J. Phys. Chem. 1994, 98, 6075-6081
6075
Evaporation of Dimers from Proton-Bound Formic Acid Clusters Wan Yong Feng and Chava Lifshitz'9t Department of Physical Chemistry and The Fritz Haber Research Center for Molecular Dynamics, The Hebrew University of Jerusalem, Jerusalem 91 904, Israel Received: February 10, 1994; In Final Form: April 5, 1994"
Proton-bound clusters of formic acid and mixed clusters of formic acid and water evaporate neutral dimers of formic acid. This attribute is shared with liquid formic acid. Clusters are considered to bridge the gap between the gas phase and condensed phases. The evaporation of dimers begins already for hexamers. Collisionally activated dissociations indicate a structure in which a central ion (e.g. HsO+)is completely solvated by a ring of hydrogen-bonded formic acids. Ring closure and dimer evaporation begin for the same cluster sizes. Thermochemical considerations suggest that the formic acid dimer is evaporated in the open-chain configuration, rather than in the ring-closed one.
Introduction High-energyion beam experimentsfurnish information about the structure and reaction dynamics of clusters. Unimolecular and collision-induced decompositions of proton-bound clusters, for example (H20),H+ and (NHs),H+, have been reviewed recently.' Reactionsare characterized by evaporationsof solvent molecule units. The loss of only one neutral molecule in the unimolecular dissociation of metastable cluster ions, on a microsecond time scale, is the general rule.2-5 Collision-induced decompositions can lead to evaporations of several solvent molecules$ but these are considered to be consecutive events. Cluster sequences demonstrate very often "magic numbers"i.e. ions of special abundance due to their unique stability. In (NH3),H+ n = 5 is a magic number due to closure of the first solvation shell. Magic number clusters such as (NH3)5H+ are characterized by maxima in kinetic energy releases (KERs) upon solvent evaporation, as a function of cluster The binding energies to solvent monomer units can be calculated, for clusters of different sizes, from the experimental KERS.'.~Structures of mixed proton-bound clusters may be deduced through KERs1.10 and through collision-induced decompositions.Iv6J' Protonated formic acid clusters and carboxylicacids in general are interesting since they possess potentially two proton binding sites-the OH and the C=O groups. We havestudied recently12 the effect of stepwise solvation on ion reactivity along the series (HCOOH),H+, n = 1-3. The results suggested the evaporation of the formic acid neutral dimer in some ion/molecule reactions of (HCOOH)3H+. Carboxylicacids are well-known to form stable cyclic dimers through intermolecular O-H.-O=C hydrogen bondsaI3J4 At room temperature and normal pressure, 95% of the formic acid vapor consists of the dimer. The binding energy of theneutral dimer is150.66 eV. Open-chaindimersofcarboxylic acids may be preferred in aqueous solutions because of hydrophilic interaction of the carboxylic group and hydrophobic interaction of the alkyl groups.16J7 Mass spectral investigations of carboxylic acid clusters have been r e p ~ r t e d . l ~ -The ~ ' ion (CH&OOH)s(H20)H+ was demonstrated to be a magic number.21.22 Calculations performed by the AM1 method2lV22 yielded a hydrogenbonded cyclic structure for the acetic acid pentamer surrounding a central H30+. Similar structures wereobtained for other (CH3COOH),(H2O)H+ clusters.21 We studied unimolecular and collision-induced reactions of the proton-bound formic acid clusters, as well as mixed cluster series, results of which will be reported here. Evidence will be
* To whom correspondence should be addressed. 7
Archie and Marjorie Sherman Professor of Chemistry. Abstract published in Aduance ACS Abstracts, May 15, 1994.
presented for dimer evaporations. Attempts at deducing cluster binding energies from KERs will be presented.
Experimental Section Measurements were performed on a high-resolution doublefocusing mass spectrometerof reversed geometry-the VG ZAB2F.23924Ions were formed by electron impact in a temperatureand pressure-variable s0urce.24.~~The typical conditions for promoting cluster ion formationhave been described previo~sly.~*~ The typical pressure and temperature employed in the present study were 0.03 Torr and 253 K. The metastable fragmentations were studied by mass-analyzed ion kinetic energy spectrometry (MIKES).3.26 An energy resolution of -4000 was employed. Metastable ion peak shapes were determined by scanning the electrostatic analyzer (ESA) and using single-ion counting. Ion countingwas achieved by a combination of an electron multiplier, amplifier/discriminator,and multichannel analy~er.~ The metastable ion peak shapes obtained were mean values of several hundred accumulated scans. This was done in a computercontrolled experiment, monitoring the main beam scan and correcting for the drift of the main beam.24 The kinetic energy spread in the parent ion beam was subtracted from the width recorded for each of the fragmentation processes. Kinetic energy release distributions (KERDs) were obtained from the first derivatives of the metastable ion peaks ~hapes.2~-29Collisional activation (CA) spectra30were obtained using air as collision gas at a pressure of 2 X 1C7mbar as measured by an ion gauge situated near the diffusion pump located between the electric sector and the gas cell; the actual gas pressure was higher by approximately a factor of 103. The nature of neutral products of unimolecular fragmentations of the clusters was determined by collisional reionization.31 Oxygen was used as the reionization gas, and an ion deflectionelectrode was used in front of the collision ce11.31b*32bJ3 Typical reionization experimentswere run at an ion translational energy of 8 kV, with zero collision cell voltage and with the ion deflector at 500 V. Formic acid was from Sigma Chemical Co. at a stated -99% purity; the main impurities were water and acetic acid.
Results and Discussion 1. Mass Spectra, Cluster Size Distributions, and Magic Numbers. Two major cluster series observed are (HCOOH),H+ ( n = 1-9) and (HCOOH),(H20),H+ (n = 1-8, m = 1; n = 1-7, m = 2; n = 1-5, m = 3; n = 1-4, m = 4). Minor series are (HCOOH),,*+ (n = 1-8) and (HCOOH),,COOH+ (n = 0-6). Typical cluster ion mass spectra are presented in Figure 1, demonstrating the dependence of the size distributions on the ion
0022-365419412098-6075$04.50/0 0 1994 American Chemical Society
6076 The Journal of Physical Chemistry, Vol. 98, No. 24, 1994
Feng and Lifshitz
100 80
-
(HCOOH)n@IzO)mH*
i ._,i
2o
0-lo..
0
,
,
y
100
d Z 80
60 40
20 0
1 2 3 4 5 6 7 8 9 Figure 2. Branching ratios (%) for monomer (M)and dimer (D) loss from proton-bound formic acid clusters as a function of cluster size. Upper part, unimolecular evaporations;lower part, collisionallyactivated
m/z 100 80
dissociations.
P1) -
1
(HCOOH)n(HzO)mp c. Td50 K. M . 0 5 Ion
p r e d i ~ t e d ~as~aJ hydrogen-bonded ~ cyclic structure. As noted above, we observe all of these ion series, including M,*+. Apparently, ionization of the neutral dimer and of higher neutral clusters leads to unstable ionic clusters; however, ionization of the neutral monomer followed by addition of neutral molecules can lead to stable clusters through collisional stabilization in the ion source, (HCOOH),
+e
-
[(HCOOH),'+]*
(HCOOH),,
H+, (HCOOH),, COOH' (1)
mh HCOOH
1M)
(HCOOH)n(HzO)mIf
HCOOH"
-0 0
IO0
200 m/Z
Figure 1. Cluster ion mass spectra as a function of pressure and temperature in the drift ion source. Formic acid was a sample containing a small (-1%) water impurity.
source temperature and pressure. The ion (HCOOH)s(HzO)H+ was observed to be particularly abundant (a "magic number"), in agreement with similar results21.22 for (CH&!OOH)5(H20)H+. Partial cluster sequences for (HCOOH),H+ and (HCOOH),(H20)2H+ at T = 250 K and p = 0.02-0.03 Torr demonstrated pronounced abundances for (HCOOH)6H+, (HCOOH)6(H20)2H+,and (HCOOH)4(H20)2H+. A 1:l HCOOH: CH3COOH mixture demonstrated the magic character of (CH3COOH)6H+,(CH3COOH)j(HzO)H+,(CH3cC)OH)6(H20)2H+, and (HCOOH)4(CH3COOH)2H+in their corresponding partial cluster sequences. Other enhanced peaks observed are (HCOOH)sCH3CO+and (CH3COOH)sCHpCO+. The CHpCO+unit is formed by dehydration of protonated acetic acid.'s Nonprotonated carboxylic acid cluster sequences Mn*+have not been observed from nozzle beam expansions.19 These ions were found to break up to M,IH+ and M,&OOH+. The existence of the ion (HC02H.C02H)+ has been theoretically
+e
-
HCOOH"
+ (n - 1)HCOOH
d. T=247 K. P d . 0 2 tom
-
-
(HCOOH),"
(2)
Staceand Moore35have found that specieswith thecombination p = n - 2 have special properties for proton-bound clusters Xn(H20),H+,where X = acetone, diethyl ketone, dimethyl ether, and diethyl ether, by virtue of a core ion which is a protonated water cluster to which the molecules X bind. The ketones and ethers have a single group each of which can hydrogen bond to one of the core ion protons. The formic acidlwater clusters do not conform to p = n - 2 as a special combination. The dual hydrogen-bonding character of the C - 0 and OH groups prefers a cyclic structure of formic acid units in which a central ion is encapsulated. The central ion may be H30+as in the case of acetic acid21322 or it may be any other ion (COOH+, CH3CO+, etc.), provided the cavity is large enough. The proton itself may beinternally hydrogen bonded as in crown ethers.36 In the coming sections we will try to support this idea. 2. Unimolecular and Collisionally Activated Reactions. The MIKE spectra of the cluster series (HCOOH),H+ demonstrate two major reactions: Evaporation of a single formic acid unit and evaporation of two formic acid units. The relative abundances of these two reactions are cluster size dependent-clusters with n = 2-5 lose a single formic acid unit preferentially while for n = 6 the loss of two units is about equal to the loss of one unit, and by the time n = 9, the only reaction is loss of two formic acid units (Figure 2). These data as such suggest evaporation of a monomer and evaporation of a dimer as the two parallel reactions observed, (HCOOH),H+
-
(HCOOH),,H+
+ HCOOH
(3)
The Journal of Physical Chemistry, Vol. 98, No. 24, 1994 6077
Proton-Bound Formic Acid Clusters
(HCOOH),H+
-
(HCOOH),,H+
+ (HCOOH),
(4)
The loss of two formic acid molecules could, in principle, take place consecutively in the second field-free region (2 FFR). We will present additional evidence, in coming sections, favoring the single step evaporation of a dimer unit. Collisionally activated dissociation (CAD) spectra enhance the unimolecular peaks due to reactions 3 and 4. CAD changes the ratio between the two channels to a limited extent (Figure 2). Evaporation of additional solvent molecules is also observed under CAD. CAD on the hexamer (HCOOH)aH+ was carried out at two ion source temperatures: 253 and 299 K. The low temperature favored the dimer loss, while the high temperature favored the monomer loss. This indicates the possible existence of two isomeric structures, in a similar manner to a previous observation from this laboratory.3’ In addition, there is some indication for an even-odd alteration (Figure 2), whereby even ions favor dimer evaporation, while odd ions favor monomer evaporation. The mixed clusters (HCOOH),(H20)H+ favor HzO loss for n = 1-3 and formic acid loss for n 1 4 (Table 1). The higher clusters in the series demonstrate formic acid dimer evaporations. Similar results were observed for the series (HCOOH),(HzO),,,H+, m = 2 4 . The cluster series (HCOOH),*+ (n = 1-8) gave two major reaction products under unimolecular MIKES: (HCOOH),lCOOH+ and (HCOOH),lH+. Additional products observed under CAD were (HCOOH),l*+ for n = 2-5 and (HCOOH),,*+ for n 1 6 . Mixed proton-bound formic acid and acetic acid clusters evaporate formicacid monomers and dimers. Neat proton-bound acetic acid clusters evaporate acetic acid monomer and dimer units. The recent investigation12 of ion/molecule reactions of (HCOOH)3H+demonstratedanalogous reaction channelsto those of the protonated methanol trimer38 and similar general trends, and an analogous open-chain hydrogen-bonded structure was suggested for the proton-bound formic acid trimer’, and for the proton-bound methanol trimer.39 Results for mixed water/ methanol clusters have shown, on the basis of both thermochemistry40 and CAD? that the most stable isomers of small mixed clusters have the methanol molecules near the charged center. For example, the largest peak under CAD for (CH30H)3(HzO)H+ is due to water loss, since the HzO molecule is in the periphery of the mixed tetramer. A similar situation is observed for the mixed formic acid/water clusters for n = 1-3; for example, (HCOOH)3(H20)H+loses water preferentially, and an openchain structure with water in the periphery is plausible. There is a controversy concerning the structures of higher alcohol/water clusters, (ROH),(HzO)H+. A central H30+ion completely solvated by a ring (or chain) of hydrogen-bonded alcohols was suggested4’for (CH30H)9(H20)H+. Mixed methanol/water clusters with lower n, e.g. n = 7, have an incomplete ring of methanols.41 The results of CAD experiments4, favor a loose chain of hydrogen-bondedmolecules and no rigid protonation site or fixed central ion. Even (CH30H)9(Hz0)H+was observed42 to lose water preferentially under CAD. Nonetheless, a “proton switch” model at a specific cluster size is fa~ored.4’-~* For methanol the critical size is between n = 9 and n = 10. The present results for formic acid suggest a similar “proton switch” model. There is a critical cluster size, below which the openchain cluster with water in the periphery is more stable and above which an H30+ion solvated by a ring of hydrogen-bondedformic acids is more stable. The critical size is between n = 4 and n = 6 ; in other words, the cavity of H30+is already large enough for rings having fewer formic acid moleculesthan methanols, because of the two hydrogen-bonding sites of formic acid. These results are in excellent agreement with predictions by AM1 calculations21v22 for proton-bound acetic acid/water clusters. CAD data for (CH3COOH),(H20)H+ gave similar data to those for (HCOOH),(HzO)H+: HzO loss is favored for small n, and acetic acid monomer or dimer loss is favored for large n.
6490
651 0
6530
ENERGY, eV
Figure 3. Metastable ion peak shape for monomer evaporation from the protonated hexamer. The reaction takes place in the second field-free region of the ZAB-2F mass spectrometer. The electrostatic analyzer voltage is scanned, and ion counts are accumulated on the multichannel analyzer. Ion counts are plotted as a function of ion energy (in the laboratory frame). The main beam [(HCOOH)6H+] had an energy of -7800 cV. 500
1
4 400
z
10
300
a W
200
c
z
g
100
0 0
5190
521 0
5230
ENERGY, eV
Figure 4. Metastable ion peak shape for dimer evaporation from the protonated hexamer. See caption to Figure 3.
TABLE 1: Percent of Daughter Ion Intensities for Water (W), HCOOH (M), and (HCOOH)z (D) Losses from CAD Swctra of (HCOOH),,(H20)H+ ions at -15 OC and 0.03 Torr n ~
1
2
3
4
5
6
7
8
W(%)
100
M(%)
0
77 23 0
60 38 2
33 58 9
21 59 20
0 94 6
0 5 95
0 3 97
D(%) 0 3. Kinetic Energy Releases. The metastable peak shapes were all pseudo-Gaussian. Typical examples are shown in Figures 3 and 4 for reactions 5 and 6 , respectively:
(HCOOH&H+
-
-
(HCOOH)6H+
+ (HCOOH),H+ + (HCOOH), (HCOOH)5H+ HCOOH
(5) (6)
The kinetic energy release distributions (KERDs) obtained were Boltzmann-like,as is seen in Figure 5 for reaction 6 . The average kinetic energy releases (KERs), ( e ) deduced from the distributions, are summarized in Table 2 and plotted as a function of cluster size in Figure 6 . The most striking result is the equality, within experimental uncertainty, of the average KERs for monomer and dimer evaporations from clusters with n = 6-8. This equality suggests that the two evaporations take place competitively and in parallel from the same ion structure. For two parallel reactions to occur in the field-free region, their rate constants have to be nearly equal. The unimolecular decompositions of clusters areconsidered to be evaporationshaving universal
6078 The Journal of Physical Chemistry, Vol. 98, No. 24, 1994
Feng and Lifshitz
TABLE 2: Kinetic Enerm Releases for Unimolecular Reaction of (HCOOHLH+ cluster size, n 2 3 4 5 6 7 8 monomer loss ( e ) , meV 9.5 f 0.6O 17.0 f 0.4 17.1 & 0.9 17.4 & 0.4 20 f 3 19&3 18.3 f 0.1 0.60 0.58 0.56 0.53 0.57 0.53 0.56 e 142 128 130 147 140 58 126 T*,K 0.38 0.53 0.45 0.45 0.40 1.48 0.80 AEvap,eV dimer loss (d,meV 62.6 f 2 19.5 f 0.4 18.7 & 0.9 19.8 f 0.2 0.47 0.67 0.60 0.55 e 450 142 142 154 T', K (1.54) 0.44 0.40 0.42 hEvapt eV The error limits quoted are deduced from the spread in several separate experiments, each of which was the result of several hundred accumulated scans. (I
.-n n
0.6
e
0.0
0.00
0.10
0.05 C.M. Kinetic Energy, eV
Product kinetic energy release distribution for metastable loss of formic acid dimer from protonated formic acid hexamer: ( 0 ) experimental; (-) model fit. Figure 5.
60 50
$
40
30 20 10
1
2
3
4
5
6
7
8
9
Cluster Size, n Figure6. Plot of the average kinetic energy release ( t ) versus cluster size n for monomer (M) and dimer (D) loss from (HCOOH),H+. 80
I
I
36M)
31W
I
3800
3900
ENERGY,CV
"Reionization" (collisionally i n d u d dissociative ionization, CIDI) mass spectrum of formic acid monomer HCOOH, from (HCOOH)zH+,on an 0 2 target. Ion source acceleration voltage, 7820 Figure 7.
V; deflection, 500 V.
preexponential A factors.43 As a result, the critical energies of activation of the two parallel reactions have to be nearly equal. For reactions having no reverse activation energies, this leads to
similar KERs, since theexcess energy required for decomposition in the metastable time window is the same. The KER for dimer loss from n = 5 is quite high, but the reaction is very weak and could very well be collision induced. Alternatively, it could be due to evaporation of the dimer from a different isomer than the monomer evaporation. A situation like this has been observed for the ammonia-triethylamine system.l0 Statistical energy partitioning in dissociationto severalproductshas been discussed.44 The peak width in the laboratory frame due to two consecutive HCOOH eliminations can be calculated, since the KERs for each of the two have been determined. The combined KER is thus calculableon the basis ofwell-knownequations for metastable ions.26A short derivation (Appendix) demonstrates that equality of the kinetic energy relases for monomer evaporation and for the consecutive evaporation of two monomers is expected. There are indeed measurements of clearly identified consecutive decay processes4swhere the kinetic energy releases are very similar to those found for a single step, however, only when the reactions were collision induced. The equality of the average KERs for evaporations of a single formic acid unit and two formic acid units from clusters with n = 6-8 is in itself not a proof for dimer evaporation, but the latter will be demonstrated unequivocably below (section 4). KERs obtained for the mixed proton-bound (HCOOH),(HzO),H+ clusters are summarized in Table 3. The three parallel reactions, HzO loss, formic acid monomer loss, and formic acid dimer loss from the same precursor ion, have equal KERs within experimental error, as is required for evaporations from a single isomeric cluster structure or from two isomers separated by an isomerization barrier which is lower than the dissociation limit.lJ0 4. CollisionalReionization of Neutral Fragments. Collisional reionization of the neutral fragments from unimolecular fragmentation of the clusters (HCOOH),H+ with n = 2-5 gave characteristic mass spectra of formic acid monomer with ions m / z = 46, 45, and 29. A partial reionization mass spectrum is shown in Figure 7. There were no peaks higher in mass than m / z = 46 (HCOOH+). This indicates the evaporation of monomer units of formic acid from these clusters. No dimer was observed for the pentamer, but this may be due to low sensitivity. From n L 6 the reionization mass spectrum changed. While no ions were observed at m / z = 92 ((HCOOH)2+), a pronounced peak appeared at m / z = 47 due to (HCOOH)H+. A similar structure characteristic ion was observed for formic acid/water mixed clusters. The spectrum for dimer reionization from (HC0OH)s(H20)H+ is shown in Figure 8. Mass resolution was not very good, but the peak at m / z = 47 was clearly reproducible. It is known that carboxylic acid dimers do not give parent ions in their mass spectra.I9~~~ The most abundant ion observed is the protonated monomer. It is thus not surprising that we do not observe theion (HCOOH),+; theion (HCOOH)H+isanexcellent indicator for reionization of the neutral (HCOOH)2 dimer. The reionization experiments and the kinetic energy releases discussed above prove that a single-step evaporation of a neutral dimer, reaction 4, takes place for proton-bound formic acid clusters (HCOOH),H+ and mixed clusters with water (HCOOH),(H20),H+, provided n L 6 or n + m 1 6 . Clusters are usually
Proton-Bound Formic Acid Clusters
The Journal of Physical Chemistry, Vol. 98, No. 24, 1994 6079
TABLE 3: KERs for Unimolecular Reactions of (HCOOH),,(H20)&+ n,m
channel H2O IOSS
(e)
E F.K
A&.p HCOOHloss
3,1 17i2' 0.56 128 0.47
(e)
E
P,K mvrp
(HC0OH)zIOSS
4,1 17f3 0.53 127 0.40 17f 1 0.53 129 0.46
(e)
e
T', K
mvap
5,1 16f3 0.52 115 0.33 17.9f0.5 0.56 131 0.38 21.3 f 0.5 0.59 162 0.48
6,1
73
8,l
18 & 1 0.56 138 0.36 15.8 f 0.2 0.58 122 0.31
52
4,2 17f2 0.51 128 0.38 18.6f 0.7 0.58 147 0.43
62
15.9f 0.2 0.58 124 0.34
16.6f 0.8 0.56 130 0.31
16.8f 0.9 0.59 126 0.33
* See footnote of Table 2.
0.05
n
0.04 0.03 0.02
1350
1400
1450
I500
ENERGY, CV
Figure 8. Reionization (CIDI) mass spectrum of formic acid dimer (HCOOH)z, from (HCOOH)s(HzO)H+,on an 0 2 target.
considered to bridge the gap between the gas phase and the condensed phase. Evaporation of dimers has recently4 been reported for carboxylic acid liquids. Our results for the clusters indicate that this bulk property is achieved already for clusters with six monomer units. 5. Metastable Fractions. Decay fractions of metastable cluster ions give the metastable peak intensities, resulting from the unimolecular decompositions, relative to the parent ion cluster intensities. They usually demonstrate a monotonic increase with cluster size.I.9 This is understood within the framework of the evaporative ensemble statistical model due to K10ts.~~The evaporative ensemble model assumes that each cluster ion has suffered at least one evaporation before it enters the field-free region of the mass spectrometer. The metastable rate coefficient window is k = 104-106 s-1. The slower the rise of the microcanonical rate coefficient k(E)with energy E is, the broader is the internal energy range 6E covered by the metastable window. Sincethe range of internal energies for each cluster in the ensemble is equal to Mvap, the vaporization energy, it is more or less independent of cluster size. However, the metastable fraction D = 6E/AEvaPincreaseswithincreasing cluster size. Themetastable fractions for reactions 3 and 4 were summed, and the resultant D values are plotted versus the cluster size in Figure 9. While it is not at all clear that an evaporative ensemble is produced in the drift ion source employed to create the clusters, the break at n = 6 (Figure 9) is quite remarkable. As noted earlier, the cluster size n = 6 is the one for which dimer evaporation becomes important; n = 6 is a magic number for partial cluster sequences of (HCOOH),H+, and the critical cluster size for a "proton switch" in the case of mixed (HCOOH),(H2O)H+ clusters is n = 4-6. In that model H30+ is the central ion solvated by a ring of hydrogen-bonded formic acids. In the neat clusters (HCOOH),H+ the central ion could be either H+ or protonated formic acid HCOOH2+. The size of the cavity has to be quite large to accommodate the protonated formic acid. In conclusion, the decay fractions observed favor a structural change at n = 6. A similar abrupt change in metastable fractions was observed for C,+ clusters at n = 30, above which fullerenes are produced and below which ring structures prevail.47
0.00 0'01
1
I
L-2* A '
1
2
3
4
5
6
7
8
9
Cluster Size, n Figure 9. Plot of decay fraction of (HCOOH),H+ as a function ofcluster size.
6. Binding Energies. The unimolecular decompositions of the proton-bound formic acid clusters and formic acid/water mixed clusters may be viewed as evaporations from small particles. This process has been treated theoretically by Klots.43 It has been proposed that the average kinetic energy with which a monomeric unit leaves the surface of an aggregate can measure the temperature of the transition state, Tt. This assumption holds, provided the decomposition reaction does not demonstrate a reverse activationenergy. The pseudo-Gaussian metastable peaks obtained for all the present decompositions (p evaporations) suggest the absence of reverse activation energies. This idea was developed further by K l o t ~ ,treating ~ ~ , ~the ~ full KERD. It allows one to extract the vaporization energies (Le. binding energies) of the clusters from the KERDs. In the model-free approach, the KERD is written in the form
oI t I 1
p(c) = e' exp(-c/k,TS)
(7)
where t is the kinetic energy, ke is Boltzmann's constant, T' is the transition-state temperature, and t is a parameter. The KERDs for all of the reactions studied could be fitted by expression 7. An example of the quality of the fit is shown in Figure 5. The parameters Tt and C were extracted from the fits, as previously explained,@and are included in Tables 2 and 3. Once Tt is extracted from the KERD, Tb may be calculated' from
(8) where Tb is the isokinetic temperature to which a heat bath must be set to yield a thermal rate constant k(Tb) equal to the microcanonical rate coefficient k(E) characteristic of the cluster decomposition; y is the universal Gspann parameter related to the preexponential A factor, y = 23.5 1 S , 5 0 and c is the cluster heat capacity. The cluster vaporization energy Uvap is calculated
*
Feng and Lifshitz
6080 The Journal of Physical Chemistry, Vol. 98, No. 24, 1994
0.0'
1
"
2
3
"
4
5
"
'
6
Cluster S i t e ,
7
8
9
n
Figure 10. Plot of calculated binding energies of (HCOOH).H+: (0) monomer (M) loss; (A)dimer (D) loss. Lines are drawn to lead the eye.
from Trouton's r~Ie,~,43.4*-50 (9)
The values for C, TI,and AEvapr extracted from the experimental KERDs,are included in Tables 2 and 3. Mvap is plotted as a function of cluster size for reactions 3 and 4 in Figure 10. As expected, the binding energies for monomer and dimer evaporations are equal within experimental error for the clusters (HCOOH),,H+ (n = 6-8) (Figure 10 and Table 2). Inspection of reactions 5 and 6 for the hexamerdemonstrates that this equality implies the equality of the sums of enthalpies of formation as follows: AH,[(HCOOH),H+]
+ AH,[HCOOH] =
AH,[(HCOOH),H+]
+ AH,[(HCOOH),]
(10)
and similarly for the higher clusters, AH,[(HCOOH),H+]
+ AH,[HCOOH]
AH,[(HCOOH),H+] AH,[(HCOOH),H+]
+
= AH,[(HCOOH),]
(1 1)
+ AHf[HCOOH] =
AHf[(HCOOH),H+]
+ AH,[(HCOOH),]
(12)
This implies further that the binding energy of each protonbound cluster in the series (HCOOH)nH+ (n = 4-7), D,,.,+I (reaction 3), is equal to the binding energy of the neutral dimer. The latter is equal15 to 0.66 eV, provided it is cyclic. However, the actual binding energies D,,,,+1determined experimentally are 0.45 eV (n = 6),0.40 eV (n = 7), and 0.38 eV (n = 8) (Table 2). These values are lower than 0.66 eV and indicate that the neutral dimer is evaporated as an open-chain species. It can evaporate as an open-chain species from an open-chain protonbound cluster, giving an open-chain product proton-bound cluster, or from a ring-closed proton-bound cluster, giving a ring-closed product cluster. Evaporation of an open-chain dimer from an open-chain proton-bound cluster would be in keeping with a loose transition state as required for y = 23.5 and the absence of a reverse activation energy. A thermochemical cycle leads to a dimer evaporation energy from the proton-boundpentamer, which is 0.53 eV. This is slightly too high to compete with the monomer evaporation but much lower than the experimental dimer evaporation energy, making that value suspect, as noted earlier. The calculated dimer evaporation energy from the protonated tetramer is 0.88 eV, in considerable excess of the monomer evaporation energy. These
calculations demonstrate internal consistency and clearly show why the dimer evaporation channel begins at n = 6. How accurate are the binding energies? We do not expect the value for the proton-bound dimer to be accurate. The binding energies for the higher clusters were calculated by Klots' model43-4"50 as well as by Engelking's modified RRK model,51 and theagreement between the twowasvery good. The parameter which is least well-known is the heat capacity. A value C,,= 6(n - 1) (in units of k ~ was ) adopted, following Castleman and cow o r k e r ~ .This ~ value takes into account only the intercluster modes. A value of C,, = 6n may by more plausible for a cyclic cluster, but the effect on the calculated Mvap is minor. The parameter C was found to be between 0.5 and 0.6 (Tables 2 and 3), indicating a dimensionality of - 3 for the KERDs, which is appropriate for an ion/induced-dipole Langevin type potential between the fragments.
Conclusion Cluster ions were formed from formic acid in a temperatureand pressure-variableion source. Reactions of these clusters were studied by tandem mass spectrometry. The cluster series observed included (HCOOH),,H+, (HCOOH),,*+,(HCOOH),(HzO),,,H+, and (HCOOH),(CH3COOH)mH+. Mass spectra revealed several magic numbers, notably (HCOOH)s(H2O)H+. Unimolecular and collisionally activated decompositions demonstrated solvent molecule evaporations. A unique reaction detected recently also for liquid formic acid is the evaporation of formic acid dimer from proton-bound clusters (HCOOH),,H+ with n L 6,as well as from the other cluster series beyond a certain critical value of n. Evaporation of thedimer as a single-stepreaction was verified by reionization of the neutral. Collisionally activated dissociations of mixed proton-bound formic acid/water clusters, (HCOOH),,(HzO)H+, yield water loss preferentially for low n and formic acid (monomer and dimer) loss for high n. A "proton switch" model is adopted according to which HzO is in the periphery of an open-chain cluster for low n, but H30+ is the central ion solvated by a ring of hydrogen-bonded formic acids for n 2 6. Kinetic energy release distributions were measured for many of the unimolecular reactions. The results were employed to extract binding energies for the clusters. In (HCOOH),H+ the monomer and dimer binding energiesare equal for n = 6-8. Thermochemicalcalculationssuggest that the formic acid dimer evaporates as an open-chain species, rather than a cyclic one.
Acknowledgment. This research was funded by The James Franck Research Center. The authors thank Professor Helmut Schwarz for helpful suggestionsand M. and T. Peres for technical assistance. Appendix Assume two consecutive reactions,
AB,'
-
+B +B
AB+
AB+ -,A+
having the same KER e. Let u stand for velocity in the centerof-mass (CM) system of AB2+, u' for velocity in the CM system of AB+, and v for velocity in the laboratory system. Conservation of energy and momentum requires that
Proton-Bound Formic Acid Clusters
The Journal of Physical Chemistry, Vol. 98, No. 24, 1994 6081 (1 1) Wei, S.; Tzeng, W.B.; Keesee, R. G.; Castleman, A. W., Jr. J. Am. Chem. Soc. 1991,113, 1960. (12) Feng, W. Y.; Lifshitz, C. J. Phys. Chem. 1994, 98, 3658. (13) Allen, G.; Caldin, E. F. Quart. Reu. 1953, 7, 255. (14) Kollman, P. A.; Allen, L. C. Chem. Reo. 1972, 72, 283. (15) Chao, J.; Zwolinski, B. J. J. Phys. Chem. Ref. Data 1978, 7, 363. (16) Ben-Naim, A. HydrophobicInteruction; Plenum: New York, 1980. (17) Yamamoto, K.; Nishi, N. J. Am. Chem. Soc. 1990, 112, 549. (18) Luczynski, 2.;Wlodek, S.; Wincel, H. Adu. Mass Spectrom. 1978,
From eqs A3, A4, and A5, A6, respectively, one obtains
u'A+
=
(
)
2m,e
7A, 297.
112
mAB+'mA+
The velocity UA+ thus has two Components uA+
=
(
2mBc
)1'2
~AB~+'~AB+
+
(
2mBe )'I2
(Ag)
~AB~++"A+
which need to be summed vectorially. The maximum and minimum values of the laboratory velocities of A+ are given by in-line vectorial addition or subtraction, respectively, of the two components of UA+ to V A B ~ + ,
(A101
(19) Mori. Y.; Kitagawa, T.; Yamamoto, T.; Yanada, K.; Nagahara, S. Bull Chem. Soc. Jpn. 1980,53, 3492. (20) Sievert, R.; Cadez, I.; Van Doren, J.; Castleman, A. W., Jr. J. Phys. Chem. 1984,88,4502. (21) Tsuchiya, M.; Teshima, S.; Kaneko, T.; Harano, T. J. Chem. Soc. Jpn. 1993, 6, 687. (22) Teshima, S.; Kaneko, T.; Yolcoyama, Y.; Tsuchiya, M. 12th International Mass Spectrometry Conference, Amsterdam. (23) Morgan, R. P.; Beynon, J. H.; Bateman, R. H.; Green, B. N. Int. J. Mass Spectrom. Ion Processes 1978, 28, 171. (24) Kirchner, N. J.; Bowers, M. T. J. Phys. Chem. 1987, 91, 2573. (25) van Koppen, P. A. M.; Kemper, P. R.; Illies, A. J.; Bowers, M. T. Int. J. Mass Spectrom. Ion Processes 1983, 54, 263. (26) Cooks,R.G.;Beynon, J.H.;Caprioli,R. M.;Lester,G. R.Metastable Ions; Elsevier: Amsterdam, 1973. (27) Holmes, J. I.; Osborne, A. D. Inr. J. MassSpectrom. Ion Phys. 1977, 23, 89. (28) Lifshitz, C.; Tzidony, E. Int. J. Mass Spectrom. Ion Phys. 1981,39, 181.
(A1 1) This leads to a kinetic energy peak width in the laboratory frame,
AKEA+=4-
mA+
AB,+
[-(l + mBteV
AB+
'/'
(A12)
where eV is the ion-source acceleration energy of AB*+ (-8000 eV). For a single-step dimer elimination,
Suppose a consecutive elimination of 2B units is mistaken for a single-step elimination of Bz, then
and e'
=e
(A151
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