WALTERJ. LEHMANN
3188
A Correlation between Vibrational Isotope Shifts and Mass Spectral Fragmentation Patterns’”
by Walter J . Lehmannlb Department of Chemistry, University of California, Los Angeles, California
90084
(Receized M a y 87, 1964)
Isotope effects on vibrational frequencies are straightforward and well understood. On the other hand, theories dealing with isotope effects on mass spectra are relatively complex and difficult to apply. Although these effects are of great concern in connection with isotope-abundance determinations, they are often disregarded; e.g., for many years the “accepted” Bll/BIO natural-abundance ratio, 4.31, was based on the direct ratio of BF2+ fragments of boron trifluoride, which the present paper shows to lead to a false ratio. The present study suggests a very simple direct correlation between vibrational frequency shifts and mass spectral isotope effects for diatomic and quasi-diatomic molecules.
In 1959 a revision of the atomic weight of boron from that these effects have not been taken into considera 10.82 to 10.811 was proposedz” several years before tion in many isotope-abundance determinations.5-l1 the International Coniniission on Atomic Weights Consideration of molecular vibrations immediately accepted such a change.2b The Commission’s report focuses attention on such effects. The BF2+ fragment was based on work by RlcMullen, Cragg, and T h ~ d e , ~ is produced when the “elastic limit” is exceeded during who reported a B1l/BIO ratio in the range of 4.04 to an asymmetric vibration of the BF3 molecule. Xatu4.07 (=t0.04), later extended to 3.95 to 4.10. (The range apparently reflects a natural variation of the (1) (a) Contribution No. 1618. Presented in part a t the Seventh European Congress on llolecular Spectroscopy, Budapest, Hungary, boron isotope ratio.) July, 1963; (b) Department of Chemistry, ‘L‘niversity of California, Riverside, Calif. 92502. Those results are based on mass spectral nieasure(2) (a) W. J. Lehmann and I. Shapiro, Nature, 183, 1324 (1959); ments of the Na2BO2+peaks of borax and were cali(b) International Commission on Atomic Weights (IUPAC, Monbrated against synthetic mixtures prepared from treal, 1961); J . Am. Chem. Soc., 84, 4175 (1962). B’O- and B”-enriched borax. (3) C. C. McMullen, C. B. Cragg, and H. G. Thode, Geochim. Cosmochim. Acta, 23, 147 (1961). The fact that these values differed significantly from (4) F. H . Field and J. L. Franklin, “Electron Impact Phenomena,” previous ineasureinents based on direct comparison Academic Press, Inc., New York, N. Y . , 1957, pp. 204-217 and list of references therein. of Bl1F2+and BIOFz+fragments from boron trifluoride (5) M.G. Inghram, Phys. Rev., 70, 653 (1946). was attributed to “mass discrimination.” Generally, (6) G. M . Panchenkov and V. D. Moiseev, Z h . F i z . Khim., 30, 1118 such discrimination in mass spectrometry is ascribed (1956). This paper contains a review of other boron isotope investigations. to instrumental conditions. It becomes evident, how(7) C. E. Melton, C. 0. Gilpatrick, R. Baldock, and R. M . Healy, ever, that an entirely different type of discrimination Anal. Chem., 28, 1049 (1956). effect is at work here-namely, an effect that is in(8) V. Shiuttse, Soviet Phys. J E T P , 2, 402 (1956) ; translated from herent in the fragmentation process itself. Z h . Eksperim. i Teor. Fiz., 29, 486 (1955). (9) N. N. Sevryugova, 0. V. Uvarov, and N . M. Zhavoronkov, J . RIass spectrometrists have long been familiar with Nucl. Energy, 4, 483 (1957); translated from A t . Energ., (USSR), 1, 113 isotope effects on molecular f r a g m e n t a t i ~ n . ~For (1956). example, it has been shown4 that in monodeuterio(10) R. W. Law and J. L. Margrave, J . Chem. Phys., 25, 1086 (1956). methane the hydrogens fragment approximately twice (11) R. M . Abernathey, Seventh Annual Meeting of the ASTM as easily as the deuterium (after allowance for statistical Committee E-14 on Mass Spectrometry, Los Angeles, Calif., May, effects). A check of the literature, however, reveals 1959. The Journal of Physical Chemistry
CORRELATION BETWEEN VIBRATIONAL ISOTOPE SHIFTS ASD M A S S SPECTRAL PATTERNS
rally, such a vibrat,ion, in which the boron atom e3sentially moves against three heavier fluorine atoms, is strongly isotope dependent, and this isotope dependency will be reflected in the fragmentation process, thus influencing the observed BI1/B1O ratio of BF2+ fragments. The same would be expected, and is observed, for trimethylborane.'2 As a matter of fact, several apparent ratios are observed, depending on the spectral region and the fragrnent species under consideration. In the BC2 region a ratio of 4.12 is obtained, but for the low-mass region 3.77 is observed. A number of other compounds similarly have been found to yield more than one apparent abundance ratio (Table I ) . l 2 - I 6
Table I : Variation of .A.pparent Isotope-Abundance R a t i o with Mass G r o u p Compound
BlO/B11
B2D6
4.00 3.85
B6Hg
4.00 3.85
MeaB
4.12 3.77
Me3B303
3.98 3.6 C135/C187
CCla
3.12 3.22
When different fragments of the same compound lead to divergent isotope ratios, obviously not both can represent a true value. But which to choose, if any? Without additional (considerations we would have 110 basis for a choice, once errors in measurements have been eliminated. It has previously been p r o p o ~ e d ' ~ ,that ' ~ these apparent abundance ratios should be resolvable into true abundance ratios and correction factors that take into account isotope effects on fragmentation. To determine true abundance ratios, we thus seek conipounds having minimail correction factors. The principal fragments of the boron hydrides, representing successive losses of hydrogens, are produced by the vibration of tihe light hydrogen atoms against the heavy boron frame. Such vibrations are approximately independent of the boron mass. Like -
3189
-
wise, the principal fragment, Me2B303+, of triniethylboroxine is produced by an out-of-phase vibration of the relatively light methyl group against a massive boron-oxygen ring. Vibrational motion again is concentrated in the methyl group and is very nearly independent of whether the ring contains BO ' or BI1. With these considerations in mind, it is not surprising that the principal peaks of the boron hydrides13>14z17-22 and of trimethylb~roxine'~yield identical values, namely, an isotope ratio of 4.00, even though the boron hydrides are produced by rupture of B-H bonds, while the latter case involves breakage of a B-C linkage. (It is to be remembered that breaking of the B-C bond in Me3Byielded an apparent ratio of 4.12.12) It would be useful to have some means for a t least a rough a priori prediction of mass spectral isotope effects, since their experimental determination is rather cumbersome. The following represents such a scheme for diatomic or "quasi-diatomic" molecules. Consider the case of molecule AB rupturing to give fragments A and B, and its isotopic relative AB* yielding A and B*. AB* will fragment less easily than AB if B* represents the heavy isotope. For example, comparison of fragments from HZ and D2 shows that the protium molecule breaks up twice as easily as the deuterium n i ~ l e c u l e ~i e~. ,~the ~ ; fragmentation ratio, f = (H+/H2+)/(D+/Dz+), is approximately 2. Table I1 lists experimentally determined relative fragmentation probabilities for a number of simple ~ o n ~ p o u n d sIt. ~can ~ ~be ~ ~seen that each f value is (12) W. J. Lehmann, C. 0. Wilson, Jr., and I. Shapiro, J . Znorg. NucZ. Chem., 11, 91 (1959). (13) V. H. Dibeler, F. L. Mohler, L. Williamson, and R . M . Reese, J . Res. NatZ. B u r . Std., 43, 97 (1949). (14) V. H. Dibeler, F. L. Mohler, and L. Williamson, ibid., 44, 489 (1950). (15) W. J. Lehmann, C. 0. Wilson, J r . , and I. Shapiro, J . Inorg. Nucl. Chem., 21, 25 (1961). (16) "Catalog of Mass Spectral Data," Carnegie Institute of Technology, Pittsburgh, Pa., American Petroleum Institute Research Project 44, Serial No. 603. (17) I. Shapiro and J. F. Ditter, J . Chem. Phys., 26, 798 (1957). (18) V. H . Dibeler and F. L. Mohler, J . Am. Chem. Soc., 70, 987 (1948). (19) F. J. Norton, ibid., 71, 3488 (1949). (20) J. F. Ditter and I. Shapiro, ibid., 81, 1022 (1959). (21) S. G. Gibbins and I. Shapiro, J . Chem. Phys., 30, 1483 (1959). (22) J. F. Ditter, E. B. Klusmann, J. C. Perrine, and I. Shapiro, J . Phvs. Chem., 64, 1682 (1960). (23) 0. A. Schaeffer and J. M . Hastings, J . Chem. P h y s . , 18, 1048 (1950). (24) 0. Schaeffer, Proceedings ofthe NBS Semicentennial Symposium on Mass Spectroscopy in Physics Research, Washington, D. C., September, 1951, published in "Mass Spectroscopy in Physics Research," NBS Circular 622, January, 1953, p. 249.
Volume 68, Number 11
iVouember, 1064
WALTERJ. LEHMANN
3190
numerically equal to the square of the ratio of the zeroonly 0.3Yo or less for a difference of one mass ~ n i t , ~ 7 , ~ 8 and even in the low-mass region it is difficult to account order vibrational frequencies (4395 and 3118 cm.-1 for an instrumental discrimination effect that is 4Yo for HZand Dz, r e ~ p e c t i v e l y or ) ~ ~the equivalent inverse greater. ratio of the reduccd masses. (The complex F'ranckCondon calculation, which can be applied only to the The value 0.25, obtained from the parent regions of a simplest of molecules, yields 2.2 for h y d r ~ g e n . ~ ~ ~ ~ ) number of boron hydrides, is probably close to the true B1@/B1'abundance ratioza because the difference Admittedly, this correlation is only approximately valid for the extreme case of tritium as compared to in fragmentation probabilities between a B"-H and protium, where the observed4 23,26 f factor is between a B1@-Hbond is negligible (since the heavy boron atom 3.3 and 3.7, while the ratio of frequencies squaredz5 participates only slightly in B-H stretching vibrations) and because the sum of BIH, fragments is relatively or reduced masses is 3.0. (On the other hand, using small compared to the sum of BzH, fragments. the Franck-Condon theory, Schaeff er and Hastings calculated the equally divergent value of 4.2.4,23) On the other hand, boron isotopes should have considerable effect on B-B bond rupture. Let us say When smaller isotope effects are involved, such as for that a BIO-B1@bond ruptures f times as easily as a Bllisotopic variants of Nz,02,and CO, reduced-mass ratios agree well with observed j values (and are at B" bond and that the B'O-B" fragmentation factor is least as good as values calculated from the Franckmidway-O.5(1 f). We can calculate j" by making only a few simplifying assumptions. Condon theory) . 2 3 ' 2 4 Probability statistics predict the compounds B1'2H6, The simple correlations of the present paper can be B"H1@H6,and BL02H6to occur in the ratio 1 :2R:R2, extended to polyatomic molecules which can be treated where R is the BIO/Bll ratio. For R = 0.25, this beas quasi-atomic, such as diborane, BzH6, which can, comes l :0.50:0.0625. Each B1lz rupture yields two for the present purpose, be considered as made up of Bll fragments. Each Bl1-B1@rupture yields one B11 two BH3 units (even though the borons are linked and one BIO fragment, both quantities being proporthrough three-center bonds with hydrogen bridges). tional to the B1lB1@ abundance (212) and the fragmenBecause of overlapping contributions to mass spectral tation factor [0.5(1 f ) ] ; L e . , R ( l f f ) . Similarly, peaks, due to successive losses of H a t o m , boronBIo2 fragmentation produces B'O fragments in the relaabundance ratios in boron hydrides must be calculated tive amount of 2Rzf. I n the low-mass region, the apthrough a "stripping" process1*>lgwhich also yields parent B1O/B1l ratio thus is the monoisotopic patterns. Most workers dealing
+
+
Table I1 : Correlation of Fragmentation Probability with Reduced Mass or Vibrational Frequencies Re1. Molecule
Hz (Dz) XZ
(P)
CO ( 0 3 ) BHa-B H,
fragm. prob.
~1.9-2,3 1.10 1.04 1.08
d P 1
(Vl/Y2) 2
2.00 1.07 1.05
1.99 ...
1.08
1.07
...
with isotopically normal boron hydrides have found the value of 0.25 to be the best B1@,/B1lratio for calculating monoisotopic fragmentation patterns from observed polyisotopic mass spectra in the higher mass regions.13~14~17--22 However, for monoboron fragments, a ratio of 0.26 has been found applicable.1a,14 Instrumental mass-discrimination effects alone cannot satisfactorily account for this 4yo difference. The high-mass fragments, representing loss of hydrogens, do not possess much kinetic energy. Hence, mass discrimination effects here should be of the order of The Journal of Phvaical Chemistry
Using the values of 0.25 and 0.26 for R and R,, respectively, we findf to be 1.08. I n other words, interpretation of mass spectral data indicates that the B102 bond ruptures 8% 1110'e readily than the B112 bond. Again, this value corresponds closely to the square of the ratio of the B-B stretching frequencies of B"zH6 and B11ZH6-816 and 788 cm. -I, respe~tively~~--vix., '1.072. A similar value, 1.077, also is obtained from the ratio of the reduced masses of B",H, ( p = 7) and B"ZH6 ( p = 6 . 5 ) when we consider them simply as consisting of two BH3 groups oscillating against each other. A word of caution: Application of this scheme is (25) G. Herzberg, "Spectra of Diatomic Molecules," D. Van S o s trand Co., Inc., Princeton, N. J., 1950, p. 532. (26) V. H. Dibeler, F. L. Mohler, E. J. Wells, Jr., and R. M . Reese, J . Res. Natl. Bur. Std., 45, 288 (1950). (27) C. E. Berry, Phys. Rea., 78, 597 (1950). (28) F. H. Field and J. L. Franklin, "Electron Impact Phenomena," Academic Press, Inc., New York, N. Y., 1957, p. 99. (29) R. C. Taylor and A. R. Emery, Spectrochim. dcta, 10, 419 (1958)
3191
ENERGETICS OF Sonm GASEOUS OXYGEXATED ORGANIC XONS
restricted to "quasi-diatomic" molecules in which the resulting fragments have approximately identical internal vibrational frequencies. (This is true for the fragments B11H3and B10H3, since their vibrations involve motions of 1ig;ht hydrogens against essentially fixed B1" or Bll atoms.) The method must not be applied when the fragment pairs differ greatly in internal vibrational energy. For example, we cannot compare CDa-CD, with CH3-CH3 bond rupture since
the fragments CD3 and CHs have quite different vibrational energies. To summarize, it seems that vibrational frequencies and masses can advantageously be used in a very simple manner to estimate isotope effects on mass spectral patterns of diatomic and quasi-diatomic molecules. In view of these effects, greater care should be taken in the application of mass spectral data for isotopic-abundance determinations.
Energetics of Some Gaseous Oxygenated Organic Ions" by M. S. B. Munsonlb and J. L. Franklin'" Research and Development, Humble Oil and Refining Company, Baytown, Texas, and Rice University, Houston, Texas (Received J u n e 3, 1864)
The heats of formation of some simple oxygenated organic compounds have been rneasured from different sources; AHf(CH,OH+) = 174 kcal./mole and AHf(CH3Q+) = 202 kcal./mole. Similar differences exist for the isoiners of mass 45. The proton affiyities of formic, acetic, and propionic acids were determined from rearrangement ions of esters as about 170-180 kcal./mole. The protonated acid ions are readily formed by ionic reactions in the gaseous aliphatic acids. Appearance potential data for H30+ and CH30Ha+ may be interpreted to give P(H,Q) z P(CH30H) S 170 kcal./nzole.
The tabulation of appearance potentials and heats of formation of simple oxygenated ions by Field and FranklinId indicated several apparent discrepancies as well as a lack of data for certain ions. It seemed worthwhile to obtain further data on energetics of oxygenated organic ions. There were also indicated several potentially interesting variations of ion energy with structure which appeared worthy of study.
Experimental The conipounds for this study were obtained from various sources (purit#yabout 99Oj,) and used with only simple further purification since the fragments under study were generally prominent in the spectrum. Some of the compounds were prepared and purified by Dr. R. H. Perry of these laboratories. The mass spectrometer was that previously described by Field.2 The appearance potentials reported in this paper were
obtained froni the threshold of a plot of ion current us. electron energy, for which the slopes of the curves of the desired ion and the calibrating ion were made about equal over a 2-v. range above the threshold or onset potential. The appearance potentials are generally the average of three or four separate determinations with two calibrating gases. Measured differences in ionization potentials of rare gases were within 1 0 . 1 v. of the spectroscopic differences. The pressures within the ionization chamber were not measured, but were never greater than about 10 b. These pressures, ~
(1) (a) Supported in part by Project SQUID under Contract No. Nonr-3623 (S-18); (b) Humble Oil and Refining Co.; (c) Rice University; (d) F. H . Field and J. L. Franklin, "Electron Impact Phenomena and t h e Properties of Gaseous Ions," Academic Press, New Tork, N. T.,1957. (2) F. 13. Field, J . Am. Chem. Soe., 83, 1523 (1961).
Volume 68, hiumber 11
November, 1964
