J. Phys. Chem. 1983,87,5059-5061
of molecular excited states.16 Experimental Synthesis and Characterization of Cr(sep)2+. Anhydrous chromium sulfate was mixed with concentrated ethylenediamine and heated in a water bath for 4 h. A solution formed by mixing equal volumes of formalin and concentrated NH40H was added dropwise to the yellow brown residue. During these additions, which included occasional ethylenediamine and continued over a period of 3-4 h, the mixture was constantly heated on a steam bath, and eventually a solid residue was obtained. This residue was dissolved in a formalin solution and NH3 gas was passed through the solution (15-20 "C). The resulting mixture was filtered and the pH of the filtrate adjusted to -5 with HC1. Following rotary evaporation and removal of the hexamethylenetetraamine side product, a crude product was obtained. This material was redissolved in aqueous HC1 a t pH 4.5 and purified with a Sephadex LH-20 ion-exchange column (preswollen in aqueous methanol; 15:85 ratio). Column separation resulted in three bands; the middle band was the desired product. Rotary evaporation of the aqueous methanolic eluate gave a solid product which was recrystallized from aqueous NaC1O4. The yield was -10%. The purified Cr(sep)(ClO,), exhibited the lower energy N-H and C-H stretching vibrations and the -2880-cm-l capping methylene stretch which are characteristic of these compounds.15 Voltammetry. Differential pulsed voltammetry was performed with a PAR Model 174 polarographic analyzer. (16) (a) Engleman, R.; Jortner, J. Mol. Phys. 1970,18, 145. (b) Freed, K. F.; Jortner, J. J. Chem. Phys. 1976, 52,6272.
5059
We used a 10 mV s-l scan rate and a modulation amplitude of 25 mV (peak-to-peak). We were able to obtain good quality quasireversible cathodic and complementary anodic waves (Epa- E,, = 80 mV) in several media, for C r ( ~ e p ) ~in+ 0.1 ; M aqueous NaCF3S03,El - 1.09 f 0.03 V vs. NHE. Under similar conditions, we o6.7 Lamed a single, broad, cathodic voltammogram for Cr(e111,~' (Epc= -1.15 V vs. NHE); the anodic wave is absent for this complex owing to the very rapid equilibration of Cr(en)32+. Emission Spectra and Lifetimes. We employed a Molectron UV-1000 pumped Molectron DL-14 tuneable dye laser for excitation at 446 nm. Spectroscopic studies employed a Princeton Applied Research optical multichannel analyzer (OMA) with a silicon-intensified detector. Gating was accomplished by using an OMA signal, generated at the start of each spectral scan, as an external trigger for the laser. We accumulated 100-300 scans for each spectroscopic determination. The first- and second-order scatterings of the excitation light were used to calibrate the wavelength scale. For the lifetime studies we passed the sample emission through a Jobin-Yvon H-100 spectrometer to remove scattered laser frequencies. An RCA 7102 photomultiplier in a Products for Research housing was used for signal detection, and signals were stored in a Nicolet Explorer I11 digital oscilloscope. Samples were thermostated to f l "C in a PRA cell holder. Qualitatively similar observations were obtained in aqueous and DMF media, but the more limited aqueous temperature range precluded acquisition of good spectroscopic data.
Correlation between the Symmetry Factor of the Electrode Reaction and the Band Shape of the Photoelectron Spectrum for Alkylamine Masao Takahashi," Iwao Watanabe, and Shigero Ikeda Deparfment of Chemistry, Faculty of Science, Osaka University, Toyonaka, Osaka 560, Japan (Received: August 9, 1983)
The width of the first band in the UV photoelectron spectrum of a free molecule, along with information on its reorganization in an oxidation reaction in vacuo, is compared with the symmetry factor, one of the parameters concerning the kinetics at an electrode in solution. There exists a correlation between them for a series of alkylamines. The correlation can be interpreted by means of potential energy diagrams for the amine and amine cation.
Introduction The purpose of this work is to examine the UV photoelectron spectrum (PES) of a free molecule for any information which can be connected with the kinetics of the electrochemical reaction in solution. A certain molecule deforms so significantly after ionization of the HOMO electron that the equilibrium or ground-state molecular geometries are quite different for the reactant and the product cation. For such a molecule we expect (1)the first band of the PES to have a large difference between the adiabatic and the vertical IPS,or no observable adiabatic IP and only a broad structureless band, and (2) the electrochemical oxidation to behave totally irreversibly because of the large activation energy needed to rearrange the molecular geometry for the oxidation to occur through a thermal electron transfer process. This implies that, if the 0022-3654/83/2087-5059$0 1.50/0
intramolecular reorganization energy contributes most of the total reorganization energy for the oxidation reaction, the band width in the PES should be correlated with the parameter for electron transfer kinetics for the irreversible electrode reaction. Alkylamines were selected for the present investigation. They undergo a large geometrical change from pyramidal to planar after ionization of the nitrogen lone-pair electron (HOMO),I and give a broad PES lone-pair band, isolated enough from the other bands to allow an exact measurement of the band width, and an irreversible oxidation wave on a cyclic v o l t a r n m ~ g r a m . ~ We ~ ~have found that there (1) (a) Aue, D. H.; Webb, H. M.; Bowers, M. T.J. Am. Chem. SOC. 1975,97,4136. (b) Ibid. 1976,98, 311. (c) Potts, A. W.; Price, W. C. Proc. R . SOC.London, Ser. A 1951, 326,181.
0 1983 American Chemical Society
5060
The Journal of Physical Chemistry, Vol. 87,No. 25, 1983
Letters
TABLE I: Vertical Ionization Potential IP,, Band Width 6 , and Symmetry Factor p of Alkylaminesa
'
1 2 3 4 5 6 7 8
9 10 11
amine
IP,leV
PrNH, BuNH, i-BuNH, t-BuNH, Am", Pr,NH Bu,NH Me,N
9.34(9.44b) 9.29(9.40b) 9.29 (9.31') 9.24 (9.26') 9.30 8.56 (8.54') 8.49 8.50 (8.53,c 8.44,d 8.54,e 8.50f) 8.08 (8.08') 7.94 (7.92') 7.88 (7.90')
Et,N Pr,N Bu,N
0.76 0.79 0.71
P 0.14 0.14 0.16 0.18 0.13 0.28 0.24 0.26
0.72 0.73 0.72
0.32 0.30 0.32
sIeV 0.86 0.83 0.83 0.83
0.81
a Symmetry factors are taken from ref 3. I n ref 3 the number of electrons per mole of reactant in the ratedetermining step times the transfer coefficient is tabulated, see text. IP,s are determined at the maximum of the first band, and those determined by others are also included in parentheses. Katsumata, S. ; Iwai, T. ; Kimura, K. Bull. C h e m . SOC.Jpn. 1973, 4 6 , 3391. Reference l b . Kimura, K.; Osafune, K. Mol. Phys. 1975, 29, 1073. e Elbel, S.; Bergmann, H.; Ensslin, W. J. C h e m . Soc., Vovna, V. I.; Vileson, Faraday Trans. 2 1974, 70, 555. F. I. Opt. S p e k t r o s k . 1974, 3 6 , 436.
exists a correlation between the symmetry factor and the band width for a series of alkylamines.
Experimental Section All samples used were obtained commercially. The ionization energy scale was calibrated with argon (IP = 15.759 eV) or xenon (IP = 12.130 eV) as an internal standard. The spectral resolution of the He I PES was kept less than 0.03 eV of the full width at half-maximum for the 2P3,2argon or xenon peak. The width 6 of the first band for the amines was defined as the full width at half-maximum. When the first band accompanies the vibrational fine structure, we measure the band width by using the envelope to the peaks of the vibrational structure. Results and Discussion The width 6s measured for the first bands in the PES for a series of alkylamines are listed in Table I. Also included are the symmetry factor Ps, which were measured by Mann,3 for the electrochemical oxidation reaction at a platinum electrode in acetonitrile. We assume that the rate-determining step of the electrode reaction under consideration is a one-step, single-electron transfer reaction and the transfer coefficient is equal to the symmetry factor. A plot of P against 6 gives a good correlation as shown in Figure 1. The correlation can be understood by introducing potential energy diagrams for the amine and the amine cation in very crude way. The geometrical structure of amines should change significantly after removal of the nitrogen lone-pair electron by either photoelectron emission or electrochemical oxidation at an electrode. Potential energy diagrams for the species involved in the photoionization or oxidation process are illustrated in Figure 2. The configurational coordinate in Figure 2 is the deformation angle 4 of the nitrogen bonds from the plane on which the three nitrogen bonds will lie when the molecule is planar. Since the nitrogen skeleton for a ground-state neutral amine molecule is pyramidal, the potential energy curye for the neutral molecule M has a double minimum (4 = f 30-40') and a maximum (4 = 0'). The potential energy curve for an (2) Barnes, K. K.; Mann, C. K. J. Org. Chem. 1967, 32, 1474. (3) Mann, C. K. Anal. Chern. 1964, 36, 2424.
9,11
I\,6 l
I_____
0.3
o
\
\
108
06
I \
0.2t
05
0.75
085
0.80 dleV
Flgure 1. Plot of the symmetry factor fl vs. the band width 6. Symmetry factors are from ref 3. The numbers correspond to the samples listed in Table I.
+
I
1
,
photoionization 1
-
eiac
1
s o l v a t i o n energy
0
+ ' f
Flgure 2. Potential energy curves for the neutral and the cation molecules which are invoked in the photoionization and electrochemical processes. The potential energy curve for (MVac+ e-) is stabilized by the solvation of the ion and the stabilization of an electron by moving into an electrode, and further by electrode potential F v .
+
ion molecule M,,,+ has a single minimum at = 0' because the ground-state nitrogen moiety for the ion molecule is p1anar.l We assume now that the shapes of potential energy curves for M in solution and in the gaseous phase are similar by neglecting the solvation effect and that the potential energy curve for Msolv+in solution, produced by electrolytic oxidation, is given by shifting the potential energy curve for Mv,,+ in the gaseous phase downward by an amount equal to the solvation energy of M+ and the work function of the electrode material. The potential energy curve for Msolv+is further shifted vertically by an energy Fv when the electrode is positively charged by 7. However, the potential of the neutral molecule M is not affected by the electrical potential. Since the absolute stabilization energy for each system is of no concern in the present discussion, the potential energy curves for both M,,, and Msolvare represented by the same curve M. To make the diagram even simpler the potential energy barrier near the intersection point is made up of straight lines as shown in Figure 3, which has been frequently used by Bockris4to interpret the symmetry factor p with regard to the potential energy profiles for the reactant and product. The electrical energy F7 introduced into the system decreases the activation energy for the oxidation reaction by pF7. When the slopes 0 and y of the potential
5061
J. Phys. Chem. 1983, 87, 5061-5064
ul
-
+
0
Flgure 3. Linearized potential energy curves for ion molecule.
Y the neutral and the
energy curves for reactant M and product M+, respectively, are used, the symmetry factor p is expressed as follows:* tan 6 (1) = tan 0 + tan y By use of the diagram in Figure 3, the origin of the band width in the PES can also be interpreted. The band width 6 is equal to the length of the potential energy curve of ion molecule M+ corresponding to the breadth d of the potential energy curve of neutral molecule M in the ground state. In order to estimate d we have to know the zeropoint energy. The zero-point energy is a function of the force constant and the reduced mass, and therefore is closely related to the potential energy profile and to the slope 0. Thus the zero-point energy for M is defined here as h(6). Now, the slopes 6 and y are given as tan 6 = 2h(6)/d (2) tan y = 6 / d (3) By substituting tan 6 and tan y in eq 1, we can give the symmetry factor p as hi01 (4) = h(0) 6/2
+
(4) Bockris, J. O’M.; Reddy, A. K. “Modern Electrochemistry”; Plenum Press: New York, 1970; Vol. 2, Chapter 8.
1
0.0
1
2h(0)
6
Figure 4. The predicted correlation between the symmetry factor /3 and the band width 6, under the assumption that h ( 0 ) is a constant.
Hence if h(0) should happen to be constant, or does not change much for molecule to molecule under study, a negative correlation must exist between the symmetry factor and the band width as shown in Figure 4. In the above discussions, however, some of the very important factors which critically control electron transfer reactions on the electrode in solution are completely neglected. Those factors, for example, are the reorganization energy in the solvation sphere and the effect of the double-layer structure which could be drastically affected by the nature of the electrode material, supporting electrolyte, and adsorption of reactants or products. Those factors, however, seem to have a minor effect on the 0-6 correlation for alkylamines because the same kind of correlation also exists with the symmetry factor taken at a glassy carbon electrode in an aqueous alkaline ~ o l u t i o n . This ~ fact indicates that most of the activation energy for the oxidation reaction of amines originates from the intramolecular reorganization energy. The system having a good p-S correlation must have a HOMO which fixes the molecular geometry firmly and because of this fact it should have a broad first band in the PES and a totally irreversible electrode reaction. (5)Masui, M.; Sayo, H.; Tsuda, Y. J. Chem. SOC.B 1968, 973.
Studies on the Statistical Behavior of Ar Clusters: The Ar4 Case S. C. Farantos Theoretical and Physlcal Chemistry Institute, National Hellenic Research Foundation, Athens 50 I/ 1, Greece (Received: August 15, 1983)
In order to test a previously made assumption that a stochastic parameter, which measures the rate of exponential divergence of two initially close trajectories, provides the time scale for energy randomization we have carried out a classical trajectory study on Ar4 clusters. This characteristic time is found to be 1.5 ps at the dissociation limit, a time scale which justifies the RRKM unimolecular dissociation of Ar4found by Brady et al. Comparison with results on Ar3 shows that the stochastic parameter increases with the size of the cluster. Furthermore comparison with chemically interesting species reveals that for argon clusters the time for energy randomization is almost two orders of magnitude larger.
Introduction The powerful technique of classical trajectories is commonly used to study the detail dynamics of triatomic molecules for which satisfactory potential energy surfaces are known.’ However, when dealing with larger poly0022-3654/83/2087-506 1$01 S O / O
atomic molecules even classical mechanics becomes difficult to aPPlY-We must define the classical analogue of (1)D. G. Truhlar and J. T. Muckerman in “Atom-Molecule Collision Theory”, R. B. Bernstein, Ed., Plenum Press, New York, 1979.
0 1983 American Chemical Society
