6440
J . Phys. Chem. 1986, 90, 6440-6446
larger with the quantum number of this mode. The acceleration of the IVR rate by the torsional mode results from the low frequency, the great anharmonicity of the torsional mode, and its strong anharmonic coupling with other vibrational modes, especially with the in-plane bending mode 25. This characteristic nature of the torsional mode contributes greatly to the increase of the density of states pb as well as to the large interaction matrix element V, leading to a great IVR rate. In this sense, the torsional mode plays the most important role in the IVR process of trans-stilbene. The measurements of the IVR rates of many levels involving the torsional mode are now in progress in our laboratory. IV. Conclusion The stimulated emission spectroscopy utilizing two-color ionization dip and fluorescence dip techniques was proved to be very useful for the studies of the vibrational energy levels of the ground-state molecule as well as of their dynamical behaviors. A large number of the ground-state vibrational levels have been observed which are not expected in the vibrational spectrum or the spontaneous fluorescence spectrum. Although the analysis of most of the observed levels except for some low-frequency levels was not attempted here, the many levels found by the stimulated emission spectroscopy certainly provide detailed information on the vibrational structure of the ground-state molecule. As mentioned in section 111, most of the bands appearing in the two-color dip spectra are those involving the overtones and combinations of the low-frequency modes. The strong appearance of these bands in the dip spectra in spite of expected small Franck-Condon factors indicates large IVR rates of the overtone and combination levels. Therefore, the most characteristic feature of the stimulated emission spectra is preferential appearance of the bands associated with the ground-state levels having large IVR rate. In the sense that overtone and combination levels usually have small optical activities in the transition from an initially prepared state, they construct a large part of the “bath” in the theory of relaxation
process. Therefore, the detailed structure of the bath can be elucidated by the use of stimulated emission spectroscopy. It was shown that trans-stilbene is a very flexible molecule in the ground state. Although the molecule has the inversion symmetry (probably C,, planar structure), it is undergoing a large amplitude motion of the phenyl groups along the out-of-phase torsional coordinate. The very low fundamental frequency and great anharmonic potential of the mode and its strong anharmonic couplings with other vibrational modes all contributes to the acceleration of the IVR rate. Although quantitative estimation of the acceleration was postponed in future study, the important role of the large amplitude motion in the IVR process has been clearly demonstrated. The IVR in a ground-state molecule is the most simple relaxation process because of the absence of electronic relaxation processes such as internal conversion and intersystem crossing which occur in an electronically excited-state molecule. The nonradiative relaxation processes of large polyatomic molecules in electronically excited states have been discussed by many investigators from both theory and experiment. However, the role of the IVR process induced by anharmonic coupling of various vibrational modes is always vague. This in turn results in ambiguity in the discussions of the electronic relaxation processes. In this sense, the study of the IVR process of a ground-state molecule has a profound significance also in understanding the relaxation processes of an electronically excited molecule. Once a relationship between anharmonicity and IVR rate is established in the ground state, we may apply it to an excited-state molecule. Then, we might gain a more clear picture of the excited-state relaxation processes. It is expected that the stimulated emission spectroscopy supplies a powerful tool for achieving this goal. Acknowledgment. We thank K. Okuyama and M. Fujii for stimulating discussions. W e also thank Prof. M . Tasumi for sending us data on the normal mode analysis of trans-stilbene prior to publication.
Complex of Pyridine with Chloroform: Deuterium Nuclear Quadrupole Coupling Ellen Goldman+ and J. L. Ragle* Department of Chemistry, University of Massachusetts, Amherst, Massachusetts 01003 (Received: June 6, 1986)
NQR measurements on nitrogen and deuterium and DTQR spectra of deuterium allow one to draw qualitative conclusions about the geometry and charge distribution of the structural unit in cocrystals equimolar in pyridine and chloroform. A corresponding isolated hydrogen-bonded dimer is discussed from the point of view of molecular orbital theory, which yields its stable comformation, information about the relaxation of the length of the chloroform C-H bond, the binding energy of the complex, and the field gradients at quadrupolar sites in the complex. The field gradient measurements are discussed in light of the charge distribution of this dimer.
This paper considers the solid 1 :1 complex of pyridine and chloroform and attempts to assess the changes in molecular structure which occur on complexation by combining experimental measurements of the electric-field gradient at various sites in the complex with theoretical calculations of this and other properties. Chloroform is an associated liquid, as shown by Lord and Stidham,’ and acts as a proton donor to nitrogen and oxygen bases, as pointed out, for example, by Savitsky and co-workers.2 In the solid state, chloroform also exhibits a propensity to form hydrogen bonds or otherwise to participate in weak complexation. For example, a search of the Cambridge Crystallographic Data Base yields a substantial number of chloroform solvates of various kinds. ‘Undergraduate Research Participant. Department of Chemistry, University of Massachusetts.
0022-3654/86/2090-6440$01,~J / 0
Chlorine nuclear quadrupole resonance studies of simple stoichiometric bimolecular examples of these complexes were apparently first reported by Grecheskin and K y u n t ~ e l ’ . ~J.L.R. subsequently reported, with co-workers, double-resonance studies of the deuterium quadrupole coupling of the hydrogen-bonded site in several examples and provided a qualitative determination of the change in local charge distribution on experimental and theoretical ground^.^" A report of some preliminary measure( 1 ) Lord, R. C.; N o h , B.; Stidham, H. D. J. A m . Chem. SOC.1955, 7 7 , 365. (2) Gregory, R. V.; Asdjodi, M . R.; Spencer. H. G.; Beyerlein, A. L.; Savitsky, G. B. J. Chem. Phys. 1984, 81, 4790. (3) Grecheshkin, V. S . ; Kyuntsel’, I . A. Z h . Struct. Khim. 1966, 7, 119. ( 4 ) Ragle. J. L.; Minott, G.; Mokarram, M . J . Chem. Phys. 1974. 60, 3 184.
t Z 1986 American Chemical Society
Complex of Pyridine with Chloroform ments on the complex of pyridine with chloroform was also made some time ago by our group.’ Only a single structure determination is available for a simple bimolecular complex of this sort, according to the Cambridge Crystallographic Data Base. Andersen and Thurman-Moe report the structure of the complex of diethyl ether with bromodichloromethane.8 Ragle and Schwartz5 have briefly discussed the shift of the deuterium quadrupole coupling constant in this complex in terms of its structure, which is a hydrogen-bonded dimer in which the bromodichloromethane proton interacts with the ether oxygen. Pyridine is also an active participant in coordination to acidic sites. Its role as electron donor in such interactions has been studied theoretically and experimentally, and Brown and coworkers have discussed the behavior of the field gradient at I4N in such c o m p o ~ n d s . The ~ present paper reports an experimental study of the deuteron NQR spectra of the 1: 1 complex of pyridine with chloroform. Preferential substitution of ring protons by deuterium shows the magnitude of the perturbation of the electronic structure which arises to the two participants in the interaction. In this sense, the complex of pyridine with chloroform is an acid-base complex in which the local structure of the acidic group is relatively simple. That is, the local environment in the dative interaction is not complicated by a large number of participating (e.g., metal) orbitals as is true of the cases studied by Brown. W e regard the phrases “acid-base” interaction and “hydrogen bonding” as synonymous in this study and feel that the chloroform complex is an appropriate representation of a limit case in which a proton is present but not transferred to pyridine as in the simple pyridinium salts we presented earlier.I0 The data obtained in this study relate to earlier work by H a and O’Konski, who first observed I4N N Q R spectra in the complex” and who presented a detailed investigation of the charge distribution and properties of pyridineI2 based on the Gaussian-lobe wave function of Petke et aI.l3 W e have previously made a preliminary report of the shift in deuterium coupling constants for the chloroform site in this complex.6
Experimental Technique The zero-field “pure quadrupole resonance” spectra reported in this work were obtained on a field-cycling spectrometer via double resonance between protons and deuterium or nitrogen. The cycle begins with the proton Zeeman reservoir a t thermal equilibrium at 77 K and in a field of ca. 1 T. The sample is then moved adiabatically and reversibly to zero field, at which point a continuous wave (CW) trial irradiation of the quadrupolar spin species is made. The cycle terminates with a remagnetization to the original field and measurement of the proton Zeeman temperature using a single 90-deg pulse. The frequency of the C W irradiation is then stepped and the entire sequence repeated under automatic control. The spectra shown are therefore plots in which the ordinate is the inverse proton Zeeman temperature a t the completion of the field cycle and the abscissa is the scanned frequency. The major constraints on this experiment are generally the values of the proton relaxation times at high field and at zero field. Measurements on solid pyridine are rather awkward because the proton spin-lattice relaxation time a t high field is very long, of the order of 1000 s a t 77 K. We have previously reported measurements on both pyridine-pyridine-ds solid solutions and on ( 5 ) Schwartz, D.; Ragle, J. L. J . Chem. Phys. 1974, 61, 429. (6) Ragle, J. L.; Minott, G.; Mokarram, M.; Presz, D. J . Magn. Reson. 1975, 20, 195. See particularly Table 5 of this reference. (7) Ragle, J. L.; Reed, E. L.; Goldstein, N . J . Mol. Struct. 1980, 58, 37. (Proceedings of the Fifth International Symposium on NQR Spectroscopy, Toulouse, France, Sept 10-14, 1979.) (8) Andersen, P.; Thurman-Moe, T. Acta Chem. Scand. 1964, 18, 433. (9) Hsieh, Y.-N.; Rubenacker, G. V.; Cheng, C. P.; Brown, T. L. J . A m . Chem. Soc. 1977, 99, 1384. Rubenacker, G. V.; Brown, T. L. Inorg. Chem. 1980, 19, 392. (10) Goldstein, N.; Ragle, J. L. J . Chem. Phys. 1979, 70, 5072. (11) Ha, T.-K.; O’Konski, C. T. Z . Naturforsch. 1970, 25, 1509. (12) Ha, T.-K.; OKonski, C. T. Intl. J . Quantum Chem. 1973, 7 , 609. (13) Petke, J. D.; Whitten, J. L.; Ryan, J. A. J. Chem. Phys. 1968, 48, 953.
The Journal of Physical Chemistry, Vol. 90, No. 24, 1986 6441 samples of specifically deuteriated pyridine. At the time that those measurements were made, only small amounts of the specifically deuteriated species were available, and this, coupled with the very long relaxation times, made it difficult to obtain clearly resolved spectra. This difficulty is further compounded by the complexity of the crystal structure of pyridine. Measurements on the complex of pyridine with chloroform are greatly facilitated by its much shorter relaxation time at high field, of the order of 100 s or less, and by the fact that its crystal structure is apparently much simpler than that of pyridine (vide infra).
Discussion Sample Preparation. Samples of the cocrystal were obtained by mixing chloroform (or chloroform-d) and pyridine (or pyridine-2,6-d2,pyridine-3,4,5-d3, pyridine-2,4,6-d3, or pyridine-4-dl) in controlled molar proportions, followed by degassing and sealing in glass ampules. Nucleation of the cocrystal phase is difficult, and the following regimen was used throughout. The sample was cooled until a portion of it became a transparent, glassy solid. At this point, the two-phase sample (e.g., glass and very viscous liquid) was allowed to warm until nucleation occurred, as evidenced by the growth of multiple spherulitic structures throughout the glass. On a substantial fraction of such occasions, phase separation occurred, and the N Q R lines of the complex were not observed. On about half of these attempts, however, nucleation occurred to the cocrystal phase, and the sample was eventually “teased” into a completely nonglassy condition by repeated gentle cooling and warming. The sample was then suspended in a basket near the top of a large liquid nitrogen storage Dewar (well above the liquid nitrogen) and annealed for several hours at least. If the deuterium line width seemed excessive, Le., if a single line of the spectrum was wider than a few tenths of a kilohertz, the procedure was repeated. This method produced usable samples more often than did a single cycle of slow cooling. Where the available amount of specifically deuteriated pyridine permitted, samples were deliberately made in mole ratios departing from 1:l. N o lines other than those reported below were seen, and the intensities of the lines present scaled properly with regard to the proportions of the two components. One concludes that the representation of this compound as a 1:l complex is justified, and in this connection Ha and O’Konski mention a phase diagram study which indicates that the complex melts congruently.” Experimental Data. The frequencies of the pure quadrupole transitions of nitrogen in pure pyridine are known from the work of Guibe.I4 Each line shows four components, in agreement with the rather complex crystal structure of pyridine.Is Quadrupole coupling data for nitrogen in the pyridine-chloroform complex are also available from the work of H a and O’Konski. In the course of the present work, we have repeated both measurements by using the double-resonance technique above and find agreement with the previous values. Barnes et al. have reported a mean value for the deuteron coupling constants of the ring positions in solid pyridine from high-field N M R powder measurements.I6 The deuteron coupling constant for solid chloroform is known from spin-echo doubleresonance (SEDOR) measurements made in this 1aboratory.l’ The crystal structure of chloroformi8at 185 K (Pnma, 2 = 4) allows a non-zero asymmetry parameter for deuterium. The material exhibits two 3sClNQR lines over the temperature range 77 K to the melting point, and using Fourier transform N Q R techniques we find them to be in the intensity ratio 2:1, corresponding to the m symmetry of the molecular site. The line at ca. 38.303 M H z at 77 K corresponds to the chlorine located in the mirror plane and that at ca. 38.247 MHz to the mirror-related pair, It is worth noting that although both lines are roughly equal in width at 200 K, the latter line is substantially broader than the (14) Guibe, L. Ann. Phys. 1962, 7 , 177. (15) Mootz, D.; Wussow, H.-G. J . Chem. Phys. 1981, 75, 1517. (16) Barnes, R. G.; Bloom, J. W. J . Chem. Phys. 1972, 57, 3082. (17) Ragle, J. L.; Sherk, K. L. J . Chem. Phys. 1969, 50, 3553. (18) Fourme, R.; Renaud, M. C. R . Hebd. Seances Acad. Sci., Ser. C 1965, 203, 69.
6442
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The Journal of Physical Chemistry, Vol. 90, No. 24, 1986
1 1 ' 1 I '
I
I
1
I
1
I 30
120 DEUTERIUN
;15
,
1 I' 1 1 ' 1
120
ktrz
19'2 k H z
NOR S P E C T R U f l
PYRIDINE-2,6-02
RT
OF
OF
77 K
Figure 1. Deuterium pure quadrupole spectrum of solid pyridine-2,6-d2 at 77 K. The structure is a result of the presence of four different molecules in the asymmetric unit of the structure. This spectrum is taken from previously unpublished work by J.L.R. and E. L. Reed, Jr. 132. 6 5
l I I l / I I I I ,' I I
1:E
I
I
D E U T E R I U M NQR S P E C T R U M CHLOROFORM S I T E I N S 0 ~
PYRID1NE:CHLOFOFORM
AT
13
COMPLEX
77 K
Figure 3. Chloroform deuterium pure quadrupole spectrum from a cocrystal of chloroform-d and pyridine-3,4,5-d3at 77 K. There is no discernible difference between this spectrum and those obtained using
pyridine-44, pyridine-2,6-d2, or pyridine-d,.
7 /----135.70 135. 8 5
130.35132. 6 5
-
138.20 138. 60
!28
OEUTERIUn SOLID
136
132
N Q R OF
SITES
PYRID1NE:CHLOROFORM
AT
I N
COMPLEX
77 K
Figure 2. Ring deuterium pure quadrupole spectra of cocrystals of chloroform-d with various ring-deuterated pyridines at 77 K. From the top, ring deuteration is at sites 4; 2,6: 2.4,6; and 3,4,5.
TABLE I: Coupling Constant Data for Pyridine-Chloroform Comolex
nu cI eu s I4N 14N
2H
site (solid pyridine) (complex) ring 4 ring 2,6 ring 3,5 chloroform
2r5
265
nt-z
D T C R S P E C T R J q 3F S O L I D F'YR1DINE:CPLOROFORP COMPLEX A T 7 7 K
lLi0 k H z
RING
l""I""!""I""I'"'~'"
225
quadrupole coupling asymmetry const, MHz parameter, 5% 4.60" 39a 4.539 38.1b 0.1789 3.4 0.1772' 5.9' 0.18 15' 5.0' 0. I549 2.3
Reference 14. Reference 11. 'Averages for two crystal sites separated in frequency by a few tenths of a kilohertz. (See Figures 2 and 3.) former a t 7 7 K, perhaps implying that the m symmetry is not precisely present a t low temperature. Despite the lack of axial symmetry, only a single narrow S E D O R line is observed for deuterium. The coupling constant and asymmetry parameter for deuterium in the C13CD fragment of the pyridine complex has been reported by us previously,6 and the ring deuterons in pyridine and the chloroform complex were observed and partially characterized.' It is clear on chemical grounds that the ring positions in pyridine are not equivalent, and Figure 1 shows the way in which the crystallographic inequivalence of ring sites further splits the deuterium N Q R spectrum of the 2,6-po~itions.'~ Deuterium N Q R spectra of the cocrystal are shown in Figure 2 (ring region) and Figure 3 (chloroform). Coupling constants are given in Table I. The observations may be summarized qualitatively as follows. First, a substantial decrease in the coupling constant of the chloroform deuteron accompanies complex formation. Second, the doublet structure of this line is well resolved, corresponding to an increase in the nonaxial component of the field gradient a t this site. Third, the quartet structure of the nitrogen site in pyridine collapses to a singlet in the complex, with a slightly diminished nitrogen coupling constant and asymmetry parameter. Finally, not only are the lines associated with the nitrogen site
Figure 4. Deuterium DTQR spectrum of an equimolar sample of chloroform-d and pyridine-2,6-d2 at 77 K. The strongest features in the
spectrum are combination bands between deuterium on chloroform and the adjacent 2,6 sites of the ring (see text). The upper spectrum is run under heavy saturation conditions for the ring-chloroform lines in order to bring out the ring-ring combination lines. not split, but the deuterium ring site 4 is a singlet, implying that the complex contains a single pyridine-chloroform unit in the unique part of the unit cell. However, both the 2,6- and 3,5positions of the ring show clearly resolved doublet structures. Thus, there is no crystal symmetry operation by which the ring sites 2 and 6 or 3 and 5 are equivalent. The lack of symmetry in the complex is further illustrated by the increase in the asymmetry parameter of deuterium on chloroform and the observation of multiple lines for ~ h l o r i n e . ~ Figure 4 shows the deuterium double-transition quadrupole resonance (DTQR) spectrum of equimolar chloroform-d and pyridine-2,6-d2. This spectrum, consisting of normally forbidden combination bands involving simultaneous transitions at two sites, gains its intensity by virtue of the direct dipolar interaction between deuteron sites and therefore reflects the proximity of adjacent deuterons. Close pairs of sites show stronger DTQR lines than do distant sites. Such spectra are several orders of magnitude weaker than the usual single-spin transitions and are observed by suitably increasing the radio-frequency (rf) field strength of the C W irradiation." Because of the high rf field required, these lines are observed under conditions of partial saturation, and the response can therefore be very nonlinear. Only partial success is to be expected in fitting observed intensities by a first-order theory.20 The intensity also depends on the relative orientations of the principle axes of the field gradient tensors of the pair. Nevertheless, from a qualitative point of view, one can draw the following conclusions from the spectrum. The origins of the individual DTQR lines are obvious from the frequencies of the single-spin "normal" spectrum. They are grouped into three types: DTQR lines arising from D-D interactions between chloroform molecules a t adjacent sites (here virtually absent), lines from 2 to 6 cross-ring or interunit interactions, and lines from interactions between D on chloroform and D on ring positions 2 or 6. One notes from the spectrum that the (19) Edmonds, D. T.; White, A. A. L. J . Magn. Reson. 1978. 31. 149 and references cited therein. (20) Hadipour, N.; Ragle, J. L. Z . Naturforsch., A 1985, 40a, 3 5 5
Complex of Pyridine with Chloroform
The Journal of Physical Chemistry, Vol. 90, No. 24, 1986 6443 TABLE II: Geometry of Pyridine-Chloroform Dimer Optimized with respect to Total Energy at STO-3G (See Figure 5)
pyridine G E O R E T R Y OF M O L E C U L A R UNIT IN SOLI0 COMPLEX OF ~ Y R 1 D I N E : C H L O R O F O R M A T 7 7 K Figure 5. Ball-and-stick drawing of molecular geometry used in the computations of Tables 11-IV. Parameters varied in the computations are shown on the figure.
ASSLIflED
latter are quite significantly stronger than either of the interunit transitions and also that the interaction between chloroform and deuteron “2” is essentially equivalent to that between chloroform and deuteron “6”. Therefore, we are consistent in supposing that the chloroform deuteron is about equidistant from the two types of ring sites and closer to both of them than the 350-pm cross-ring distance. A chemically reasonable way to form such a structure is to place the chloroform molecule so that the proton points toward the nitrogen site. This is the structure shown in Figure 5. On chemical grounds, one can also reach some qualitative conclusions about the features of the electron density in the complex which are responsible for the spectral features. We ignore small changes in the intermolecular contribution to the field gradient. This is consistent with the difference between the small splitting (ca. 0.4 kHz) of the 2,6 or 3,5 sites and the somewhat larger “chemical” shift (ca. 3 kHz) between the coupling constants of the two. The decrease in the coupling constant of the chloroform deuteron is the result of changes in the C-D bond length, of polarization of the charge distribution in the C-D bond, and of the presence of the basic (Le., negative) nitrogen. In our previous work we modeled this shift by summing the observed chloroform field gradient and the field gradient produced by the ring a t an estimated N-D distance of 200-210 pm. This model qualitatively reproduces the observed shift in deuteron coupling constant. Structure from the Theoretical Viewpoint. The geometry of the complex was refined and its charge distribution further studied by using a b initio theoretical methods, assuming the gross features of the geometry outlined above to be correct. The size of this species only permitted the following treatment. Calculations were performed by using the QCPE distribution version of GAUSSIAN-76, with a standard STO-3G basis which did not include d-orbitals on chlorine. Although this basis set is likely to be fairly adequate for deuterium, it is open to objection on several grounds, particularly that the environment around nitrogen and in the hydrogen bond is rather constrained. As will be evident from the results of these calculations, this forces the field gradient at nitrogen to respond in a rather peculiar fashion to the formation of the adduct. The representation of the local charge distribution around chlorine is of course even more severely constrained in this basis, and we only expect a very qualitative agreement between theory and experiment for chlorine. In preliminary work, the molecular complex was taken to contain a pyridine molecule with the “average” geometry reported by Mootz and Wussow. This molecule is constrained to mm symmetry, with bond lengths equal to the averages of those of the four independent molecules per asymmetric unit in crystalline pyridine, to which a rigid-body thermal motion correction was applied. The heavy atom geometry of the chloroform moiety was taken from the structure of Renaud and Fourme, and the structure was locally optimized with respect to the chloroform C-H bond length and the H-N hydrogen bond length. The results of this set of calculations are a binding energy of ca.26.4 kJ/mol, a H-N hydrogen bond length of 190 pm, and a C-H bond length of 11 1 pm. By use of the same basis set, the C-H bond length in chloroform is 109 pm. In a second series of calculations, the structures of both monomer units were optimized theoretically, again at STO-3G and not including d-orbitals on chlorine. The structure of the complex was then optimized, holding the ring geometry and the heavy-atom
chloroform complex
189.20
109.84 111.35
-243.638 61 -1 401.698 37 -1654.34762
90
Distances A and B are the hydrogen ...nitrogen and carbon-hydrogen bond lengths. 6 and 9 are the angle between the C-H ...N axis and the perpendicular to the ring and the twist angle about this axis, respectively. The total energy of the complex is essentially independent of this parameter.
il -1.0
li
F I E L D GRADIENT
vs DISTANCE FROM NITROGEN
Figure 6. Field gradient at a test point along the z axis as a function of distance from ring nitrogen. The ordinate is in atomic units. The abscisssa is the Ne-H distance in angstrom units. For distances greater than ca. 1.2 A, the field gradient is positive; e.g., the ring acts as a negative charge (base). For distances less than this, the field gradient is dominated by the positive nitrogen nuclear charge. The curve labeled IOX has been expanded 10-fold in the ordinate.
geometry of the chloroform rigid and allowing the C-H bond and the H.-N distance to relax while assuming the 3-fold axis of the chloroform fragment to be collinear with the N-C(4) axis. These three optimizations were done by Prof. J. DelBene (Youngstown University) by using the gradient search capability of GAUSSIAN-82. Using these bond lengths, we then further explored the energy surface, finding that the total energy of the complex is very insensitive to small departures from this orientation. For example, a tilt of the 3-fold axis of the chloroform by 30’ out of the ring plane holding the He-N distance constant only costs ca. 4-5 kJ/mol. As expected, the energy of the dimer is also found to be essentially independent of the angle of rotation about the chloroform 3-fold axis. Results of this series of optimizations are shown in Table 11. In most further computations, the 3-fold axis of the chloroform group is assumed to be collinear with the N-C(4) axis, although it is obvious that this complex is very flexible and may be somewhat distorted from this structure by crystal packing forces. The shortened proton relaxation time of the ring sites probably reflects this flexibility. Comments on Pyridine as a Proton Acceptor. When a proton is transferred to pyridine to form the pyridinium ion, the sign of the field gradient at this proton is controlled by the nitrogen nucleus. However, a t somewhat longer N-H distances, of the order of those involved in the hydrogen bonding interaction in the complex, a basic site such as this one does in fact act as a negatively charged center from the point of view of the sign of its contribution to the field gradient, as shown in Figure 6. The large positive nuclear charge of nitrogen is effectively screened by the electron density associated with the lone pair. The nitrogen lone pair is not particularly obvious in a contour map of charge density and is not associated with special points
6444
Goldman and Ragle
The Journal of Physical Chemistry, Vol. 90, No. 24, 1986
TABLE 111: Major-Axis Principle Field Gradient and Asymmetry Parameter Calculated for Pyridine, Chloroform, and Complex at the Geometry of Table 11"
complex Dosition H (on chloroform) H (on ring carbon 2) H (on ring carbon 3) H (on ring carbon 4) N (ring) C1 (in ring plane) CI (mirror pair)
monomers
field gradient, au
asymmetry parameter, 5%
-0.210 592 -0.323 353 -0.328814 -0.327 276 +0.975 057 -3.706 432 -3.702 927
0.95 2.92 3.41 1.89 52.41 2.06 2.05
field gradient, a u -0.296 737 -0.325 752 -0.329 754 -0.327 813 +1.087571 -3.809 568
asymmetry parameter, % 0
(-0.382) (-0.382) (-0.390) (+1.887)
1.98 (2.6) 3.24 (3.7) 2.1 1 (2.6) 38.23 (13.7) 1.80
"The second pair of columns refers to isolated monomers, with numbers in parentheses taken from ref 12. TABLE IV: Selected Mulliken Charges for STO-3G Pyridine, Chloroform, and Complex at the Geometry of Figure 2"
charge position H (on chloroform) H (on ring carbon 2) H (on ring carbon 3) H (on ring carbon 4) N (ring) CI (in ring plane) CI (mirror pair)
complex
monomers
+0.206 85
+0.155 416 +0.073 390 +0.073 191 +0.073658 -0.239057 -0.074 577
+0.08069 +0.080 327 +0.081013 -0.260 884 -0.100 38 3 -0.101 304
I 12
SELL:-EL
- _ .^
r
L;;
-
,~
-*
Figure 7. Selected equipotentials of the charge distribution of STO-3G pyridine in the ring plane. Units of electrostatic potential are atomic units, and the zero used in labeling contours is taken at the bottom of
the well corresponding to the nitrogen lone pair (see text). This zero lies at -0.143 047 au with respect to the potential at infinite distance. The contours are constructed on a 1600-point grid with mesh size 0.25 X 0.25 au, and very small-scale features are accordingly not resolved. Only two-thirds of the ring including the nitrogen is shown in the figure. in the charge distribution. That is, although the charge distribution has a number of critical points of rank 3 and signature -3 (at the nuclei), -1 (in the bonds), and + 1 (at the ring center), there is no critical point or other obvious topological feature associated with the charge density in the lone pair region. Nevertheless, its presence is dramatically evident in plots of the scalar electrostatic potential. A contour map of selected equipotentials in the plane of the pyridine ring is shown in Figure 7. In this figure, generated from the STO-3G wave function discussed above, there is a prominent well a t 103.8 pm from the nitrogen associated with a potential value of -0.143 047 au. This is a critical point of the scalar potential with rank 3 and signature 3 (that is, a positive ion trap), clearly associated with a ''latent'' tendency of pyridine to bind a proton. The field gradient a t this well is closely related to the Hessian matrix of the potential, values reported in NQR experiments differing from these by the factor of 4ap(0)/3 conventionally omitted from such work. At this well, the charge density is -0.041 023, and the field gradients are -0.1988 and +0.0924 (in the plane of the ring) and +0.1063 (transverse to ring). The innermost contours of the well shown in the figure are essentially contours of the Morse form of the potential around this critical point, and it is evident from the figure which direction corresponds to which field gradient component in the ring plane. It is interesting to note that one recovers a substantial portion of the proton affinity of pyridine from the static, unpolarized charge distribution of the base. The well location, 103.8 pm from the nitrogen, and the coupling constant calculated from the above gradient, 133.6 kHz, also coincide well with expectations for pyridinium ion.I0 This type of observation has been made previously by Bonnacorsi, Politzer, Pullman, and others,21and maps (21) See, for example: Politzer, P.; Daiker, K . C. In The Force Conrepf B. M., Ed.; Van Nostrand Reinhold: New York, 1981; Chapter 6 .
I
bo
W
0
IO
20
30
Figure 8. C-H bond length and bond energy vs. I\--H distance for the complex in which the C-H bond length is relaxed to its equilibrium value a t each N-H distance. The abscissa is the N-sH distance in angstrom units.
such as this may be obtained directly from experimental X-ray structure factors, as pointed out by Stewartz2 Field Gradients and Additional Comments on the Complex. The charge distributions resulting from the theoretical minimum-energy geometries were used to calculate field gradients at quadrupolar nuclei in the complex and the monomers. These results are shown in Table 111, where the STO-3G calculations are compared to those of H a and O'Konski.I2 Some qualitative feeling for the way in which charge is redistributed on complexation can be gained from a Mulliken population analysis of the wave functions used to generate these gradients. Selected examples are shown in Table IV. Examination of the data in Tables I and I11 shows that although the shifts in field gradient a t all quadrupolar sites are qualitatively in agreement with experiment, the theoretical model overemphasizes the effects of complex formation. The bonding energy has the correct order of magnitude, but all shifts in field gradient are too large. At nitrogen, this can be understood as a result of
in Chemistry; Deb,
( 2 2 ) Stewart, R . F. Chem. Phys. Left. 1979, 65, 335
The Journal of Physical Chemistry, Vol. 90, No. 24, 1986 6445
Complex of Pyridine with Chloroform -0.2
.
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Figure 9. Field gradient at the chloroform and ring deuteron sites as a function of N-H distance. The ordinate is in atomic units. The abscissa is the Ne-H distance in angstrom units. The curve labeled ring alone is that shown in the previous figure but redrawn so that its zero corresponds to the field gradient for isolated chloroform, indicated by the hashmark on the right ordinate. The curve labeled total is the field gradient at the chloroform deuteron in the complex for which the C-H bond length is relaxed to its equilibrium value at each N-H distance. The relaxed C-H bond lengths are given in Table I1 and shown in a previous figure.
a tendency for nitrogen to utilize the local region to attempt to compensate for inadequacy in basis size, particularly in the region of the hydrogen bond. As a result, the hydrogen bond length is too short and field gradient shifts are overemphasized, particularly at nitrogen. For this reason, further computations were undertaken in which the N-H distance was frozen at values somewhat longer than the minimum energy value, and relaxation was permitted in the C-H bond. Figure 8 shows the relaxed C-H bond length and the total energy over a range of N-H distances. Figure 9 shows the behavior of the computed field gradients a t deuterium sites for the relaxed complex as a function of N.-H distance over the same range. In this figure, the field gradient a t the site of the chloroform hydrogen is broken into two contributions; a corresponds to the contribution of the ring charge distribution at this site and b to the total field gradient computed for the relaxed complex. At all distances, the response of the monomer charge distributions to complex formation is substantially larger than the contribution of the rigid pyridine base alone. It should be noted that the field gradients at the ring proton sites, also shown to the same scale in Figure 9, are essentially independent of complex formation in this model. In Figure 10 the local reponse of the charge distribution around the ring nitrogen site in terms of field gradient and asymmetry parameter of the relaxed complex is plotted as a function of N.-H distance. Although the I4N field gradients are reasonable for the pyridine monomer, they respond in an exaggerated way to complex formation. That is, the behavior shown in the figure is in strong contradiction to experiment, which shows little change at nitrogen in either the coupling constant or the deviation from axial symmetry. As discussed above, we feel that this is due to the fact that the limited basis set, particularly a t nitrogen, is inadequate to deal with the changes which accompany hydrogen bond formation. This defect could be partially remedied either by incorporating floating basis functions in the hydrogen bond region or by augmenting the nitrogen basis, but it is well-known that use of such an unbalanced basis set may lead to other undesirable effects. The computations discussed in the preceding paragraph were extended to chlorine and are itemized in Table 111. Synthesis of Data with Theory. Experimental and theoretical quadrupole coupling data agree qualitatively. In the case of deuterium, although the scalar quadrupole moment of the nucleus is known, the fact that the field gradient comes largely from neighboring atoms means that a very precise prior knowledge of
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I
Figure 10. Upper section: field gradient at the ring nitrogen vs. N-.H distance for the complex for which the C-H bond length is relaxed to its equilibrium value at each N-eH distance. The ordinate is in atomic units. The abscissa is the N.-H distance in angstrom units. The curve labeled CHCI, alone is the EFG which arises at the nitrogen site from the unrelaxed chloroform charge distribution alone. Lower section: asymmetry parameter at the ring nitrogen vs. N-H distance, as above.
geometry is necessary before one begins the task of generating a charge distribution. We have pointed out previously that an error of 0.01 8, in the nearest-neighbor distance may mean an error of the order of 20 kHz in the computed coupling constant at deuterium. In addition, approximate Hartree-Fock wave functions underestimate the electronic contribution to the field gradient at D, giving coupling constants which are usually too high. The net result is that, while shifts in field gradient at deuterium are computed to be in the correct direction, the computed changes in magnitude are somewhat too large. I n the present case, we wish to compare the observed chloroform-deuteron coupling data for chloroform and the 1:1 chloroform-pyridine complex to the shift of -57.9 kHz computed for the static isolated molecules. As Savitsky and co-workers have pointed out, it is unreasonable to use the measured deuterium coupling constant of 166.9 kHz for solid chloroform* to represent the uncomplexed chloroform molecule. A much more reasonable value of 1864 kHz is obtained by them by Raman and NMR relaxation measurements in hexane solution. The experimental difference between the coupling constant of uncomplexed chloroform and the pyridine complex is therefore -324 kHz. In view of the crudeness of the theoretical model, e.g., limitations of basis, neglect of vibrational effects, neglect of the effects of incorporation into the condensed phase, etc., this may probably be regarded as satisfactory agreement. The calculated asymmetry parameter from the data of Table I11 (0.95%) may be compared to the experimental value of 2.3%,the discrepancy probably arising from a low site symmetry in the lattice. In the case of the ring deuterium sites in the complex, calculation indicates only very small perturbations of the field gradient from the corresponding values in the monomer. We have previously published spectra of ring deuterium in pure pyridine,’ but the complexity of the unit cell renders them of rather poor quality. Only in the case of the 2,6-positions were we able to partially resolve the four inequivalent molecular sites shown in Figure 1. Because of the small values of the computed shifts relative to the spread in intermolecular crystal field contributions shown in the
J . Phys. Chem. 1986, 90, 6446-6451
6446
figure, we may regard the information obtained on the pyridine ring in the complex studied in the present work as pertaining equally well to pure pyridine. That is, we regard the chloroform as a label which facilitates the examination of the pyridine ring positions by simplifying the crystal structure and increasing the proton relaxation rate, as explained in the Experimental Section. This allows direct comparison to the earlier work of Ha and O'Konski. For nitrogen and chlorine, it is much more difficult to make contact between experimental and theoretical field gradient data, since neither nuclear quadrupole moment is known with notable precision. Since the corresponding field gradients arise mainly from charge in the immediate neighborhood of these nuclei, a prior knowledge of the geometry plays a less important role here than in the deuterium case. The calculated values of the shifts in field gradient agree with the experimental result that the semimajor tensor axis length decreases a t both the chlorine' and nitrogen sites. This parallels the slight increase in calculated total atomic charge. As discussed above, the asymmetry parameter at nitrogen is predicted to increase substantially, in disagreement M ith the
experimental observation. Our experience is that nitrogen field gradients and the directions and relative magnitudes of the semiminor axes are very basis dependent for calculations done with such limited bases and in which symmetry does not fix the tensor directions, and although we report the computed values, we do so only for completeness. Values for the asymmetry parameters at the chlorine sites are not known experimentally, and the dubious nature of the theoretical results for nitrogen indicates that some mistrust of the very small computed asymmetry parameters for chlorine is justified.
Acknowledgment. We would like to thank Prof. Del Bene for her interest in this work, for several lively discussions, and for undertaking the calculations mentioned in the text. Thanks are also due to Evan Miller for undertaking field gradient calculations a t nitrogen in several nitrogen heterocycles with a variety of Gaussian bases.23 (23) Evan D. Miller, unpublished Undergraduate Honors Thesis, University of Massachusetts, Amherst, MA, 1986.
Ab Initio Studies of Hydrocarbon Peroxyl Radicals Brent H. Besler, Michael D. Sevilla,* Department of Chemistry, Oakland Unicersity, Rochester, Michigan 48063
and Perry MacNeille Ford Motor Scientific Research Laboratory, Dearborn, Michigan 481 21 (Received: June IO, 1986; In Final Form: July 29, 1986)
Extensive ab initio molecular orbital calculations have been performed for the important series of peroxyl radicals (02'7, H02', CH302*,(CH3)2CH02',and (CH3CH2),CH02'. Parameters calculated include equilibrium geometries, harmonic vibrational frequencies, dipole moments, and isotropic and anisotropic hyperfine couplings. Equilibrium geometries were of primary interest. In the two large hydrocarbon peroxyl radicals the carbon atoms and appropriate hydrogen atoms were constrained to be coplanar and the 0-0 group was forced to be perpendicular to the carbon chain in order to stimulate the presence of a peroxyl radical site in a polyethylene chain. Calculations were performed with large Gaussian basis sets (up to 6-3 1 l++G(d,p)). Calculations for HO: including electron correlation utilizing Moeller-Plesset perturbation theory were performed at the following levels: MP2(6-31G(d)) and 6-31 lG(d,p), MP3(6-31 lG(d,p)) and MP4SDTQ(6-31 l(d,p)). Calculated values are compared against the highly accurate experimental data for HO,' known from microwave, laser magnetic resonance, and diode laser studies in order to determine the level of calculation necessary for accurate predictions. Comparison of the various calculations shows that MP2(6-3 1 G(d)) compares favorably with MP4SDTQ(6-31 lG(d,p)) at a considerable savings in computation time. Corrections to the H F bond distances and bond angles for the largest structures due to electron correlation are estimated from correlated calculations on the smaller peroxyl structures. Semiempirical calculations were also performed but were found to give poor agreement w>ithexperiment.
Introduction Peroxyl radicals play an important role in the chemistry of a variety of systems. Among these are the oxidation of hydrocarbons,' the chemistry of the upper atmosphere,* and the oxidative degradation of polymers and lipid^.^,^ The small peroxyl radicals H02' and CH302' appear in hydrocarbon oxidation as well as atmospheric chemistry, while those involved in polymer degradation involve large alkyl chains. The closely related 02'-radical ( I ) Benson, S. W.; Nangia, P.S. Arc. Chem. Res. 1979. 12, 223. (2) Heicklen, J. Atmospheric Chemisrry; Academic: New York, 1976. (3) Carlsson, D. J.: Dobbin, C. J . 8.: Wiles, D. M. Macromolecules 1985, 18, 2092. (4) (a) Sevilla, C. L.; Becker, D.; Sevilla, M . D. J . Phys. Chem. 1986, 90, 2963. (b) Yanez, J.: Sevilla, C. L.; Becker, D.: Sevilla, M. D. J . Phys. Chem., in press. (c) Becker, D.; Janez, J.: Sevilla, M. D.: Schlick, S.; Alonso-Amigo, M. G . J . Phys. Chem., in press. (d) Bors, W . , Saran, M.. Tait, D., Eds.; Oxygen Radicals in Chemistry and Biology, Proceedings Third International Conference; Waltern De Grupter: Berlin, 1983.
0022-365418612090-6446$01.5010
also appears in many oxidation p r o ~ e s s e s . ~Peroxyl ,~ radicals may also be used as electron spin resonance (ESR) probes in polymer chains and on metallic surfaces.6 Over the past decade a large amount of experimental data and a b initio calculations have appeared for the H02' radical.'-I4 In the cases of 02'-,CH302*, and the larger alkyl peroxy radicals data have been scarce and widely scattered among different areas of research. In this work ( 5 ) Bielski, B. H. J.; Richter, H. W. J . A m . Chem. SOC.1977, 99, 3019. (6) Kevan, L.; Schlick, S. J . Phys. Chem. 1986, 90, 1998. ( 7 ) Bair, R. A.; Goddard, W. A. J , A m . Chem. SOC.1982, 104, 2720. ( 8 ) Jackels, C. F.; Phillips, D. H. J . Chem. Phys. 1986, 84, 5013. (9) Cohen, D.; Basch, H.; Osman, R. J . Chem. Phys. 1984, 80, 5684. ( I O ) Beers, Y . ; Howard, C. J. J . Chem. Phys. 1976, 64, 1541. ( I I ) Lubic, K. G.; Amano, T.: Lehara, H.; Kawaguchi, K.; Hirota. E. J . Chem. Phys. 1984, 81, 4826. (12) Barnes, C. E.: Brown, J. M.; Radford, H. E. J . Mol. Spectrosc. 1980. 84. 119.
( 1 3 ) Saito, S. J . Mol. Spectrosc. 1977, 65, 229. (14) Adrian, F. J.; Cochran, E. L.; Bowers, V. A . J . C h e m Phys. 1967. 17. 5441
0 1986 American Chemical Society
