J . Phys. Chem. 1985,89, 1499-1504 mention two representative values. These values yield relaxation times of 25-60 ns for 1.6 torr of CDF3, which compared with a total pulse length of about 6 ns means that 10-20% of the molecules have changed their rotational states during the pulse. For the long pulse, with a total duration of 300 ns and pressure of 0.065 torr, 2 0 4 0 % of the molecules are affected during the pulse. Also, considering the above relaxation times in the experimental results with 500 torr of Ar (short pulse) and 20 torr as Ar (long pulse), the rotational relaxation of CDF, should be complete and hence the need of fractionation has to vanish. This is what the calculations show; i.e., the simple master equation approach satisfactorily reproduces the experimental results. Calculations with the simple master equation then imply that all the molecules are in resonance with the radiation, or, stated in other words, all the limitations imposed by rotational fractionation and anharmonicity are relaxed or not important, which in fact is equivalent to take J;. = 1 and X5,= 0. The effect of collision is also important in the analysis of the wavelength dependence of uL($). These data were obtained with a 6 ns fwhm pulse a t a pressure of 5.5 torr of CDF,, so that collisions should be important, mainly at those wavelengths in which the fraction of active molecules is low, i.e., in the low absorption cross-section region. The calculated uL($) are also lower than the experimental, and this is also indicative of the effect of collisions. Notwithstanding, the general shape of the v5 band
1499
is well reproduced. In conclusion, the main finding of this work, along with the effect and introduction of anharmonicity in the master equation, is the predictive power of this approach. To our knowledge, no previous work has analyzed data obtained under such different conditions as are available for CDF3, as to provide such a test of the use of the master equation. Even though only more fundamental experiments might achieve a better understanding of multiphoton processes, most of the information presently available rely on bulk data, such as reaction probabilities and absorption cross sections, analyzed with the master equation formulation. We have shown that this method is reliable for small molecules only when essential properties controlling absorption, such as rotational fractionation and anharmonicity, are explicitly considered and that the calculated results, based on a rather restricted set of experimental conditions, can be successfully extended. This includes different pulse length, wavelength, and also pressure effects. The application of the method to obtain rotational relaxation rates seems possible, and efforts in this direction are presently being made in this laboratory.
Acknowledgyent. We thank the Consejo Nacional de Investigaciones Cientificas y T h i c a s (CONICET) for partial financial support. Registry No. CDF3, 558-22-5.
Generation of All Homo- and Heteronuclear Alkali Dimers in Supersonic Nozzle Beams. Ionization Potential Measurements Manfred M. Kappes, Martin Schar, and Ernst Schumacher* Institute for Inorganic and Physical Chemistry, University of Bern, CH- 301 2 Bern, Switzerland (Received: September 12, 1984)
Ionization potentials were determined for 11 alkali dimers. All species were generated in supersonic molecular beams and probed by photoionizationm a s spectroscopy. Most molecules were produced via adiabatic expansions out of an oven containing sodium metal and one or more alkali chlorides. The data set together with previous measurements allows for a comprehensive characterization of the 15 alkali dimers. Of particular interest are differences in dissociation energy between neutral and ionic ground states. Photoionization efficiency curves beyond ionization threshold were obtained for several molecules. These measurements allow insight into photodissociation processes, in particular for LiK.
Introduction Ligand-free metal clusters have recently become the focus of a great deal of attention.’ Their importance to many areas of physics and chemistry is well-known. The simplest metal clusters in terms of their bonding, theoretical tractability, and ease of preparation are alkali molecules. While interesting in themselves, they can serve as model systems for the more complicated transition-metal clusters. In the past, this laboratory has been involved in particle-specific studies of many of the aspects of alkali clusters. Homonuclear clusters of up to 65 sodium atoms have been generated in molecular beam^.^,^ Various heteronuclear clusters were also produced, particularly of sodium and pota~sium.~ All molecules were detected via photoionization mass spectroscopy, and usually an ionization potential was determined. In some cases data were obtained on rovibronic energy levels via laser spectroscopic studies. (1)
See Ber. Bunsenges. Phys. Chem. 1984, 3 for a representative com-
pendium of ongoing experimental and theoretical research efforts in the field of metal clusters. (2) Kappes, M.;Kunz, R.; Schumacher, E. Chem. Phys. Lett. 1982, 91, dl 3
(3) Herrmann, A.; Schumacher, E.; Woste, L. J. Chem. Phys. 1978, 68, 2327.
0022-3654/85/2089-1499$01,50/0
Resonant two-photon ionization (R2PI) measurements resulted in the first observation of autoionizing Rydberg series for Na2, Kzand NaK.4” R2PI was also used to characterize five new singlet states in LiNa as well as to study Na3.’v8 In this paper we present ionization potential determinations for 11 alkali dimers, several of which had not been observed previously. All were generated in supersonic expansions. Two were formed by coexpansion of alkali metal vapor^.^ All others were generated by adiabatic expansion from a high-temperature oven containing alkali metal and alkali chloride vapor. This turns out to be a generally applicable method for the production of mixed alkali dimers (and larger mixed alkali species) in a supersonic molecular beam. Interesting byproducts of these expansions were neutral dimer chlorides (MM’Cl). A comprehensive study of this class (4) Leutwyler, S.; Heinis, T.; Jungen, M.; HBrri, H.-P. Schumacher, E. J . Chem. Phys. 1982, 76,4920. (5) Leutwyler, S.; Herrmann, A.; Whte, L.; Schumacher, E. Chem. Phys.
--. (6) Leutwyler, S.; Hofmann, M.; HBrri, H.; Schumacher, E. Chem. Phys.
1980. 48. --, 253.
Lett. 1981, 77, 257. (7) Kappes, M.; Marti, K.; Radi, P.; Schir, M.; Schumacher, E. Chem. Phys. Leti.-1984, 107, 6. (8) Herrmann, A.; Hofmann, M.; Leutwyler, S.; Schumacher, E.; WBste, L. Chem. Phys. Lett. 1979, 62, 216. (9) Dagdigian, P.; Wharton, L. J. Chem. Phys. 1972, 57, 1487.
0 1985 American Chemical Society
1500 The Journal of Physical Chemistry, Vol. 89, No. 8, I985
of molecule will be. presented in a future publication.1° Several alkali dimers could be generated in sufficient amounts to allow for measurement of low-resolution photoionization efficiency curves. These data were obtained for LiNa, LiK, NaRb, and NaCs. The LiK measurements indicate appreciable photodissociation above threshold. Together with previous measurements for Liz, Na,, NaK, and Kz, the data from this study allow for a complete I P characterization of the 15 alkali dimers. There have recently been significant advances in quantum chemical calculations on simple A number of predictions have been made systems of this regarding the ionization potentials of the lighter alkali dimers."J2 These predictions are in excellent agreement with our measurements.
Experimental Section Metal molecules were generated by supersonic expansions from cartridges containing alkali metal vapors (and alkali chloride vapors). The resulting molecular beams were probed 50 cm from the source by crossing them with UV radiation from a 1-kW Xe/Hg arc lamp within the ion source of a quadrupole mass spectrometer, perpendicular to both molecular and light beams. Table I lists the molecules characterized, together with the type of expansions used to generate them. Mixed lithium/scdium and lithium/potassium molecules resulted from coexpansions of the two respective alkali vapors. All other molecules were formed in mixed expansions from cartridges containing one or more alkali metals with one or more alkali chlorides. Clusters were produced by using a high-temperature source and beam machine which has been previously de~cribed.~ Oven temperatures of between 700 and 750 "C were necessary to obtain adequate fluxes of the desired molecules. Experiments requiring lithium metal were done by using cartridges that were welded shut to circumvent corrosion problems due to lithium vapor. All other measurements were performed with cartridges sealed with chrome-plated copper gaskets. Beam clogging was never observed throughout the series of experiments with alkali chlorides. This is unusual for high-temperature nozzle beams involving metal vapors (and the associated contaminants). Alkali halides may act as a flux preventing buildup of oxides and other refractory contaminants in the nozzle channel. Beam intensity was monitored with a surface ionization detector. During the course of an experiment slow changes in beam intensity were observed (at constant oven temperature). Similarly, slow changes in beam composition also occurred. These variations were taken into account in ionization potential measurements (via null measurements at appropriate intervals). Ionization thresholds were determined in two modes. Both used a 1-kW Xe/Hg arc lamp. For small signals (ion currents at the detector with 1-kW Xe/Hg A) the full output of the lamp was used together with a set of UV cutoff filters. This resulted in a rough bracketing of the appearance potentials (f0.1 eV). In the case of larger signals a monochromator was placed between the lamp and the molecular beam machine. It was then possible to continuously scan ionizing wavelength, resulting in photoionization efficiency curves with much higher resolution (20 nm) and in I P S with typical uncertainties of f0.04 eV. Deconvolution of data to yield ionization potentials is described below. Chemicals used were from commercial sources. All alkali chlorides (KCI, RbCI, and CsCI) were of spectral purity. At a typical oven temperature of 750 OC, chloride vapor pressures were roughly KCI 0.2 torr, RbClO.2 torr, and CsCl0.5 torr.I4 In each case, this is less than 1% of the sodium vapor pressure at that oven temperature (260 torr). (10) Kappes, M.; Radi, P.; SchPr, M.; Schumacher, E. Chem. Phys. Lerr. 1985, 113, 243.
(1 1) v. Szentpaly, L.; Fuentealba, P.; Preuss, H.; Stoll, H. Chem. Phys.
Leu. 1982, 93, 555. (12) Milller, W.; Meyer, W. J. Chem. Phys. 1984, 80, 3311. (13) Stevens, W.; Konowalow, D.; Ratcliff, L. J . Chem. Phys. 1984, 80, 1215. (14) Landolt-Bbmstein. 'Zahlenwerte und Funktionen"; Springer-Verlag: West Berlin, 1960; Band 11, Teil 2, Bandteil a.
Kappes et al.
I
I
I
1
320
300
280
I
260
210
223
Wovelengti-
jrnl
01
C
'?
-0
9
wl
1
3CO
326
I
210
260
280
1
220
Wove:ength
:nT]
I
I
I
I
I
I
1
I
320
300
280
260
210
220
Wove~engh
Inn]
Figure 1. Photoionization efficiency curvesfor LiNa (a), NaRb (b), and NaCs (c). These data can be deconvoluted as described in the text to yield the vertical ionization potentials listed in Table I. The resulting computer fits (smooth lines) are shown in each case.
Wavelength [nrnj
Figure 2. Photoionization efficiency curve for LiK. The measured data (a) is again plotted together with the computer fit (b). Agreement with the fit is poor above threshold. This is indicative of a secondary process, perhaps formation of an ion pair.
The experimental setup used for two-photon ionization studies on Na, and NaCs has been previously described? One-color R2PI experiments were done using an excimer-pumped pulsed dye laser. For two-color RZPI studies we made use of a C W laser system consisting of an Ar+-pumped DCM dye laser and a separate Arf
Homo- and Heteronuclear Alkali Dimers
TABLE I: Vertical Ionization Potentials. Comparison with Theoretical Predictions and Previous Experimental Determinations' molecule IP (meas) IP (theor) IP (prev) expansion LiNa 5.05 (4) 5.001: 5.000d 4.94 (IO)' E18 Li/Na LiK LiRb
4.57 (6) 4.3 ( 1 )
4.502,* 4.496d 4.69 (10)' EIS
LiCs
4.1 (1)
4.20d
NaRb NaCs KRb
4.32 (6) 4.05 (6) 3.9 (1)
4.341d 3.92d 3.97d
KCs
3.9 (1)
3.79d
Rb2 RbCs
3.9 (1) 3.7 (1)
3.92d 3.766
cs2
3.7 (1)
3.59d
Li/K Li/Na/ RbCl Li/Na/ CSCl Na/RbCl Na/CsCl Na/KCl/ RbCl Na/KC1/ CSCl 3.44 5 IP 5 3.9Y Na/RbCl Na/RbCl/ CSCl 3.59 5 IP 5 3.82' Na/CsCl
a Ionization potentials in eV. Experimental uncertainties in the last figure(s) are given in parentheses. Reference 12. cReference 32. dReference 11. CReference 25. fBased on calculations for De(X22 RbCs+) (ref 1 l ) , and measurements of D,(X'Z RbCs) (ref 33). SEI = electron impact ionization.
laser. Details are described below.
Results (a) Data. Figures 1 and 2 present the photoionization efficiency curves obtained in these measurements, together with the respective computer fit used to obtain the ionization potential. Peaks and minima in the raw data generally correspond to band structure in the lamp spectrum. The cutoff filter data are not given in detail. The filters used had high-frequency cutoffs centered at 230,214, 280, 299, 302, 305,320,335,345, 360,310, and 315 nm. Measurement of an ion signal with filter was always followed by a determination without, so as to take neutral cluster intensity variations into account. Vertical ionization potentials resulting from these data are given in Table I together with error bars and previous experimental determinations where available. A selection of recent theoretical predictions is also listed. Very accurate ionization potential determinations have been published for Lib Na2, NaK, and K2$,1s-18 These numbers were obtained by laser two-photon ionization (R2PI) or optical double-resonance techniques, and we make use of them together with our new determinations in Table 11, which provides a summary of ground-state spectroscopic data for alkali dimers. (b)Deconuolution. Appearance potentials were obtained from the experimental data by one of two deconvolution procedures. Short wavelength cutoff filter measurements can be interpreted to a first approximation in terms of upper and lower bounds to the IP. A more accurate determination can be achieved by using a computerized deconvolution procedure. Here, one unknown quantity and one unknown functional are taken into account: the position of the onset of ionization and the functional dependence of ionization probability upon radiation frequency beyond threshold. The computer fit assumes a step function for the ionization threshold and beyond. Ratios of ion signal with filter to ion signal without were obtained experimentally for a series of cutoff filters with well-characterized transmission function. These numbers are compared to the ratio of integrated light intensity (times step function) with and without cutoff filters. Integrals are calculated for an array of different step locations. The optimum threshold value is determined via a least-squares (IS) Bernheim, R.; Gold, L; Tipton, T. J. Chem. Phys. 1983, 78, 3635. (16) Eisel, D.; Demtrbder, W.; Miiller, W.; Botschwina P. Chem. Phys. 1983, 80, 329.
(17) Broyer, M.; Chevaleyre, J.; Delacretaz, G.; Martin, S.; Woste, L. Chem. Phys. Left. 1983, 99, 206. (18) Martin, S.; Chevaleyre, J.; Valignat, S.; Perrot, J.; Broyer, M.; Cabaud, B.; Hoareau, A. Chem. Phys. Lett. 1982,87, 235.
The Journal of Physical Chemistry, Vol. 89, No. 8, 1985 1501 error minimization routine. As a rule determinations of ionization potentials with this method are good to within 0.1 eV. Deviations of ionization probability above threshold from a step function will be discussed in more detail below. The deconvolution of monochromator measurements is more ~omplicated.~ For the threshold region we assume that ionization probability can be expressed as a step function with PIE(X) = 0 X > XIp PIE(X) = 0.5 PIE(X) = 1
X =
X
Alp
X1p
where XIp corresponds to the ionization threshold. Deconvolution is based on the following considerations. The wavelength-dependent radiation density of the lamp, L(X),must be multiplied by the unit step function so as to obtain the number of photons (with energy hc/X) emitted between X and X dX that are capable of ionizing the molecule: Fx(X) = L(X)PIEx(X)
+
This term represents a photon flux, F(X), which must in turn be convoluted with the slit function of the monochromator, M ( X , A), to give the ion current for the molecule of interest (M,) at XO
Cx+(Xo) = KJ:Fx(X)M(Xo - A) dh
where K comprises all the wavelength-independent apparatus functions. Analysis of experimentally derived ion currents proceeds as follows. The slit function is first obtained by measuring the ion current of a particle with a well-known ionization potential-usually an atomic species or dimer with a fully analyzed Rydberg spectrum. By use of these data, the slit function can be calculated via discrete Fourier transformation with 1-nm increments, deconvolution in Fourier space (a simple division), and the inverse transform:
Convoluting the slit function and photon flux for different ionization potentials, i.e., locations of the step, gives an approximate reconstruction of the ion current. The optimum fit is arrived at as follows: convolution for a specific threshold is carried out in Fourier space via a simple multiplication; the numbers obtained are converted back to real space where a least-squares minimization takes place.
Variation of Alp in F,(X) lead to an optimum (least-squares minimized) simulation of the measured ion current and thus to the ionization potential of the particle of interest. Only the region near threshold is important for this evaluation. Fits were never carried further than the first maximum (beyond threshold) in the photoionization efficiency curve. In the postthreshold region, comparison between simulated (constant ionization efficiency) and measured curves can afford further information about ion dissociation and fragmentation, as will be discussed below for the case of LIK. Discussion (a) Ionization. The mechanics of how we convert our data into ionization potentials has been described above. The underlying assumption, namely that ionization probability can be described as a unit step function near threshold, needs to be elaborated on. It is well-known that two distinct processes can lead to the production of ions in energy regions close to (above) the onset of photoionization: autoionization and continuum i0nizati0n.l~ (19) Berkowitz, J. "Photoabsorption, Photoionization and Photoelectron Spectroscopy"; Academic Press: New York, 1979.
1502 The Journal of Physical Chemistry, Vol. 89, No. 8, 1985
Kappes et al.
TABLE II: Alkali Dimers: Spectroscopic Constants"
MN IP, eV De, cm-l we, cm-I re, A
MN
IP, eV De, cm-I we, cm-'
re, A
MN IP, eV De, cm-I we, cm-'
Li2 5.1451 (7)* 8522 (4)< 351.4 (0)d 2.673 (0)d
LiNa
Na2
5.05 (4) 7068 (4)c 257.0 ( l ) c 2.885
4.8951 (2)' 59879 159.1 (0)g 3.079 (0)s
LiK
NaK
K2
re, A
4.57 (6) 6150 (120)h 211.91 (2)" 3.322 (2)h
4.4164 (2)' 5268.1 (8)' 124.0 (0)k 3.498 ( l y
4.0637 (2)' 4192' 92.0 (0)' 3.924"
MN
LiRb
NaRb
KRb
Rb2
IP, eV De, cm-l
4.3 (1)
we. cm-'
-185'
4.32 (6) 5263 (5)"' 106.97'" 3.558'"
3.9 (1) -4033' -75.5'
3.9 (1) 3950 (160)"-a 57.747(2)P 4.17 (3)P
MN
LiCs
NaCs
KCs
RbCs
IP, eV De, cm-'
4.1 (1) -5810' 167'
4.05 (6) 4950 (100)9 98.89 (O)9 3 850 (1)q
3.9 ( 1 ) -3790' -66.2'
3.7 ( 1 ) 3833 (5)' 49.922' 4.3'
re, A
we, cm-l
re, A
cs2 3.7 (1) 3648 (8)s 42.019 (0)' 4.65 (0)s
'For each molecule in its ground electronic state (XlZ)we give an ionization potential (ev), dissociation energy (cm-I), vibrational constant (cm-I), and equilibrium internuclear separation (A). Where available, experimental uncertainties are given in parentheses. Reference 15. CReference26. dReference 34. 'Reference 35. /Reference 6. gReference 36. "Reference 37. 'Reference 25. 'Reference 38. kReference 39. 'Reference 17. mReference40. "Reference 41. "References cited in ref 41. PReference 42. 9Reference 21. 'Reference 33. "eference 43. 'Reference 18. "Personal communication from Engelke, F. to Meyer, W.; ref 12. Autoionization proceeds by way of neutral Rydberg electronic states. There exist many series of such states which converge on the ground state of the molecular ion. For the higher lying members of these electronic series, vibrationally (and rotationally) excited molecules may have energies above the adiabatic ionization potential. Vibrational-to-electronic energy conversion can occur with very high transition probability, resulting in ion formation. The probability of the direct process, continuum ionization, is lower. Depending on the molecule and excitation energy, autoionization can contribute more than 80% to the observed ion current. While the frequency dependence of autoionization probability is highly structured, continuum ionization probability is generally broad with hints of structure due to vibrational energy levels in the ionic electronic state accessed. An accurate prediction of the functional dependence of ionization probability near threshold is not possible. This would require spectroscopic information on the contributing electronic potentials so as to take into account Franck-Condon effects, which are important for both ionization modes. For most molecules in this study we do not have that information. Furthermore, the present state of theory in this area would already preclude prediction of an ionization probability curve for all but the simplest diatomics. Consequently, we need to make some approximations. The accepted continuum photoionization threshold law for small molecular species is a step function.20 Unfortunately it is rigorously valid only very close to threshold (0.05 cm-' or less depending on the onset of autoionization) whereas we would like to fit experimental data measured over a range of more than 3000 cm-'. At the low resolution of these measurements, however, the autoionization structure is effectively smeared out. Smoothing of several high-resolution spectra with Rydberg structure (Na2, NaK, K2) shows that ionization probability may indeed be represented as a step function up to 3000 cm-' beyond threshold for measurements with 300-cm-' resolution. With this assumption we can determine a vertical ionization potential which is generally good to within 0.04 eV.
(b)Internal Temperatures. To convert an appearance potential into an adiabatic IP we need to have accurate spectroscopic data on both neutral and ionic ground states. In addition we need to know the relative populations in excited vibrational and rotational levels of the initial state. The higher the internal temperature, the greater the difference between measured vertical IP and actual adiabatic IP. It is safe to assume that the molecules characterized here are in their ground electronic state. The question of rovibrational excitation was probed in two separate experiments. In the first we measured one-color two-photon ionization spectra of Na2 present in a Na/RbCl expansion. These measurements, using an excimer-pumped pulsed Coumarin 102 laser, indicated that the Na2 produced under these conditions had vibrational and rotational temperatures comparable to those of Naz generated in pure sodium expansions. This means in effect that for Na2 only the lowest vibrational level is significantly populated. The second experiment was performed on NaCs generated in a Na/CsCl expansion. Here we measured two color, one-photon resonant, two-photon ionization spectra using an Ar+-pumped DCM laser for the excitation step and an Ar' (501 nm) laser for the ionization step. NaCs is still poorly characterized spectroscopically. There exist accurate data only for the ground electronic state and for an excited D'n states2' Our measurements resulted in the observation of a previously uncharacterized electronic state in the red region of the spectrum, which will be the subject of a future communication.22 Preliminary analysis indicates that NaCs is vibrationally slightly hotter than Na2. An accurate vibrational temperature could not be assigned because of lack of FranckCondon factors for this transition. Very roughly we estimate that internal excitation cannot contribute more than 0.03 eV to the measured IP. Similar considerations would be expected to apply to all other dimers in this study which were generated by coexpansions of metal and metal chloride vapors. Were there no other factors involved, the vibrational excitation (21) Diemer, U.; Weickenmeier, H.; Demtriider, W. Chem. Phys. Lett. 1984, 104, 489.
(20) Wigner, E. Phys. Rev. 1948, 73, 1008.
( 2 2 ) Kappes, M. M.; Radi, P.;SchBr, M.; Schumacher, E., to be published.
The Journal of Physical Chemistry, Vol. 89, No. 8, 1985 1503
Homo- and Heteronuclear Alkali Dimers
TABLE 111: One-Electron vs. Two-Electron Bonds in Alkali Dimers and Dimer Cations for X'Z (MN) and MN Liz LiNa LiK LiRb LiCs NaZ NaK NaRb NaCs K2
KRb KCs Rb2 RbCs CS2
D,"(MN) 1.057 (0) 0.8763 (4) 0.763 ( i s j
D,'(MN') 1.304 (1) 0.965 (40) 0.534 (6oj
0.72 0.7423 0.6532 (0) 0.6525 (6) 0.614 (12) 0.5197 -0.50 -0.47 0.490 (20) 0.4752 (6) 0.4523 (10)
0.51 (10) 0.986 0.5777 (2) 0.509 (60) 0.457 (60) 0.797 -0.78 (10) -0.46 (10) 0.766 (20) 0.67 (10) 0.65 (10)
A(Di - D,") +0.247 (1) +0.089 (40)' -0.229 (60k -0.12 (l0)C -0.21 (10)' +0.244 -0.0755 (2) -0.144 (60)' -0,157 (60)' +0.277 -+0.28 (10)' - 4 . 0 1 (10)C +0.28 +0.19 (1O)e +0.20 (10)'
r,(MN) 2.673 (0) 2.885 (1) 3.322 (2j
re(MN+) 3.12 (0)b
3.079 (0) 3.498 (0) 3.558 3.850 (1) 3.924
3.60 ( 0 ) d
4.59 (0)t
4.17 (3) 4.37 4.65 (0)
%E (MN')" 4MN) 351.4 (0) 257.0 ( 1 ) 211.91-(2) 185 167 159.1 (0) 124.0 (0) 106.97 98.89 92.0 (0) -75.5 -66.2 57.747 (2) 49.922 42.019 (0)
--
%(MN+) 262.2 (20)
120.8 (5)
73.4 (5)
"Calculations of D,(X22) are based on the thermodynamic cycle given in the text. Atomic IP's used are from ref 44, and molecular ionization potentials are given in Table 11. Uncertainties are given in parentheses. Dissociation energies are in eV, vibrational constants in cm-I, and q u i librium internuclear separations in A. bBased on Be(X2Z Li2+) = 0.496 f 0.002 cm-l (ref 15). CNocorrection made for differences in zero point energies. dBased on B,(X2Z Na2+) = 0.113 f 0.002 cm-l (ref 45). CBased on B,(XzZ K2') = 0.041 f 0.002 cm-l (ref 17).
argument would imply that the adiabatic ionization potential of NaCs is roughly 0.03 eV higher than the appearance potential. However, the shape of neutral and ionic potential curves is an important but unknown variable. It seems to be generally the case for alkali dimers that the ionic ground state has a larger equilibrium internuclear separation than the neutral ground state (see Table III).12*15-18This would bring the adiabatic I P down by several hundredths of an electron volt due to (ill-defined) Franck-Condon effects. We conclude that the respective adiabatic ionization potentials are probably not greatly different from our determinations.23 However, in the absence of higher resolution data, we restrict ourselves to reporting one-photon vertical ionization potentials in this study. ( c ) Formation Mechanisms. How are mixed alkali dimers produced in supersonic expansions from a high-temperature mixture of sodium and alkali halide? At a temperature of 1100 K, the vapor-phase equilibrium within the cartridge, reaction la, is strongly in favor of Na: AGlloo = +4.2 (KCl), AGlloo = +4.0 (RbCl), and A G l l o o = +8.0 kcal/mol ( C S C ~ ) .Nevertheless, ~~ significant amounts of the other alkali atoms will be present in all cases. Upon adiabatic expansion to form a supersonic molecular beam, the species present within the cartridge (Na, M, NaCl, and MC1-negligible amounts of clusters), will undergo multiple collisions. Collisions involving M, Na, and a third body to remove excess energy are possible. The result is a mixed dimer (reaction 1b). The generation of M N in expansions of N a with MCl and NCl can be explained analogously.
-
+ N a NaCl + M M + N a + T - MNa + T MCl
(la) (lb)
Reactive collisions between two or more molecular species could also occur during the adiabatic expansion stage. The only way this would lead to N a M species is via reaction between Na2 and MCl (reaction 2). MC1+ Na2
-+
MNa
+ NaCl
(2)
observed in mixed expansions with more than one chloride. (d) Dissociation Energies. Using the ionization potential determinations it becomes possible to calculate differences in dissociation energy between the neutral and ionic ground states. Dissociation energy of the ion ground state is given by D,(MN+)
IP(M)
+ D,(MN)
- IP(MN) (-A)
where IP(M) is the lower of the two atomic ionization potentials and A is the difference in zero point energies (between neutral and ionic ground states). In the absence of accurate spectroscopic data on the ion ground state we set A equal to zero. This is not a major approximation given spectroscopic determinations of the vibrational constants in Li2/Li2+,Na2/Naz+, and K2/K2+, which show that the maximum error introduced by neglecting zero point energies in these systems would be 50 cm-1.6715917725-27 We list the resulting ionic ground-state dissociation energies in Table 111. We also indicate the difference in dissociation energies between ionic and neutral ground states for all 15 dimers, including those for which we do not as yet have neutral groundstate spectroscopic data. In addition to dissociation energies, we list equilibrium internuclear separations and vibrational frequencies. It has long been recognized that the one-electron bonds in Liz+, Naz+, and Kz+ are respectively stronger than the corresponding two-electron bonds in their precursor neutrals.28 The present study indicates that this phenomenon is not limited to homonuclear diatomic alkalis. The data suggest that LiNa, KRb, and RbCs are all stabilized by ionization, while the remaining mixed dimers are not. Interestingly, high-resolution laser spectroscopy via autoionizing Rydberg states has shown that, as in the case of H2, equilibrium internuclear separation in Liz, Na2, and K2 increases upon ionization. That this is a general effect for alkali dimers is implied by recent ab initio calculations (with predictive power, as discussed below)."J2 Bonding "anomalies" in M N vs. M N + have been explained in terms of charge-induced dipole attractions, core orthogonalization effects, and valence electron p e n e t r a t i ~ n . ~ ~ , ~ ~ In addition to experimental ionization potential determinations,
Free energy changes for this process (at 1100 K) are +9.5,+9, and +13.7 kcal/mol for KCl, RbCl, and CsC1, r e ~ p e c t i v e l y . ~ ~ Apart from being more thermodynamically unfavorable than (25) Huber, K.; Herzberg, G. 'Molecular Spectra and Molecular Structure"; Van Nostrand: New York, 1979; Vol. IV. reaction 1, reaction 2 cannot give rise to M N species as were (23) In this context it is informative to compare one-photon IP determinations with accurate two-photon measurements via autoionizing Rydberg states. This can be done for Na2 and K, (see ref 3 and Table 11). The numbers are 4.8951 (2)/4.934 (1 1) and 4.0637 (2)/4.05 (5) eV for Na2 and K2.respectively (IPI/ZPI). (24) Barin, I.; Knacke, 0. 'Thermochemical Properties of Inorganic Substances"; Springer-Verlag: New York, 1973.
(26) Verma, K. K.; Koch, M. E.; Stwalley, W. C. J . Chem. Phys. 1983, 78, 3614. (27) Verma, K. K.; Vu, T. H.; Stwalley, W. C. J . Mol. Specrrosc. 1981, 85, 131. (28) See,for example: James, H. M. J . Chem. Phys. 1935,3,9. Hudson, R. J. Chem. Phys. 1965.43, 1790. Roach, A. C.; Baybutt, P. Chem. Phys. Lerr. 1970, 7, 7 . (29) A good qualitative description of bonding in alkali dimer neutrals and cations can be found in: Lowe, J. J . Am. Chem. SOC.1977, 99, 5557.
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The Journal of Physical Chemistry, Vol. 89, No. 8, 1985
v .....
L,+K+
-
..--... -L,-+
K+
3 74 L 3L
L.88
-Li+K
Figure 3. Term diagram showing electronic ground states for LiK and LiK+. From our measurements of the appearance potential for LiK', we determine a vertical ionization potential of 4.57 eV. Above a photon energy of 4.88 eV a significant reduction in ion yield is observed. This can be attributed to dissociation into an ion pair (see text).
Table I gives a selection of computer calculations published prior to these measurements which predict ionization potentials. Two particular studies are selected to highlight the degree of accuracy with which state-of-the-art computational methods can predict physical properties for simple systems of this kind. The earlier, pseudopotential, calculations" are the more extensive, providing I P predictions for all alkali dimers except LiRb. In this study only the ground electronic state of the molecular cation was calculated and experimental determinations of dissociation energy in the neutral ground state were used to arrive at an ionization potential. Agreement with our experimental determinations is generally good to within 0.1 eV. More recently,12 ab initio calculations using an effective core polarization have been performed for neutral and ionic ground states of all alkali dimers containing Li, Na, and K. The ionization potential predictions which result from these computations are in excellent agreement (0.06 eV) with our measurements. Very recently this method has also been used to calculate the five lowest singlet states of LiNa.30 Agreement with our recent experimental determination of these states' is remarkable. ( e ) Photodissociation of U K . Figure la-c shows the experimentally determined photoionization efficiency curves for LiNa, NaRb, and NaCs. In the case of LiNa and NaCs, when we superimpose the computer fit from which we assign appearance potentials, agreement is good far beyond the threshold region. This indicates that for both species at this resolution, ionization efficiency can be described as a step function with its onset at the appearance threshold and continuing well into the UV. For NaRb, there is a moderate discrepancy between predicted and measured curve in the postthreshold region. In the case of LiK (Figure 2) this discrepancy is very large. The observed ion signal is much lower in the postthreshold region than what one would expect from a unit step function ionization probability, indicative of some process which reduces LiK+ yield. When we attempt to fit a second step function to this data we obtain an appearance potential for LiK+ loss of 4.88 eV. Quantitatively, this secondary process must account for about 89% of the LiK+ which would otherwise have been produced. The dissociation energy of the electronic ground state of LiK+ is 0.53 eV (Table 111). The onset of the postthreshold reduction (30) Schmidt-Mink, I.; Miller, W.; Meyer, W. Chem. Phys. Lett. 1984, 112, 120.
Kappes et al. in ionization efficiency lies roughly 0.3 1 eV above the IP, consequently still almost two-tenths of an electron volt below the ion dissociation limit (see Figure 3). Interestingly a similar effect has been observed in a photoionization study on NaK.3 This molecule has an ionization potential of 4.41642 (2) eV. Its photoionization efficiency curve shows normal step function behavior near threshold. However, above 4.8 eV there is a secondary deactivation mechanism which serves to reduce the amount of NaK+ produced upon photoexcitation of NaK by up to 70%. Here also, the dissociation limit of the molecular ion ground state is well above threshold for the secondary process. The most plausible explanation for this effect was thought to be dissociation into an ion pair (reaction 3) which should have an adiabatic threshold of 4.42 eV.3 NaK NaK* Na- K+ (3) The presence of large amounts of NaK' between 4.42 and 4.80 eV was explained by smaller transition probabilities into NaK+ below the threshold of 4.8 eV. An analogous process in LiK might be expected to occur somewhere above a threshold of3' Elhr= D,(LiK) IP(K) - EA(Li) = 4.48 eV
- -
+
+
+
The mechanism by which a dissociative ion-pair state could be accessed over an energy range as broad as that observed is not clear. Predissociation into ion pairs below the adiabatic ionization potential has been observed for various diatomic molecules, e.g., F2, Iz, HCI, and HF.I9 In all cases ion-pair formation occurs at a curve crossing between neutral Rydberg states and either the inner or the outer limb of an ion-pair potential. Typically these regions are energetically narrow. Another possible cause for LiK+ depletion is a two-photon process. Absorption of a second photon by the nascent molecular ion could access a purely dissociative electronic state. This mechanism seems unlikely as measurements were carried out at low radiation intensity. Transition probabilities for both steps would have to be extremely high to account for the large reduction in molecular ion yield observed.
Acknowledgment. We thank the Swiss National Science Foundation for financial support of this work (Grant No. 2.6 17.82). Registry No. LiNa, 12333-49-2; LiK, 12030-83-0; LiRb, 12031-70-8; LiCs, 12018-59-6; NaK, 12056-29-0; NaRb, 12333-61-8; NaCs, 12018-60-9; KRb, 12333-39-0; KCs, 12331-81-6; RbCs, 12331-83-8; Liz, 14452-59-6; Na,, 25681-79-2; Kz,25681-80-5; Rb2, 25681-81-6; Csz, 12184-83-7. (31) Calculated using IP(K) = 4.34 eV (ref 44), D,,(LiK) = 0.755 eV (Table 11), and EA(Li) = -0.609 eV. Sims, J. S. et al. Phys. Rev. A 1976, 14, 1965. (32) Zmbov, K.; Wu, C.; Ihle, H. J . Chem. Phys. 1977, 67, 4603. (33) Kato, H.; Kobayashi, H. J . Chem. Phys. 1983, 79, 123. (34) Hessel, M. M.; Vidal, C. R. J . Chem. Phys. 1979, 70, 4439. (35) Engelke, F.; Ennen, G.; Meiwcs, K. H. Chem. Phys. 1982,66, 391. (36) Kusch, P.; Hessel, M. M. J . Chem. Phys. 1978, 68, 2591. (37) Engelke, F.; Hage, H.; Sprick, U. Chem. Phys. 1984, 88, 443. (38) Breford, E.; Engelke, F. J . Chem. Phys. 1979, 71, 1994. (39) Wormsbecher, R.; Hcssel, M. M.; Lovas, F. J. J . Chem. Phys. 1981, 74, 6983. (40) Takahashi, N.; Kato, H. J . Chem. Phys. 1981, 75, 4350. (41) Breford, E.; Engelke, F. Chem. Phys. Lett. 1980, 75, 132. (42) Caldwell, C. D.; Engelke, F.; Hage, H. Chem. Phys. 1980, 54, 21. (43) Raab, M.; Weickenmeier,H.; Demtrider, W. Chem. Phys. Lett. 1982, 88, 377. (44) Moore, C. E. "Atomic Energy Levels"; Natl. Stand. Re$ Dafo Ser. (US.Natl. Bur. Stand.) 1971, NSRDS-NBS 35, Vol. 1 . (45) Martin, S.; Chevaleyre, J.; Bordas, M.; Valignat, S.; Broyer, M.; Cabaud, B.; Hoareau, A. J . Chem. Phys. 1983, 79, 4132.
