J. Phys. Chem. 1996, 100, 14655-14660
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Dipole-Bound Electron Attachment to Uracil-Water Complexes. Theoretical ab Initio Study Johan Smets,† William J. McCarthy, and Ludwik Adamowicz* Department of Chemistry, UniVersity of Arizona, Tucson, Arizona 85721 ReceiVed: January 31, 1996; In Final Form: March 25, 1996X
Ab initio calculations performed in this work found positive electron affinities for all three possible doubly H-bonded complexes of the uracil molecule with a single water molecule. In all cases the excess electron is bound by the the dipole field of the complex. No conventional stable “valence” anionic states were found with the theoretical procedure used in this work (SCF + second-order perturbation theory corrections for the electron correlation effects). The attachment of the excess electron lowers the relative energy differences between the three complexes, making their coexistence more probable. Structural changes in the uracilwater complex upon attachment of an electron were also found. The anion’s equilibrium geometry had noticeably shortened hydrogen-bond lengths and a shifted orientation of the water molecule with respect to the uracil molecule compared to the neutral system.
1. Introduction The ability of nucleic acid bases and their complexes to form anions has significant biological implications. Ionizing radiation interacting with living organisms can lead to release of free radicals, including free electrons, into the cell environment and to attachment of those radicals to DNA and RNA components. The reaction of the nucleic acid bases with free electrons may lead to permanent damage, which can be linked to induced mutagenesis of the genetic material.1 The present study on electron-adducts of the uracil-water complex is undertaken to gain understanding of where excess-electron localization occurs relative to the molecular frame. The present study has also been motivated by recent experimental studies by K. H. Bowen’s group at Johns Hopkins University to measure the electron affinity (EA) of uracil-water complexes.2 In our previous studies of the electron affinities of uracil, thymine, guanine, and adenine,3-6 we found that excess electrons are attracted to and bound by the dipole field of the nucleic acid base. We also noted that the extra electron has a very diffuse charge distribution. Our calculated electron affinity values for uracil and thymine have recently been confirmed by two independent experimental measurements performed by K. H. Bowen and collaborators7 and J. P. Schermann and collaborators.8 These two groups, with the use of different experimental techniques, detected dipole-bound anions of uracil and thymine. J. P. Schermann also claims that his data give evidence that for both uracil and thymine “conventional” anions are formed as well. The term “conventional”, or “valence”, anion is used to describe an anion where the excess electron is localized within the confines of the valence orbitals of the molecule. Conversely, the excess electron in “dipole-bound” anions is located mostly outside the molecular frame. Valence anions typically have larger electron affinity values than their dipole-bound counterparts. Schermann’s findings were not confirmed by either our calculations or Bowen’s experimental results. However, it is evident from our calculations that even in the dipole-bound state part of the excess electron charge distribution is localized around the atoms, giving the anion a partial valence character. Scher† Present address: MPI-Strahlenchemie, Stiftstrasse 34-36, Muelheim a.d. Ruhr, D-45470, Germany. X Abstract published in AdVance ACS Abstracts, August 1, 1996.
S0022-3654(96)00309-7 CCC: $12.00
mann’s experiment also seems to indicates that the degree of interplay between the “dipole-bound” and “valence” electron attachment increases as the size of the molecule or molecular complex grows (see Schermann et al.11). Apart from our own studies,3-6 there have been several others attempting to theoretically determine the electron affinity of the four DNA bases.12-18 Only in the recent work of Sevilla et al.15-18 were the calculations done without resorting to a semiempirical approach. However, Sevilla’s calculations utilized a standard basis set that did not include the sufficiently diffuse functions necessary to describe dipole-bound anions. Sevilla’s calculated energies for the anions of all the nucleic acid bases were higher than the energies of the neutral systems. As we demonstrated in our previous work,3-6 dipole-bound electron attachment to nucleic acid base molecules and their complexes results in a very diffuse anionic wave function. In the biological environment, this kind of wave function will be significantly perturbed by the presence of other molecules, particularly by the solvent molecules. There is experimental evidence that for some systems with the increasing size of the complex the valence character of the attachment will eventually become more dominant over the dipole-bound attachment.8 Here it would be in order to mention some works on the electron affinities of nucleic acid bases in solutions where more significant positive electron affinity values were reported for all the bases.9,10 This change in the electron attachment mechanisms is an interesting feature that can be investigated theoretically. Sevilla et al.17 has argued that the increase in valence character over the dipole-bound character of the state of the excess electron results from a downward shift in energy of some bases’s antibonding orbitals of up to several electronvolts through polarization. This downward shift in energy can increase the localization of the excess electron on the antibonding orbitals of the base molecule. Although such energy lowering will be more significant in the solvent, for the first few solvent molecules, it will certainly depend on the relative positions of the solvent molecules and the charge distribution of the electron occupying the particular antibonding orbital, which, in some cases, may even lead not to an energy decrease but to an energy increase. A more intuitive reason why the excess electron may become more strongly attached for solvated base molecules is the increasing size of the system and increased © 1996 American Chemical Society
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Smets et al.
number of electronegative atomic centers, which become available for the excess electron and can lower its potential and kinetic energy by delocalization over these centers. In the present study we consider electron affinities of isomeric complexes of uracil. Our interest in this system was piqued by the recent experimental study of Bowen’s group involving detection of the uracil-water anion with the use of photoelectron spectroscopy. The question, which we address here, is whether the calculations predict formation of a valence, or dipole-bound, complex anion. This work, as well as the work performed before,20 is aimed at characterizing the states of the excess electron in 1:1 water complexes with polar nucleic acid bases. This is the first step toward considering larger multimolecular complexes involving more solvent molecules around the base molecule and toward considering clusters of base molecules. There has recently been an increase in experimental interest in studies of dipole-bound states or larger polyatomic molecules and complexes. The measurements performed by Desfranc¸ ois et al., based on the charge transfer collisions between laserexcited xenon Rydberg atoms and acetonitrile molecules and clusters, have shown that dipole-bound states of CH3CN- and (CH3CN-)3 are formed.19 There have been some additional reports on other molecular dipole-bound anionic states coming from that research group.21 One should also mention recent photoelectron spectroscopy studies by Bowen’s group on dipolebound anions of the (HF)2-, (CH3CN‚‚‚H2O)-, (HCl(H2O)n)-, (HCN‚‚‚(H2O)n)-, and (H2S)n- clusters,2 as well as contributions of others to this area.22 Stable anions of larger biological molecules and complexes, particularly those dipole-bound with the excess electron causing no significant perturbation to the structure of the molecule, may offer a valuable tool to study biological systems with the use of mass-spectroscopic methods. 2. Method of Calculation and Numerical Results The computational procedure used in this study is similar to the one employed previously in calculations of the electron affinities of uracil, thymine, guanine, and adenine.3-6 The use of very diffuse basis functions and an account for part of the electron correlation energy are essential in such calculations because the dipole-bound excess electron is usually significantly delocalized along the direction of the molecular dipole moment. The extent of the delocalization depends on the dipole moment size and orientation, which in turn depends on the accuracy of the calculation and on an accounting of the electron correlation effects. The calculations in this work have been performed with the use of the GAUSSIAN92 program package.23 1. The geometries of three possible complexes of uracil with water were first optimized at the SCF/6-31+G* level of theory. The obtained structures are depicted in Figure 1 and called complex A, B, and C, respectively. Next, MP2/6-31++G** (second-order Moller-Plesset perturbation theory) level calculations were performed to determine the relative stability of the complexes and their dipole moments. The results are presented in Table 1. Comparison of the relative energy values reveals that the most stable complex is labeled A, with B and C being 1.88 and 1.55 kcal/mol less stable, respectively. In all three complexes the water molecule is connected to the base molecule with two hydrogen bonds with the structure of intermolecular bonds assuming a cyclic geometry. At the SCF/6-31++G** level, complex B has the largest dipole moment of 5.21 D; however, the dipole moments of both complexes A and C are not significantly smaller and are equal to 4.53 and 4.38 D, respectively. All three dipole moments significantly exceed the theoretically determined threshold value of 1.625 D24-26 for formation of stationary anionic states. The three dipole moments
Figure 1. Three possible H-bonded, cyclic water complexes of uracil considered in this work.
also exceed the value of 2.5 D, which is considered to be a practical lower limit for detection of molecular dipole-bound anions by the most advanced experimental methods.21 2. To determine the electron affinities of the uracil-water complexes, SCF and MP2 calculations have been performed for each complex with the use of the standard 6-31+G* basis set augmented with an additional set of three diffuse sp shells with exponents equal to R, 0.1R, and 0.01R, where R is a scaling factor. The additional set was selected on the basis of the analysis presented in refs 27-29, where numerical orbitals
Dipole-Bound Electron Attachment to Uracil-Water
J. Phys. Chem., Vol. 100, No. 35, 1996 14657
TABLE 1: Electron Affinity (EA) Calculations of Water Complexes with Uracil: Total Energies in Hartrees, Relative Energies in kcal/mol, Electron Affinities and LUMOs in meV, and Dipole Moments (µ) in Debyes complex A SCF/6-31+G*//SCF/6-31+G* SCF/6-31++G**//SCF/6-31-G* MP2/6-31++G**//SCF/6-31+G* ∆E(MP2) SCF/6-31+G*X//SCF/6-31+G* MP2/6-31+G*X//SCF/6-31+G* ∆E(MP2) -LUMO/6-31+G*X µ/SCF/6-31+G* µ/SCF/6-31++G**
complex B
complex C
-488.5122209 -488.5367210 -489.9373608 1.88 -488.5122474 -489.8802697 2.06 16 5.2115 5.2192
-488.5127124 -488.5371645 -489.9378900 1.55 -488.5127328 -489.8808717 1.68 10 4.3832 4.3957
-488.5158607 3
-488.5129059 18
-488.5131793 12
-488.5158706 -489.8837617 0.0
-488.5131477 -489.8818829 1.18
-488.5134212 -489.8822110 0.97
Neutral System -488.5157408 -488.5400366 -489.9403621 0.0 -488.5157479 -489.8835464 0.0 3 4.5264 4.5105 Anion
(at the geometry of the neutral) SCF/6-31+G*X vertical EA SCF/6-31+G*X (at the geometry of the anion) SCF/6-31+G*//SCF/6-31+G*X MP2/6-31+G*X//SCF/6-31+G*X ∆E(MP2) adiabatic EA SCF/6-31+G*X MP2/6-31+G*X
3 6
produced by the Hartree-Fock and MCSCF procedures for some dipole-bound diatomic polar systems were projected onto Slater-type atomic orbitals. The presence of the additional diffuse functions will be indicated by X in the basis set designation (e.g., 6-31+G*X). The value of the scaling factor, R, was determined through minimization of the orbital energy of the LUMO (lowest unoccupied molecular orbital) for each of the neutral complex structures in the SCF calculation with the 6-31+G*X basis set. The optimal value was found to be equal to 0.05 for complex A, 0.08 for complex B, and 0.075 for complex C. (The smaller values of R indicate a more diffuse orbital.) Interestingly, even though the dipole moment of A is higher than for C, the optimization of the scaling factor gave a lower value. This is an indication that the size of the dipole moment is not the only determining factor for the wave function and the energy of the excess electron. From previous calculations,3-6 it was determined that the results are rather insensitive to the position of the diffuse orbitals, provided that they are located somewhere along the direction of the positive side of the molecular dipole. Therefore, in determining the vertical electron affinities, no optimization of the position of the diffuse set was performed, and similar to the previous calculations, the position of the X set was centered on the coordinates of the dipole moment vector (in the center-of-mass coordinate system). In the calculation of the adiabatic electron affinities of the complexes, the position of the diffuse orbital set for each system was optimized together with the positions of the nuclei by minimizing the total SCF/6-31+G*X energy of each of the anions. In Table 1 the energy results are presented for the neutral and anionic complexes. The table also contains the calculated values of the vertical and adiabatic electron affinities. One notices that the energies of the LUMO orbitals are negative for all three complexes, but very small (3, 16, and 10 meV for complexes A, B, and C, respectively). Examination of the spatial extent of the LUMO orbitals indicates that all represent dipole-bound states. Again, the LUMO energies do not follow exactly the variation of the values of the dipole moments. Complex A, with a larger dipole moment, has a lower LUMO energy than complex C, with a smaller dipole moment. It should be mentioned that in the calculation performed to determine very small energy effects, such as those mentioned
24 44
19 36
above, it is essential to maintain high precision at each computational step. This criterion includes sustaining the accuracy in calculating the atomic integrals, maximizing the convergence criteria in the SCF and post-SCF calculations, etc. Those features were closely monitored in our calculations. 3. The electron affinity calculation was done by subtracting the total energy of the neutral system from the energy of the anion. The total energies calculated at the SCF (RHF for the neutral system and UHF for the anion) and MP2 levels of theory are presented in Table 1. One can notice by comparing the Koopmans’ EA (i.e., the LUMO energy of the neutral) values with the SCF vertical EA values that there is a small stabilizing relaxation effect for complexes B and C. There is also some structure relaxation and adiabatic EA lowering for B and C (none for A), indicating that the geometry of the complex changes as a result of the electron attachment. The most striking effect is an almost 2-fold increase of the EA value for all the complexes after inclusion of the correlation effect at the MP2 level. The electron correlation contribution to EA can result from two effects. It can be related to the change of the dipole moment value of the neutral system, which in turn may lead to a stronger bonding of the excess electron. It can also result from the stabilizing contribution of the correlation between the excess electron and the electrons of the neutral system. From the results presented in Table 1, one notices that attachment of the excess electron, although it does not change the stability order, significantly reduces the relative energy differences between the three isomeric complexes (from 2.06 kcal/mol for complexes A and B to 1.18 kcal/mol, and from 1.68 to 0.97 kcal/mol for complexes A and C; the MP2/ 6-31+G*X results; see Table 1). This effect should result in increased concentration of anions of B and C in the mixture in comparison with B and C neutrals. Our best estimates of the adiabatic EAs of complexes A, B, and C calculated at the MP2/6-31+G*X//SCF/6-31+G*X level of theory (the notation denotes the following: (level of the theory for the energy calculation)//(level of theory for the optimization of the structure)) are 6, 44, and 36 meV for complexes A, B, and C, respectively. One notices a remarkably low EA for the most stable complex. This may result from the fact that complex A (see Figure 1) is almost planar and complexes B and C are not (the water hydrogen not participating
14658 J. Phys. Chem., Vol. 100, No. 35, 1996 in the H-bond is significantly distorted from the plane). A consequence of the nonplanar geometry is that the direction of the dipole moment vector for B and C is also off-plane, leading to the excess electron approaching the molecule not in the plane of the ring, as in complex A, but from an off-plane direction. 4. The electron attachment to the field arising from the molecular dipole moment leads to an orbital for the excess electron that is diffuse and localized along the dipole moment direction. In Figure 2 we present a contour plot of HOMOs (highest occupied molecular orbital) from the SCF/6-31+G*X calculations for all three anionic complexes. One can see that in the case of complexes B and C the excess electron is localized on the opposite side of the uracil molecule from the water molecule. In addition to a significant portion of the electron being located outside the molecular frame, there is some noticeable fraction of the electron charge localized on the uracil molecule. In complex A, however, the excess electron attaches to the same side of the uracil molecule as water and the orbital occupied by the electron is much more diffuse (this is manifested by fewer contour lines on the plot). It is seen that the maximum of HOMO for each system is located several bohrs away from the molecular frame. As expected, and as in all previously studied dipole-bound anions, the orbital has the shape of an sp hybrid oriented along the positive direction of the molecular dipole. 5. The adiabatic EA results for complexes B and C indicate that there is some relaxation of their geometries after electron attachment. This effect can be important for the interpretation of the photoelectron spectroscopy experiment. Broader spectral features result in those cases where significant geometry changes of the anion occur in comparison with the neutral system. In Table 2 are presented the results of an analysis of the structural differences between the anion and neutral equilibrium geometries of complex C. Since the difference between the adiabatic and vertical EAs are similar for B and C, we have performed our analysis only for C since the anion of this complex has lower total energy. As there is a significant correlation energy contribution to the electron affinity of all the complexes, which almost doubles the EA values, we first reoptimized the geometry of the anion including the position of the diffuse orbital set for complex C at the MP2/6-31+G*X. Next we also reoptimized the geometry of the neutral complex C at the same level of theory with the diffuse set X being placed at the same point as for the anion and not being optimized. This approach allowed us to minimize the nonequivalency in the geometry optimizations of the neutral and anionic systems. The results of the optimizations are presented in Table 2. One can notice that the structure reoptimizations at the MP2 level further increase the electron affinity value from 36 meV (the MP2 value calculated with the SCF geometries; see Table 1) to 39 meV. The structural parameters, which we found to be the most different between the neutral and the anionic systems, are those related to the relative position of the water molecule with respect to the uracil molecule. The parameters are shown in Table 2. Upon examining the numerical values, one can see that in the anion the hydrogen bond is noticeably shorter than in the neutral system (by more than 0.07 Å). Also, the relative angular orientation of the water molecule with respect to the uracil molecule is somewhat different in the two systems. For example, the hydrogen-bond O14-H13-O8 angle in the anion is by almost 7° larger than in the neutral complex.
Smets et al.
3. Discussion and Conclusions
Figure 2. HOMOs of the anions of water complexes of uracil. The contours depicted range in value from the outermost inward from 0.0020 to 0.0060 in increments of 0.0005.
In this work we demonstrated, based on ab initio calculations, that all three possible double H-bonded complexes of the uracil
molecule with a single water molecule possess positive, but very small, electron affinities. In all three cases the excess electron
Dipole-Bound Electron Attachment to Uracil-Water TABLE 2: Results of MP2/6-31+G*X Optimization of the Neutral and Anion of Complex C MP2 (hartrees)
relative geometry of the water molecule in the complexa
Neutral -489.8888521 H13 R(13-8) ) 1.9806 Å ∠(13-8-4) ) 111.000° ∠(13-8-3) ) 2.893° O14 R(14-13) ) 0.9818 Å ∠(14-13-8) ) 141.421° ∠(14-13-8-4) ) 3.380° H15 R(15-14) ) 0.9712 Å ∠(15-14-10) ) 132.256° ∠(15-14-10-3) ) 116.680°
adiabatic EA (meV) a
Anion -489.8902905 H13 R(13-8) ) 1.9138 Å ∠(13-8-4) ) 110.976° ∠(13-8-4-3) ) -0.879° O14 R(14-13) ) 0.9845 Å ∠(14-13-8) ) 148.317° ∠(14-13-8-4) ) 0.275° H15 R(15-14) ) 0.9710 Å ∠(15-14-10) ) 124.337° ∠(15-14-10-3) ) 103.176° 39
See Figure 1 for atom numbers.
is attached to the molecule through the attractive interaction with the molecular dipole moment. The predicted values of the electron affinities of the complexes allow us to speculate on the outcome of a photoelectron spectral experiment performed in the gas phase of this system. We can predict that there will be a sharp feature due to the anion of complex A, which according to our evaluation, should be the most stable and shows very little structure relaxation when the excess electron is removed. We can also predict that anions of complexes B and C will give rise to broader features located near each other, or overlapping. The broadening will result from much more significant geometry relaxation for B and C than for A, which is predicted to happen when the excess electron is detached. It is also quite possible that the spectral manifestation due to the anions of all three complexes will appear as a single broader feature in the spectrum. As mentioned before, this work has been motivated by the photoelectron experiment performed on the uracil-water system by Bowen and co-workers.30 The spectrum obtained in this experiment is qualitatively different than the spectrum obtained for the uracil dipole-bound anion. It is much broader and is shifted toward higher energies. Based on previously studied conventional anions of molecules and clusters, Bowen’s group interprets the result as a clear manifestation of a conventional and not dipole-bound anion of the uracil-water system. This result could be the first remarkable observation of a transformation of a dipole-bound anion to a conventional anion upon hydration. A question arises as to why all our calculations on the uracil-water complex converged to dipole-bound states and none to a valence state. The procedure that we applied in the present studies is heavily based on the SCF wave function as the reference for the post-SCF correlated calculations. This is definitely an appropriate procedure to study dipole-bound anionic states because the SCF function provides a good representation of such states. If there is a significant covalent component in the dipole-bound attachment of the excess electron, or if the dipole moment of the molecule changes by a considerable amount with the inclusion of the electron correlation, the SCF representation of the dipole-bound anion states may fail. In the case of the covalent anions, however, it is quite
J. Phys. Chem., Vol. 100, No. 35, 1996 14659 possible that the bonding effect of the excess electron results from a dispersion interaction, which is not at all represented at the SCF level of theory. In such cases the electron correlation effect should be present in the wave function at the very first stage of the calculation for the anion (the reference function should be a correlated function or there should be a mechanism in the computational method used to modify the SCF reference function in order to reflect its adjustment to better describe the covalent state of the bonded excess electron). This kind of approach has not been used in the present work, and this might be the reason why the covalent anions of the uracil-water complexes were not described. An investigation of this point will continue to be carried in our group. It is interesting to compare the dipole-bound EAs of the water complexes of uracil with the EA of uracil (86 meV) monomer calculated in our previous work.3 One notices that the water attachment destabilizes the anion. This is contrary to what one usually expects to happen for conventional anions, where the increasing size of the system usually leads to a larger EA. Although the dipole moment is not the only factor that determines EA for a dipole-bound anion, it is clear from our calculations that when the dipole moment decreases, the EA usually decreases too. In the case of uracil-water complexes the dipole moments for the two most stable structures, A and C, are lower than for the uracil molecule (the uracil SCF/ 6-31++G** dipole moment value is equal to 4.94 D, and for the A and C complexes they are 4.51 and 4.40 D, respectively; see Table 1). The dipole moment of the third less stable complex, B (5.22 D), is slightly larger than for uracil. The lowering of the dipole moment due to the hydration provides a possible explanation of the decrease of EA for the complexes. Acknowledgment. This study was inspired by work of Prof. Kit Bowen and collaborators. We would like to thank Prof. Bowen and Mr. Jay Hendricks for making their results available to us prior to publication and for commenting on our manuscript. We acknowledge support by a grant from the office of Health and Environmental Research, Department of Energy, under Contract DEFG 0393ER61605. References and Notes (1) von Sonntag, C. In Physical and Chemical Mechanisms in Molecular Radiation Biology; Glass, W. E., Varma, M. N., Eds.; Plenum Press: New York, 1991. (2) Bowen, K. H. Private communication. (3) Oyler, N. A.; Adamowicz, L. J. Phys. Chem. 1993, 97, 1122. (4) Oyler, N. A.; Adamowicz, L. Chem. Phys. Lett. 1994, 219, 223. (5) Roehrig, G. H.; Oyler, N. A.; Adamowicz, L. Chem. Phys. Lett. 1994, 225, 265. (6) Roehrig, G. H.; Oyler, N. A.; Adamowicz, L. J. Phys. Chem. 1995, 99, 14285. (7) Hendricks, J. H.; Lyapustina, S. A.; de Clercq, H. L.; Snodgrass, J. T.; Bowen, K. H. J. Chem. Phys., in press. (8) Schermann, J. P.; et al. J. Chem. Phys., in press. (9) Wiley, J. R.; Robinson, J. M.; Ehdaie, S.; Chen, E. C. M.; Chen, E. S. D.; Wentworth, W. E. Biochem. Biophys. Res. Commun. 1991, 180, 841. (10) Steenken, S. Chem. ReV. 1989, 89, 503. (11) Desfranc¸ ois, C.; Abdoul-Carime, H.; Schultz, C. P.; Schermann, J. P. Science 1995, 269, 1707. (12) Pullman, B.; Pullman, A. Quantum Biochemistry; Wiley-Interscience: London, 1963. (13) Younkin, J. M.; Smith, L. J.; Compton, R. N. Theor. Chim. Acta 1976, 41, 157. (14) Compton, R. N.; Yoshioka, Y.; Jordan, K. J. Theor. Chim. Acta 1980, 54, 259. (15) Colson, A.-O.; Besler, B.; Close, D. M.; Sevilla, M. D. J. Phys. Chem. 1992, 96, 661. (16) Colson, A.-O.; Besler, B.; Sevilla, M. D. J. Phys. Chem. 1993, 97, 13852. (17) Sevilla, M. D.; Besler, B.; Colson, A.-O. J. Phys. Chem. 1995, 99, 1060.
14660 J. Phys. Chem., Vol. 100, No. 35, 1996 (18) Sevilla, M. D.; Besler, B.; Colson, A.-O. J. Phys. Chem. 1994, 98, 2215. (19) Desfranc¸ ois, C.; Abdoul-Carmine, H.; Adjouri, C.; Khelifa, N. Europhys. Lett. 1994, 26, 25. (20) Smets, J.; McCarthy, W. J.; Adamowicz, L. J. Chem. Phys., submitted for publication. (21) Desfranc¸ ois, C.; Abdoul-Carmine, H.; Khelifa, N.; Schermann, J. P. Phys. ReV. Lett. 1994, 73, 2436. (22) Mead, R. D.; Lykke, K. R.; Lineberger, W. C.; Marks, J.; Brauman, J. I., J Chem. Phys. 1984, 81, 4883. Haberland, H.; Ludewigt, C.; Schindler, H.-G.; Worsnop, D. R. Phys. ReV. A 1987, 36, 967. Hashemi, R.; Illenberger, E. J. Phys. Chem. 1991, 95, 6402. Dessent, C. E. H.; Bailey, C. G.; Johnson, M. A. J. Chem. Phys. 1995, 103, 2006. (23) Frisch, M. J.; Trucks, G. W.; Head-Gordon, M.; Gill, P. M. W.; Wong, M. W.; Foresman, J. B.; Johnson, B. G.; Schlegel, H. B.; Robb, M. A.; Replogie, E. S.; Comperts, R.; Andres, J. L.; Raghavachari, K.; Binkey,
Smets et al. J. S.; Gonzalez, C.; Martin, R. L.; Fox, D. J.; Defrees, D. J.; Baker, J.; Steward, J. J.; Pople, J. A. GAUSSIAN 92, Revision C; Gaussian Inc.: Pittsburgh, PA, 1992. (24) Fermi, E.; Teller, E. Phys. ReV. 1947, 72, 406. (25) Crawford, O. H. Mol. Phys. 1971, 20, 585. (26) Barrett, W. R. Chem. Phys. Lett. 1979, 62, 35. (27) Adamowicz, L.; McCullough, E. A., Jr. Int. J. Quantum Chem. 1983, 24, 19. (28) Adamowicz, L.; McCullough, E. A., Jr. J. Phys. Chem. 1984, 88, 2045. (29) Adamowicz, L.; McCullough, E. A., Jr. Chem. Phys. Lett. 1984, 107, 72. (30) Hendricks, J. H.; Lyapustina, S. A.; de Clercq, H. L.; Bowen, K. H., Private communication.
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