9274
J. Phys. Chem. 1993,97, 9214-9219
Estimation of the Probability Distribution of End-Group Distances of Chain-Linked Electron Donor-Acceptor Molecules and Radical Ion Pairs: A Monte-Carlo Approach Udo Werner and Hubert Staerk' Abteilung Spektroskopie und Photochemische Reaktionskinetik, Max- Planck- Institut f u r Biophysika lische Chemie, Postfach 2841, 0-37070 Gattingen, Federal Republic of Germany Received: April 6, 1993"
Probability distributions of center-to-center and edge-to-edge distances of chain-linked electron donor-acceptor molecules have been calculated applying a simple Monte-Carlo method. The donor is N,N-dimethylaniline, and the acceptor is pyrene. The linkages, in one study, are different flexible polymethylene chains, (CH& with n = 5-16. In the systems with n = 5-10, the appearance of an odd-even effect in the calculated population of conformations of short distances below 10A correlates well with the fluorescence lifetimes measured recently. Molecules with a partly rigid chain, (CH2)n-trans-cyclohexane-(CHz),, with n = 2, 3 and m = 2-4, were enclosed in the systematic investigation in order to find a molecule which, after generation of the radical ion pair by intramolecular electron transfer, would show a particularly narrow distribution of the exchange interaction between the unpaired electron spins in the paramagneticspecies. In the probability distribution of the compound with n = m = 3, virtually no conformations are observed at short distances if highly polar solvents are considered.
Introduction
interval. The distribution is
In the case of chain-linked electron donor-acceptor (A-D) systems in an appropriate solvent, the linear chain having more than four saturated carbon atoms with no aromatic intermediate structure, it may be assumed that electron transfer (ET) will take place through the solvent (through space) rather than through the chain (through bond). In that case, among the essential parameters determining the reaction are the geometrical orientation and, in particular, the mutual distance of the end groups. It is, however, not sufficient to characterize the distance of the end groups of the stretched or folded chains; more important is knowledge of the relative probability of the appearance of all the possible molecular conformations. Only this prior information about the probability distribution curve for the distances permits more far-reaching explanations of experimental results. One simple way for obtaining pair distribution functions of alkane chain end groups is the Monte-Carlo (MC) method, as described earlier by La1 and Spencer.' This method, which had been applied by others2 and in our laboratory3 for chain-linked A-D systems, is the basis for the treatment described below, with essential modifications and extensions beyond the descriptionsin refs 1-3. The principle of the MC method is to generate a multitude of random conformations and to calculate for each of the conformations its conformational energy, UK as well as the parameters of interest (here, the center-to-center distance r, and the edgeto-edge distance r, of the end groups of one chain-linked donoracceptor system), namely, pyrene-1inkageDMA (N,N-dimethylaniline), in which the linkage comprisesflexible aliphatic chains or flexible chain groups with incorporated trans-cyclohexane. The probability of finding a certain conformationK in an ensemble of such molecules is given by e-&/kT
P(K) =
(1)
xe-uKm/kT m
The probability of finding the distance of the end group in a certain interval, r,,, of width Ar is the sum of the probabilities of all conformations whose end-group distances fall within this
* Correspondence and reprint requests may be addressed to this author. Abstract published in Aduunce ACS Absrracrs, August 15, 1993.
p(r,) = s ( i )
with rm- Ar
< r, < rm
(2)
i
with the mean value for the distance
(3)
Consideration of Forces and Energies The geometry of a polyatomic molecule is sufficiently characterized by the lengths of the bonds between various chemically bonded atom pairs, the bond angles, and the bond rotation. In the case of alkane molecules, the bonds in question are C-C and C-H; the currently accepted value for the C-C bond length is 1, = 1.54 A, and the carbon-carbon bond angle is 8, = 112". The geometries of the end groups, pyrene, Nfl-dimethylaniline, and cyclohexane in the chair conformation are provided by the molecular mechanics program PCModel.4 Only the rotations about the bond between twocatoms, theso-calleddihedralangle, are allowed to ungergo changes. For the dihedral angle in alkanes, three enery minima arise at 4 = 0" (trans), 4 = 120" (gauche-), and 4 = 240" (gau~he+).~ These energy minima are caused by the interaction between the H-atoms and the chain atoms, respectively. The angles are defined in Figure 1. An alkane chain with all dihedral angles in the trans-position is a fully stretched chain, withal1C-atoms locatedin one plane. Onegauche position leads to a kink in the chain. In successive bonds, the additional conformational energy for a specific dihedral angle depends on the preceding dihedral angle. From a detailed calculation, La1 and Spencer' obtained the conformational energies for n-pentane; their data set is reproduced in Table I. The conformational energy was scaled such that the energy would be equal to zero, when 41 = 42 = 43 = 4 4 = 0. The energy values in Table I designate excess conformational energies with respect to the all-trans conformation. Our treatment ignores the high-energy regions g*gF, since the energy of 3 120 cal/mol would merely contribute to a negligible Boltzmann factor. Thus, only the first five possibilities in Table
0022-3654/93/2091-9214$04.00/0 0 1993 American Chemical Society
The Journal of Physical Chemistry, Vol. 97,No. 37, 1993 9275
Probability Distribution of End-Group Distances CH3
CH3
Building Up a Conformation
CH3
Chi3
H
H
+= O( t rans)
m = l 2O0(goucne-)
0 =240°(gauc he+)
Figure 1. n-Alkane dihedral angles with minimal energy (definitions).
TABLE I: Dihedral Angles with Minimal Energies According to Ref 1 conformation 4 2 (deg) 43 (de&!) U (cal/mol) tfF g+g+
0 4 356 112
i3-g
248
248
8+F rg+
114 282
282 114
tt
tg+
0 112
248 112
0
495 495 1376
The starting point is the pyrene molecule. The coordinates of its atoms have been calculated with the aid of the molecular mechanics program PCModel and transferred to the Pascal program written for calculating conformations. The pyrene molecule lies in the xy-plane; the bond leading to the first chain atom is on the x-axis. La1 and Spencer furnished the transformation formalism for the attachment of a new alkane atom to the chain. To begin with, a unit vector is set up which gives the direction of the new bond:
x0 = (-cos e)xl( 1 - cos 6)+ x2cos 6 + (zly2 - zzy,) sin 4
+
yo = (-cos e ) y , ( i - cos 6) y2 cos 4 + (x1z2- x2zl) sin 6
zo = (-cos e)z,(l - cos 4)
+ z2 cos + (ylx2- y2x1) sin 4 I$
1376
(5)
3120 3120
I are considered. The widths of the energy minima permit a deviation from the trans angle of f13O and of * 9 O from the gauche angle, corresponding to an energy variation of 400 cal/ mol with respect to the minimum-energy positions. Therefore, in order to build up individual conformations, in each case one of the angles Oo, 112', and 248' was chosen at random; then a deviation angle A 4 was randomly selected in the range -13O to +13O and in the range -go to +go, respectively, and was added to obtain the final angle 4. The sum of conformational energies resulting from this selection is formed after completion of the conformation. In addition to these short-range conformational energies, long-range energy terms are included between nonneighbored atoms constituting the CH2 segments. A LennardJones potential (4)
was used to determine the intersegmental interactions where the segments are assumed to behave like spherical beads interacting with one another in accordance with this potential appropriate to nonpolar spherical molecules. The same potential is applied to account for the forces between the atoms of the end groups pyrene and DMA and the forces between these end-group atoms and thechain atoms, respectively. Thecorresponding forces within pyrene, DMA, and cyclohexane have already been included in the PCModel treatment. At this point, we emphasize that the primary objective of this work is a comparative study of probability functions for the pair distribution of linked uncharged and charged end groups of A-D systems. From these calculations,we require only that differences in the probability functions, p(r), between aliphatic chains of different chain lengths and between flexible aliphatic chains and partly rigid chains (with trans-cyclohexane), respectively, be sensitively distinguishable. To achieve this sensitive distinction, the values of the parameters e* and r* were carefully chosen. Using€*= 305cal/molandr* = 4.19AfromLalandSpencerl and based on the published work of others, one obtains rather unrealistic results for our molecules with their relatively large end groups. Since these parameters describe the intramolecular forces in the gas phase, simulations already lead to associations of the end groups, indicating complex formation even for uncharged pyrene and DMA. In solution, where intramolecular associations compete with solvation, a smaller value for e* must be chosen. In the following computations, we reduced the value of €* by a factor of one-third, i.e., to 100 cal/mol.
= ( ~ ~ 0 designates ~ 0 ) the direction of the ne_w Whileyector bond, P1= (xlylzl) is the direction of the preceding one, and P2 = (XU~ZZ) is the predecessor of the latter. These nonorthogonal vectors are normalized. They represent the bond angle 0 = 112O, and 4 is the dihedral angle. Hence, the position of the new atom can be plotted according to
Aj = Aj-, + P0b
(6)
The vectors Aj give the positions of the alkane molecules in a spatially fixed coordinate system, where b is the bond length of theC-C bondofthealkane (1.54A). Applying the transformation ofeq 5, the position ofthenew C-atomisdeterminedafter selecting the angle 4 randomly from the permissible range, as described above. Subsequently,the distance to thealreadyestablished atoms is calculated. With the exception of the two closest neighbors on each side, if an atom appears positioned closer than the contact distance of 3 A, the conformation is abandoned and a new posit@ calculation is initiated. To establish a bond with the pyrene, P2 is arbitrarily rotated, since it is assumed that the first bond rotates freely. After the alkane chain is constructed to the desired number n of chain elements in this manner, the electron donor DMA is finally tied up to the chain end. To accomplish that linkage, the molecule, energy minimized by the PCModel routine, is incorporated and placed in the xy-plane with its tie-up atom localized in the origin of the coordinate system. To rotate the molecule into the position determined by the last bond and angle 4, it is necessary to firs; construct an orthonormal local coordinaie system. Its axis P1 points in the direction of the last bond, P2 is the perpendicular projection of the preceding bond, and P3 is a unit vector orthogonal to both preceding vectors
PIJ= Pl 3; = P2- Pl(PlP2)
Pi = PIJX P;
(7)
Next, the DMA is rotated by 4 about the x-axis:
0 -sin 4 cos4
(8)
DMAjdesignates the positionof thejth DMA atom. The rotation in the direction of the last bond is achieved by multiplication with the matrix containing the components of the local basis vectors
9276 The Journal of Physical Chemistry, Vol. 97, No. 37, 1993
Werner and Staerk
TABLE lk Mean End-Group Distances and Short-Range Probability.
Figure 2. Structure and dot-cloud model of Py3(C6)3DMA in the conformation of minimal energy. The atoms are shown with their van der Waals radii. The arrowsrefer to the center-to-center distance r, and edge-to-edge distance ra, as used in the text.
pY5 pY6 pY7 418 pY9 4110 4111 4112 4113 4114 pYl5 4116 2pY9 2q.10 Py2(C6)2DMA Py3(C6)2DMA Py3(C6)3DMA Py3(C6)4DMA
10.1 12.2 11.6 13.1 13.1 14.0 15.4 15.0 16.5 17.0 16.6 17.3 13.8 14.6 16.7 16.1 15.5 16.1
2.7 3.7 4.1 5.4 5.7 6.5 7.5 7.6 8.7 9.3 9.3 10.0 6.0 6.9 7.2 7.4 7.9 7.7
8.5 11.3 9.3 12.4 11.6 12.6 13.8 12.9 14.5 14.7 14.4 14.8 12.2 12.9 16.7 16.0 15.3 15.3
2.2 3.4 3.0 4.9 4.7 5.5 6.5 6.2 7.3 7.7 7.6 8.1 5.1 5.8 7.2 7.4 7.9 7.4
30 16 26 11 23 13 9 7 9 10 10 10 19 11 0.0 0.4 0.4 2
Estimated from 250 OOO conformations. Columns 2 and 3 refer to the uncharged molecules (mol), columns 4 and 5 to the radical ion pairs (RIP) in ACN. bpw (short-range probability) gives the fraction of the p(r,) distribution of the uncharged molecule with distances smaller than i o A.
The starting point for the chain, (CH2),-trans-~yclohexane (CH2),, is the construction of a (CH2), group. Then, the transcyclohexane in chair form is attached at a position where both chain extensions point equatorially from the ring. This is performed analogously to the procedure described above for the attachment of the DMA molecule. The dihedral angle 4 is chosen from among one of the 60°, 180°, or 300’ angles which are related to the energy minima as provided by the PCModel program, designating the dihedral angle between alkane bond and the hydrogen atom at the respective bond position of the cyclohexane ring. The 1 80° angle has a conformational energy which is higher by 900 cal/mol; that value would enter into the sum when this angle is selected. The boat conformation and the cyclohexaneconformation with both chain extensions in the axial position have not been considered here, since their conformational energies are much too high (6 and 4.2 kcal/mol)6 and would therefore only negligiblycontribute to the total distribution. After completion of the ring connection, the construction of the chain is continued with the addition of the (CH2)m section and of the DMA with the same applicable angles for the first bond as above.
Evaluation of a Conformation After a valid conformation is found, the distance (r,) and the edge-to-edge distance (re) are calculated. They are defined as follows (cf. Figure 2): r, is the distance betwen the Enter ofpyrene and the nitrogen atom in DMA and r, is the smallest of all pairwise calculated distances (minus the contact distance of 3 A) between the carbon atoms of pyrene and the carbon atoms in the aromatic ring of DMA, as well as the nitrogen in DMA. The distance between pyrene and the CH3 groups in DMA is not considered here, since the electron to be transferred in an electron-transferprocess, or the unpaired electron in the DMA cation (relevant for the spin dynamics of the donoracceptor pair), has only a negligible residence probability within the methyl group. Conformations yielding distances smaller than the contact distance of 3 A are rejected. In all other instances, the conformational energy UK is calculated from the following contributions: (i) from the energy associated with the dihedral angles; (ii) from the energy associated with the Lennard-Jones potential between atoms which are neither directly bonded nor have a common bonded neighbor, i.e., are separated by at least two intermediate atoms; the Lennard-Jones potentials contribute only for chain members which are separated by at least three
joints, since the short-range forces are already included in Table I as contributing in connection with the conformational energies. (In the structures of pyrene, cyclohexane, and DMA, already energy-minimizied, these energies are not calculated.) (iii) The probability distribution for chain-linked radical ion pairs (2A-dD+) is obtained in the calculations by considering the Coulomb energy
uc= e2/cr, between two elementary charges, localized in the center of pyrene and at the nitrogen atom, respectively. Finally, the Boltzmann factor is determined according to eq 1, both for the uncharged molecule and for the radical ion pair, followed by the final summation in the correspondingchannel for r, and r,. After arriving at the desired possible number of conformations, usually 250000 in the present work: one sees that four distributions become apparent: the cc-distance distributions of the uncharged molecule and of the radical ion pair, respectively, and the ee-distance distributions for both types. Furthermore, within certain distance ranges, the minimum-energy conformations together with the coordinates of all atoms and bond parameters are stored in a file format readable by PCModel. On the propr construction Of the One hand, this Serves to and On the Other conformations during program hand, a review of these conformations can provide insight into the Of the distributions.
Simulation Results Continuous and reproducible distance distributions were obtained if about 250000 conformations were computed and distributed into 400 distance intervals (channels). Thus, about 600conformations per channel were accumulated on the average. This was done with a PC 486 DX/33MHz requiring 1-5 h to calculate 2.5 X lo5conformations,depending on the chain length. Repeated runs on the same molecule gained essentially identical curves, and the error in the mean distance (cf. Table 11) was about 0.3 A. All distributions shown are unfiltered and unsmoothed, and the traces reflect the “noisenthat derives from the discrete computation. Smoother traces are approached with increasing number of conformations evaluated. An example, covering the r, distributions of the radical ion pair (RIP) and the uncharged molecule, is shown in Figure 3 for
Probability Distribution of End-Group Distances
"-
The Journal of Physical Chemistry, Vol. 97, No. 37, 1993 9277
Py9DMA 0 025
0.020
a
0015
-I:
0.010
o 01
0.005
o.Oo0
0
5
10
15
cc-dlstanm [A]
Figure 3. Center-to-center distance probability distribution of pyrene-
(CH2)vDMA. Radical ion pair (RIP),solid line; uncharged molecule, dotted line. Representative molecular conformations with r, = 7.3 A and r, = 17 A are depicted. I-pyrene(CH2)g-DMA (Py9 in short notation). For the calculation of the Coulomb energy of the radical ion pair (cf. eq IO), E = 37 is used, corresponding to the highly polar solvent acetonitrile (ACN). A distribution having two maxima results, one in the range of the stretched all-trans conformation and one in which pyrene and DMA are closely adjacent. In the distance distributions of the RIP, the short-distance range is favored due to the stronger influence of the Coulomb energy. This difference between RIP and uncharged molecule is characteristic for all molecules investigated and for both types of distances ( r , and rsc). Respective representative molecular conformations are depicted whose center-to-center distances are 7.3 A for the folded conformation and 17 A for the stretched one. Distributions for the uncharged molecules PySDMA to Pyl lDMAandforPy16DMAareshowninFigure4. Thecurves for the molecules Pyl2DMA to PylSDMA are removed from the displayed series, because no qualitative changes appear between Pyl lDMAandPyl6DMA. Thedistributionsrepresent the probability of finding the molecule in a distance interval at the distance (in A) marked on the x-axis. The area under each curve is the same and refers to the interval width of 0.0625 A. Each graph contains the r, distribution in solid lines and the r, distribution in dashed lines. Table I1 summarizes the mean values of the center and edge distances for the uncharged molecules and the radical ion pairs. In addition to the molecules with the chain substituted in the I-position of the pyrene, we also estimated the distributions for 2-pyrene(CH2)g-DMA (2Py9) and the corresponding 2Py10. Their distributions, not shown in the figures, are very similar to those for the Py9 and PylO molecules; the noteworthy difference is a broadening, together with a shift to larger distances. This is reflected in the mean distances, Table 11, by an increase of 0.3-0.7 A, when the different substitution positions are compared. A series of chain-linked A-D molecules containing a cyclohexane ring between two alkane groups, namely, I-pyrene (CHz),,-trans- 1,4-~yclohexane-(CH&DMA, in short notation Pyn(C6)mDMA or n(C6)m, was enclosed in the investigation in order to find a molecule which, after generation of the radical ion pair by intramolecular electron transfer, would show a particularly narrow distribution of the exchange interaction between the unpaired electron spins in the paramagnetic species (Le., a more pronounced J-resonance in the magnetic field effect); for explanations, cf. refs 10 and 11. Three requirements are to be met therefore: (i) a narrower distance distribution than that provided by the alkanes, (ii) the center of the distribution in the
I dillawe [AI
dewwe [A]
Figure 4. End-group distancedistributions for 1-pyrene(CHz),,-DMA, n = 5-1 1 and n = 16. The center-to-centerdistance r, is traced in solid lines, the edge-to-edgedistancer,indottedlines. 250 OOOconformations were evaluated for each of the distributions. The areas under all
distributions are the same. Fy2(C42DMA
Fyl(CW)ZDMA
Figure 5. End-group distance distribution for l-pyrene-(CH2),,-rranr1,4cycIohexane-(CH2),,,-DMA, abbreviated Pyn(C6)mDMA(cf. Figure 2), gained from 250 000 conformations.
same region as that for Py8...PylO, and (iii) a part of the distribution in the region where effective electron transfer can occur. The calculated distributions for 2(C6)2,3(C6)2,3(C6)3, and 3(C6)4 are shown in Figure 5 . While 2(C6)2 to 3(C6)3 show narrower distributions, due to the restricted mobility of their chains, the distribution of 3(C6)4 is almost as broad as that for the comparable alkane chain compounds PylO and Pyl 1. The restrictions in 2(C6)2 are so strong that this molecule almost behaves like one with a completely rigid chain, as far as the end-groupdistance (and not the relativeorientation) is concerned. For 2(C6)2 and 2(C6)3, a very small electron-transfer rate is
9278 The Journal of Physical Chemistry, Vol. 97, No. 37, 1993
Werner and Staerk
TABLE HI: Fluorescence Lifetimes T of Pvrene. Connected
I
20
O C
in ACN
.
.
.
.
I
2.4
to the wencher DMA with Varying Chains,-at 377 om and at
e .
20
P
2.0 2.1 2.3 2.3 1.8 1.8 36.3 190
0.43 1.13 1.44 1.33 1.7 1.5 1.7 1.8 1.9
16
1.2
E "
!ia a m fa?
g
10
0
expected, and 3(C6)4 does not satisfy the first requirement (see above). The molecule which, in fact, meets all three conditions best is Py3(C6)3DMA. Its stretched length is intermediate between that of Py9 and PylO and may therefore be compared with thesestructures. The 3(C6)3 distributionisclearly narrower, having virtually no conformations in the low-distance range, in contrast toPy9andPylOwith27%and 14%oftheconformations, respectively, contributing in this range. In order to give an illustration of the substantially reduced mobility of the 3(C6)3 chain with the incorporated cyclohexane ring, the structure with the lowest energy is represented as a dot cloud model in Figure 2; the diameters of the spheres correspond to their van der Waals radii.
Discussion and Comparison with Experimental Data The underlying principle of the Monte-Carlo simulation is rather more appropriate for conformation distributions of a molecule at thermal equilibrium in vacuum. The weakening of the attractive component of the Lennard-Jones potential has provided plausible results for molecules with large end groups in liquid solutions. Ongoing control of the resultant conformations by a molecular mechanics program (PCModel) prevented fundamental errors in our program of calculations. Possible shortcomingscan be encountered (i) through inappropriate choice of initial basis vectors, which would lead to varying rather than fixed bond lengths, and (ii) by limiting the total number of calculated conformations to C50 OOO.* By incorporating the full end-group geometries, the information base used for our calculations is substantially broader than that in ref 3. The transformations described in eqs 8 and 9 additionally permit arbitrary substituents to be built into the molecular geometry, as has been demonstrated for the cyclohexane chain in the present work. Within the context of the present numerical study, we will first discuss earlier results obtained in intramolecular fluorescence quenching experiments on compounds 1-Py-(CH*),-DMA, n = 5-16. In nonlinked and in a certain class of flexibly linked A-D systems, electron transfer (ET) depends on the distance between acceptor A and donor D. In the literature, the transfer probability or rate constant for ET as a function of distance is often expressed as an exponential dependence: kET = ko exp(-Or) with the coefficient fl of the order of 1.6 A-1.9 With this value, one obtains in the distance range between 7 and 10 A a drop in the transfer probability of about 2 orders of magnitude. With decreasing distance, ET is favored and the fluorescence lifetime from the excited pyrene is decreased. From experiments, the rate constant for ET is obtained according to
k,, = -1 _17
To
with the measured lifetime T and the lifetime of the unquenched molecule TO. Table I11lists fluorescence lifetimesof the molecules Py4 to Py16 measured earlier" in the solvent ACN at 20 OC. These data are depicted in the upper graph of Figure 6. A very interesting result of the above computer simulation is the appearanceof an odd-even effect in the distributionsof alkane-
Figure 6. "Odd-even effect". Upper graph experimental fluorescence lifetimes 7 of the compounds PynDMA, n = 5-16; n is marked on the x-axis. Lower graph: short-range fraction pu of the simulated r, distributions (in %), where r, C 10 A. The odd-even effect is evident in both graphs in the region from n = 5 to n = 10.
linked molecules with chain lengths n = 5-10. This suggests that chains with an even number of chain elements must behave differently than their neighbors with an odd number of chain elements. This becomes evident in the differences of the fluorescence decay times, which show larger incremental increases between Py5 and Py6, Py7 and Py8, and Py9 and PylO than incremental decreases between Py6 and Py7, etc. In the computed distributions, this is indicated in a variably strong population of conformations at short distances,as becomesobvious when viewing the last column of Table I1 and the lower graph of Figure 6. There, the fractionof ther,distributionof theuncharged molecule where the distance is below 10A is shown, since it can be assumed that mainly that part contributes to the ET process. Clearly, the compounds with odd chain lengths contribute stronger to the distance range r, < 10 A than those with even chain lengths. Over the same range, this agrees rather well with the fluorescence decay times (cf. Table I11 and Figure 6). For n > 10, this effect vanishes, both in the simulated and in the experimental data. For n > 10, the short-range part of the distributions almost stays constant, while the mean distances still increase. This can explain the further, now steady, increase of the fluorescence lifetime. It is through these observations that we can now interpret previously measured data," which could not be explained satisfactorily at the time. Now, these earlier results can be ascribed on purely geometric grounds to the higher probability of finding short end-group distances in the chains with odd numbers of chain elements. Further agreement between simulation and fluorescence decay times is the fact that the mean values for the distances are increasing, up to about PylO. From there on, changes are reduced significantly; the fluorescence lifetimes exhibit the same behavior. In 2-Py9 and 2-Py10, the distributions shob a shift to larger distances. This behavior is reflected in the decay times and also in the magnetic field effect of the corresponding radical ion pairs that is shifted to lower magnetic field ~trengths.~JO This supports the hypothesis that in these molecules interactions between end groups take place through space and not through the chain bonds, for it is the chain which is completely identical in both bonding variations. The distance distributions of the first three cyclohexaneincluding compounds (cf. Figure 5 ) are distinctly different from those of the alkane-linked molecules. We selected Py3(C6)3DMA for synthesis and measurements, with the expectation of finding a magnetic field effect with characteristic and interesting features. Although the stretched length of 3(C6)3 lies between that Py9 and PylO, virtually no conformations are observed at short distanw in the probability distribution. When oneenvisions a mechanical molecular model, the absence of occupied confor-
Probability Distribution of End-Group Distances mations at short distances remains unclear as the various rotational degrees of freedom are contemplated. In that mechanical model, the end groups can readily be brought into close proximity or near contact. The fact that our calculations do not lead to such near-contact conditions is due to the relatively high conformational energy with the associated low Boltzmann factor of specific rotational angles. In the above-mentioned strictly mechanical model, such rotational motions can be readily exaggerated, without awareness of constraints. We see from Figure 2 how the cyclohexane ring restricts the intramolecular mobility of the entire molecule, thereby preventing a close-proximity condition. The emphasis of conformations with large end-group distances is experimentally confirmed by a fluorescence decay time of 36 ns in ACN. That corresponds to a 21-fold smaller fluorescence quenching factor than that seen with PylO, since Py3(C6)3DMA generates no contributions from narrower conformations. The following paper in this issuelo addresses the effects of such a distribution on the spin dynamics and on the magnetic field dependent reaction yield from radical ion pairs.
Acknowledgment. The compound pictured in Figure 2 has been synthesized by Dr. W. Ktihnle. The synthesis is described
The Journal of Physical Chemistry, Vol. 97, No. 37, 1993 9279 in ref 10. We thank B. Frederichs and A. Wiessner for checking the lifetime data.
References and Notes (1) Lal, M.; Spencer, D. Mol. Phys. 1971, 22,649.
( 2 ) de Kanter, F. J. J.; den Hollander, J. H.; Huizer, A. H.; Kaptein, R. Mol. Phys. 1977,34,875. (3) (a) Busmann, H.-G.; Staerk, H.; Weller, A. J. Chem. Phys. 1989, 91,4098. (b) Busmann, H.-G. Dissertation, University of G&tingen, 1987. (4) PCModel, Molecular Modeling Software, Serena Software, Bloomington, IN, 1990. (5) Morrison, R. T.; Boyd, N. Lehrbuch der organischen Chemie; 5. Aufl. Verlag Salle und Sauerllnder: Frankfurt/Main, 1982. (6) Christen, H. R. Grundlagender organischen Chemie;2. Aufl. Verlag Chemie: Weinheim, 1978. (7) Werner, U. Dissertation, University GBttingen (to be presented), 1993. (8) The number conformations (10 OOO) calculated in ref 3 was much too low. (9) (a) Rau, H.; Frank, R.; Greiner, G. J. Phys. Chem. 1986,90,2476. (b) Dexter, D. K. J. Phys. Chem. 1953,21,836. (c) Inokui, M.; Hyrayama, F. J. Chem. Phys. 1965,43, 1978. (d) Gnarr, T.; McGuire, M.; Strauch, S.; McLendon, G. J . Am. Chem.Soc. 1983,105,616. (e) Marcus, R. A.; Siders, J. P. J. Phys. Chem. 1982, 86,622. (10) Werner, U.; Kilhnle, W.; Staerk, H. J . Phys. Chem.,following paper in this issue. (11) Staerk, H.; Busmann, H. G.; Ktihnle, W.; Treichel, R. J. Phys. Chem. 1991, 95, 1907.
