAL DISCUSSION A lower bond can be estimated for the barrier to internal rotation because re- orientations would average out the electronic differences of the two CH3 groups and give a single line if the reorientations were fast enough.The general theory 1 for the averaging effects of dynamic processes shows that the doublet separation of about 5 c/s would not be observed if the reorientation frequency Y was itself faster than 5 CIS. The reorientations are undoubtedly thermally activated and the reorientation frequency is given by a rate equation of the form : Y = vo exp (- V~/RT). vo is a frequency factor the order of kT1h or 6.25 x 1012 at room temperature and the activation energy is the potential barrier VO, which is related directly to the contribution of the double bond to the N-C bond energy. If we rcquire that v be less than 5 c/s, then Vo must be greater than 16 kcal. We are obtaining a more definite value for VO by observing the temperature dependence of the doublet separation.At higher temperatures the reorientation frequency increases enough to coalesce the doublet; so we can determine the temperature at which v is actually 5 c/s and this will give us VO. This general method is limited in its applications by the separation of the chemically shifted and multiplet resonances which are averaged by the dynamic processes in question, These separations range from a few cycles to the order of several kc. If the dynamic processes have normal frequency factors, the cor- responding range of barrier heights or activation energies is between 10 and 20 kcal mole-1. Prof. H. S. Gutowsky (University of Illinois) said: The results of Ford and Richards on the broad proton resonance in solid diketene provide an interesting confirmation of the molecular structure in the solid phase.However, there is some infra-red evidence 2 for the presence of a second form in thc liquid phase with increasing concentrations at higher temperatures. The versatility of nuclear magnetic resonance is illustrated by the fact that we could apply high resolution techniques in our laboratory 3 to the question of the structure of diketene in the liquid phase. At various times the following five structures have been proposed for diketene : 0 - G C H I II I I H2C--C=O C H 2 a H 2 I I I I o r - 0 O&O The number and relative intensities of the chemically shifted components in the proton magnetic resonance absorption spectra for these structural models are given simply by the number of non-equivalent structural sites and the fraction of protons in each type of site.Thus, structure (I) would have two resonance components with relative intensities of 3 : 1 ; (Ir) 2: 1 : 1 ; (111) 4 ; (IV) 3 : 1 ; and (V) 2 : 2. At room temperature the proton resonance of the liquid was found to consist of two components, with equal intensities, and with chemical shift &values 4 1 Gutowsky and Saika, J. Chem. Physics, 1953, 21, 1688. 2 Miller and Koch, J. Amer. Chem. Soc., 1948,70, 1890. 3 Bader, Gutowsky, Williams and Yankwich, unpublished results. 4 Meyer, Saika and Gutowsky, J. Amer. Chem. SOC., 1953,75,4567.GENERAL DISCUSSION 249 referred to H20 of - 0.07 and - 0.16. This proves that the structure of the liquid is (V), the 3-buteno-/%lactone as found in the solid. Moreover, the position of the - 0.07 line is close to that found 1 for vinyl groups while the - 0.16 line is not far removed from CH2 groups in cyclic compounds, confirming structure 03.At elevated temperatures, the spectrum became more complex indicating the formation of one or more new species. However, most of these effects were irreversible. In any event, it appears that no more than 5 to 10 % of the sample at room temperature could have been other than structure 0. And this estimate is based on a conservative value for the sensitivity of our measurements. Prof. W. N. Lipcomb (University of Minnesota) said: Confirmation of the structure for diketene is indeed pleasing, and some comments on the values of the interatomic distances may be of interest. Cox, Cruickshank and Smith have found that if the effect of torsional oscillations of benzene molecules in the crystal is ignored, an apparent shortening of the bonded C-C distance by about 0.0158, occws.An estimate of this same effect in diketene indicates that OW published valucs of bonded distances in the four-membered ring are about 042A shorter than the correct values, and that the correct external C=C and C=O distances are probably about 0.015 8, shorter than we reported. If these correc- tions are made the bonded distances in our X-ray diffraction study agrec to within an average of -i. 0.02A with the electron diffraction results for dimensions of this model.2 Finally, a small similar effect occurs in our X-ray diffraction study of pentaborane. While these changes are probably significant they do lie within the limits of errors assigned by us.Dr. Peter Gray (Cambridge University) said: Dr. Drain reports a value 1.042 f 0.01 8, for the N-H distance in N&F (in NH4C1 the value 3 is 1,038 f 0.004 A) and suggests that the change in dimensions of the ammonium ion produced by the strong hydrogen bonding in ammonium fluoride is small. On the other hand the change in the N-H distance in hydrazinium fluoride in which there is also strong hydrogen bonding is appreciable ; 4 the N-H distance is 1.075 f0.02 A. In hydrazinium fluoride this is accompanied by an appreciable4 shift in the 3000 cm-1 N-H frequency. A similar effect is observed in ammonium fluoride where, as a result of hydrogen bonding, the N&+ vibration frequency normally in the neighbourhood of 1400cm-1 has the value 1484cm-1 in NH4F, markedly different from its 1397 cm-1 in NI&Cl. Such a shift would again be expected to be associated with an appreciable lengthening of the N-H bond.Is it possible that the value reported here for the N-H bond length in NH4F is somcwhat low ? Prof. D. P. Hornig (Math. Inst., Oxford University) said : It is surprising that the N-H distance obtained in NI&F should be so close to that in N&Cl since the N-H stretching frequencies differ considerably, occurring at about 2850 cm-1 in NH4F and 3100 cm-1 in N€&CI. In hydrazine fluoride, according to Deeley and Richards, the N-H distance is 1.075A and the mean N-H stretching frequency is 2670 cm-1. These considcrations suggest a value for rNH of 1-05-1.06 A.The considerable increase in thc bending frequency of the NH4+ ion from 1400 cm-1 in NH4Cl to 1494 cm-1 in N&F also indicates the presence of a moderately strong hydrogen bond in the latter. The infra-red spectrum yields a torsional frequency of 523 cm-1 (1.7 x 1013 sec-1) for the NH4+ ion in the lattice, moderately close to the value 1.4 X 1013 estimated by Dr. Drain. The change should not greatly affect his calculations. Dr. Mansel Davies (Aberystwyth) said: The urea molecule is of particular interest as it is possibly one of the simplest compounds showing the planar form 1 Meyer, Saika and Gutowsky, J. Amer. Chem. SOC., 1953,75,4567. 2 Bauer, Bregman and Wrightson, J. Amer. Chem. Soc., 1955, to be published. 3 Gutowsky, Pake and Bersohn, J. Chern. Physics, 1954,22, 643.4 Deeley and Richards, Trans. Faraday Soc., 1954, 50,560. 5 Bovey, J. Chem. Physics, 1950, 18, 684.250 GENERAL DISCUSSION of the amide nitrogen valencies found by X-ray methods to occur in a variety of peptide and protein-like structures. At Aberystwyth we have been interested in the bonding within the simplc amide group and the changes which occur in it. Thus formamide, the simplest amidc, is certainly not planar in the vapour state 1 -the hydrogens of the NH2 group are symmetrically disposed about the OCN plane-but it may possibly become so in the liquid or solid state. The planar structure of the urea molecule in the crystal presumably involves the sp2 hybridized valency state of the nitrogen atom : this means that what might have been regarded as the lonepair electrons of the nitrogen are in pz orbitals and delocalized n-bonding takes place between the 0, C and N atoms-a picture which accounts qualitatively for the high order of the C-N bonds when compared with singIe bonds, and the somewhat reduced bonding in the C 4 linkage.Mr. L. H. Hopkins, who has been studying urea in the infra-red, has considered the possible implications of this valency state of the nitrogen upon the stretching v(N-H) frequency and he has also made some experimental observations to which I should like to refer. Compared with ammonia r(N-H) == 1-014& v(N-H) = 3372 cm-1 if we accept the bond length of Andrew and Hyndman, the stretching frequency in urea is remarkably high r(N-H) = 1.046 A, v(N-H) = 3396 cm-1; the increased N-H bond length would have been expected to decrease the frequency by about 300 cm-1.However, by analogy with the case of carbon, the hybridiza- tion change p3 + sp2 for nitrogen might shorten r(N-H) by about 4 %. Taking this and the influence of ionic tcrms into account, one then finds that, in the absence of hydrogen bonding the v(N-H) frequency in urea could be in the neighbourhood of 3650cm-1. Compared with the quoted frequency (which is the arithmetic mean of thc symmetric and asymmetric modes), this would be indicative of appreci- able hydrogen bonding. But this suggestion is by no means satisfactory either in itself or in the light of at least two other observations. The X-ray data show that the relevant 0-N distances in the solid are 2-99A and 3.04 A : thesc correspond to weak hydrogen bridges and, moreover, suggest that the two N-H bonds of the NH2 groups in crystalline urea are not strictly equivalent.Again, as Mr. Hopkins has found, there are no very pronounced changes in the urea spectrum on going from the solid to the vapour-at least, not in the region of the carbonyl frequency. Thus it is very difficult, if not impossible, to reconcile the N-H bond length deduced from the proton magnetic resonance spectrum with other observations on the urea structure. Prof. H. S. Gutowsky (University of Illinois) said : In their determination of the structure of the urea molecule, by observing the proton magnetic resonance in a single crystal, Andrew and Hyndman assumed the lattice to be "rigid" at room temperature.This was supported by the similarity of results at liquid air and room temperature, so observations made at the latter temperature were used in the analysis. However, Kromhout and Moulton,2 at the University of Illinois, have observed a transition in the proton line width in urea crystal powder, centred at about 50" C. The width changes from 14 to 7 gauss, as would be expected for rotation of the NH2 groups about the C-N bond. The transition to the broad line may not be complete at 25" C. In fact, the second moment measured at 0" C is 20.8 & 0.6 gauss2, from which Kromhout and Moulton calculate an N-H bond distance of 1.010 f 0-007 A, if the planar rnolccule with an H-N-H bond angle of 120" is assumed. 1 Evans, J. Chem. Physics, 1954, 22, 1228. 2 Kromhout and Moulton, J.Chem. Physics, in press.GENERAL DISCUSSION 25 1 This is somewhat less than the 1.046 f 0.01 A found by Andrew and Hyndman, as would be the case if a slight amount of motional narrowing were indeed present at room temperature. Such narrowing would not affect in any way the con- clusions as to the planarity of the molecule. However, the N-H distance and the bond angles may require some modifications. I believe that resolution of the small discrepancies would be useful in establishing the dependence of the N-H bond distance on hydrogen bonding, which is an important problem. Prof. E. R. Andrew (University College of North Wales) (comniiinicnted) : Kromhout and Moulton (private communication) have recently reviscd their N-H bondlength of 1-010&0-007 A quoted by Prof.Gutowsky to 1*036:1:0*009 A, which, within the combined limits of error is not in disagreement with our value of 1.046 f 0.01 A. Nevertheless, it is possible that our second momcnt values may be slightly less than the rigid lattice values, though our measurements were made at a rather lower temperature (18-20°C) than the tempcraturc suggested by Prof. Gutowsky. A correction to the observed second moment values which might help to explain the discrepancy mentioned by Dr. Davies is concerned with the vibration of the atoms within the molecule. Deeley and Richards 1 have treated the case Of atoms vibrating along the line joining them, which causes only the length of the inter- nuclear vector to vary. If this correction is applied the bondlength is further increased.However, in our casc the vibration of the protons also causes the directions of the internuclear vectors and their angles with respect to the applied field to vary, leading to a more complicated corrcction which might have opposite sign. We are extending thc work on monocrystalline urea to lower and higher tem- peratures to find out more definitely than can be done using polycrystalline material the nature of the motion responsible for the narrowing of the spectrum at higher temperatures. Dr. J. A. S. Smith (Leedr University) said: I think that the question of the mechanism of the transitions ip PTFE is still an open one. I should like to discuss briefly some of the evidence which seemed to us relevant to the problem. In the first place, the first nuclear resonance transition decrcases the second moment by about 6 gauss2, which seems too large to be accounted for by a change in the so-called amorphous regions of the polymer alone, for these constitute only about 30 % of the bulk of the material.This point is brought out by inaking a rough calculation of the percentage of the polymer which has undergone the transition at 270°K at which temperature the second moment is 5.5 gauss2. If we assume that the second moment of a specimen of the polymer in which the helices are effectively stationary is 11.4 gauss2 and one in which the helices are undergoing hindered rotation is 2.3 gauss2, and assume thesc values to be the Same for both amorphous and crystalline regions, this percentage comes to 67.This figure agrees better with a model in which two-thirds of the chains are rotating and the remainder are stationary. In the second place, the experimental evidence shows that this is a roughly quantitative explanation, for as already mentioned the total width of the line falls by about 5 gauss between 200" and 250" K. The line-shape at these inter- mediate temperatures is apparently not a simple superposition of two curves, one of which is due to a rigid lattice and the other to a lattice affccted by molecular rotation, but both to some extent must be affected by thc molecular motion. The comparison of the results for PTFE with those for polythene may throw Some further light on the nature of the transitions. It must be remembered, however, that as many as four in a hundred carbon atoms in the polythene chain may be branch mcthyl groups, so that extra complications may occur because of the presence of CH3 or CH groups in the polymer.1 Deeley and Richards, Trans. Furuduy Soc., 1954, 50, 560.252 QENERAL DISCUSSION Prof. G. E. Pake (Washington University, St. Louis) said : As noted in Dr. Smith's excellent paper, Dr. C. W. Wilson 1 and 1 investigated the nuclear magnetic resonance of polytetrafluoroethylene (PTFE) in 1952. Since the published report of this work was extremely brief, it should be of interest to compare here the Washington University data with those of Dr. Smith. The Washington University data agree very well with the curves presented in fig. 3 and 4 of Dr. Smith's paper. In addition, Dr. Wilson measured the spin- lattice relaxation time TI and, as mentioned by Dr.Smith, interpreted both line width and T1 studies to indicate that there are two distinct F19 environments in PTFE, each giving rise to a TI and a T;! (inverse line-width parameter). Thus the resonances which appear to have structure or an inflection peak were inter- preted as resulting from a superposition of two simple bell-shaped absorption curves which have, in certain temperature ranges, different widths. The strongest support for this interpretation comes from the TI measurements. At a temperature of 170" K, for example, no resolvable structure has appeared in the resonance, and the data indicate that both kinds of F19 nuclei are sufficiently " frozen in " to give the full rigid lattice second moment.However, the resonance intensity alters in a complex way when one makes a saturation measurement2 to determine T I , as indicated by the experimental curve shown in fig. 1. We Siqoal qenerator output voltaqe FIG. 1.-Saturation curves for the P 9 resonance in PTFE showing a normal type of curve (135" K) and the complex type (170" K). Measurements were made at 30 Mc/sec. suggest that the 170" K curve illustrates the saturation first of those F19 nuclei in an environment which contributes about 28 % of the low-power resonance intensity, followed at higher power by saturation of the resonance from the re- maining 72 % of the nuclei. The occurrence o f a normal curve at 135" K is explained when one plots the TI values against temperature, for one finds that the T1 of the 28 % region increases rapidly with decreasing temperature, and at 135" K, power sufficiently low to avoid saturation gives totally inadequate signal-to-noise ratios for its signal observation. Other complex saturation curves support these general conclusions, although the saturation measurements require more care in interpretation to find T1 values where the line shape is complex, one region having developed a narrower resonance.1 Wilson, Ph.D. Thesis (Washington University, St. Louis, Mo., U.S.A., 1952) ; 2 see Bloembergen, Purcell and Pound, Physic. Rev., 1948, 73, 679 for a discussion J. Polymer Sci., 1953, 10, 503. of the saturation technique for measuring TI.GENERAL DISCUSSION 253 We were able to saturate selectively either the broad line or the narrow line at temperatures where the one was still at the rigid lattice width (T2 = 0.9 X 10-5 sec) and the other had progressed to considerable narrowness (T2 = 5 X 10-5 sec).This progressive narrowing of the one line, it should be pointed out, renders the inflection peak ratio of the derivative ineffectual as a means of fixhg the percentage of F19 nuclei in each environment, since the area under the absorption curve is proportional to, for a given line-shape function, the product of the square of the width and the derivative maximum. The derivative maxima of fig. 1 are an indication of intensity at 170" K only because both lines are found to have the same width (that corresponding to a rigid lattice). The decomposition of the complex line shapes into a derivative of a broad curve and that of a narrow curve, which were then subsequently integrated as described in the published account of this work, is admittedly a somewhat arbitrary procedure.However, numerous curves at different temperatures gave results gratifyingly consistent with each other and with the 72-28 distribution obtained from fig. 1. If these procedures all measure the same quantity, we can quote 72 rt 5 % as including all experimental determinations of this quantity. On the basis of these data, we suggest that 72 % of the F19 nuclei contribute to a resonance with distinct TI and T2 against temperature curves, and the remaining F19 nuclei possess different TI and T2 against temperature curves. The further suggestion that these different fluorine environments are the crystalline and amorphous regions of the polymer is, we think, plausible, but additional work is certainly necessary to substantiate this hypothesis.Dr. N. Sheppard (Cambridge University) said : I am particularly interested in the application of nuclear magnetic resonance (n.m.r.) to the study of the structure of complex molecules. It appears to me that, even when allowance is made for the fact that the normal nuclei of carbon and oxygen atoms are not accessible by this method, n.m.r. may well be the technique of next usefulness for the study of organic molecules after the universally applied methods of infra-red and ultra-violet spectroscopy. Dr. Shoolery has given us some very good examples of this type of work. He has studied a number of cyclobutane derivatives (his compounds A, B and C) in which it is probable that there are CF2 and CH2 groups adjacent to each other.The n.m.r. spectrum shows that the two fluorine nuclei are not in chemically equivalent positions in the molecule and the spectrum due to one of these shows extra triplet fine-structure. It is suggested in the paper that this fine structure is due to the stronger interaction of this fluorine nucleus with the adjacent protons cause of non-planarity of the cyclobutane carbon skeleton, the CF2 and CH2 groups assume relative positions with respect to each other between the extremes of (1) F- - ~ ~ - - - eclipsed and staggered configurations. Looking along the connecting C--C bond below. 1s it likely that the fluorine atom one would then observe a structure as (1) which lies between the two hydrogen atoms is the one that is more strongly coupled with the protons? It may be that there are difficulties in this type of inter- pretation of the spectra which I have not appreciated. In case this is so I would like to generalize my question and to ask if, in a more favourable case such as a substituted cyclohexane molecule, it might be possible to tell from the fine structure due to interaction with neigh- bouring protons whether a F atom (or other suitable nucleus) is in an axial or of the CH2 group.It is possible that, be- / / @\\ / I H /' I I (2) F254 GENERAL DISCUSSION an equatorial position on the ring? If from high resolution n.m.r. measurements one is likely to be able to deduce in this type of manner not only the chemical nature of adjacent groups, but also their spatial relationships, the method is going to be a very powerful one for the study of molecular structure.Dr. J. N. Shoolery (Varian Associates, California) said : The cyclobutane carbon skeleton can indeed assume a non-planar configuration and the adjacent CF2 and CH2 groups very probably do assume some position other than the sym- metrical eclipsed configuration. One of the fluorine nuclei is then coupled more strongly to the protons. Since the fluorine atom (1) pictured by Dr. Sheppard lies between the hydrogens, and since experimentally the coupling appears to be about equally strong to the two hydrogens, there is a temptation to pick fluorine (1) as the more strongly coupled. However, the details of the coupling mechanism are not fully understood and such an interpretation is certainly open to question. In the general case, I would say that with sufficient experience we may eventually be able to deduce spacial relationships, at least in favourable cases, as well as the chemical nature of adjacent groups. Mr. R. P. Bell (Oxford University) said : It is of great interest that Ogg finds it necessary to invoke rhe tunnel effect in order to explain the apparent identity of the protons in AlB3H12. Calculations made about 20 years ago 1 indicated that this effect might be important in chemical reactions involving protons, and recent experimental work (Bell, Fendley and Hulett, to be published shortly) on proton and deuteron transfer in solution provides experimental support for this view. However, I am not sure that the case is proved for AIB3H12. The total frequency of interchange will be of the form zP(.i) exp (- Ej/kT), where p(.i) is the probability of tunnelling associated with the energy level ei. This will be temperature independent only if most of the transitions take place from the lowest level : this is certainly not the case in our own theoretical or experi- mental work, where the most important levels at ordinary temperatures appear to be those only a few kilocalories below the top of the barrier. This is probably also true for the problem treated by Ogg ; on the other hand, the observed spectrum could be independent of temperature even if the tunnelling rate is temperature- dependent, provided that the latter rate is great enough over the temperature range investigated. It would be of interest to know the actual rates of non- classical transfer estimated by Ogg in his problem. i 1 Bell, Proc. Roy. Soc. A , 1933, 139,466 ; 1935, 148, 241 ; 1936, 154,414.

ISSN:0366-9033    

DOI:10.1039/DF9551900246

出版商:RSC    

年代:1955

数据来源: RSC

摘要:

IV. QUADRUPOLE SPECTROSCOPY THE INTERPRETATION OF QUADRUPOLE SPECTRA BY IB. P. DAILEY Dept. of Chemistry, Columbia University, New York Received 1 1 th February, 1955 The nuclear quadrupole coupling constant, eqQ, may be obtained by the analysis of several types of radio-frequency spectroscopy. It has been pointed out that eqQ for an isolated molecule is largely determined by the number of electrons which occupy p atomic orbitals in the valence shell of the atom in which the quadrupolar nucleus is located. Several approximate relations between the quadrupole coupling constant, the amount of ionic character and the type of hybridization occurring in the bonding orbitals formed by an atom in an isolated molecule will be critically discussed. The difficult question of the role of the overlap integral in such approximate calculations has been discussed by a number of authors and their arguments will be reviewed.In a few cases the components of quadrupole coupling tensor have been determined for crystalline substances whose crystal structure is known. For several of these cases it has proved possible to determine the nature and type of intermolecular chemical bonding which occurs in these molecules. In the specially interesting case of 12, several conflicting points of view have been advanced. The bulk of the quadrupole coupling data for solids has been obtained using crystals of unknown structure. Here in order to interpret the data it is necessary to neglect solid-state effects. In spite of this, interesting information on the electronic structures of series of aliphatic and aromatic halides has been obtained from a consideration of the results of quadrupole spectra and this work will be briefly reviewed.Certain nuclei, such as C135 and Br81, have distributions of nuclear charge which have less than spherical symmetry and are said to possess a quadrupole moment. These nuclei interact with the electrons and other nuclei in a molecule or crystal to produce a variation in the electrostatic energy of the system with nuclear orientation. Transitions between these orientational energy levels give rise to hyperfine structure in molecular rotational spectra and in crystalline solids to what have been termed direct quadrupole spectra. It can be shown rigorously that the energy of orientational interaction between a nucleus having a quadrupole moment and the electric field in the molecule or crystal depends on the value of the nuclear spin I, on the nuclear quadrupole moment Q, and on the tensor quantity V V V, where V is the electrostatic potential due to all charges external to the nucleus having a quadrupole moment. A set of co-ordinate axes are usually chosen so that the symmetric tensor may be described in terms of the three components qzz = 32V/3z2, qyy = 32V/3y2 and qxx = 32V/3x2, with 1 qz2 I the largest.In the analysis of the experimental data for cases where the field is symmetric about the z axis then qxx = qVu = - 1/2qzz and the experimental results are given as values of e QqZz which is called the quadru- pole coupling constant. If the field does not have symmetry about the z-axis the data are usually reported in terms of eQqZz and an asymmetry parameter -> + 7 = (4x3 - q l d q z z .These quantities, eQqzz and 7, which may be derived from experimental data, are functions of the electrostatic field at the nucleus and can, at least in principle, 255256 INTERPRETATION OF QUADRUPOLE SPECTRA be used to study the distribution of electronic and nuclear charge in a molecule or crystal. In a study of the direct quadrupole spectra of a molecular crystal, the analysis must divide the contributions to eQqzz and 31 into those due to charges within the molecule and those due to the other charges in the crystal external to the molecule in question. If this separation can be carried out successfully then the electronic structure of both molecule and crystal can be studied.In order to relate the quadrupole coupling constants to the electronic structure of a molecule in a rigorous and precise fashion, it would be necessary to have accurate wave functions for each of the molecular electrons and to carry out a precise evaluation of the necessary integrals. This has been done for the hydrogen molecule but becomes a problem of great complexity for any larger or more complicated molecule. Townes and Dailey 1 in a semi-empirical discussion have attempted to develop a simple relation between eQq and approximate wave functions for the bonding electrons in a molecule. They point out that the magnitude fo qz2 is largely determined by the way in which the valence electrons fill the available p orbitals of lowest energy.An s orbital or an undisturbed closed shell of electrons make no contribution to the energy of nuclear orientation because of their spherical symmetry. It has also been established that the contribution due to charges associated with neighbouring atoms in a molecule or with distortions of the nonbonding closed shells of electrons can be neglected in comparison to the larger effects. In a crystal the effects due to electrostatic interaction between neighbour- iiig ions is large enough to make itself evident. In their first paper Townes and Dailey derived for the special case of a diatomic chlorine compound an expression equivalent to the following approximate equation e Q q E (- 1 - S2 + s - d)(l - i)eQq310. In deriving this equation it has been assumed that the wave function for the bonding electrons may be represented in the neighbourhood of the chlorine atom by # d 1 - s - d & rt: 2/S$s & d Z $ d . s is the amount of s character in the bonding orbital, d the amouiit of dcharacter. i is the ionicity and S2 is the value of the square of the overlap integral. The general form of this relation has not been challenged but methods of using it have differed widely.Townes and Dailey in the analysis of experimental values of quadrupole coupling constants have neglected overlap effects and the possible occurrence of d hybridization. Shatz 2 has stressed the importance of including the overlap integral in discussing (212, HC1 and CH3Cl. Gordy 3 has argued that overlap effects should be ignored and maintains that s hybridization is unimportant also.Obviously personal preference plays an important role in the task of evaluating three parameters, s, d and i from one experimentally determined constant eQq. Schatz’s calculations of eQq including overlap effects are straight-forward applications of the method of Heitler and London. S2 may be as large as 0.3 or 0.4 so that the inclusion of overlap effects should result in relatively large values of s - d. The validity of this procedure, however, is open to question. The molecular wave functions used are adequate to describe the distribution of charge in the overIap region between the two bonded atoms. But the contribution to qzz produced by a given element of charge at a distance r from the nucleus is pro- portional to l/d.Therefore it is important that the molecular wave functions accurately describe the distribution of electronic charge near the nucleus. This is a requirement that the usual approximations to molecular wave functions do not meet. Furthermore, it is required that the introduction of overlap effects accurately describe the redistribution of charge near the nucleus due to the formation of the chemical bond.B. P. DAILEY 257 It is probably significant that those workers who have made surveys of large bodies of quadrupole coupling data have been reluctant to include overlap effects. If they are included the amount of s hybridization must be increased by 20 or 30 % and the resulting values begin to seem implausibly large. Considerations of promotional energy argue against the presence of large amounts of s character and presumably influence Gordy in minimizing it or rejecting it altogether.Certain quadrupole coupling data are available which make it seem probable that the values of the s hybridization obtained, neglecting overlap effects, are only slightly smaller than the correct values. Dailey and Townes4 assume that Cl, Hr and I bonds have 15 % s character, when the halogen is bonded to an atom which is more electropositive than the halogen by as much as 0.25 unit, in their discussion of the quadrupole coupling data for diatomic halides. This assumption is in good agreement with the values of 10 % s character for the As bonding orbitals in AsC13 and 15 % s character for the s bonding orbitals in H2S found by an analysis of quadrupole coupling data which does not depend on the presence or absence of overlap effects.Gordy 5 has in several places argued the merits of his simple relation between ionicity and the quadrupole coupling constant in which s character is neglected completely. Using it he obtains as the relation between ionic character and electronegativity difference for a bond A-B ionic character = 3 I X, - X, I . The values of the s character found for AsC13 and H2S argue as strongly against the complete absence of s character as they do against the excessively large values found in Schatz’s calculations. Dailey and Townes 4 have derived an S-shaped curve for the relation between ionicity and electronegativity differences. Gordy s straight line relationship is a fairly good rough approximation to the S-shaped curve over most of the range of electronegativity differences.However, at the top of the curve, in the region I AX1 -2, the large number of points available for alkali halides indicates a definite deviation from a simple linear relationship. In the middle of the curve near 1 AX I -- 1, points for the molecules FC1 and FBr show a considerable differ- ence between the two curves. The role of d-hybridization in the formation of halogen bonds is difficult to evaluate on the basis of quadrupole data. However, since the factor s - d is the one which actually enters into the equation for the quadrupole coupling constant, the preceding discussion of an upper limit to the s character would seem to limit d character to 5 % or less.In attempting to interpret the quadrupole coupling data obtained from the direct quadrupole spectra of crystalline substances, the uncertainty of the con- tribution of solid state effects is added to the uncertainties attending the attempt to unravel i, s and d for an isolated molecule. For the majority of solid substances whose crystal structures have not been determined the analysis is nearly impossible. The only practical recourse is to try to establish trends in the data for a series of similar substances and assume that solid state effects can be neglected. In a number of interesting cases fortunately the crystal structure data are available. Some of these have been discussed by Townes and Dailey6 and by Schawlow.7 Most substances which have been measured in both the gaseous and solid state, experience an increase in ionic character upon the formation of the crystal.An exceptional case is ICN for which the quadrupole data indicate lower ionicity in the solid. This effect is apparently caused by the presence of the resonant structure I=&=N. An additional factor of interest in this molecule is the presence of linear polymeric chains of molecules having the struc- ture -I-C=N-I-kN-. The existence of the =N-I- bond is in- dicated by the unusually close approach of these two atoms in the crystal, + - + - + I258 INTERPRETATION OF QUADRUPOLB SPECTRA The pure quadrupolc spectrum of 12 is of spccial interest bccause a rather large valuc of the asymmetric parameter 7 is found.Tomes and Dailey6 attempted to explain this asymmetry as arising from the formation of weak inter- molecular bonds in the solid. Thc known crystal structurc of iodine supports this hypothesis quite well since in solid iodine thc molcculcs are arrangcd in planar sheets with each I atom having two ncighbours at a distance of only 3.54 8, as well as its molecular partner at a distance of 2.70A. 3-54,4 is considcrably shoi ter than the sum of two van dcr Waals' radii and 2.70 A is slightly longcr than 2.67 A, the inteinuclcar distance in the gaseous 12 molecule. This analysis of the quadrupole coupling data for molecular iodinc has been criticizcd by Robinson, Dehmelt and Gordy 8 and by Stevens.9 Robinson, Dehmelt and Gordy point out that the s-p hybrid bonds suggested by Towncs and Dailcy 6 make it difficult to undcrstand thc formation of planar sheets of 12 molecules in the crystal.If it is assumed that the bonding orbitals are rcsonancc hybrids formed from a 5.~5~145~1 configuration the planar arrangement can bc morc naturally explained. Stevens' interpretation of the quadrupole coupling data is rathcr different in that, while using d hybridization, he finds it possible by a rather unconventional at gument to account for thc asymmetry without using intermolecular bonds. Tn this picture, thc close approach of certain of thc iodine atoms is accounted for by a " lock and l e y " fitting together of lobes of the clcctronic charge clouds. A number of interesting studics have been made of series of molcculcs whose crystal structure is not known.It is usually assumed in interpreting the rcsults of thcsc investigations that the solid state effects arc not large and do not vary greatly from molecule to moleculc in a scrics of similar moleculcs. The cvidcnce so far accumulated bearing 6n athis point seems to indicatc that qualitative conclusions drawn from a considcration of solid state eQq valucs are equally valid whcn applied to quadrupolc coupling data obtained for gas molccules. For example, Livingston,lo studying the dircct quadrupolc spcctra of some substituted methanes and other aliphatic chlorine compounds, arrived at thc following conclusions. The replaccmcnt of a H in one of these compounds by a more clcctroncgativc atom such as a halogen reduced thc ionicity of thc C-Cl bond.Thc replaccmcnt ofa H with thc more electropositivc CH3 group increased the ionicity of the C-Cl bond. Thc replacement of a H atom by F causes structures such as F-C=CI 1- to becomc important. Thcsc generalizations also hold true for the small number of compounds in this series whosc quadrupolc coupling constants have bccn obtained from thc analysis of microwavc rotational spectra. While all four molccules in the series CH3C1, CzHsCI, CH3Br, CzHsBr show an increase in ionic charactcr upon formation of the crystal there are casily measiirable diffcrenccs in thc amount of the change. For CH3Cl the changc is 8.5 %, for CH3Br it is 8.0 "/;I, for C21-IsCI it is 4.6 "/o and for C2HsBr it is 7 "/;I. With the use of a ccrtain amount of caution the neglect of solid state effects in the interpretation of eQqzz derived from direct quadrupolc spcctroscopy is apparently justified.Schawlow 6 has carried out a similar study of the group 4 tctrahalides, among other compounds. The analysis is complicated hcre by thc prescnce of resonant structures with double bonds to thc halogcns. Howevcr, using bond distance data to supplcment thc quadr upole coupling data, Schawlow obtaincd a rather reasonable steady increasc in ionic character in going from carbon to tin with a corrcsponding decrease in double-bond charactcr from silicon to tin. Carbon having no d orbitals in the valcnce shell, exhibits no double bond character. A number of interesting studies of quadrupole coupling have been made which use the experimentally determincd asymmetry paramcter to cvaluatc the importance of structures having double bonds to thc halogen.The first of these studies was that of Bragg and Goldstein 11 on vinyl chloride which foundB . P . DAILEY 259 approximately 5 % double-bond character in the C-Cl bond. This value is quite significantly lower than the value of 15 % indicated by the bond length. Berson 12 has discussed systems of this kind using molecular orbital theory to relate the electron loss to the halogen coulomb integral, the carbon-halogen resonance integral and the wave functions and energies of the system to which the halogen atom is bonded. Duchesne and Monfils 13 suggest that the increase in the quadrupole coupling constant in going from m-dichlorobenzene to o-dichlorobenzene is due to decreased double-bond character in the C-CI bonds of the oriho compound because of its lack of phanarity or twisting by 18".Berson makes a strong case, however, for a much smaller effect due to double-bond character and suggests that an inductive effect is responsible for the change in eQq. Meal 14 established a correlation between e Qq values for substiiutcd chloro- benzenes and Hammett's substituent parameter 0. 0 is defined by means of the equation log (k / k") = op where k and k" are the rate or equilibrium constants for the aromatic compound and its substituted derivative. p is a constant characteristic of the reaction. Jaffe 15 has shown that G values can be correlated with electron densities calculated using molecular orbital methods. This conclusion is supported by the correlation Gutowsky and co-workers 16 obtained between G values and chemical shifts in the fluorine magnetic resonances for substituted fluoro benzenes.Studies of the Zeeman effect 17 in direct quadrupole spectroscopy have been made in several laboratories. A small external magnetic field splits each line in the direct quadrupole spectrum into either two or four components whose splitting depends on the relative orientations of the magnetic field and the electric field gradient at the nucleus giving rise to the quadrupole interaction. In the usual polycrystalline sample the result is to smear out the resonance over a range of frequencies. This effect is frequently used to distinguish between spurious and authentic resonances. fn work with a single crystal, however, it is possible under favourable circum- stances, to observe distinct and different Zeeman spectra for each structurally different atom giving rise to a direct quadrupole spectrum.Information on the crystal structure of the sample can be obtained by the analysis of a series of direct quadrupole Zeeman spectra for selected orientations of the magnetic field. Another important feature of the analysis of the direct quadrupole Zeeman spectra of C1 and Br compounds is the possibility of obtaining values of the asymmetry parameter 7. The direct quadrupole resonant frequencies of C1 and Br do not involve this quantity in the absence of the magnetic field. As indicated above much important information about the pattern of chemical bonds in a molecule can be obtained from the analysis of values of the asymmetry parameter.Additional solid-state information can be obtained from the study of the temperature dependence of the nuclear quadrupole resonant frequencies. These have been related to torsional motions in the crystal by Bayer.18 The abrupt changes in resonant frequency observed for certain crystals can be correlated with phase changes. The changes in molecular orientation for one such change in p-dichlorobenzene have been studied by Lutz19 using the Zeeman effect for additional help. To summarize, there is much potentially valuable information on the electronic structure of molecules and on crystal structure which can be made available by the analysis of quadrupole spectra. To some extent, however, it is fair to say that the experimentalists have outstripped the theoretician since a number of aspects of the interpretation of quadrupole spectra are still rather poorly understood.260 ELECTRIC FIELD IN HCN 1 Townes and Dailey, J. Chem. Physics, 1949, 17, 782. 2 Shatz, J. Chem. Physics, 1954,22, 695 ; 1954, 22,755 ; 1954, 22, 1974. 3 Gordy, J. Chem. Physics, 1954, 22, 1470. 4 Dailey and Townes, J. Chem. Physics (to be published). 5 Gordy, J . Chem. Physics, 1951,19,792. Gordy, Smith and Trambarulo, Microwave 6 Townes and Dailey, J. Chem. Physics, 1952, 20, 35. 7 Schawlow, J. Chem. Physics, 1954,22, 1211. 8 Robinson, Dehmelt and Gordy, J. Chem. Physics, 1954,22,511. 9 Stevens, Nuclear Quadrupole Resonance and Crystal Structure of Solid Iodine (Cruft Laboratory, Harvard University, Cambridge, Mass., Technical Report No. 197, 1954). Spectroscopy (John Wiley and Sons, Inc., New York, 1953), p. 272. 10 Livingston, J. Chem. Physics, 1951, 19, 1613 ; 1952, 20,496. 11 Bragg and Goldstein, Physic. Rev., 1949, 75, 1453. 12 Berson, J. Chem. Physics, 1954, 22,2078. 13 Duchesne and Monfils, J. Chem. Physics, 1954, 22, 562. 14 Meal, J. Amer. Chem. SOC., 1952, 74, 6121. 15 Jaffe, J. Chem. Physics, 1952, 20, 279. 16 Gutowsky, McCall, McGarvey and Meyer, J. Chem. Physics, 1951, 19, 1328. 17 Dean, Physic. Rev., 1954,96, 1053. 18 Bayer, 2. Physik, 1951, 130, 227. ZQLutz, J. Chem. Physics, 1954, 22, 1618.

ISSN:0366-9033    

DOI:10.1039/DF9551900255

出版商:RSC    

年代:1955

数据来源: RSC

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260 ELECTRIC FIELD IN HCN AN ANALYSIS OF THE GRADIENT OF THE ELECTRIC FIELD IN HCN BY ANDRE BASSOMPIERRE Laboratoire d’Electronique et de Radioklectricite Received 31st January, 1955 Numerous data from nuclear quadrupole resonance experiments and Hertzian spectro- scopical techniques are now available on nuclear quadrupole couplings. The chief difficulty in obtaining the quadrupole moments lies in our ignorance of the electrical gradients acting on the nuclear quadrupole in molecules and solids. We have 1 tried here to solve this problem in a case which is attractive in its relative simplicity, the molecule HCN. Evaluation of the gradient of the electric field, to which the nucleus of nitrogen is submitted, requires a rather accurate knowledge of the electronic structure. Ordinary valence schemes are not sufficient for this purpose.For instance, they are not able to provide information on the perturbations of inner atomic shells. Such perturbations, which have small effects on the usual properties of molecules, cannot be neglected here, since they destroy the spherical symmetry of these shells. This is especially important for nitrogen, since the 2s atomic electrons give a lone pair coupling with the quadrupolar moment of the nucleus which is quite considerable. The method of self-consistent field 2 extended to molecules by Roothaan, provides a convenient way for obtaining a suitable electronic wave function. This method being now well known, we shall give only a brief account of it. The molecule HCN is linear and the intemuclear distances 3 are H-C = 1*064& C-N = 1*156& The axis Oz is directed from H to N.A N D R ~ BASSOMPIERRE 2 6 1 We consider an antisymmetric normalized wave function for the fourteen elect- rons of the molecule of the form where the #i are an orthonormal system of space functions and a, p the two functions of electronic spin.P is an operator which permutes the electrons, designated by upper indices, and p its parity. We suppose that the functions +f are developed in an arbitrary subspace X, described by functions X,, +i = xqcqi- 4 The function $ is now determined only by the parameters Cgi. The best values of these parameters may be obtained by searching for those for which the electronic energy is a minimum. For this purpose, we use the complete Hamiltonkin in- cluding all electronic interactions ; we neglect only the spin orbit coupling, which gives a fine structure.It is now easy to show that the unknown parameters C g j , written as column matrices Ci, verify the equation S-lFCi = EiCj, where F and S are the following matrices : The ej are scalars whose values (with change of sign) give the energies of vertical ionization, that is to say, before disturbances of nuclei and other electrons of the molecule occurs. For solving eqn. (1) we must first choose a sub-space X. If it were complete, the equation would be equivalent to Fock's equation. We have taken as a basis eleven real atomic functions : ( 1 s ) C ~ (1s)N7 (1s)H7 (2s>C7 (2pz)C7 (2s)N, (2pZ)N, (2pX)G (2pX)N, (2py)C7 (2p,)N The indices designate the corresponding nuclei.We shall take the functions xq in the order written above. We have used the atomic functions of Duncanson and Coulson.4 These functions are orthonormal for each atom, and so the base x is not orthogonal on the whole. The atomic functions are used only as a vectorial basis which permits one to introduce easily the singularities in space constituted by the nuclei and also the correct symmetry conditions around these singularities. The introduction of these functions into the equation allows the evaluation of many integrals. In spite of all the studies which have been made by many authors, their evaluation remains tedious, especially because the molecule is heteronuclear. We have tried to calculate each of them as carefully as possible; the approximation introduced in these calculations is probably the main limitation to the precision of our wave function.When these integrations have been performed, it is possible to solve the equation. It has the form of an ordinary eigenvector equation of the eleventh order, and moreover, its operator S-1F is a quadratic function of some of the eigenvectors Ci (we count those corresponding to effectively filled levels only). Such an equation may be solved by iteration. Taking a set of vectors Ci we form262 ELECTRIC FIELD I N HCN the operator S-1Fand then solve the eigenvector equation, and so on, until the field becomes self-consistent. The order of the equation may be reduced by symmetry arguments, since the functions s, p z and px, py belong to different irreducible representations of the group C,, of the molecule.In this way we get one equation of seventh order and two of second order. In addition, a simple perturbation calculation shows that 1s states are not appreciably mixed with the other states. Finally, the cquation is reduced to a set of equations whose orders are respectively 1, 1, 5, 2, 2. The levels which are filled are only those corresponding to the fin-st-order equations, the three lowest levels of the fifth order equation and also the lowest one of each of the two last equations. We shall give to these levels respectively the numbers 1, 2, 3, 4, 5, 8, 10 (according to the preceding notations these are the second indices in the parameters Cpi). We have solved the fifth order eigenvectors equations using the excellent method of M a y ~ t .~ At the tenth iteration the field becomes self-consistent. The con- vergence is alternate ; probably it would be possible to accelerate the rate of con- vergence by taking mean values of the results of two preceding iterations. We obtained C33 = 0.165, c34 = 0.002, c35 =- 0.159, c88 = c10, 10 = 0.575, C43 = 0.439, c44 = 0.001, c45 = 1.200, c98 == c11, 10 == 0.657, C53 =- 0.388, C54 = 0.267, C55 = 0,189, C11 = C22 = 1. c63 =- 0.680, c@ = 0.016, c65 =- 0.037 C73 = 0.324, C74 =: 1.042 C75 = 0.484, (the other parameters are zero). Kusch, Hustrulid and Tate 6 have found experimentally that the energies for vertical ionization of levels 8 and 5 are equal to 13-7 and 26-3 eV. We have obtained for these levels 17.3 and 26-4eV.The evaluation of the first of these levels is apparently less satisfactory than the second one mainly because of a differentiation effect. In fact, the eighth iteration gave for the level 8 an energy of 14.1 eV in better agreement with the experimental result 13.7. On the other hand the corresponding parameters Cgg and c98, given by the eighth iteration, were very close to those of the last iteration (c88 = clo, 10 = 0.569, cgg = c11,10 = 0.662). So we may consider that the agreement with experiment is good. With the preceding wave function it is now possible to calculate the gradient of the electric field acting on the nucleus of nitrogen. The molecule having a cylindrical symmetry around the axis Oz, we need only to calculate the mean value of b2V/3z2. The part qe of this due to the electrons may be written as the spherical co-ordinates being centred at the N nucleus.For evaluating each of these integrals, we have developed the function X, and X4 in spherical harmonics around the N nucleus. This may be achieved with the help of some of CouBson's formulae 7 using Bessel functions of half order and imaginary argument. We have calculated the radial integrals by numerical integration. Seeking a high precision we were obliged to integrate rather far from the nucleus, more than 1 A ; this proves that, if the main part of the quadrupolar coupling comes from electrons surrounding the nucleus, all the electrons of the molecule must, in fact, be considered. At a distance from the nucleus of the order of h/mc, our wave function is no longer valid due to the relativistic perturbation, which introduces a spin-orbit coupling.It is difficult to obtain information on the electronic structure inside this sphere; nevertheless we think that the relative error is rather small. We have still to consider the gradient of the electric field due to the nuclei H and C. For its evaluation, we have taken account of the vibrations of the molecule.ANDRE BASSOMPIERRE 263 A study of the normal modes of vibration 8 shows that at ordinary temperature we need only to take an average value over zero-point rotations of the H atom. It was possible to neglect the influence of these vibrations on electrons, since the electrons being mainly concentrated on the CN group are not appreciably per- turbed by small rotations of the H atom.Finally we obtain the gradient q of the total electric field equal to q = - (2-729)e (the first Bohr radius being the unit of length). Simmons, Anderson and Gordy 9 have found experimentally that the nuclear quadrupole coupling eqQ is -4.58 Mc/s. From this, we may infer that the nuclear quadrupolar moment of N14 is Q = (0.0071) x 10-24cm2. It is quite difficult to state the accuracy of this result. We hope to check it by calculations on other molecules. We intend to try and extend the preceding results to give an approximate understanding of the electronic structure of solids such as ICN and BrCN. 1 Bassompierre, J. Chim. Phys., 1954,51,614 ; Compt. rend., 1954,239,1298 ; 1955,17. 2 Roothaan, Rev. Mod. Physics, 1950, 23, 69. 3 Simmon, Anderson and Gordy, Physic. Rev., 1950 77, 77. Nethercot, Klein and Townes, Physic. Rev., 1952, 86, 798L. 4Duncanson and Coulson, Proc. Roy. SOC. Edin., 1944, 62, 37. 5 Mayot, Ann. Astrophys., 1950, 13,282. 6 Kusch, Hustrulid, and Tate, Physic. Rev., 1937, 52, 840. 7 Coulson, Proc. Cumb. Phil. Soc., 1942, 38, 210. 8 Penney and Sutherland, Proc. Roy. SOC. A, 1936, 156, 654. 9 Simmons, Anderson and Gordy, Physic. Rev., 1950,77, 77.

ISSN:0366-9033    

DOI:10.1039/DF9551900260

出版商:RSC    

年代:1955

数据来源: RSC

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ANDRE BASSOMPIERRE 263 NUCLEAR QUADWUPOLE RESONANCE IN SOLIDS * BY H. G. DEHMELT Dept. of Physics, Duke University, Durham, N.C., U S A . Received 8th February, 1955 Nuclear quadrupole resonance-also called pure electric quadrupole spectra-is a recently developed branch of radio-frequency spectroscopy. It is concerned with mag- netic resonance absorption in crystals. This absorption is due to reorientation of the non-spherical atomic nuclei against crystalline electric fields. Related phenomena in free molecules are briefly discussed. This is followed by a treatment of the electrostatic interaction of a non-spherical n~icleus with an axially symmetric electric field. Such a field is found, e.g. in crystalline Clz, a crystal whose structural units are very nearly undisturbed Clz molecules.Electrostatic torques are shown to exist, which cause a precession of the nuclear angular momenta around the molecular axes. This motion is accompanied by a precession of the magnetic and electric moments of the nuclei, which may interact with alternating electromagnetic fields of the proper frequency. Thus one arrives at the transition mechanism between energy levels which are derived from the corresponding Hamiltonian. Then some experimental aspects are described and examples of absorption lines are given. The significance of the experimental information obtained, namely, the quadrupole coupling constant eQq, and the asymmetry parameter is pointed out. The fundamental point is emphasized that these quantities are character- istic of the electron density distribution around a single nucleus which is closely related to the bonding of the corresponding atom.The advantages and disadvantages of quadrupole resonance studies are discussed. It is seen that the class of dipole-less E = 1 (4xx - 4yU)/qzz I 9 * supported by the Office of Ordnance Research.264 RESONANCE IN SOLIDS molecules which exhibits no rotational spectra is well suited for this method, as inter- actions between neighbouring molecules are small here. This class comprises all element molecules and highly symmetrical molecules which are especially accessible to structural analysis. The recent determinations of the quadrupole couplings for the halogen mole- cules Clz, Br2 and 12-important because of their simplicity-contributed materially to the understanding of their structure.Furthermore, a multitude of molecules, molecular addition compounds, molecular ions as well as crystals with covalently bonded lattices, which can be obtained in the gaseous state only with difficulty or not at all, are most conveniently studied by quadrupole resonance and typical cases are given. Finally, all atoms investigated by this method are reviewed. 1. INTRODUCTION Nuclear quadrupole resonance (NQR), a recently developed 1-4 branch of radio-frequency spectroscopy, has already contributed significant information on molecular and crystalline structure. Experimentally, it is concerned with the detection of radio-frequency magnetic resonance absorption in suitable crystals In this and many other respects it is similar to nuclear magnetic resonance.(NM39.5~6 However, while jn nuclear magnetic resonance one has to do with transitions between levels corresponding to different orientations of the nuclear magnetic moments against a static field applied from the outside, no such field is needed in NQR. The place of the magnetic field is taken by an inhomogeneous (axially symmetric) electric field generated by the charge cloud of the (diatomic) molecule containing the nucleus. This electric field now interacts with the electric quadrupole moment of the nucleus instead of its magnetic dipole moment. The quadrupole moment measures the deviation from spherical symmetry of the nuclear charge distribution. Again, different relative orientations of nuclear axis against field axis correspond to different energy levels. For free molecules such nuclear quadrupole effects have been observed earlier in molecular beam resonance experiments 7 and in rotational absorption spectra in the microwave region,8 where they lead to a hyperfine structure of the lines.2. MOTION AND ENERGY HGENVALUES IN A QUADRUPOLE SYSTEM 99 lo We now consider in more detail a system which consists of a non-spherical nucleus in a diatomic molecule forming part of a molecular crystal, to be specific, one C1 nucleus in solid C12. In such a crystal the molecules essentially retain their identity and the electrostatic field generated at the site of the CI nucleus is practically determined by the molecular electron cloud alone. Therefore it is very nearly axially symmetric, even though the surroundings in the lattice have lower symmetry.We introduce a frame of reference xyz fixed in space (see fig. l), the z-axis coinciding with the molecular axis and in the point of origin the 61 nucleus under consideration, which in fig. 1 and 2 is represented as a highly en- larged ellipsoid. Further, a second frame x‘, z’, z’ with z’ fixed along the nuclear axis is chosen. Since both nucleus and surrounding molecular field q are axially symmetric, the electrostatic interaction energy can only depend on the angle 8 between nuclear and molecular axis. To simplify the calculation we therefore let the y and y’ axes fall together. Quantity PN denotes the charge distribution in the nucleus. If the potential q as function of x‘y’z’ is expanded around the origin.W takes the formH. G . DEHMELT 265 The first constant term in this expression is of no interest to us. The following (dipole) terms containing the first derivatives of q vanish, as the integrals are zero because of the symmetry of the nucleus. The (quadrupole) terms with the second derivatives of q are the ones of interest, while higher terms can be neglected in excellent approximation as proven by the experiments. Since the integrals 1 pNx’2dY’ . . . constitute the components of a tensor-henceforth abbreviated eQxpxt, eQ,t,t . . .-whose principal axes coincide with x’, y‘, z‘, no mixed terms C’2 FIG. I‘ - X 1 .-Non-spherical C1 nucleus in C12 molecule. I FIG. 2.-Precession of nuclear moments I, p, eQ around symmetry axis of molecular electric field. Q,t,t, Q,t,#, Qytzt appear in formula (2.2).Without referring to their tensor character, it can also be seen directly that these integrals ‘y‘dV . . . vanish for the assumed symmetry of the nucleus. We now make use of the Laplace equation qxtx’ + qytyt + qZt2t = 0 holding at the site of the nucleus. With Q,t,t I- &,~ because of the axial symmetry we obtain for the quadrupole inter- action energy, s p x since The integral ~~(32’2 - r2)dV’ defines an inherent property of the nucleus and is customarily called “ the ” nuclear quadrupole moment and denoted by eQ. It measures the deviation from spherical symmetry of the nuclear charge cloud. A nucleus elongated with respect to its axis has a positive, a flattened nucleus a negative quadrupole moment. For a spherical nucleus eQ vanishes of course.lr*266 RESONANCE IN SOLIDS Quantity q2y in eqn. (2.4) can be expressed as with qxx = qYy = -- +qZz this reduces to q2rzt = qxx sin2 8 -I- qZ2 C O S ~ 8, (2.5) Here qZ2 represents an inherent molecular quantity which, because of the axial symmetry, completely suffices to describe the electric field at the site of the nucleus. Finally we have obtained for the classical quadrupole interaction energy the formula Because of the dependence of the energy WQ on 8 there must result a torque, which for the appropriate sign of eQqz2 tends to align the nuclear and the molecular axes. As in the Zeeman effect, the nuclear angular momentum I, whose direction coincides with the figure axis of the nucleus, will respond to this torque by a pre- cession around the z-axis (see fig.2). However, while in the Zeeman effect the precession frequency is constant, independent of 8, we find for the quadrupole system a precession which slows down with growing 8, comes to a standstill for 8 = ~ / 2 , reverses its sense and between 8 = 4 2 and T again increases in frequency. Quantum mechanically this is reflected in the spacing of the energy levels, which is not equidistant as in the Zeeman effect, but increases with growing values of the magnetic quantum number m. This precession of the angular momentum --compare fig. 2-will also be accompanied by rotating components of the magnetic dipole p, as well as the electric quadrupole moment eQ of the nucleus, which in the classical picture must lead to the respective radiations.It can be seen, however, that only the rotating magnetic dipole experiences any appreciable coupling with an electromagnetic radiation field of the appropriate low frequency of a few megacycles while the coupling of the electric quadrupole is many orders of magnitude smaller. Now we shall try to derive the quantum-mechanical energy eigenvalues of our quadrupole system-abbreviated QS. We note that the z component of the angular momentum Iz is a constant of the motion-compare fig. 2-whose eigen- values m therefore can be used to label the energy eigenvalues of the QS. By substituting the operators Iz/I for cos 8 in the classical expression (2.7) we obtain the Hamiltonian from which follow the energy eigenvalues H = +eQ*qzz(3I,2 - P)/X2, (2.8) In eqn. (2.9), Q has been marked with an asterisk in order to show that in this formula it has been evaluated with respect to the figure axis of the nucleus.This deviates somewhat from the customary definition of the nuclear quadrupole moment Q, which is to be taken for the aligned state m = I of the nucleus with respect to the axis of alignment z. Even though quantum-mechanically complete alignment is not possible, the charge distribution pm is axially symmetric with respect to the z axis, the axis of the electric field. This is due to the fact that Pm = represents an average of the nuclear charge distribution over the motion which has not completely ceased even for rn = I. In this case the interaction energy can easily be written down independent of eqn. (2.9) using eqn.(2.4) for 8 = 0 and substituting pm = I for pN. Thus we obtain for the energy eigenvalue Em =iE I : n Here the integral is identical with the customary eQ. Comparing this with E' from eqn. (2.9) we find Q* == 2Q(I + 1)/(2I - 1). (2.1 1)H . G . DEHMELT 267 Since the square of the total nuclear angular momentum is a constant of the system, we can substitute for the operator 12 in the denominator of eqn. (2.8) its eigenvalue I ( Z 4 l), and using eqn. (2.1 1) we obtain from eqn. (2.8) and (2.9) the final expressions H = eQqzz(31z* - 12)/4(21- 1)I, (2.12) and Em = eQqZz[3m2 _- I(I -t- 1)]/4(21- 1)I. (2.13) The energy levels following from eqn. (2.13) are sketched in fig. 3 for integer and half-integer I values. For I < the quadrupole interaction energy vanishes.This follows from formula (2.11) for I = 4 while for I = 0 the nuclear charge distributing in eqn. (2.10) becomes spherically symmetric which reduces the integral to zero. In case the axial symmetry of the electric field is only approximate, an asymmetry parameter may be defined : E = I (4xx - sj?v>/szz I’ (2.14) This asymmetry causes, as a perturbation calculation shows, a first-order splitting only of the degenerate m = f 1 levels, while all other levels experience only small second-order shifts.11-13 In all cases E can be determined from the observed spectra, provided a Zeeman effect is produced for I = z.22 I nteger I m I I I I I 7- 5 2 2 + 3 + l C 0 4 b 4 FIG. 3.-Energy levels arising from the interaction of a quadrupole nucleus with an axially symmetric electric field. The diagram is drawn for eQqzz > 0, the unit of energy being 3eQqzz/(41 - 1).3. TRANSITIONS AND R.F. SUSCEPTIBILITY In order to bring about transitions between these energy levels which we have just described, we apply a magnetic r.f. field perpendicular to the z-axis whose frequency corresponds to the energy difference between two consecutive levels (selection rule Am = & 1). The action of the magnetic r.f. field can be under- stood best by decomposing it in two oppositely rotating components. While the component whose sense of rotation is identical with that of the nuclear pre- cession in the classical picture exerts a steady torque on the nuclear magnetic moment which changes the angle of the precession cone, the effects of the other component average out. The energy which the spin system is able to extract from268 RESONANCE I N SOLIDS the r.f.field in this way is then dissipated into the crystal lattice through relaxation processes. This absorption is conveniently described by an imaginary r.f. sus- ceptibility of the sample whose magnitude is given by I ( I + 1) - mm' v (3.1) In this formula NO denotes the number of nuclei per cm3 and p their magnetic moment. The frequency of the absorption line and its width between half-power points are given by v and Av. The temperature Tenters, since only half of the small surplus in the lower of the Boltzmann populated levels can be lifted up in the higher one before stimulated emission completely cancels absorption. The ratio of 2~ times the r.f.energy stored in the volume of the sample to the energy ab- sorbed per cycle, which is commonly called the Q of the sample is connected with XI by the relation Here x' has been given for a polycrystalline material, in which the axes of the molecular electrical fields are randomly oriented with respect to the linear r.f. field. 2 N0P2 "= 3 (21 -t- 1)kT .-I2 &- xa = 114nQ. (3 .a Gauss 0 200 kc FIG. 4.-NQR absorption line due to the 1271 nuclei in Snb (from ref. (16)). 50 cis capacitive frequency modulation and oscilloscopic display was used. The two lower traces show the Zeeman pattern for both of the occurring tran- sitions. The frequency scale for all three traces is the same. It might be emphasized that no single crystals are required in NQR which greatly adds to the convenience of such experiments. 4.EXPERIMENTAL ASPECTS Exactly as in NMR, NQR absorption lines are detected by making the sample the core of a r.f. coil which is part of a tank circuit and displaying in some way the reduction of the Q of this circuit when it is tuned over an absorption line. However, as opposed to NMR where it is possible to keep the frequency constatlt and shift the energy levels by varying the static magnetic field, in NQR experiments the spectro- meter must have a sufficiently wide frequency range. This calls for simple and easily tunable circuits. The effects to be detected are not strong and can easily be lost in the noise generated in the tubes and other parts of the detection circuit. In a good spectrometer the noise is essentially only the thermal noise of the tank circuit containing the sample.However, at the same time the circuit should be able to develop a r.f. power as high as possible, since the absorbed power is pro- portional to the r.f. power incident upon the sample. While regenerative oscillators 149 15 are quite satisfactory at low power levels, they do not allow the generation of higher r.f. powers without generating an excessive amount of tube noise at the same time so that nothing in signal-to-noise ratio can be gained in this way. In NMR this is not too serious, as the early onset of saturation in the small samples usually employable forbids the use of higher power anyway. A different situation is encountered in NQR where in many cases saturation canH. G .DEHMELT 269 easily be avoided by the use of large samples or need not be feared because short relaxation times are to be expected. Here the use of super-regenerative oscil- lators 1617 has proven especially advantageous, The obvious shortcomings of these circuits are not serious as long as the experimental aim is not the exact measurement of line shapes or relaxation times, but highest sensitivity in detecting unknown lines. Higher sensitivity of course can be achieved by reducing the band width of the amplifying circuits in order to suppress the noise. While capacitative modulation can also be used in conjunction with narrow band recording circuits, H e u p t o i g n o l FIG. 5.-Recording of the NQR absorption line in polycrystalline B(CH& at 2589.0 kc/s (from ref.(18)). The line corresponds to the transitions rn = f 2 -+ & 3 of the 10B isotope. 30 c/s Zeeman modulation and a lock-in amplifier employing a time constant of 40 sec were used. if a few precautions are taken, it appears more satisfactory to use Zeeman modulation 18919 of the nuclei. With this type of modulation the lines in a poly- crystalline sample are periodically smeared out by zero based field pulses of about 100 gauss. No previous knowledge of the line width is necessary to obtain optimum modulation efficiency, and response to spurious signals is greatly reduced also. 5. DISCUSSION OF mFORMATION OBTAINABLE FROM NQR EXPERIMENTS As frequencies in the r.f. region can easily be measured with accuracies of 10-5 or better, the coupling constants eQqzz can be obtained from NQR spectra with comparable accuracy, provided the asymmetry E is known.For nuclei with spins other than I = 3/2 this parameter can also be deduced from the spectrum with considerable accuracy. Quite generally these two quantities provide information on the shape and density of the electron cloud in the neighbowhood270 RESONANCE IN SOLIDS of a single (quadrupole) nucleus, as (in the axially symmetric case) qzz can be expressed as (5.1) containing the electron-nucleus distance R in the inverse cube. As E and eQqzz are closely related to the electron-configurations around a single quadrupole atom which, in turn, is characteristic of the state of bonding of this atom20121 these data frequently turn out to be of a more fundamental character than other molecular quantities like dipole moments, bond distances and force constants which are of a more complex nature involving two or more atoms. How well the NQR data can be interpreted now depends naturally upon how well the make-up of the whole crystal, which contains the quadrupole atoms, can be understood.Also in order to realize the full value of NQR data the corres- ponding couplings for the free atoms should be known which, however, is not the case always. Purely practical reasons appear to limit NQR experiments to crystals in which the atoms of interest are covalently bonded to one or more neighbour-atoms, because only in these cases the NQR frequencies are likely to be high enough to allow their observation. The small quadrupole effects occurring for atomic ions with inert gas configurations are usually more conveniently observed with NMR techniques? We shall now try to illustrate, with the help of some selected cases, to what kind of problems NQR has been applied, and to what use the experimental results may be put.One might begin with the rather general type of information which the experiments provide, like the number and symmetry of non-equivalent lattice sites in a crystal 16 which are occupied by the same atomic species but generally do not have identical qzz values. Furthermore, when single crystals are available the a m a n effect 11-13 of NQR lines can be used in determining the direction of qzz = J Pelectron ~ - 3 (3 ~ 0 ~ 2 8 - 1 ) d ~ P 1/2 *A 3/2 f 3/2 -+k 512 FIG. 6.-NQR spectrum of 1271 in Sn14. n - The doublet structure is explained by the occurrence of the two non- equivalent lattice sites I, II.The relative population and the local symmetry of these sites can be determined as 1 : 3 from the in- tensities and as trigonal or higher for I and lower than trigonal for I1 203.00 2 0 4 . 0 0 405.95 4 0 8 . 0 0 from the frequency ratios of the two ( I = 5/2) transitions f 112 -++ rt: 312 and rt: 312 +-+ f 512. II I I I I _GL Frequency (m c/sec) covalent bonds with respect to the lattice,16,22 as it depends strongly on the angle between the external magnetic field and the axes of the molecular electric field gradients. In quite a few cases these things can be learned comparatively easily from the NQR spectrum and then be used to simplify and corroborate the X-ray analysis of crystal structures.23 A related application is the study of phase transi- tions 24.34 by observing the NQR spectrum while the temperature is changed. We shall now proceed to cases where it is possible to make use of the coupling constants measured in the solid in a more refined way by comparing them with the corresponding couplings for the free atoms.One class of crystals interesting in this respect is that formed by the dipole-less element molecules and other highly symmetric molecules as far as they form molecular crystals held together only by weak van der Waals’ forces. The very fact that these molecules have no dipole moments because of which they exhibit no rotational spectra insures here a minimum of interaction between neighbouring molecules.Nevertheless the concept ofH. G. DEHMELT 271 non-interacting molecules in the solid state must of necessity only be an approxi- mate one. Its justification, however, can be checked by sufficient other data, namely, low heat of sublimation, independence of associated Raman spectra on the state of aggregation and so on, not to mention the asymmetry parameter E which for an end-atom forming a single bond should approach zero, and the narrowness of the multiple lattice site splitting of NQR lines mentioned earlier. There the theory of Townes and Dailey relating quadrupole coupling constants to molecular bonding can readily be applied. As discussed by Gordy in another paper pre- sented at this meeting, one striking result to come out of work with crystals of this kind is the fact that the coupling constants for the molecular halogens, C12,25 Br2,26 I2,16* 28 agree within a percent with the free atom values.This demonstrates that overlap effects must have but little influence on the density of the electron FIG. 7.-Quadrupole coupling constant, molecular bonding and solid state perturbations. The decrease in the ratio of molecular to atomic coupling constant in the series CF31, CF3Br, CF3C1, shows the in- creasing importance of ionic structures which do not con- tribute to the field gradient q. The correlation of decreasing intermolecular effects on the coupling in the solid with decreasing dipole moments is demonstrated also. 0 Solid I L l %=I X=0r X=Cl cloud around the nucleus, quite contrary to the predictions of present bonding theories. Appreciable experimental work has also been done on the tetra- halides.27~ 28 Besides in the nonpolar molecular crystals just discussed the situation of fairly weak interaction may also be expected for slightly polar constituents as, e.g., the organic halogen compounds.Comparison of the coupling constants for such molecules in the gaseous and the solid state usually show the differences to be not bigger than a few percent 28 and in selected cases it has even been possible to account for them in a satisfactory way.29 Thus a large number of halogen compounds have been systematically investigated 279 2% 30 and it has been possible to correlate these data to molecular structure theories. Sometimes 20 it is possible to reduce the interaction between appreciable polar ’ molecules (Sb13) by the insertion of inert fillers (s8) as 28 in SbI3 .3s8. This leads to studies of the effects of complex formation on quadrupole coupling which turned out to be rather small for SnC14 against SnC14 . 02NcsH5.31 The concept of well-defined isolated groups may even be extended to molecular ions like BrO3- and C103- in the corresponding metal salts. The NQRfrequencies here have been shown to depend very little on the metal i0n.27 For crystals in which no clear-cut sub-groups can be identified and where the bonding between the atoms is intermediate between the covalent and ionic extremes272 RESONANCE IN SOLIDS as, e.g., in SbC13, the interpretation 32 of the quadrupole coupling becomes ex- ceedingly complex along with most other crystal properties. Cu20 may represent a more favourable case 33 as it can be considered as a covalently bonded macro- molecule.In this compound the Cu atom forms two clearly distinguishable linear covalent bonds after acquiring a positive charge of one. FIG, 8.-Bonding in the Cu20 lattice. The Cu-' ion forms two linear bonds which can be explained as pd bonds derived from to a sizeable axial field gradient. In order - 6 2 cub Q __ the excited 3d94p configuration and give rise to cxpIain the 4 tetrahedral bonds formed by the 02-ion as sp3 bonds one has to assume s P3 Pd s P3 the rather high excitation to the 2p43s3p configuration. -2 I 1 I I In highly ionic crystals which contain atomic ions with filled electron shells NQR frequencies may sometimes be large enough for observation.34 This is likely for heavier atoms with large couplings for low-lying excited states of the free ion, which may be sufficiently polarized by asymmetric surroundings. How- ever, very few clues are available to estimate the expected NQR frequencies unless a NMR experiment with a suitable single crystal is performed.Therefore not much work has been done here. compound, quadrupole nucleus underlined 33s8 predominant electron configuration of quadrupolc atom 2.92p2 22p2 2.+2p3 292p3 3s23p4 3s23p5 3s23p5 3d94p 3dlo4s4p 4s4p3 4s24p3 4s24p5 4s24p5 4s24p6 5s25p3 5s25p5 5s25p5 6s6p 6 ~ 2 6 ~ 3 TABLE 1 calculated from free atom data for pre- dominant configuration NQR data - e % 0 0.9 0 0 - - I - - - - - 80.6; 0 19 17.3 0 ; 0.9 - 8.9 eQqz.? Mcls 10.36 10.43 3.40 4-54 45.8 109.0 81.9 53.4 65.3 58 232.5 765 529 23.1 ; 16.0 489 2153 1363 724 669 ref.18 18 19 19 35 36 30 33 33 37 38 26 3 34 32 16 16 39 40 eQqzz Mc/s 11.22 11.22 0 0 - 109.8 109.8 - - 0 0 769.8 769-8 0 0 2292 2292 780 0 ref. 41 41 42 42 43 43 44 44 45,46H . G . DEHMELT 273 Knowledge of the cxperimental asymmetry parameter E has been most helpful for the understanding of the bonding in solid iodine.28n29 Experimental E values also can be used to determine double bond character expected for theoretical reasons.22 A measurement of E for the I atoms in B13, e.g., should provide rather conclusive evidence for the 33 % double bond character demanded for the B-I bond by covalent bond theories. A table of all atoms for which NQR has been observed so far giving the values of the coupling constant in one or two representative compounds as well as that calculated from free atom values for the predominant electron configurations used in the bond formation should round off this qualitative discussion of selected experimental work in NQR./ A ‘ f; Y ‘5 ?’ 2’ FIG. 9.-Bonding in solid 12. The axial symmetry of the 12 molecules-the intramolecular bond represented by a full line-is destroyed by the appreciable formation of weak intermolecular bonds-dashed lines - -. These additional bonds are responsible for the formation of infinite plane layers which, stacked over each other with rather wide spacing, make up the 12 lattice. The author is indebted to Dr. Walter Gordy for stimulating discussions. The help extended by the Bell Telephone Laboratories in preparing the manuscript is gratefully acknowledged.1 Dehmelt and Kruger, Nuturwiss, 1950, 37, 11 1. 2 Pound, Physic. Rev., 1950,79, 685. 3 Dehmelt and Kriiger, 2. Physik, 1951,129,401. 4 Dehmelt, Amer. J. Physics, 1954, 22, 110. 5 Bloembergen, Purcell and Pound, Physic. Rev., 1948,73, 679. 6 Bloch, Physic. Rev., 1946, 70,460. 7 Kellog, Rabi, Ramsey and Zacharias, Physic. Rev., 1939, 55, 318. 8 Cola and Good, Physic. Rev., 1946, 70, 979. 9 Casimir, On the Interaction between Atomic Nuclei and Efectrons (Bohn, Haarlem, 10 Casimir, Physicu, 1935, 2, 719. 12 Bersohn, J. Chem. Physics, 1952, 20, 1505. 13 Cohen, Physic. Rev., 1954, 96, 1278. 14 Pound and Knight, Rev. Sci. Instr., 1950, 21,219. 15 Livingston, Ann. N.Y. Acud. Sci., 1952,55, 800. 16 Dehmelt, 2. Physik, 1951, 130,385. 17 Whitehead, Superregenerutive Receivers (Cambridge University Press, Cambridge, 18 Dehmelt, 2. Physik., 1952, 133, 528 ; 1953, 134, 642. 19 Watkins and Pound, Physic. Rev., 1952, 85, 1062. 20 Tomes and Dailey, J. Chem. Physics, 1949, 17, 782. 21 Barnes and Smith, Physic. Rev., 1954, 93, 95. 22Dean, Physic. Rev., 1952, 86, 607. 23 Geller and Schawlow, to be published. 24 Dean and Pound, J. Chem. Physics, 1952,20, 195. 25 Livingston, J. Chem. Physics, 1951, 19, 803. 26 Dehmelt, 2. Physik, 1951, 130,480. 27 Schawlow, J. Chem. Physics, 1954,22, 1211. 28 Robinson, Dehmelt and Gordy, J. Chem. Physics, 1954,22, 51 1. 29 Tomes and Dailey, J. Chem. Physics, 1952, 20, 35. 30 Livingston, J . Physic. Chem., 1953, 57, 496. 31 Dehmelt, J. Chem. Physics, 1953, 21, 380. 32 Dehmelt and Kruger, 2. Physik, 1951, 129,401. 33 Kruger and Meyer-Berkhout, 2. Physik, 1952, 132, 171. 34 Cotts and Knight, Physic. Rev., 1954, 96, 1285. 1936). 11 Kriiger, 2. Physik, 195 1, 130, 371. 1950).274 GENERAL DISCUSSION 35 Dehmelt Physic. Rev., 1953, 91, 313. 36 Livingston, J . Chem. Physics, 1951, 19, 803. 37 Dehmelt, Physic. Rev., 1953, 92, 1240. 38 Kruger and Meyer-Berkhout, 2. Physik, 1952, 132,221. 39 Dehmelt, Robinson and Gordy, Physic. Rev., 1954, 93, 480. 40 Robinson, Dehmelt and Gordy, Physic. Rev., 1953, 89, 1305. 41 Wessel, Physic. Rev., 1953, 92, 1581. 42 Jaccarino and King, Physic. Rev., 1951, 83,471. 43 King and Jaccarino, Bull. Amer. Physic. Soc., 1953, 28, 11. 44 Jaccarino, King, Satten and Stroke, Physic. Rev., 1954, 94, 1798. 45 Schuler and Schmidt, 2. Physik, 1935, 98, 239. 46 Murakawa and Suwa, J . Physic. SOC. Japan, 1950,5,429.

ISSN:0366-9033    

DOI:10.1039/DF9551900263

出版商:RSC    

年代:1955

数据来源: RSC

摘要:

274 GENERAL DISCUSSION GENERAL DISCUSSION Prof. B. P. Dailey and Prof. C. H. Townes (Columbia University) said: It would be unfortunate if the disagreement over details among the various authors who have discussed the interpretation of quadrupole coupling constants were allowed to obscure the fact that there are considerable areas of agreement and that certain conclusions seem fairly well established by consideration of quadrupole coupling effects. For the interesting attempt tc obtain a relation between ionic character and electronegativity differences using quadrupole coupling data the general nature of the curve is well determined even though questions relating to s-p and s-p-d hybridization make the exact nature of some parts of it a bit doubtful. The accompanying figure will show most simply how the proposal of Gordy’s paper compares with our own.The solid curve shown in this figure is the one which we believe to be best from examination of presently available quadrupole data, especially that for Univalent diatomic gaseous molecules, which appear to lend themselves most readily to reliable interpretation. This curve has already been published 1 and its basis discussed in some detail,2 but it may be worth while to emphasize which features are rather certain and which are not. One can show theoretically under simple, but rather general assumptions, that the curve of ionic character against electronegativity difference should start linearly for small electronegativity difference and end asymptotically for large differences.Simple theoretical arguments about the curve shape in intermediate regions can be made, however, only under special assumptions. Quadrupole coupling data show that the alkali halides are largely ionic, and that those involving larger electronegativi ty differences such as KCl are almost complete ionic. As was pointed out in both the present paper by Prof. Gordy and by the authors,2 complications involving effects of overlap and of hybridiza- tion arc unimportant in the region of large ionicity. The curve in this region, then, is rather well determined by the data for the alkali and group 3B monohalides. The central part of the curve (electronegativity difference of 1.0 to 1.5) suffers from a lack of quadrupole data for molecules that can be simply interpreted, and hence may perhaps not be very well established.The region of smaller ionicity is subject to uncertainty because of the sensitivity of the quadrupole coupling constants to hybridization. Here the differences between Prof. Gordy’s interpretation of quadrupole coupling constants and our own become important. Gordy’s proposal that ionic character equals one-half of electronegativity difference (straight line in the figure) represents a convenient and easily remembered approximation. However, the solid S-shaped curve is probably more accurate. 1 Townes, Symposium on Molecular Physics, (Maruzen Co., Ltd., Tokyo, 1954). 2 Dailey and Townes, J. Chem. Physics, 1955, 23, 118.GENERAL DISCUSSION 275 On the other hand, our early proposals 112 for such a curve, based on the few quadrupole coupling constants initially available, probably indicates too small an ionic character in the region where hybridization can produce large un- certainties. It is hoped that additional data will allow the relation between ionic Character and electronegativity differences to be still better established.How- ever, it must be noted that ionic character certainly depends on other variables in addition to electronegativity difference 3 so that a unique curve relating these two quantities cannot be expected. FIG. 1 .-Various curves proposed for ionic character as a function of electronegativity. The solid curve represcnts the authors' choice based on quadrupole coupling constants of diatomic gaseous molecules.314 The dashed straight line is a relation proposed by Gordy, and the dashed curve that proposed in his present paper.Electroneqativiry difference Mr. B. Dreyfus (Institut Fourier, Grenoble) said: Prof. Dailey has told in his papcr of the necessity of taking into account the solid state effects in order to get thc true molecular coupling constant, which is only of interest to chemists. One of thcsc solid state cffects is the variation of the effective, electric field gradient duc to thcrmal vibrations of the molecule; 5 consequently the resonance frequency dccrcascs when ternpcrature riscs. One of the principal features is the fact that thc thcorctical curve becoines a straight line above temperatures of the ordcr kv/k (20" K to 80" K). But the experimental curves are not straight lines. Wc have bcen abic with Mr.Dautreppe, in Grepoble, to show that it is necessary to taltc into account, the variation of the vibrational frequencies of the molecule with Icmperaturc due to the contraction of the crystal at low temperature. Our work 6 on P - C ~ H ~ C I ~ and p-CGH4Br2 shows that a variation of external Raman frequencies of the order of 40 tc 50 %, between room and liquid nitrogen temperatures, is requircd to explain our experimental curves. Such an import- ant increase seems to be confirmed by the few direct Raman measurements. 1 Townes and Dailey, Physic. Rev., 1950, 78, 346. 2 Dailey, J. Physic. Chem., 1953, 57, 490. 3 Townes, Symposium on Molecular Physics (Maruzen Co., Ltd., Tokyo, 1954). 4 Dailey and Townes, J. Chem. Physics, 1955, 23, 11 8. 5 Bayer, 2.Physik, 1951, 130, 227. 6 Dreyfus and Dautreppe, Compt. rend., 1954,239, 1618.276 GENERAL DISCUSSION Dr. H. 0. Pritchard (Manchester University) said: It is often assumed in simplified treatments that the dipole moment of a molecule may be divided into four components which arise from (i) ionic character, (ii) hybrid character of bonding orbitals, (iii) hybrid character of lone pairs, (iv) overlap (see, e.g. Gorcly, this Discussion, ref. (14) and eqn. (23)). The first term is generally agreed to be related to the difference in electronegativity between the bonding atoms. Taking terms (ii) and (iii) together, suppose we have excited the atom under consideration to its appropriate valence state, say s m p : the electron dis- tribution in this atom, which may be represented by a determinantal wave function, does not give rise to any dipole moment.We now prepare it for bond formation by hybridization, and still the atom has no dipole moment because, although any bonding orbital we may pick out is unsymmetrical, the other electron wave functions for the atom change simultaneously to leave the total electron distribu- tion unchanged-hybridization only consists of adding or subtracting columns of the determinant and this operation leaves the value of the determinant unchanged. Looking at the problem pictorially, consider the configurations spxpy and s2pxpy2 represented by I and 111: if we pick out an sp2 orbital in the x-direction from I and allow the remaining two orbitals to become equivalent to each other, they adopt wave functions equivalent to the first, 120" apart, and the atom has no dipole; again, if we pick cut an sp2 orbital from I![ and allow the two remaining lone pairs to become equivalent, their form is not that obtained by putting two electrons in each of the II(xy) orbitals, but becomes as in IV where the dipole moment of the unpaired orbital is exactly cancelled by the resolved moments of the lone pairs.Hence, at this level of approximation, we may eliminate (ii) and (iii) from our discussion of dipoles as they are only a function of the way in which we arc looking at the problem. Furthermore, it is difficult to say how far (iv) is a real effect. Suppose we have a bond formed between two atoms each using a pure 2p orbital : this bond has an overlap moment only if the radial dependences of the two orbitals differ, i.e.if the two atoms have differing effective nuclear charges ; but the effective nuclear charge at the covalent radius boundary is one of the successful measures of electronegativity suggested by Gordy 1-these two orbitals, so long as they have the same principal quantum number, can only have different radial dependences if they differ in electronegativity, so that part at least of the overlap moment is an electronegativity effect. 1 suggest that the significance of the overlap moment is that it represents the potential which brings about the charge transfer and that if a suitable pair of atomic wave functions were constructed by the methods suggested recently by Moffitt,2 then the overlap 1 Gordy, Physic.Rev., 1946, 69, 604. 2 Moffitt, Ann. Report Prog. Physics, 1954, 17, 173.GENERAL DISCUSSION 277 moment would disappear. Thus the electronegativity difference between the two orbitals forming the bond would still remain the major source of the dipole moment. Also, it must be emphasized that hybridization in the sense I --> I1 or 111 + IV can have no effect on the quadrupole coupling constant because it leaves the electron distribution in the atom, and hence the field gradient, totally unchanged. The only form of “ hybridization ” which can affect the quadrupole coupling constant is one which actually changes the electron distribution, i.e. isovalent hybridization where we have a hybrid valence state as opposed to a hybridized valence state; for example, in nitrogen this would mean that the valence state is not s2p3, suitably hybridized, but a mixture of s2p3 and the excited sp4 state.Thus, if ionic character is not sufficient to account for the variation in coupling constant, we must infer that the valence state is not a simple configuration, but that excited structures, such as those of Voge for methane,l must be included as an integral part of our description of every molecule. Prof. C. A. Coulson (Oxford University) said: There are two points in Dr. Pritchard’s contribution which seem to justify a further comment. In the first place it is evidcntly most desirable to distinguish between hybridization in which we merely rearrange already occupied atomic orbitals of s, p , d . . . type, keeping one electron in cach for the purposes of bond formation; and hybridization in which one or more of the new orbitals is occupied by two electrons (lone-pairs).Moffitt has referred to these as first-order and second-order hybridization re- spectively. It is easy to see, along the lines pointed cut by Pritchard, that the total atomic hybridization moment is zero in the first case, whereas it is very far from being zero in the second. Several authors (e.g. Pople, Danielsson, Fischer- Hjalmars, Grcenwood and the present writer) have shown that a large part of the total molecular dipoIe moment in molecules such as water and ammonia may be attributcd to the extra contributions arising from the fact that the lone-pair hybrids involve two electrons, and the bonding hybrids only one. Thus, whenever there are non-bonding electron pairs in the valence shell the components (ii) and (iii) of Dr.Pritchard’s list must be regarded seriously. But these components arc still significant for cases of first-order hybridization as soon as we try to discuss bond-moments in a polyatomic molecule. Large parts of chemistry depend on the concept of a bond, as described by the mutual pairing of two appropriate atomic orbitals, and the additivity relations for dipole moment, energy, refraction, etc., as wcll as recent accurate intensity measurements in infra-red and Raman spectra, urge us to try to account for these properties in terms of individual bond charge densities. Such a description does not seem possible without reference to the hybridization in the bonding orbitals, even though when we make a sum- mation over all the bonds which terminate on a given atom, these hybridization moments may frequently canccl out to a give zero value. My second comment concerns the overlap moment, Pritchard’s component (iv). It is perfectly true that this contribution to the bond dipole moment depends on the sizes of the overlapping charge-clouds, and hence on the electronegativity differencc of the atoms being bonded together.But this does not make it re- dundant, nor does it imply that it is insignificant. Some recent unpublished calculations of Prof. M. T. Rogers and the writer lead to the view that overlap dipole moment valucs of 4-1 D are frequently found. This means that what we call the electronegativity difference dominates both the pure ionic character of the bond and also the overlap moment.Yet here again the type of hybridization is important since it is not the electronegativity differencc of the atoms that is concerned, but the electronegativity difference of the particular hybrids in the atoms that are involved in the bond formation. And this, as MofEtt has stressed, is closely related to the hybridization in the bond. 1 Voge, J. Chem. Physics, 1936, 4, 581.27 8 GENERAL DISCUSSION Prof. B. P. DaiIey and Prof. C. H. Towncs (Colund~in University) said : It should be emphasized that in deriving an empirical relation between two such loosely defined quantitics as ionicity and electronegativity grcat care must be taken to avoid unconscious bias in influcncing thc results through the arbitrary choice of data or the introduction of various corrections in a non-systematic way.It is for this reason that thc curve which we present is based only on gaseous diatomic molecdcs, and uses Huggins’ values of electronegativities without any modification. The usc of sclectcd polyatomic molccules to provide points on the curvc, as in Gordy’s discussion, leads to certain dangcrs. There is no generally accepted method for deriving the elcctronegativity of the central atom in a poly- atomic molecule. Gordy has used his cmpirical relation between force constants and elcctronegativities to introduce a corrcction of 0.3 unit in the electronegativity of C in the methyl halides, due to the prescncc of the thrce hydrogens. Although it is dificult to evaluate quantitatively, somc such change probably takes place.However, for the sake of consistency i t would bc valuable to apply similar correc- tions to thc other polyatomic niolecules such as SiH3C1, as well as to allow specifically for thc double bonding which occurs in SiH3C1. There is also considerable doubt that the empirical relation between force constants and electronegativitics can be uscd to provide reliable values for the correction to elcctronegativity due to adjacent atoms. In the original paper 2 which established the empirical relation used between form constant and electro- negativity, the average deviation of the calculatcd force constant from the observed was 2 %. The deviation for HCI of 4.1 %, where no correction is indicated, is appreciably larger than that of 2.7 % for CH3CI or similar deviations for other methyl halides or for methanc.The deviation for CH3F is in the opposite direction from that in CH3CI which would seem to make it difficult to derive a consistent correction for C in CH3. It is unfortunately true that at present data for diatomic molecules with electro- negativity diffcrences between 1.0 and 1.5 are quite scarce. However, one cannot expect to fill the gap with much certainty by data from a limited number of poly- atomic moiecules . lnterprctation of quadrupole coupling data for solids is difficult because of the influence in some cases of intermolecular bonding. Gordy’s conclusion, from a consideration of eQq for solid Br2 and Cl2, that no hybridization occurs in these molecules may be questioned since no account was taken of the inter- molecular bonding which is clearly indicated in these solids.39 4 Prof.D. F. Mornig (Math. Inst., Oxjord University) said : The question raised in my mind is whcther thc “ ionic character ” and “ hybridbation ” found from quadrupok coupling constants are coiinectcd with valence theory. All of the authors have eniphasi7ed that thc quadrupole coupling constant is sensitive only to the charge distribution war the nucleus and not to the outer regions of the atom important in the formation of chcrnical bonds. Townes and Dailcy have put this in quantitativc form by expanding the wave function neat. the nucleus in telnis of atomic configurations. For example, jf the standard value of eQq in C1 is due to the 2P configuration (3s)2(3p)5, the change when the atom is in- corporated in a molecule is caused by admixture of the ionic configuration (3s)2(sp)6 and the 2s configuration (3s)(3p)6.The question thcn is how the pro- portion of these configurations is related to the nature of the chemical bond. The rejection of the overlap contribution by both Dailey and Gordy implies that neither the valence bond nor molecular orbital theories provide an adequate link between atomic and molecular wave functions for this purpose. In that case one cannot carry ovcr thc terms “ ionic character ” and “ hybridization ” to 1 I-fuggins, J. Amer. Cliem. Soc., 1953, 75, 4123. 2 Gordy, J . Chem. Physics, 1951, 19, 792. 3 Townes and Dailey, J . Chem. Physics, 1952, 20, 35. 4 Tsukada, J. Physic. SOC.Japan, 1954, 9, 872.GENERAL DISCUSSION 279 the bonding regions without formulating such a link. Nevertheless, it is commonly done and Gordy has quite explicitly assumed that thc hybridization he finds near the nucleus can be carried over to such quantitics as the dipolc moment which depend on the outer clectrons. The chief argument against the inclusion of overlap has becn that the normal- ization changes the electron density near the nuclcus whereas the major effects of bonding should occur only in a distortion of the charge in thc outer regions of the atom. This argument seems reasonable but it should be noted that the other atomic configurations, for example in C1, also change the charge density near the nucleus and the ionic configuration quite considerably.Consequently it is partly a question of how one prefers to change this charge density. It appears, thcrcforc, that although the quadrupole coupling constant gives valuable information about the asymmetry cf the charge distribution near thc nucleus, quantitative inferences about the chemical bonds must be made with caution until some of these questions have been answcred more quantitatively. It is gratifying that Dr. Bassompierre has made a start in this direction. Prof. B. B. Dailey and Prof. C. H. Townes (Columbia University) said : The role of overlap effects in determining quadrupole coupling constants is a puzzling onc. Schatz,l by making a calculation of the Heitler-London type, found that the overlap integral played an important part in determining the value of eQq.Wc have formed the opinion, as has Prof. Gordy, from a consideration of cmpirical data that overlap does not usually contributc in an important way to the quadrupole coupling constant. Gordy’s suggested explanation of why this is so may have some validity but his statement as to why the argumcnt does not apply to hybridization appears to be incorrect. Gordy states : “ a pure covalent bond through scrambling (hybrid- ization) of the atomic orbitals can alter the angular distribution of the electronic charge cloud near the nucleus and thus can influence the coupling without lifting charge density appreciably away from the nucleus ”. Actually even a small amount of s-character added to a p orbital increases enormously the charge density of the particular clectron involved in the immediate vicinity of the nuclcus.Similarly a 15 % addition of J character to a p bond would decrcase chargc density near the nucleus by about this fractional amount. The primary difficulty with the Schatz approach would seem to be that near thc nucleus of the first atom involved in a bond the atomic wave function of the second atom is very far from being a correct solution to Schroedinger’s cquation. Furthermore, the charge density near the nucleus due to this part of the wave function is sufficiently large to contribute importantly to the quadrupole coupling constant. Hybridization is quite different in this respect. For example, near the nucleus a combination of s and p atomic wave functions corresponding to cnergy levels that are not very different represents a reasonable approximation to a solution of Schroedinger’s equation.The approximation is particularly gocd near the nucleus where the potential energy is very much larger than the differcnce in atomic binding energy for the s and p electrons. Prof. B. P. Dailey and Prof. C. H. Townes (Columbia University) said : Two points are evident to all of the authors who have discussed the interpretation of quadrupole coupling data. First, that it is not possible to scparate effects due to ionicity and hybridization in the general case using quadrupole data alone. Secondly, that s hybridization definitely exists in certain molecules such as PF3, H2S, AsC13, etc. We would like to emphasize that hybridization probably also occurs commonly in the halogens and will appreciably affect the quadrupole coupling constants.This procedure seems doubtful at best. 1 Schatz, J. Chem. Physics, 1954, 22, 695 ; 1954, 22, 755 ; 1954, 22, 1974. 2 Townes and Dailey, J. Chem. Physics, 1949, 17, 782.280 GENERAL DISCUSSION Schatz and Gordy have attempted to use dipole moment data to determine the amount of s hybridization for certain molecules such as HCI where both dipole moment and nuclear quadrupole coupling data are available. Such an attempt to obtain a theoretical relation between the electric dipole moment and the nuclear yuadrupole coupling constant must be evaluatcd with some caution because normally two different types of wave functions are being used in the two halves of the calculation. In the estimation of eQq atomic wave functions are implied which accurately describe the charge distribution in the immediate neighbourhood of the nucleus.In the dipole moment calculations it is customary to use Slater atomic orbital (a.0.) functions or something similar which are reasonably successful in describing the charge distribution in the overlap region but are considerably less accurate near the nucleus. The procedure used in calculating the dipole moment has been described by Mullikcn, who applied it to the special case of HCl. The ability of this method of calculation to reproduce experimental values of the dipole moment has not been established. Gordy’s discussion of the dipole moments of the hydrogen halides is based on Mulliken’s,l using values of thc overlap moment derived from values of the overlap integral obtained by Mulliken from Slater a.0.functions. If the wave functions are correct and Mulliken’s methods of calculation are satisfactory, it is also possible to calculate the primary moment and the cor- responding ionicity directly. Mulliken’s value of the ionicity for HC1 is 16 % compared to the value of 41 % Gordy derives from the dipolc moment using Mulliken’s calculations as a basis. It is interesting to note that Mulliken’s conclusion from the failure of his theoretical calculation to reproduce thc observed dipole moment of HCI was that either the theoretical approach was inadequate to deal with the moment or that the Cl bonding orbital in HC1 must contain a rather large amount of s character. Robinson 2 arrives at essentially the same result, which seems to be inconsistent with Gordy’s discussion.In his treatment of the dipole moment of IC1 Gordy points out that it would be very difficult to account for the observed dipole moment if only the C1 bonding orbital involved s-p hybridization. However, the argument previously made by Dailey and Townes was that the s hybridization of the negatively ionic atom could be expected to be greater than the s hybridization of the positively ionic atom from considerations of promotional energy but that even for the positively ionic atom the s character in reality might not be zero. It can easily be shown that a few per cent of s character on the much larger iodine atom would completely overbalance the hybridization moment produced by 15 % .r character for chlorine.Gordy proposes that s hybridization occurs when a halogen is positively ionic much more readily than when it is negatively ionic because the primary molecular dipole moment would interact with the hybridization moment. There is, of course, some interaction of this type. However, a somewhat quantitative examina- tion does not make it more important than the promotional energy associated with hybridization as indicated by Gordy. Rather it seems to be somewhat less important. If a halogen is negatively ionic, this type of interaction does not occur in first approximation, since the primary and hybridization moments occur in different resonant structures. If a halogen is positively ionic, then its hybridization moment would interact with the primary moment as suggested if hybridization of the non- bonding electrons is assumed to occur in the positive ion as in the covalently bonded atom.Consider the particular case of FCI, where the internuclear 1 Mulliken, J. Chem. Physics, 1949, 46, 497. 2 Robinson, J. Chem. Physics, 1949, 17, 1022. 3 Gordy, J. Chem. Physics, 1951, 19, 792.GENERAL DISCUSSION 28 1 distance is approximately 1.6& the radius of F 0*7& the energy required to promote an electron from 2s to 2p about 20eV, and the hybridization moment produced by 25 % s hybridization is about 2 D. Then with 25 % hybridization of the two non-bonding electrons, the energy is lowered by approximately 3 eV by the interaction between hybridization and primary moment. However, it is raised by about 10eV due to promotional energy.Hence one would expect promotional energy to be the more important. Hybridization of this type may well occur when a halogen is positively ionic. Certainly the situation is so complex that any final statement about it from simple considerations is not possible. However, it seems unreasonable to suppose that s hybridization occurs when the halogen is positively ionic but not when it is negatively ionic. Energy considerations appear to favour the reverse. Dr. Lurcat (Fortenay-aux-Roses (Seine)) said : It is generally admitted that pure quadrupole transitions cannot be observed in liquids, because of the averaging to zero of quadrupole interaction by the molecular motion. However, Prof. Ubbelohde has recently shown 1 that in some liquids, composed of planar molecules, the movements of the molecules are restricted.Rotation is not possible; only the sliding of molecules over each other. This phenomenon should make possible the observation of pure quadrupole resonance in liquids. Dr. Seiden, of OUT laboratory, developed this idea2 and showed that the intervals between the quadrupole levels are reduced by the restricted rotation. If the rotation becomes free, all the levels collapse. Hence the frequency of quadrupole resonance is reduced in the liquid with restricted rotations, compared to the frequency measured in a solid; and it becomes zero when the rotation becomes unrestricted. This is due to the fact that molecular motions are so quick that quadrupole levels are determined by a Hamiltonian averaged over these motions. (More precisely, the correlation time 7c of molecular movements is small, compared to the period of quadrupole resonance : rc < 2.rr/o~.) So it must be possible, not only to observe quadrupole resonance in liquids of this type, but also, using Seiden’s calculations, to obtain, by comparing the frequencies in solid and liquid states, information concerning the degree of restric- tion of molecular rotation in those liquids. Prof. C. H. Townes (Columbia University) said: The results of Dr. Bassom- pierre’s calculation are interesting and the quadrupole moment he obtains not far different from that obtained from considerations of more primitive type. It should be noted that nitrogen is such a light atom and its bond structure suf- ficiently complicated that the approach of Townes and Dailey to obtaining Q cannot be especially accurate. It would be valuable to have an estimate of the accuracy of Bassompierre’s result for Q. In calculations of this type, it is important to use a set of wave functions which approximate fairly closely to atomic wave functions near the nucleus. It is well known that many wave functions used in molecular calculations are very far from accurate near the nucleus. They need not be for molecular energy and many other calculations. However, they should be fairly close to atomic wave functions near the nucleus for calculations of q, since this quantity is so sensitive to electron charges in the immediate vicinity of the nucleus, This is especially true for heavier atoms. 1 Ubbelohde and A1 Mahdi, Proc. Roy. SOC. A, 1953, 220, 143. 2 Lurcat, Compt. rerid., 1955, 240, 1419.

ISSN:0366-9033    

DOI:10.1039/DF9551900274

出版商:RSC    

年代:1955

数据来源: RSC

摘要:

282 AUTHOR INDEX Agar, J. N., 100. Anderson, W. A,, 226. Andrew, E. It., 195,25 1. Arnold, J. T., 226. Bak, B., 30. Bassompierre, A., 260. Bassov, R'. C., 96. Bell, R. P., 100, 254. BCne, G., 184. Bennett, J. E., 140. Bleaney, 13., 64, 112, 173, 175. Conibrisson, J., 181. Coulson, C . A., 65, 277. Cox, J. T., 52. Dailey, l3. P., 255, 274, 278, 279. Dainton, F. S., 101, 183. Davics, M., 249. Dehmelt, H. G., 263. Denis, P., 184. Dousmanis, G. C., 56. Drain, I,. E., 200. Drcyfus, B., 275. Extermann, C. R., 184. Ford, P. T., 193, 230. GHumann, T., 52. George, P., 177, 184. Gordy, W., 14, 182. Gray, P., 249. Griffith, J. S., 178. Griffiths, J. H. E., 106. Gutowsky, H. S., 187, 246, 247, 248, 250. Gwinn, W. D., 43. Hansen, L., 30. Heath, G. A., 38. Hornig, D. F., 249, 278. Hyndman, D., 195.Ingrain, D. ,J. E., 104, 140, 176, 178. Kozyrev, 13. M., 135. Lipscomb, W. N., 249. AUTHOR INDEX * * The references in heavy type indicate paper submitted for discussion. Lhingst on, R., 166, 183. Longuet -Higgins, H. G., 9. Lurcat, 28 I . Millen, D. J., 66. Ogg, R. A., 239. Orville-Thomas, W. J., 52, 66. Owen, J., 127. Page, F. M., 87, 101, 102. Pake, G. E., 147, 179, 181, 154, 252. Pritchard , H. O., 276. Prokhorov, A. M., 96. Ray, Jr., J. D., 239. Rastru p-Anderscn, 30. Richards, R. E., 193, 230. Runciman, W. A., 176. Schneider, E. E., 158, 173, 174, 176, 183. Schwarz, R. F., 56. Slicppard, N., 247, 253. Shcridan, J., 38. Sherrard, E. I., 38. Shoolery, J. N., 215, 254. Sinnott, K. M., 66. Smith, J. A. S., 207, 251. Sugden, 'I. M., 68, 76, 100, 101, 105. Taylor, IS. H., 166, 183. Thomas, I,. F., 38. Tinkhani, M., 174. Townes, C. H., 56, 66, 104, 185, 274, 278, To wnsend, J., 147. Ubbelohdc, A. R., 99. Uebersfeld, J., 181. Warhurst, E., 101. Weissmann, S. I., 147. Wheeler, K. C., 76. White, R. L., 56. Wieringen, J. S. van, 118, 177. Zeldes, H., 166, 183. 279, 281.

ISSN:0366-9033    

DOI:10.1039/DF9551900282

出版商:RSC    

年代:1955

数据来源: RSC