Pyrimidic Dimers - American Chemical Society

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Use of the Dual Potential to Rationalize the Occurrence of Some DNA Lesions (Pyrimidic Dimers) Christophe Morell,*,† Vanessa Labet,† Paul W. Ayers,‡ Luigi Genovese,§ Andre Grand,† and Henry Chermette|| †

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INAC/SCIB/LAN (UMR-E n°3 CEA-UJF FRE3200 CNRS), CEA-Grenoble, 17, rue des Martyrs, F-38054 Grenoble Cedex 9, France ‡ Department of Chemistry and Chemical Biology, McMaster University Hamilton, Ontario, L8S 4M1, Canada § SP2M, UMR-E CEA/UJF-Grenoble 1, INAC, Grenoble, F-38054, France Sciences Analytiques Chimie Physique Theorique, Universite de Lyon, Universite Lyon 1 (UCBL) et UMR CNRS 5180, bat Dirac, 43 bd du 11 novembre 1918, F-69622 Villeurbanne Cedex, France ABSTRACT: Exploiting the locality of the chemical potential of an excited state when it is evaluated using the ground state Density Functional Theory (DFT), a new local descriptor for excited states has been proposed (J. Chem. Theory Comput. 2009, 5, 2274). This index is based on the assumption that the relaxation of the electronic density toward that of the ground state drives the chemical reactivity of excited states. The sign of the descriptor characterizes the electrophilic or nucleophilic behavior of atomic regions. Through an exact excited state DFT formalism provided by Gross, Oliveira, and Kohn, a mathematical argument is given for this descriptor only for the first excited state. It is afterward used to rationalize the occurrence and the regioselectivity of some DNA lesions based on the [2 þ 2] cycloaddition between two adjacent bases.

1. INTRODUCTION Conceptual Density Functional Theory (DFT) is a mathematical framework in which qualitative theories are developed to understand chemical reactivity and selectivity.1,6 Basically, the overall chemical reactivity is assessed by several global descriptors79 that stem from derivatives of the energy with respect to the number of electrons. Local reactivity parameters, of paramount importance for the understanding of chemical selectivity, arise from the response of the energy as the external potential experienced by the electronic system changes. Within Conceptual DFT, numerous organic and inorganic rules have been rationalized as purely electronic effects.10 Moreover, different chemical reactivity principles have arisen from a better understanding of the nature of DFT descriptors. Nevertheless, in spite of three decades of great success,11,12 two kinds of chemical reactions are still difficult to apprehend within this framework. Specifically, the way radical and excited state species evolve during a chemical process is not yet totally understood. For the former, a whole new mathematical framework1317 has been set up but so far the results obtained are not totally convincing. For the latter, the issue is inherent in the mathematical foundation of DFT. Indeed, the two foundational theorems r 2011 American Chemical Society

of DFT, namely, the first and the second HohenbergKohn theorems,18 are only valid for the ground state of an electronic system. Thus, for excited states, the physical and mathematical equations are still to be developed, even though different tentative studies have already been undertaken.1924 Very recently, the present authors have proposed an alternative way to rationalize the chemical selectivity of an excited state species.25 That analysis starts by hypothesizing that relaxation of the electronic density of the excited state species toward the ground state can be facilitated by a chemical reagent. This is merely an update of the Fukui’s idea2628 that for the first excited state the highest occupied molecular orbital (HOMO) becomes the lowest unoccupied molecular orbital (LUMO) and vice versa. Indeed a crude model for the first excited state consists to show the promotion of an electron from the HOMO to the LUMO. Thus, the new HOMO is the former LUMO, while the new LUMO is the former HOMO. This approach was successful and the regio-selectivity of different chemical reactions, mainly Received: March 27, 2011 Revised: May 31, 2011 Published: June 02, 2011 8032

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[2 þ 2] cycloadditions has been predicted using the descriptor derived from this approach. Unfortunately, the mathematical arguments in this previous paper are suspect because they use traditional DFT, which cannot properly describe the energy of an excited state, except in rare cases,29,30 even though it might be sufficient for the reactivity. In this paper we present a different approach to the problem, starting from an exact excited-state version of DFT. This provides a different, and arguably better way, to understand the power of the descriptor we already found to be useful for excited state. The descriptor is then applied to the rationalization of the occurrence and the selectivity of very important DNA lesions based on [2 þ 2] cycloadditions between adjacent bases.3133 So in the next part, the general equations leading to the excited state local descriptor are exposed. Afterward, it is shown how this approach elegantly solves the problem of the occurrence of different dimeric cycloproducts.

2. PHYSICAL GROUND FOR THE USE OF THE DUAL POTENTIAL FOR EXCITED STATES Generally an excited state is produced through a two-step process. As electrons are much lighter than nuclei, in the first step, a vibronic excited species is produced by a vertical electronic transition. The electronic density of this species differs from that of the ground state while the external potential (defined by the position of the atomic nuclei) remains unchanged. This step is described by the well-known FranckCondon principle.34,35 The excited state so produced is called Hot Excited State (HES). During a second step, the HES decays toward the vibrational ground state of the electronic excited state. As this vibrational relaxation process occurs, the external potential adapts itself to the new electronic density, creating an Optimized Excited State (OES). Traditional DFT is based on the first and second Hohenberg Kohn theorems. Unfortunately, these theorems have only been proven for the electronic ground state and, therefore, cannot be applied to excited states. However, the situation is not as bad as it seems because different formulations of the excited state DFT have been published.3642 In this paper we focus on the approached excited states propounded by Gross, Oliveira, and Kohn.43 Following the example of Theophilou,44 they generalize the first HohenbergKohn theorem and the Rayleigh-Ritz principle to an ensemble of fractionally occupied states. In their approach, they have been able to provide an easy calculation of excitation energies and related properties. In this section, starting from their formalism for a nondegenerated two-state ensemble with energies E1 and E2, we will provide a new perspective for why the dual descriptor is relevant for excited state chemistry. Arbitrarily it has been decided that the energies follow this inequality: E1 < E2. Thus, state is the ground state, while state is the first excited state. For this electronic system ensemble, the electronic density is given by Fω ¼ ð1 ωÞF1 þ ωF2

ð1Þ

in which ω is the weight of state 2. To comply with the variational principle, the weight ω is limited to the interval 0 e ω < 1/2. F1 and F2 are the electronic densities of states 1 and 2, respectively. The global energy of the system is related to the energy of state 1 (E1) and that of state 2 (E2) by EðωÞ ¼ ð1 ωÞE1 þ ωE2

ð2Þ

Assuming that the expected values of eq 2 are known for at least two ω, it is possible to compute the exact excitation energy because E is a linear function of ω. Specifically, DEðωÞ ¼ E2 E1 ¼ Eexc ð3Þ Dω Finally, within the KohnSham framework, Gross, Oliveira, and Kohn45 found Eexc ¼

DEðωÞ DEω ¼ E2 E1 ¼ εNþ1 εN þ exc Dω Dω

ð4Þ

where Eω exc is the ensemble’s exchange-correlation energy. By identifying the two first terms with the hardness, Nagy46 showed that DEðωÞ DEω ¼ E2 E1 ¼ ηKS þ exc ð5Þ Dω Dω In eq 4, ηKS stands for the KohnSham hardness, which is computed from frontier orbital eigenvalues as Eexc ¼

ηKS ¼ ðεLUMO εHOMO Þ

ð6Þ

47

In the original paper, the definition of hardness differed by a factor of 2, but this is now the preferred definition.48,49 It would be convenient to neglect the last term of the righthand side in eq 5 and assume the excitation energy was equal to the hardness. This approximation is valid in the frozen frontier orbital approximation, but the computation of eq 5 without the exchange-correlation contribution always gives excitation energies higher than the experimental ones, at least for atomic systems. Another link between the excitation energy and the hardness can be inferred from the extension of the GrochalaAlbrecht Hoffmann50 bond length rule to energies that was proposed by Ayers and Parr.51 Following up on those theoretical arguments, we recently showed52 that the first exited state potential energy surface can often be approximated by the following relation: EN2 ðξgs Þ EN1 þ 1 ðξgs Þ þ EN1 1 ðξgs Þ EN1 ðξgs Þ þ C

ð7Þ

Here the exponent indicates the electron number of the electronic system considered, ξgs is an arbitrary reaction coordinate, and C is a constant independent of the reaction coordinate. By subtracting EN 1 (ξgs) on both sides of eq 7 and identifying the chemical hardness one gets EN2 ðξgs Þ EN1 ðξgs Þ ηðξgs Þ þ C

ð8Þ

Comparing eq 8 to eq 5, one can state that eq 7 works only when, during the chemical process, the exchange correlation contribution is either constant or its variations are negligible. Thus, the variations of the first excited state energy can be monitored using the reaction force:53,54 dE2 ðξgs Þ dηðξgs Þ dE1 ðξgs Þ þ dξ dξ dξ

ð9Þ

According to eq 9, there is a way to evaluate the variation of the first excited state potential energy surface through an adiabatic connection between the ground state and the first excited state. This is schematically represented in Figure 1: For the ground state, the reactants are always at the bottom of a potential energy well, so the last term in eq 9 will be zero. This term then becomes positive until the transition state, after which it is negative. On the contrary, when a reaction happens in the excited state, the activation energy is generally either nil or small 8033

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Table 1. Chemical Behavior Related to the Sign of the Dual Potential for the First Excited State sign [VΔf]

chemical behavior for the excited state

þ

nucleophile

electrophile

64,65 created at position x is then defined as The dual R potential V (x) = (Δf1(ξgs,r))/(|r x|)dr. Just as has been argued for the Fukui function, one may argue that the dual potential is a better measure of the chemical reactivity than the dual descriptor itself. Because the reagent is going to approach the molecule as the reaction proceeds, (dx)/(dξ) is always positive and does not affect the analysis for eq 12. It is generally accepted that the charge of the active site of an electrophile (respectively, nucleophile) is positive (respectively, negative). Therefore, the best interaction between an electrophile (q(x) > 0) and the excited molecule is reached when the nucleophile R is located in a position where the dual potential is positive ( (Δf1(ξgs,r))/(|r x|)dr > 0). Conversely, the best interaction between a nucleophile (q(x) < 0) and the excited molecule is achieved when the former is located in a position where R the dual potential is negative ( (Δf1(ξgs,r))/(|r x|)dr < 0). The sign of the dual potential is therefore a nice indicator of the chemical behavior of an excited state atomic site. Positions that exhibit positive values act as a nucleophile, while positions with negative values act as an electrophile. These results are gathered in Table 1. The results in this table are consistent with the arguments that have been made previously using the dual descriptor itself. These results also suggest that higher order derivative of the energy,66 like the dual descriptor, are just as interesting in excited states as they are in ground states. To demonstrate the utility of these concepts, we will study the occurrence and the selectivity of some DNA lesions arising from [2 þ 2] photocycloadditions between two adjacent bases. To do this, we need understand how one should choose the charge q in a molecule with multiple reactive sites. It is now well established that the dual descriptor is an efficient indicator of the electrophilic versus nucleophilic behavior of an atomic site within a molecule. Sites exhibiting positive values of the dual descriptor act as electrophile, while positions with negative value react as nucleophile.67 Following the concept developed in this paragraph about the reactivity of the first excited state, the fundamental quantity that governs photochemical reactions such as [2 þ 2] photocycloadditions is the interaction between the dual descriptor of one reagent and the dual potential of another reagent,68,69 Z ε¼ Δfg, s ðrÞVesΔf ðrÞdr Δf

Figure 1. Schematic representation of the adiabatic connection between the ground state and the first excited state.

because one reactant has been photochemically activated and electronic energies are usually much larger than activation energies for chemical reactions. One therefore expects the first term of the right-hand side of eq 9 to be negative. (One arrives at the same conclusion by invoking the principle of maximum hardness, which suggests that transition states are generally less hard than reactants or products.) The following discussion focuses on the sign of this first term. By decomposing the hardness derivative into its electron-transfer and external-potential-responses contributions, one may write, ! Z dE2 ðξgs Þ δηðξgs Þ δvðrÞ Dη dN þ dr þ D ð10Þ DN v dξ dξ dξ δvðrÞ In eq 10, D is a positive defined constant that replaces the second right-hand term of eq 9, recall that D is negligible for structures sufficiently close to the reactant and positive for any structures that precede the transition state. The derivative of the hardness in eq 10 may now be identified with the well-known chemical descriptors, namely, the hyperhardness55 and the dual descriptor5658 Z dE2 ðξgs Þ dN δvðrÞ þ Δf1 ðξgs , rÞ dr þ D ð11Þ γ1 ðξgs Þ dξ dξ dξ This methodology can easily be extended to other excited states by replacing Δf(ξgs,r) by the electron density difference between the excited state of interest and the ground state. ΔkgsthesF(ξgs,r) and γ1 by ((∂Eexc)/(∂N)). For well-separated molecules, Ayers and Parr59 argued that the variation of the external potential can be replaced with the electrostatic potential of the reagent. If we assume that the reagent is so far away that it can be approximated by a point charge6063 located at the position x, then (δv(r))/(dξ) ≈ ( (q(x))/(|r x|))((dx)/(dξ)), one gets dE2 ðξgs Þ dN1 γ1 ðξgs Þ dξ dξ

Z

Δf1 ðξgs , rÞ dx þ D ð12Þ dr qðxÞ: jr xj dξ

The best matching is then obtained when positions with opposite reactivity are aligned.

3. COMPUTATIONAL DETAILS All the molecules were fully optimized at the B3LYP/6-31G** level of theory using the Gaussian software package.70 The optimization process was checked by a frequency calculation. No imaginary frequency has been found. Both the excited and ground state electronic densities have been obtained through a CIS single point calculation with the same basis set. Then the 8034



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Figure 2. Four kinds of bipyrimidine sites in a DNA strand.

Figure 4. Imino tautomeric form of cytosine involved in the formation of 64PP with a cytosine at the 30 -end.

Figure 3. Chemical structure of the main UVB-induced dimeric photoadducts produced at a 50 -TT-30 bipyrimidine site.

3-dimensional cube files of the difference have been generated using the cubgen facility program. The dual descriptor for the ground state has been calculated from the density of the radical cation and anion using the formula: Δf ðrÞ ¼ FNþ1 ðrÞ þ FN1 ðrÞ 2FN ðrÞ

The dual potential has been computed from the electron density difference using a Poisson’s solver based on interpolating scaling functions.71 This is an efficient and accurate formalism, optimal for electrostatic problems, explicitly conceived with free boundary conditions. For all the isodensity maps, the positive regions are colored in red while the negative regions are colored in yellow. Therefore, favorable interactions are achieved when regions with same colors are aligned. On the contrary, unfavorable interactions are achieved when regions with different colors are aligned. 8035



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Table 2. Chemical Structures and Notations of the Main UVB-Induced Dimeric Photoproducts

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Figure 5. Yield of formation of the main photoproducts within isolated DNA exposed to UVB radiations (dose range: 03.4 kJ 3 m2).

4. APPLICATION TO DNA LESIONS We shall see now how the concepts developed in section 2 can be applied to rationalize the occurrence of some DNA lesions based upon [2 þ 2] photocycloaddition. UV radiation is a strong physical genotoxic agent, implicated in the development of human skin cancers.7274 Exposure of DNA to UVB radiation (290320 nm) leads to the electronic excitation of the nucleobases,75 allowing among others the occurrence of photocycloaddition [2 þ 2] between two adjacent bases. Dimeric photoproducts are thus formed, very mostly at the bipyrimidine sites76 (Figure 2). Two main kinds of damage are produced: cyclobutadipyrimidines (CPDs) and pyrimidine (64) pyrimidone photoproducts (64PPs;77 Figure 3). The former are the result of a [2 þ 2] photocycloaddition between the C5C6 π-bonds of two adjacent pyrimidic bases. Alternatively, the latter 64PP adducts involve in a first stage a Paterno-B€uchi [2 þ 2] cycloaddition between the C5C6 π-bond of the 50 -end pyrimidine and the exocyclic carbonyl or imino group at position 4 of the 30 -end pyrimidine, depending on whether it is a thymine or a cytosine. This leads to the formation of either an oxetane or an azetidine intermediate which rearranges to give the pyrimidine (64) pyrimidone photoproduct. It is worth noting that in the case where the 30 -end pyrimidine is a cytosine, this latter has to be in an imino tautomeric form to exhibit a π-bond character at position 4 (Figure 4). As a result, there are eight potentially important kinds of pyrimidine dimers. Their structures as well as the notations used in the following of the subsection are given in Table 2. The distribution of these photoproducts in isolated DNA, determined experimentally,78 is reported in Figure 5. Three main observations can be made: (1) The CPDs are produced more efficiently than the related 64PPs. This is particularly true at the 50 -TT-30 and

50 -CT-30 bipyrimidine sites, i.e. when the 30 -end pyrimidine is a thymine. (2) Thymines appear more reactive than cytosines toward the formation of dimeric photoproducts. Indeed, TTCPD are the main dimeric photoproducts observed, whereas CC CPD and CC 64PP are rather infrequent. (3) There is a sequence effect because photoproducts are not produced in the same yield at 50 -TC-30 and 50 -CT-30 sites. Geometric considerations are probably at the origin of the sequence effect. The fact that 50 -TT-30 bipyrimidine sites are more reactive than the others toward the formation of CPDs has been studied from a theoretical point of view by B. Durbeej and L.A. Eriksson through DFT and TDDFT calculations.79,80 Other authors have reached the same conclusion using “ab initio” methods.81 The rationalization of this difference of reactivity with conceptual DFT tools would necessitate the use of local size-consistent descriptors for the excited states, which is beyond the scope of this paper. Indeed, the dual potential defined in the previous section is relevant only to study selectivity inside the same molecular system. So, it must be an appropriate tool to try to understand why, at the same bipyrimidine site, the cyclobutadipyrimidine and the pyrimidine (64) pyrimidone photoproduct, which are isomers, are not formed in the same yield. To form CPDs and 64PPs, a pyrimidic base in its first excited state interacts with an adjacent pyrimidic base in its ground state. The favorable/unfavorable character of the interactions between the two partners should be deduced from the interactions between the dual descriptor of the base in its ground state and the dual potential of the base in its first excited state. In Figure 6 are represented the interactions between dual descriptor and dual potential, at the level of atoms involved in the formation of the 2 σ-bonds of the [2 þ 2] cycloadditions leading to the eight photoproducts represented in Table 2. We arbitrarily selected 8037



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Figure 7. Interactions at 50 -TC-30 and 50 -CC-30 bipyrimidine sites between the dual descriptor of the 50 -end pyrimidic base in its ground state and the dual potential of the 30 -end pyrimidic base in its first excited state to form either a cyclobutadipyrimidine or a pyrimidine (64) pyrimidone photoproduct. The symbol * indicates the base that is in its first excited state. Red lobes correspond to positive values of the dual descriptor/potential, whereas yellow lobes correspond to negative ones. Dashed lines correspond to the interactions leading to the formation of the σ-bonds during the cycloadditions [2 þ 2]. Dot lines correspond to secondary interactions.

Figure 6. Interactions at the four kinds of bipyrimidine sites between the dual descriptor of the 50 -end pyrimidic base in its ground state and the dual potential of the 30 -end pyrimidic base in its first excited state to form either a cyclobutadipyrimidine or a pyrimidine (64) pyrimidone photoproduct. The symbol * indicates the base that is in its first excited state. Red lobes correspond to positive values of the dual descriptor/ potential, whereas yellow lobes correspond to negative ones.

the 30 -end base to be excited. Because the dual descriptor and the dual potential are quite identical (see Figure 6), the reader will not be surprised to learn that the results would be the same if the other reagent is excited instead. In the case of the formation of the four CPDs, there is one interaction between carbon C5 of the base in its ground state that corresponds to a negative value of the dual descriptor (yellow), and carbon C5 of the excited base corresponding to a negative value of the dual potential (yellow). Simultaneously, an interaction takes place between carbon C6 of the base in its ground state, which exhibits a positive value of the dual descriptor (red), and carbon C6 of the base in its first excited state, associated with a positive value of the dual potential (red). In section 2 of this article it has been shown that the interpretation of the sign of the dual descriptor for the ground state and the dual potential for the first excited state are reversed. Consequently, both interactions correspond to an interaction between a nucleophilic site and an electrophilic one, which is favorable.

In the case of the 64PPs, it appears that the formations of TC 64PP and CC 64PP involve two favorable interactions, whereas those of TT 64PP and CT 64PP involve only one favorable interaction (between carbon C6 of the 50 -end base and carbon C4 of the 30 -end one) and an unfavorable one (between carbon C5 of the 50 -end pyrimidine and OC4dO of the 30 -end thymine). This is completely in agreement with the experimental observation according to which TT 64PP and CT 64PP are produced in much smaller yields than TT CPD and CT CPD respectively. If both the carbonyl group of thymine at position 4 and the exocyclic imino group of the cytosine tautomer can be involved in a Paterno-B€uchi cycloaddition, their reactivity is not the same at all. Indeed, at the first excited state, in both cases, carbon C4 is electrophilic but whereas the nitrogen of the imino group of the cytosine tautomer is more nucleophilic than electrophilic, that is the reverse for the oxygen of the carbonyl group of thymine. Consequently, thymine is less likely than the imino tautomer of cytosine to undergo a [2 þ 2] photocycloaddition with the C5C6 π-bond of an adjacent pyrimidic nucleobase exhibiting in its ground state an electrophilic site at position 5 and a nucleophilic one at position 6. In DNA, the WatsonCrick conformation of the double strand imposes the relative orientation of two adjacent pyrimidic bases. Different secondary interactions involved in the formation of CDP and 64PP at the same bipyrimidine site could be the cause of the fact that CPDs are produced more efficiently than 64PPs even when the two interactions leading to the formation of the 2 σ-bonds are favorable in both cases. Those secondary interactions are represented in Figure 7 at 50 -TC-30 and 50 -CC-30 bipyrimidine sites. It can be seen that four favorable secondary 8038


The Journal of Physical Chemistry A interactions are involved in the formation of TC CPD and CC CPD whereas an unfavorable one takes place in the formation of TC 64PP and CC 64PP. Again, this is in total agreement with the experimental observations. Finally, it appears that the use of the dual potential to characterize the chemical behavior of reactive sites of a molecular system in its first excited state gives good qualitative results in the case of the formation of dimeric photoproducts in DNA.

5. CONCLUSION The goal of this paper was 2-fold. First, we provided a more satisfying motivation for the utility of the dual potential in describing excited state reactivity by invoking the exact ensemble-excited-state DFT theory of Theophilou, Gross, Oliveira, and Kohn and the excited state additivity rule of Ayers and Parr. By monitoring the variation in the first excited state energy, it was shown that positive values of the dual potential indicate nucleophilic sites, while negative values indicate electrophilic sites. Second we checked whether the dual descriptor could describe properly the reactivity of some photocycloadditions of adjacent DNA bases. By analyzing the interactions between the dual potential and the dual descriptor, both the occurrence and the regioselectivity of [2 þ 2] cycloadditions between adjacent DNA bases have been rationalized. ’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

’ REFERENCES (1) Geerlings, P.; De Proft, F.; Langenaeaker, W. Chem. Rev. 2003, 103, 1793. (2) Gazquez, J. L. J. Mex. Chem. Soc. 2008, 52, 3. (3) Ayers, P. W.; Andeson, J. S. M.; Bartolotti, L. J. Int. J. Quantum Chem. 2005, 101, 520. (4) Gazquez, J. L. J. Mex. Chem. Soc. 2008, 52, 3. (5) Liu, S. Acta. Phys. Chem. Sin. 2009, 25, 1. (6) Chermette, H. J. Comput. Chem. 1999, 20, 129. (7) Mulliken, R. S. J. Chem. Phys. 1934, 2, 782. (8) Parr, R. G.; Donnelly, R. A.; Levy, M.; Palke, W. E. J. Chem. Phys. 1978, 68, 3801. (9) Parr, R. G.; Pearson, R. G. J. Am. Chem. Soc. 1983, 105, 7512. (10) Morell, C.; Grand, A.; Gutierez-Oliva, S.; Toro-Labbe, A. In Theoretical Aspects of Chemical Reactivity; Toro-Labbe, Ed.; Elsevier: New York, 2006; Vol. 19. (11) Morell, C.; Hocquet, A.; Grand., A.; Jamard-Gregoire, B. J. Mol. Struct. (THEOCHEM) 2008, 849, 46. (12) Morell, C.; Ayers., P. W.; Grand, A.; Guttierez-Oliva, S.; ToroLabbe, A. Phys. Chem. Chem. Phys. 2008, 10, 7236. (13) Ghanty, T. K.; Ghosh, S. K. J. Am. Chem. Soc. 1994, 116, 3943. (14) Garza, J.; Vargas, R.; Cedillo, A.; Galvan, M.; Chattaraj, P. K. Theo. Chem. Acc. 2006, 115, 257. (15) Garza, J.; Robles, J. Int. J. Quantum Chem. 1994, 49, 159. (16) Perez, P.; Chamorro, E.; Ayers, P. W. J. Chem. Phys. 2008, 128, 204108. (17) Pinter, B.; De Proft, F.; Van Speybroeck, V.; Hemelsoet, K.; Waroquier, M.; Chamorro, E.; Veszpremi, T.; Geerlings, P. J. Org. Chem. 2007, 72, 348. (18) Hohenberg, P.; Kohn, W. Phys. Rev. 1964, 136, B864. (19) De Proft, F.; Fias, S.; Van Alsenoy, C.; Geerlings, P. J. Phys. Chem. A 2005, 109, 6335. (20) Sengupta, D.; Chandra, A. K.; Nguyen, M. T. J. Org. Chem. 1997, 62, 6404.

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(21) Mendez, F.; Garcia-Garibay, M. A. J. Org. Chem. 1999, 64, 7061. (22) Fuentealba, P.; Simon-Manso, Y.; Chattaraj, P. K. J. Phys. Chem. A 2000, 104, 3185. (23) Chattaraj, P. K.; Poddar, A. J. Phys. Chem. A 1999, 103, 1274. (24) Chattaraj, P. K.; Poddar, A. J. Phys. Chem. A 1998, 102, 9944. (25) Morell, C.; Labet, V.; Grand, A.; Ayers, P. W.; De Proft, F.; Geerlings, P.; Chermette, H. J. Chem. Theory Comput. 2009, 5, 2274. (26) Fukui, K.; Yonezawa, T.; Nagata, C. Bull. Chem. Soc. Jpn. 1954, 27, 423. (27) Fukui, K.; Yonezawa, T.; Nagata, C. J. Chem. Phys. 1953, 21 (1), 174. (28) Fukui, K.; Yonezawa, T; Shingu, J. J. Chem. Phys. 1952, 20 (4), 722. (29) Perdew, J. P.; Levy, M. Phys. Rev. B 1985, 31, 6264. (30) Ayers, P. W.; Levy, M. Phys. Rev. A 2009, 80, 012508. (31) Eisinger, J.; Lamola, A. A. Biochem. Biophys. Res. Commun. 1967, 28, 558. (32) Eisinger, J.; Shulman, R. G. Science 1968, 161, 131. (33) Shreier, W. J.; Shrader, T. E.; Koller, F. O.; Gilch, P.; CrespoHernander, C. E.; Swaminathan, V. N.; Carell, T.; Zinth, W.; Kohler, B. Science 2007, 315, 625. (34) Frank, J. Faraday Soc. 1926, 21, 536. (35) Condon, E. Phys. Rev. 1926, 27, 640. (36) Nagy, A. Int. J. Quantum Chem. 1998, 70, 681. (37) Chattaraj, P. K.; Gosh, S. K.; Liu, S.; Parr, R. G. Int. J. Quantum Chem. 1996, 60, 535. (38) Gross, E. K. U.; Oliveira, L. N.; Kohn, W. Phys. Rev. A 1988, 37, 2805. (39) Nagy, A.; Levy, M.; Ayers, P. W. In Chemical Reactivity Theory: A Density Functional View; Chattaraj, P. K., Ed.; Taylor and Francis: Boca Raton, FL, 2009; p 121 (40) Gorling, A. Phys. Rev. A 1996, 54, 3912. (41) Casida, M. E.; Chong, D. P. Recent Advances in Density Functional Theory Methods, Part 1; World Scientific: Singapore, 1995; p 155. (42) Runge, E.; Gross, E. K. U. Phys. Rev. Lett. 1984, 52, 997. (43) Gross, E. K. U.; Oliveira, L. N.; Kohn, W. Phys. Rev. A 1988, 37, 2809. (44) Theophilou, A. K. J. Phys. C 1979, 12, 5419. (45) Gross, E. K. U.; Oliveira, L. N.; Kohn, W. Phys. Rev. A 1988, 37, 2809. (46) Nagy, A. J. Chem Sci. 2005, 117, 437. (47) Parr, R. G.; Pearson, R. G. J. Am. Chem. Soc. 1983, 105, 7512. (48) Pearson, R. G. Inorg. Chim. Acta 1995, 240, 93. (49) Ayers, P. W.; Parr, R. G.; Pearson, R. G. J. Chem. Phys. 2006, 124, 194107. (50) Crochala, W.; Albrecht, A. C.; Hoffmann, R. J. Phys. Chem. A 2000, 104, 2195. (51) Ayers, P. W.; Parr, R. G. J. Phys. Chem. A 2000, 104, 2211. (52) Morell, C.; Labet, V.; Ayers, P. W.; Jorge, N.; Grand, A. Chem. Phys. Lett. 2010, 485, 371. (53) Toro-Labbe, A. J. Phys. Chem. A 1999, 103, 4398. (54) Toro-Labbe, A.; Gutierrez-Oliva, S.; Concha, M. C.; Murray, J. S.; Politzer, P. J. Chem. Phys. 2004, 121, 4570. (55) Fuentealba, P.; Parr, R. G. J. Chem. Phys. 1991, 94, 5559. (56) Morell, C.; Ayers, P. W.; Grand, A.; Chermette, H. Phys. Chem. Chem. Phys. 2011, 13, 9601. (57) Morell, C.; Grand, A.; Toro-Labbe, A. J. Phys. Chem. A 2005, 109, 205. (58) Morell, C.; Grand, A.; Toro-Labbe, A. Chem. Phys. Lett. 2006, 425, 342. (59) Ayers, P. W.; Parr, R. G. J. Am. Chem. Soc. 2001, 123, 2007. (60) Anderson, J. S. M.; Melin, J.; Ayers, P. W. J. Chem. Theory Comput. 2007, 3, 358. (61) Anderson, J. S. M.; Melin, J.; Ayers, P. W. J. Chem. Theory Comput. 2007, 3, 375. (62) Chattaraj, P. K.; Ayers, P. W.; Melin, J. Phys. Chem. Chem. Phys. 2007, 9, 3853. (63) Cedillo, A.; Contreras, R.; Galvan, M.; Aizman, A.; Andres, J.; Safont, V. S. J. Phys. Chem. A 2007, 111, 2442. 8039



ARTICLE

(64) Berkowitz, M. J. Am. Chem. Soc. 1987, 109, 4823. (65) Ayers, P. W.; Levy, M. Theo. Chem. Acc. 2000, 103, 353. (66) Geerlings, P.; De Proft, F. Phys. Chem. Chem. Phys. 2008, 10, 3028. (67) Toro-Labbe, A.; Gutierrez-Oliva, S; Murray, J. S.; Politzer, P. Mol. Phys. 2007, 105, 2619. (68) Ayers, P. W.; Morell, C.; De Proft, F.; Geerlings, P. Chem.— Eur. J. 2007, 13, 8240. (69) Cardenas, C.; Rabi, N.; Ayers, P. W.; Morell, C.; Jaramillo, P.; Fuentealba, P. J. Phys. Chem. A 2009, 113, 8660. (70) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; M. A. AlLaham, Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; , Pople, J. A. Gaussian 03, Revision B.3; Gaussian, Inc.: Pittsburgh, PA, 2003. (71) Genovese, L.; Deutsch, T.; Neelov, A.; Goedecker, S.; Beylkin, G. J. Chem. Phys. 2006, 125, 0704105. (72) De Gruijl, F. R. Methods Enzymol. 2000, 319, 359–366. (73) Van Der Leun, J. C.; De Gruijl, F. R. Photochem. Photobiol. Sci. 2002, 1, 324–326. (74) Matsumura, Y.; Ananthaswamy, H. N. Toxicol. Appl. Pharmacol. 2004, 195, 298–308. (75) Fasman, G. D., Ed. Nucleic Acids. In Handbook of Biochemistry and Molecular Biology, 3rd ed.; CRC Press, Inc.: New York, 1975; Vol. I. (76) Cadet, J.; Vigny, P. The Photochemistry of Nucleic Acids. In Bioorganic Photochemistry: Photochemistry and the Nucleic Acids; Morrison, H., Ed.; Wiley and Sons: New York, 1990; pp 1272. (77) Cadet, J.; Sage, E.; Douki, T. Mutat. Res. 2005, 571, 3–17. (78) Douki, T.; Cadet, J. Biochemistry 2001, 40, 2495–2501. (79) Durbeej, B.; Eriksson, L. A. J. Photochem. Photobiol., A 2002, 152, 95–101. (80) Durbeej, B.; Eriksson, L. A. Photochem. Photobiol. 2003, 78, 159–167. (81) Serrano-Perez, J. J.; Gonzalez-Ramirez, I.; Coto, P. B.; Merchan, M.; Serrano-Andres, L. J. Phys. Chem. B 2008, 112, 14096.

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