J . Phys. Chem. 1993, 97. 543-5444
5443
COMMENTS Comwat 00 Theory of CollIsiolul Activation of
Macromdecules Helen J. Cooper,Peter J. Derrick,' and H. Donald B. Jenkins
These lead to the final velocities in the xdirection (eqs 18 and 19 of ref 1) being expressed as
Department of Chemistry, University of Wamick, Cooentry, CY4 7AL West Midlands. U.K.
Einar Uggerud Department of Chemistry. University of Oslo, P.O. Box 1033. Blindern. N-0315 Oslo, Norway
-- m, - m,(2 cos2cp - 1)
u:,
Received: December 29. I992
2m1 cos2 cp m , + m , us
m, + m8
(6)
Thevelocity of the atom within the ion (eq 26 of ref 1) should be given as
This comment refers to a r e n t publication by Uggerud and Derrick,' which develops an impulsive collision-transfer theory for collision between a gas atom and a macromolecular ion. The theory provides, in the case of a single collision, expressions for the uptake of internal energy, Q.by the macromolecular ion, the loss of kinetic energy, AE,of this ion. and the angle, 8. through which this ion is scattered. According to this theory the relationship between Q and AE is independent of 8. The original paper fails to emphasize perhaps the most important consequence of this angular independence; namely, that the energy loss AE,characterizing any particular fragment ion, can be converted to the internal energy, Q, of that fragment's parent ion. Further we point out that theoriginal articlecontainsa number of typographical errors, the most important of which is an error in thecited relationshipbetween Qand AE. The true relationship remains of the form
(7) while the y a m p o n e n t of the velocity of the ion after collision (eq 32 of ref 1) should be expressed as
The energy of the ion after collision is then given by E' = [mm2(m, + m,)'
- 4m8m,(m,m, + mumHm-
m,m,) ox2c ~ ~ ~ / [ m l o n ~+ (m m,)'~ g (9) A simpler way of expressing eq 9 is
E'=
Q = (rI2t)AE
(1) where t and p are constants. t is, however, defined by eq 2, and not as stated in eq 38 of ref 1, where m, = mass of the atom that is 'hit", m, = mass of ion, and m, = mass of gas atom.
[1
4m,m,(m,m,,
+ mlmlon- m 8 m # ) cos 2
m,, (m, + m,12
cp
] E (10)
TheexpressionforcosO(eq 36ofref l),whereOisthescattering angle in the laboratory system, should be written
me=
[m,(m,
+ m,) - 2m,m,
cos2 cpl~/m,,)
+ mg)(2"/m,)"2
112
( 1 1)
which can be simplified to The results of the original study have been cited in the literature.' Use of the incorrect version would not in itselfcause gross errors in the calculation of Q. since for macromolecular ions m, >> m, and so t tends to (m,+ m1)/2m,. The computer simulations described by Uggerud and Derrick' have taken note of the true relationship between internal energy uptake, Q, and translational energy loss, AE. Simpler expressions for internal energy, Q, and energy loss. AE, given by Jarrold and Honeas concern the limiting case when the collision is end-on. so that the impact angle, cp, is zero. There are a number of errors in the equations given at various stages of the derivation. Equation 13,' which introduces the impact angle, cp, should read
Two further simplifications can be made by writing eqs 24 and 25 of ref 1 as 2m, cos cp sin cp
' 2m, cos cp sin cp
=
m,+ m,
(14)
Further eq 47 of ref 1 should take the form m8(Ul,I2
= m,(u,$
Bhllh = arcsin(p - 1)
(15) Both the translational energy loss, AE,and the internal energy uptake, Q, are functions of the scattering angle, 8, according to
- m , ~ , , )2 (3)
while eq IS of ref 1 describing the velocity of the ion should read oo22-3654/93/2o97-543S~.oo/O
(6
1993 American Chemical Society
5444 The Journal of Physical Chemistry, Vol. 97, No. 20, 1993
impulsive collision-transfer theory. The dependence upon the scattering angle is, however, the same in each case. In a typical tandem mass spectrum of a complex molecule, each fragment ion exhibits an identifiable translational energy loss,AE. Therefore provided that the fragment ion in question is formed as a result of a single collision, rather than multiple collisions, the translational energy loss, AE, can be converted, by virtue of eq 1, to a corresponding internal energy, Q. This internal energy can be properly considered to be the internal energy associated with the formation of that particular fragment ion. It is the internal energy of a decomposing ion which is the key physical quantity of interest in understanding fragmentation dynamics in tandem mass spectrometry.
Additions and Corrections
References and Notes (1) Uggerud, E.; Derrick, P. J. J . Phys. Chem. 1991, 95, 1430. (2) Bradley, C. D.; Curtis, J. M.; Derrick, P. J.; Wright, B. Anal. Chem. 1992,64, 2628. (3) Jarrold, M.F.; Bower, J. E. J. Chem. Phys. 1992, 96, 9180. (4) Mowrey, R. C.; Ross,M. M.; Callahan, J. H. J. Phys. Chem. 1992, 96, 4155. (5) Jarrold, M.F.; Honea, E.C . J . Am. Chem. SOC.1992, 114, 459. (6) Jarrold, M.F.; Honea, E. C. J . Phys. Chem. 1991, 95, 9181. (7) Bradley, C. D. Ph.D. Thesis, University of Warwick, 1992. (8) Winger, B. E.; Laue, H.J.; Homing, S.R.; Julian, R.K.;Lammert, S.A.; Riederer, D. E.; Cooks, R. G. Rev. Sci. Instrum. 1992, 63, 5613. ( 9 ) Derrick, P. J.; Colburn, A. W.; Sheil, M.M.;Uggerud, E. J . Chem. Sac., Faraday Trans. 1990,86, 1533.
ADDITIONS AND CORRECTIONS
1993, Volume 97
Douglas G. Frank, Oliver M. R. Chyan, Teresa Golden, and Arthur T. Hubbard': Probing Three Distinct Iodine Monolayer Structures at R(111) by Means of Angular Distribution Auger Microscopy: Results Agree with Scanning Tunneling Microscopy Pages 3830and 3835. Figures 1 and 8 on these two pages were inadvertently switched during the printing process. However, the captions are correct as printed.
