Coulomb Potentials Have Strong Effects on Anion Electronic States

May 1, 2013 - Coulomb Potentials Have Strong Effects on Anion Electronic States. Jack Simons*. Chemistry Department and Henry Eyring Center for ...
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Coulomb Potentials Have Strong Effects on Anion Electronic States Jack Simons* Chemistry Department and Henry Eyring Center for Theoretical Chemistry, University of Utah, Salt Lake City, Utah 84112, United States ABSTRACT: The Coulomb destabilization of intrinsic electron binding strengths and in forming repulsive Coulomb barriers (RCB) that can act to trap an excess electron are overviewed for a variety of anionic systems that include (i) multiply charged anions in which the charged sites are spatially well separated, (ii) multiply charged anions that have negative electron binding energies but in which the RCB decreases the rate of electron detachment, (iii) multiply charged superhalogen anions, (iv) positively charged polypeptides in which positive sites’ Coulomb potentials stabilize antibonding orbitals allowing an electron to attach, (v) DNA duplex oligomers containing a thymine dimer damage site that is repaired by electron attachment, and (vi) DNA fragments in which an electron attached to a base π* orbital results in formation of a strand break. Special attention is paid to the degree to which such Coulomb interactions are screened, especially in the latter two cases.

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INTRODUCTION

The effects of Coulomb interactions among negatively charged centers within multiply charged molecular anions in the gas phase have been the subject of several recent experimental1 and theoretical2,3 studies. In the present paper, we attempt to unify the key concepts that apply in such cases by first reviewing several findings of earlier investigations and then discussing how such Coulomb effects also arise, albeit in attenuated strength, in systems probed in condensed media. The latter cases involve repair of thymine dimer damage in DNA as well as electron-induced strand break formation in DNA. Of particular interest is the extent to which Coulomb interactions are screened by polarization of the electron distributions and reorientation of dipoles within the anion itself and within the surrounding medium. To begin, let us briefly review two examples in which the effects of Coulomb energies are very clear. In ref 1, results of a beautiful set of photoelectron spectroscopy experiments on dicarboxylate anions −OOC−(CH2)n− COO− having aliphatic methylene spacers were reviewed. The data discussed there nicely illustrate two effects arising from the Coulomb interactions between the two negative carboxylate centers. The first effect is summarized in Figure 1 where the electron binding energies (EB) determined in the photoelectron spectroscopy experiments are plotted vs the inverse of the distance between the two COO− groups’ carbon atoms for various values of n. (These distances were estimated assuming an all-trans quasi-linear extended geometry for the −(CH2)− backbone. Because these experiments were carried out in the gas phase, it is likely that the Coulomb repulsion between the two terminal −COO− groups causes the backbone to adopt geometries near this idealized estimate.) © XXXX American Chemical Society

Figure 1. Plot of electron binding energies (EB) and repulsive Coulomb barriers (RCB) for dicarboxylate dianions as functions of inverse distance between the two negative centers. Taken from Figure 7 in ref 1. Reprinted with permission from ref 1. Copyright 2000 American Chemical Society.

Special Issue: Ron Naaman Festschrift Received: March 11, 2013 Revised: April 30, 2013

A

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The fact that the EB data points appear to fall on a straight line was taken to suggest that the energy required to remove an electron from either of the carboxylate groups is (i) a value (ca. 3.2 eV) representative of the intrinsic electron binding strength of a singly charged R−COO− unit (e.g., as for H3C−COO−) and (ii) reduced by the Coulomb interaction between the two carboxylate groups. The Coulomb energy C (in eV) for two units having charges Q1 and Q2 separated by a distance R (in Å) is given by

C=

14.4Q 1Q 2 RÅ

eV

(1)

Figure 2. Qualitative depiction of the repulsive and attractive potentials experienced by the second excess electron the n = 3 dicarboxylate dianions as a function of distance R from the other negatively charged site. Redrawn following Figure 8 in ref 1.

so the slope of the plot of EB vs 1/R in Figure 1 should be 14.4 rather than the value of 16.7 shown there. However, if, rather than taking R to be the distance between the oxygen atoms of the terminal carboxyl groups, one realizes that the orbitals occupied by the two excess electrons extend beyond the oxygen nuclei, somewhat larger R-values would be calculated. Using such a modified definition for R can be shown to then produce a slope very close to 14.4. So, the first conclusion to draw from these experimental data is that the Coulomb potential generated by surrounding charges can indeed alter the intrinsic electron binding energy, and the amount by which the binding energy is changed can be expected to be very well approximated by the mutual Coulomb interaction energy of eq 1. An important point to take note of is that the Coulomb interaction for the dicarboxylate systems discussed here has no dielectric screening even though there are methylene groups between the two −COO− groups. In other words, the plot in Figure 1 is consistent with a local dielectric constant ε = 1. This fact will be important to keep in mind when we later discuss cases in which the charged groups reside within hydrophobic regions of DNA or of peptides. In Figure 1, there is a second plot whose origin we now discuss using the data for −OOC−(CH2)3−COO− to illustrate. This n = 3 dianion was found to have an electron binding energy of 0.6 eV. However, when photons having energy of 2.33 eV (532 nm) are used in an attempt to detach an electron from this dianion, no electron detachment is detected. In contrast, when photons having energy of 3.49 eV (355 nm) are used, electron detachment occurs. In Figure 2 we illustrate what is causing these observations. Figure 2 is meant to describe the interaction potential for the second excess electron of the −OOC−(CH2)3−COO− dianion as a function of its position R relative to the other negatively charged site. As this electron approaches from large R, it experiences a repulsive Coulomb interaction due to the other negative site. Only once this electron resides in regions of space near the two oxygen atoms to which it is bound in the dianion does it experience the valence-range attractive potential of these two oxygen atoms. As a result, the second excess electron feels a repulsive Coulomb potential at long-range and an attractive potential in the valence range of the two oxygen atoms. This is the potential that Figure 2 describes. We know from the EB = 0.6 eV value associated with this dianion that the minimum in this potential lies ca. 0.6 eV below its large-R asymptote. The height of the repulsive Coulomb barrier (RCB) above the large-R asymptote can be estimated by using eq 1 with R defined in the manner described above.

For −OOC−(CH2)3−COO−, R is approximately 6 Å, so eq 1 predicts the height of the RCB to be 14.4/6 = 2.4 eV. The data summarized in Figure 1 thus illustrate two important effects of Coulomb interactions in multiply charged anions: 1. The internal Coulomb interactions are unscreened in the gas phase and reduce the electron binding energies by amounts that can be estimated via eq 1. 2. The Coulomb interactions produce repulsive Coulomb barriers that cause electron photodetachment to not occur near the electron binding energy threshold but at photon energies in excess of the threshold by an amount approximately equal to the RCB. To further emphasize the importance of the RCB, we will use data on a multiply charged anion shown in Figure 3 consisting

Figure 3. Structure of quadruply negatively charged Cu phthalocyanine complex containing four sulfonate groups. Taken from Figure 4 in ref 6. Reprinted with permission from ref 6. Copyright 2000 American Chemical Society.

of (i) a copper atom at the center, surrounded by (ii) a phthalocyanine ligand having (iii) sulfonate groups on its four peripheral apexes. When all four sulfonate groups are rendered neutral (e.g., by protonation) and the resulting neutral complex B

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the electron density of the phthalocyanine framework resides between the Cu atom and the four sulfonates, the Coulomb interaction is best described using a dielectric constant of unity. This system was recently studied theoretically4 where excellent agreement with the experimental findings described above was obtained. Having used examples from recent gas phase experiments to introduce the concepts of Coulomb destabilization of intrinsic electron binding strength and of Coulomb stabilization behind the RCB, in Results we turn attention to a few small inorganic multiply charged anions whose stabilities involve more than these two effects. We discuss how internal Coulomb interactions can play important roles in how electrons attached to DNA induce damage (e.g., strand breaks) or cause repair (e.g., thymine dimer repair) not in the gas phase but in condensed media. We also discuss to what extent these Coulomb interactions are screened in such cases. In Discussion and Conclusions, we offer a summary of our main points.

is studied by photoionization spectroscopy, an ionization potential of 6.3 eV is determined. When three of the sulfonate groups are negatively charged (i.e., with one group being protonated) and photodetachment experiments are carried out, one finds that the energy needed to remove an electron from the Cu atom is reduced due to the Coulomb repulsions created by the three sulfonate groups. In fact, by using photons having various energies, and measuring the kinetic energies of the detached electrons, it was determined that the triply charged species has an electron binding energy of 1.2 eV (for example, when photoelectrons are observed to have a kinetic energy KE and result from photons having energy hν, the electron binding energy is given by hν − KE) and the RCB height is ca. 2.5 eV [this value agrees well with an estimate reached by summing the Coulomb interaction energies (as from eq 1) between two of the sulfonate sites on the third site]. These facts are summarized in Figure 4.

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RESULTS A. The Superhalogen Effect. Let us begin by considering the bonding in alkaline earth halide dianions such as MgF42−, BeF42−, or CaF42−, the first of which is isoelectronic with SiF4. These dianions have been observed in mass spectrometry and Coulomb explosion experiments.5 The relative energies of MgF42− and MgF4− species as a function of extension of one M−F bond (with the remaining geometrical degrees of freedom relaxed to minimize the energy) are shown in Figure 5.

Figure 4. Qualitative depiction of potential experienced by most weakly bound electron in the neutral (a), triply charged (b) and quadruply charged (c) complex whose structure is shown in Figure 3. Taken from Figure 5 in ref 6. Reprinted with permission from ref 6. Copyright 2000 American Chemical Society.

When the quadruply negatively charged species is subjected to similar experiments using photons having energy 6.4 eV (193 nm), electrons are ejected with kinetic energies near 7.3 eV. When 4.7 eV photons are used, electrons having kinetic energies of 5.6 eV are ejected. These remarkable findings tell us that the Cu electron in the quadruply charged species has a negative electron binding energy of −0.9 eV! This species, therefore, is electronically metastable, but its Cu electron is trapped within the RCB caused by the four surrounding negatively charged groups. The height of the RCB can be estimated by summing eq 1 with R taken as the distance from each of the four sulfonate groups to the Cu atom. Alternatively, an upper bound to the RCB can be determined from the fact that 4.7 eV photons eject electrons, so the barrier must be no higher than 4.7 + 0.9 = 5.6 eV. Of course, by tuning the photons’ energy and determining the threshold for observing electron detachment an even more precise estimate can be achieved. As was the case for the gas phase dicarboxylate species, the destabilization of the intrinsic electron binding energy (6.3 eV) as well as the height of the RCB that traps the excess electron are consistent with unscreened Coulomb energies derived from the negative sites within the inorganic complex. Even though

Figure 5. Energy (eV) of MgF42− and of MgF4− as functions of elongation (Å) of one Mg−F bond with the remaining geometrical parameters optimized to minimize the energy of the dianion. Recreated following Figure 5 in ref 2.

As shown in ref 2, very similar potential surfaces are found when Mg is replaced by Be or Ca. The main things to notice in Figure 5 are as follows. 1. The MgF42− species is metastable (i.e., unstable but having a barrier to surmount) with respect to F− + MgF3−. The barrier to dissociation is substantial (ca. 1 eV for MgF42−), which is why this dianion persists long enough to be amenable to mass spectroscopy detection. 2. The vertical electron detachment energy is in the 2 eV range, and the monoanion formed upon detachment is not geometrically stable (i.e., its potential surface is repulsive). For BeF42−/BeF4− and CaF42−/CaF4−, very similar energy profiles were found in ref 2. A more recent study of the MgF42− system6 sheds more light on the nature of the electronic structure in these alkaline earth C

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3. For MgF42−, we take the intrinsic electron binding energy of a fluoride ion (3.4 eV) and reduce it by the Coulomb repulsion from the three other fluoride ions and increase it by the Coulomb attraction from the Mg2+ ion: BE = 3.4 −

3 × 14.4 2 × 14.4 + = 3.4 − 13.6 3.17 2.51

+ 11.5 = 1.3 Figure 6. Examples of valence bond structures contributing to the electronic structure of MgF42−.

14.4 = 3.4 − 4.5 = −1.1 3.17

eV

(3)

4. For MgF4−, we take the fluoride ion binding energy and reduce it by Coulomb repulsion from two other fluoride ions and increase it by the Coulomb attraction from the Mg2+:

halide anions. In Figure 6 the fact that MgF42− is isoelectronic with SiF4 and may be viewed as having strongly ionic bonding is emphasized. In ref 6, the vertical electron detachment energy of MgF42− was determined to be 2.6 eV. In addition in ref 6, by freezing the geometry at the equilibrium geometry of MgF42− and calculating the energies of the MgF4− anion and of the MgF40 neutral, it was determined that to vertically remove an electron from MgF4− requires 7.1 eV. There are two aspects of the data shown in Figure 6 for MgF42− that merit attention. We note that the difference between the (vertical) electron binding energy of MgF42− and of MgF4− (7.1 − 2.6 = 4.5 eV) is very close to the Coulomb energy 14.4/RFF = 4.54 eV one computes for the interaction between two F− ions residing as they do in MgF42−, again using an unscreened Coulomb formula. This again supports the picture in which the Coulomb repulsion destabilizes the intrinsic electron binding strength (in this case of a fluoride ion ligand). The second issue that needs to be pointed out relates to the energy needed to remove an electron from the singly charged MgF4− anion 7.1 eV. This is a very large electron detachment energy, exceeding by a considerable amount that of the fluoride ion 3.4 eV, whose origin deserves further discussion. In Figure 6 we see several valence bond structures that likely contribute to the electronic state of MgF42−. One structure involves purely ionic bonding of four fluoride ions and a Mg2+ cation; the other six equivalent structures (not all are shown in Figure 6) have two fluoride ions, two neutral fluorine atoms and a neutral Mg atom. Although all of these structures, in principle, contribute, it is worthwhile to explore what the electron detachment energies (2.6 and 7.1 eV) discussed above tell us about their relative importance. If the six valence bond structures containing two fluoride ions were dominant, one would estimate the energies needed to remove an electron from MgF42− or from MgF4− as follows. 1. For MgF42−, we take the intrinsic electron binding energy of a fluoride ion (3.4 eV) and reduce it by the Coulomb repulsion from the other fluoride ion: BE = 3.4 −

eV

BE = 3.4 −

2 × 14.4 2 × 14.4 + = 3.4 − 9.09 3.17 2.51

+ 11.5 = 5.8

eV

(4)

In summary, the electron binding energies of the dianion and monoanion as calculated by ab initio theory are 2.6 and 7.1 eV, respectively. The valence bond structures with neutral Mg predict −1.1 and 3.4 eV, which clearly are very far from the ab initio predictions although the anion−dianion difference is essentially identical to the ab initio result. In contrast, the purely ionic valence bond structure predicts binding energies of 1.3 and 5.8 eV, both of which are close to but smaller than the ab initio results by 1.3 eV, with an anion−dianion difference that agrees with ab initio theory. These observations suggest that (i) the bonding in MgF42− is best described as purely ionic and (ii) Coulomb interactions adequately account for differences in the electron binding strengths between the anion and dianion, but (iii) something else causes the two binding strengths to be larger than expected based upon the purely ionic model. Another thing to notice is that the electron binding strength for the singly charged MgF4− ion (7.1 eV from ab initio theory; 5.8 eV from the Coulomb model estimate) exceeds by a considerable amount that of the fluoride ion ligand (3.4 eV). It is for this reason that such anions are called superhalogens. They have such large electron binding strengths as a result of the Coulomb attraction from the Mg2+ center being stronger than the Coulomb repulsions from the two fluoride ligands. Other examples7 of superhalogen anions include FLiF−, ClLiCl−, FNaF−, and ClNaCl−, which have vertical electron binding energies of 6.5 eV, 5.9 eV, 6.2 eV, and 5.8 eV, respectively, all of which are considerably in excess of halogen atom electron affinities. Two more extreme examples of unusually high electron binding strength are provided by the TeF82− and SeF82− dianions. (The geometries of these dianions each have four fluorine ligands arranged in a square above a central metal and four fluorine ligands in another square below the metal, with the two squares rotated by 45° relative to one another. The interatomic distances needed to compute the Coulomb repulsion energies of these species are given in ref 6.) These dianions have electron binding energies of 4.9 and 5.7 eV, respectively. The energies required to remove an electron (vertically at the dianion’s equilibrium geometry) from the corresponding monoanions are 10 and 11 eV. These data suggest Coulomb repulsion energies of 5.1 and 5.4 eV, respectively. Indeed, using the geometry information given in ref 6 within eq 1, one calculates internal Coulomb energies of 5.3 and 5.5 eV, which are very close to the 5.1 and 5.4 eV deduced from the difference in

(2)

2. For MgF4−, we would expect the electron binding energy to be that of a fluoride ion (3.4 eV) because there exists no Coulomb repulsion in this ion. Clearly, these predictions are not in line with what is reported above for MgF42− and MgF4−; they even say that the dianion is electronically unstable. If, alternatively, the valence bond structure containing four fluoride ions and Mg2+ is dominant, one would estimate the electron binding energies as follows. D

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electron binding energies. The superhalogen character of these species is illustrated by their anion-to-neutral electron binding energies 10 and 11 eV, which are much larger than that of their fluoride ligands. A large number of such dianions displaying unusually high electron binding energies have been studied.3 B. Sometimes the Coulomb Repulsion Makes the Multiply Charged Anion Unstable. Another species that is isoelectronic with SiF4 and MgF42− is the sulfate anion SO42−. In Figure 7 we show some of the resonance structures likely to

Figure 8. Experimental vertical (top) and adiabatic (bottom) electron binding energies of SO42−(H2O)n for n > 2. Taken from Figure 2 of ref 8. Reprinted with permission from ref 8. Copyright 2000 American Institute of Physics.

binding energy of SO42− using the so-called charge stabilization method in which 1. one increases the nuclear charge Z of the sulfur atom by a fractional amount (doing so differentially stabilizes the energy of XO42− relative to XO4−, where X is the sulfur nucleus having charge Z > 16), and then 2. one uses the equilibrium geometry of SO42− and calculates the energy E1 of the XO42− and E2 of the XO4−, after which 3. one computes the electron binding energy as E2 − E1. 4. One then plots these electron binding energies as a function of the nuclear charge Z, making sure to only use data for which E2 − E1 is positive (i.e., corresponds to a true bound electronic state), and extrapolates this plot to Z → 16 to obtain the predicted electron binding energy for the actual sulfate ion. An example of such a charge-stabilization plot9 is shown in Figure 9 for calculations on sulfate carried out at the

Figure 7. Examples of resonance structures contributing to the electronic structure of sulfate.

be involved in the electronic structure of this doubly charged ion, and we specify the O−O interatomic distance at the equilibrium geometry of the sulfate ion. Proceeding as we did earlier in analyzing the effects of Coulomb repulsion for MgF42−, we consider the energy needed to remove an electron from the singly charged SO4− ion at the equilibrium geometry of the sulfate dianion, which has been predicted on the basis of ab initio calculations6 to be 5.1 eV. Using the O−O distance of 2.45 Å given in Figure 7, we compute a Coulomb repulsion energy of 5.9 eV for the SO42− dianion. (Recall from our discussion of MgF42− that the same value for the Coulomb repulsion contribution to the dif ference in electron binding strengths between the anion and dianion is obtained using either the totally ionic valence bond structure or the structures containing a neutral central atom.) Combining these two data allows us to predict the electron binding energy for SO42− to be 5.1 − 5.9 = −0.8 eV. In other words, the sulfate ion is predicted to be not electronically stable as an isolated (i.e., gas phase) species. Two things make sulfate unstable whereas MgF42− was stable (by 2.6 eV): (i) the Coulomb repulsion energy in sulfate (5.9 eV) is larger than in MgF42− (4.5 eV) because the O−O distance is shorter than the F−F distance, and (ii) the oxygen ligands have lower intrinsic electron binding strength than the fluorine ligands. There have been photoelectron spectroscopy experiments8 carried out on sulfate ions that have three or more water molecules attached to them, SO42−(H2O)n. In Figure 8 we show the vertical and adiabatic electron binding energies obtained for such systems containing from 3 to 13 water molecules. In the electrospray mass spectrometry ion source used in the experiments of ref 8, no SO42−(H2O)n ions were observed for n < 3, which suggests that sulfate may indeed be unstable with respect to electron loss unless it is sufficiently solvated. If the electron binding energies shown in Figure 8 for n > 2 are extrapolated to n → 0, one estimates the electron binding energy for SO42− to be negative and to be ca. −1 eV, although the data do not vary linearly with n in this range of n-values, so this extrapolation may not be all that accurate. Alternatively, it is possible to theoretically estimate the (negative) electron

Figure 9. Plot of charge-stabilized electron binding energies of SO42− as functions of the nuclear charge on S for various treatments of the electronic structure. Taken from Figure 1 of ref 9. Reprinted with permission from ref 9. Copyright 2002 American Institute of Physics.

Hartree−Fock self-consistent field (SCF), Møller−Plesset second or fourth order perturbation theory (MP2, MP4) and coupledcluster (CCSD(T)) levels of theory. The highest-level CCSD(T) data extrapolate to an electron binding energy of −1.1 eV. Using the Coulomb energy 5.9 eV quoted above for SO42− as an estimate of the height of the repulsive Coulomb barrier, in ref 9 the lifetime for electron loss in SO42− was estimated to be ca. 10−10 s. E

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This example shows us that some multiply charged anions, including some most chemists assume to be intact species, can have so much internal Coulomb repulsion energy that they are rendered electronically unstable. In such cases, it is the RCB that may produce a lifetime with respect to electron loss that is sufficiently long to make the anion amenable to experimental detection. In the SO42− case, the 10−10 s lifetime may be too short to make detection feasible. However, for the quadruply charged Cu phthalocyanine complex discussed earlier, the RCB was high enough to extend this species’ lifetime sufficiently to allow for its spectroscopic detection and characterization. C. Coulomb Effects in Species Studied in Condensed Media Can Sometimes Be Strong. Before discussing species surrounded by solvent molecules (containing perhaps significant electrolyte concentrations), let us consider a biological molecule whose mass spectroscopy fragmentation behavior has been studied using electron capture dissociation (ECD) methodology. In Figure 10 we show a depiction of a doubly

Figure 11. Example of duplex DNA oligomer used in ref 11. Taken from Scheme 1 in ref 12 Reprinted with permission from ref 12. Copyright 2013 American Chemical Society.

In Figure 11, we show a sequence of a double strand DNA oligomer that contains a thymine dimer damage site denoted T=T as well as DNA’s four bases (C, G, T, and A) and a modified base denoted O (whose chemical name is 8oxoguanosine). In Figure 12, we show the molecular structures of the thymine dimer, of two separated thymines (T), and of the

Figure 10. Structure of doubly protonated (AcCA15K+H)22+ showing the two charged Lys termini and the disulfide linkage at the center. Taken from Figure 1 of ref 10. Reprinted with permission from ref 10. Copyright 2003 American Chemical Society. Figure 12. Structures of thymine dimer (T=T), two separated thymines (T + T), and the modified base (O).

charged polypeptide consisting of (i) two protonated terminal lysines (Lys) and (ii) two polyalanine (Alan) helices, connected in the center by a cystine disulfide linkage. In ECD experiments, the gas-phase positively charged peptide undergoes collisions with low-energy (thermal) electrons, an electron is captured by the peptide, and the peptide is observed to fragment. In ECD studies of the peptide shown in Figure 10, abundant fragment ions produced by cleavage at the central disulfide bond were detected. A mechanism for such S−S bond cleavage has been proposed10 in which an electron enters an antibonding S−S σ* orbital to initiate the bond breaking event. In ref 10 it was emphasized that vertical electron attachment into an S−S σ* orbital is endothermic by ca. 1 eV, so there appears to be no way for a thermal electron to enter such an orbital. However, the Coulomb potentials originating at the positively charge Lys termini can act to increase (by 2 × 14.4/R eV, where R is the distance from each Lys to the S−S bond midpoint) the electron binding strength of the S−S σ* orbital. Therefore, even when there are 20 Ala units in each of the two helices and the distance from the terminal Lys and the S−S bond is ca. 30 Å, there can be enough (2 × 14.4/30 = 1 eV) Coulomb stabilization to render electron attachment to an S−S σ* orbital exothermic, which is consistent with the ECD observations discussed in ref 10. So, even in such a large molecule, the Coulomb potential estimated using a dielectric constant ε of unity produces predictions that are in line with what is seen experimentally. Now, let us extend our considerations to large biological molecules that are studied experimentally under conditions where they are surrounded by highly polar (e.g., aqueous) solvent that may even contain electrolyte ions in substantial concentrations.

modified base (O). In these structures, the symbol R is used to show where the O, T=T, or T is linked to a sugar unit within the DNA duplex shown in Figure 11. In recent experiments,11 samples of duplex oligomers similar to those in Figure 11 (with the O placed in various locations relative to the T=T damage site) were subjected to radiation from photons having energy 0.2 eV, corresponding to rates >1013 s−1) are high enough to make accessing the barriers on the π*−σ* crossings the rate limiting process for these systems. In turn, the barriers have been found16 to be as low as 5 kcal mol−1 (for cleaving the C−O bond in aqueous solvation). For the temperatures at which the experiments13 were performed, the rate of C−O bond cleavage can be estimated by multiplying the C−O vibrational frequency (ca. 3 × 1013 s−1) by a barrier-accessing probability exp(−E/RT) to obtain ca. 1010 s−1. The barriers to cleaving base−sugar N1−C bonds are higher (because the electron affinity of the base N1 radical is lower than that of the phosphate O radical), so the rates for breaking these bonds are predicted to be lower. Although the earlier experiments showing stand breaks in DNA induced by low-energy electrons were not able to determine which bonds are broken, more recent studies17,18 on small double stranded nucleotide oligomers bombarded by electrons as in ref 14 did indeed experience sugar− phosphate C−O (primarily) and base−sugar N1−C (secondarily) bond cleavage as illustrated in Figure 21.

Figure 21. Numbers proportional to the yields of bond cleavages involving N1−C (base release) or C−O (phosphate) bonds. Taken from Figure 12 in ref 15. Reprinted with permission from ref 15. Copyright 2006 American Chemical Society.

Although the experiments and theoretical modeling on DNA strand breaks discussed above contain no significant Coulombpotential effects, they do suggest roles that Coulomb interactions could play under different (and probably more relevant to how DNA behaves in living organisms) conditions. Specifically, it is important to keep in mind that the DNA samples subjected to electron bombardment as discussed in refs 13 and 17 had been subjected to desiccation conditions. This means that all other than a few water molecules bound tightly (e.g., within major or minor grooves or near phosphate groups) had been removed. Under such conditions, it is most likely that the phosphate units are neutralized (e.g., by a nearby Na+ ion or by protonation) rather than negatively charged. As a result, there would be no strong Coulomb repulsion between the baseattached excess electron and the backbone phosphate groups, as a result of which the barrier at which the base π*-attached and sugar−phosphate σ*-attached curves undergo an avoided crossing can be low as found in ref 14. I

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The species used to illustrate these concepts include the following: a. multiply charged anions in which the charged sites are spatially well separated (e.g., dicarboxylate dianions); b. multiply charged anions that have negative electron binding energies but in which the RCB lengthens the rate of electron detachment (e.g., the Cu phthalocyanine complex and the sulfate ion); c. multiply charged superhalogen type anions (e.g., MF42−, where M is an alkaline earth element); d. positively charged polypeptides in which positive sites’ Coulomb potentials stabilize antibonding orbitals allowing an electron to attach to such orbitals (e.g., (AcCA15K+H)22+); e. DNA duplex oligomers containing a thymine dimer damage site that is repaired by electron attachment; f. DNA fragments in which an electron is attached to a base π* orbital and results in cleavage of a sugar−phosphate C−O or base−sugar N1−C bond. By gathering together data and insights from such a broad spectrum of systems, we hope to inspire others to consider utilizing the effects of Coulomb potentials in designing new anionic fragments whose chemical and physical properties can be tuned through their Coulomb interactions.

In contrast, if the phosphate group closest to the base to which an excess electron has attached is negatively charged, as it is most of the time in living systems, the base π*-attached electron will be repelled by the negative phosphate group. [Although the equilibrium constants Keq for binding and unbinding ions (e.g., Na+, K+, H+) to phosphate groups k binding −

(RO)(R′O) − POO + I

+

→ ←

(RO)(R′O) − POOI

k unbinding

may be known, it is the unbinding rate constant kunbinding that determines how long a given phosphate group remains neutralized, and these rates are largely unknown.] As a result, the energy of the C−O σ*-attached curve will be shifted upward, thus increasing the barrier that needs to be accessed to effect electron transfer from the base to the sugar−phosphate C−O bond. Of course, the energy of the N1−C σ* curve will also be shifted to higher energy. These considerations of Coulomb potentials would thus suggest the following. 1. Unless the rate of accessing the base π* to C−O σ* or N1−C σ* crossing point exceeds the rate constant kunbinding describing forming negatively charged phosphate from its neutralized form, C−O or N1−C bond cleavage will be substantially reduced. Depending on the degree to which the Coulomb interactions between the base π*-attached electron and the phosphate group are dielectrically screened, the formation of strand breaks via C−O cleavage or of base excision by N1−C bond breakage may even be eliminated for all practical purposes. 2. Because the distance from the N1−C bond to the phosphate group is larger than from the C−O bond to the phosphate’s center of negative charge, these Coulomb effects should differentially destabilize the C−O σ*-attached state relative to the N1−C σ*-attached state. This, in turn, should decrease the fraction of C−O bond cleavage and increase the fraction of N1−C cleavage. Unless both bond-breaking rates are rendered too small to be detected, it should be possible to test this hypothesis. In summary, although the experimental data on desiccated DNA samples has little to do with internal Coulomb potentials, the theoretical interpretation of that data allow us to suggest what will occur if similar experiments were carried out on samples that are strongly solvated. In particular, it is suggested that the Coulomb potentials would have major influences on the yields of strand break formation and of base excision.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel: (801) 581-8023. URI: http://simons.hec.utah.edu. Notes

The authors declare no competing financial interest.

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REFERENCES

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DISCUSSION AND CONCLUSIONS The primary concepts reviewed and analyzed in this paper include 1. Coulomb destabilization of intrinsic electron binding strengths; 2. the repulsive Coulomb barrier that can act to trap an excess electron behind it; 3. the role of attractive and repulsive Coulomb interactions that produce superhalogen compounds; 4. the fact that Coulomb interactions may be unscreened or only weakly screened even for species embedded in condensed media; 5. Coulomb stabilization of antibonding orbitals that renders electron attachment exothermic. J

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