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Calculations of rate constants for ion—molecule reactions in a pulsed-source mass spectrometer
Inlernatiotzai
of Mass
JOLUM~
Spectrometry
and Ioon Physsrcs
385
Eisevier Publishing Company, Amsterdam - Printed in the h’etheriands
CALCULATIONS
REACTIONS
OF
BRYAN G. REUBE?!*, Department
RATE
CONSTANTS
Ibi A PULSED-SOURCE
of Physical
ASSA
LESWTZ
Chemistry,
AKD
Hebrew
FOR
MASS
CH.%VA
Unicersity.
ION-MOLECULE
SPECTROMETER
LIFSHITZ Jerusalem
(israei)
(Received Nobember Zlst, 1968)
ABSTRACT
A method is described for calculating the rate constants of ion-molecule reactions in a pulsed-source mass spectrometer where parent and daughter ions differ markedly in mass. The rate of loss of ions in the ion source is mass dependent, but a correction can be made for this using experimentally determined decay curves
for ions cf masses similar to those of the primary
and secondary
ions.
The rates of thermal ion-molecule reactions can conveniently be determined in a pulsed ion source mass spectrometer, as has been demonstrated by Harrison and coworkers’. if only a small proportion of primary ions is lost by reaction, the rate constant can be obtained from the equation [S+]/[P’]
= k[M]i
0)
where [M] is the concentration of neutral molecules in rhe ion source, and [S’]/ [PT] is the ratio of secondary to primtry ion concentrations’. In the absence of mass discrimination the ion concentratton ratio can be equated to the ratio of collected ion currents (i,,,/i,,:, )_ Most of the reactions studied so far involve proton transfer, so that the primary and secondary ions have been of similar mass. For such reactions, mass discrimination in a pulsed ion source can be neglected. This is not possible, however, when the masses of reactant and product ions differ by more than 50 %‘. During the delay time between ion-formation and ionwithdrawal, the ions of lower mass decay much faster than those of higher mass. We have recently carried out a mass spectrometric investigation of ion-molecule reactions in benzene3, where, for some of the reactions, the masses of reactant and product ions differed by as much as I00 %, e.g. C,H,++C,H,
--, C12H,,+
(2)
l Permanent address: Department of Chemistry, University of Surrey, London, S.W. 11, England.
3. Mass
Spectrometry
and Ion Physics,
2
(1969) 385-390
386
B. G. REUBEN,
A. LIFSHITZ,
C. LIFSHITZ
Though our mass discrimination was smaller than that found by Harrison and coworkers4 , it was essentially similar. It was not, therefore, legitimate to take the ratio iscJiprim as a tr ue measure of t le ratio of concentrations of reactant and product ions in the source. This prob!em has been considerti briefly by Lampe and his coworkers. In one paper’ he assumed that the ratio of observed ion currents could in fact be equated to the ratio of ionic concentrations, and in another6 he constructed mass discrimination c~urvl:s for primwy ions of different masses and applied a correction to the secondary ions basal on these. Neither of these methods is enr rely satisfactory and the following analysis was carried out in order to overcome the difficulties_ Consider a pulsed system containing a gas M which, on electron bombardment gives ions P’ whici can undergo reaction to give secondary ions S’. In addition to M, let the system contain a substance R \\hich gives ions R’ of similar molecular weight tc, S-. If the ion currents due to P’, R- and S’ are measured at various delay tixes, 2 series of decay curves is obtained. Let the initial coxzxtrations of primary, secondary and marker ions be [P-lo, [S’], and [R-l,, and the measured concentrations after delay time :,, be Assuming only a smsil proportion of primary ions is [P-L,, WI,, and W’j,,,. lost by rextion, we can write:
F-lr,
= F-lOfPWr=fD
(3)
/3-I,,
= P’loliCi)r=rD
(4)
where&(t) represents the value of the decay function for P’ ions at time t, the same symbols applying to Rf and S * ions, mutatis mutandis. At zero time the various decay functions have the value unity. The rate of reaction at any moment t for A simple bimolecular reaction IS given by:
=
k[Ml
F’l,
=
k[Ml
F’loh@)
After time t, a proportion of the P’ ions will have been lost according to the decay function f&l). Th e secocdazy ions formed at this instant by reaction of some of the remaining P’ ions will then be lost according to a different decay function for the remaining time (to- f) before the drawout pulse is applied. A feasible hypothcsis is that they will be lest at the same rate as R* ions between times t and I,,. If this is so, then the fraLrion of secondary ions lost over this period (tD-t) will and the number of ions d[St], formed between t and b equal to MD)&(~) f tdt wiii be related to the number of them d[S-I,, actually collected at time t,, by the relationship
W’lr, 3. Mass
= (fRbJifi(f 11d IS - It
Sprctrometr~
and Iorr Physics, 2 (1969) 355-390
(6)
RATE
CONSTAXTS
Substituting
IN
A PULSED-SOURCE
MASS
SPECTROhlETER
387
d[S- j, from eqn. (5) into (6), we obtain:
G’l,,
= U&).&~~)~ klM1 D’ - lo_fXW
Substituting [P- j,, from eqn. (3) in (7) and integrating to, we obtain:
(7) between zero deiay time and
(8) Suppose. to take an extreme case, that 211 primary ions were to react simultaneously the instant before the drawout pulse; then t = t, = constant and the above equation reduces to [S- 1,,w-
I,, = kWlt,
(9)
and a graph of i,ecjicr,m against fD would give a straight line of gradient k[M]. This i; equi\aIent to one of tSe methods ,idopted by Lampe et al.’ SubstitutingJ,(t,) from eqn. (4) in (7), rearranging and integrating we get:
WI:,
[R’lt,
ff’l, = kW1 IR’l,
s
IDfP(d o fR(I)df
(10)
The supposition at the opposite extreme from the one above is that all primary ions reset at the instant immediately after they have been formed i.e. t = 0. In this case, (10) reduces to
[S-lt,~tR’l,,
= kCdl (PrlolWlok,
(10
lo. and a graph of isec/irmrkerv ould gike a straight line of gradient k[M] [P’],/[R’ This appears to bt the ecuivalent of the various experiments in which a marker of the same mass as the wcondary ion is used to suggest the way in ~nich secondary icns decay. Rate constants obtained by these methods for reaction (2) differed by a facto? of 2. A more accurate rate constant may however be obtained by exact integration of eqn. (7):
E-l,,
= kfM,[P-
]oJR(tD)j;D z dt
(12)
A Fortran programme was written to fit polynomials to the experimental decay curves of the primary and marker ions P’ and R+‘, respectively. The decay curves were fitted to a poiyr,omial expansion of the fifth power of the delay time. Fig. 1 represents experiment-al decay curves (full circles) for ions of m/e = 77 and the computed curves for these same ions (C,H,-) and nzle = 150 (C,F,I), 1. .Uzs Specrrome&yand Ion Pl;ysicr, 1 (1969) 385-390
388
B. G. REUBEN,
obtained from the polynomial fit. The following m/e = 77 and m/e = 150, respectively:
A.
LIFSHITZ,
expressions
C. LIFSHITZ
were obtained
for
m;c! = 77
f(t)= 1.00796
- 6.5439x10-‘t + 2.7949 x iO-?’
5.2657 x 10-3t’
-
S.i86xIO-'t' + 3.5396x10-'t" 1.13)
m,‘e = 150 f(t) = 0.9983 1.3125 x 10-3t4 where t is expressed
-
5.622: x lo-‘; + 6.15429 x IO-‘t5
2.9465x
lo-‘t’
f
9.865 x 10-3t3
(14)
in microseconds.
Fig 1. Experimental decay curves (a) for ions of m/e = 77 (cH,-) and m/e = 150 (C,FsL) and the computed curves obtained from the pcl_ynomial fit. The zero of the time scale is arbitrary and corresponds to the minimum delay (- 2.2 +x) of which the pulsing system was capable.
A second programme evaluated k at each delay time by the use of eql. (12). The input data for this programme included the experimentally measured [S’II, vaIues, the expressions obtained for the decay curves of primary and marker ions (i.e. expressions such as (13) and (I4)), the concentration of neutral m&cuies, [M ]. fp’] at zero delay time and the experimental value forf,(t,). Each delay time interval was divided by one thousand and the integration of eq>. (12) carried out 1. MULSS’ctrome!~-
ad
fan Physics,
2 (1969)
3CL-390
RATE
CONSTANTS
A PULSED-SOCRCE
IN
h¶ASS
389
SPECTRO>fETER
numerically. The derived k values are fairly constant and iie between the maximum and minimum values obtained by the previous two methocis3. They lie nearer to the minimum than to the maximum value, since the majority of ions which eventually react will do so in the early stages of the reaction. TABLE
1
ZA-l?Z COSsTc\?‘i~ AT DIFFEREXT
Delay
FOR -IX’0
OF Tii
TPMES DURIhG
time
T fjlsec)
ION--.MOLECULE
A SINGLE
k x IO’O (cd
molecule-l
=:aHa’ + c-6 Ha -
RJiACliONS
CEHIO-
0.266 0.301 0.297
3.0
1.21
0.323
3.2 3.4 3.6 3.8
1.30 1.32 1.28 1.35
0.341 0.357 0.370 0.381
4.0 4.2 4.4
1.36 1.28 1.29
0.389 0.405
4.6 4.8
1.27 I.34
0.395 0.41 I
5.0 5.2 5.4 5.6
1.27 1.24 1.25 1.28
0.411 0.401 0.387 0.385
0.371
5.8
1.29
0.389
6.0 ?.O 8.0
i -25 1.23 1.25 1.23
0.380 0.342 0.289 0.249
1.27 $4.3
EVALUATED
C,H,--rC,H, + C,,H,+;C:H,
1.55 1.17 1.17
Mean Q
IN BENZENE,
set-1)
2.4 2.6 2.8
9.0
OCCURRltiG
RUN
0.366
%
& 10.2 %
Two examples are shown in Table of delay times for the reactions C,H,‘+C,H,
-+ C12HIc,*
C6H5-+C6H6
+ C,.H,++C,H,
1 which gives the k values at a number
and
The former shows one of the best sets of results, the latter one of the worst. The values at the highest and iawes& delay times are the ieast reliable because of the nature of the potynomial fit. J. Mars
Spectromefry
and fan Physics.
2 (1969)
385-390
B. C.
390
REL’BEX:.
A. LlFSHlT
L. C.
LIFSHITZ
Considering the assumptions involved, the k values are sat sfactorily constant: nonethelss, in both cases (and in the other experiments) a --rend is discernible in that the valve of the rare constant appears to go through 3 maximum at intermediate deIay tines. The theory of pulsed sources developed by Harrison et al. considers only what happens in the volume element directly behind the exit slit from the ion source, and assumes that any ion lost from this region can afterwards be neglected. This is valid as long as ion-molecule collisions are few and the popuiation of ions outside the electron beam is small. At intermediate delay tims, ho\\e\er, secondary ions formed by collisions outside the above-mentioned volume element might well drift bsck into it thus increasing the apparent rate constant. At very Iong delay times, the rate of loss of primary ions becomes sma!l (see Fig. 1) and something approaching equilibrium is reached behveen loss and gain of primary
the ions which tials
in the
secondary critically
ions from
are gained
element
back
way occurring
to the region
above
It was not
of the source. and as both
the slit, a drop
found
possible
it was assumed
to them
Nonetheless
reactant
the slit. It is unclear
whether
wai! or by stray poten-
to caIculate
reflection
and product
in rate constant
but because our rate constants lay, as minimum values obtained by the previous value,
behind
by the source
source. They are unlikely to arise by gas-phase collision (unlike the ions) since the shape of the curve in Fig. 1 at long delay times depends
on the cttsnliness
is in some
the volume
are reflected
of primary
ions
ions are now returning
occurs.
the magnitude
of these
two effects,
predicted, between the maximum and two methods but close to the minimum
th:tt they were of set ondsry
importance
and the trends
due
were neglected.
REFERENCES 1 A. G. H. UGUSON, 3. J. MYHER .:?cm3. C. f. THYSIE, Ion Moolecule Keacrions in the Gas Phase. Adrtx. Ckm. Ser.. 58 (1966) 15&166. 2 A. G. HARRISOS, A. IVKO AND T. W. SHAXSOU, Cm. J_ Chenr.. 44 (1966) 135!. 3 C. hFSHrrZ AXD B. G. REum, J. Chem. Ph~s., in press. 4 T. W. SHA?GSOS, F. MEIER ASD A. G. HARRISON, Can. J. Chem., 43 (1965) 159. 5 34. C. Cxs, P. M. BECKER .+LX~DF. W. LAMP E, J_ Chem. Ph_~s., 44 (1966) 2212. 6 F. W. L.MAPEASP G. G. ASS, J. Am. Chem. Sm., 86 (19G) 1952. 1. _~s.u
Specrromerry
and Ior: Ph_vsics. 2 (1969)
X5--39il
of Mass
JOLUM~
Spectrometry
and Ioon Physsrcs
385
Eisevier Publishing Company, Amsterdam - Printed in the h’etheriands
CALCULATIONS
REACTIONS
OF
BRYAN G. REUBE?!*, Department
RATE
CONSTANTS
Ibi A PULSED-SOURCE
of Physical
ASSA
LESWTZ
Chemistry,
AKD
Hebrew
FOR
MASS
CH.%VA
Unicersity.
ION-MOLECULE
SPECTROMETER
LIFSHITZ Jerusalem
(israei)
(Received Nobember Zlst, 1968)
ABSTRACT
A method is described for calculating the rate constants of ion-molecule reactions in a pulsed-source mass spectrometer where parent and daughter ions differ markedly in mass. The rate of loss of ions in the ion source is mass dependent, but a correction can be made for this using experimentally determined decay curves
for ions cf masses similar to those of the primary
and secondary
ions.
The rates of thermal ion-molecule reactions can conveniently be determined in a pulsed ion source mass spectrometer, as has been demonstrated by Harrison and coworkers’. if only a small proportion of primary ions is lost by reaction, the rate constant can be obtained from the equation [S+]/[P’]
= k[M]i
0)
where [M] is the concentration of neutral molecules in rhe ion source, and [S’]/ [PT] is the ratio of secondary to primtry ion concentrations’. In the absence of mass discrimination the ion concentratton ratio can be equated to the ratio of collected ion currents (i,,,/i,,:, )_ Most of the reactions studied so far involve proton transfer, so that the primary and secondary ions have been of similar mass. For such reactions, mass discrimination in a pulsed ion source can be neglected. This is not possible, however, when the masses of reactant and product ions differ by more than 50 %‘. During the delay time between ion-formation and ionwithdrawal, the ions of lower mass decay much faster than those of higher mass. We have recently carried out a mass spectrometric investigation of ion-molecule reactions in benzene3, where, for some of the reactions, the masses of reactant and product ions differed by as much as I00 %, e.g. C,H,++C,H,
--, C12H,,+
(2)
l Permanent address: Department of Chemistry, University of Surrey, London, S.W. 11, England.
3. Mass
Spectrometry
and Ion Physics,
2
(1969) 385-390
386
B. G. REUBEN,
A. LIFSHITZ,
C. LIFSHITZ
Though our mass discrimination was smaller than that found by Harrison and coworkers4 , it was essentially similar. It was not, therefore, legitimate to take the ratio iscJiprim as a tr ue measure of t le ratio of concentrations of reactant and product ions in the source. This prob!em has been considerti briefly by Lampe and his coworkers. In one paper’ he assumed that the ratio of observed ion currents could in fact be equated to the ratio of ionic concentrations, and in another6 he constructed mass discrimination c~urvl:s for primwy ions of different masses and applied a correction to the secondary ions basal on these. Neither of these methods is enr rely satisfactory and the following analysis was carried out in order to overcome the difficulties_ Consider a pulsed system containing a gas M which, on electron bombardment gives ions P’ whici can undergo reaction to give secondary ions S’. In addition to M, let the system contain a substance R \\hich gives ions R’ of similar molecular weight tc, S-. If the ion currents due to P’, R- and S’ are measured at various delay tixes, 2 series of decay curves is obtained. Let the initial coxzxtrations of primary, secondary and marker ions be [P-lo, [S’], and [R-l,, and the measured concentrations after delay time :,, be Assuming only a smsil proportion of primary ions is [P-L,, WI,, and W’j,,,. lost by rextion, we can write:
F-lr,
= F-lOfPWr=fD
(3)
/3-I,,
= P’loliCi)r=rD
(4)
where&(t) represents the value of the decay function for P’ ions at time t, the same symbols applying to Rf and S * ions, mutatis mutandis. At zero time the various decay functions have the value unity. The rate of reaction at any moment t for A simple bimolecular reaction IS given by:
=
k[Ml
F’l,
=
k[Ml
F’loh@)
After time t, a proportion of the P’ ions will have been lost according to the decay function f&l). Th e secocdazy ions formed at this instant by reaction of some of the remaining P’ ions will then be lost according to a different decay function for the remaining time (to- f) before the drawout pulse is applied. A feasible hypothcsis is that they will be lest at the same rate as R* ions between times t and I,,. If this is so, then the fraLrion of secondary ions lost over this period (tD-t) will and the number of ions d[St], formed between t and b equal to MD)&(~) f tdt wiii be related to the number of them d[S-I,, actually collected at time t,, by the relationship
W’lr, 3. Mass
= (fRbJifi(f 11d IS - It
Sprctrometr~
and Iorr Physics, 2 (1969) 355-390
(6)
RATE
CONSTAXTS
Substituting
IN
A PULSED-SOURCE
MASS
SPECTROhlETER
387
d[S- j, from eqn. (5) into (6), we obtain:
G’l,,
= U&).&~~)~ klM1 D’ - lo_fXW
Substituting [P- j,, from eqn. (3) in (7) and integrating to, we obtain:
(7) between zero deiay time and
(8) Suppose. to take an extreme case, that 211 primary ions were to react simultaneously the instant before the drawout pulse; then t = t, = constant and the above equation reduces to [S- 1,,w-
I,, = kWlt,
(9)
and a graph of i,ecjicr,m against fD would give a straight line of gradient k[M]. This i; equi\aIent to one of tSe methods ,idopted by Lampe et al.’ SubstitutingJ,(t,) from eqn. (4) in (7), rearranging and integrating we get:
WI:,
[R’lt,
ff’l, = kW1 IR’l,
s
IDfP(d o fR(I)df
(10)
The supposition at the opposite extreme from the one above is that all primary ions reset at the instant immediately after they have been formed i.e. t = 0. In this case, (10) reduces to
[S-lt,~tR’l,,
= kCdl (PrlolWlok,
(10
lo. and a graph of isec/irmrkerv ould gike a straight line of gradient k[M] [P’],/[R’ This appears to bt the ecuivalent of the various experiments in which a marker of the same mass as the wcondary ion is used to suggest the way in ~nich secondary icns decay. Rate constants obtained by these methods for reaction (2) differed by a facto? of 2. A more accurate rate constant may however be obtained by exact integration of eqn. (7):
E-l,,
= kfM,[P-
]oJR(tD)j;D z dt
(12)
A Fortran programme was written to fit polynomials to the experimental decay curves of the primary and marker ions P’ and R+‘, respectively. The decay curves were fitted to a poiyr,omial expansion of the fifth power of the delay time. Fig. 1 represents experiment-al decay curves (full circles) for ions of m/e = 77 and the computed curves for these same ions (C,H,-) and nzle = 150 (C,F,I), 1. .Uzs Specrrome&yand Ion Pl;ysicr, 1 (1969) 385-390
388
B. G. REUBEN,
obtained from the polynomial fit. The following m/e = 77 and m/e = 150, respectively:
A.
LIFSHITZ,
expressions
C. LIFSHITZ
were obtained
for
m;c! = 77
f(t)= 1.00796
- 6.5439x10-‘t + 2.7949 x iO-?’
5.2657 x 10-3t’
-
S.i86xIO-'t' + 3.5396x10-'t" 1.13)
m,‘e = 150 f(t) = 0.9983 1.3125 x 10-3t4 where t is expressed
-
5.622: x lo-‘; + 6.15429 x IO-‘t5
2.9465x
lo-‘t’
f
9.865 x 10-3t3
(14)
in microseconds.
Fig 1. Experimental decay curves (a) for ions of m/e = 77 (cH,-) and m/e = 150 (C,FsL) and the computed curves obtained from the pcl_ynomial fit. The zero of the time scale is arbitrary and corresponds to the minimum delay (- 2.2 +x) of which the pulsing system was capable.
A second programme evaluated k at each delay time by the use of eql. (12). The input data for this programme included the experimentally measured [S’II, vaIues, the expressions obtained for the decay curves of primary and marker ions (i.e. expressions such as (13) and (I4)), the concentration of neutral m&cuies, [M ]. fp’] at zero delay time and the experimental value forf,(t,). Each delay time interval was divided by one thousand and the integration of eq>. (12) carried out 1. MULSS’ctrome!~-
ad
fan Physics,
2 (1969)
3CL-390
RATE
CONSTANTS
A PULSED-SOCRCE
IN
h¶ASS
389
SPECTRO>fETER
numerically. The derived k values are fairly constant and iie between the maximum and minimum values obtained by the previous two methocis3. They lie nearer to the minimum than to the maximum value, since the majority of ions which eventually react will do so in the early stages of the reaction. TABLE
1
ZA-l?Z COSsTc\?‘i~ AT DIFFEREXT
Delay
FOR -IX’0
OF Tii
TPMES DURIhG
time
T fjlsec)
ION--.MOLECULE
A SINGLE
k x IO’O (cd
molecule-l
=:aHa’ + c-6 Ha -
RJiACliONS
CEHIO-
0.266 0.301 0.297
3.0
1.21
0.323
3.2 3.4 3.6 3.8
1.30 1.32 1.28 1.35
0.341 0.357 0.370 0.381
4.0 4.2 4.4
1.36 1.28 1.29
0.389 0.405
4.6 4.8
1.27 I.34
0.395 0.41 I
5.0 5.2 5.4 5.6
1.27 1.24 1.25 1.28
0.411 0.401 0.387 0.385
0.371
5.8
1.29
0.389
6.0 ?.O 8.0
i -25 1.23 1.25 1.23
0.380 0.342 0.289 0.249
1.27 $4.3
EVALUATED
C,H,--rC,H, + C,,H,+;C:H,
1.55 1.17 1.17
Mean Q
IN BENZENE,
set-1)
2.4 2.6 2.8
9.0
OCCURRltiG
RUN
0.366
%
& 10.2 %
Two examples are shown in Table of delay times for the reactions C,H,‘+C,H,
-+ C12HIc,*
C6H5-+C6H6
+ C,.H,++C,H,
1 which gives the k values at a number
and
The former shows one of the best sets of results, the latter one of the worst. The values at the highest and iawes& delay times are the ieast reliable because of the nature of the potynomial fit. J. Mars
Spectromefry
and fan Physics.
2 (1969)
385-390
B. C.
390
REL’BEX:.
A. LlFSHlT
L. C.
LIFSHITZ
Considering the assumptions involved, the k values are sat sfactorily constant: nonethelss, in both cases (and in the other experiments) a --rend is discernible in that the valve of the rare constant appears to go through 3 maximum at intermediate deIay tines. The theory of pulsed sources developed by Harrison et al. considers only what happens in the volume element directly behind the exit slit from the ion source, and assumes that any ion lost from this region can afterwards be neglected. This is valid as long as ion-molecule collisions are few and the popuiation of ions outside the electron beam is small. At intermediate delay tims, ho\\e\er, secondary ions formed by collisions outside the above-mentioned volume element might well drift bsck into it thus increasing the apparent rate constant. At very Iong delay times, the rate of loss of primary ions becomes sma!l (see Fig. 1) and something approaching equilibrium is reached behveen loss and gain of primary
the ions which tials
in the
secondary critically
ions from
are gained
element
back
way occurring
to the region
above
It was not
of the source. and as both
the slit, a drop
found
possible
it was assumed
to them
Nonetheless
reactant
the slit. It is unclear
whether
wai! or by stray poten-
to caIculate
reflection
and product
in rate constant
but because our rate constants lay, as minimum values obtained by the previous value,
behind
by the source
source. They are unlikely to arise by gas-phase collision (unlike the ions) since the shape of the curve in Fig. 1 at long delay times depends
on the cttsnliness
is in some
the volume
are reflected
of primary
ions
ions are now returning
occurs.
the magnitude
of these
two effects,
predicted, between the maximum and two methods but close to the minimum
th:tt they were of set ondsry
importance
and the trends
due
were neglected.
REFERENCES 1 A. G. H. UGUSON, 3. J. MYHER .:?cm3. C. f. THYSIE, Ion Moolecule Keacrions in the Gas Phase. Adrtx. Ckm. Ser.. 58 (1966) 15&166. 2 A. G. HARRISOS, A. IVKO AND T. W. SHAXSOU, Cm. J_ Chenr.. 44 (1966) 135!. 3 C. hFSHrrZ AXD B. G. REum, J. Chem. Ph~s., in press. 4 T. W. SHA?GSOS, F. MEIER ASD A. G. HARRISON, Can. J. Chem., 43 (1965) 159. 5 34. C. Cxs, P. M. BECKER .+LX~DF. W. LAMP E, J_ Chem. Ph_~s., 44 (1966) 2212. 6 F. W. L.MAPEASP G. G. ASS, J. Am. Chem. Sm., 86 (19G) 1952. 1. _~s.u
Specrromerry
and Ior: Ph_vsics. 2 (1969)
X5--39il