Reaction enthalpies for M+L = M+ + L, where M+ = Na+ and K+ and L = acetamide, N-methylacetamide, N,N-dimethylacetamide, glycine, and glycylglycine, from determinations of the collision-induced dissociation thresholds

Article abstract of DOI:10.1021/jp9608382

With electrospray (ES), ions present in solution can be transferred to the gas phase. The method provides unique opportunities for studies of hitherto inaccessible ions. Collision-induced dissociation threshold measurements of gas phase ions produced by ES are described. The thresholds for the reactions M⁺L = M⁺ + L, where M⁺ is Na⁺ or K⁺ and L is acetone, dimethyl sulfoxide, acetamide, N-methylacetamide, N,N-dimethylacetamide, glycine, glycinamide, succinamide, and glycylglycine, were determined. Enthalpy changes for the reaction were derived from these data.

Full text of DOI:10.1021/jp9608382

14218
J. Phys. Chem. 1996, 100, 14218-14227
Reaction Enthalpies for M+L ) M+ + L, Where M+ ) Na+ and K+ and L ) Acetamide,
N-Methylacetamide, N,N-Dimethylacetamide, Glycine, and Glycylglycine, from
Determinations of the Collision-Induced Dissociation Thresholds
John S. Klassen, Stephen G. Anderson, Arthur T. Blades, and Paul Kebarle*
Department of Chemistry, UniVersity of Alberta, Edmonton, Alberta, Canada T6G 2G2
ReceiVed: March 19, 1996; In Final Form: May 31, 1996X
With electrospray (ES), ions present in solution can be transferred to the gas phase. The method provides
unique opportunities for studies of hitherto inaccessible ions. Collision-induced dissociation threshold
measurements of gas phase ions produced by ES are described. The thresholds for the reactions M+L ) M+
+ L, where M+ is Na+ or K+ and L is acetone, dimethyl sulfoxide, acetamide, N-methylacetamide, N,N-
dimethylacetamide, glycine, glycinamide, succinamide, and glycylglycine, were determined. Enthalpy changes
for the reaction were derived from these data.
Introduction
can be transferred into the gas phase and subjected to mass
spectrometric detection, was developed by Fenn and co-
workers.11 Electrospray affords the production not only of ions
such as Na+ and K+ and other singly charged ions but also that
of doubly and triply charged transition metal and alkaline earth
ion-ligand complexes,12 multiply protonated peptides and
proteins,13 doubly charged anions14 like SO42- and HPO42-, and
multiply deprotonated nucleic acids.15 The latter are also of
paramount importance in solution chemistry and biochemistry
but could not be obtained in the gas phase prior to the
development of ES.
The bond enthalpies corresponding to reaction 1, where M+
ML+ ) M+ + L
(1)
) Na+, K+ and L ) CH3NHCOCH3, are of special interest
because of attempts to understand the microscopic factors
controlling the passage of these ions through transmembrane
channels such as the gramicidin channel. The permeation of
the ion through the channel involves partial dehydration of the
ion, where the endoergicity of the dehydration is offset by
attractive interactions of the ion with polar groups in the
channel.1 The ion-channel interactions are believed to involve
mainly the carbonyl oxygens of the peptide backbone.2-4
Theoretical investigations of the Monte Carlo and molecular
dynamics techniques rely on the development of realistic pair
potential functions representing the microscopic interactions.
For ion-solvent molecule interactions, such as ion-water
molecule interactions, the pair potential functions were devel-
oped on the basis of ab initio calculations of the ion-molecule
interactions.5 Of considerable help to this approach were the
experimentally determined free energy, ∆G°1, enthalpy, ∆H°1
and entropy, ∆S°1 changes obtained from ion-solvent molecule
equilibria observed by mass spectrometric techniques.6 These
experimental data helped establish the quality of the basis set
and electron correlation required in order to obtain values5 in
agreement with experiment.
The interactions of the ions with peptides such as the
transmembrane channels are also amenable to this approach,
but in this case, rather than the actual peptide, a model
compound such as methylacetamide is used to obtain informa-
tion on the dominant interactions.7 Previous experimental ion-
equilibria determinations are available only for K+ and dimeth-
ylacetamide.8 It is therefore desirable to extend the equilibria
determinations, which lead to the bond enthalpy and free energy
changes ∆H°1 and ∆G°1, to N-methylacetamide, acetamide and
Na+ ions.
ES generates ions in ambient gas at ∼1 atm, and the
determination of ion concentrations with a mass spectrometer
in gas at such high pressure is difficult. A successful design
where the gas is transferred to a reaction chamber at 5-10 Torr
pressure, where the ion-molecule equilibria establish, was
described recently.16
The ion-equilibrium method is not well suited for determina-
tions where the bond enthalpies are high, i.e. greater than ∼40
kcal/mol, because of the very high temperatures required for
the equilibrium to establish. However, many ion-ligand
complexes can have such high bond enthalpies particularly when
multiply charged ions are involved.11 Therefore, it is very
desirable to have a method with which the bond energies of
strongly bonded ion-ligand complexes, produced by electro-
spray, can be determined.
Determination of the threshold of the product ion, M+, where
the reactant ion, ML+, is accelerated to known kinetic energies,
experiences a collision with a noble gas atom and undergoes
dissociation, is a method with which bond enthalpies, e.g., ∆H°1
values, can be determined. This collision-induced dissociation
(CID) threshold method18,19 is applicable also when high bond
energies are involved. The present work describes some of the
first results with this method as applied to ions generated by
ES. The determinations for M+ (Na+, K+) and L (acetamide,
AA; N-methylacetamide, MAA; and N,N-dimethylacetamide,
DMA) are described in subsequent sections.
The previous determinations8 were obtained with alkali ions
produced in the gas phase by thermionic emission of the ions
from a heated metal filament painted with the alkali ion salts.9,10
This apparatus was dismantled several years ago. Recently, the
electrospray (ES) method with which ions present in a solution
Determinations for K+ and L ) acetone and dimethyl
sulfoxide were also made for the purpose of comparing the CID
threshold data with available previous determinations based on
ion equilibria. Determinations involving Na+ and K+ and L )
glycine, glycine amide, succinamide, and the dipeptide, gly-
cylglycine, were also made. The last three ligands may lead to
X Abstract published in AdVance ACS Abstracts, July 15, 1996.
S0022-3654(96)00838-6 CCC: $12.00 © 1996 American Chemical Society

Reaction Enthalpies for M+L ) M+ + L
J. Phys. Chem., Vol. 100, No. 33, 1996 14219
(1) The electrospray generator, ES, produces charged droplets
and ultimately gas phase ions from an electrolyte solution which
flows through the ES capillary.
Solutions of electrolytes NaCl or KCl at 10-4 mol/L in
methanol and the ligand L at 10-3 mol/L were used to generate
the ions NaL+ and KL+.
(2) The low-pressure ion source, LPS, is maintained at 10
Torr by means of a pump. Atmospheric pressure gas containing
ES produced ions is admitted through the sampling capillary
CAP. The clustered ions such as M+Ln or M+Ln(H2O)x entering
the chamber can be partially declustered to a given desired
species such as M+L, by applying a high ion drift field between
the tip of CAP and the bottom plate IN of the low-pressure
source LPS.
Figure 1. Front end apparatus. Electrospray generator, ES, consisting
of electrospray capillary with stainless steel tip at high electric potential,
generates charged droplets and ultimately gas phase ions. ES is partially
surrounded by glass tube providing flow of dry air. Capillary, CAP,
transfers gas and ions from 1 atm to a low pressure ion source LPS
maintained at 10 Torr. Ions can be partially declustered by applying
a high drift field between CAP and interface plate IN. Ions are allowed
to thermalize in low drift field, 10 Torr pressure, ion thermalization
chamber IT. Orifice OR, 100 µm diameter leads to vacuum. First
electrode and skimmer, CB. RF only ion guide quadrupole Qo. First
quadrupole Q1. Cryosurfaces CR for cryopumping.
(3) The ion thermalization chamber IT is at the same pressure
as the low-pressure source. The ion drift field between IN and
the orifice OR is low, E/p < 6 V/(cm Torr), so that thermal-
ization of the ions can occur in this region.20
(4) The triple quadrupole mass spectrometer is where ions
entering the cryopumped vacuum region are subjected to mass
analysis and CID. Precursor ions selected by Q1 are accelerated
to the RF only collision cell Q2 where product ions are created
by collisions with Ar gas. A given product ion is mass selected
with Q3 and detected with an ion counting system.
bi- and tridentate complexes and provide an interesting extension
of the CID threshold results.
It was shown20 that the precursor and product-ion kinetic
energy profiles are independent of the potential difference CAP-
IN used for the declustering of ions in the low-pressure ion
source LPS. The profiles were also independent of the potential
drop between IN and OR when E/p < 6 V/(cm Torr). This is
consistent with the assumed ion thermalization in the IT
chamber.
It was found20 that the kinetic energy profiles of the precursor
ions are somewhat broadened, i.e., develop a tail toward higher
kinetic energies. The broadening increased with the magnitude
of the radial dc field in the first quadrupole Q1. Collisions of
the parent ions with neutral gas molecules of the gas jet present
in Q1 were assumed to be responsible for the broadening.20 The
broadening was reduced by working at low radial dc fields, i.e.,
low mass resolution in Q1. It was found, in the present work,
that the broadening could be further reduced by selecting a
specific offset potential for the Q1 quadrupole, i.e. by controlling
the axial kinetic energy of the precursor ions entering Q1. For
an ion of mass to charge ratio m/z ) 110, the selected kinetic
energy was typically 12 eV. The selected energy decreased as
m/z decreased. The exact cause for the observed behavior is
under investigation.
Mass spectral analysis of electrospray produced ions from
aqueous and methanol solutions containing low concentrations
of peptides or proteins and Na+ ions due to the presence of
electrolytes Na+ + X- in the solutions has shown11 that the
peptides and proteins form sodium ion adducts. Multiple
sodium ion addition occurs with polypeptide and protein
molecules. The number of sodium ions increases with the
number of the peptide units in the molecule.11 The sodium ions
evidently form complexes with polar regions of the peptides,
although the complexation may be largely occurring as a
consequence of the ion transfer from solution to the gas phase.
Therefore, data on the bonding forces between alkali ions and
peptides or models of peptides, such as described in this work,
are of interest also from the standpoint of electrospray mass
spectrometry and the mechanism of electrospray mass spec-
trometry. One should not fail to notice that there are certain
analogies between the transfer of sodium and potassium ions
from solution to the transmembrane channels and the transfer
from solution to the gas phase when the solution contains
peptides or proteins.
Experimental and Curve-Fitting Procedure
It was also established20 that collisions of the ions with gas
molecules in the front end space between the electrodes OR,
CB, and Q0 lead to kinetic energy broadening. This broadening
was eliminated by setting equal potentials to OR, CB, and Q0.
While the mass analyzed parent ion intensity is reduced under
these conditions, the signals obtained, ∼20 000 ions/s, are
sufficient for the threshold measurements.
(a) Apparatus and Conditions. As mentioned in the
Introduction, with electrospray one obtains gas phase ions in
ambient gas at 1 atm pressure. The transfer of these ions to
the vacuum of the mass spectrometer used for the CID studies
presents some special challenges because the accelerated ions
entering the collision cell must have a known internal energy
distribution, preferably a Maxwell-Boltzmann distribution at
a known temperature. Furthermore, the translational kinetic
energy of the ions must be well-defined and have a narrow
distribution. The present measurements were performed with
a modified triple quadrupole mass spectrometer.20 A detailed
account which describes how and to what extent the above
challenges could be met is given elsewhere.20 Here, we give
only a brief description of the apparatus and conditions of the
present measurements.
The collision gas argon was at a pressure of ∼0.1 mTorr
(collision cell length 8 cm). At such a pressure single collisions
are dominant and the contribution of double collisions to the
foot of the threshold curve are negligible. This was verified
by making threshold measurements at decreasing pressures and
observing that the E0 value obtained increased by less than 0.02
eV for a decrease of the pressure from 0.2 to 0.1 mTorr.20
(b) Determination of Threshold Energies E0. Determina-
tions of the energy thresholds E0 were obtained by fitting the
product ion energy profiles with the CRUNCH program
developed by Armentrout and co-workers.18,22 The fitting
procedure is based on the equation
The mass spectrometer used was a SCIEX Trace Atmospheric
Gas Analyzer 6000 E, triple quadrupole mass spectrometer.21
The front end was modified as shown in Figure 1. There are
four sections:

14220 J. Phys. Chem., Vol. 100, No. 33, 1996
Klassen et al.
TABLE 1: Energies for the Reaction M+L ) M+ + L from
CID Threshold Determinationsa
∆H°298
(lit.)
b
b
c
d
E0(0 K) ∆H°298 ∆H°298 ∆H°298
M+ ) K+
Me2CO
Me2SO
HCONMe2
MeCONH2
24.2
31.3
32.0
29.7
32.3
32.9
29.2
24.4
31.6
32.0
29.6
31.9
32.2
30.1
24.4
30.2
27.1
29.6
28.3
25.5
29.4
24.4
31.1
29.5
29.7
30.4
29.0
30.0
26.0e
35 ( 3e
31.0e
(26.2)f
(24.8)f
31e
MeCONHMe
MeCONMe2
H2NCH2COOH
M ) Na+
MeCONH2
34.3
38.9
46.9
36.3
34.7
39.0
46.7
37.5
45.1
61.8
64.7
34.7
33.7
35.2
35.7
39.5
41.5
40.1
34.7
35.7
37.5
36.6
41.4
44.5
42.9
(36.0)g
(38.4)g
MeCONHMe
MeCONMe2
H2NCH2COOH
H2NCH2CONH2 45.1
(H2NCOCH2)2 62.3
H2NCH2CONH- 64.6
CH2COOH
(38.5)h
Figure 2. Appearance curve of K+ from CID of K+ acetone. Also
shown are three calculated cross-section curves (a-c), obtained by
fitting the cross-section model, eq 2, to different portions of the
appearance curve. Curve a (- -), fitted from 0.6 to 1.4 eV,
corresponds to n ) 1.46 and E0 ) 0.99 eV (22.8 kcal/mol). Curve b
(- ‚ -), fitted from 0.6 to 3.0 eV, corresponds to n ) 1.05 and E0 )
1.09 eV (25.1 kcal/mol). Curve c (s), fitted from 1.0 to 3.0 eV,
corresponds to n ) 1.00 and E0 ) 1.11 eV (25.5 kcal/mol). Expanded
scale used for insert at lower right in figure provides a better view of
the three curve fits at the threshold.
a All energies in kcal/mol. b Without correction for kinetic shift, E0
internal energy change, ∆H° enthalpy change for reaction eq 1. c With
correction kinetic shift, two lowest frequencies, 30 cm-1, for both K+
and Na+ complexes. d With correction for kinetic shift, two lowest
frequencies, 10 cm-1, for Na+ complexes and 5 cm-1 for K+ complexes.
This set is considered to be the best. e Experimental determinations
based on ion-molecule equilibria (Sunner et al.).8 f Theoretical calcula-
tions, HF/6-31G, combined with a semiempirical correction (Roux and
Karplus).7 g Theoretical calculations, HF/6-31G*, combined with a
semiempirical correction (Roux and Karplus).7 h Theoretical calcula-
tions, 6-31+G(2d)MP2 (Jensen).28 i Succinamide.
σ ) σ g (E + E + Erot - E0)n/E
(2)
∑
0
i
i
i
where σ is the cross section, which is proportional to the
observed product ion intensity at single collision conditions. E
is the kinetic energy in the center of mass frame. Ei is the
internal vibrational energy of the precursor ion whose relative
abundance at a given temperature is gi, where ∑igi ) 1. E0 is
the threshold energy, corresponding to the energy required for
the dissociation reaction, i.e., eq 1 in the present work, at 0 K.
The fitting procedure based on eq 2 treats n and E0 as variable
parameters which are determined through the best fit. The
vibrational energies Ei are calculated from the frequencies of
the normal vibrations of the precursor ion. The frequencies are
generally obtained from quantum chemical calculations.
An important feature underlying eq 2 is the assumption that
due to the relatively long residence time of the excited ions in
Q2, dissociation at the threshold involves the process where the
internal energy of the products is close to 0 K, i.e., essentially
all the internal energy of the precursor ion is used up in the
dissociation at the observed threshold.
Figure 3. Appearance curve of K+ from CID of K+N-methylacetamide.
The calculated curve (solid line), fitted from 1.1 to 2.5 eV, corresponds
to n ) 1.02 and E0 ) 1.40 eV (32.2 kcal/mol). Cross-section model,
eq 2.
other reactants. The frequencies used are given in Table 2. A
temperature of 298 K was assumed for the precursor ions.
Illustrations of alternate fitting results are given in Figure 2.
The different values of n and E0 for K+ (acetone) given in the
figure result from different choices of the range of points, at
the foot of the threshold and near the maximum of the cross
section, which were included in the fit.
The observed precursor ion kinetic energy profiles were fitted
to a Gaussian distribution and the zero center of mass kinetic
energy was taken at the maximum of the Gaussian curve.
In general, we have excluded the experimental points of very
low intensity at the very end of the foot because these probably
originate from precursor ions of higher than thermal energies.20
The very small difference observed between the E0 values
obtained for the fits b and c, E0 (b) ) 1.09 eV and E0 (c) )
1.11 eV, which differ by points excluded at the foot, provide
assurance that points of very low intensity at the foot can be
excluded. The relatively close values for the fits a and b, E0
(a) ) 0.99 eV and E0 (b) ) 1.09 eV, demonstrate that inclusion
of experimental points past the steeply rising portion of the curve
does not affect the E0 values very significantly. Thus, while
there is a certain arbitrary element in the choice of the fit, the
E0 values agree within ∼0.1 eV. The E0 values quoted in Table
Results and Discussion
(a) Results: Evaluation of the Threshold Energies. Effect
of Kinetic Shift. Threshold curves for the product ions Na+
and K+ from the dissociation of the sodium and potassium
complexes M+L are shown in Figures 2-8. The values of the
exponents n and the E0 values obtained by fitting the data to
the expression, eq 2, are given in the figures and Table 1. The
vibrational frequencies for the M+L complexes required for the
evaluation of the internal energies Ei, see eq 2, were obtained
with ab initio calculations (3-21 G basis set) for Na+‚CH3-
CONH2 and CH3CONH2 and the semiempirical MNDO for the

Reaction Enthalpies for M+L ) M+ + L
J. Phys. Chem., Vol. 100, No. 33, 1996 14221
TABLE 2: Vibrational Frequenciesa
acetoneb
K+acetoneb
DMSOb
K+DMSOb
DMFc
K+DMFc
37
69
90
71
81
155
36
45
59
86
160
406
150
186
425
148
179
220
187
191
263
82
105
149
80
117
182
549
553
556
561
238
304
280
315
247
335
277
341
806
981
819
991
633
700
644
700
435
649
437
654
1019
1201
1257
1315
1553
1562
1627
1630
1638
1662
1940
3199
3206
3249
3258
3306
3307
1015
1203
1261
1337
1561
1573
1617
1622
1625
1655
1891
3204
3212
3258
3267
3307
3308
712
881
1024
1036
1160
1166
1169
1190
1404
1426
1431
1432
1433
1520
1527
1540
1567
2083
3215
3217
3236
3247
3267
3308
3325
1032
1036
1156
1160
1175
1189
1403
1426
1427
1428
1431
1511
1524
1537
1588
2043
3230
3231
3249
3254
3271
3318
3327
1027
1061
1104
1155
1493
1520
1610
1623
1628
1643
3239
3240
3342
3342
3345
3347
1040
1080
1121
1161
1499
1527
1604
1618
1618
1634
3243
3243
3350
3351
3353
3355
AAb
K+AAc
Na+AAb
MAAb
K+MAAc
Na+MAAc
DMAd
K+DMAd
Na+DMAd
44
57
67
92
103
124
29
43
57
55
55
101
25
35
47
40
45
80
147
451
530
142
360
417
328
489
591
108
137
194
103
131
173
111
133
174
108
108
137
203
103
131
111
111
133
590
596
448
583
609
710
308
457
302
423
304
457
194
194
173
173
174
174
735
874
616
849
902
619
672
682
930
156
617
651
999
159
621
652
308
457
619
672
682
930
302
423
156
617
651
999
304
457
159
321
1032
1077
1099
1220
1425
1436
1483
1542
1804
2056
3268
3276
3346
3608
3630
1090
1193
1247
1442
1556
1637
1658
1814
1917
3208
3263
3337
3784
3910
1128
1207
1258
1530
1571
1628
1650
1806
1846
3215
3276
3327
3748
3866
1000
1085
1098
1170
1233
1308
1421
1422
1423
1436
1476
1482
1530
1707
2040
3233
3259
3269
3279
3328
3349
3568
1051
1190
1192
1262
1289
1380
1554
1596
1630
1658
1663
1686
1708
1895
3198
3205
3248
3262
3322
3344
3807
1085
1098
1172
1234
1311
1421
1424
1425
1438
1472
1492
1530
1702
2043
3229
3257
3269
3278
3328
3349
3575
352
1000
1085
1085
1098
1170
1233
1308
1308
1421
1422
1422
1423
1436
1436
1476
1476
1482
1530
1707
2040
3233
3259
3269
3233
3259
3269
3279
3328
3568
1051
1051
1190
1192
1262
1289
1289
1380
1554
1554
1596
1630
1658
1663
1663
1686
1686
1708
1895
3198
3205
3248
3198
3205
3248
3262
3322
3807
1085
1085
1098
1172
1234
1311
1311
1421
1425
1424
1425
1438
1472
1492
1492
1530
1530
1702
2053
3229
3229
3257
3257
3269
3269
3278
3328
3575

14222 J. Phys. Chem., Vol. 100, No. 33, 1996
Klassen et al.
TABLE 2 (Continued)
glycinec
K+ glycinec
Na+ glycinec
glycinamidec
Na+ glycinamidec
succinamidec
Na+ succinamidec
Gly2
Na+Gly2
e
23
53
57
39
59
84
50
73
94
31
49
69
39
42
63
65
162
295
65
232
300
103
218
307
54
227
294
103
193
291
18
36
167
77
100
103
35
42
56
72
92
96
427
476
426
498
459
533
372
431
410
441
235
267
220
275
99
167
98
157
590
741
589
739
592
674
567
689
498
577
321
414
380
390
226
287
221
248
991
987
988
783
987
989
742
977
991
433
490
501
529
540
589
596
740
429
451
501
518
582
589
694
755
324
454
485
510
540
588
612
638
365
399
486
528
549
604
624
660
766
872
943
962
1030
1055
1164
1199
1272
1313
1336
1349
1356
1418
1434
1442
1472
1575
1657
1722
1961
2062
2944
2980
3013
3038
3384
3441
3446
3486
1000
1118
1214
1302
1363
1417
1462
1474
1596
1810
2109
3192
3279
3536
3587
3953
1003
1148
1213
1310
1636
1390
1456
1471
1609
1810
2084
3195
3255
3538
3581
3974
1002
1169
1222
1322
1367
1387
1429
1477
1619
1805
2074
3206
3272
3534
3585
3930
1128
1214
1262
1298
1359
1457
1466
1513
1812
1813
2098
3206
3272
3551
3579
3594
3606
1123
1190
1228
1316
1364
1453
1471
1553
1808
1811
2045
3200
3266
3547
3593
3613
3627
922
935
901
939
703
917
953
1048
1065
1143
1181
1194
1208
1246
1366
1379
1398
1404
1561
1564
1704
1705
1985
2000
3015
3019
3081
3093
3487
3524
3542
3546
1058
1067
1168
1196
1216
1231
1264
1404
1415
1458
1466
1538
1546
1806
1809
2054
2071
3222
3236
3293
3303
3592
3607
3635
3636
1006
1039
1070
1161
1195
1256
1315
1339
1345
1381
1408
1431
1455
1474
1547
1644
1724
2001
2081
2952
2958
3024
3028
3416
3437
3475
3481
a The vibrational frequencies (in cm-1) of the ligand and ion-ligand complexes were obtained by evaluating the Hessian of the corresponding
optimized geometries using the GAMESS program. Only frequencies below 1000 cm-1 are significant in the fitting procedure, eq 2, and in the
calculation of the internal energies needed in eq 3. Furthermore, the fitting procedure and internal energy calculations are not sensitive to the
values of the frequencies and errors of 20% are expected to have only a small effect on the energy determinations. b The vibrational frequencies
were obtained from HF calculations done using a 3-21G basis set. c The vibrational frequencies were obtained from semiempirical calculations
(MNDO). d The frequencies for CH3CON(CH3)2 (DMA), K+CH3ON(CH3)2 (K+DMA), and Na+CH3CON(CH3)2 (Na+DMA) were estimated by
comparing the calculated frequencies for CH3CONH2 (AA) and CH3CONHCH3 (MAA) and the corresponding metal ion complexes. e The frequencies
for H2NCH2CONHCH2COOH (Gly2) and Na+Gly2 were obtained from semiempirical calculations (AMI).
1 correspond to the averages between two or three of the fits,
considered as best. We assign an error of (0.1 eV to these
results.
is conserved, a decrease of rotational energy for these rotations
is expected and this energy will be converted into internal
energy, on formation of the transition state. Therefore, these
two rotational energy terms 2/2RT should be included in the fit.
We have included the thermal rotational energy of the
precursor ion, Erot ) 3/2RT, see eq 2, in our curve-fitting
procedure. Armentrout et al.24 who fit the threshold curves right
to the very bottom of the threshold, do include this term.
Squires et al.,19 who omit points from the bottom i.e., the foot
of the curve, which are presumed to be due to above thermal
ions, do not include the rotational energy, making the assump-
tion that the rotational energy will affect only the bottom of
the curve, i.e., the portion that is omitted from the fit. Since in
our experiments we also do not fit the foot of the curve,
following Squires et al., we should have omitted the rotational
energy. However, the transition states involved in the present
work, vide infra, are expected to have two very large moments
of inertia, and since the angular momentum quantum number
3
For simplicity, we have included /2RT.
The E0 values, which correspond to the dissociation energy
at 0 K, were converted to enthalpy changes at T ) 298 K, with
use of eq 3 (Armentrout22).
∆H° ) E0 - Evib(ML+) + Evib(L) + 5/2RT
(3)
Equation 3 is based on a thermodynamic cycle for the
enthalpy change, ∆H°, of reaction 1 between 0 and T K. The
required vibrational thermal energies Evib(ML+) and Evib(L) were
evaluated from the corresponding vibrational frequencies which
are given in Table 2. Due to cancellation of heat capacity terms

Reaction Enthalpies for M+L ) M+ + L
J. Phys. Chem., Vol. 100, No. 33, 1996 14223
Figure 4. Appearance curve of Na+ from CID of Na+N-methylaceta-
mide. The calculated curve (solid line), fitted from 1.4 to 4.0 eV,
corresponds to n ) 1.25 and E0 ) 1.69 eV (38.9 kcal/mol). Cross-
section model, eq 2.
Figure 7. Appearance curve of Na+ from CID of Na+glycine. The
calculated curve (solid line), fitted from 1.6 to 3.4 eV, corresponds to
n ) 1.20 and E0 ) 1.58 eV (36.3 kcal/mol). Cross-section model, eq
2.
Figure 5. Appearance curve of Na+ from CID of Na+succinamide.
The calculated curve (solid line), fitted from 2.8 to 4.5 eV, corresponds
to n ) 1.25 and E0 ) 2.70 eV (62.3) kcal/mol). Cross-section model,
eq 2.
Figure 8. Appearance curve of Na+ from CID of Na+glycinamide.
The calculated curve (solid line), fitted from 2.0 to 3.5 eV, corresponds
to n ) 1.31 and E0 ) 1.96 eV (45.1 kcal/mol). Cross-section model,
eq 2.
residence time t of the ion before entering the mass analyzer
Q3. For the present apparatus, t is estimated to be between 30
and 40 µs and complete dissociation within that time, for ions
with energies just above E0 can be expected only for relatively
small polyatomic ions. Ions with many internal degrees of
freedom will attain the required dissociation rate only at internal
energies which are somewhat higher than E0. This “kinetic
shift”,23 if not taken into account, will lead to E0 values that
are too high.
Armentrout et al.24 have developed a method with which the
kinetic shift can be taken into account in the curve-fitting
procedure. This fitting procedure includes only to the fraction
of the precursor ions which decompose during the residence
time t. This fraction is given by, 1 - exp(-kt), where k is the
rate constant for the decomposition. k can be evaluated with
the RRKM formalism.25 k is a function of the internal energy
of the ion and the threshold energy E0, i.e., k(E + Ei - ∆E -
E0), where E is the kinetic energy in the centre of mass frame,
Ei is the internal energy of the ion prior to the collision, and
∆E is the center of mass kinetic energy which was not converted
into internal energy of the ion. The dependence of ∆E on the
center of mass energy, E, was obtained24 on the basis of an
assumed relationship, since an accurate theoretical expression
for that dependence is not available.
Figure 6. Appearance curve of K+ from CID of K+glycine. The
calculated curve (solid line), fitted from 1.2 to 2.0 eV, corresponds to
n ) 1.07 and E0 ) 1.27 eV (29.2 kcal/mol). Cross-section model, eq
2.
in the cycle, the values of E0 at 0 K and ∆H° at 298 K turn out
to be very similar.
The fits of the experimental profiles with eq 2 are based on
the assumption that the energized reactant ions, whose total
energy is equal or larger than E0, will decompose within the

14224 J. Phys. Chem., Vol. 100, No. 33, 1996
Klassen et al.
For the evaluation of k with RRKM one needs to know the
vibrational frequencies of the transition states occurring in
reactions eq 1. These were estimated as follows. Examination
of the frequencies of the M+L species in Table 2 shows that
these contain three lowest frequencies which are associated with
motions of M+ relative to L, while the rest of the frequencies
are all quite close to those of L. Since the transition state for
the dissociation is a “late” transition state which resembles the
separated M+ and L, its frequencies can be obtained by dropping
one of the three low frequencies of M+L and reducing the
remaining two to low values. Energy changes, based on fits of
the experimental threshold curves obtained with this procedure,
are given in Table 1.
Comparison of the ∆H° data without and with kinetic shift
correction, Table 1, provides an illustration for the magnitudes
of the corrections. The corrections for small ligands, Me2CO,
Me2SO, MeCONH2 are small, i.e., less than 1 kcal/mol, and
the exact value of the frequencies used is not important. Larger
corrections are required for the bigger and the more strongly
bonded ligands. Succinamide (H2NCOCH2)2 is an extreme case
where the strong bonding and the large size of the ligand require
a correction which is 15-20 kcal/mol. Due to the uncertainty
of the choice for the transition state frequencies, the ∆H data
for this compound might be in error by as much as (5 kcal/
mol.
The choice of the two lowest frequencies for the Na+
complexes (10 cm-1) and K+ complexes (5 cm-1), although
justified to a certain extent in the discussion above, is also a
semiempirical choice. As will be seen in the next section, these
values lead to the closest agreement with available ∆H° data
in the literature.
The energy values obtained with the correction for the kinetic
shift are dependent on the choice of the value of the two lowest
frequencies of the transition state. Two sets of kinetic shift
corrected ∆H° values are given in Table 1. The first set uses
30 cm-1 for all K+ and Na+ complexes. This frequency was
based on the choice of 25 cm-1 made by Wenthold and Squires
in a study of the CID of chlorophenyl radical anions26 leading
to Cl- as product ion where a late transition state is also
expected to occur. The authors26 made the choice of 25 cm-1
on the basis of literature data for experimentally measured ∆Sq
values of similar reactions.
A somewhat different procedure was used in a very recent
CID threshold study of Li+(CH3OCH3)x complexes, by Armen-
trout and co-workers.27 These authors also used the frequencies
of the complex as the starting point for the transition state
frequencies. For x ) 1, they dropped the frequency which
corresponded to the reaction coordinate and divided the two
other lowest frequencies by 2 and by 10 obtaining thus two
sets of frequencies. The two threshold values obtained with
these two choices were considered as the limits of the true value.
There are significant differences between the chloride dis-
sociation and the dissociation of the alkali ion-ligand com-
plexes. The ion-dipole and induced dipole interactions which
dominate the bonding in the alkali complexes involve weaker
but longer range forces. Furthermore, the bonding modes
involving the alkali ion and the ligand have lower frequencies
due to the less directional character of the electrostatic, relative
to the covalent bond. At the large distances between the ligand
and the alkali ion expected for the transition state, the frequen-
cies associated with the bonding should be considerably lower
than is the case for the chlorophenyl anion transition state.
The quadrupole collision cell used in the present work has
some drawbacks relative to the octapole cell used by Armentrout
and co-workers.18 These have been discussed.18 The major
advantage of the octapole is the type of energy well that it
produces. The ac potential well in the octapole increases very
slowly, inverse sixth power, with radial distance R, from the
octapole axis, while in the quadrupole, this field increases much
faster, with the inverse square power of R. The flat bottom of
the octapole well leads to a lesser pickup of kinetic energy in
the radial direction by ions which are off center from the
multipole axis. Part of the tailing toward low energies observed
in the threshold curves Figures 2-8 is undoubtedly due to
pickup of such kinetic energy in the quadrupole cell Q2.
However, the tailing is small and can be avoided by omitting
points at very low energies; see Figures 2 and 3 and discussion.
Evidence that the tailing due to excess internal energy in the
precursor ions is small is provided by a comparison of the
theoretical fit based on eq 2 and the experimental points; see
Figures 2-7. The experimental points at the very onset coincide
quite closely with the threshold fit. While the accuracy achieved
with the quadrupole trap is lower than that obtained with the
apparatus of Armentrout,18 the main uncertainty in the data
obtained for the measurements which involve larger molecules
is not the energy spread but the modeling of the kinetic shift.
To obtain frequencies for a looser transition state, the
following procedure was used. ab initio calculations at the 3-21
G level of the energies and frequencies of the complex,
Na+‚CH3CONH2 were performed for different ion-oxygen
atom distances extending from the equilibrium distance (2 Å)
to a maximum distance of 14 Å. For this distance, the bond
energy of the complex had reduced to ∼2% of the equilibrium
distance energy. At this distance, the average of the two lowest
frequencies, which did not correspond to the reaction coordinate,
was ∼10 cm-1. Assuming that the contribution of the rotational
barrier to the transition state energy is very small, such that the
transition state occurs very near to the complex dissociation,
the value of 10 cm-1 can be adopted for the two lowest transition
state frequencies. For the K+ complex, the frequencies should
be somewhat lower and a value of 5 cm-1 was chosen. ∆H°
values obtained with these frequencies for all the Na+ complexes
and K+ complexes are given in Table 1; see second last column,
∆H°.
Squires and his co-workers19 who have used a triple quad-
rupole for threshold measurements for many years have shown
that such an apparatus can provide many measurements of great
interest, with sufficient accuracy. The present apparatus allows
threshold measurements involving a large variety of ions that
at present can be obtained only by electrospray. We believe
this capability justifies its use even at the cost of some reduced
accuracy of the measurements.
The entropy change associated with the formation of the
transition state at 1000 K, ∆Sq1000, is often quoted26 and used
as a measure of the “looseness” of the transition state, where a
loose transition state is assumed to have a value, ∆Sq
> 0.
1000
The vibrational frequencies used for the transition state of
Na+‚CH3CONH2, lead to a ∆Sq ≈ 3.7 cal/(deg‚mol). The
vib
(b) Comparison of Threshold-Based Energies with Lit-
erature Data. Types of Bonding Present in the Complexes.
The ∆H°298 data obtained from the CID thresholds, discussed
in the preceding section, can be compared with previous
determinations in the literature.7,8,28 Previous determinations
are available from ion equilibria studies8 for complexes of
potassium with acetone, dimethyl sulfoxide, dimethylformamide,
transition state has two moments of inertia which are much
larger than those for the precursor ion and this rotational change
leads to ∆Sq ≈ 5 cal/(deg‚mol), for a total of ∆Sq
) 8.7
rot
1000
cal/(deg‚mol). This value corresponds to a very loose transition
state and appears appropriate for the electrostatically long range
bonding prevailing in the present ion-ligand complexes.

Reaction Enthalpies for M+L ) M+ + L
J. Phys. Chem., Vol. 100, No. 33, 1996 14225
and dimethylacetamide (Table 1). There is relatively good
agreement between the equilibrium derived ∆H° values and the
present CID results, particularly so with the set shown in the
second last column, ∆H°, which we consider as the best values
and which were obtained with the low-frequency choice for the
transition states. These CID values are found to be ∼1.5 kcal/
mol lower than the equilibrium data. Only for dimethyl
sulfoxide is there a larger difference of ∼4 kcal/mol. However,
the error limits given for the dimethyl sulfoxide equilibrium
determination8 are quite high, (3 kcal/mol. Examination of
the original data8 indicates that the slope of the van’t Hoff plot
was based on experimental points covering a narrow temperature
range. In such cases, the ∆H°i values obtained are less certain
than the ∆G° values at the experimental temperature. The
experimental points8 are also compatible with a lower ∆H°1
and a lower ∆S°1 value. A lower ∆H°1 value is also suggested
by a correlation with lithium ion affinities determined by Taft
and co-workers.29,30 A plot of the Li+ affinities29 vs ∆H°1 values
involving K+ complexes determined by ion equilibria8-10 leads
to a fairly good correlation. This correlation indicates for L )
Me2SO a value of ∆H°1 ≈ 31 kcal/mol, while the value ∆H°1
) 35 kcal/mol lies outside the curve. We conclude that the
CID threshold result of 31.1 kcal/mol is to be preferred over
the equilibrium value.8
discussed, can be considered as substituted carbonyl compounds.
Because of the expected dominance of electrostatic interactions
and the large bond dipole and polarizability of the carbonyl
group, the major contribution to the bonding in the complex
should be due to this group. The other polar groups i.e. -NH2,
NHCH3, N(CH3)2, and OH, also make contributions to the
bonding as indicated by the observed changes of ∆H°1 values
in Table 1.
Acetone may be considered as the simplest of the ligands
involved. Unfortunately, recent theoretical results for the
structure and energies of the acetone sodium and potassium ion
complexes do not seem to be available. Early work32 for the
Na+ complex predicts that the ion lies on the same axis as the
C-O bond, as expected on the basis of electrostatics. The same
structure can be expected for the potassium complex.
The bond with acetamide as the ligand is stronger. An
increase from 24.4 kcal/mol (acetone) to 29.7 kcal/mol (aceta-
mide) is observed for the potassium ion complexes (Table 1).
The theoretical calculations of Roux and Karplus7 predict a
structure in which the Na+ ion is close to coaxial with the C-O
bond. There is a tilt of a few degrees away from the C-O
axis, in the plane of the N-C-O atoms as shown in structure
I. This tilt approximately aligns the ion with the axis of the
Na+
Energy values from theoretical calculations, HF/6-31G,
obtained by Roux and Karplus7 are available for K+ and L )
acetamide (26.2 kcal/mol) and N-methylacetamide (24.8 kcal/
mol). Both of these values are lower than the threshold results
(29.7 and 30.4 kcal/mol). However, the authors7 were primarily
interested in developing pair potential functions for molecular
dynamics simulations and therefore did not refine their ab initio
calculations as much as they could have. The values7 quoted
in Table 1 are not the actual ab initio results which were
considerably higher, but results obtained after a semiempirical
correction based on the experimental and theoretical dipole
moment.7 Therefore, we believe that the CID threshold results
are to be preferred.
Roux and Karplus7 have obtained energy values (HF/6-31G*)
also for the sodium ion complexes with acetamide (36.0 kcal/
mol) and N-methylacetamide (38.4 kcal/mol). Also in this case,
the semiempirical correction was applied to obtain the quoted
results. These results are somewhat higher than the threshold
values of 34.7 and 35.7 kcal/mol. Again, we believe that the
threshold results should be preferred.
A theoretical result obtained by Jensen28 is available for the
complex of the sodium ion with glycine (H2NCH2COOH). The
calculations performed at the MP2/6-31G* and MP2/6-31+G-
(2d) level predict a complexation energy of 38.5 kcal/mol. A
zero point energy correction was not included, but the correction
should be small. Also, the conversion from ∆E at 0 K to ∆H°
at 298 is expected to be small (∼1.2 kcal/mol) (Table 1). This
theoretical result, which is ∼2-3 kcal/mol higher than the
threshold result (36.6 kcal/mol), is within the expected combined
error limits of the two determinations. Bouchonnet and Hop-
pilliard31 have also performed calculations for the Na+‚glycine
complex. These authors carried their calculations only to the
MP2/6-31G* level at which they obtained an energy of 45.2
kcal/mol. A very similar result (46.0 kcal/mol) was obtained
by Jensen28 with the same basis set. However, when the
calculation was carried to the higher, MP2/6-31G+(2d) level,
Jensen obtained the value, 38.5 kcal/mol, which is quoted in
Table 1 and used in the present discussion.
O
C
H
H3C
N
H
I
molecular dipole of acetamide, which is due to the combined
effect of the C-O and the C-N partial charges, the latter being
due to the partial electron pair shift from the lone pair of the
nitrogen to form a partial C-N π bond.
Substitution of H with methyl on the nitrogen in acetamide
may be expected to strengthen somewhat the interaction with
the sodium and potassium ion due to electron donation by the
methyl group and to the increased polarizability of the ligand.
Lithium ion affinities determined by Taft et al.29,30 exhibit such
increases. Thus, the Li affinity increases by ∼3.4 kcal/mol from
acetamide to N,N-dimethylacetamide.29 For Na+ this value may
2
be expected to become reduced by a factor of ∼ /3 on the basis
of comparisons between energies of Li+ and Na+ complexes.33
This leads to an expected increase of 2.3 kcal/mol between Na+
acetamide and Na+ dimethylacetamide which is close to the
observed difference of 2.8 kcal/mol between the corresponding
∆H°298 values in column 5 of Table 1. It is important to note
that in the absence of a kinetic shift correction (see ∆H°298 in
column 3) an increase of 12 kcal/mol would have been predicted
which is clearly an erroneous result.
Methyl substitution in the potassium acetamide complexes
1
2
should have a smaller effect roughly /2 to /3 of the effect
expected for sodium because of the increasing remoteness of
the methyl groups from the positive charge. On this basis, one
can expect an increase by ∼1.5 kcal/mol for two methyl
substitutions. The observed ∆H°298 (column 5) values are 0.7
kcal/mol increase for the first methyl and a decrease of 1.4 kcal/
mol for the second methyl. This is probably an erroneous trend
but the expected changes are small, i.e., within the experimental
error of (3 kcal/mol of the threshold determinations.
The threshold energies of the Na+ or K+ complexes with
acetic acid were not determined. They are expected to be lower
than those for acetamide because the more electronegative
oxygen atom leads to significantly lower π and σ electron
donation from -OH relative to -NH2. The relatively high
∆H°1 values observed for the complexes of K+ and Na+ with
The structures of the sodium and potassium ion complexes
and their relationship to the observed bond energies are of
interest and will be discussed in the following text. All ligands
in Table 1 except dimethyl sulfoxide, which will not be

14226 J. Phys. Chem., Vol. 100, No. 33, 1996
Klassen et al.
the R amino acetic acid (glycine) indicate that the R amino group
makes an important contribution to the bonding of the complex
and this suggests dicoordination involving the carbonyl and the
amino group as shown in structure II.
V
The theoretical calculations for the sodium glycine complex
by Jensen28 at the MP2/6-31G* level predict structure II to be
the most stable one. The distances, shown in Å, indicate a
stronger bond to the carbonyl oxygen. Two other structures,
III and IV, have only slightly lower stabilities. The glycine
VI
ecules, and the bond energy of such a complex would set the
upper limit for the energy of the sodium succinamide complex.
Data for the complexation of a second ligand molecule are often
available from ion equilibria measurements.8-10,34 Unfortu-
nately, such results are not available for the sodium ion and
acetamide. However, data are available for sodium and
acetone.34 These show that the enthalpy required to fully
dissociate the two acetone complex equals 1.75 times the
enthalpy for the dissociation of the one molecule complex.
Applying this factor to sodium and acetamide and using ∆H°298
) 34.7 kcal/mol, (column 5 of Table 1) one obtains 60.7 kcal/
mol as an upper limit for the dissociation of the sodium
succinamide complex. The experimental value, ∆H°298 ) 44.5
kcal/mol (column 5 of Table 1) equals approximately 75% of
the upper limit. The orientation of the two C-O dipoles in
structure V is far from optimal and a bond energy that is ∼75%
of the optimal energy appears quite reasonable.
II
III
The structure VI shown for the sodium-glycylglycine
complex indicates strong interactions only with the two carbonyl
groups. Examination of space models of glycylglycine indicates
that an alignment of the three groups: the two carbonyl groups
and the terminal amino group, leading to interactions with the
sodium as a tridentate complex, cannot be achieved.
IV
The bond energy of complex VI is expected to be fairly close
to that of the succinamide complex V, i.e., 44.5 kcal/mol. A
somewhat smaller bond energy is expected for structure VI on
the basis that succinamide has two NH2 groups acting as π and
σ electron donors while in glycylglycine there is only one amino
group and a weaker donating hydroxy group. The value
obtained, ∆H°1 ) 42.9 kcal/mol (column 5 of Table 1), is
smaller, in agreement with the expected substituent effects.
zwitterion structure III is only 2.2 kcal/mol higher in energy
while the related structure IV in which a proton transfer has
not occurred but a hydrogen bond interaction is present is higher
by 4.7 kcal/mol.28 Very similar results were obtained also by
Bouchonnet and Hoppilliard.31 The variety of interactions
leading to similar bond energies is interesting. Thus, the lowest
energy structures II and III provide information on the interac-
tions of a sodium ion with the N-terminal (structure II) and
C-terminal (structure III) of neutral peptides.
The bond energy of the glycinamide complex with sodium
was also determined (Table 1). The enthalpy change obtained
is 41.4 kcal/mol, which is close to 6 kcal/mol higher than the
36.6 kcal/mol value observed for the sodium glycine complex
(Table 1). As pointed out above, a higher value is expected
because the amide NH2 group is a better π and σ electron donor
than the -OH group of glycine.
Threshold-based enthalpy changes for the sodium ion com-
plexes with the dipeptide glycylglycine and the diamide of
succinic acid (succinamide) were also obtained (Table 1).
Theoretical calculations for these complexes are not available
in the literature. Probable structures for the two complexes are
shown below. Structure V for the succinamide is based on an
optimized MNDO geometry determination, and structure VI was
obtained using the AM1 method.
On the basis of the above considerations, one may conclude
that the interactions of a sodium ion with two adjacent carbonyl
groups in a polypeptide will be somewhat stronger than those
observed for the glycylglycine complex and very close to those
for the succinamide complex because in the polypeptide and
the succinamide complex stabilization is provided by two amide
nitrogens.
Very recent and as yet unpublished work by Beauchamp and
co-workers36 has provided evidence that the most stable
structures of the sodium ion complexes with the tri and higher
polyglycines are zwitterion structures. These are similar to
structure III for glycine but include an additional interaction
where the terminal ammonium group is close to and thus
stabilizes the negatively charged carboxy group. No results for
glycylglycine are available yet.36 If the zwitterion is the most
stable structure also for glycylglycine, then the arguments given
above concerning the agreement between the observed ∆H and
expected bonding for structure VI will be invalidated, but only
partially. Theoretical calculations36 for the two structures
indicate that the zwitterion is lower in energy but not by much;
see also structures II and III due to Jensen28 which were very
close in energy as discussed above. This “coincidence” of
energies would partially validate the discussion of structure VI.
The closeness of the ∆H values for the sodium complexes with
The enthalpy change obtained for dissociation of the succin-
d
amide complex is ∆H°1 ) 44.5 kcal/mol (Table 1). One can
examine whether this value is reasonable. Geometric constraints
in structure V hinder the optimum orientation of the two
carbonyl groups relative to the Na+ ion. Such an optimum
orientation can be achieved by two separate acetamide mol-

Reaction Enthalpies for M+L ) M+ + L
J. Phys. Chem., Vol. 100, No. 33, 1996 14227
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succinamide where a zwitterion structure is not expected and
glycylglycine also supports this view.
Assuming that the glycylglycine complex has the zwitterion
structure, one might be concerned that structure VI will not
provide the correct frequencies for the threshold fitting proce-
dure. However, the frequencies of the zwitterion structure and
structure VI will not be all that different and since the fitting
procedure is not very sensitive to the frequencies, the error will
be small. Concerning the transition state, the choice of
frequencies will be the same for both cases.
One may ask whether the gas phase experiments can be
extended to complexes which more closely model the interac-
tions of the sodium and potassium ions in the gramicidin
channel. Achieving a close correspondence seems impossible
at the present time. However, the gas phase experimental data
may provide some limiting complexation energy values. Ac-
cording to 2D NMR evidence35 and theoretical work,2-4 the
ion-channel interactions are principally due to interactions with
four carbonyl oxygens of the peptide backbone and two water
molecules which accompany the ion. A crude model for the
optimum complexation energy may be provided by the com-
plexation energy of the sodium ion with two suitable dicarbonyl
molecules, such as glycylglycine amide (GGAm) and two water
molecules, leading to Na+(GGAm)2(H2O)2. Experimental work
presently underway in our laboratory has shown that such a
complex can be produced in the gas phase. The dihydration of
the complex Na+(GGAm)2 can be determined by ion equilibria
measurements,16 while the complexation energies of the Na+-
(GGAm)2 would be amenable to CID threshold measurements
and also ion molecule equilibria, for the addition of the second,
less strongly bonded GGAm molecule. Determination of the
free energy changes rather than only the enthalpy changes will
be desirable because the transfer of the sodium ion from an
aqueous medium to the transmembrane channel depends on the
free energy change.
(20) Anderson, S. G.; Blades, A. T.; Klassen, J. S.; Kebarle, P. Int. J.
Mass Spectrom. Ion Processes 1995, 141, 217.
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1993, 115, 12125.
(23) Chupka, W. A. J. Chem. Phys. 1959, 30, 191.
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P. B. J. Phys. Chem. 1996, 100, 1605.
Acknowledgment. The present work was supported by
grants from the Canadian National Sciences and Engineering
Research Council NSERC. The authors are indebted to Profes-
sor P. Armentrout for making the CRUNCH program available
to them and for informative discussions with Professor P.
Armentrout and Professor R. R. Squires. The authors are also
indebted to Professor B. Roux, who provided the impetus for
this study.
(28) Jensen, F. J. Am. Chem. Soc. 1992, 114, 9533.
(29) Taft, R. W.; Anvia, F.; Gal, J. F.; Walsh, S.; Capon, M.; Holmes,
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1990, 62, 17.
(30) The Li+ affinity differences given in ref 29 correspond to free
energy differences, i.e., changes in the -∆G°1 at 298 K for reaction 1.
(31) Bouchonnet, S.; Hoppilliard, Y. Org. Mass Spectrom. 1992, 27,
71.
References and Notes
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