FROTCN MAGNE'F‘EC REWCE 0F SQME CYCLC‘PRCPANE DERIVATIVES AND FLUORINE MAGNETIC RESONANCE OF SOME PERFLUQROALKYL DERIVATIVES OF SULFUR HEXAFLUGRIBE AND SOME FLuORocARaoN NITRQGEN COMPOUNDS ~ rhesus!” 1h; Degree pf Dh; D. , . meg-mm mm UNEVERSETY ' John David Graham , 1.96.1. ' LIBRARY . Michigan State University F.’I!CHIGAN EAST LA! ABSTRACT PROTON MAGNETIC RESONANCE OF SOME CYCLOPROPANE DERIVATIVES AND FLUORINE MAGNETIC RESONANCE OF SOME PERFLUOROALKYL DERIVATIVES OF SULFUR HEXAFLUORIDE AND SOME FLUOROCARBON NITROGEN COMPOUNDS by John David Graham The proton magnetic resonance absorption of several derivatives of cyclopropane was studied with a Varian high—resolution nuclear magnetic resonance spectrometer operating at a fixed radiofrequency of 60. 000 mcs. The fluorine magnetic resonance absorption of some perfluoroalkyl derivatives of sulfur hexafluoride was studied at fixed radiofrequencies of 60. 000 mcs, and 560445 mcs. and the fluorine magnetic resonance absorption of some fluorocarbon nitrogen compounds was studied at 56.445 mcs. The syntheses of some of the cyclopropane derivatives which were studied in this research are reported here including three compounds whose preparations have not been previously reported. The methods by which the proton and fluorine magnetic resonance spectra were analyzed are discussed and theoretical spectra for the spin systems which were analyzed are presented. The following cyclopropane de- rivatives were studied: 1, l—dichloro-Z-methyl—2-phenylcyclopropane, £i_s—1, l-dichloro—Z—methyl-3-phenylcyclopropane; 1, l—dichloro-Z- methoxycyclopropane; 1, l-dichloro-Z-ethoxycyclopropane; trans-l, Z, 3- tribenzoylcyclopropane; cyclopropane—l, l, Z-tricarboxylic acid; and trans—3-methylenecyclopropane-l, Z—dicarboxylic acid. The fluorine magnetic resonance absorption of the following derivatives of sulfur hexafluoride was studied: (C2F5)ZSF4; CF35F4C2F5; CF3SF4CFZCOOCH3; Abstract - John David Graham C3F5SF5; C4F9$F5; and CF3SF4CFZSF5. Fluorine magnetic resonance spectra of the following fluorocarbon nitrogen compounds were obtained: (CF3)ZNF; (C2F5)ZNF; (CZF5)3NI; CZF5N=NC2F5; C4F9N=NC4F9; (CF3)2NCF= NCF3; (CF3)2NCOOCH3; and (CF3)ZNHgN(CF3)2. The fluorine magnetic resonance absorption of CF3CC12CFC1CF3 and CFClZCClZCFzCl was also studied. The observed chemical shifts and nuclear spin-— spin coupling con— stants have been interpreted in terms of substituent effects and the structures of the molecules. Although the structure of the cyclopropane ring is considered to be somewhat unusual the observed proton—proton coupling constants for ring protons in the cyclopropane derivatives are not anomalous. The magnitude of, and variations in, the proton—proton coupling constants can be satisfactorily explained on the basis of the geometry of the molecules. Substituent effects have not been found to be important in the consideration of the proton-proton coupling constants but the chemical shifts of the ring protons have been found to be sus- ceptible to the nature of the substituents on the ring. The fluorine chemical shifts have been found to vary with the electronegativity of the substituents in a predictable manner. Fluorine- fluorine spin coupling constants have been found, in general, to be quite large. Spin—spin coupling constants between fluorine atoms four and five bonds removed have an appreciable magnitude. However, in almost all cases where the perfluoroethylgroup is present there is no measurable fluorine—fluorine coupling constant between the CF3 and CFZ groups. Furthermore, the fluorine-fluorine coupling constants do not vary in any coherent manner with a change in the number of bonds separating the interacting nuclei. The angular dependence of some fluorine—fluorine coupling constants has been discussed as well as the effect of rapid rotation around the carbon— carbon single bond. ACKNOWLEDGMENTS The writer acknowledges with sincere appreciation the counsel of Professor Max T. Rogers under whose direction this investigation was conducted. He also wishes to express his gratitude to the Monsanto Chemical Company and the National Science Foundation for fellowships, and to the Atomic Energy Commission for grants subsidizing part of this research. ii VITA John David Graham candidate for the degree of Doctor of Philosophy Dissertation: Proton Magnetic Resonance of Some Cyclopropane Derivatives and Fluorine Magnetic Resonance of Some Perfluoroalkyl Derivatives of Sulfur Hexafluoride and Some Fluorocarbon Nitrogen Compounds. Outline of Studies: Major: Physical Chemistry Minor: Physics and Inorganic Chemistry Biographical: Born, March 21, 1936, New Haven, Connecticut Undergraduate Studies: B. 5., Chemistry, Providence College, Providence, Rhode Island, 1957 Professional Affiliations: American Chemical Society The Society of Sigma Xi iii TABLE OF CONTENTS INTRODUCTION .......... . . . . . ..... HISTORICAL REVIEW . . ............ THEORY....... .............. Nuclear Energy Levels Relaxation . . . . . . . . . . . . ..... Line Broadening . . . ..... Saturation . . . . . ....... . . . ...... . The Chemical Shift . . . . ...... . . . . . . . Nuclear Spin-Spin Interactions ......... Analysis of Spectra ....... . . . . . ..... EXPERIMENTAL ..... . . . ...... Spectrometer . . ..... . . . . . . Compounds Studied .......... Sample Preparation . . . . . . . . ........ Determination of Spectral Parameters . . ....... RESULTS...................... ..... High—Resolution Proton Magnetic Resonance Spectra . High-Resolution Fluorine Magnetic Resonance Spectra. DISCUSSION ...... . . . . . ..... SUMMARY ........ BIBLIOGRA PHY . . .................. iv 10 13 14 15 20 31 54 54 59 60 62 62 77 112 119 121 LIST OF TA BLES TABLE Page I. Theoretical Coupling Constants for Ethane as a Function of Dihedral Angle .......... . . . . 28 11. Theoretical Coupling Constants for CH2 Fragment as a Function of the HCH Angle ........... .. . 29 III. Basic Product Functions and Diagonal Matrix Elements for the AB Spin System . ......... 40 IV. Eigenfunctions and Eigenvalues for the AB Spin System ....... 41 V. Transition Frequencies and Relative Intensities for the AB Spin System ............ . . . . . . 42 VI. Basic Symmetry Functions for the AZB Spin System . 43 VII. Eigenvalues and Eigenfunctions for the AZB Spin System..... ....... ............44 VIII. Transition Frequencies and Relative Intensities for the AZB System .............. . . . . . . 45 IX. Line Frequencies and Relative Intensities for the A4B Spin System ............... . . . . 47 X. Basic Product Functions and Hamiltonian Matrix Elements for ABX Spin System . . . . . . . . . . . 49 XI. Eigenfunctions and Eigenvalues for the ABX Spin System ......... ..... 50 XII. Line Frequencies and Relative Intensities For the ABX Spin System . . . ........... . . . . 51 XIII. Fluorine Compounds Studied ........ . . . . . 57 XIV. Cyclopropane Derivatives Studied ......... . 57 LIST OF TABLES — Continued TABLE XV. XVI. XVII. XVIII . XIX. XX. Ring Proton Coupling Constants In Cyclopropane Derivatives . . . . . . . . ........ Chemical Shifts of Ring Protons In Cyclopropane Derivatives ............. Spin—Spin Coupling Constants in Perfluoroalkyl Derivatives of Sulfur Hexafluoride .......... Fluorine Chemical Shifts in Perfluoroalkyl Deriva- tives of Sulfur Hexafluoride . . . . . . . . . . . . . . Spin-Spin Coupling Constants in Fluorocarbon Nitrogen Compounds . . . . . . . . . . ..... Fluorine Chemical Shifts in Fluorocarbon Nitrogen Compounds . . . . . . ........ . ....... vi Page 78 FIGURE 1. 3. 10. LIST OF FIGURES Experimental and theoretical I-I1 magnetic resonance spectra of 1, l-dichloro—2-methy1-2-pheny1cyclo— propane . 2 -methyl- 3 —pheny1cyclopr opane . I-I'1 magnetic resonancie spectrum of phenyl groups of trans— 1, 2, 3- itribenzoylcyclopropane . Experimental and theoretical H’ magnetic resonance spectra of ring protons of trans-1, 2, 3-tribenzoyl- cyclopropane. . Experimental and theoretical H‘ magnetic resonance spectra of the low-field proton'resonance of 1, l-dichloro—Z-ethoxycyclopropane . . Experimental and theoretical II1 magnetic resonance spectra of the high—field proton resonance of 1, L-dichloro-Z-ethoxycyclopropane . .. .7 Experimental and theoretical H1 magnetic resonance spectra of the low-field proton resonance of l, 1-dichloro—2-methoxycyclopropane . . Experimental and theoretical H‘ magnetic resonance spectra of the high-field proton resonance of l, 1~dichloro—2-methoxycyclopropane . . Experimental and theoretical I-I1 magnetic resonance spectra of the low—field proton resonance of Cyclopropane — l, l, 2—tricarboxylic acid Experimental and theoretical I-I1L magnetic resonance spectra of the high-field proton resonance of cyclopropane-l, 1,2-trica'rboxy1ic acid . vii Page 63 . H1 magnetic resonance spectrum of cis-l, l—dichloro- 65 66 67 69 7O 71 72 74 75 LIST OF FIGURES - Continued FIGURE 11. 12. l3. 14. 15. 16. 17. 18. I9. 20. 21. 22. 23. Page I-I1 magnetic resonance spectrum of trans-3— methylenecyclopropane- l, 2—dicarboxy1ic acid . 76 F19 magnetic resonance spectrum of the CF3 and CFZ groups of (C2F5)ZSF4. 80 F19 magnetic resonance spectrum of the SE, group of (C2F5)ZSF4 . 81 Theoretical F19 magnetic resonance spectrum of the SR, group of (CZF5)SF4 . 83 F19 magnetic resonance spectrum of the SCF3, CCF3 and CFZ groups Of CF3SF4C2F5 . 84 F19 magnetic resonance spectrum of the SF4 group of CF3SF4CZF5 . 85 Theoretical F19 magnetic resonance spectrum of the SF4 group Of CF38F4C2F5 . 86 F19 magnetic resonance spectrum of the CF3 and CF: groups of CF3SF4CF2COOCH3 . 87 Experimental and theoretical F19 magnetic resonance spectra of the SF4 group of CF3SF4CF2COOCH3 . 87 Experimental and theoretical F19 magnetic reson- ance spectra of the apex fluorine of CZFSSFs . 88 F19 magnetic resonance spectrum of the base fluorine atoms (SF4) of C2F5SF5 . 89 F19 magnetic resonance spectrum of the CF3 and CFZ groups of CZF5$F5 . 90 Experimental and theoretical F19 magnetic reson- ance spectrum of the apex fluorine atom of C4F98F5 92 viii LIST OF FIGURES — Continued FIGURE 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. F19 magnetic resonance spectrum of the base fluorine atoms (SF4) of C4F9SF5 . ...... F19 magnetic resonance spectrum of the CF3 and v B u Q—CFZ groups Of CF3CF2CF2CF28F5 . . F19 magnetic resonance spectrum of the [3-CF2 7 F5 <1 group of CF3CF2CF2CFZSF5 ..... F19 magnetic resonance spectrum of the y-CF2 I“ 5 ° group of CF3C ZCFZCFZSF5. . . . . . . ..... F19 magnetic resonance spectrum of the apex and base fluorine atoms of the SF5 group of CF3SF4CFZSF5 . . Fl9 magnetic resonance spectrum of the SF4, CF3, and CFZ groups of CF38F4CFZSF5 . . . F19 magnetic resonance spectrum of (CF3)2NF. . F19 magnetic resonance spectrum of CZF5N=NCZF5 . F19 magnetic resonance spectrum of the CF3 and 7 a o. -CFz group of CF3CFZ€F2CFZN=NC4F9. . F19 magnetic resonance spectrum of the B—CFZ and ’Y (1 'y—CFZ groups of CF3CFZCFZCFZN=NC4F9 . F19 magnetic resonance spectrum of (CF3)2NHgN (CF3)2 . F19 magnetic resonance spectrum of (CF3)2NCOOCH3 Experimental and theoretical F19 magnetic reson- ance spectra of the CF3(a) and CF3(b) groups of a b CF3CCIZCFC1CF3 . ix Page 93 93 94 94 96 96 100 100 101 101 103 103 104 LIST OF FIGURES - Continued FIGURE 37. 38. 39. 40. 41. F19 magnetic resonance Of CF3CCIZCFC1CF3 . - 1 . F 9 magnetic resonance 19 . F magnetic resonance 1 . F 9 magnetic resonance 1 . F 9 magnetic resonance Page spectra of the CFCl group ......... . . . . . . . 104 spectrum of CFCIZCCIZCFZCI 106 spectrum of (CF3)ZNCF=NCF3 106 Spectrum of (CZF5)ZNF. . . . 107 spectrum of (C2F5)3N . . . . 107 INTRODUC TION The investigation of molecular structure has been fruitfully pursued through the use of many physical methods. Among these are infrared, Raman, ultraviolet, microwave, and nuclear—magnetic resonance spectroscopy, X—ray and electron diffraction, and electric dipole moments. Nuclear magnetic resonance spectroscopy can supply information concerning the nuclear configurations and electronic structures of mole— cules if those molecules contain nuclei which possess magnetic moments. There are many examples in the literature of the application of nuclear magnetic resonance spectroscopy to structural problems (1, 2, 3). The research reported in this thesis consists of the following: (1) examination of the nuclear magnetic resonance spectra of several substituted cyclopropanes in order to determine what features of the nuclear and electronic configurations present in this series of compounds are reflected in the observed spectra, (2) investigation of the nuclear configuration of several fluorocarbon derivatives of sulfur hexafluoride and fluorocarbon nitrogen compounds by the method of nuclear magnetic resonance spectroscopy, and (3) determination of the manner in which the nuclear magnetic resonance spectra of some fluorine compounds vary with changes in molecular structure. HIS TORICAL REVIEW The cyclopropane ring has been shown to undergo many reactions characteristic of an unsaturated molecule and for this reason the Sug— gestion has been made that there is some similarity between the electronic structure of the cyclopropane ring and the olefinic bond (4). Theoretical investigations (5, 6) and physical measurements (7, 8) have lent support to this conclusion. Rogers has obtained evidence of the conjugating power of the cyclopropane ring through studies of electric dipole moments and ultraviolet absorption spectra (7). At the time this research was initiated there was no published work on nuclear spin- spin coupling constants in three-membered rings. Recently, Reilly and Swalen have published a paper dealing with the nuclear magnetic resonance spectra of some simple epoxides (9). They found that the cis coupling constants were larger than the trans coupling constants and that the nature of the substituents on the ring had only a minor effect on the magnitudes of the coupling constants. Mortimer has obtained the cis and trans coupling constants in ethylene oxide, ethylene sulfide, and ethylene imine by observing carbon-13 satellite lines in these compounds (10). In each case he has assigned the larger coupling constant to the protons is to one another. Gutowsky, Karplus, and Grant have reported the coupling constants in some epoxides and in N-methyl ethylenimine but they were not able to assign specific values to cis and trans interactions (11). Jackman has reported that the spectrum of trans-dibromocyclopropane consists of two triplets from which he concluded that the cis and trans coupling constants are equal with a value of 6. 0 cps (12). However, as has been pointed out by Gutowsky, the invoking of accidentally equal coupling constants to explain an experimental spectrum is not always valid (13). In the particular case discussed by Jackman the assumption of equal coupling constants is most probably incorrect. Muller and Pritchard have observed the natural-abundance carbon—l3 satellite lines in cyclopropane which appear as "normal“ quintets. They obtained a coupling constant . of 7. 5 i 0. 5 cps. presumably from a first-order perturbation theory analysis (14). Closs has reported the proton magnetic resonance spectra of several mixtures of substituted cyclopropanes as well as the spectra of two pure compounds, 1, 1-dimethyl-2-chlorocyclopropane and trans- l, 2—dimethyl-3—chlorocyclopropane (15). The coupling constants for the v'ic'inal protons were found to be 7.0 cps. and 4.0 cps. for the former compound and 6. 5 cps and 3. 5 cps for the latter compound with the larger coupling constant for each compound assumed to be for trans protons. In both spectra the peaks due to the ring protons were partially obscured by the methyl resonance and a complete analysis of the spectra does not seem to be possible. The assignment of the larger value to the trans coupling constant does not agree with the results of the research reported in this thesis or with theoretical predictions. This point will be discussed further in another part of this thesis. Smidt and de Boer have examined the proton magnetic resonance spectra of some derivatives of nitrocyclopropane (16). In the analysis of the spectrum of trans—1- nitrocyclopropane-l, Z—dicarboxylic acid the authors assumed that the cis and trans coupling constants were equal and that the chemical shifts of the two geminal protons were identical. The validity of these assump— tions is highly questionable and their results are undoubtedly in error. The spectrum of l-nitrocyclopropane—l, 2-dicarboxylic anhydride was analyzed to give values for the cis and trans coupling constants of 9. 0 cps and 6. 3 cps. The assignment of a specific value to the cis or trans coupling constant was not made. Ullman has reported the coupling constant between the methylene protons and the ring protons in trans—3- methylenecyclopropane—l, 2-dicarboxylic acid to be 2. 5 cps (17). In the case of fluorine magnetic resonance spectroscopy the emphasis has been on obtaining and correlating chemical shift data. It has been found theoretically (18) and experimentally (19, 20) that, in general, covalently bonded fluorine atoms tend to be less shielded than fluorine atoms participating in an ionic bond. For example, in fluorocarbons the fluorine nuclei experience increased shielding in the series CF3, CFZ, and CF which is opposite to the order of proton chemical shifts in hydro- carbons. In the case of chlorofluorocarbonsthe subStitution Of a chlorine atom for a fluorine atom results in a decrease in shielding of the remain- ing fluorine nuclei on the carbon atom being considered (21, 22). This is the reverse of what would be expected from electronegativity considerations. Gutowsky has suggested that the explanation for this effect is that fluorine has a greater tendency to form partial double bonds than does chlorine and in doing so the fluorine nuclei become less shielded (22). Spin-spin coupling constants between fluorine atoms are much larger than proton coupling constants and as a result coupling between fluorine atoms four or five bonds removed may often be observed. The magnitude of the coupling constant between fluorine atoms two bonds removed varies from 30 cps to 400 cps (23). McConnell has found that the cis coupling constants between two fluorine atoms in substituted ethylenes are in the range 33-58 cps and the trans coupling constants vary from 115—124 cps (24). An extensive study of the proton and fluorine coupling constants in substituted fluorobenzeneshas been carried out by Gutowsky, Holm, Saika, and Williams (25). These authors found that the magnitudes of the fluorine-fluorine coupling constants decrease in the order ortho> para > meta while for the proton—proton and proton-fluorine coupling constants the order is as expected, ortho > meta > para. The amount of information available concerning coupling constants involving fluorine atoms separated by more than two bonds in acyclic Systems is limited. Roberts has found that the coupling constant between vicinal.fluorine atoms in CFzBrCBrzF is 18 cps (26). In (CF3)ZCHCFZOCH3 the coupling constant between the fluorine atoms in the CF3 and CFZ groups is 11 cps (19), while in CF3CFZCFIC1 the coupling constant between the fluorine atoms of the CF3 group and the fluorine atom of the CF group is 10.8 cps (27). There are several anomalies in the relative magnitudes of fluorine spin- spin coupling constants. As the number of bonds between inter- acting fluorine nuclei increases the magnitudes of the coupling constants often increase whereas in proton coupling constants there is a severe attenuation in magnitude of the coupling constant with increase in number of bonds betWeen coupled nuclei. Another striking peculiarity is found in the perfluoroethyl group, CF3CF2, where the magnitude of the coupling constants between fluorine nuclei in the CF3 and CFZ groups is usually so small that it is not measurable. In (CF3)ZNCFZCF3 the fluorine coupling constant between the N(CF3)2 group and the CF; group is 16 cps and between the N(CF3)2 and CF3 groups the coupling constant is 6 cps. (28). However, there is no detectable coupling between the CF3 and CFZ groups. In the molecule CF3CFZCFIC1 the coupling constant between the fluorine nuclei in the CF3 and CF: groups is zero (27). The low-resolution fluorine magnetic resonance spectra of most of the fluorine compounds studied in this work have been previously reported. With two exceptions, the fluorine spin- spin coupling constants have not been reported. Preliminary studies performed in this laboratory on the fluorine magnetic resonance of some perfluoroalkyl derivatives of sulfur hexafluoride have been reported by Dresdner and Young (29, 30). Other fluorine ,magnetic resonance spectra of perfluoroalkyl derivatives of sulfur hexafluoride have been published by Muller, Lauterbur and Svatos (31). The fluorine chemical shifts in some fluorocarbon nitrogen com— pounds have been reported by Muller, Lauterbur, and Svatos (19), and some results of preliminary studies of the fluorine magnetic resonance spectra of several fluorocarbon nitrogen compounds obtained in this laboratory have been published by Dresdner and Young (32, 33). THEORY Nuclear Energy Levels It is known that certain nuclei possess magnetic moments and intrinsic spin. Pauli suggested this in order to account for hyperfine splittings found in the optical spectra of some atoms (34). Subsequent experimental investigations have confirmed this hypothesis. If such a system of magnetic nuclei is placed in a magnetic field the nuclei will experience a torque which will tend to line them up with the field. It is then possible for these nuclei to absorb energy from a magnetic field which oscillates at the proper frequency and this absorption gives rise to the phenomenon of nuclear magnetic resonance. It is convenient to first consider this system classically as a charged spinning particle in a magnetic field. The time rate of change of the angular momentum is equal to the torque applied d M. where M is the angular momentum and P is the applied torque. The M motion of charge which results from the spinning particle sets up a current which can interact with the magnetic field. The torque, P, will be ’11: u X H (2) where u is the magnetic moment due to the current and H is the magnetic M field intensity. Equation (1) now becomes dM ow H dt fixm (3) For a volume distribution of current the magnetic moment is defined as (35) 7 l = ' dV 4 if. a. / LXI < ) Where j is the current density. The relation used for the current density is , e 2.: a P x ‘5’ where p is the mass density and xthe velocity. Equation (4) now becomes e 1 , i—ZmC/flxpde. (6) The integral in equation (6) is the total angular momentum and the relation between magnetic moment and angular momentum can be written H: e M (7) w- 2mc M It can be seen that the ratio of u to M is a constant. This constant will have to be modified when a magnetic nucleus is considered since its spin angular momentum is quantized. Using relation (7), equation (3) becomes CIM _ e dt _Mx2mc (8) This is the equation of motion of a vector of constant magnitude which is rotating with respect to a space-fixed axis with an angular velocity 2).. given by es :2 = - (9) 2mc Therefore, the effect of a magnetic field on a charged body is to cause the angular momentum vector M to precess about the field direction E with an angular velocity given by equation (9), which is known as the Larmor frequency. If a magnetic field rotating with a frequency equal to the Larmor frequency is impressed perpendicular to the field Ii it will exert a torque on M and energy will be absorbed by the system. The system is then said to be in resonance. Alternatively, magnetic resonance can be described in quantum mechanical terms. The magnitude of the nuclear spin angular momentum vector, ’1” , is MW ’6 and the maximum observable component of the nuclear spin angular momentum vector along a spacenfixed axis is I (1', where I is the nuclear spin quantum number. The component of the nuclear spin angular momentum vector along the space—fixed axis can take any of the 21 + 1 values of m m: 1, 1—1, 1-2, ., . . , —1+ 1, -1 (10) where m is the nuclear magnetic quantum number. The magnetic moment can be related to the spin angular momentum by an expression similar to the classical relation (7) H=ge 1’6 (11) N- 2 mc ”- where g is the nuclear g factor which is analogous to the Landé factor for electrons. Equation (11) can be written in the form #:71’3 (12) where 'y is the magnetogyric ratio. Referring to equation (12), it is seen that the magnetic moment can assume 21 + 1 orientations with respect to a space-fixed axis. The energy of a dipole in a magnetic field is E : _ .1- H (13) which can be rewritten as E=-HZHo=-Vlz’fiHo (14) by using equation (12) and assuming that the applied field, H0, is in the z direction. IZ can be replaced by the magnetic quantum number, m, which gives the allowed values of IZ. The selection rule for allowed 10 transitions is Am 2 + l (15) which leads to AE v41 Ho (16) for the energy difference between adjacent energy levels. Since AE=hv=yZ—h—n- Ho (17) the frequency of electromagnetic radiation required for a transition is H 7. .° (1.. v: where v is in cycles per second (cps). Equation (18) can be recast into the form 2nv=yHo=w (19) where w is in radians per second. It can be seen that equation (19) is the same as the classical expression (9) for the Larmor frequency. Relaxation The discussion presented in the last section was devoted to the behavior of a single nucleus, possessing a magnetic moment, in a magnetic field. In practice, however, one must consider a system of interacting nuclei in a magnetic field. If an assembly of nuclei, each here chosen to have spin quantum number of ;— for convenience, is placed in a magnetic field and allowed to come to thermal equilibrium, the ratio of the number of nuclei in the lower energy level (N+) to the number of nuclei in the upper energy level (N_) will be given byithe Boltzman fac to r N+ ’Y’leo EH0 ZHHo r: e kT II (D H W 1-1 II (D W H (20) 11 Equation (20) shows that there is a slight excess of nuclei in the lower energy level. It is well-known that the Einstein transition probability coefficients for induced emission and absorption of electromagnetic energy are equal (36). Furthermore, Purcell has shown that the probability of spontaneous emission is negligible in this case (37). Thus, it is because of the slight excess of nuclei in the lower energy level that nuclear magnetic resonance absorption occurs. The rate at which a system of magnetic nuclei reaches its equiv librium distribution is also of importance. Suppose that the system of nuclei (I = i— ) is not in a magnetic field,in which case the populations of the two spin states are equal (in fact, the two energy levels are degenerate). When the system is placed in a magnetic field it will proceed to its equilibrium distribution at a certain rate. The excess number of nuclei in the lower state is n = N+ - N- (21) and it is the time rate of change of n that is of interest. The transition probabilities per unit time for absorption and emission are represented by W+ and W, respectively. It should be noted that in the absence of a perturbing radiofrequency field, which is the case being discussed here, transitions take place through the interaction of the magnetic nuclei with other degrees of freedom, that is, with the lattice. The term lattice means the molecular system in which the nuclei are imbedded. At equi- librium the total number of upward transitions per unit time must be equal to the number of downward transitions per unit time. Therefore W+ N+ = W — N- (22) and from equation (20) L %j-—=e kT =1+—2“H°~ (23) From equation (23) we obtain __4 12 _ HHo W-—W(1+ kT ) (24) and _ _ HHo W+—W(l kT ) (25) where W is the mean of W+ and W_° Thus one can see that in the absence of a radiofrequency field the probability of a downward transition per unit time is greater than the probability of an upward transition. It is for this reason that our system can come to equilibrium when it is suddenly immersed in a magnetic field. A downward transition increases the excess number of nuclei in the lower level, n, by two and an upward transition decreases n by two. Thus the rate of change of n is (In dt = 2 N_W_ — 2N+W+ (26) Using equations (24) and (25) this becomes dn __ |-L Ho l-L I{0 dt _ 2N- [W(1+ kT )] -2N+[W(l- kT )] (27) Equation (27) can be cast into the form dn '51-;— — Z W (neq - n) (28) where neq, the excess number of nuclei when the system is in thermal equilibrium with the lattice, is given by _ |~L Ho A time T1 can be defined 1 T1= W (30) which is a measure of the rate at which the spin system approaches thermal equilibrium with the lattice. This time is referred to as the spin-lattice relaxation time. For nuclei of spin one-=half the magnetic l3 moments can interact with magnetic fields only and thermal equilibrium between the spin system and the lattice can arise only from interaction with local magnetic fields. There are several mechanisms through which spin-lattice relaxation can take place (38). The magnetic moments of nuclei which are rotating and translating produce local fluctuating magnetic fields which may have a component whose frequency is equal to the resonance frequency of the nuclei in question. This component is able to induce transitions between energy levels analogous to an applied radiofrequency field. In this case we may have intramolecular relaxation as well as intermolecular relaxation. The presence of paramagnetic ions in a sample affords another mechanism for spin-lattice relaxation. The magnetic moment of a paramagnetic ion is of the order of 103 times as large as a nuclear moment. Thus the local fluctuating magnetic field is larger and the relaxation time shorter. Another possible mechanism for spin—lattice relaxation is the effect produced by the anisotropic shielding of a nucleus (39, 40). In this case the secondary magnetic field due to electronic currents will have a component perpendicular to the applied magnetic field and as the mole- cule rotates this component may cause transitions between the nuclear energy levels. For nuclei with spini> ;— there is another mechanism through which spin-lattice relaxation can take place. These nuclei possess quadrupole moments which interact with electric field gradients and produce shorter relaxation times. Quadrupole effects and spin-lattice relaxation are discussed in detail by Andrew (41). Line Broadening There are several causes of line broadening in nuclear magnetic resonance spectroscopy. The natural line width of any spectral line is l4 determined by the lifetime of the upper state since there is a finite prob- ability of spontaneous emission. As was mentioned previously this effect is not important in nuclear magnetic resonance. Due to the possibility of the nuclei undergoing transitions as a result of interactions with the lattice, the finite lifetimes of both states is important. This is the spin-lattice relaxation process discussed above. The magnitude of 1 the broadening can be estimated from the uncertainty principle to be -— T from which one notes that shorter relaxation times lead to greater line1 widths. In some instances direct magnetic dipoleadipole interactions lead to line broadening greater than that which may be accounted for by spin- lattice relaxation. This results from nuclei staying in the same relative positions for a long time as in the case of solids or highly viscous liquids. In these situations another relaxation time T2 is defined which is shorter than T1 and this is often given the name of spin= spin relaxation time. In liquids and gases the rapid movement of the molecules tends to average out the direct dipole-dipole interaction and T2 is approximately equal to T1. As was mentioned above, nuclei withl> %— have quadrupole moments which interact with electric field gradients and this results in shorter relaxation times and broader lines. Variations in the applied magnetic field will induce nuclear transitions at slightly different frequencies and lead to broad resonance lines. Saturation If a radiofrequency field of large amplitude is applied to a system of nuclei the excess number of nuclei in the lower level becomes very small and the spin system is said to be saturated. A saturation factor may be defined as (42) 15 2o = = I 1+ 72 H12 Tszlu1 (31) eq where H1 is the radiofrequency field. If suitable values are substituted in equation (31) one finds that saturation becomes appreciable for protons when H1 is of the order of 10”4 gauss. Saturation will distort the observed signal in such a way as to broaden it as well as reduce the overaall intensity. The Chemical Shift In 1949 Knight found that the resonance frequency of certain metals in a magnetic field depended upon the manner in which the metals were chemically combined (43). This same effect was found by Dickinson (44) and Proctor and Yu (45) for non-metallic elements in different compounds. Soon afterward Arnold, Dharmatti, and Packard (119) found that structually different protons in the same molecule give rise to separate resonance signals and as an example they showed that the proton magnetic resonance spectrum of ethyl alcohol consisted of three distinct peaks. This effect arises from the magnetic shielding of the nuclei by the atomic or mole= cular electrons and is known as the chemical shift. The motion of electrons when placed in a magnetic field results in a secondary magnetic field which acts on the nucleus. This secondary magnetic field is proportional to the applied magnetic field and the proportionality constant, or , is called the screening constant. The net magnetic field experienced by a nucleus, H, can be expressed as H=Ho-GHO:Ho(l-6) (32) where H0 is the applied magnetic field and 0* H0 is the secondary magnetic field produced by the circulating electrons. The field dependence of the chemical shift given by equation (32) has been demonstrated experimentally. Most high resolution nuclear magnetic resonance studies have been l6 concerned with H1, F19, P31, B“, N14, and Cl3 and,of these, proton and fluorine chemical shifts have been the most widely investigated. The ‘ experimental data show that the chemical shifts associated with protons are much smaller than those of other nuclei and this may be attributed to the lower electron density around the proton as compared with other nuclei. There have been many attempts to relate experimental chemical shifts to physical properties. Dailey and Shoolery (46), and Narasimhan and Rogers (47) have shown that there is a general correlation between chemical shifts of u-methylene protons and the electronegativity of the substituent in ethyl compounds. The relation of chemical shifts to dipole moments and Hammett's a- values has also been discussed in the literature (48). Although the experimental determination of chemical shifts has been quite successful the theoretical calculation of these quantities has proven to be difficult. By using second-order perturbation theory Ramsey has developed an expression for the magnetic shielding constant (49) z e l 4 3 2 <0 -- 0>— -- <0 -- r: 0> 6 —-—23 c I E r I (3 /A E) If mJ mk/ I (33) where 6‘ is an average screening constant and Ink has components such as Insz _ e’h/Z mci (Xkd _ yk L ). (34) dyk dxk AE is an average excitation energy and rk is the distance of electron k from the nucleus being considered. The first term in equation (33) is the same as Lamb's term for the diamagnetic shielding of atoms (50). The second term is often called the second—order paramagnetic term because it arises from the lack of spherical symmetry of the electron distribution and hence diminishes the effect of the diamagnetic circulation of the electrons. The difficulty in calculating shielding constants is v.- 17 caused by a lack of knowledge of ground state Wave functions which are needed to evaluate the paramagnetic term. If the average energy approximation is not used wave functions for excited states of molecules are also required. The screening of a nucleus depends upon the orientation of the molecule in the magnetic field and the screening constant should be expressed as a tensor. However, in high-resolution nuclear magnetic resonance spectroscopy the molecules are rotating and tumbling quite rapidly and the screening tensor will assume an average value (51) which is given in equation (33). Ramsey has applied equation (33) to the calculation of the screening constant in the hydrogen molecule where he was able to avoid the calcu= lation of the paramagnetic term by evaluating it from experimental data. The results are in good agreement with experiment. Several authors have used a variational procedure to calculate the screening constants in Hz and other diatomic molecules with fair success (52, 53, 54). However, quantitative application of this method to larger molecules is very diffi- cult. The problem of computing chemical shifts can be approached in a semi-quantitative manner by assuming that the total screening can be treated as a sum of separate contributions. This was first done by Saika and Slichter who divided the screening into three terms: (1) the diamagnetic correction for the atom in question; (2) the paramagnetic term for the atom in question; and (3) the contribution from other atoms (18). These authors applied this method to the analysis of fluorine chemical shifts. In 1951 Gutowsky and Hoffman (55) showed experimentally that there is a linear relationship between the chemical shift of fluorine and the electronegativity of the atom to which it is bound. This was presumed to be a reflection of the ionic character of the bond in question, the more l8 covalent the bond the less shielded is the fluorine atom. Saika and Slichter estimated that changes in the diamagnetic term could not account for the large range of fluorine chemical shifts and they therefore attributed the observed chemical shifts to the variation of the local paramagnetic term. For the F' ion the paramagnetic term is equal to zero and for a covalently bonded atom this term would give a negative contribution to the screening constant. By using simple valence bond wave functions the paramagnetic term was evaluated for F2 and found to be of the correct order of magnitude, that is, it agreed fairly well with the chemical shift between F2 and HF. This treatment also accounts for the variation in chemical shift with the electronegativity of the substi— tuent atom. Although the observed fluorine chemical shifts may be interpreted as due to a change in the local paramagnetic contribution to the screening constant, no simple explanation of proton chemical shifts has been forth- coming. The local paramagnetic contribution to the shielding would not seem to be important in the case of protons because of the lack of low energy 3 states. BecauSe of the low electron density around the proton, electron currents in other parts of the molecule may be expected to contribute significantly to the magnetic shielding of a proton and such long-range shielding would account for the lack of a general correlation between proton chemical shifts and ionic character of the bond. The most useful treatments of long—range shielding of protons are those OchConnell (56) and Pople (57, 58). The electron currents on other atoms in the molecule are replaced by point magnetic dipoles and the dipolar field at the nucleus being considered is calculated. It is found that this shielding depends upon the anisotropy of the diamagnetic sus- ceptibility of the group which is contributing to the shielding and upon the relative orientation of the shielding group and the nucleus being shielded. If the shielding group, G, has axial symmetry the expression for the contribution to the shielding of nucleus N has the form . 19 G G A' 2 _ —£— < 1- 6N 3R Lo 3 COS 9 > av (35) G. where A39 is the anisotropy of the molar susceptibility of group G G G G AQL : 7‘11 ' 711. ~ (36) 9 is the angle between the symmetry axis of group G and R, where R is the magnitude of the radius vector from nucleus N to the electrical center of gravity of G. Equation (35) leads to the result that for linear molecules there will be a positive contribution to the proton shielding and the proton signal will be shifted to high field. This has been con— firmed experimentally for acetylene and the hydrogen and alkyl halides (56, 58, 59) . The proton shieldings in aromatic molecules have also received considerable attention (57, 60, 62). In these molecules there are inter= atomic electron currents flowing around closed loops which set up secondary magnetic fields at the protons. The contribution of these fields to the shielding can be estimated by replacing the current with a magnetic dipole at the center of the ring. As an example, for benzene the contri- bution to the screening constant from this interatomic circulation of electrons is (57) ezaz 2mczR3 A6‘ = — (37) where a is the radius of the ring and R is the distance from the center of the ring to the proton. One can note from equation (37) that aromatic protons are deshielded by these electron currents. Other authors have refined this model by recognizing that the current distribution is in the form of two rings above and below the plane of the carbon atoms (60, 61). In order to investigate further the validity of the ring—current model, Waugh and Fessenden measured the proton chemical shifts of some 1, 4-polymethylenebenzenes(60). Some of the methylene groups will be directly above the ring in which case the protons of these groups should 20 be positively shielded if the proposed model is correct. Upon examina- tion of the nuclear magnetic resonance Spectra of these compounds it was found that the resonances of some of the methylene protons were shifted to higher field. The ring current model has also been successful in explaining the chemical shifts in polyaromatic molecules (62) and in some porphyrins (6 3). Nuclear Spin- Spin Interactions Soon after the discovery of the chemical shift it was found that some spectral lines possessed fine structure and that these multiplets were field independent and hence were not due to chemical shifts (64, 65, 66). Since in high-resolution nuclear magnetic resonance direct magnetic dipolar interactions between nuclei are averaged to zero by molecular motions the observed fine structure must have its origin in some other interaction. Experimental investigations have supported the original proposal of Gutowsky (66) and Hahn and Maxwell (65) that the energy of interaction is of the form ENN' = h JNN'AIN'ILNI (38) where the energy, ENN" has units of ergs and JNN" the Spln— Spln coupling constant, is in cycles per second. 'LN and “I“N' are the spin angular momentum vectors of nuclei N and N'. The interaction energy as given by equation (38) has the desired property of rotational invariance. ' The theoretical basis for the mechanism of spin—- spin coupling has been given by Ramsey and Purcell (67) and Ramsey (68). By employing second-order perturbation theory they have shown that the nuclear spin- spin interaction proceeds through the molecular electronic system. The Hamiltonian for an electronic system in the presence of nuclei possessing magnetic moments is fi=fil+fiz+fi3+fi4 (39) where Hl : ifl— mk][(!h/i) Ak + (e/c) ill-1 'YNINX ikN/rgkNF + V + HLL+ H +£1— (40) LS 55 H2 : 2.816 ENYN{3(§k DEkN) (.I.N°5§kN) rkN - El: “..I.N rkN 3 (411 H3=(16n(541/3)2 v 6 (r )s oi <42) kNN kN k N . 3 '- _ _ 3 1 ,, . =5 _ . " H4 ‘ ’5 ZNN' INVN' [ 3(1N £NN1) (~I-N' ~r4NN') rNN‘ lN lN'rNN'] (43) The term in equation (40) involving 2k gives the total electronic kinetic energy and magnetic interactions between electronic orbital motions and nuclear moments. V is the elctrostatic potential energy and ELL” HLS, and fiSS are, respectively, the electron orbital—orbital, spinaorbital, and spin-spin interactions. I is the nuclear spin angular momentum in units “N of Ahand «likN is r - 5N where 21k designates the coordinate of the k'th electron. Hz represents the magnetic dipolendipole interactions between electrons in non-s orbitals and nuclear moments. «5k is the electron spin vector and Bis the Bohr magneton. H3 gives the Fermi interaction between electron spins in s—states and nuclear spins (69). This is often named the contact term as it depends upon the electron density at the nucleus. H4 is the term for the direct magnetic interaction of the nuclei with each other. As was mentioned previously, this interaction averages to zero for liquids and gases which are the states of matter employed in high resolution nuclear magnetic resonance. The nuclear spin-= spin interaction energy arises from the terms involvinglN and l-N' when the above Hamiltonian is treated by second—order perturbation theory. For a molecule in a '2 state Hz and H3 do not give any first-order perm turbation of the ground state electronic energy (70). By second=order permrbation theory E=- Z'<0II-—l|n> n En- E0 (44) It is found that by using this expression the energy of interaction of two magnetic nuclei is of the form (68) ENN' : h JNN' lN'iN' + thN ' lNN1'lN' (45) where’iNN' is a dyadic of zero trace. In high—resolution nuclear magnetic resonance frequent collisions, which average the molecular orientation over all directions, make iNN' average to zero and as a result : . 4.6 ENN' h JNN'rl‘ lN' ( ) Consider the energy of interaction arising from the Fermi contact term. Using equations (44) and (42) (3) 2 E : — 1 NN, 2 ( 6Tr (Mi/3) yNyN, an’j < 0 | 5 (ka)~S-k.~I-N|n> <21) 5(ng‘) ~s-j .lego > (47) E - E n 0 where the terms involving “I'N and IN' simultaneously have been picked out. This equation is in the form of equation (46) provided (3) _ JNN' _ 42/31.) (16V (326/3) YNYN: mi,- < 0 l6(£kN)§k|n > ' (48) E-E n o Since wave functions for excited states of molecules are not well-known it is assumed that the triplet excitation energies En—Eo can be replaced by a Suitable mean excitation energy AE. Karplus (71) has recently answered criticism of the use of this closure approximation (72). With this approximation equation (48) becomes Jgiw : -(2/3 h) (16 TI 5.5/3): 7:911 < o | EjéukN) 6 (LquNgke §j (o; 3 9 (49) The other terms in the Hamiltonian which involve the nuclear Spin can be treated in the same manner as the Fermi contact term. The total coupling constant will be a sum of these terms g (1a) (1b) (2) (3) JNN’ — JNN' + JNN' + JNN' + JNN' (50) 3 where JIVIV' is the coupling constant due to the Fermi contact interaction, 3:12), and J(1:I]I\)I‘ are the contributions to the coupling constant due to the interaction of the electron orbital motion with the nuclear moments, (z) and JNN' between nuclear and electronic spins. is the contribution due to the direct magnetic dipole interaction Ramsey has applied this theory to the molecule HD where he found that the electron orbital terms made a negligible contribution to the coupling constant. The contact term was found to have a magnitude of 40 cps whereas the experimentally determined value is 43. 5 cps (73). This result suggests that the contact term makes, by far, the most important contribution to the coupling constant in the HD molecule. Stephen (74) and Ishigiuro (75) have calculated the coupling constant in HD using a variational procedure and obtained similar results. It may be seen from the above equations that the contributions to the spin- spin coupling constants can be calculated provided the ground state wave function for the molecule concerned is available. In general, these wave functions are not available and approximation methods must be used. The molecular orbital approximation as developed by McConnell will be discussed first (76), and then in more detail the valence bond approach of Karplus (77,78, 79,11). The Fermi contact term would be expected to give the largest contribution to the interaction energy of two protons not directly bonded to one another. This is because the electron distribution around a proton in a. molecule can be adequately described by a liatomic orbital while the other terms in the Hamiltonian depend upon angular properties of electron orbitals. The wave function used by McConnell was an anti- symmetrized product of molecular orbital and spin functions. The mole- cular orbitals were taken to be linear combinations of atomic orbitals (LCAO-MO's). Using these functions equation (49) becomes (3) _1_6 2 ~ 2 2 where the bond order, nHH' is nHH' : 2 Ti aI-lo. aH'u (52) and < ¢H I 5(r) I ¢H > = «ti, (r = 0) = film) (53) The ac are coefficients of the atomic orbitals 43H If one takes AE = 10 ev and an effective nuclear charge of 1.00 for the in the LCAO-MO. proton the result is Jéfg. : 200 772' . (in cps) (54) McConnell has used this expression to obtain an order of magnitude estimate for the coupling constant in H2 and CH4. In general, this equation can be used if it is possible to obtain or estimate the proton- proton. bond orders. It does seem that bond orders could be obtained from equation (54) by using experimental values for the coupling con- stants and, in fact, Eyring (80) has estimated the barrier to internal rotation in ethane by using observed HCCH' coupling constants and Linn-mi \\ equation (54). The use of this equation always leads to positive proton- proton coupling constants but there is, however, experimental evidence that this coupling constant may have either Sign (11). McConnell esti— mated qualitatively the importance of the electron-orbital and electren.= dipole terms for fluorine nuclei and found that these terms can make significant contributions to the total coupling constant. Pople has estimated the contribution of the electronworbital term to the coupling constant for several fluorine—containing groups by relating this term to the anisotropic shielding of the fluorine nuclei (81). The results indicate that the electron orbital term does make a positive contribution to the coupling constant although it is still a small part of the total coupling constant. Williams and Gutowsky have discussed some experimental H-l-l, H—F, and F—F coupling constants in fluorobenzenes in terms of molecular orbital theory. By using the experimental magni- tudes and relative signs of these coupling constants they were able to determine the relative importance of the various interactions which con- tribute to the coupling. They were able to estimate the various bond orders in these molecules as well as to determine that the amount of 2 _s_ character in the C-F bonding orbital was of the order of 5%. It was found that the largest contribution to the coupling constant came from the Fermi contact term. As was noted above, the use of LCAO—MO wave functions for calculating spin— Spin coupling constants does notgive quantitative results. Further, the estimated proton-proton coupling constants are always positive when this model is used. The valence bond method gives results which agree quantitatively with experimental coupling constants and ( also yields negative proton-proton coupling constants in some instances. In equation (49) the ground state wave function required to evaluate the matrix elements can be expressed according to the methods of the valence bond approximation (82, 83, 84). The system considered involves 2n electrOns and Zn orbitals with spin degeneracy only and the molecule in a singlet state. The ground state wave function can be expressed as a linear combination of independent valence bond structures ((1 , J _ ,_ (2n)! Y°_?Cj\1/j J—l,2,...,m (55) where 1 R 1 1— P +1]. : :1: ER (—1) R[( (211,212 2P (~1) Pa(1)(3(1)b(2)a(2) . . - 2n(2n)c1(2n)] (56) The spin functions c1 and [3 correspond to the spin components of +4; and '1 "g“ respectively, R is the operation of interchanging the spin functions 0. and B of orbitals bonded together, and P is the permutation operator representing the permutation of the electrons among the orbits and associated spins. The factor (—l)R is equal to +1 for an even number of interchanges and -l for an odd number and (-1)P is equal to +1 or -1 according to whether P corresponds to an even or odd permutation. The Rumer-Pauling diagrams allow one to determine the complete set of canonical structures and afford a method of calculating the coefficients of the Coulomb and exchange integrals which occur in the secular equation. The ~S»j - Sk term in equation (49) can be replaced by using the Dirac equation (85) s l . : — 1 . ° PJk 2 ( + 4 §., sk) (57) s where ij represents [the exchange of spins of electrons j and k. Using equation..(55), equation (49) becomes _ 1 2 16 n M; z .. JHHI“'(4AEH3hH 3 )‘Ylemclcm ’ «(21) Ekwer) 5(rkH.)(2ijk - 1) I \ym > (58) 27 There are two types of integrals which must be evaluated h =<%th u%£ Mnfldlwnf> 6% and S 12 = < (pl IJZ’k 6 (,IgJ-H) 6(5kI-l') ij I \Fm > (60) I} is in the form of a Coulomb integral and I; has the form of an exchange integral. Thus, with the assumption of orthogonal orbitals, the Rumer— Pauling diagrams can be used to evaluate the coefficients of these integrals as was mentioned above. The result is _ 1 2 l6wfifi , JHH' ‘ (m) (371;) (-—3'—)Z'Y;_I¢H(o) (til—160) Emclcm(—;—’.-l_‘: ) c [1+ 2 f (P’ l] (61) l, m HH‘ where i1 is the number of islands in the superposition diagram of , m structures 1 and m and fl m between the HCC plane and the H‘CC plane. The exchange integrals, which must be evaluated in order to compute the coefficients in the ground state wave function, were expressed in terms of the angles 9 and 4) where 0 is the HCC angle and was chosen as tetrahedral for ethane. In this manner the ground state wave function was obtained for values of 4) from 00 to 1800 at 300 intervals. The results for ethane are shown in Table I. Table 1. Theoretical Coupling Constants for Ethane as a Function of Dihedral Angle (79) Dihedral Angle (o) Coupling Constant, JHCCH' (cps) 0° 8.2 30° 6.0 60° 1.7 90° -O.28 120° 2.2 150° 6.9 180° 9.2 —-——————————__—____________ 29 It may be noted from Table I that the coupling constant goes through a minimum at 900 and that the values for the coupling constants are not symmetric about this value. The angular dependence of .I H1 has HCC been confirmed to some extent experimentally (86, 87). A more thorough discussion of the agreement between theory and experiment will be con— sidered in a later section. In the case of ethylene the ground state wave function was computed for 9 equal to 1200 (s3Z hybridization) and for values of 4) equal to O0 and 1800. All 0‘- 1T interactions were neglected. Although the calculated values are somewhat lower than the observed values, the ratio of cis- __ to trans coupling constants is in excellent agreement with experiment. In addition to the HCCH' system, Karplus has treated the HCH! fragment by the valence bond method (11). In place of performing a separate calculation for every XYCHH' molecule the treatment is re- stricted to a four—electron, four-orbital problem. In this approximation, which is valid provided substituent effects are not important, there are only two independent valence bond structures to be considered. The exchange integrals are computed as a function of the HCH' angle (6) from which arises the angular dependence of the ground state wave function. The results are given in Table II. Table II. Theoretical Coupling Constants for CH2 Fragment as a Function of the HCH Angle (79) HCH Angle Coupling Constant, JHCH' (cps) 100° 32.3 105° 19.7 110° 12.1 115° 6.91 1200 3.05 125° 0 130° -2.62 \—————————————.—_—_—_——_—_ 30 For this system the agreement between theory and experiment is very good. The theory predicts that the coupling constant should become negative when the HCH angle reaches a value of 1250 and this has been confirmed for the molecule vinyl bromide. The results indicate that HCH‘ bond angles may, be determined fairly accurately by measuring the HCH' coupling constants. In the methods used above, the electronic coupling of nuclear spins Was treated as arising from S-type electrons. The contribution of Tr-electrons to the proton spin— spin coupling mechanism for aromatic systems has been discussed by McConnell (88, 89) and for non-aromatic molecules by Karplus (90). In order for the Tr—electrons in a molecule to participate in the proton spin— spin coupling the 17 system would have to interact with the O‘electronic system. If this 6117 interaction is taken into account when writing the molecular wave function the calculation of the coupling constant becomes very difficult because each molecule would have to be treated separately. McConnell and Karplus have made use of the fact that the mechanism of the nuclear spin— electron spin hyperfine interaction observed in the electron spin resonance of aromatic and unsaturated free radicals corresponds closely to the mechanism involved in the ‘IT electron contribution to proton spin—spin coupling. Use of this correspondence permits one to neglect configuration interaction in the molecular wave function and this simplifies the calculations. The results for aromatic molecules indicate that the TT electron contribution to the coupling interaction is small but that this coupling does not rapidly diminish with distance between protons as is the case in saturated mole— cules. For unsaturated non-aromatic molecules, the proton spin— spin coupling mediated by Tr electrons is often found to be appreciable for protons four or five bonds removed in certain molecules. The above theoretical treatments of nuclear Spin— Spin interaction energies allow one to interpret experimental spin- spin coupling constants in terms of molecular electronic structure and nuclear configuration. 31 Knowledge of the parameters involved in spin- spin coupling also aids in the interpretation of nuclear magnetic resonance spectra. Karplus has adopted the procedure of using the agreement between experimental and theoretical spin— spin coupling constants as a criterion for the validity of approximate molecular wave functions. In the valence bond approxi- mation, deviations from perfect pairing which appear in the total ground state wave function give rise to hyperconjugation. It has also been shown that the nuclear spin- spin coupling constant is sensitive to the presence of non-perfect pairing structures (11, 78, 79). Thus a compari- son of the calculated and observed coupling constants for vicinal protons should indicate the validity of the valence bond model in treating hyper— conjugation in ethane. Karplus has computed the hyperconjugation energy in ethane and found it to be of the order of 3 kcal/mole (91, 92). He has also shown that it is possible to obtain information concerning bond polarization parameters from experimental coupling constants between directly bonded atoms (92). Details concerning orbital hybridization may also be obtained from nuclear spin— spin coupling constants (93, 94, 95). Analysis of Spectra In order to obtain information concerning chemical shifts and spin— spin coupling constants from high-resolution nuclear magnetic resonance spectra it is necessary to treat the transition frequencies and intensities as a quantum mechanical problem. There has been a large amount of work published in the literature on the analysis of the spectra of various spin systems. The basis for this work has been given by Gutowsky, McCall, and Slichter (96),) McConnell, McLean, and Reilly (97), and others (98, 99). Pople, Schneider, and Bernstein (100), and Corio (51) have published extensive reviews on the analysis of nuclear magnetic resonance spectra. In this section the analysis of spin systems which have been experimentally studied in this work will be reviewed. '32 As was mentioned previously, the intrinsic spin vector Lb magnitude '\( I (1+1) IE and I is the component of the spin vector i z z direction. It can be shown that the square of the intrinsic spil 12, and I commute ~ z 2; _ 2:12 :0 IIZ IZI LIZ] and that if a set of operators commute with one another there e): set of functions which are simultaneously eigenfunctions of all t] is a set of eigenfunctions of I2 and I ‘ I, m ’V‘ 2 form an orthonormal set then operators (101). If 4) ,Ifcbl = I(1+1) ¢ ,m l,m where I, the spin quantum number, can have integral or half—im positive values or be equal to zero. I is the maximum componer. spin vector in the z direction. The eigenvalue equation for I is z 1z q)I,m: m qDI,m where m, the magnetic quantum number, has the values, m=I, I-l, I—Z, . . . , —I+1, -I Thus for every value of the spin quantum number, I, there are L values of the magnetic quantum number, m. The matrix e1eme1 the operator IZ can be evaluated by using equation (65) <4) llzl¢1m>=m6 1, m' mm' Where .6 mm' is the Kronecker delta. It may be noted from eq1 (67) that the Iz matrix is diagonal when the basis is the set (1)1 n Two other operators which will be found useful are the so-calle‘ (+) and lowering (-) operators + __ _ i _ I — IX 11Y 33 where Ix and Iy are, respectively, the x and y components of the vector. The result of operating on <1) "with Ii is (101, 102) l,m = W Im)(I—:Fm+ 1) ¢ i I. 4)I, m I, mil and the matrix elements for these operators are + __ < _ > = I? _ + 1 dim" I 1 «him «H m) (I m ) for m' = m i 1. The nuclei which are to be considered here are F19 both of which have I = -21- and m = i 1' . The eigenfunctions-f0 nuclei may be written ¢1,1 :0 TT and ¢1_,_1 :5 z 2' Equations (64), (65) and (69) become H N p I - ‘r(:—+ 1) a Izu:-;—q Izfi=-%-fi I uzl'fizo I‘a=[3 I+[3:u also (0.6): (5,0) = 0 (F3.B)=1 (and) 34 There is an important theorem in quantum mechanics which will be used in this section: if B is an operator which commutes with A and if h)! i and Y.) are eigenfunctions of A then the matrix element < \i’: lBl‘l’j > is zero unless ai :2 aj, where ai and aj are eigenvalues of A. Consider = aj. (82) If A is Hermitian <\.y:"'lBAl\)Jj> <\+’i*lABHYj>:::lLyi*> (s3) and < quj | AZ: (4);" > = ai <41," (13le >. (84) Hence (a1 - aj) = 0 (85) and if ai a! aj then <(Yi*|B|\yj> =0. (86) The discussion so‘far has dealt with the problem of a single nucleus whereas the actual systems consist of collections of nuclei. For this latter case the pertinent operators for a system of n spins are n I = z I. (87) n IS = i3 Isj ( S : X, Y: Z) (88) Z n 2 1:1.I=zg.+z.z,;.._1, (89) f n i I = 2 I. (90) J J The operators If and Is commute and it is thus possible to construct a set of functions which are simultaneously eigenfunctions of both Operators (103). The simpler representation which is used here is the products of the functions ¢I m given by equations (64):and (65).. Each 35 nucleus is represented by a ¢I m and the entire spin system is described by a number of products such as : l Mm) Tr,- ¢I,,,m; (9 ) J J These product functions are eigenfunctions of Iz : ? Izj IZ @(m) : mg) (m) (92) where the quantum number m is m=Zm_ (m=ZIj,ZI.-1,...-ZI-)(93) J J j j J j 3 It is possible to construct linear combinations of these product spin functions which are also eigenfunctions of“;Z As mentioned above, the systems of interest are those for which the spin quantum number of a nucleus I = é— . In this case, the product functions have the form §(m) = MN (3(2) 6(3) . .. (94) which will be abbreviated by @(m)=at3[3... (95) where the nuclear spin functions are written in serial order. The high—resolution nuclear magnetic resonance Hamiltonian Operator can be written as H Vii H:—[? 21v 21 I.+;_Z}.~I.I.°I-] (96) 1 where the first term comes from the expression for the energy of a nuclear dipole in a magnetic field and the second term is the electron- coupled nuclear spin— spin interaction term. Hi is the magnetic field at nucleus i and both terms are in units of cycles per second. 36 Note that the spin- spin coupling constant, J, also has units of cy per second. The Hamiltonian can be rewritten in the form H2-[Zvil.+$_E.JijI.-»I.] ( where vi (cps) is the resonance frequency of nucleus i in the ab: spin-spin coupling. The eigenfunctions and eigenvalues of this 'Hamiltonian mu found. The eigenfunctions will be expressed as linear combinati the basic product functions N 1 Wm: Z amn @n (m:1,ZJ° ° ° 7 2 n=1 where N is the number of spin states and is equal to 2P for a sy: P nuclei of spin one-half. The eigenvalues of the Hamiltonian c; found by solving the secular equation II_Irnn'6mnEml:o where Hmn is given by Hmnz<¢m|HI¢n> ( and the 43m, ¢n are basic products functions. The coefficients i1 equation (98) are obtained from the solutions of the N simultanec equations :5 B :3 The matrix elements expressed in equation (100) are easily eval for nuclei with I = %-. By using equation (68), equation (97) beco 37 -I H= - [ pvilzi+ an JijIZl +12 13311 T1 + _ + .. . . :1 . . 10 . Fifi J1J(Il IJ + 111,] )] ( 3) Zj As was stated previously, the basic product functions are eigenfunctions of IZ and hence the first tWo terms in equation (103) will have only diagonal matrix elements <¢IH|¢> = ~[Ev-mi+Z_).ZoJijmimj] (104) Using equation (70), the off-diagonal elements of the Hamiltonian in equation (103) are < ¢(mi+1, . . . , mj-l, . . .) IHI¢(mi,...,mJ-,...)> :- - ;— Jij «I (Ii-mi)(Ii+mi+1)(Ij+mj)(Ij-m-+1) (105) J For the case where all nuclei have I = i‘: equations (104) and (105) become (97) .] (106) NlH M 'M C—l I—] < ¢|fi|¢>=-)—[zi;sivi+ <¢ilHl¢>=-%- JijU (107) where Si = i 1 accordingly as spin i is a or B, T.. = :1 accordingly 1 as spins i and j are parallel or antiparallel, and I1}: 1 if ¢' differs from 4) only in the permutation of spins i and j and U: 0 in all other cases. By using time-dependent perturbation theory it can be shown that the transition probability per unit time for induced emission or absorption in a nuclear spin system is proportional to the square of the matrix element of the magnetic dipole moment (97, 51, 36) (ppm: <¢ H541 (>1, > (108) where Rx: :fi 27,1xi - (109) 38 The relative intensities are thus proportional to the square of any of the following matrix elements |<¢milxl¢n >| (110) + |<¢mll l¢n>| (111) |<<1>mlI‘l<)>n >l . (112) Furthermore the selection rule for allowed transitions is Am =i 1. (113) In determining the matrix elements of the Hamiltonian the theorem expressed by equation (86) will be used. Since IZ commuteswith the Hamiltonian (51), and since the basic product functions are eigenfunctions of IZ, there will be no matrix elements of the Hamiltonian between functions which have different eigenvalues of IZ, that is, different values of m. Thus, for p nuclei each with I : 21— the secular equation will factor into p + 1 separate equations. If a group of nuclei have the same chemical shift these nuclei are said to be equivalent and to constitute an equivalent set. Equivalent nuclei may or may not be coupled equally to other nuclei. The spectrum due to two equivalent sets of nuclei, with all coupling constants between nuclei in different sets equal, will be independent of the coupling constant within the set (96, 100). In nuclear magnetic resonance spectroscopy many Spin systems give rise to first order spectra, that is, the experimental line frequencies and intensities can be interpreted on the basis of first-order perturbation theory. If the spin- spin coupling term is treated as a perturbation of the external field Hamiltonian then the first-order corrections to the energy are just the diagonal elements of the coupling term. As an example, 39 if the spin system consists of two groups of equivalent nuclei, [5 the energy levels of the system to first-order are given by E:-](Vm+vm+J A A B B ABmAmB) If there is a transition from a state mA to a state mA=1, the fre of the transition is Equation (115) can be extended to more than two groups of equiv nuclei n n n r r r = m m =—— -——1 -— VVA+iJARR (R 2’2 ’ ’2) where nr is the number of nuclei in group R, all nuclei having I It may be noted from equation (115), that the number of lines in group spectrum depends upon the number of values the quantum mB can assume, and the spacings between adjacent lines are eq the coupling constant, J The intensity of a given line will d AB' upon the number of ways in which the n spins can be arranged B the required mB, and the relative intensities of all the lines in multiplet will be given by the binomial coefficients of n Simii B° remarks can be made concerning equation (116). The first—0rd approximation will be valid when the chemical shift between two is much larger than the spin— spin coupling constant between the This will always be the case when the nuclei of one group are of ferent species than the other nuclei. The notation used in classifying spin systems will be to us A, B, . . . , for non-equivalent nuclei whose relative chemical sh of the same order of magnitude as the spin- spin coupling consta between them. The letters X, Y, . . . , will be used for nuclei wh resonance signals are not close to the set A, B, . . . . The nuclei i 40 set X, Y, . . . , may or may not be of the same species as A, B, . . . . The number of nuclei in a given set will be noted by a subscript. The simplest spin system to be studied is one containing two nuclei with I = 21- having resonance frequencies VA and VB and coupling constant J AB=JBA:J' The Hamiltonian for this system is El __ 1 + - - + — [VAIAZ+VBIBZ.+JIAZIBZ+TJuA IB +IBIA)] (117) The basic product functions and diagonal matrix elements for this AB spin system are given in Table III. Table III. Basic Product Functions and Diagonal Matrix Elements for the AB Spin System Basic Function In Diagonal Matrix Element 1.0.0. 1 -g—(vA+vB+%-J) 2.a(3. 0 —=%(vA~vB—1rJ) 3.001 0' ——%(-VA+vB-~)-J) 4.00 -1 -21-(-VA..VB+ITJ) Since there can only be matrix elements between states which have the same values of m, it can be seen from Table III that states 2 and 3 will have matrix elements between them. These off-diagonal elements are <031H|Ba>==—%—J (118) The secular determinant is 41 Tau)fi|au->-E 0 0 0 0 —E 0 i o < 3.1131111» <0.) E110. >—E o 3 0 0 0 <(3mfi {MD—E Because of the absence of mixing of spin states with different valu the secular determinant has factored into two 1 x l determinants a 2 x 2 determinant. The functions with m = 1 and m = —1 are eigen with eigenvalues equal to their respective diagonal elements. The two eigenvalues are found by solving the quadratic equation. The : coefficients of the two product functions can be found by using one two simultaneous equations and the normalization condition. The functions and eigenvalues for this System are given in Table IV. Table IV. Eigenfunctions and Eigenvalues for the AB Spin System Eig enfunc tion Eig envalue 0° —%(vA+vB>—1J 0:“?- (013+Qfiu) )— (%-J - W + J ) I+Q “—1 Zen...) 1— c? , +W ) l+Q (515 i‘(vA+vB)-i'~T The expression for Q is ___J__ __l_ _2_2____ 5+~lé +J 6+R D (1 n where 6: v -v andR='\/<'SZ+Jz 42 The transition frequencies can be found from the selection rule Am 2 =1, and the relative transition intensities from the expression (l< m-l )I'-Im>|2 Table V gives the transition frequencies and intensities for the AB spin system. Table V. Transition Frequencies and Relative Intensities for the AB ‘Spin System W Relative Transitions in Limit J 40 Intensity Frequency J 1. A , B —> A B 1 - - ‘— + + J + R imi— i’i i'"ir iri- R 2("A ”B ) 2 A1 1 B1 1 '9 A1 1B1 1 1+9.— “1-(V +V “J+R) ‘2'": 2‘”:— 2"-z— 7':- R Z A B 3A B 4A B 1 1+1 1—(v +v +JR) 1.1? 1-4— 1712‘— ;—: 7 R 2 A B 4A B _-_>'A B 1-J- 1—(v +v -J—R) ' i'"i‘ 1:"? 1"1- iv":- R 2 A B The notation for the spin functions is AIA’ mA BIB’ mB where IA, IB, mA and mB are the total spins and z—components of angular momenta. for A and B nuclei, respectively. It is evident from Table V that the AB spin system consists of four transitions symmetrical about the frequency%— (v + VB). The separation A of transitions 1 and 2, or transitions 3 and 4, is always equal to the spin— spin coupling constant and the separation of transitions 2 and 3 is R-] J) . Thus the values of J and 6 can be easily obtained from an experimental AB spectrum. Apart from a scale factor, the spectrum can be described J by the ratio 3 as is the case for all ABn or AnB spin systems. 43 The spin system of three nuclei, two of which are equivalent, is quite common and will be discussed next. This AZB spin system possesses a plane of symmetry and it is convenient to use basis functions which reflect this symmetry. The use of basic symmetry functions is advan= tageous because it becomes possible to reduce the order of the secular equation and further restrict the number of allowed transitions. The factoring of the secular equation comes about because there are no matrix elements of the Hamiltonian between functions belonging to different irreducible representations. The number of allowed transitions is restricted because transitions between states of different symmetries are forbidden. The basis functions can thus be classified according to their symmetries and to their values of m. The basic symmetry functions for the AZB system are given in Table VI. Table VI. Basic Symmetry Functions for the AZB Spin System Spin Function In Symmetry Notation cum '2— 0. A1, 1B1 1 Z"? (1016 21- 0. A1, 15%, ..%_ l :(ofia+(30.a) %‘ a. A1,0B1 ’ 1 «la 7 7 l —(C113)3+ (30(3) 'i— 0’ A1, 0B1 , -1 ,.__Z 2" 7 55“ 'i‘ a’ A1, =-1]321_,%_ (3513 "g— Q, A1, —iBzi_, -;_ l :(aBa-Bau) fi— 8 A0, 0B1 , 1 \/ 2 7 T l — (oars-(Bus) -1.— 8 A. 0 B1 ,1 r_2 ’ '2' T >‘.< CL and@ signify symmetric and antisymmetric wave functions, respectively. 44 One notes from Table VI that the secular equation factors into four linear equations and two quadratic equations. The eigenvalues and eigen- functions for the AZB system are given in Table VII. Table VII. Eigenvalues and Eigenfunctions for the AZB Spin System Eigenfunction Symmetry Eigenvalue A1 1B1 1 Q 1 ' ' — + + 2- T {(ZVA VB J) l J —— (A B_+QA B <1 1—(-v +—-R) 1+0 1’1 i, %_ 1,0 21_";_) a A Z —1— (QA B A B ) 01 1 ( v + J—+ R) r—HQ. 1,11,“, 11°11.) T A 2 1 a l—(v +5 + R') — (A1 -1B1 1 ‘ Q'Ai 0B1 -1) 2 A Z .)1+Quz 2"!— 2'" 2" ——1— (QA B + A B 1 ( + J— R') 0—11“). “11.1. 101-1.) CL “A 2 A B C\. 1 _ 1’ _1 %_, _%_ '2-(ZVA + VB J) A0,0131,21_ (B %(-VB) 1 A0, 013%,-) (B 2'(VB) where R=\(62- 6J+2— J2 R'='\(62+6J+Z—JZ J? J Q:6-%J+R _J? J ___T____ 6+7J+R' The transition frequencies and relative intensities £01 has been chosen a system are given in Table VIII where v origin (v = 0)) and thus v Table VIII. Transition Frequencies and Relative Intensitie AZB System Transition in Limit J --—90 Intensity Transitions in Group A (QV?P (1) A1,1131 ,1 '—> A1,0 T T T1752— (QL+J?V --rAl.-IBI W (2) AI, OB%! 2" _2_ [anfonmfr (1+QM1+Qfl [QNTCJHWTF u+dm+ofi Transitions in Group B (JTQ+1V ____z____ 1+Q u-Jfofi ____r___ 1+Q' [J?KLQ%HZ (1+QW1+Qfi (3) A1,1131 , -1 —'>Ai, 0B1 _ T T, (4) A1,0131 1* A1, -1B1 "2"2' 2"? (MARAB (7) A1,051 ,1 fiAl . 2' Mixed Transition WN——QLVTQF (1+ Q:) (1 + Q'z) 6+ 6+ 6 —: 46 It may be noted from Table VIII that the mean of transitions 3 and 4 gives J the chemical shift. It is then only necessary to adjust the ratio of :5- to get the best agreement with experiment from which the coupling constant may be obtained. Tables of theoretical AZB spectra have been published for various-% ratios (51,100). Expressions for the line frequencies and intensities for the general An B spin system have been given by Corio (51). These expressions A have been used to obtain the transition frequencies and relative intensities for the A4B spin system. This system has been discussed in the literature by Bannerjee, Das, and Saha (99). There are twelve transitions of A origin, nine B transitions, and four mixed transitions. Apart from a scale factor, the spectrum is only a function of the .— ratio. The line <5 frequencies and relative intensities are given in Table IX, where 2 R1: «((a——§J)z+4JZ Q. J 5-i-J+R1 2 R2 = ~/( 6+ T3 J)2 + 4J2 QZ ——J3—— II «M J : I\)' : R3 (‘6—%)Z+ .zJ2 Q3 5.7! J+ R3 r————————— ~/2J : 2 R4 (<5+%)Z+2JZ Q4 6+2—IJ+R4 6J RS:,——— Q5=(_:_ '22 2 (5'2) +6J 6-£+R5 2 6J R...r————- OPEL. (5+-:—)Z+6J2 5+TJ+R6 47 Table IX. Line Frequencies and Relative Intensities for the A4B Spin System Transition in Limit J —> 0 Intensit Fre uenc Transitions in Group A o -2 z 5 1:1; AZ,ZB}_,21__§AZ,1B%_,%_ (Ill-Q)? 17(VA'1‘ VB+EJ+R1) 2 ' [2 +Q1(1+Q N/6 )]2 1 . 2 + R - R Z Az'zBé—"%—’ A2! 1B1”.— (1 + 0200 + 052) 7‘ VA 1 5’ [Q5(ZQI'1) + ’\/—6]2 1 3.A B —9A B —‘—z——z—— —(2v +R—R) 2.1%,;— 2:°;—.;— (1+Q,)(1+o,) 2 A 5 1 N 6 + 05(1 + 20.)]2 1 — 2 + R - R 4. A2,1131 _1_-->A2‘0B_1_ —1_ —‘—z—"““‘T—'(1 + Q5)(1 + Q6) 2( VA 5 6) 10. 11. 12. {\J 7’2 2’2 Q r\/—6_Q-1+~/6_2 . A2,0B1 ’1 eAZ,_lB1,1 [ 6( 5 ) ] 2-2- 2-2- (1+Q5)(1+Q6) [061 o.(1+2c22)]2 . , _ B _‘r—‘z—r’ AZ,0B;_, ,_%_%AZ, 1 .1: —-;- (1+ Q6)(1+ Q2) mania—1) +2]z . A »_ B A - B —‘-2'—‘—‘—z—' 2" 1 :§:"r—> 2’ 2 Hr (1+ Qz)(1+ Q.) (Q + 2)2 . Az,—1B. -1 —>Az,—2B1_ _1_ 717—- T' 2‘ 2 ’ 2 2 3(Q -~/2 )2 A1,1131 _1__ ">A1,oB1 ,1_ _erl + Q 7’2 2 3 2 3(04 + N/ Z ) A10131 -%__)A1,-1Bl ,-%_ W— Transitions in Group B (201 + 1)z .9 _ __,__ AZ’ 2131’ 1 AME): i- 1 + 01 3[~/‘Z+ Q,(1+~/TQ,)]Z (1+Q3) (1 + (X ) 3[Q4(N/TZ_Q3-1)+~/—2—]2 mm?)— [ZQi-(l+'\/—6—Qs)lz (1+Q1) (1+ Q5) [ON—6— =.(1 + 0.467)]2 1 :- (1+Q_=,z) (1+0?) A 1(1) +11 -=3—J+R) T A B 2 4 1(v+v +-5—J—R) 7 A B 2 1 ‘r (sz -= 3. - RI) :— (ZVA .. R6.- R5) Continued 48 Table IX - Continued Transition in Limit J 4-—> 0 Intensit Fre uenc Transitions in Group B [Q.~fF-(1+2Q~.)]Z 4. AZ,_1B%_’21. —>A,’ ,,B%_, “i- W)— %(2VA= R2 — R6) 5. A2, _ZB%_’%_ —>Az, -zB%_,_21_ ggaficé—Df— %- (VA + VB“:‘J“R2) 6. A1’1B%_,_;_-—)A1,1Bé_,_%_ W -,‘—(vA+vB+%J=R,) 7 AWBM ‘3 “1°31: '1- (3103403111: 3:)? ,1. i‘ZVA " R4 ‘ R3) 8 A“ "BB;— RAB-131:).— W M + VB “3 J - R4) 9. AO’OB%_”,%_ —>AO,OB%_’ '7)? 2 VB Mixed Transitions '[Q5(Z+Q1)=’\[Z)—Q1]Z ’ 7’2- (1+‘ 03.)(1 + Q?) [Q3(’\/6—+ Qg,)-ZQ{,]z 15(2 vA+R1+R5) 2 A B _ —>A _ B _____2___2___ 1 2 + R + R 2,0 i_’ %_ Z: Z %’%_ (1 + Q3) (1+ Q6) ?( VA 6 2) ' [om/6+ (25)—«ls Q5]? 1 ‘ _ A B —-)-A _ B , ——Z—_2——" 2 +R +R 3 2,1 i_;—%_ Z, 1 %_’%_ (1+ Qé) (1+ Q5) T( VA 5 6) 3[Q4(‘( 2 + Q3)=\(Z Qslz 1 4. A B —>A -B 2 +R +R . 1,1 %_,_;_ 1,1 .12,’%_ “—r———z————(1+04)(1+Q3) 2'( VA 3 4.) 483 It can be seen from Table IX that transition nine in the B group gives the resonance frequency for the B nucleus unmodified by spin— spin coupling. The mean of transitions ten and eleven gives the corresponding frequency for the A nuclei. It is convenient to set v = 0 in which case B VA = 6 and the mean of transitions ten and eleven gives the chemical shift. The spin— spin coupling constant can be obtained from the% ratio which best fits the experimental spectrum. The last system to be discussed is the asymmetrical three spin system ABX (51,100, 25). This consists of three non— equivalent nuclei, the Larmor resonance frequency of one of the nuclei being well separated from those of the other two nuclei. For this system there will be no mixing of basic product functions unless these functions have the same values of m and mx. The restriction imposed on mx is essentially a result of second-order perturbation theory. For functions with different values of mX the off-diagonal elements are of the order of the coupling constants while the diagonal elements depend largely upon the resonance frequencies. The second-order correction to the energy is equal to the square of the off—diagonal element connecting two energy levels divided by the difference between the diagonal matrix elements of the two levels. For the case of two nuclei whose resonance frequencies are well separated this ratio is vanishingly small. Since this system has no elements of symmetry the. simple product functions may be used as a basis and they will be written in serial order, 49 0GB =0(A)a(B))3(X) (121) The basic production functions and the matrix elements of the Hamiltonian are given in Table X. Table X. Basic Product Functions and Hamiltonian Matrix Elements for ABX Spin System Spin Off-diagonal Function In Diagonal Matrix Elements Matrix Elements 3 1. .. _1_ “a“ 2 2 [V A+”B+”X+2— MHJAB AX JBXH 1 2 — -1. - _ - .. “a” 2 '2'[”A+”B ”X+; (JAB JAX JBXH 1 3 — -1 _. + +— °Ba 2 T[” A ”B ”X?- (' "JAB+ JAX JBXH 2 1 J 4 (3110. 1— -1—[- v +v +v +—(J +J )] 34 2- AB ' 2 2 A B X AB JAX BX 1 1 l 5 “5B '2 '2 [”A'”B'”X +T('J AB 'HAX JBX” H _ _1_ J 6 l 1—[.+ 1(J +J J)] SG-ZAB ' ”a” '2 '2 ”A ”B'”X+T ' AB AX' BX 1 1 7' 55“ '2 'T['” ”A'”B+”X+Z_(JAB'J AX 'JBXH 3 1 8' F359 '2 'Z['” ”'A ”%’B'”X+ (JABH AX +JBX)] It may be noted from Table X that the secular equation has factored into four linear equations and two quadratic equations. The eigenvalues and eigenfunctions for the ABX spin system are given in Table XI where the eigenstates are numbered in the limit JAB —->O. 50 Table XI. Eigenfunctions and Eigenvalues for the ABX Spin System Eigenfunction m Eigenvalue 1 out). 2 n)- [v +v B+v +é-(J +J +J )] ' 2 A X AB+ AX+ BX 2 out) —1- =--1-[v +1! -v +1 (J —J -J )] ° 2 Z A B X 7 AB AX BX 1 1 ' —— _ _l. 1 _ 3. {—21 + Q+(ofiu+Q+(30.u) 2 2 vX-l- 2;- JAB D+ l v — _ l 1 1 4' Jm‘QfiBG'BW’ 2 'T ”X + r JAB “3+ 1 1 ,, __ _ 1- , .. 5. m (0.6(3+Q_(3ufi) -2 Z vx+f JAB D, 1 1 u _— _ .1. l. 6- m(Q.GF3)3'(3GF3) '2 a VX+4 JAB+D- 7 BBa -1 .1—[.v —v +v +. (J J )1 ' 2 3 ”A B X AB' JAX BX 2 1. ~- 1_ 8' 55$ ' 2 '2 1“”A'”B'”X+ 2 (JAB+JAX+JBX)] where Q: — —;—r—————— 6 — T(JAX— JBX)+ZD+ Table XII gives the transition frequencies and relative intensities for the ABX spin system. Table XII. Line Frequencies and Relative Intensities For the ABX Spin System Transition in Limit JAB—i 0 2. 3' —>5' 3. 4' —>6' 4. 7-—>8 5.1—94‘ 6. 2-—>6' 7. 3'—>7 8. 5'-—)8 9.1——>3' 10. 2———>5' 11. 4'—§7 12. 6' —>8 13. 3' —>6' 14. 4' ——> 5) Intensity Frequency Transitions in Group X l +21-(J +JB X) ”X AX+ i%f%ffi) vX+D+-D_, %% vanm+ 1 ' ”X' iTUAX +JBX) Transitions in Group A (147292 1+Q+ i7(”AJ’”B)+"JAB+1'11'(“TAX+JBX)+D+ i%§{£ f(vA+vB )+§— JAB” fi-(JAX+JBX)+D_ ($04.; )2 é7"(”A+”B) 3' JAB+T1 (JAX JBX)+D+ (11:35:32 ;(VAW B” TJAB ' 21’(JAXJ’JBXHD‘ Transitions in Group B (1122+; )2 “”A‘L” B)+TJAB+41_ (JAX+JBX)'D+ (if—2%): é—(”A+”B)+%'JAB' zHJAXJ’ JBX)'D' (ii-(2%)Z 2_(VA+1)B)-Z_JAB+ i'(JAX‘L JBX)'D+ i:bQZ_)z %-(VA+VB)- %JAB-%(JAX+JBX)_D‘ Mixed Transitions 2 MT— VX+D++D" (1+Q+)(1+Q-) 2 -(—-Qj-—-ZC-2)-—)—1—) VX—D+-D_ (1+Q+ (1+Q.- 52 The two mixed transitions may be considered as X lines for purposes of grouping in which case the X group consists of six lines symmetrical . ' ' d about vX The most intense lines, 1 and 4, are separate by (JAX+ J'BX) Transitions 2 and 3 are separated by 2 |D+—D_l and transitions 13 and 14 are separated by 2(D++D_). In the spectra studied in this research transitions 13 and 14 were never observed and as a result, from Table XII (Q.r - of _ (1 + 01) (1 + oz.) ' 0 ”22) or (2+ = Q_ (123) From the definition of Q). J J ———1—* = _ (124) 6 +T(JAX_ JBX) + 21)+ 5 ' 2(JAX— JBXH JF'ZD which leads to ZlD+-D_l = IJAX-JBXI (125) Therefore, the separation of transitions 2 and 3 is approximately )J ) when transitions 13 and 14 have very low intensities. With AX JBX this information the relative signs of the JAX and JBX coupling constants may be determined. If the magnitude of (JAX+ JBX) is greater than the ma nitude of 2ID -D_) then the si ns of the cou lin constants are the g + g P g same. The relative signs of the coupling constants are different if < . IJAX+ JBXI 2113+ -_D| There are eight lines in the ABpart of the ABX spectrum. These lines form two quartets, which often overlap, each of which is identical in appearance with a two-spin AB spectrum. The two quartets are (5, 7, 9,11) and (6, 8,10,12). One quartet has a central spacing of 2D+—J AB and the other quartet has a central spacing of 2D'_JAB . Thus the 53 difference in central spacings of the two quartets is 2|D+-D_| which may be compared with the X part of the spectrum. The separation of the centers of the two quartets is equal to %—(J ) which may also AX+JBX be compared with the X spectrum. The J coupling constant occurs AB four times in the AB part of the ABX spectrum. It is equal to the separations between the transitions 5 and 7, 9 and 11, 6 and 8, and 10 and 12. In the analysis of an ABX spectrum there may be more than one way to make an assignment of the two quartets. It is usually necessary to use the information obtained from the X spectrum to make the correct choice. After obtaining J the chemical shift (vABvB) and the coupling AB’ constants, J and JB may be obtained by solving the equations in AX x1 I. V‘ I ‘n EXPERIMENTAL Spectrometer The proton and fluorine magnetic resonance spectra were obtained using a high-resolution nuclear magnetic resonance spectrometer, ’ Varian Associates (VA) Model V-4300-2. A VA Model V—4311 fixed- frequency RF unit and a VA Model V-4331A RF probe were used to obtain spectra at a fixed radio frequency of 60. 000 mcs. Some fluorine spectra were obtained at 56.445 mcs.using a modified VA Model V-4311 RF unit and a VA Model V—4331A RF probe. The RF unit was modified by installing a VA crystal set 904564-01 in the VA Model V—43ll RF unit. This permits use of the spectrometer for obtaining fluorine spectra with- out the necessity of changing the magnetic field strength. Some prelimi— nary investigations of fluorine nuclear magnetic resonance were per- formed at a fixed frequency of 40. 000 mcs. using a VA Model V—431‘0C. fixed frequency RF unit and a VA Model V-4331A RF probe. The constant magnetic field was obtained with a VA twelve-inch high—resolution electromagnet, Model V-4012A. A VA Model V—ZlOOA regulated magnet power supply equipped with a field—reversing mechanism was used in conjunction with this magnet. A VA Model VK-3513 field trimmer was bolted to the magnet yoke. This permitted shimming the magnet in the y (vertical) direction which increases the homogeneity of the applied magnetic field. A VA Model V—4365 field homogeneity control unit and pole cap covers containing four sets of coils were installed. This provided a way for electrically shimming the field along the x, y, and z directions (the magnetic field direction is taken as the z axis) as well as producing the desired shape of the field. The use of these coils made frequent cycling of the field unnecessary and also gave rise to highly homogeneous fields. 54 55 In order to be rewarded with satisfactory high-resolution spectra, stability of the various components of the system must be obtained. Of paramount importance is the stability of the applied magnetic field. This stability was obtained by using a VA Model V-K 3506 magnetic flux stabilizer. The line voltage to the spectrometer unit was regulated with a Sorenson lOOOS A.C. voltage regulator. The cooling system for the electromagnet consisted of distilled water which, after passing through the cooling coils, was recycled through a refrigerated copper tank. The temperature of the water was maintained at 21.0 i . 150C. The room temperature was regulated by a commercial air-conditioning unit. Two safety devices were employed in the magnet cooling system. If the water pressure entering the cooling coils fell to an unsafe value or if the water temperature became too high, the magnet current would shut off. A VA Model V-3521 NMR integrator and base line stabilization system was added to the spectrometer unit. The stabilization system produced extremely stable base lines which are necessary when signal intensities are integrated. Audio frequencies from a Hewlett—Packard Model ZOOCD wide range oscillator were used to modulate the magnetic field. This audio-frequency modulation produces side-bands on either side of the main signal, the separation of the side-bands from the main peak being equal to the modulation frequency. In this manner nuclear magnetic resonance spectra can be calibrated (104). The audio frequencies were counted using a Hewlett-Packard Model 521 A electronic counter. The spectra were recorded on either a VA Model G-lO graphic recorder, a Sanborn Model 151 recorder, or a Moseley Model 2 X—Y recorder. With the twelve—inch high-resolution magnet and the regulated magnet power supply applied magnetic fields of sufficient strength to observe fluorine magnetic resonance at 60. 000 mcs. were obtained. However, at these high magnetic field values, the magnet could not be 56 properly cycled and the homogeneity of the field was only fair. To correct this condition shim coils were constructed which consisted of two pairs of coils, each pair containing two concentric circular coils (105). Each pair of coils had one circular coil four inches in diameter and the other circular coil had a diameter of l. 5 inches. Each pair was fastened with celluloid tape to separate sheets of stiff) paper and these sheets were taped to the sides of the probe in such a manner that the axis of the circular coils passed through the center of the receiver coil inside the probe. Ten turns of No. 40 pure copper wire were used for each coil and the coils in each pair were connected to the D. C. so that the current in the larger coil flowed in the opposite sense to that in the smaller coil. The constant voltage of about 15 volts for the D. C. was obtained from a battery of Edison cells. The direction of the D. C. could be reversed and the magnitude of the current was adjustable. The magnitude of the D. C. flowing in the coils could be divided between the coils of large and of small diameter so that there would be zero field at the sample due to the circular coils. The magnitude of the current flowing through the coils was adjusted until the desired shape of the field was obtained. Without these coils the field was always undercycled (dorne-shaped) and with the coils it was possible to make the shape of the field flat. Compounds Studied The compounds which were studied in this research are listed in Tables XIII and XIV. Table XIII lists the compounds for which fluorine magnetic resonance spectra were obtained. The compound 2, 3, 3—trichloro- 1, l, l, 2, 4, 4, 4—heptafluorobutane was purchased from Columbia Organic Chemicals Co. , Inc. , and the compound 1, 1, 2, 2, 3—pentachloro—l, 3, 3—tri- fluoropropane was purchased from Halogen Chemicals Inc. All of the other compounds listed in Table XIII were obtained from Professors J.,A. Young and R. D. Dresdner of the University of Florida. V 57 Table XIII. Fluorine Compounds Studied m Compound Boiling) Point Molecular (OC.) Weight czrssr5 14. 3 ‘ 246 (C2F5)ZSF4 70. 0 346 CZFSSF4CF3 47. 1 297 CF3SF4CFZCOOCH3 123. 0 C4F9SF5 70. 9 346 CF3SF4CFZSF5 88. 0 352 (CF3)2NF -35.0 171 C2F5N=NC2F5 C4F9N=NC4F9 (CF3)ZNCF=NCF3 37=39 266 (CF3)ZNHgN(CF3)2 127 (CF3)ZNCQOCH3 76 CFCIZCCI’QCFZCI CF3CC12CFC1CF3 ( C215‘5)3N 76 371 (C2F5)2NF 22 In Table XIV the cyclopropane derivatives whose proton magnetic resonance spectra spectra were obtained are listed. Table XIV. Cyclopropane Derivatives Studied qHZCCBCHOCH, H H C 2cc1zc OCZH5 cis _ C6H5CHCC12CHCI-I3 — 'l ___.1 H3 HZCCIZ c61415 C(0)c.,115 trans _ C6H5C(O)EHCHSHC(O)C6H5 HoochCHZ_cr(c00H)2 OOH trans—CH2 = E HSHCOOH 58 The compounds trans-3-methylenecyclopropane—l, Z—dicarboxylic acid (Feist's acid) and cyclopropane-=1, l, 2=tricarboxylic acid were obtained from Dr. L. Brady of Abbott Laboratories, Chicago, Illinois. "trans - l, 2, 3-Tribenzoylcyclopropane was obtained from Professor W. G. Brown of the University of Chicago. The other compounds listed in Table XIV were synthesized in this laboratory. Doering and Henderson have reported the synthesis of l, l—dichloro—2-ethoxycyclopropane by the addition reaction of dichlorocarbene to vinyl ethyl ether (106). This method has been used in this research to synthesize the dichlorocyclo- propanes listed in Table XIV. Except for the above—mentioned compound, the other dichlorocyclopropanes have no'tbeen previously reported. Potassium i-butylate was prepared by dissolving potassium metal in dry i-butyl alcohol contained in a three—neck flask equipped with a reflux condenser (107). The flask was heated on a steam bath at reflux temperature until the potassium had dissolved. The excess alcohol was distilled off and the product was left as a white powder. The re- action with each olefin was carried out in a one liter three—neck flask equipped with a Dry Ice condense r and dropping funnel and immersed in a Dry Ice-methanol bath. Stirring was accomplished with a magnetic stirrer. To the flask containing 20 grams (0. 27 mole) of potassium i—butylate 200 grams of olefin was added. The temperature of the bath- was maintained between -20 and -100C while 30 grams of Baker reagent grade chloroform was added slowly to the stirred solution over the period of one hour. After letting the reaction mixture stand for thirty minutes it was washed twice with equal volumes of water. The water extracts were washed with pentane and the combined organic layers were dried over sodium sulfate. The product was distilled at a reduced pressure. 1, l-dichloro-2-methoxycyclopropane was prepared by the addition of dichlorocarbene to vinyl methyl ether (Matheson Co. , Inc.). The boiling point of this compound is 510C. at a pressure of 47 mm. of mercury 59 and the refractive index n3 ; 1.4490. The product was analyzed for carbon, hydrogen, and chlorine content (108). Calculated for VC4H60C12: C, 34.07; H, 4.26; Cl, 50.22. Found: C, 33.95; H), 4.37; Cl, 50.20. The reaction of u—methylstyrene (Eastman Kodak Co. , white label) with dichlorocarbene afforded l, l—dichloro—2-methyl-2—phenylcyclo— propane which boiled at 55-56OC. at 0. 3 mm. and had a refractive index Cl, 35.32. Found: C, 59.77; H, 5.03; Cl, 35.19. 03 = 1.5448. Analysis: Calculated for cmHch: c, 59.70; H, 4.98; B—methylstyrene was obtained from Columbia Organic Chemicals Co. and was determined to be > 99% pure by gas chromatography. The 20 D value for the cis isomer (109). The product of the reaction of the olefin refractive index of this material, )7 = l. 5430, agrees with the literature with dichlorocarbene was cis—1, 1—dichloro-2-phenyl-3-methylcyclopropane where the two ring protons are ci_s to one another. The boiling point of this compound is 54-56OC at O. 2 mm. and the refractive index n20 .= l. 5440. Analysis. Calculated for CloHloClz: C, 59.70; H, 4.98; Cl, 35.32. Found: C, 59.78; H, 5.06; Cl, 35.18. Vinyl ethyl ether, purchased from Matheson Co. , Inc. , added dichlorocarbene to give 1, 1~dichloro—2—ethoxycyclopropane which boiled at 53-54OC. at 28 mm. with a refractive) index 'nzo ,= 1.4440. Analysis: Calculated for C5HBOC12: C, 38.73; H, 5.16; Cl, 45.77. Found: c, 38.89; H, 5.40;’c1, 45.84. Sample Preparation All of the fluorine spectra were observed with pure liquid samples. The sample tubes used were either custom-manufactured Pyrex sample tubes purchased from the Wilmad Glass Co. , Inc. (110), or tubes made from selected 5 mm. o.d. Pyrex glass tubing. The custom—manufactured tubes had the following dimensions: 0.192 i . 002 inches 0. d.; 0.1604 inches i. d.; straight within 0. 003 inches; and hemispherical bottoms. 60 Each of the fluorine samples was degassed under reduced pressure at the boiling point of air and sealed at the top of the sample tube. All proton spectra were taken using sample tubes purchased from the Wilmad Glass Co. , Inc. Spectra were obtained for the following pure liquids: l, 1-dichloro-2—methoxycyclopropane; l, l—dichloro-Z—ethoxy- cyclopropane; l, l-dichloro-2-methyl-2—phenylcyclopropane; and c_i_s- l, l—dichloro-Z-methyl-3—phenylcyclopropane. Spectra were obtained for solutions of cyclopropane-1, l, 2—tricarboxylic acid and trans—3- methylenecyclopropane— 1, 2-dicarboxylic acid in dilute sodium hydroxide and for a solution of trans-l, 2, 3-tribenzoylcyclopropane in trifluoroacetic acid. Determination of Spectral Parameters The proton spectra reported in this thesis were obtained at a fixed frequency of 60.000 mcs. The fluorine Spectra were obtained at 60.000 mcs.for some spectra and 56.445 mcs.for other samples. The spectra were recorded on either a Sanborn 151 recorder, a VA Model G-lO recorder, or a Moseley Model 2 X-Y recorder. The line separations in cycles per second were obtained by the side-band technique using a Hewlett—Packard Model 200 CD audio-frequency oscillator. Several spectra were recorded for each sample and the values of the chemical shifts and spin-Spin coupling constants reported here are average values. The recording of several spectra is necessary to average out any instabilities of the slow-sweep unit or magnetic field. External fluorine chemical shifts were measured using the fluorine magnetic resonance of trifluoroaceticacid as a reference standard. Proton chemical shifts were measured with respect to tetramethylsilane (TMS) as the reference standard. For the dichlorocyclopropanes and for trans- l, 2, 3-tribenzoyl- cyclopropane TMS was dissolved in the sample and internal chemical shifts were obtained. The insolubility of TMS in aqueous solution precluded 61 the possibility of measuring internal chemical shifts for cyclopropane- l, 1, 2-tricarboxylic acid and trans =3-methy1enecyclopropane-1, 2- carboxylic acid. External chemical shifts were obtained for these compounds by placing a small capillary containing TMS within the sample tube. Chemical shifts and spin—spin coupling constants were determined by using the methods of analysis described in a previous section. Theoretical spectra were calculated from these data and compared with the experimental spectra. RESULTS High-Resolution Proton Magnetic Resonance Spectra All of the proton magnetic resonance spectra displayed in this thesis were obtained at room temperature at a fixed radiofrequency of 60. 000 mcs. and with the linear sweep field increasing from left to right. The positions of the proton magnetic resonance lines are given in cycles per second (cps) with respect to the resonance position of tetramethylsilane which was used as an internal standard except for compounds dissolved in aqueous solutions. For the latter solutions tetramethylsilane was sealed in a small capillary which was placed within the sample tube. All of the proton signals were found to beat a lower field than tetramethylsilane whose resonance position was arbitrarily chosen as zero cps. The frequencies of lines to the low—field side of tetramethylsilane are given positive values. The average error in the separation between individual lines in a spectrum is in the range of 0. l to 0. 25 cps. and the average error in the spin- spin coupling constants is in the same range. Theoretical spectra were calculated from para- meters obtained from the experimental spectra. - l, 1—dichloro-2—methyl—2-phenylcyclopropane — The high-resolution ' proton magnetic resonance spectrum of l, l-dichloro—2-me-thyl-2-phenyl- cyclopropane is shown in Figure 1. The resonance line at 429. 7 cps arises from the resonance of the phenyl group while the intense line at high field is due to the methyl resonance. The remaining four lines arise from the resonance absorption of the two ring protons. These lines com- prise a typical multiplet for two non-equivalent protons whose spin- spin coupling constant is comparable in magnitude to the chemical shift between 62 m _i was mo; 3 6 .m e E O . _ m 8 m . _ m U m . M l ., IO m “ <1 «mo . . . H m . oemdmffifiofimbg Hoocohvwou . 608600.00 u o> HO HQ .939me woddGOmoH oflonmmg Hm Hoofimuoofi new Hducoafihomxm 3. ohsmfirm 64 them. This is an example of the AB spin system discussed in a previous section of this thesis. , The coupling constant, Jgem: is 7.03 cps. and the chemical shift between the g_e_r_n protonsis 16. 65 cps. It is not possible to determine from the spectrum which proton is more shielded. However, Curtin, Gruen, and Shoulders have shown that in diphenylcyclopropanes a proton cis to a phenyl group comes at higher field than a proton trans to a phenyl group (111) and this is assumed to be true here. The theoretical spectrum for the two ring protons is shown in Figure l. fl-l, l-Dichloro-2-methyl—3-phenylcyclopropane - The proton magnetic resonance spectrum of (ls—l, l-dichloro-Z-methyl-3-phenylcyclo— propane is shown in Figure 2. The low field resonance line at 448. 2 cps. is due to the phenyl group and the unsymmetrical doublet at 71. 3 cps. is due to the resonance of the methyl group which is spin-coupled to the ring proton on the carbon atom to which the methyl group is bonded. The phenyl resonance line was recorded at a lower gain than that for the other lines. The multiplet centered at 103. 3 cps. arises from the resonance of the ring proton which is coupled both to the methyl group and to the other ring proton. The unsymmetrical doublet at 132. 3 cps. is due to the resonance of the ring proton trans to the methyl group. This is the low- field part of the AB spin system formed by the two ring protons. The ci_s_ coupling constant obtained from the separation of these two lines is 8. 28 cps. Because of the additional splitting by the methyl group the other half of the AB system can not be directly analyzed and the chemical shift between the two ring protons has been estimated as 28. 3 cps. trans- l, 2, 3- Tribenzoylcyclopropane- - The proton magnetic resonance spectrum of trans-l, 2, 3-tribenzoylcyclopropane is shown in Figures 3 and 4. Figure 3 is the Spectrum due to the resonance of the phenyl groups and Figure 4 shows the resonance lines of the three cyclopropane ring protons. The unsymmetrical doublet centered at 247. 5 cps is due to the two (I11). (1)111.) .)()))|.1( 2.1. 11(5).)WMUIW)NIMHH)) . 9.: ((1. mmo mm. .w msmflmfimfluoamtou n30 “museum“; . .moe 00085 n o; m mo 55.30on ooddSOmoH oflocmmg um .N omdwfih mmso 6.6.4.34 6.66.45. 66 Tom memfimfififieamfiou Househoweh . .mog 000 .00 n o> £665 £8065 < . m CH mooo mo . mom .vm m.oH..oN 67 ii mac we .m .0528 mmo om.m m o m e (32.569338. “ooeohowon m 065 m 05 .o :86 08.3 n 5 $4 m < . n I E 3000 MD a: < mmoOAOVO Ho meOuOHm mafia m0 .930on I ouBmCOmou ofleewwa Hm Hmoflopoofi poo Hmuoogflomxm .w ondwfim 68 equivalent protons on the same side of the ring and the multiplet at 269. l cps. , which is at higher gain, arises from the remaining ring proton. The resonance peak at 508 cps. from the solvent, CF3COOH, is not shown. The analysis of this spectrum as an AZB system gives 5.61 cps. for the trans coupling constant and 21. 57 cps. as the chemical shift between the A and B protons. The theoretical spectrum of the ring protons calculated from these parameters is shown in Figure 4. A 40 mcs. spectrum of this compound has been reported by Shoolery(112) and the trans coupling constant has been reported as 6. 0 cps. by Closs (15). l, 1—Dichloro-2-ethoxycyclopropane - The high—resolution proton spectrum of l, 1-dichloro-2—ethoxycyclopropane is shown in Figures 5 and 6. This is an example of an ABX spin system. The group of lines in Figure 5 consists of the resonance lines from the methylene protons of the ethoxy substituent and of the resonance lines of the proton on the carbon atom to which the ethoxy group is bonded. The methylene peaks are identifiable by their small second-order splittings. The ring proton resonance lines are the four lines symmetric about 208. 8 cps. In Figure 6 the three intense peaks at high field, which have relative intensities of 1:2: 1, are due to the methyl group of the ethoxy substituent. The remaining resonance lines are due to the ring protons cis and trans to the ethoxy group. These form the AB part of the ABX spin system which can be analyzed exactly. The analysis of this spectrum gives J 's = 8.25 cps, J c1 = 5.25 cps., and J = 8.09 cps with the (is trans gem and trans coupling constants having the same sign. The theoretical spectrum for the ring protons is shown in Figures 5 and 6. l, 1-Dichloro-2-methoxycyclopropane - The high—resolution proton magnetic resonance spectrum of l, l-dichloro—2—methoxycyclopropane is shown in Figures 7 and 8. This is another example of an ABX spin system. The intense resonance line in Figure 7 is due to the methyl group $11? Tom .0933 11338830“ ”0 oeouowoh :88 80.3 n 9. ~30 Cam < . m N m 00 HO 3 HO mo 00emo0w0p couosm UHoEIBOH 063 m0 9&0“me ooedcomon ofloewdefl «mm 30309005. pew Hmocofifihomxm .m end—mam if); 70 .momfimafiesmfioo Hooeouowon . .moa ooo .oo n o: XE <3 . m N g m nu ma .m m 00 m w _ <3 HOHO Z we 00GMQOm0H BOBOBQ pfioflugmfia may «0 .930on .. anaemoh 0Uocmm5 HE fimoflonoonu pod Hmucoafiuomxm .w ondmmh Alan-Iii. , ., wmo o .FHN 30 86, .l. T cm 7 Km Jamfim -Tfifimcfldhumu “025980..” ~ .mog ooooow u o: . XE < .n 300 #0 mm 2 HO mo oqufiOmmu neuona 303-33 Bi wo anuommm confinemou ofloswda mEO «E Maoflohoofiu flaw fiducogimmxm .N. madman '72 . ocmflmfwnuogmuug ”muaohomoy . .wua ooo.oo u 0; xm ¢H mac ow.slm Tom .m.o mimhm 76 Tom NmUH 25 3;.“ m3 3.... mo . x 29.3. 79 Table XVI. Chemical Shifts of Ring Protons In Cyclopropane Derivatives" d Compoun 6A 6B 6X H C1 c1 CH 5% 3 102.36 85.53 B C6H5 C1 H 01 H A 132.34 103.30 CH3 6H5 C1 C1 HMCHZ. 99.80 90.52 217.01 HA X EA; CHZCH3 90.47 81.62 208.8 COOH COOH COOI—I 137.78 145.53 190.47 C(O)C6H5 H H A B HA 247.53 269.10 C(0)C(,H5 (0)C6H5 CH2 H /'\ COOH 109.50 COOH HA 3k Chemical shifts are in cps. relative to tetramethylsilane and are taken to be positive for protons on the low field side of TMS. 8O EQQOJN [I'll Emmmé 2 rl Mao Till 6334. who 36 8.2 «~000th Hmchouxm “mononomon . .moE ooo .oo 0 o> .vhmnAmMNUv mo, mQSOHm who «:5 mrAU 95 mo 8.3.30on oocmGOmoH 0.30”“me firm .NH ohdwmh 81 can 0631 mmo mm .0 EOOOMMU HmsHouXo “035.8on . .moa 000 .00 n o; .«hmmAmrmwov mo 03on Nam 05 mo 5530on oodeHOmoH oflosmmg Sh .mH ohdmfirm 82 coupling constant of 15.7 cps. Figure 13 shows the spectrum of the SF4 group and Figure 14 'shows the theoretical spectrum of the SF4 group calculated by first—order perturbation theory. CF3SF4CF2CF3 - The 60. 000 mcs. high-resolution fluorine magnetic resonance spectrum of CF3SF4CF2CF3 is shown in Figures 15 and 16. In Figure 15 the quintet centered at -11.4 ppm. is due to the CF3 group bonded to sulfur. The spin—spin coupling constant between this CF3 group and SF4 is 24. 0 cps. The five-line multiplet at 4. 5 ppm arises from the CF3 group of the Cst substituent. This group is spin—coupled to the SF; group with a coupling constant of 9.40 cps. The multiplet at 21.4 ppm. arises from the CFZ group which is coupled to the SF4 group with a coupling constant of 15.1 cps. Figure 16 shows the experimental spectrum for the SF4 group and Figure 17 gives the theoretical spectrum for the SF4 group calculated by first-order perturbation theory. At higher gain the two lines which appear at either end of the theoretical spectrum may be observed experimentally. CF3SF4CFZCOOCH3 - The 56.445 mcs. high-resolution fluorine magnetic resonance spectrum of CF3S'F4CF2COOCH3 is shown in Figures 18 and 19. In Figure 18 the five-line multiplet at —12. 6 ppm is due to the CF3 group which is coupled to the SF4 group with a coupling constant of 23. 5 cps. The group of five lines centered at 12. 1 ppm. arises from the CFZ group which is coupled to the SF4 group with a coupling constant of 13.6 cps. Figure 19 shows the experimental and theoretical spectra for the SF4 group. First-order perturbation theory was used to calculate the theoretical spectrum. There is no measurable fluorine—proton spin- spin coupling in this molecule. CF3CFZSF5 — The 60. 000 mcs. high—resolution fluorine spectrum of CF3CFZSF5 is shown in Figures 20, 21, and 22. The fluorine atoms in the SF5 group form a square pyramid with the sulfur atom in the plane of .vhmAmhmov mo adonm «hm 08. mo 8.9.500mm ouzwcomon 33¢me Sh Hmoflouoogfi .«l madman 84 m .111 a . n moo 606 3.6 6 oo .3. 00m .mooommo 1.5308 "60.566060 :88 08.8 n f .mmnoermnmo mo deOHm Nho paw nhUU 8th 0:0 mo fishbomm 00cma0mmh 0305me Sh .mH mud—warm 85 mmo v6 mooomho 1.32386 ”mononowou . £08 000 do u o: .mrmuowhmnrmo Mo QSOHM «hm 05 mo 53500mm 00cmcowoh 030Gon Em A: mudmfih 86 OMn ON... o .. o .H mm . m 3. a... m ““.~.__m~.w___ .mmnofimmmo do 96% «mm 6.: wo 85.30096. 0099.80“: 0306”de Sh Houflonoodfi .NA ohdmfih . . _|.. 36 9.1.3.. EOOOth $98303 ”00:0.H0m0a . .008 minim n o: .MEOOOONMUmeth mo mooyw «hm 05. mo 0300mm 000088000 0309m0§ Sm 3030.505 0cm 3300830me .mL 00.93pm Emmddwfin .11 , , ll .15! .11 who om .MM EOOUnrAU #0830303 “00c0n0m0h . Smog mwvom u o; .mEDOODnhOvhmth mo masonm NED cum «MD 05 3195309? 0235000“ 0300939 87A .2 0hdmfih 88 5.. 0.0.21 c." .1 666 0 .sm mOOUnuHO 09.30303 “000000000 . .mug 000.00 0 0; .mhmmnmNO 00 0500.30 x000 03 00 0.30000 000000m0h 030Qm05 Sh 30300004.. 0:0 H030083H0mxm .8. 0.305. Hp.. m.wHH- 89 _ mmo 0.0mH _ EOOUMMU #95038 n00n0n0m0h . .008 000 .00 u o: .mhmmh~0 mo Awhmv 0880 0dmhosd 000n— 05Mo 85500mw 00525000 030nw08 SM .HN 0H5mfih 90 Son cam 90 $11.3 _ m3 310 N00 , n00 “00G0H0m0n . .005 000 .00 n 3. .mhmmhuo .mooommo :05on m0 009200000 030Gm0§ Sh .NN 003mfim mo masonm NhU 090 «HMO 00% mo 8.9.500 .111 Tom 91 the four base atoms. The base atoms are chemically shifted from the apex fluorine atom and therefore the SF5 group is an A4B spin system. The spectrum of the apex fluorine atom shown in Figure 20 consists of nine lines which arise from interaction with the base fluorine atoms each of which is split into a triplet by the CF; group. The theoretical spectrum of the apex fluorine atom due to the spin—spin interaction with'the base fluorine atoms is shown in Figure 20. The experimental spectrum was analyzed by the method discussed in a previous section (Analysis of Spectra, page 46) and it was found that {the coupling constant between the apex and base fluorine atoms is 152. 19 cps. and the chemical shift is 19. 5 ppm. The coupling constant between the CF; group and the apex fluorine atom is 4. 82 cps. Figure 21 shows the spectrum of the four base fluorine atoms. These atoms are spin—coupled to the apex fluorine atom, to the CFZ group, and to the CF3 group. In Figure 22 the quintet centered at 5. 6 ppm is due to the CF3 group which is spin—coupled to the base fluorine atoms with a coupling constant of 8. 56 cps. The multiplet centered at 24. 0 ppm. arises from the CFZ group which is spin coupled to four base fluorine atoms with a coupling constant of 14. 36 cps. Each line is further split into a doublet by spin— spin interaction with the apex fluorine atom as was mentioned above. The spectrum of the CF; group was obtained at a higher gain than was the spectrum of the CF3 group. CF3CF2CFZCF2SF§ - The 56.445 mcs. high-resolution fluorine magnetic resonance spectrum of C4F9SF5 is shown in Figures 23, 24, 25, 26, and 27. The spectrum of the apex fluorine atom is shown in Figure 23. This fluorine atom is spin-coupled to the base fluorine atoms to give a nine line spectrum each line of which is split into a triplet by coupling with the CF; group which is adjacent to the sulfur atom (a-CF3). Each of these lines is split into a triplet by the B-CFZ group. The theoretical spectrum for the apex fluorine atom which arises from coupling to the base fluorine atoms is shown in Figure 23. The coupling tin»; acme p.0m2- illliii- 411. .0 i- iiililiiiiliiii4liiiw 92 $iiii|iiiiiil mao «N.mm o M . 300% MO H0CH00X0 00:000000 . .005 m¢¢.0m u 0: .mhmohvo 00 800.0 0GEOSG x0 .0 030 m0 93.300000 0050200000 omuoawma 07m 100300093 000 H00c0gam0mxm~ .MN waswfim Il'li. .. :l'lll.‘ ~00-.. Tl. Tl... 0QU . 0 NH 0&0 00.0H .mU .mooomho $5808 "80338 :38 3.0.0... u f .mrmmamofionmonmo .o a \r m0 09.5mm NMOI0 090 NMD 0A» 00 5.9.3025 0099500.." 03090.05 Sb. .mN 0.3%er as, m ._2 .1... 93 jfljiiliiii .ZOOOMMU 100.336 “000000000 . .005 3.0.00 u 0; .mmmohmd mo Avhmv 0800.0 0030de 00.00r 003 m0 85.50005 0000Q000H 030Gm05 07m .vm 0Hdmfirm 94 mumfiofiofiommo 0 a x. mo 98am NrmDJr 003 mo E5300m0 00Qdd000H 030cwm§ 2h .FN 0Hdmfih Sam M H00 . _ $0-0 000 0.0. mooonmo :22on ”85033 :88 03.00 u s. .mhwfimononommo .o a x. . modicum NhUua 0% mo 95.500Q0 0ocwnO00H 0UOGmmg Sh .0N 0Hdwfih 1.1... 95 constant between the apex and base fluorine atoms is 145.46 cps. and the chemical shift is 17.4 ppm. The coupling constant between the apex fluorine atom and the <1~CFZ group is 4. 93 cps. and between the apex fluorine atom and the B-CFZ group is 2.47 cps. The magnetic resonance spectrum of the base fluorine atoms is shown in Figure 24 and in Figure 25 the multiplet centered at 5. 0 ppm is due to the CF3 group. This group is coupled to the B-CFZ group with a coupling constant of 10. 80 cps. and it is coupled to the a-CFZ group with a coupling constant of Z. 42 cps. This Spectrum was recorded at a lower gain than were the others. The multiplet centered at 17. 8 ppm in Figure 25 arises from the c-CFZ group which is coupled to the base fluorines with a coupling constant of 16. 99 cps. The spectrum of the [S—CFZ group is shown in Figure 26 and the spectrum of the y-CFZ group is shown in Figure 27. CF3SF4CFZSF5 - The 56. 445 high-resolution fluorine magnetic resonance spectrum of this compound is shown in Figures 28 and 29. The structure of this compound is based upon its molecular weight and the nuclear magnetic resonance spectrum reported here. In Figure 28 the multiplet centered at — 141. 6 ppm. is typical of an apex fluorine atom coupled to four base fluorine atoms and to an a-CFZ group. An analysis of this multiplet (page 46) shows that the coupling constant between the base and apex fluorine atoms is 151. 87 cps and the coupling constant between the apex atom and the a-CFZ group is 5. 28 cps. In Figure 28 the multiplet centered at —125. 8 ppm is due to the four base fluorine atoms of the SF5 group. In Figure 29 the multiplet at —lQ3. 9 ppm. arises from the four equivalent fluorine atoms of the SF4 group which are spin- coupled to other groups in the molecule. The five-line multiplet at —11. 9 ppm in Figure 29 is due to the CF3 group which is spin—coupled to the adjacent SF4 group with a coupling constant of 22. 92 cps. The resonance lines centered at -10. 3 ppm arise from the CF; group which is ~00 .00 m0 0 _ . _ m MN M 0m n00 TI. . EOOOth 000000003 ”000000000 000 00.00 :8E 34.0... n s. 000.000.00.000 0o 0Q500w 0&0 000.0 .nrmO $.mm 05 No 0005000003 0000000000 00000m0§0 3h .0m 005me 6 0! 000mm 0 . mNH .. .Iil, 000mm 0 $101.. .EOOUth 000000000 “000000m0w . .00000 mvv.0m .I. 3., .mhwthvhmth mo @500m mhm 05 mo 000030 000000de 0003 0G0 x090 00$ 00 0050000000 0000000000 0000Gm0q0 Sh .mN 00Dm0h 97 coupled to the four base fluorine atoms of the SF5 group and to the SF4 group with a Spin- spin coupling constant of 21. 31 cps. The CF; group is also coupled to the apex fluorine atom as was mentioned above. Some of the lines in this multiplet are obscured by the CF3 resonance lines. The spin—spin coupling constants for the above compounds are summarized in Table XVII and the chemical shifts are listed in Table XVIII. - The high-resolution fluorine magnetic resonance spectra of some fluorocarbonsnitrogen compounds have been obtained at a fixed radio— frequency of 56.445 mcs. The spectra of other fluorine-containing com- pounds are also reported here. (CF3)2NF - The 56.445 mcs. high-resolution fluorine magnetic resonance spectrum of (CF3)2NF is shown in Figure 30. The doublet at -3. 8 ppm. arises from the resonance of the CF3 groups which is split by the fluorine atom on nitrogen with a coupling constant of 14. 97 cps. The broad septet at 12. 8 ppm. is due to the fluorine atom bonded to nitrogen. CF3CFZE=NCFZCF3 - The 56.445 mcs. high-resolution fluorine magnetic resonance spectrum of CF3CFZN=NCFZCF3 is shown in Figure 31. The peak at 7. 5 ppm. is due to the two equivalent CF3 groups and the peak at 35. 9 ppm. is due to the equivalent CFZ groups. There is no measurable spin— spin splitting in the perfluoroethylgroup nor is there any spin-spin interaction between CF3 and CFZ groups on opposite sides of the double bond. CF3CFZCFZCFZN=NCFZCFZCFZCF3 - The 56.445 mcs. high—resolution fluorine magnetic resonance spectrum of C4F9N=NC4F9 is shown in Figures 32 and 33. The multiplet at 5. 3 ppm. in Figure 32 is due to the CF3 group which is split by the CF; group a to the nitrogen atom with a coupling .9500m mhm 030 00 0000000 000000de 00.00r .000 x005 00.3 00003009 000000000 mfifimdoo 08. 00 th0hm an .m500w mhm 00.? 00 00000.0 00000.30 N090 0% 0000000000 .0050 98 000000 009 00H0>0 00 000003 000 00>0m 000 000000.000 mcflmdoo lillllllll'lllll‘lllllllll'llllllll $.02 002m . 3.0... 8.00 m00~0owmmm00 o 2. .30 . E. .0 mo .0. N0. .0 ow .2 o .: m00~00~00~00000 o 3 .02 mm .0. cm .0 om .E m00~0om00 8 .2 om .8 00000000000900 2. .o S .3 oo .00 M.WGNr.00..r00£n0 0 mm .o o» .2. 10020000000 llllllllllll'lllllllllllll‘lllll N in 0— u0 0 - N 0 iN. 0 i n N i n w i n 0. N w m r00 .mD .m .m .m i u 0 Mb hm O ”0000 .mm MWH. MD 00 hob. 000 0 bob hm O huh. hm huh. hm mob. , 0050000000 E OUMHOSGNNOHIH .HSMHHHW HO w®>fiwd>fikvg kavHHdOHSHMHOAH QM muqmuwmfioo MCQUHQSOU memlfifiam .HH>VA GHQ—NH. vw Q500m mnHm 00 0000000 0000.06 00.00. 00 000000 0000000000. @500w mrAm 06. no 000000 000000.30 X0000 00 0300 00000000000 $000...th 0000000000 00000 700090: 00020000 000 00000.0 000 00>0m 00.0 000000 0000000000... lull!!!" 00.000- 0.2- 0.2- 0.80- 0.2.0- mmmumodmnmo W 30.00. 800.8. o.m 30.: 0.00.0. 0.02- 300.00.00.00000 .o a x. 0.... 0.0.0 90:- 0.02- $0000.00 0.2 0 .2 - 0 do- m$00.00.00.00.00 0.0. 0.40 0.40- 0.8- m00...00..00n00 m .0. o . E. o .02. - .00NAN000000 f!!! u 0 l N -n :0 In a. 0 0 00 00mg 0 0000 0 000. 0 mos 0 00... 00.... 000 9500800 d til-Iii; *0000050000003 05:05 00 00>0u0>0000 H>MH00005d00m 000 0.300% 0000000000 0000.00.3h .HHECA 030R. M MD .EOOOnhU 0000000000 “0000000000 . .0090 00.0.00 n o: .mMNDZanhno mo 00050000Q0 00000000000 00000m0c0 Sh .Hm 00dm0h .qmmww.~wiiiii-iiiii., iii :1. ._. , .. . . .. . i . . - Filliililiil i .. VIII.iinitii:iiliiiiliiii 100 T11 30 1.0.5. 02 ¢iiom £00002 Tiiiil mmo 00.00 .EOOOMMD #0000038 ”000000000 . .mmo 0.3.0.000“ n o> .MZNAMMDV 00 0005000090 00000000000 000000w000 Sb .om 005m0h .000 0000 m 4: 0800800 :88 3.0.60 u f émdz “2000.0QN00000 d a .0 mo 0&500m NED-.0 000 uhoua 05. 00 0005000000 0000000000 00000w0000 Sm .mm 00dm0h 0000.00 0058.8 33.0 . -- i— i. 101 1000mm 0 .m iilliilili i ii , -- iii-1.1-5!- .ii-ira-l—ilil-lli'inilii:ii.-i W ill 3%.... , Ti 000 00.00 000 00.0 00000000 0203.8 028802 :85 3.0.0... n f 50.02 ”2.00.00.00000 .0 a x. 00 0&500m NhUnd 000 th 00$ 00 000.900.0090 0000000000 0000cm0000 Sh .Nm 005m0h 102 constant of 4. 27 cps. and by the B-CFZ group with a coupling constant of 9. 90 cps. The multiplet of 31. 6 ppm in Figure 32 arises from the resonance of the a-CFZ group which is assumed to be Split into a triplet by the a—CFZ group with a coupling constant of 10.. 97 cps., In Figure 33 the multiplet centered at 47. 8 ppm. is due to the B-CFZ group and the resonance lines at 49.1 ppm. are due to the ‘Y—CFZ group. (CF3)ZNHgN(CF3)2 - The 56.445 mcs. high—resolution fluorine magnetic resonance spectrum of (CF3)ZNHgN(CF3)z is shown in Figure 34. The Spectrum consists of a triplet centered at _18. 9 ppm. This compound might be expected to give a single magnetic resonance line because of the equivalence of the CF3 groups. However, the mercury isotope, Hg199, which has a natural abundance of 16., 86%, possesses a nuclear spin of one-half. This isotope is spin-coupled to the CF3 groups with a coupling constant of 73.0 cps. (CF3)2NCOOCH3 — The 56.445 mcs. high-resolution fluorine magnetic resonance spectrum of (CF3)2NCOOCH3 is shown in Figure 35. The spectrum consists of a single line at -21. 3 ppm. from CF3COOH. There is no measurable proton-fluorine spin- spin coupling. CF3CC12CFC1CF3 - The 56.445 high-resolution fluorine magnetic resonance spectrum of CF3CC12CFC1CF3 is shown in Figures 36 and 37. In Figure 36 the multiplet centered at —5. 5 ppm. is due to the CF3 group adjacent to the CFCl group to which it is coupled with a coupling constant of 11.69 cps. The coupling constant between the two CF3 groups is 7'. 20 cps. The multiplet at -4. 0 ppm- in Figure 36 is due to the remaining CF3 group. This group is spin-coupled to the CF group with a coupling constant of 5. 54 cps. as well as to the other CF3 group. The theoretical spectra, calculated by first—order perturbation theory, for these two groups are given in Figure 36. Figure 37 shows the experimental and first-order theoretical magnetic resonance spectra of the CF group. .EOOOnhO Hmmhofino ”monogamon . .mog mmluiwm n c> .mEUOOUZfimMUV mo 93.50on ouCMQOmoH oflonmddfl Sh .mm oadmfim .vagnm.®uWWHUiéz. 11.. 2.1.1. . . . . . .. . -21- _. 103 c .EOOOnhD Hmanouxw 638.8%»; . .moE mwwcm n 3. .NAthVZmEZNAthV mo 8.9.30on ooGdCOmon oflocmmg Sh .vm whdmfih nmmo 0o4m.fl mooonmo :22me ”88083 :88 mitem u f .nmoaomosoommo mo mfioum HOMO mafia mo mun—00mm moddGOmon oflocmmdfl Sh adoflohooafi paw Hmucogfinomxm .wm oudmfim M -illlllllflmlonlwli I: . ill..- .2 l . l--. .-l.l-l llllll..|~mlmnmlwl.lmillll I_J_:___m_ _l. . --...--lll--l_... n--. .. ll: - . . m . . Emmo 31.8 Tall. TI on Tl. mmo 0o . AH . m3 3. .m .EOODth 13.838 .wucohomog . .moE m3... om n o; .thHOhOJOUth mo wQSOHm n 3;th pad @3th 2i m0 930on oucMGOmmh oBocmg Sh 1856.893 pad amunoawhomxm .om mhdwflh illlllllll 9.1.. .l . .. llllllllli .lv . .l {1... . lillllllll'llllllllllz..lll . I. l . . .ll...||l _ 105 CFClzCCIZCFzCI - The 56.445 mcs. high—resolution fluorine magnetic resonance spectrum of CFClZCCIZCFzCl is shown in Figure 38. This is an example of an AZB spin system. The doublet centered at -23.83 ppm. is due to the CFZ group which is spin-coupled to the CF group with a coupling constant of 14.44 cps. The multiplet at —22.0 ppm is due to the CF group. (CF3)ZNCF=NCF3 - The 56. 445 mcs. high resolution fluorine magnetic resonance spectrum of (CF3)2NCF=NCF3 is shown in Figure 39. The multiplet at -57. 0 ppm. is due to the CF group which is spin- coupled to the three CF3 groups. The multiplet at high field consists of two overlapping doublets. The more intense doublet centered at -l9. 84 ppm. is due to the two equivalent CF3 groups bonded to the same nitrogen atom which are coupled to the CF group with a coupling constant of 13. 25 cps. The coupling constant between the remaining CF3 group and the CF group is 13. 97 cps. One line of this doublet is obscured by the resonance absorption of the other CF3 groups. (CZF5)ZNF - The 56.445 mcs. high—resolution fluorine magnetic resonance spectrum of (CZF5)2NF is shown in Figure 40. The resonance line at 7.4 ppm.is due to the CF3 groups and the peak at 11. 6 ppm. arises from the resonance of the NF group. The resonance line of 35.4 ppm is due to the CFZ groups. There is no observable spin— spin coupling in this molecule. (C2F§)3N - The 56.445 mcs. high-resolution fluorine magnetic resonance spectrum of (CZF5)3N is shown in Figure 41. The multiplet centered at 5. 2 ppm. is due to the CF3 groups and the multiplet at 12. 7 ppm. arises from the resonance of the CFZ groups. The origin of the spin- spin splitting present in Figure 41 will be discussed in the next section. llllLlllllllll lllllllll -llllllilllllrlllllllllllllll ho" m u MDZ I . mmo e.sm , w, _ Ammovz .mooonmo mmo fl Hanson—N0 ”0200.330 . .008 mfiwom H o: .nhDZHhOZNAthV mo 5.9.30on 009065.000 ofipocmma 3h .0m 00.9mm” Ema o.dm... . , -Emmwam- 106 ......... . . .. l zillllllll. . .lll .llilPI.llll.li-[ll.l_l lllllllllllllllllll .mU mac N¢.w~ fimu EOODth Hmanofinm 0900.830 . .005 mvvbm n o> .HONMUNHOONHOMU mo 85.3.0005 00G0Q000n ofiuocmwa Sh .wm madman o mho T E .l. 090 00.0 .EOODth $950000 “00G0H0m0h . .008 mwvbm n o: .ZmathOv mo 89.30090 0300:0000 ofloflmmg 07m .3. 0993M £0 .EOOOth .H0GH0ux0 “00000300 . .008 mwwbm u o> .thAmMNOV mo 59.30%? 005200009 0309w08~ 07m .o¢ 0993mm 108 The spin—spin coupling constants for these molecules are listed in Table XIX and the chemical shifts in parts per million with CF3COOH as the external standard are summarized in Table XX. 109 Table XIX. Spin-Spin Coupling Constants in FluorocarbonNitrogenCompound: <|| C d " ompoun JCF3C-NF Jch—NF JCFg-CF JCF3C-CF (CF3)ZNF CF3CFZN=NCFZCF3 CF3CFZCFZCF2N=NCFZCFZCFZCF3 (CF3)ZNHgN(CF3)z (CF3)ZNCOOCH3 CF3CC1ZCFCICF3 11.69. 5.54 CFCichzcr'chl . (CF3lzNCF=NC‘F3 .{CZF5)3NF o . o * . Spin-spin-coupling constants are in units of cycles per second. 110 W CFzC-CF JCF3C-CFZ JCF3CC—CF3 JNCFz-CFZ JNCFZCC—CF3 JCF3—NF JCF3N-CF 13.97 9.90 10.97 4.27 7.20 1.44 13.25 Confinued 110a Table XIX - Continued compound JCF3N=CF JCF3—CF2 JCF3N=Hg JH-F (CF3)ZNF CF3CFZN=NCF2CF3 o CF3CFZCFZCFZN=NCFZCFZCFZCF3 o (CF3)2NHgN(CF3)2 73.0 (crglchoocn3 o cr3cc1ZCFC1CF3 croizcc1zcrzc1 (CE‘3)ZNCF=NCF3 13. 97 (CsthNF 0 (CZF5)3N 7.0 _‘________________________________.__———————-——-—-——— .EOOUth #0900003 50¢ 75%: 903399 HOQ 00.909 99. 90.3% 090 mufiflm 3009330,. 52. . Nd 22.0.00 0.: «.3 E . 92%va 33.3- m N. . - a ”a z 00 i. 3...: .wz o i .V o..-.. 0.8- 90.00.900.90er n scams. 1 ~13. 320.? mmofiomomoommo Q .0 m .5- M900093.000 a .2 - 2.002.092.1000 e .3 E: .3. m .m mmowmoflmoamozuzfiofiofiofio a; S. s a _u «0 .mm m .s mmofimozuzfiommo was ma- 02.1000 iiillllliiiilii Show. .9000”. 5.00”. zumo 02 77.00... 2:00... 9.00”. 05900 e e 09909900 0 ...mpcsod§ou cwmofizz connwoonogm E mtfim #0005005 oaflogm .xx 033. DISCUSSION The data presented in Table XV show that the ci_s and trans coupling constants are relatively insensitive to the nature of the sub— stituents while the data presented in Table XVI indicate that substituent effects are important in the case of chemical shifts. Although the cyclopropane ring is considered to have some Tr-electron character the results for the coupling constants given in Table XV indicate rather clearly that the most important mechanism for spin- spin coupling takes place through the 0’ electronic structure. This follows because substituents would be expected to perturb the more easily polarized Tr—electrons, and hence the coupling constant, if the mechanism for spin— spin coupling proceeded through a Tr-electronic system. The results for the cis and trans coupling constants are in good agreement with the predictions of valence-bond theory (79, 92). In particular, Table I shows that for the dihedral angle 0 equal to 00 the coupling constant is calculated to be 8. 2 cps. The average value for the cis coupling constant (0:00) for the cyclopropane derivatives is 8. 44 cps.( Table XV). The calculated value for <1) 2 146. 50 is 6. 3 cps (92) and the average trans coupling constant (0 : 146. 50) has a value of'5. 68 cps. The values of 0 quoted above are those which exist in the cyclopropane molecule when the HCH angle is 1180. For the HCH angle equal to 116‘,3 <1) has the values of 00 and 144. 50. A change of 20 in the dihedral angle changes the calculated vicinal coupling constant by only 0. 25 cps. Thus, the conclusion may be drawn that the vicinal coupling constant is not very sensitive to small variations in the dihedral angle. The amount of data available concerning vicinal proton—proton coupling constants in molecules with known dihedral angles is limited. Musher has found that in l, l, 4, 4-tetramethylcyclohexyl-ci__s-2, 6-diacetate 112 113 the vicinal proton-proton coupling constants for 4): 600 and <1) = 1800 are 4. 25 cps. and 12. 35 cps. , respectively (113). Lemieux it a_l. have studied a series of acetylated sugars and found that the average coupling constant for <13, = 1800 is 7 cps. and for d: = 600 the average coupling constant is 3 cps. (87). Cohen, Sheppard, and Turner have estimated the proton-proton coupling constants in dioxane to be 9.4 cps. for 1 ¢ = 1800 and 2.7 cps. for <1>= 600 (114). The use of molecules such as these to study nuclear spin- spin coupling constants is limited because of the possibility of the conversion of one conformation into another. This often results in nuclear magnetic resonance spectra which can not be completely analyzed and the coupling constants must then be approxi- mated. On the other hand, the use of cyclopropane derivatives to study experimentally the angular dependence of proton=proton coupling con- stants has the decided advantage that the nuclear framework is rigid. From the results reported here and from the above data it may be con- cluded that the theoretical values for vicinal proton—proton coupling constants are of the correct order of magnitude and that the angular dependence of these coupling constants is as predicted. The general agreement of the vicinal proton-proton coupling constants in cyclopropane derivatives with theory indicate that the 0‘ electronic structure of the cyclopropane ring is not radically different from that of other siaturated hydrocarbons. .‘N The ginproton-proton coupling constants summarized in Table XV vary over a larger range than do the cis and trans coupling constants. According to valence-bond theory the gem coupling constant is a sensitive function of the HCH angle (Table II) and alterations in this angle should be reflected by changes in the value of the gem coupling constant. ' Table II shows that as the HCH angle increases the gem coupling con- stant should decrease. From the observed coupling constants one would 1 conclude that the HCH angle varies from 1130 to 117. 50 with an average 114 angle of 1150. These angles are in the range of those calculated (5) and observed experimentally (115) for cyclopropane and its derivatives. It may be noted from Table XV that there is some variation in the value of similar coupling constants in different molecules but that in those molecules where the cis, trans, and gem coupling constants are observable the sum of these coupling constants is virtually constant. Also, in the molecule 1=nitrocyclopropane—l, 2=dicarboxylic anhydride the sum of these three coupling constants is 21.70 cps. (16). These data indicate that the increase in the HCH angle, which reduces the gem coupling constant and decreases the CCH angle, increases the vicinal coupling constants. The dihedral angle would also be affected but as was mentioned above the vicinal coupling constant is not very sensitive to small variations in the dihedral angle. It must be kept in mind that the theoretical coupling constants listed in Table I were calculated using tetrahedral carbon orbitals. The HCC angle is 116029“ when the HCH angle is 1180. If the vicinal protonnproton coupling constants increase in magnitude when the HCC angle decreases as is proposed above, then the valence—bond theory predicts coupling constants which are lower than those observed experimentally. Musher has also concluded that the valence-bond theory predicts proton-proton coupling constants which are somewhat low (113). It would be of interest to learn if theoretical calculations would predict an increase in the vicinal coupling with a decrease in the CCH angle. The large coupling constant of 2. 63 cps. in Feist‘s acid between protons four bonds removed is of some interest. The coupling constants for protons four bonds removed fall in the range of 1.4 cps. to l. 8 cps. in substituted propenes, and for allenes the coupling constants are in the range of 6.1 cps. to 7.0 cps. (90). A possible explanation for the magnitude of the coupling constant in Feist's acid is that the nature of the electronic structure of the cyclopropane ring imparts an allene-type 115 character to this molecule. However, the role which the geometry of the molecule plays is hard to ascertain and this might be the source of the large coupling constant. As was mentioned previously the chemical shift data presented in Table XVI vary over a wide range. The chemical shift of the protons of cyclopropane is 13. 2 cps. with respect to tetramethylsilane (116). One may note from Table XVI that substituents on the cyclopropane ring shift the resonance positions of the ring protons to lower field. Sub— stituents which are magnetically anisotropic, such as a phenyl or a carbonyl group, have a marked effect on the chemical shifts. It is interesting to compare the ring proton chemical shifts in 1, 1-dichloro—2— methoxycyclopropane to those in 1, l—dichloro—2-ethoxycyclopropane. The replacement of a methoxy group by an ethoxy group increases the shielding of HA' 11B, and HX by 9.33 cps. , 8.90 cps. , and 8.21 cps. , reSpectively. This change in shielding may be interpreted as a measure of the relative electron-releasing power of these two substituents. It is rather surprising that the changes in shielding are essentially equal for all three ring protons. It may also be noted that the proton cis to the substituent in these two compounds is more shielded than the trans proton while in cyclopropane—l, 1, 2-tricarboxy1ic acid the trans proton is more shielded. In these three compounds the proton adjacent to the substituent is always less shielded than the other ring protons. Because of the dissimilarity of the molecules listed in Table XVI a more extensive correlation of chemical shifts can not be made. The fluorine-fluorine coupling constants listed in Table XVII for the perfluoroalkyl derivatives of sulfur hexafluoride show that similar coupling constants in different molecules have a characteristic value. The only exception to this observation is J in the molecule CFz—SF4 CF3SF4CFZSF5 where the CF; group is situated in a unique position bonded to two SF4 groups. With the exception of J the coupling CF3-CF2 116 constants decrease with an increase in the number of bonds separating the interacting nuclei. In all sulfur hexafluoride derivatives where the CF3CFZ group is present J is equal to zero. Narasimhan CF3-CFZ has shown theoretically that this is a result of the cancellation of terms of opposite sign when the CF3 group is considered to be freely rotating with respect to the CF; group (117). The largest contributions to this coupling arise from the Fermi contact term and from the two—electron term of f1; (equation 41), which is the magnetic dipole-dipole interaction term between nuclei and electrons in non-s orbitals. These two contri- butions are of comparable magnitude but of opposite sign. The spin- spin interaction between the apex fluorine of the SF5 group and other groups in the molecule results in some interesting coupling constants. It can be noted from Table XVII that J is of the order CFz-SF4 of 15 cps. while J is about 5 cps. This illustrates the remark- CFz-SFa able angular dependence of the spin- spin coupling constants. There is a change of 900 in the CSF angle as one goes from the CFZSF4 fragment to the CFZSFa fragment. Also, there is no rotational averaging possible in the CFZSFa fragment because the CSFa angle is 1800 while in the CFZSF4 case the magnitude of the coupling constant results from an averaging process dependent upon the dihedral angle. It may also be noted that JCF3C-SFa ls zero and JCF3C~SF4 15 8156 cps. 1n CF3CFZSF5 even though the number of bonds separating the interacting nuclei is the same in both cases. In C4F98F5 the coupling constant JCFzC-SFals 2.47 cps. and in CF3CFZSF5 the J coupling constant is zero. CF3C-SFa Reference to Table XVII shows that J is always greater than CF3-SF4 J presumably as a result of differences in the averaging process. CFz-SF4 The comparison of coupling constants between nuclei separated by the same number of bonds allows one to ascertain the importance of the geometry of molecules in the determination of the magnitude of coupling constants. 117 The chemical shifts listed in Table XVIII agree well with those published by Muller, Lauterbur, and Svatos (31). In general, as the electronegativity of a substituent on an atom to which fluorine is bonded increases the fluorine nucleus becomes less shielded. This is borne out quite well by the chemical shift of the CF; group in CF3SF4CFZSF5. In this molecule the CFZ group is bonded to two SF4 groups and the resonance absorption of this group experiences a large down-field shift. In the molecule CF35F4CF2COOCH3 the chemical shift of the CF; group is also at a lower field than is usual for an S~CFZ group presumably because of the neighboring carbonyl group. In all SF5 groups the apex fluorine is less shielded than the base fluorine atoms which indicates that the S—Fa bond is more covalent than the Swa bond (18). It may be noted from the coupling constants listed in Table XIX is again equal to zero with the possible exception of h . t at JCF3-CFZ (C2F5)3‘N. However, in CF3CC13CFC1CF3, J is equal to 11.69 CF3~CF cps. and in C4F9N=NC4FQ, J is equal to 10.97 cps. These three ' Cqu-CFZ coupling constants involve fluorine atoms on adjacent carbon atoms and for J , where one of the interacting groups is CF3, the magnitude CF3-CF is unexpectedly large. Because of the trigonal symmetry of the CF3 group the energies of the staggered conformations are equal and this coupling would be expected to vanish as in JCF3-CF2° If there is free rotation in the J case the spectrum would be of the Azxz type CFz—CFZ and if the coupling constants are approximately equal then the a-CFZ resonance should be a triplet as is observed. Because of the complexity of the spectra of the fi-CFZ and y-CFZ groups one can not eliminate completely the possibility that the observed CFz-CFZ coupling constant is between the a—CFZ and 'y-CFZ groups. There is also a large variation in the coupling constants when the interacting nuclei are four bonds removed. The coupling constants for J and cr3cucr’ JCF3C-CF2’ JCFZC-CF are 5. 54 cps. , 9. 90 cps. , and 14.44 cps. , respectively. 118 For interacting nuclei which are five bonds removed JCF3CC—CF3 is equal to 7.20 cps. and J is equal to 4. 27 cps. (Table XIX). CFZCC-CFZ An interesting comparison of coupling constants exists in the molecules (CF3)ZNF and (CZF5)ZNF. In (CF3)ZNF the coupling constant J is CF3-NF equal to 13. 97 cps. while in (CZF5)ZNF the coupling constantSJ 0 CFz-NF = CF3C-NF = 0. Also JCF3-CFZ is equal to zero in this molecule. The one apparent exception to the general result that J = 0 is in CF3-CFZ the molecule (CF3CFZ)3N. A possible explanation for the observed and J spectra is that the CFZ group is split equally by all CF3 groups and the CF3 group is split equally by all CFZ groups. This leads to the result that JCF3-CFZ = 7.0 cps. The existence of a double bond in (CF3)ZNCF=NCF3 in which . = 1 . . = l . . d JCF3N-CF 3 25 cps and JCF3N=CF 3 97 cps oes not appear to affect the magnitude of the coupling constant. The value of 73. 0 cps. for JCF3N—Hg 1n (CF3)ZNHgN(CF3)z 18 small in comparison w1th J in (C2H5)2Hg (118). This is a case where the nitrogen atom has CH3C-Hg attenuated the magnitude of the coupling constant although a strict com- parison can not be made since information concerning the sign of mercury-fluorine coupling constants is lacking. In general, there is no apparent correlation of the fluorine coupling constants listed in Table XIX with the number of bonds separating the interacting nuclei. Also, there are no observable trends in the coupling constants between fluorine atoms which are separated by the same number of bonds. The presence of a nitrogen atom separating inter- acting nuclei does not produce any coherent effect on the magnitudes of the coupling constants. The chemical shifts presented in Table XX generally agree with the results given by Muller, Lauterbur, and Svatos (19). The only serious deviations are in the molecules which contain chlorine atoms and these chemical shifts have been explained by Gutowsky as being due to the tendency for fluorine atoms to form double bonds and hence become less shielded (22). SUMMARY The proton magnetic resonance absorption‘of several derivatives of cyclopropane was studied with a Varian high—resolution nuclear magnetic resonance spectrometer operating at a fixed radiofrequency of 60. 000 mcs. The fluorine magnetic resonance absorption of some per- fluoroalkyl derivatives of sulfur hexafluoride was studied at fixed radio- frequencies of 60. 000 mcs. and 56. 445 mcs. and the fluorine magnetic resonance absorption of some fluorocarbon nitrogen compounds was studied at 56.445 mcs. The syntheses of some of the cyclopropane derivatives which were studied in this research are reported here including three compounds whose preparations have not been previously reported. The methods by which the proton and fluorine magnetic resonance spectra were analyzed are discussed and theoretical spectra for the spin systems which were analyzed are presented. The proton magnetic resonance absorption of seven cyclopropane derivatives was studied and the fluorine magnetic resonance absorption of six perfluoroalkyl derivatives of sulfur hexa- fluoride was studied. Fluorine magnetic resonance spectra of eight fluorocarbon-nitrogen derivatives and two substituted fluorocarbons were obtained at a fixed radiofrequency of 56.445 mcs. The observed chemical shifts and nuclear spin— spin coupling con— stants have been interpreted in terms of substituent effects and the structure of the molecules. Although the structure of the cyclopropane ring is considered to be somewhat unusual the observed proton-proton coupling constants for ring protons in the cyclopropane derivatives are not anomalous. The magnitude of, and variations in, the proton—proton coupling constants can be satisfactorily explained on the basis of the geometry of the molecules. Substituent effects have not been found to be 119 120 important in the consideration of the proton—proton coupling constants but the chemical shifts of the ring protons have been found to be suscept- ible to the nature of the substituents on the ring. The fluorine chemical shifts have been found to vary with the electronegativity of the substituents in a predictable manner. Fluorine- fluorine spin coupling constants have been found, in general, to be quite large. Spin— spin coupling constants between fluorine atoms four and five bonds removed have an appreciable magnitude. 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