J . Phys. Chem. 1989, 93, 3624-3630
3624
approximation to S and P, taking d[P]/dt = 0 and d[S]/dt = 0, then one has the simplification J I. = J C = J 0 (6.22)
If the rate of removal of P is first order in P, one has d(,/dt = -w[P]
or dtO/dt = A " + B"[,
+ C"(,
(6'21)
Then (6.19) and (6.21) would represent two coupled equations in the two variables 5, and E,. If one applies the steady-state
The case of coupled open systems is of great importance in biology. This paper has tried to illustrate a simple means by which the time course of such reactions can be calculated. Registry No. Dihydrofolate reductase, 9002-03-3.
Influence of Initlal Electrostatic Interactions on Final Product Distributions in Gas-Phase Organometallic Ion/Molecuie Reactions. 2. The Cr+/n-Butyl Chloride System Deborah J. Hankinson: Clifford B. Miller,? and John Allison* Department of Chemistry, Michigan State University, East Lansing, Michigan 48824 (Received: August 8, 1988)
Electrostatic interactions between a transition-metal ion and n-butyl chloride are studied to investigate the possible relationship between initial ion/molecule interactions and final product distributions that have been reported for low-pressure bimolecular reactions. It is proposed that before bond cleavage, bond formation, and/or electron reorganization begins, metal ions and organic molecules form a complex that is sufficiently long lived such that various geometries may be sampled. Localization of the ion about some parts of the molecular framework may be more likely than about others, due to interactions of the ion with polarizable portions of the molecule as well as with the charge distribution throughout the system. Various configurations of butyl chloride are considered, to investigate the dominant reaction mechanism, insertion into the C-CI bond. Also, configurations are considered that allow for a six-membered cyclic intermediate to be sampled. These have been proposed to be important in the chemistry of larger polar molecules with first-row transition-metal ions.
Introduction In the past 15 years, the gas-phase, bimolecular chemistry of transition-metal ions such as Fe', Co+, and Ni+ with polar and nonpolar saturated, unsaturated, and aromatic organic compounds has been extensively studied.' This area of research may provide unique insights into how transition metals react in homogeneous and heterogeneous catalysis. However, even gas-phase systems are complex, and our understanding is not yet to the point at which the products (and their distribution) for a given transition-metal ion/organic molecule system can be predicted. The key mechanistic component in these systems appears to be an insertion step,'P2 in which the transition-metal ion (M+) reacts with an organic molecule, AB, to form A-M'-B. Following this step, products formed may be due to either charge- or H-atom transfer processes. Specific thermochemical information is increasingly more available due to experimental and theoretical efforts; however, thermodynamic considerations alone frequently do not correlate with products distribution^.^*^ One aspect of these reactions that must be considered is the relationship between the chemistry observed and the nature of the experiment. That is, the aspects of the chemistry that are due to the fact that the reactions occur in the gas phase and that one of the reactants is an ion must first be understood. With this, those aspects of the chemistry due solely to the electronic structure of the metal can be identified-and it is these latter insights that will be most useful in understanding condensed-phase systems. We focus here on early events in transition-metal ion/organic molecule reactions-interactions that occur before the chemistry (bond cleavage and bond formation) begins. There are both geometric and thermodynamic aspects to these early portions of the reaction coordinate. The geometric factors may be important in controlling branching ratios. When the ion and molecule first 'Current address: Department of Chemistry, Princeton University, Princeton. NJ 08544.
0022-3654/89/2093-3624$01.50/0
come together, the resulting complex is dynamic, allowing the ion to sample the various local chemical environments that the molecule has to offer. The ion/molecule complex will be more stable in some geometries than in others. The ion may find some "hot spots" about the molecular framework that are highly attractive and will thus spend a larger fraction of time in these regions (close to certain atoms/bonds). Thus, initial interactions determine the likelihood of the ion being in close proximity to various bonds, and the thermochemistry of the situation would determine whether an insertion at that site would follow. This concept has been developed in the context of chain-length studies for such system^.^ For example, consider the reactions observedS for Co+ reacting with a small alkyl chloride, n-propyl chloride, and one with a larger chain, n-heptyl chloride (eq 4-9). Co'
+ n-C,H7C1
-
-
C3H7++ CoCl (72%)
(1)
COC,H6+
(2)
+ C3H6
(5%)
(3)
Co+ + n-C7HI5C1 C4H9+ [CoC3H6C1] (41%)
(4)
--
+
CoHCI'
HC1 (23%)
+
+ [COCI + C2H6] C7Hls++ CoCl (18%) C5H9'
(7%)
(5)
(6)
CoCSHro++ C2HsCl (19%)
(7)
+ H2 + C3HTCI (6%) CoC3H,+ + C4H9C1 (9%)
(8)
COC,H6+
(9)
( I ) For a recent review, see: Allison, J. Prog. Inorg. Chem. 1986, 34, 627, and references contained therein. (2) Allison, J.; Ridge, D. P. J . Am. Chem. SOC.1977, 98, 7445. (3) Radecki, B.; Allison, J. Organometallics 1986, 5, 41 I. (4) Hankinson, D. J.; Allison, J. J . Phys. Chem. 1987, 91, 5307. (5) Tsarbopoulos, A,; Allison, J. J . Am. Chem. SOC.1985, 107, 5085.
0 1989 American Chemical Society
Cr+/n-Butyl Chloride System The reaction of propyl chloride suggests that all products are formed via the insertion intermediate C3H7-Co+-C1. One might expect the results for small molecules to be useful in predicting those for larger molecules; however, in the case of heptyl chloride, insertion into C-C bonds "far" from the polar C-Cl bond is observed. It has been proposed that the ion first complexes with the electronegative C1, and, if the chain is sufficiently long, parts of the chain can then interact with the metal ion via cyclic intermediates, bringing such remote sites into close proximity, making them candidates for insertion.' This model also suggests why some bonds are not attacked and why sites even farther from the functional group are attacked in nitriles6s7(due to the linear geometry about the atoms in the cyano group). These observations support the concept that upon approach of the reacting species, insertion is not immediate, but there is sufficient time for the reacting pair to sample various geometries (at least, for thermal energy reactions). Thermodynamic aspects of these early events have also been considered. It has been suggested that the energy released upon initial M+-AB complexation is important in overcoming early barriers leading to the intermediate8 A-M+-B. That is, there is interest in knowing not only where the "hot spots" are about the molecule but also the depth of the potential well at these locations. For example, the unreactive behavior of Pr+ and Eu+ with small alkanes was discussed by Schilling and Beauchamps using these concepts. Adduct formation may not yield a complex that is sufficiently "activated" because these metal ions are relatively large, thus ion-molecule separations are large, and the resulting electrostatic interaction energies are small. With this background on the importance of "early events" in these ion/molecule reactions, a few comments should be made on the suitability of an electrostatic model for probing such processes. Is an electrostatic description appropriate for studying ion/molecule complex geometries, or must an ab initio molecular orbital (MO) calculation be performed? Here we focus on the interactions of a transition-metal ion with a polar organic molecule, butyl chloride. An M O calculation would allow interactions such as dative bonding (M++-:ClR) to be considered between the metal ion and a lone pair of electrons on the halogen. We suggest that the contributions of such interactions are minor compared to electrostatic interactions. To support this, we have recently reported results of multiconfigurational self-consistent field (MCSCF) calculations on a variety of M+CO molecular ions.9 The traditional Dewar-Chatt modelt0 of metal-ligand bonding certainly suggests that a synergistic interaction should take place, with electron donation in the u-system from the lone pair on the C, and metal-to-ligand backbonding through the mystem. While this is, in fact, the case for neutral MCO complexes,I' the bonding scheme collapses to one dominated by electrostatic interactions when an electron is removed from the metal. This has been observed for a number of metal ionsI2 and supports the concept that prior to that point where the chemistry begins, electrostatics may dominate these systems and an electrostatic model is appropriate. The model that we use4 is simple. The expression used in this work for the ion/molecule electrostatic potential does not limit the size of the molecule and allows for the consideration of specific configurations. The molecule is not treated as a point polarizable dipole, but the calculation allows for the fact that the ion cannot (6) (a) Lebrilla, C. B.; Schulze, C.; Schwarz, H. J. Am. Chem. SOC.1987, 109, 98. (b) Drewello, T.;Eckart, K.;~Lebrilla,C. B.; Schwarz, H . Int. J . Muss Spectrom. Ion Proc. 1987, 76, R1. (c) Lebrilla, C. B.; Drewello, T.; Schwarz, H. J . Am. Chem. SOC.1987, 109, 5639. (d) Lebrilla, C. B.; Drewello, T.; Schwarz, H . Int. J . Mass Spectrom. Ion Proc. 1987, 79, 287. (7) Stepnowski, R.; Allison, J. Orgunometallics 1988, 7 , 2097. (8) Schilling, J. B.; Beauchamp, J. L. J . Am. Chem. SOC.1988, 110, 15. (9) (a) Allison, J.; Mavridis, A,; Harrison, J. F. Polyhedron 1988, 7 , 1559. (b) Mavridis, A.; Harrison, J. F.; Allison, J. J . Phys. Chem., in press. (10) (a) Dewar, M . J. S. Bull. SOC.Chim. Fr. 1951, 18, C71. (b) Chatt, J.; Duncanson, L. A. J. Chem. SOC.1953, 2939. (1 1) Bauschlicher, C. W. J . Chem. Phys. 1986, 84, 260. (12) Merchan, M.; Nebot-Gil, I.; Gonzalez-Luque, R.; Orti, E. J . Chem. Phys. 1987,87, 1690.
The Journal of Physical Chemistry, Vol. 93, No. 9, 1989 3625 be simultaneously close to parts of the molecule that are spatially well separated. The molecule is treated as a collection of polarizable bonds and as a collection of atoms. On the atoms, small partial charges are localized. Also, ion/atom repulsive interactions are included. We certainly recognize that all of these aspects are approximations, and their strengths and weaknesses are understood. Nonetheless, their utility in considering how the various interactions behave, in terms of directionality and magnitude have been substantial. For a good discussion of the strengths and limitations of electrostatic models for studying ion/molecule interactions, the work of Tomasi13 should be consulted. In the first paper in this series: the Cr+/n-butane system was studied. The metal ion Cr+ is used since it is spherically symmetric (ground-state electronic configuration is a 6S, [core]3d5). Butane was selected because it is the simplest organic molecule that contains two types of skeletal bonds, the interior and terminal C-C bonds. An electrostatic description of the interaction suggests that the potential well about the interior C-C bond is deeper (more attractive) than that about the terminal C-C bond, which correlates with the fact that insertion into the interior bond occurs to a greater extent (while other thermodynamic considerations do not correlate with product distributions). The "bond strengths" determined with this model appear to be larger than what would be expected. We certainly did not expect this simple model to accurately predict bond energies of electrostatic complexes-its strength lies in the intuition it helps us to develop. Also, comparison of numbers obtained in this way are useful, reflecting the relative energies of various "hot spots". The reader should keep in mind that the computations are being done to explore possibilities, not as definitive calculations. Also, it should be made clear that while the calculations presented are for Cr+ as the first-row transition-metal ion, the specific gas-phase chemistry of this metal is not the subject of the investigation. The ion was chosen only because of its electronic configuration, which simplifies the calculation. In the gas phase, transition-metal ions such as Co+ react with n-butyl chloride5 as follows:
-
Co+ + n-C4H9C1
-+
+
C4H9+ CoCl (81%)
+
C O C ~ H ~ ' HCl
+ H2
(10)
(19%)
(11)
The products of reactions 10 and 11 are both formed via Co+ insertion into the C-C1 bond. From the C4H9-Co+-CI intermediate, charge transfer can occur, or a P-H can shift from the butyl group, yielding (C4H8)Co+(HC1). There is apparently a rapid dehydrogenation of the butene ligand to form butadiene. This has also been observed in the bimolecular reaction of Co+ with butene,14 reaction 12, so it is not unexpected. cO+
l-C4H$
-
COC4H6'
+ Hz
(12)
The chemistry of butyl chloride is much different than that for butane, and the model used here may be used to determine to what extent these systems differ due to (1) the negative charge on the C1, (2) the size of the C1 atom, (3) the polarizability of the C-CI bond, and (4) the charge distribution within the alkyl group.
Computational Details The electrostatic interactions between Cr+ and n-butyl chloride are calculated, for fixed configurations of the molecule, with the ion at some specific position relative to the molecule, by using an equation of the form E = XEiid
+ XEip+ X E ,
Three sets of terms are calculated. The first are ion/induced dipole terms, which all lead to attractive interactions. In this model, the bond-polarizability approximation is used. The ion interacts ~~
~~~
(13) Tomasi, J. In Quantum Theory of Chemical Reactions I . Collision
Theory, Reaction Path, Static Indices; Daudel, R., Pullman, A., Salem, L., Veillard, A,, Eds.; D. Reidel Publishing: Boston, 1980; p 191. (14) Armentrout, P. B.; Halle, L. F.; Beauchamp, J. L. J . Am. Chem. SOC. 1981, 103, 6624.
3626
The Journal of Physical Chemistry, Vol. 93, No. 9, 1989
TABLE I: Atomic Charge Distribution (millielectrons) on Atoms of n-Butyl Chloride designation scheme for atoms:
Hankinson et al. charges on the H's. The C bonded to the CI is very positive, and the other C atoms are negative. This description is consistent with the one discussed by Pople et in which the distribution of positive charge in the alkyl group of polar compounds of this type is not distributed as CI6-CH 6+CH 66+CH 666+CH 6666+ 2
atom
C(1) C(3) H(1) H(3)
H(5) H(7) H(9)
charge
atom
charge
-384.0 -233.3 124.8 124.5 +111.9 +114.4 +112.9
C(2) (74) H(2) H(4) H(6) H(8)
-209.5 +170.0 +124.5 +111.9 +114.4 f112.9 -395.3
+ +
c1
with each of the 13 bonds in the molecule, leading to 13 terms having the formI5 &(r) = - a z 2 e 2 / 8 ~ t o r 4 In this description, an ion with a charge ze at a distance r from a bond center induces a dipole in the polarizable bond. The bond polarizability, a , has the form16 a = a,, cos2 8
+ a i sin2 8
where 8 is the angle formed between the ion-to-bond-center and bond vectors. Each bond is characterized by a parallel and perpendicular polarizability, a,,and aI. In units of cubic centimeters per molecule, the following polarizability components16 and aI = 0.2 X were used: for C-C bonds, a,, = 18.8 X for C-H bonds, a,I = 7.9 X and a L = 5.8 X for C-CI bonds, ail = 36.7 X and aI = 20.8 X The strengths and weaknesses of this bond-additive description of molecular polarizability have been addressed.]' The numerical values used here suggest that (1) C-CI bonds are the most polarizable of the three types of bonds in the molecule and (2) C-C bonds are unique in that they exhibit very little polarizability if the applied field is perpendicular to the bond. This latter point becomes important in these calculations, since the metal ion may be close to a C-C bond, but the Eiidterm for that ion/bond pair may be small if the approach is perpendicular to that bond. The second set of terms recognizes the fact that the molecule has a permanent dipole moment. The chlorine atom is the negative end of the dipole, carrying a negative charge, and a positive charge of equal magnitude is distributed among the atoms of the butyl group. Here, point charges are localized on the atoms and are computed by using an extended Hiickel calculation.l* The ion interacts with each of these atom-localized charges to yield repulsive or attractive interactions having the formIg Eip(r) = zlz2e2/4mor where the ion with a charge zle interacts with an atom with a charge z2e, separated by a distance r. The charges on the atoms used, as well as the numbering scheme for the atoms in butyl chloride that will be used, are listed in Table I. At this level of description of the distributed charges in the molecule, the chlorine is negative, and the positive charge is distributed throughout the butyl group. The charges on the C atoms vary more than the ( 1 5 ) Benson, S. W. The Foundations of Chemical Kinetics; McGraw-Hill: New York, 1960. (16) (a) Hirschfelder, J. 0.;Curtiss, C. F.; Bird, R. B. Molecular Theory of Gases and Liquids; Wiley: New York, 1954. (b) Denbiegh, K. G. Trans. Faraday SOC.1940, 36, 936. (17) (a) Smith, R. P.; Mortensen, E. M. J . Chem. Phys. 1960, 32, 502. (b) Smith, R. P.; Mortensen, E. M. J . Chem. Phys. 1960,32, 508. (c) Wang, S . N . J . Chem. Phys. 1939, 7, 1012. (d) Le Fevre, R. J. W. In Aduances in Physical Organic Chemistry; Gold, V., Ed.; Academic Press: New York, 1965; Vol. 3, p I. (18) Code written by J. F. Harrison at Michigan State University. (19) Halliday, D.; Resnick, R. Physics; Wiley: New York, 1966; Parts I and 11.
2
2
3
Instead, inductive effects along the chain lead to alternation of charge of adjacent groups. That is, the CH2 group attached to the CI has a net positive charge, the next CH2 group has a net negative charge, and so on. Again, any model that forces charges onto the atoms has limitations;20,2'however, these approximations have been useful in predicting and understanding molecular features such as dipole moments. To represent the repulsive interactions between the ion and the atoms in the molecule, an rI2-dependent term was chosen, similar to that used in the Lennard-Jones 6-12 potential.22 The repulsive interaction takes the form E,(r) = 4d(a/r)I2
where the ion and atom are separated by a distance r . Values of a and d a r e extracted from ab initio potential curves for Cr+-H, Cr+-C, and Cr+-CI that were reported by Harrison et al.23 We have chosen the following values: for the Cr+--H interactions, J atom-' and a = 1.18 A; for Cr+--C interd = 17.44 X J atom-' and a = 1.41 A; for Cr+--CI actions, d = 22.78 X J atom-] and a = 1.65 A. interactions, d = 32.71 X These repulsive terms reflect the relative size of the atoms, CI > C > H. For each position of the ion, the distance from the ion to all 14 atoms is computed, and 14 repulsive terms calculated. These may be insufficient to account for repulsive interactions, which would lead to total energies that are larger (more attractive) than they should be. Again, we certainly realize the limitations of this model, but find it useful in suggesting possibilities. Calculations were performed using AT&T and DEC equipment. An AT&T PC (Model 7300) and an AT&T 3B2-400 computer are used for creating input files and manipulating/plotting final results. The computations are currently performed on either a DEC VAX 11/750 or the 3B2-400 at a double-precision level. Consider the configuration of butyl chloride shown in Table I, which will be referred to as configuration 1. The calculation requires atomic coordinates, which are calculated by placing the center of mass of the molecule at the origin and using the following geometric parameters: C-C bond lengths = 1.54 A, C-H bond lengths = 1.10 A, C-CI bond length = 1.78 A, and tetrahedral angles. As shown, the "major plane" is the X Y plane, which contains all four C atoms, the chlorine atom, and one H atom, with the remaining eight hydrogens symmetrically located outside of the major plane. With the molecule thus defined, a plane is selected. Suppose we chose the X Y plane. The next step is to define a rectangular region within that plane in which calculations are performed, such as a 10 A X 10 A rectangle centered at the origin. The metal ion is then placed at a starting point such as (-5,-5,0), and the potential calculated. The ion is moved through this region in 0.05-8, steps, and a (position, potential energy ( E ) ] array is generated. From this array, the positions at which the ionic center may be placed corresponding to, for example, -10 kcal/mol can be collected and their positions plotted. In this way, families of constant-potential curves can begenerated in a selected plane. With these results, potential grzdients can be studied, and the regions of highest attractive potential can be identified. The (20) Pople, J. A,; Gordon, M. J . Am. Chem. SOC.1967, 89, 4253. (21) (a) Fliszar, S . Charge Distributions and Chemical Effects; Springer-Verlag: New York, 1983. (b) Del Re, G. J . Chem. SOC.1958, 4031. ( c ) Smith, R. P.; Mortensen, E. M. J . Am. Chem. Soc. 1956, 78, 3932. (d) Smith, R. P.; Ree, T.; Magee, J. L.; Eyring, H. J . A m . Chem. SOC.1951, 73, 2263. (e) Hehre, W. J.; Pople, J. A. J . Am. Chem. SOC.1970, 92, 2191. (f) Smith, R. P.; Eyring, H . J . Am. Chem. SOC.1952, 74, 229. (22) Daniels, F.; Alberty, R. A. Physical Chemistry, 3rd ed.; Wiley: New York, 1966. (23) (a) Alvarado-Swaisgood, A. E.; Allison, J.; Harrison, J. F. J . Phys. Chem. 1985, 89, 2517. (b) Harrison, J. F. J . Phys. Chem. 1986, 90, 3313. (c) Alvarado-Swaisgood, A,; Harrison, J . F. J . Phys. Chem. 1988, 92, 5896.
The Journal of Physical Chemistry, Vol. 93, No. 9, 1989 3627
Cr+/n-Butyl Chloride System -10
I30”
F
a)
-3 I
-40
Figure 1. Data for potential energy contours for configuration 1 of butyl chloride in the XY plane.
program allows either E vs position, or any component of the function vs position, to be investigated. A second type of calculation can be performed that is a radial search for potential minima, yielding “minima plots”. A radial calculation in the X Y plane is performed as follows: A ray is extended from the center of mass, initially along the +Y axis (“up”)-this initial ray corresponds to an angle of 90’. The ion is brought toward the molecule along that ray, and a potential curve is computed. The most attractive point, the bottom of the well for that approach, is identified. The ray is then moved counterclockwise by O S 0 , and the calculation repeated. The ion is moved along each ray in 0.02-A steps. The calculation is repeated as the ray is swept through 360°, yielding the points about the molecule, in this plane, that correspond to the bottom of the attractive potential well about the molecule. The location of these points and the energies computed for each can be plotted.
Results and Discussion To investigate the various “local environments” that this molecule may present to the ion and to determine which of these are most attractive, calculations are performed in a variety of planes for a variety of configurations. The types of data calculated for configuration 1 will be presented in detail, and selected results will be presented for the other configurations. Configuration 1 of Butyl Chloride. Figure 1 shows a family of potential curves in the X Y plane for this configuration of butyl chloride. (Note that in this figure and all others the projection of all the atoms and bonds onto the plane under study are shown, with the C1 atom at the right end of the molecule.) If this is compared to the results previously reported for the analogous configuration of b ~ t a n ea, ~number of features are apparent. The potential curves resemble somewhat those obtained for butane but are “skewed” toward the negative halogen. There are still positions on the alkyl group that are attractive to the ion, as in butane, such as “atop” the methyl group (situated between the three C-H bonds), atop the C(l)-C(2) bond (where the ion is in close proximity to three C-H bonds), and atop the C(2)-C(3) bond. Of these three, the latter is the most attractive. When the ion is close to the C(2)-C(3) bond in this plane, it can polarize the four C-H bonds (between which it is nested) and polarize the C( 1)-C(2) and C(3)-C(4) bonds (which have significant cyll values). Since the CI carries a negative charge, one might expect that a linear arrangement of C-Cl-Cr+ would be very attractive, when the ion is farthest from any parts of the positively charged alkyl group. However, in addition to carrying a negative charge, the halogen is relatively large, preventing a very close approach and a large attraction. The most attractive “hot spots’’ are above and below the C-CI bond in Figure 1 , with the location “below” being by far the most attractive location in this plane. Here, the ion remains close to the negative C1 atom, somewhat away from C(4), which carries the largest positive charge, can polarize two C-H bonds [these being C(3)-H(6,7)], and polarizes the C(2)-C(3) bond. This model predicts what one might expect. The most attractive environments place the ion “atop” the various skeletal bonds in this plane, since, at these locations, the atom will be close to a number of C-H bonds and can frequently interact with one or
I
-!E
I
i
I
1
1
:
I
I
,
/\I 1‘1
I
W
-53
’
””&
I
!BO“
I
do’
1:
I
3dO“
450‘
ANGLE
Figure 2. Results of the search for potential energy minima about configuration 1 of butyl chloride in the XY plane. Figure 2a shows the location of the points; Figure 2b shows the potential energy corresponding to placement of the Cr’ ion at those various points. An angle of 90’ corresponds to the calculation along a ray extending from the origin to the +Y direction. The ray is rotated counterclockwise,corresponding to larger values of the angle.
more C-C bonds with substantial Eildterms. For configurations of the molecule in which the skeletal bonds can be confined to one plane, such studies in that plane are important since only in the plane will contributions due to ion/induced dipole terms involving the C-C bonds play a major role. Outside of this plane, the ion will always be approaching the C-C bonds perpendicular to the bond vectors, and this geometry does not allow for interaction with the C-C bonds, due to their small c y I . An important feature to note is that the most attractive location brings the ion perpendicular to the C-Cl bond, apparently “set up” for insertion into that bond to follow. That is, this nspect of the description is consistent with the observed chemistry of transition-metal ions with butyl chloride. Figure 2 shows the result of the minima calculation in this plane. Figure 2a shows the location of the points corresponding to the most attractive points about the molecule, with the energies corresponding to these points shown in Figure 2b. An angle of 0’ corresponds to approach toward the center of mass (the origin, indicated by the plus sign in Figure 2a), along the X axis, from positive values of X . Two points, labeled A and B, have been selected, with A being the most attractive point in this plane, and B being the location close to the C(l)-C(2) bond. The breakdown, showing how the overall values arise from the contributing terms, for these two points are listed in Table 11. In the previous work on b ~ t a n esuch , ~ calculations in the three major planes allowed for the various local environments about the molecule to be easily studied. In butyl chloride, the symmetry is much different, and studies in the three major planes may be insufficient to locate the “hot spots” outside of the X Y plane. Because of this, we have found it useful to do calculations in a number of parallel planes. (Actually, these can be plotted on transparencies, stacked, and separated to give a graphic threedimensional overview of the potential about the molecule.) Figure 3 shows computational results for a collection of planes, all parallel to the X Y plane. These results show how E varies for ionic approach from the “side” of configuration 1. The planes are
3628 The Journal of Physical Chemistry, Vol. 93, No. 9, 1989
Hankinson et al.
TABLE II: Breakdown of Individual Terms (kal/mol) for Points A and B point A
point B
E::. Terms
bond
-3.4466 -2.17340 -20.6215
C(4kH(8,9)
Ei, Terms +7.60 +9.23' -28.88 +9.61' -20.42 +22.88' 42.10 +I 1.69' +23.45 -60.39
atom
n
II
ri I
-10.7412 -3.5 154' -1.8966 -14.4255. -7.8640 -0.6912' -0.5524 -0.3393. -0.9497 +24.63 +l4.21'
-61.00 +2l.65' -38.91 +9.73* -22.84 +8.75' +13.22 -21.80
E, Terms
+o.ooooo
atom
0.00002~ 0.00024 0.00014' 0.00535 3.58195' 8.65416 0.00133' 0.34627 11.12388 -54.52
3.05107 0.00429' 1.87656 2,33459. 12.23523 0.00013' 0.00564 0.00004' 0.00036 0.00005 -36.22
*Each hydrogen. arranged about the molecule as shown in Figure 3a, moving to negative values of Z. As the plane moves away from the major XY plane, other hot spots appear. In Figure 3e, a position corresponding to a side-on approach of the butyl group hecomes important. Here, the ion is nested among all four C C bonds and is relatively close to the four C-H bonds that lie 'behind" t h e m plane. Again, variations of the scenario discussed in Figure I, where the ion is situated below the C C I bond, are attractive. At Z = -3.0 A, the dominance of the electronegative CI atom can be seen, suggesting that initial approach may be controlled by the CI and directed toward the C-CI bond, in addition to having a very attractive position close to that bond. We have found that the approach used in Figure 3, consideration of data for parallel planes, is the most efficient for locating the most attractive ion/molecule geometries with this model. Configuration 2 of Butyl Chloride. Rotation about the C(2)-C(3) bond of configuration 1 by 180° yields the second extreme configuration for butyl chloride. Results of the calculation in the XY plane are shown in Figure 4. In this configuration, a new environment is created, in which the ion is nested between four C-H bonds; it could also he thought of as forming, electrostatically, a four-membered ring structure, I. There are two
H
\
H
Cr'
I
I of these, centered about [C(l)C(2)C(3)] and [C(Z)C(3)C(4)]; the potential energy associated with each varies because of the charge distribution in the alkyl group. Actually, for this con-
Figure 3. Potential energy contours for a family of parallel planes. Figure 3a shows the orientation of the planes about the molecule. Figures 3 b h wntain the results faw e n olanes. which extend to -3 A 'behind" the major (Xu)plane. The canto& on each part are separated by -10 kcal/mol.
-3
Figure 4. Potential energy wntours f a configuration 2 of butyl chloride in the XY plane.
figuration, this environment at [C(l)C(Z)C(3)] is slightly more attractive than the point that is equivalent to position A in configuration I, *atop" the C-CI bond. In calculations out of the major (XY) plane for configuration 2, no locations more attractive than those shown in Figure 4 are found. Confieuration 3 of. Butvl . Chloride. Rotation of the C ( 3 ) C ( 4 ) bond b;lROO in configuration I yields the third configuration of but11 chloride that W A S considered. This was of interest since it allows a preliminary investigation of the types of intermediates that have been proposed for longer chain polar compounds. where the ion may first complex with the halogen and then interact with parts of the chain remote from the functional group via a cyclic intermediate. One can conceive of such a six-membered ring being formed electrostatically with hut11 chloride (the a t o m in the "ring" being the four C atoms. the CI, and the metal ion). Figure Sa
The Journal of Physical Chemistry, Vol. 93, No. 9, 1989 3629
Cr+/n-Butyl Chloride System
a)
\@ -3
Figure 5. Two potential energy contour plots for configuration 3 of butyl chloride in (a) the XY plane and (b) for a parallel plane, corresponding t o Z = 1.25 A.
shows the results of the calculation in the XY plane for configuration 3. The cyclic ring, 11, is very asymmetric, due to the -I-
Cr
:.t:.::.i:.::...,, :.:::.:
....
\C-
C
/
I1 relatively long C-C1 bond and the size of the C1 atom. While the position atop the methyl group is only moderately attractive, when the additional interaction with the C1 is added, it becomes very attractive. It has been suggested that, in longer chains, C - C bonds containing the C identified as C(1) here are candidates for i n ~ e r t i o n . This ~ intermediate, in which multiple parts of the molecule interact with the ion simultaneously, is the most attractive point found for all of the configurations studied, which is certainly not surprising. There is another very attractive spot for the ion, for configuration 3, that corresponds to approach from the Z direction toward the interior of the molecule. This can be seen in the computational results for a plane parallel to the XY plane, for Z = -1.25 A (of course, the results are identical for Z = + 1.25 A, since the molecule is symmetric on either side of the XYplane). This is shown in Figure 5b. The ion is close to the four C-H bonds that lie “behind” the XY plane and is also close to the C-Cl bond and the C1 atom. Again, this is not unexpected, since this relatively compact configuration 3 allows for a large number of attractive interactions to occur simultaneously, unlike the extended form, configuration 2. From these calculations with this simple model, realizing its limitations, a number of conclusions can be drawn. When a positive ion approaches a polar molecule, the charge distribution within the molecule may strongly influence the interaction. For a molecule RX, as the electronegativity of X increases and the charge on X increases, the positive charge on the C attached to X increases as well-thus attack of/insertion into the C-X bond is not straightforward since, while the M+-X interaction is attractive, the M+-C interaction is repulsive. Nonetheless, interactions with various parts of the alkyl group can place the molecule in close proximity to the C-X bond. Also, compared to butane, the preference of M+ for “sampling” the various skeletal bonds
Figure 6. Potential energy contours for configuration 3 of butyl chloride in the X Y plane, showing lines of constant positive potential. Most positive values are found close to C(1), the atom with the highest positive charge.
can be very different for BuX compounds, because of the charge distribution in the butyl group. Also, cyclic intermediates such as the one that could be studied with this small polar compound definitely should be favored, if the ion/molecule complex is sufficiently long lived such that they may be formed. We believe that such studies may provide insights into many features of the chemistry of polar compounds with gas-phase metal ions. There are a number of cases where the reactivity of n-PrX and i-PrX with a given metal ion differ. For example, Co+ inserts into the C-CN bond of i-PrCN but not n-PrCN.’ The increased reactivity of the branched compound may be related, in part, to the charge distribution in the alkyl group. Smith et al.24have proposed that the C1 in i-PrC1 is more negative than in n-PrC1, consistent with the fact that the ionization potential of the isopropyl radical (7.55 eV) is less than that of the n-propyl radical (8.10 eV). Thus, for such polar propyl compounds, X is more negative in i-PrX. Since the C attached to the C1 is a secondary C atom, the positive charge associated with it may be less than that for the analogous C in n-propyl chloride. These differences in the charge distribution may contribute to the increased reactivity for the branched compound. The question remains as to whether the results presented here correlate with the observed reactivity of n-butyl chloride with metal ions. This model shows in, e.g., Figure 1, that the ion is more attractive to a position close to the C-Cl bond than to other positions about the molecular framework, and this is where insertion appears to occur. However, other “hot spots” were identified as well, from which insertion does not appear to occur. We have been focusing, to this point, on ion/molecule configurations that are attractiue. Are there locations about a given configuration of these molecules (other than those very close to atoms) where the overall interaction is repulsiue? The answer is yes. Figure 6 shows the results of a calculation for configuration 3 in which attractive contours are shown and also the positions at which the ion may be placed such that the overall electrostatic interaction energy is 0, +2, +4, and +6 kcal/mol. As one might expect, these regions yielding positive values of E lie close to the most positive parts of the alkyl group-Le., C(4). This shows another very important aspect of the fact that the molecule possesses a permanent dipole moment. While there may be attractive sites close to the molecular framework, longer range repulsive forces should also be considered when attempting to extend the results of these “static” descriptions, in considering the dynamics of the collision. Conclusions The use of a simple model for the electrostatic potential suggests (24) Smith, R. P.;Eyring, H. J . Am. Chem. Soc. 1953, 75, 5183.
3630
J . Phys. Chem. 1989, 93, 3630-3634
some important interactions between an ion and a polar molecule that may affect the chemistry of this reacting pair. The electrostatic attraction of the ion to various locations about the molecule obviously depends on the size of the atoms involved and the distribution of charge throughout the molecule. It is reasonable from these considerations that the ion will be attracted toward the functional group and the C-X bond. The relative importance of other sites about the molecule depend upon the length of the chain and the probability that multiple interactions via cyclic intermediates may occur. This first study with a small polar molecule will serve as the basis for future studies of longer chain molecules,25which possess (25) Preliminary results for Cr* with n-hexyl chloride have been presented. Allison, J.; Hankinson, D. J.; Miller, C. B.; Hooper, E. J.; Tsarbopoulos, A.; Wyatt, T. L. Presented at the 36th American Society for Mass Spectrometry Conference, June 5-10, 1988, San Francisco; paper TPB 68.
different charge distributions and which can form a variety of cyclic intermediates involving parts of the alkyl chain far from the functional group. Also, if the limitations of the model are understood, its use in suggesting such possibilities are important in considering the influence of early events on reaction product distributions. Acknowledgment. The assistance of T. Wyatt and D. Becker in computer-related aspects of this project is gratefully acknowledged. Also, we are grateful to the AT&T University Equipment Donation Program and Professor P. M. Hunt, Director of Academic Computing at Michigan State University, for the gift of the AT&T hardware used in performing these calculations. The National Science Foundation Grant No. CHE-8722111 is acknowledged for partial support of this work. Registry No. Cr', 14067-03-9; n-butyl chloride, 109-69-3.
Ligand-Assisted Electron Transfer from the Triplet State of Zinc Tetraphenylporphyrin to
Hiroshi Seki,* Mikio Hoshino, and Haruo Shizukat The Institute of Physical and Chemical Research, Wako, Saitama 351-01, Japan (Received: September 6, 1988)
Effects of axial ligands on the electron transfer from excited triplet state of zinc tetraphenylporphyrin (ZnTPP) to benzoquinone (BQ) have been studied by using a laser flash technique. For the reactions of pyridinate complex of ZnTPP (Py-ZnTPP) as well as ZnTPP, quantum yields of the porphyrin cation radicals resulting from the electron transfer, @ion, were determined in various solvents of different dielectric constant (e). Remarkable enhancement in aion due to axial ligation of pyridine has been found in the solvents having relatively moderate dielectric constant (9 < t < 18). A comparison of the t dependence of aion for the reaction of the triplet ZnTPP to that for the triplet Py-ZnTPP has demonstrated that the axial pyridine causes partial neutralization of the effective charge of Py-ZnTPP cation radical. When the axial pyridine is replaced by several kinds of substituted pyridines having different pK,, chloride ion, or ethanol, a significant change in aion is revealed in dichloroethane. The change in aion was found to depend on the ability of the ligand to transfer negative charge toward the porphyrin ring via the zinc ion. The ligand ability should cause reduction of effective charge on the porphyrin ring moiety of the ligand-bound ZnTPP cation radical which interacts with the BQ anion radical. Consequently it has been concluded that the enhancement in @ion due to axial ligation is ascribed to the reduction of the effective charge of the cation radical which results in easier separation of the cation radical from its complex paired with BQ anion radical.
Introduction The excited states of metalloporphyrins as well as numerous aromatics in polar solvents have been recognized to cause electron transfer in the presence of suitable electron acceptors.'" Particular attention has been paid by Harriman and his co-workers to solvent effects on electron transfer from the excited state of zinc tetraphenylporphyrin (ZnTPP) to 1,4-benzoquinone (BQ).7 Their results have shown that the relative yield of the porphyrin cation formed by electron transfer strongly depends on the dielectric constant of solvent, although the absolute quantum yield was not determined. On the other hand, Roy and Whitten have found that addition of only small amounts (0.1-0.5 M) of a polar solvent to the benzene solution of zinc etioporphyrin I causes conversion from the exciplex, formed between the triplet porphyrin and a quencher, into separated ions.8 They have indicated that a change in bulk dielectric constant of the solvent was not responsible for such a marked effect of the additive.s Fajer and his co-workers have demonstrated that significant spin delocalization occurs on the axial pyridine in the cation radicals of pyridine-bound ZnTPP.9 It is consequently expected that a specific interaction between a metalloporphyrin and its axial ligand may play an important role in the electron-transfer process where the excited porphyrin participates. However, the electro'Department of chemistry, Gunma University, Kiryu, Gunma 376, Japan.
0022-3654/89/2093-3630$01.50/0
chemical data obtained by Kadish and his co-workers have shown that the half-wave oxidation potential of ZnTPP is less affected by axial ligation of a number of nitrogenous bases.I0 In any case, there have been few studies about the effects of axial ligands on the photoinduced electron transfer of metalloporphyrin.ll~lz In the present study, our attention is focused on the effects of an axial ligand on efficiency of electron transfer from the triplet state of ZnTPP to BQ. Any absolute value for efficiency of the electron-transfer reaction has not yet been reported prior to the (1) Seely, G. R. Photochem. Photobiol. 1978, 27, 639-654. (2) Holten, D.; Windsor, M. W.; Parson, W. W.; Gouterman, M. Photochem. Photobiol. 1978, 28, 951-961. (3) Shinozawa, M.; Yamamoto, H.; Fujita, Y. Bull. Chem. SOC. Jpn. 177, 50, 2177-2178. (4) Ottolenghi, M. Acc. Chem. Res. 1973, 6, 153-160. (5) Masuhara, H.; Mataga, N. Acc. Chem. Res. 1981, 14, 312-318. (6) Fox, M. A. Advances in Photochemistry; Wiley: New York, 1986; Vol. 13, pp 237-327. (7) Harriman, A,; Porter, G.; Searle, N. J. Chem. Soc., Faraday Trans. 2 1979, 75, 1515-1521. (8) Roy, J. K.; Whitten, D. G. J. Am. Chem. Soc. 1972, 94, 7162-7164. (9) Fujita, I.; Hanson, L. K.; Walker, F. A,; Fajer, J. J. Am. Chem. SOC. 1983, 105, 3296-3300. (10) Kadish, K. M.; Shiue, L. R.; Rhodes, R. K.; Bottomley, L. A. Inorg. Chem. 1981, 20, 1274-1277. (11) Hoshino, M.; Seki, H.; Shizuka, H. J. Phys. Chem. 1985, 89, 470-474. (12) Hoshino, M.; Seki, H.; Yasufuku, K.; Shizuka, H. J. Phys. Chem. 1986, 90, 5149-5153.
0 1989 American Chemical Society
