4310
J . Phys. Chem. 1987,91, 4310-4317
diationless transfer of the excitation photon energies takes place having a much larger diameter than those mentioned above, inless efficiently than for saturated coordination, because the ions creased with decreasing diameter of Ti02. However, such an in high coordination sites have a larger number of bonds to the increase may be ascribed to a morphological and/or a compooxide and couple more strongly with the phonon transitions of the sitional effect on the contact between Pt and TiOz particles, not lattice, providing a high probability for nonradiative d e ~ a y . ~ ~ .from ~ ~ the size quantization effect. Therefore, the smaller the particle size of the catalyst, the higher Although it is well-known that the semiconductor particles lose the efficiency of photoreaction, since, on decreasing the particle their semiconductor properties in their photophysics as they besize, the concentration of unsaturated surface sites such as corners come smaller and ~ m a l l e r this , ~ ~is ~the ~ ~first report to indicate and/or edges increases, and photon energies absorbed by the that the photocatalytic activity of the semiconductor particle is catalyst contribute effectively to the surface reactions. dependent on particle size. Sakata et Tsai et and Harada et aLZ9have reported that yields of the photocatalytic reactions on Pt-loaded TiOz, Acknowledgment. M. Anpo is indebted to Professor A. Henglein of Hahn-Meitner-Institute fur Kernforschung Berlin for drawing his attention to this problem. The authors thank Professor (27) Sakata, T.; Kawai, T.; Hashimoto, K. Chem. Phys. Lett. 1982, 88, 50. T. Minami of the University of Osaka Prefecture for Thermal (28) Tsai, C. C., Chung, Y. W J . Catal. 1984.86, 231 Gravimetric Analysis. Thanks are due to the Ministry of Edu(29) Harada, H.; Ueda, T. Chem. Phys. Lett. 1984, 106, 229. cation of Japan (Grant No. 59470007 and 59550558). The au(30) The authors thank a referee for suggesting a value of a effective mass of TiO:. thors thank referees for their useful comments and suggestion.
~~
Photoionization Mass Spectroscopy with Synchrotron Radiation of Hydrogen-Bonded Alkylamine Clusters Produced in Supersonic Beams Peter G. F. Biding, Eckart Ruhl, Bernhard Brutschy, and Helmut Baumgartel* Institut fur Physikalische und Theoretische Chemie, Freie Universitat Berlin, D- IO00 Berlin 33, FRG (Received: December 1, 1986; In Final Form: April 3, 1987)
Hydrogen-bonded clusters of methyl-, ethyl-, dimethyl-, and diethylamines are synthesized in a seeded supersonic expansion for a mass spectroscopic study. The mass spectra are compared by ionizing either with 21-eV electrons or with photons from dispersed synchrotron radiation. Photoionization efficiency curves are measured to determine threshold energies for the ionization and fragmentation of the clusters. The threshold values yield gas-phase proton affinities, association, and dissociation energies by thermochemical calculations. The derived thermochemical quantities of cluster ions depend on the amount of the association energies of the neutral clusters. The association energy data found in this study are compared with previously calculated values. Lower bounds to the bond dissociation energies of alkylamine cluster ions are presented. The absolute proton affinity values of CH3NH2(930 i 15 kJ/mol), C2H5NH2(940 f 15 kJ/mol), (CH3)2NH(955 f 15 kJ/mol), and (C2H5),NH (965 f 15 kJ/mol) determined in this study are about 30 kJ/mol higher than the currently recommended reference data. The proton affinities of molecular aggregates are determined in order to quantify the first steps of gas-phase proton solvation energetics.
Introduction Among the intermolecular interactions between molecules forming weakly bound molecular complexes in gaseous or condensed phases the hydrogen bonding is of fundamental importance to physical, chemical, and biological processes. Hydrogen bonding between molecules is observed when the region of negative charge due to lone-pair electrons of one molecule attracts the proton of another hydrogen-containing molecule. In condensed matter it is often difficult to isolate the intrinsic effects of the hydrogen bond from other solvent effects.] In the last decade investigations of gas-phase van der Waals and hydrogen-bonded clusters were initiated to overcome this difficulty using the supersonic molecular beam method for cluster production.2 Efficacious concentrations of isolated clusters were obtained in a sufficiently low-density region for experimental investigation by spectral dispersed vacuum ultraviolet light.3 The predominant processes such as ionization and dissociation allow to elucidate the energetics, the structures, and frequently the dynamics of clusters, thus promoting the basic understanding of intermolecular interactions.
A large number of gas-phase equilibrium constant measurements is available giving comprehensive information on the central role of proton-transfer reactions in intermolecular proce~ses.~J The free energy change, AG, associated with proton-exchange reactions defines the relative proton affinity, PA, of a molecule M by the negative of the corresponding enthalpy change, -AH. Rarely, absolute PA's have been measured by appearance energy measurements giving heats of formations of MH' ions derived from photon or electron impact induced molecular fragmentation or ionization. For example, new experimental results reconciled previous attempts to determine the HCO' heat of formation for the absolute PA of CO on the basis of a clear analysis about energy conservation associated with the photofragmentation process.6 The ionization energy of the C(CH3)3 radical was carefully analysed by photoelectron spectroscopy.' Following this study, a value of 871.9 kJ/mol was recommended for the PA of NH3, to which the absolute PA scale is most often related as a standard. The molecular beam photoionization mass spectrometry was used to determine the heat of formation of NH4' based on its AE from
(1) Schuster, P.; Zundel, G.; Sandorfy, C., Eds. The Hydrogen Bond North-Holland: Amsterdam, 1976; Vol. 1-3. (2) Mark, T. D.; Castleman, Jr., A. W. Adu. At. Mol. Phys. 1985, 20,65. (3) Ng, C Y . Adu. Chem. Phys. 1983, 52, 263.
(4) Kebarle, P. Annu. Reu. Phys. Chem. 1911, 28, 445. ( 5 ) Taft, R. W. Prog. Phys. Org. Chem. 1983, 14, 247. (6) Traeger, J. C. In!. J . Mass Spectrom. Ion Processes 1985, 66, 271. (7) Houle, F. A.: Beauchamp, J. L. J . Am. Chem. SOC.1979, 101, 4067.
0022-3654/87/2091-43 lO$Ol.50/0
0 1987 American Chemical Society
The Journal of Physical Chemistry, Vol. 91, No. 14, 1987 4311
Spectra of Hydrogen-Bonded Alkylamine Clusters
DEFLECTOR
McPHERSO lm-N
SG
Figure 1. Experimental setup: SR,synchrotron radiation; SM, spherical mirror coated with osmium; SG, spherical grating (1800 lines/") coated with aluminum and MgF,; LiF, lithium fluoride filter; TM, toroidal mirror coated with gold; w, quartz window coated with sodium salicylate; EG, effusive gas inlet.
an ammonia dimer. This technique yielded the absolute PA(NH3) = 851.9 kJ/mo18 and this novel approach provided additional valuable results on intermolecular bond dissociation energies and proton solvation energies from cluster beams of H 2 0 9 and hydrogen halides.1° In the present study this method is applied to investigate primary and secondary alkylamines. Thereby additional standards are obtained for the absolute PA scale, which is still in doubt above the ammonia value." To minimize problems in establishing a scale of relative PA values by extended sequences of AG determinations it is desirable to know as many reliable local standards over the course of the PA scale as possible. Moreover, measuring the ionization energies of larger aggregates and appearance energies of their protonated fragments enables the energetics of the first solvation steps to be quantified. The experimental evidence of proton-bound dimers stabilized under equilibrium conditions was used to determine molecule-pair proton affinities as found in a collection of data.12 The free energy changes released for the association of proton-bound dimers of alkylamines are known from 1iterature.l3*l4 The results of these two different methods can be compared. Furthermore, theoretical studies can be called in to complement the interpretation; properties of isolated molecules, microclusters, and the related ions in the gas-phase allow quantitative comparisons with recent calculations on their ground-state energetics, equilibrium geometries, and absolute proton affinities.
Experimental Section The molecular beam apparatus is essentially the same as previously described It is adapted to the Berlin electron storage ring for synchrotron radiation BESSY as shown in Figure 1. A spherical mirror (SM) focuses the undispersed synchrotron radiation (SR) onto the entrance slit of the nearnormal-incidence vacuum monochromator (1m-NIM, McPherson (8) Ceyer, S.T.; Tiedemann, P. W.; Mahan, B. W.; Lee, Y. T. J. Chem. Phys. 1979, 70, 14. (9) Ng, C. Y.; Trevor, D. J.; Tiedemann, P. W.; Ceyer, S. T.;Kronebusch, P. L.; Mahan, B. H.; Lee, Y. T. J. Chem. Phys. 1977,67,4235. (10) Tiedemann, P. W.; Anderson, S.L.; Ceyer, S.T.; Hirooka, T.; Ng, C. Y.; Mahan, B. H.; Lee, Y. T. J. Chem. Phys. 1979, 71, 605. (11) Lias, S. G.; Liebman, J. F.; Levin, R. D. J. Phys. Chem. Ref. Data 1984, 13, 695. (1 2) Aue, D. H.; Bowers, M. T. In Gas Phase Zon Chemistry; Bowers, M. T., Ed.; Academic: New York, 1979; Vol. 2, Chapter 9. (13) Yamdagni, R.; Kebarle, P. J. Am. Chem. SOC.1973, 95, 3504. (14) Zielinska, T. J.; Wincel, H. Chem. Phys. Lett. 1974, 25, 354. (1 5) Rademann, K.; Brutschy, B.; Baumgartel, H. Chem. Phys. 1983,80, 129. (16) Ding, A.; Cassidy, R. A.; Cordis, L. S.; Lampe, F. W. J. Chem. Phys. 1985,83, 3426. (1 7) Riihl, E.; Bisling, P.G. F.; Brutschy, B.; Baumggrtel, H.; Chem. Phys. Lett. 1986, 126, 232.
Figure 2. Mass spectra of PrNH,: (A) PIMS of the effusive beam, (B) PIMS of the cluster beam, (C)EIMS of the effusive beam, (D) EIMS of the cluster beam. The vertical intensity scale is fivefold enlarged for m/z >70. The spectra are normalized to their base peaks without regard to the Ar+ peak of the seed gas. The spectra are not corrected for the transmission function of the quadrupole.
225) equipped with a holographically ruled spherical grating (SG; 1800 lines/") of 1 m focal length, coated with aluminum and MgF2. A bandwidth between 1 and 5 A (fwhm) is chosen depending on the photon flux required for measuring the different ion species. A lithium fluoride cutoff filter (LiF) with a thickness of 0.5 mm is inserted to eliminate spectral impurities by second-order and stray light contributions in the wavelength range beyond 1050 A. A gold-coated toroidal mirror (TM) refocuses the dispersed SR onto the cluster beam giving a stigmatic focus with a cross section of 1.5 mm2. Finally, a quartz window (W) coated with sodium salicylate combined with a photomultiplier tube (PMT) monitors the photon flux independently of the photon energy.'* The pulses of the PMT are fed into a preset timer to normalize the photoion count rates. The monochromator usually is scanned with a wavelength increment of 2.0 A. In this stud the absolute wavelength scale is calibrated to better than 0.1 by recording the Ar+ autoionization structure.19 The alkylamine clusters are synthesized in a continuous supersonic nozzle beam. The sample vapors are seeded into argon at partial pressures varying between 200 and 700 mbar and giving total stagnation pressures typically in the range from 1 to 1.5 bar. The distance between the sonic nozzle (75 pm diameter) and the Campargue-type skimmer (500 pm inner diameter) is varied between 5 and 10 mm in order to maximize the individual cluster intensities. The commercial alkylamine samples (BASF, Fluka, Messer-Griesheim, and Merck) are used without further purification. Significant impurities are not observed in the mass spectra. The ions are detected with a modified, commercial quadrupole mass analyser (Balzers QMA 160) mounted coaxially to the cluster beam. The focused SR intersects the molecular beam at about 40 mm downstream of the nozzle. The ion source consists of a three-element ion lens and a repeller plate with a 3 mm diameter aperture for the molecular beam. The repeller is separated from the subsequent electrodes by 6 mm to avoid photoelectrons from metal surfaces and to guarantee optimal pumping efficiency. An acceleration voltage of 20-30 eV is maintained between these electrodes. For measurements with an effusive beam an additional gas inlet (EG) is mounted near the photoionization volume. A deflector directs and focuses the mass-analyzed ions into a paraxially mounted particle multiplier (SEM) connected to the conventional pulse counting equipment. The photoion source can be replaced by a crossed-beam ion source allowing mass analysis by electron impact ionization. The mass scale is carefully calibrated with the mass spectrum of Am+, n = 1-6, cluster ions and the mass peaks are resolved at full width to better than 240:l.
x
Results 1 . Muss Spectra. The photoionization mass spectra (PIMS) and electron impact ionization mass spectra (EIMS) of primary amines RNH2 (R = Me, Et, and n-Pr) and of secondary amines (18) Samson, J. A. R. J. Opt. SOC.Am. 1964,54,6. (19) Hudson, R. D.; Carter, V. L. J. Opt. SOC.Am. 1968,58,227.
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TABLE I: Ionization Energies, IE(M,,) in eV, of Alkylamines and Their Clusters this work M MeNH2 EtNH, Me,NH EtZNH
ref 24 8.97 f 0.02 8.86 f 0.02 8.24 f 0.03 8.01 f 0.01
ref 25 8.95 f 0.02 8.78 f 0.02 8.18 f 0.02 7.99 f 0.02
R2NH (R = Me, Et) are recorded at the wavelength of 600 A, Le., at a photon energy of E = 20.65 eV, and at the electron energy of 21 eV, respectively. These two methods are applied both to an effusive and a supersonic nozzle beam to investigate the differences in the mass spectra due to adiabatic cooling and to cluster formation. The relative ionization yield curves are measured exclusively by photoionization. Figure 2 represents the PIMS (A, B) and EIMS (C, D) of M = n-PrNH2. Some features characteristic for the compounds under investigation should be pointed out. The EIMS and PIMS of M from the effusive nozzle have very similar fragmentation patterns; simple P-bond cleavage provides the base peak at m / z 30.20,21The ion abundances of the PIMS from the supersonic beam (B) are qualitatively comparable to both PI- and EIMS from the effusive nozzle in the overlapping mass range up to the monomer ion at m / z 59. Beyond that additional mass peaks appear, the most abundant of them corresponding to M,H+, n = 1, 2, 3, Le., to protonated clusters. Using the supersonic beam in place of the effusive beam, the abundance of MH+ ions is more than one order of magnitude larger. Thus, these ions are not due to associative ionization or collision-induced ion-molecule reactions, but rather originate from the following intracluster ion-molecule reaction (PrNH2),+,+,
hu
(PrNH2),H+ + PrNH'
+ mPrNH2
8.1 f 0.2 7.8 f 0.2 7.5 f 0.2
8.82 f 0.05 8.22 f 0.05 8.01 f 0.05
. --
Ln
,
7.0
7.5
7.0
7.5
.
. . ..
7.9 f 0.2 7.7 f 0.2
4
/
,
8.0 8.5 9.0 9.5 PHOTON ENERGY / e V
10.0
(1)
The signal of the unprotonated dimer ion M2+ is one order of magnitude smaller than the MH+ signal and 5 times smaller than the M2H+ signal. The EIMS recorded from the cluster beam (D) reveal some important differences relative to the other mass spectra (A, B, and C). The most abundant ion is the monomer ion and there are many fragment ions in the mass range between the monomer and dimer ions. The dotted lines in Figure 2 compare the relative ion abundances of m / z 30 with m / z 59 in the normalized mass spectra as recorded by the four different methods. Firstly, they demonstrate that the monomer signal is enhanced by a factor of 4 in the EIMS from the cluster beam (D) compared to the other mass spectra (A, B, and C). Secondly, the fragment ions occurring at m / z 30 do not change their abundances significantly. The relative ionization or fragmentation cross sections for PI and E1 of the molecules from the effusive beam do not differ substantially as shown in Figure 2, A and C. Thus, the relative increase of the monomer's ion abundance in the EIMS of the cluster beam (D) results from additional fragmentation of larger clusters. Therefore, the fragmentation from larger clusters is considered to be substantially smaller for PI than for EI. Numerous mass spectrometric studies on related properties of ammonia clusters in a supersonic beam using photoionization22 or electron impact ionizationZ3were profoundly discussed.24 2. Photoionization Efficiency Curues. Figure 3a shows the photoion efficiency (PIE) curves of (MeNH2),+ cluster ions and Figure 3b those of the (MeNH2)H,+ cluster ions, n = 1, 2, 3. The ion yields of the unprotonated clusters rise rather slowly above
TABLE II: Appearance Energies, AE(M,H+) in eV, of the Protonated Alkylamines and Their Protonated Clusters according to Reaction 3 M AE(MH+) AE(M,H*) AE(M,H+) 8.55 f 0.10 8.25 f 0.10 8.2 f 0.1 MeNH, 8.5 f 0.1 8.15 f 0.10 8.0 f 0.1 EtNH, 8.1 f 0.1 7.85 f 0.10 7.8 f 0.1 Me,NH 7.75 f 0.1 Et,NH 8.0 f 0.1
(20) Gohlke, R. S.; McLafferty, F.W. Anal. Chem. 1962, 34, 1281. (21) Chupka, W. A.; Berkowitz, J. J . Chem. Phys. 1960, 32, 1546. (22) Cook, K. D.; Taylor, J. W. Int. J . Mass Spectrom. Ion Phys. 1979, 30, 345. (23) Stephan, K.; Futrell, J. H.; Peterson, K. J.; Castleman, Jr., A. W.; Wagner, H. E.; Djuric, N.; Mark, T. D. Int. J . Mass Spectrom. Ion Phys. 1982, 44, 167. (24) Breen, J. J.; Kilgore, K. K.; Stephan, K.; Hofmann-Sievert, R.; Kay, B. D.; Keesee, R. G.; Mark, T. D.; Castleman, Jr.. A. W. Chem. Phys. 1984, 91. 305.
background, making the determination of the ionization threshold uncertain by several 100 meV, whereas the ion yields of the protonated clusters rise steeper but still smoothly with uncertainties < 100 meV. A linear function is fitted by a least-squares fit to the background count rate. A second linear function is found in a semilogarithmic plot of the PIE curve by a least-squares fit to the first ion count rate above background (about 50 points). The intersection of the two fitted lines is defined as the threshold. Its uncertainties are taken as the standard deviations of the individual
8.0 8.5 9.0 9 5 10 0 PHOTON ENERGY / e V Figure 3. Photoionization efficiency curves of (a) the unprotonated MeNH, clusters and (b) the protonated MeNH, clusters.
Spectra of Hydrogen-Bonded Alkylamine Clusters TABLE 111: Fragment Appearance Energies, FE(M,H+) in eV, Deduced from the Curves of the Protonated Alkylamines and Their Clusters according to Reaction 4
M MeNH, EtNH, MezNH Et2NH
FE(MH")
FE(M2H')
FE(M,H+)
8.85 f 0.10 8.75 f 0.10 8.35 f 0.10 8.3 f 0.1
8.5 f 0.1 8.4 f 0.1 8.1 f 0.1 8.0 f 0.1
8.4 f 0.1 8.2 f 0.1 8.0 f 0.1
100
I /
, , '
1arb units
'
1
0
'' , I
0
0 10 100 E-AE/eV
10 0
8.5
Figure 4. Double logarithmic plot of the MeNH3' PIE minus background ion counts vs. photon energy minus AE(MeNH,+).
points to the fit functions. Threshold values thus determined in at least two separate measurements are reproduced within these statistical error limits. The following tables summarize the threshold energies of the alkylamines measured for this study: Table I gives the ionization energies, IE(M,), of the alkylamine clusters M, according to the reaction
WMd
M,+
+ e-,
n = 1, 2, 3
For the monomer the I E s are compared with values from photoionization threshold measurement^^^ and from photoelectron spectroscopy.26 Table I1 gives the appearance energies, AE(M,H+), of the protonated alkylamine clusters M,H+ according to the reaction AEWJ-IH? M,+, M,H+ R' e-, n = 1, 2, 3 (3)
-
+
+
R' is the radical separated after the proton transfer. Table 111 gives the fragment appearance energies, FE(M,H+), according to the reaction M,+2
l o o t a'
1
ICH3Nti2IH'
0 01
M,
4313
I
-
I - I,
The Journal of Physical Chemistry, Vol. 91, No. 16, 1987
FE(MP+)
M,H+
+ M + R' + e-,
n = 1 , 2 , 3 (4)
The fragmentation reaction (4) contributes to the M,H+ yield and is superposed on the PIE curves of the proton transfer (3). However, the FE values are shifted to higher energies compared to the AE values by the amount of the bond dissociation energy of M in the neutral precursor M,+2. As an example, the ion yield curve of MeNH3+is depicted in Figure 4. The double logarithmic plot of the PIE curve minus background count rate vs. photon energy minus AE reveals the superposition of two straight lines. The second onset is interpreted as the threshold for the fragmentation process (4), and the intersection of the two lines found by least-squares fits gives the corresponding FE value.* An alternative explanation for this biexponential behavior by hot bands is less likely, because the molecules are expected to be very cold and the hot band region should be much smaller. The reliability of the threshold measurements is checked by further tests. One of the most instructive tests is the variation of the total stagnation pressure, which influences the size distribution of the neutral clusters and their final temperature. For example, in the case of van der Waals clusters such as argon dimers with weak association energies of about 1 kJ/m01,~' no apparent shift of IE(Ar2) and IE(Ar3) with increasing nozzle stagnation pressure was observed; it was the shape of the PIE curve (25) Watanabe, K.; Nakayama, T.; Mottl, J. J. Quant. Spectrosc. Radiat. Transfer. 1962, 2, 369. (26) Takahashi, M.; Watanabe, I.; Ikeda, S.J . Electron Spectrosc. Relar. Phenom. 1985, 37, 275. (27) Aziz, R. A,; Chen, H. H. J . Chem. Phys. 1977.67, 5719.
9.0 95 10.0 10.5 PHOTON ENERGY l e v Figure 5. D(E)of the PIE curves of (a) MeNH,' and (b) MeNH,'.
that changed dramatically.28 Significant contributions from dissociative ionization of Ar,, n > 2 or n > 3, falsified the photoionization cross sections of Ar2 and Ar3, if the photon energy exceeded the threshold by an energy equal to association energies of additional molecules in the larger clusters. As a function of merit, the difference D ( E ) between the normalized PIE curves of the monomer from the cluster beam I,@) and from the effusive beam 12(E)is determined by the equation
W E ) = [ I , ( E )- I2(E)I/[Il(E) + I2(E)1
(5)
The normalization cannot easily be accomplished because of different target gas densities in the ionization volume and different transmission functions of the mass spectrometer during the two measurements. Determining the integrals of the recorded PIE curves for an equal energy range yields an approximate normalization factor for the PIE curves. The resulting normalized curves I , @ ) and Z2(E) are substituted into eq 5. It should be noted that, if any differences between the PIE curves occur, then D(E) indicates only the energy values where fragmentation sets in. The amount of fragmentation is given arbitrarily, because the normalization works only approximately in this case. D ( E ) reaches unity or 100% for only I , contributions and -100% for only I , contributions. Figure 5a shows D(E)of MeNH,' in the energy range between 9.0 and 10.3 eV. The signal-to-noise ratio near threshold is intrinsically poor as shown by the error bars. Hot molecular ions with a thermal energy distribution from the effusive beam contribute to the PIE curve Z2(E)in the post threshold region between 9 and 9.15 eV.29 Applying different fit functions upward from 9.2 eV, values of D ( E ) = 0% f 1% are calculated for the investigated energy range. This gives strong evidence that the PIE curve of the monomer is not affected by fragmentation in the threshold region under the present experimental conditions. The result for the protonated monomer ions generated at two different stagnation conditions of the expansion is shown in the Figure 5b. Here the PIE curve of MeNH3+from a cluster beam seeded in Ar is designated as Z,(E) and that recorded from the expansion of the pure sample gas as Z2(E). In this case D(E) demonstrates likewise that the PIE curves in the onset regions are independent of the currently used cluster source conditions, Le., the stagnation pressure and the nature of the seed gas. From the above result may follow that reaction 3 is the distinctive feature of the dimer precursors in the threshold region and the larger clusters in the supersonic beam do not influence the IE(M) and AE(MH+) values by fragmentation. The poor count rate statistics of the dimer and trimer ions inhibit this pressure dependences measurements of the PIE curves. (28) Dehmer, P. M.; Pratt, S . T. J . Chem. Phys. 1982, 76, 843. (29) Guyon, P. M.; Berkowitz, J. J . Chem. Phys. 1971, 54, 1814.
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Bisling et al.
TABLE I V Association Energies, AE(M,) in kJ/mol, for Alkylamine Clusters‘ M MeNH2 EtNH, Me,NH Et,NH
AE(M*) 15.68 (14) 17 (15) 14 (13) 15 (14)
AE(M1) 43.10 46 39 42
AE(MJ 70.8 1 75 65 69
A.EG(Mq) 5 0 f 10 4 0 f 10 40 10 40f IO
A.E,(Md) 7 0 f IO 70f IO 6 0 * 10 7 0 f 10
*
AE.(Mc) 90f IO 8 0 f 10 80 f 10
“The AE(M,) values of M = (MeNH,),, n = 2, 3, 4, were c a l c ~ l a t e d . ~The ’ AE(M,) values in parentheses result from second virial coefficient measurements.” All other AE data are extrapolated values. Semiempirical association energies, AES(Mn+Jin kJ/mol, for alkylamine clusters are calculated by eq 7
[ FEIM,H+)
i M+mM
= 8 85 t 0 10)
i- _ _ _ _ iM 3 + (m-2)M
dE,IM,+21
M,,
-
+
,
8 4 ~ 0 e1 V
85201
lm-3)M
M5+lm-4)M
= 05
[‘-:2:i”a-i”’”
A_--I
-1-
M*mM
AEIM,)
t, n+ , ~
0 16
Figure 7. Energy diagram of the M,+ = (MeNH2)n+cluster system, n = 1, 2, 3.
is estimated to be better than 10 kJ/mol. The ground-state bond dissociation energies of the neutral clusters, D(M,-,-M), defined as D(M,I-M) = AE(M,) - AE(Mn_l), n = 2, 3, 4 (7) result from the threshold measurements of protonated cluster ions as illustrated in Figure 6. Starting with AE(M2) of Table IV Mn+2),is the row of semiempirical association energies, Us( calculated from the threshold data (Tables I1 and 111) by n+ 1
AEs(Mn+2) = AE(M2)
+ r=2 CD(M,-M)
(8)
n
= AE(M2)
(30) Shinohara, H.; Nishi, N.; Washida, N. J . Chem. Phys. 1985, 83, 1939. (31) Echt, 0.;Dao, P. D.; Morgan, S.; Castleman, Jr., A. W. J . Chem. Phvs. - , 1985. 82. 4016. (32) Brinklb.;Glasser, L. J . Mol. Struct. 1981, 85, 317. (33) Odutola, J. A.; Viswanathan, R.; Dyke, T. D. J . Am. Chem. Soc. 1979.,~ 101. ~.4787. (34) Lambert, J. D.; Strong, E. D. T. Proc. R. Soc. London A 1950, 200, ~~~
~
+ rC[FE(M,H+) - AE(M,H+)], =l
= 1, 2, ...
These semiempirical association energies for the alkylamines are summarized in Table IV; they agree within 10 kJ/mol with the extrapolated values. Possibly, this reflects an inductive effect of the alkyl groups. In particular it confirms the structure concepts based on the EPEN computation and the measured polarity of the amine clusters. Obviously, the calculation of the association energies in terms of the number of hydrogen bonds in a complex differs for a linear and a cyclic cluster of the same size by the binding energy of one bond. Thus, assuming linear structures for the amine trimers and tetramers, the calculation of the association energies differs by more than 20 kJ/mol with the extrapolated AE(M,) values. This disagreement supports the conceptions of cyclic trimers and tetramers. In the following these 4E(Mn)values are used for the further thermochemical calculations. 2. Intermolecular Bond Dissociation Energies of Ionic Clusters. The ionization of an amine with C, symmetry in its singlet electronic ground-state ]A’ by removing an electron from the nonbonding 2p lone-pair orbital localized on the nitrogen atom ends up in a molecular amine cation of C, symmetry in the *A‘ ground state. The N-H distance increases from 1.03 to 1.05 A and the C-N-H angle increases from 119.1’ to 177.5O in MeNH2 upon ionization so that MeNH,’ has a nitrogen open to nearly planar geometry similar to the ammonia cation.34 This considerable change in the equilibrium geometry of the monomer may have a drastic influence on the N-H-N bonds upon ionization of the amine clusters. Furthermore, if a nonbonding electron is removed from the proton-donor site of the dimer, the dimer ion relaxes by proton transfer to the acceptor site thereby shortening the intermolecular d i ~ t a n c e . ) ~The Franck-Condon factor for an adiabatic transition thus will be very small. This explains the
566.
(35) Lathan, W. A,; Curtis, L. A,; Hehre, W. J.; Lisle, J. B.; Pople, J. A. Prog. Phys. Org. Chem. 1974, 11, 175.
(36) Tomoda, S.; Kimura, K. Chem. Phys. Lett. 1984, 111, 434.
TABLE V: Bond Dissociation Energies, D(M,,+-M), n = 1, 2, in kJ/mol, of the Alkylamines Cluster Ions from Threshold Measurements Calculated from Eq 9 M D(ivl+-M) D(M 2+-M) MeNH, 100 f 20 50 f 20 EtNH, 90 f 20 50 f 20 Me2NH 50 f 20 35 A 20 Et2NH 60 f 20
smooth increase of the ion yield of the unprotonated clusters (Figure 3a). Using the measured ionization energies (Table I) and the corresponding association energies (Table IV), the bond dissociation energies, D(MW1+-M), of the ionic ground state according to the reactions
-
+
M,+ M M,-l+, can be calculated by means of eq 7 D(M,I+-M)
n = 2, 3
= IE(MW1) - IE(M,)
+ D(M,_l-M)
(9)
(10)
As an example Figure 7 shows the energetics for the methylamine cluster system. Table V lists the corresponding data for all alkylamines studied. In order to predict the temperature effects on derived thermochemical values, the temperature of the clusters beam must be known. The translational temperature is related to the stagnation parameters of the molecular beam source and the ratios of heat capacities of the sample gas at constant pressure and at constant volume.37 The terminal translational temperature ( Tt) is estimated to be lower than 100 k.The vibrational and rotational temperature distribution encountered in the nonequilibrium environment of the cluster beam is difficult to elucidate. For a crude estimate of the temperature influences, Kirchhoff s law is applied. The enthalpy change AHt for reaction 9 is related to the enthalpy change AH, at 0 K by
AHo = AHt - LT'[Cp(M) + C,(M,,+)
F+z-T
The Journal of Physical Chemistry, Vol. 91, No. 16, 1987 4315
Spectra of Hydrogen-Bonded Alkylamine Clusters
- C,(M,+)] d T (1 1)
with Tt = 100 K as an upper value for the beam temperature, the integrated Cp(M) values amount to about 2 and 3 kJ/mol for MeNH238and Me2NH,39respectively. This small contribution may be expected to be in the same order of magnitude as the difference of the other integrated C p contributions in eq 11. Therefore, the derived values appear to be related to 0 K. Thus, the common practice of discussing the derived values in terms of bond dissociation energies instead of, strictly speaking, bond dissociation enthalpies is adopted for the present. A comparison of the bond dissociation energies for neutral and ionic clusters shows characteristic differences. In order to describe the energetic stabilization of the neutral clusters per additional molecule, the dependence of the bond dissociation energy on the cluster size is examined by using the data based on the EPEN calculation (Table IV) by means of eq 7 . The deduced values are increasing with the cluster size and converging to an average, upper limit of D(M,,-M) = 30 f 3 kJ/mol. This clearly demonstrates the nonadditivity for the energetic stabilization already for the first association steps.40 On the other hand, the bond dissociation energies of the ionic clusters, D(M,-l+-M), show considerably increased stability (Table V) reflecting the influence of additional ion/dipole and resonance interaction. The D(M,,+-M) values are obviously decreasing per additional bond, the ratios D(M+-M)/D(M,+-M) being 2 for primary and 1.4 for secondary amines. A convergence of the D(MnyI+-M)values to the corresponding D(M,-,-M) values may be expected for the larger clusters. (37) Anderson, J. B.; Fenn, J. B. Phys. Fluids 1964, 8 , 780. (38) Aston, J. G.; Siller, C. W.; Messerly, G. H. J . Am. Chem. SOC.1937, 59, 1743. (39) Aston, J. G.;Eidinoff, M. L.; Forster, W. S . J . Am. Chem. Soc. 1939, 61, 1539. (40) Beyer, A.; Karpfen, A.; Schuster, P. In Hydrogen Bonds; Schuster, P., Ed.; Top. Curr. Chem. Ser. Springer-Verlag: Berlin, 1984; Vol. 120, p 1.
PSlnMI= 9 6 2 0 2 R, = 13 598 e V
1
1 0 6 t O 2 eV
102t02
M3H'+R+im-31M
DIN-HI ;=H: 4R4 4 ? 0 10 e V
M3 + lm-2iM
AE(M,,~I
ML + lm-31M
= 0 16
Figure 8. Energy diagram of the M,H+ = (MeNH2),H+ cluster system, n = 1, 2, 3.
A comparison of the experimental value of D(Mwlf-M) with the theoretical values found by optimizing the ionic stabilization energies and based on assumed structures confirms the assignments of the structures. An ab initio calculation of the equilibrium geometry of the ammonia dimer cation optimized the ,A' ground state as a complex between the NH4+ammonium ion and the NH2 aminyl radical and strongly suggested negligible small FranckCondon factors for an adiabatic transition to the equilibrium geometry of the dimer cation.41 It is reasonable to assign the H4N+-.NH2 structure to the ionic amine dimers as well. Furthermore, this considerable change in equilibrium geometry explains the discrepancies in D(M+-M) values evaluated from calculations and experimental threshold determinations. Thus, the calculated bond dissociation energy is D(H4N+-NH2) = 160 f 20 kJ/mol for the ionic ground state. This is about 60 and 100 kJ/mol larger than the results deduced from threshold values for primary and secondary amines, respectively (Table V). Certainly, the photoionization values yield only lower bounds to D(MWI+-M). 3. Absolute Profon Affinities. Analogous to the definition of the absolute proton affinity, PA, which is the negative of the enthalpy change for the reaction M + H+ MH', it is possible to define the proton affinity of clusters PA(M,). The appearance energies AE(M,H+) from reaction 3 together with reactions 12 and 13
-
M
-+ D(N-H)
R'
H
Rc
R'
+ H+ + e-
(13) enable the calculation of PA(M,) by thermodynamic cycles using
The negative of the overall enthalpy change of reaction 14 is the proton solvation energy PS(nM) for n molecules, which is related to the PA(M,) by -AHt = PS(nM) = PA(M,)
+ AE(M,),
n = 2, 3 (15)
The energy diagram of the protonated MeNH2 cluster system in Figure 8 illustrates the thermochemical cycles, which relate the threshold data of Table I1 to the additional thermochemical information necessary for the evaluation. The association energies for the reaction 12 are found in Table IV and the N-H bond dissociation energies, D(N-H), for reaction 13 are taken from literature data4, together with the Rydberg constant, R,. The D(N-H) values for MeNH, and Me2NH are 428 f 10 kJ/mol and 41 1 f 10 kJ/mol, re~pectively.~~ According to the additivity rules for the estimation of thermochemical properties, D(N-H) is not influenced on alkyl substitution of the methyl groups.43 Then, the absolute PS(nM) values are evaluated by (41) Tomoda, S.;Kimura, K. Chem. Phys. Lett. 1985, 121, 159. (42) Batt, L.; Robinson, G. N. In Chemistry ofFunctional Groups; Patai, S . , Ed.; Wiley: Chichester, U.K., 1982; Suppl. F, p 1035. (43) Benson, S . W.; Cruickshank, F. R.; Golden, D. M.; Haugen, G. R.; O'Neal, H. E.; Rodgers, A. S.;Shaw, R.; Walsh, R. Chem. Rev. 1969, 69, 279.
4316 The Journal of Physical Chemistry, Vol. 91, No. 16, 1987 PS(nM) = D(N-H)
+ R, + AE(M,+,) - AE(M,H+),
PA(M,) = D(N-H)
+ R, + D(M,-M)
n= 2, 3 (16) The absolute PA(M,) follows from eq 15 by applying eq 7 - AE(M,H+), n = 1, 2, 3 (17)
The PA values deduced from the measurements of appearance energies are reliable, if the thermochemical thresholds are obtained, as discussed for protonated cluster fragments by Lee and coworkers.1° Complying with this condition, firstly the stable precursor ions M h l + are observed for ionization energies IE(Mn+J below the appearance energies AE(M,H+) (Table I and 11) for the dissociative reaction M,+l+ -.+ M,H+ + R', and secondly the reverse reaction has a negligible activation barrier compared with the forward reaction. The latter is implied at least in the case of the cationic dimers as discussed above on the basis of the intermolecular structure.41 The present results of PA(M,) and PS(nM) are shown in Tables VI and VII, respectively. They are compared on the one side with the most recently NBS recommended compilation for the monomer PA data" and on the other side with molecule-pair proton affinity (MPPA) valuesI2 for the PS(2M) data, both determined in equilibrium measurements. In order to compare the PA values obtained in this work at the nonequilibrium temperature TI with values obtained by ion-molecule reactions at equilibrium, it is necessary to convert the former to the standard temperature of 298 K by PA(M) = -AH, -
s
298
ACp d T
Tt
Biding et a]. TABLE VI: Absolute Proton Affinity Values, PA(M,) in kJ/mol, Obtained for Alkylamines and Small Clusters Calculated from Eq 17 this work M ref 11, PA PA(M) PA(M,) PA(M,) MeNHz 896 930 i 15 970 f 15 975 f 15 EtNH, 908 940 i 15 980 15 -995 f 15 990 f 15 995 iz 15 Me2NH 923 955 f 15 Et2NH 945 965 i 15 1000 f 15
*
TABLE VII: Absolute Proton Solvation Energies, PS(nM) in kJ/mol, of Alkylamines Calculated according to Eq 16 and Compared with MPPA Datal2 M MeNH, EtNH, Me,NH Et,NH
(19) If M and M H + possess the same number of rotational degrees of freedom and if vibrational and electronic contributions to the difference Cp(MH+) - Cp(M) are neglected, then the last term in (18) reduces to the small H+ contribution of 3R(298 K - Tt)/2, where R is the gas constant. However, this assumption may fail for n = 2, 3. A clear trend of the molecular PA values can be seen in Table VI: The present absolute PA values for MeNH,, EtNH2, Me2NH, and Et2NH are found to be on the average 30 kJ/mol higher than the NBS recommended values. This deviation is outside of the error limits. The absolute PA values of the NBS compilation in the region of the PA scale above ammonia (PA > 850 kJ/mol) seem not to be reliable for want of reliable absolute standards. Throughout the NBS scale, absolute values derived from equilibrium constant measurements should be taken for granted only when AG is
