THE JOURNAL OF
PHYSICAL CHEMISTRY
Regiatered in U.5'. Patent Ofice @ Copyright, 1967, by Me Am&n
Chemical Society
VOLUME 71, NUMBER 4 MARCH 15, 1967
The Electronic Structure of Ionized Molecules. VI.
n-Alkylamines
by J. C. Leclerc and J. C. Lorquetl Instaut de Chimk de l'Universitt5 de LOge, quai Rooaevelt, Lidge, Belgium
(Received November 8, 1966)
Contour maps of the potential energy hypersurfaces of the ethylamine ion in its ground and first excited states are presented in an effort to understand its dissociation processes.
Introduction The dissociation of n-alkylamine ions has already been studied extensi~ely.~-~ The mass spectra of these substances are very different from those of the corresponding saturated hydrocarbons. The CC bond adjacent to the CN bond is much more easily broken than any of its neighbors. No other dissociation process competes with this one, at least within 3 ev above the ionization threshold. In a previous paper of this series,Bit was shown that the use of charge-density diagrams to predict dissociation mechanisms does not always give the correct answer. In the case of the amines, a rough equivalent orbital calculation was tried. The necessary diagonal matrix elements were estimated from relations suggested by Peters' and the remaining ones were obtained from existing ionization potential values. One finds that in the ground state of the molecular ion most of the positive charge is supported by the lone pair and the CN bond, whereas the adjacent CC bond is almost unaffected. This failure was attributed to the fact that the electronic charge distribution may vary considerably when the point representing the system moves over the potential energy hypersurface. A method was then developed to determine which normal modes of vibration were most likely to transform into a reaction coordinate. Unfortunately, the
method is useful only in the case of symmetrical molecular ions and when electronic rearrangements are not important. Moreover, the behavior of electronically excited states was not investigated. It was therefore decided to calculate straightforwardly the potential energy hypersurfaces of the molecular ion. This imposed the choice of a very simplified quantum mechanical mebhod, to be described in the next paragraph, which does still yield useful results if some elementary precautions are taken and if our ambitions remain limited.
Method The only method presently capable of handling this 19-electron problem is the extended Huckel theory. Several versions of it have been proposed.8~9 (1) T o whom inquiries should be addressed. (2) (a) J. Collin, Bull. SOC.Roy. Sci. Lidge, 21, 446 (1952); Bull. SOC.Chim. Belges, 62, 411 (1953); 63, 500 (1954); 67, 549 (1958); J. E. Collin and M. J. Franskin, Bull. SOC.Roy. Sci. Liige, to be published; (b) H. Hurzeler, M. G. Inghram, and J. D. Morrison, J. Chem. Phys., 28,76 (1958). (3) W.A. Chupka, ibid., 30, 191 (1959). (4) W.A. Chupka and J. Berkowitz, ibid., 3 2 , 1546 (1960). (5) H.Sjogren, A ~ k i vFysik, 29, 565 (1965). (6) J. C. Lorquet, Mol. Phys., 10, 489 (1966). (7) D.Peters, J . Chem. SOC.,2901,2908 (1964). (8) R. Hoffmann, J . Chem. Phys., 39, 1397 (1963); 40, 2474,2480, 2745 (1964).
787
788
J. C. LECLERC AND J. C. LORQUET
We use a basis of pure atomic orbitals and neglect the overlap everywhere, as suggested by Pople and Santry. The Coulomb integrals H I ;= afare chosen as valencestate ionization potentials*s10-12(azSc = -21.4 ev; azPc= -11.4 ev; a 2 S N = -26.0 ev; aZpN = -13.4 ev; alsH= -13.6 ev). A great number of relations between the off-diagonal elements, H t , = Pir, and the corresponding overlap integral, Sll, have been suggested. Most of them assume direct proportionality between these two q u a n t i t i e ~ . ~ * 'Different ~?'~ algebraic relations have also been tried. 16-17 The following one was found to be the most satisfactory. H t j = '/Z(Hti
+ H,,)KSf,(l - I &I
(1)
In the preceding relation, K is an arbitrary parameter. Orbitals i and j belong to neighboring atoms. The advantage of this relation is that it gives potential energy surfaces with a minimum (compare with the case of diatomic molecules, e.g., Hz, mentioned by Hoffmann (ref 8, footnote 10)). The overlap integrals were taken from the tables by Sahni and Cooley.18 The orbital exponents were chosen as 1.20 for H, 1.625 for C, and 1.95 for N. The relationship between the extended Huckel theory and elaborate SCF calculations has been discussed by Boer, Newton, and Lipscomb.lg These authors conclude that the Huckel method is fairly well adapted to the calculation of dissociation energies. Their analysis supports the hope that the shape of the potential energy hypersurface (i.e., the variation of the atomization energy with the internuclear distances) will be satisfactorily reproduced by the extended Huckel method if the necessary parameters (Le., K ) are chosen for that purpose. But, conversely, the obtained wave function will yield poor results in the calculation of other quantities. The parameters K were chosen to reproduce the energies of dissociation of the CC bond of CH&H3+ and of the CN bond of CH3NH2+. In the case of CH and NH bonds, fairly extensive calculations were made on a series of small molecules, radicals, and ions. It was soon realized that different values of K had to be Table I : Dissociation Energies Caled, ev
+
CzHe+ 4 CHa' CHI CHaNHz+ -t CHs+ NHz C?HsNHz++ CHzNHz+ CHa CzHsNHz+ + CzHs+ NHz +4 CIH~NH ~ CHrCH=NH2 CHsNHz+ 4 CHzNHz+ H
+ + + +
+
The Journal of Physical Chemistry
+H
Exptl,'*fo ev
(1.85) 1.86 f 0.07 (4.36) 4.35 f 0.14 0.8 - 1.0 0.90 4.66 >4.4 r t 0 . 2 3.08 3.0 1.71 1.63 - 1.90
given to bonds of a different nature. This agrees with the conclusions of Boer, et al. The values chosen were KCC= 0.37; KCN = 0.55; KCH = K" = 0.58. The dissociation energies of the CzH6NH2+ ion obtained with these values are given in Table IS2O The obtained agreement, together with the analysis of Boer, Newton, and Lipscomb, supports our hope that the main features of the potential energy hypersurface will be reasonably well reproduced.
Molecular Geometries The equilibrium internuclear distances depend essentially on the form of the relation between H f , and Sf,. In the present approximation, the bond lengths are found to be the same in the neutral molecule and its molecular ion. The following values were calculated for all molecules, radicals, and ions: RcH = 1.10 A; RNH = 1.02 A; Rcc = 1.22A; R C - N = 1.06 A; Rc-N = 1.01 A. There is no barrier to internal rotation in the present approximation. The valence angles appear to be fairly well reproduced,21the most conspicuous exception being the CH3 radical which is predicted to have HCH angles of 110", with an inversion barrier of 0.42 ev. The CH3+ ion and the excited CH3* radical, however, are predicted to be planar. Otherwise the method predicts inversion barriers of 0.70 ev for NH3, of 0.17 ev for CHINH~,and of 0.18 ev for C2H5NH2. In the corresponding ions, the nitrogen atom is predicted to be coplanar with the atoms attached to it. The CNHlf ion is found to have an ethylene-like structure. In the C2H5+ ion, the stable configuration is predicted to be flat around the carbon of the methylene group. (9) J. A. Pople and D . P. Santry, Mol. Phys., 7, 269 (1964). (10) G. Pilcher and H. A. Skinner, J . Inorg. Nucl. Chem., 24, 937 (1962). (11) J. Hinse and H. H. JaffB, J. Am. Chem. SOC.,84, 540 (1962); J. Phys. Chem., 67, 1501 (1963). (12) H. 0. Pritchard and H. A. Skinner, Trans. Faraday SOC.,49, 1254 (1953); Chem. Rev., 55, 745 (1955). (13) M. Wolfsberg and L. Helmhols, J . Chem. Phys., 20, 837 (1952). (14) L. L. Lohr and W. N. Lipscomb, ibid., 38, 1607 (1963); J . Am. Chem. SOC.,85, 240 (1963). (15) L. C. Cusachs, J . Chem. Phys., 43, 5157 (1965). (16) M. Zernerand M. Gouterman, Theoret. Chim. Acta, 4,44 (1966). (17) J. A. Pople, D . P. Santry, and G. A. Segal, J. Chem. Phys., 43, 5129 (1965). (18) R. C. Sahni and J. W. Cooley, "Derivation and Tabulation of Molecular Integrals," Supplement I, NASA Technical Note D-146-1. (19) F. P. Boer, hl. D. Newton, and W. N. Lipscomb, Proc. Natl. Acud. Sci. U.S., 52, 890 (1964). (20) J. Collin and M. J. Franskin, unpublished results. (21) J. C. Leclerc and J. C. Lorquet, Theoret. Chim. Acta, 6 , Q l(1966).
789
ELECTRONIC STRUCTURE OF IONIZED MOLECULES
‘CN (b
~i
i
d j
,
I
Figure 1. Contour map of the potential surface of C2HsNHn+ in its ground state. The contour interval is 0.3 ev.
3
2
‘ccci, I
4
‘cad
Figure 2. “Corrected” potential energy surface of C2HsNHz in its ground state. (The atoms are allowed to relax to their equilibrium positions during the dissociation process.) The contour interval is 0.3 ev.
+
Potential Energy Hypersurfaces
of the C2H8H2+Ion Ground Slate. Figure 1 represents a contour map of the potential energy surface as a function of the length of the CC and CN bonds. The contour interval is 0.3 ev. One sees immediately that the CC bond is more easily broken than the CN bond. The dissociation energies determined from this diagram are, respectively, 2.07 and 5.12 ev. These values are not directly comparable to the experimental ones, since the dissociating ion and its fragments are constrained to retain the same geometry as they had at the bottom of the surface (ie., tetrahedral angles for the carbon atoms, etc.) and are not allowed to assume their equilibrium configurations. It is therefore necessary to correct Figure 1 and to calculate a surface representing the potential energy of the CnHsNHz+ion as a function of the extension of the CC and CN bonds when the other atoms are allowed to relax to their equilibrium position during the dissociation process. We shall call it the “corrected” energy surface. It would be very tedious to vary every internuclear distance and angle for each point, and we only did this in two or three instances. We instead applied the following approximate correction method. (1) The bottom of the surface does not require any correction. (2) The points corresponding to the infinite extension of one of the bonds ( i e . , to dissociated fragments) were calculated in their correct configuration. (3) The energy of intermediate points was calculated with a Morse function as an interpolation function. This process was tested in two or three instances by the more exact method of varying the geometries and found to be accurate within 0.01-0.03 ev.
‘CN
(jj
1.o
-8.0
1.0
1.2
1.4
rcc
Figure 3. Bottom of the “corrected” potential energy surface of C2HsNH2+in its ground state. The contour interval is 0.05 ev.
The final corrected potential surface is given in Figure 2. The corresponding dissociation energies are now 0.90 and 4.66 ev for the CC and CN bond, respectively, in good agreement with the experimental values. The bottom of the corrected surface is reproduced on a greater scale on Figure 3. The contour interval is 0.05 ev. One sees that in the immediate neighborhood of the minimum (ie., for very small elongations) the contour lines are oriented along the CN bond, whereas for larger vibrational amplitudes they are oriented along the CC bond. In other words, the CN bond has the smallest force constant, but the CC bond dissociates first. This stresses again the necessity of studying carefully the potential energy hypersurface in a certain range of internuclear distances and not only the point corresponding to the Franck-Condon transition in order to predict dissociation processes. Electronically Excited States. It is well known that the Hiickel method is not well adapted to the study of excited states. Errors by a factor of two or even Volume 7lZNumber 4
March 1967
790
three may easily happen in the estimation of energy intervals. However the general behavior, which we shall presently describe, is believed to be significant. The first excited state is calculated to be at 1.24 and 1.35 ev above the ground state for CH3NHz+and CzH,NH2+, respectively. According to the measurements of Al-Joboury and Turner,22these figures should be 2.98 and 2.67 ev, respectively. From rpd measurements, Collinzadetermined a value of 2.90 ev for CH3NH2+. Similar experiments were not made for ethylamine, but the photoionization measurements of Huraeler, Inghram, and Morrisonzbgive a lower estimate of about 2 ev for this energy interval. Immediately above this first excited state, we find a quasi-continuous set of electronic states (average spacing: 0.15 ev for CH3NH2+ and 0.1 ev for CzHsNH2+). This is in total disagreement with the values reported by Al-Joboury and Turner and by Collin, who both find energy intervals of the order of 1 or 2 ev above the first excited state. Our calculation may be in error by a factor of two or even three, as already said, but certainly not by a factor of ten. A calculation of the electronic levels of N2+ and CO+ by the same method gave values in rough qualitative agreement with the spectroscopically reported levels. Furthermore, a more elaborate calculation would tend to increase the density of electronic states, since a Hiickel calculation only deals with electronic configurations, which represent an average of several electronic states. We therefore conclude that our results are qualitatively correct and that the values reported by AlJoboury and Turner and by Collin and attributed by them to discrete levels are correct only for the first excited state. Beyond they correspond only to regions characterized by a high probability of transition within a continuum. This explanation is confirmed by the fact that the number of “states” detected by AlJoboury and Turner does not increase with the complexity of the molecule. For example, they detect seven “states” for ethylamine and only four for cyclohexylamine. This is hardly understandable if we accept the current interpretation of these experiments. We therefore restricted ourselves to the consideration of the lower envelope of the potential energy surfaces of the different excited states of the molecular ion. This corrected surface is given in Figure 4. The calculated dissociation energy of the CC bond is 0.20 ev (giving an excited CH, radical and the CHzNH2+ ion in its ground state). The dissociation energy of the CN bond is calculated to be 4.34 ev (the fragments being an excited NH2 radical and the CZH6+ ion in its ground state). The Journal of Physical Chemistry
J. C. LECLERC AND J. C. LORQUET
1
0.5
1D
1.5
2.0 rcc
Figure 4. Envelope of the potential energy surfaces of the excited states of CaHaNHz+ (corrected). The contour interval is 0.1 ev.
C H ~ ’+ C H ~ ~ H ;
‘CC
(
I
Figure 5. Cross section of the potential energy surfaces of the ground state and of the envelope of the excited states along the reaction coordinate.
Figure 5 shows a cross section of the potential energy surfaces of the ground state and of the envelope of the excited states along the reaction coordinate corresponding to the dissociation of the CC bond. The abscissas are not strictly comparable for the two curves, since they correspond to the stretching of the CC bond, together with the movement of the attached atoms towards the geometry of the final products, which is different for the two surfaces.
Radiationless Transitions According to our calculations, stretching or bending the CC, CN, or CH bonds does not induce any crossing between the potential energy surfaces of the ground and first excited states. However it was found that the stretching, symmetrical or antisymmetrical, of the NH bonds leads to such an intersection. This happens even if the CC bond is simultaneously stretched. The crossing takes place, according to our calculations, when the NH bond reaches a value of 1.82.0 A (a rather unreliabIe estimate, since our method is not adapted to the calculation of interatomic distances). The energy difference between the lowest point of intersection and the bottom of the potential energy surface of the ground state is of the order of 3 ev for CH8NH2+ and 2.5 ev for C2H6NH2+ (same (22) M. I. AI-Joboury and D. W. Turner, J. Chem. Soc., 4434
(1984). (23) J. Collin, IX Colloquium Spectroscopicum Internationale, 1961, p 696.
791
ELECTRONIC STRUCTURE OF IONIZED MOLECULES
tu
Figure 6. View of the potential energy surfaces of the ground state and of the envelope of the excited states of CzHsNH*+.
warning as above concerning the accuracy). These figures correspond to the antisymmetrical vibration of the NH bonds. The important point is that they are lower than the energy required for the next dissociation process (Le., loss of a hydrogen atom). Figure 6 pictures the situation.
Conclusions The evolution of the C2H5NH2+ion can be described as follows. (a) Ions in their ground state will dissociate into a CH3 radical and a CH2NH2+ion when the vibrational energy in the CC bond exceeds 0.9 ev. (b) If the ion is created in an electronically excited
state, radiationless transitions will tend to convert this electronic energy into vibrational excitation, since the density of states is very high. Some of these states will be repulsive; others will be predissociated. The remaining ones will be converted to the first excited state. Dissociation of the CC bond in this state requires only a very low amount of energy (about 0.2 ev, according to our calculations). If a sufficient amount of vibrational energy, calculated as about 2.5 ev, affects the NH bonds, a further radiationless transition to the ground state of the ion becomes possible. The vibrational energy in excess of 0.9 ev will eventually find its way on the CC bond, and a dissociation of the latter bond will occur. The appearing fragments will carry a certain amount of kinetic energy, a lower estimate of which can be calculated as 2.5 - 0.9 = 1.6 ev. One-third of this quantity (ie., about 0.5 ev) will affect the CH2NHz+ ion. Preliminary measurements seem to confirm this p r e d i ~ t i o n . ~ ~ The previous description does not pretend to be a complete one, since other processes, such as autoionization, were not considered. Also the kinetics of these dissociations were not taken into consideration in this study.
Acknowledgment. The authors wish to thank Professor L. D’Or, Dr. J. Collin, and Dr. J. Momigny for many helpful discussions. This work has been supported by the Fonds de la Recherche Fondamentale Collective. (24) J. Momigny, private communication.
Volume 71, Number 4
March 1967
