1060
J. Phys. Chem. 1995, 99, 1060-1063
Ab Initio Molecular Orbital Calculations of DNA Radical Ions. 5. Scaling of Calculated Electron AMinities and Ionization Potentials to Experimental Values Michael D. Sevilla,*,+Brent Besler,t and Anny-Odile Colsont Department of Chemistry, Oakland University, Rochester, Michigan 48309, and Department of Chemistry, Wayne State University, Detroit, Michigan 48202 Received: September 13, 1994; In Final Form: November 8, 1994@
Ab initio molecular orbital calculations of the electron affinities (EAs) and ionization potentials (IPS) of the DNA bases are presented in this work. Comparisons of calculated and experimental values are made for a series of compounds of size and/or structure similar to the DNA bases. Excellent correlations between calculated and experimental values are found for both Koopmans EAs at the 6-31G* and D95v levels and calculated vertical EAs of the model compounds. Several basis sets are considered: 6-31G*, 6-31+G(d), and D95v. The best correlation overall is found for Koopmans D95v EAs and the worst for Koopmans 6-3 1+G(d) EAs; however, both 6-3 1G* and 6-3l+G(d) vertical electron affinities also have good to excellent fits to experiment which allows for estimation of the vertical electron affinities of the DNA bases. Calculations at 6-31G* and 6-31+G(d) using both ROHF and ROMP2 theories show a consistent difference between calculated vertical and adiabatic EAs. This allows for a good estimate of DNA base adiabatic EAs, i.e., -0.7, -0.3, 0.2, 0.3, and 0.4 eV; from the vertical EAs -1.23, -0.74, -0.40, -0.32, and -0.19 eV for G, A, C, T, and U respectively. While EAs must be scaled, we find that Koopmans IPS calculated at the simple 3-21G level predict vertical IPS of the DNA bases with only a 0.15 eV average absolute deviation from the experimentally reported values and calculations at MP2/6-3 1+G(d)//6-3 1G* for the adiabatic ionization potentials of the DNA bases are all within 0.1 eV of experiment.
Introduction Although experimental gas phase ionization energies of the DNA bases have been measured by a number of inve~tigators,l-~ experimental gas phase electron affinities of the DNA bases have not as yet been r e p ~ r t e d .A ~ variety of molecular orbital calculations predict the pyrimidines have higher electron affinities than the purine^^-^ with recent calculations suggesting the following order; T > C >> A > G.5 Ab initio calculations reported thus far predict negative electron affinities for all the DNA bases5 (Le., unstable toward dissociation) which may seem inappropriate for such polar molecular structures.1o Since the anion radicals of the DNA bases have been observed by ESR spectroscopy in aqueous solution,’1-14 one might expect positive electron affinities for the DNA bases. However, it is largely the additional energy of solvation of these species (ca. 3 eV) that results in species stable toward dissociation to the aqueous electron and DNA base.l53 l6 As shown in this work, to a high degree of certainty the vertical electron affinities of all DNA bases are negative and only two of the adiabatic electron affinities are likely to be positive. Although there are no reported EAs for DNA bases in the gas phase there are many other determinations of gas phase negative electron affinities for similar structures. For example, EAs for benzene, pyridine, pyrimidine, naphthalene, and uracil are found to be all negative (-1.1, -0.7, -0.3, -0.2, and -0.2 eV). The calculation of gas-phase electron affinities can be a difficult problem for HF-MO theory.17-19 This is even true for small structures for which HF electron affinities are undzrestimated.17-19 In more recent work however, Staley and StmadZ0have considered a series of hydrocarbons negative ion resonance states, or “negative electron affinities”, and have Oakland University.
* Wayne State University. +
@Abstractpublished in Advunce ACS Absrructs, January 1, 1995.
0022-3654/95/2099-1060$09.00/0
employed HF theory with various basis sets under the Koopmans approximation. While the calculations still underestimate the EAs, they are successfully scaled to experimental electron affinities with the excellent fits to experiment found using the D95v basis set.21 In this work we employ ROHF22923and ROMP224-26calculations at various basis sets to investigate the gas-phase IPS and EAs of the DNA bases. Scaling of these calculations to experiment shows that excellent predictions of electron affhities can be obtained by simply applying the Koopmans theorem. Scaling is not found to be necessary for ionization potentials.
Methods Our approach is straightforward and as follows: The four DNA bases, and several model compounds of experimentally known electron affinity (uracil8 benzene,20n a ~ h t h a l e n e , ~ ~ - ~ ~ p ~ r i d i n e ,and ~ ~ p, ~y ~ i m i d i n e , ~were ~ , ~ ~geometry ) optimized at the ROHF/6-31G*35level for the neutral and ion (anion, cation) radical forms. Single point calculations at ROHF and ROMP2 level were then performed using the 6-31G* and 6-31+G(d)36 basis sets for the ion radicals and neutral species in their optimized ROHF/6-3lG* geometries. In addition the energy of the anion and cation radicals were calculated at the ROW/ and ROMP2/6-31+G(d) levels in the optimized 6-31G* geometry of the neutral species. These calculations were also performed for the anion radicals employing the 6-31G* basis set. Furthermore, single-point calculations at the D95v//6-3 lG* level were performed on the neutral species. The Gaussian 9237 and 9038sets of programs on Cray-YMP, Cray-C90, and IBM RS 6000 computers were employed in this work. Both the adiabatic and vertical electron affinities were calculated. The vertical values are usually reported experimentally, and the adiabatic electron affinities are of primary interest to OUT end point which is the localization of charge in DNA. 0 1995 American Chemical Society
J. Phys. Chem., Vol. 99, No. 3, 1995 1061
MO Calculations of DNA Radical Ions
TABLE 1: Calculated and Experimental Ionization Potentials of DNA bases (eV) 6-31G*//6-3 lG* 6-31+G(d)//6-31G* 3-21G" D95v//6-31G* adiabatic adiabatic vertical HF MP2 Koopmans HF MP2 HF MP2 Koopmans Koopmans Koopmans guanine 8.04 8.47 6.68 7.33 7.99 6.87 7.66 7.29 8.04 8.23 adenine 8.48 8.87 7.19 7.88 8.37 7.35 8.18 7.73 8.58 8.58 cytosine 9.00 9.42 7.81 8.43 9.15 7.99 8.74 8.45 8.82 9.40 thymine 9.45 9.75 7.95 8.51 9.52 8.10 8.85 8.99 10.33 9.70 a Reference 5. Reference 1. Reference 2.
experiment vertc 7.77 8.24 8.26 8.44 8.68 8.94 8.87 9.14
adia'
TABLE 2: Calculated and Experimental Adiabatic and Vertical Electron Affinities of DNA Bases and Model Compounds (eV) 6-31G*//6-3lG* 6-3l+G(d)//6-3 lG* HF MP2 HF MP2 experiment adia vert adia vert adia vert adia vert adia vert guanine -2.72 -3.37 -2.55 -3.06 (-2.27)" (- 1.79)" - 1.47 adenine -2.62 -3.08 -2.23 -2.31 -2.17 cytosine -1.73 -2.35 .-1.58 -2.15 -1.27 -1.82 -0.83 -1.34 thymine -1.52 -2.20 -1.28 -1.95 -1.07 -1.64 -0.54 -1.08 uracil -1.46 -2.09 -1.25 -1.90 -1.00 -1.58 -0.51 -1.12 -0.19' naphthalene -2.05 -2.30 -1.25 -1.52 -1.59 -1.81 -0.68 -0.94 0.14' -0.19 pyridine -2.46 -2.75 -1.95 -2.27 -1.89 -2.08 -1.20 - 1.46 -0.67' - 1.06 -0.29 pyrimidine -2.02 -2.32 -1.40 -1.79 -1.51 -1.75 -0.72 benzene -3.28 -3.42 -2.13 -2.91 -2.56 -2.67 -1.89 -2.05 -1.138 a Extrapolated from trends at the 6-31G* level. Reference 8. Average of three experimental values 0.15:' 0.14,28and 0.12 eV.29 Average of three experimental values -0.19,32 -0.20,30 and -0.19 eV.31e Average of three experimental values -0.59,33 -0.62,30 and -0.79 eV.34f Average of two experimental values -0.33,34 and -0.25 eV.308 Average of nine experimental values.20
'
The adiabatic EA is the difference in energy between the optimized anion and neutral species, whereas the vertical electron affinity is the difference in energy between the anion and the neutral species both computed at the neutral optimized geometry. The adiabatic and vertical IPS are similarly defined from the neutral and cation radical states. Koopmans value^,^^^^ which are simply the energy of the highest occupied molecular orbital for IPS and the lowest unoccupied orbital for the EAs, were also calculated. They provide an estimate of the vertical IP and EA. Vertical EAs are always smaller and vertical IPS always larger than their adiabatic counterparts as they differ by the nuclear reorganization energy on ion f ~ r m a t i o n .The ~ ~ sign convention used for the electron affinities is such that positive values indicate a thermodynamically stable state.
Results and Discussion
1. Ionization Potentials. In Table 1 we show the calculated Koopmans, vertical, and adiabatic IPS for the DNA bases and a comparison with known experimental values. At the MP2/ 6-31+G(d)//6-31G* level, each of the adiabatic IPS is within 0.1 eV of the corresponding experimental value. Clearly the MP2/6-3 1+G(d) level appears sufficient for accurate predictions of adiabatic IPS. Each of the vertical IPS is also well predicted at this level (within 0.2 eV) except for thymine which is 1.2 eV too high. Vertical IPSare less reliable from a computational standpoint since vertical values require that the structures not be geometry optimized in the cationic radical form and are less reliable from an experimental standpoint as well since some nuclear reorganization may take place during measurement. Koopmans predictions of the vertical IP are in best agreement with experiment at the lowest basis set (3-21G).5 Apparently the cancellations of orbital relaxation and electron correlation corrections are best at this level. 2. Electron Affinities. In Table 2 we show the adiabatic and vertical EAs resulting from our calculations at 6-31G*N631G* and 6-31+G(d)//6-31G* levels, and in Table 3 we report the Koopmans EAs at 6-31G*//6-31G*, D95v//631G*, and 6-3 1+G(d)//6-3 lG* levels. The HF calculations with the
TABLE 3: Koopmans Electron Affinities of the DNA Bases and Model ComDounds (eVY 6-31G*//6-31G* D95~//6-3 lG* 6-31+G(d)//6-31G* guanine -4.32 -3.63 - 1.22 -3.03 -1.62 adenine -3.74 cytosine -2.62 -1.36 -3.30 -2.52 -1.28 thymine -3.17 -2.36 -1.21 uracil -3.02 naphthalene -2.41 -2.00 -2.81 -2.93 -2.01 pyridine -3.45 pyrimidine - 1.82 -2.45 -3.03 -3.52 -2.30 -4.07 benzene Koopmans EAs are estimates of the vertical EAs. 6-3 l+G(d)//6-3 lG* basis set for the vertical calculations of the purine anions and the adiabatic calculation for guanine anion failed to reach self consistency. The 6-31+G(d) guanine adiabatic electron affinities for both HF and MP2 levels are estimated from trends observed in the 6-3 lG* calculations, as the differences in electron affinities between DNA bases do not significantly change with the basis sets used in this study. This is an important point since the trends as well as the differences between individual DNA bases electron affiities are maintained at each level of calculation. This suggests scaling may yield good predictions of DNA base electron affinities even at lower levels of c a l ~ u l a t i o n . ~The ~ ~ known experimental electron affinities for the model compounds and uracil are reported in Table 2. While for uracil only one experimental report is available,8 EA values for the other compounds appear to be quite accurately known (see Table 2). Experimental data are available for the vertical electron affinities of the model compounds chosen here with only naphthalene having both ~ e r t i c a l and ~ ~ -adiabatic ~~ value^.^'-^^ Since we wish to predict adiabatic electron affinities, it is significant to note that the experimental difference between the vertical and adiabatic EAs for naphthalene (0.34 eV) is close to that predicted theoretically regardless of the level of calculation. In fact the differences between the adiabatic and vertical EAs are constant across computational levels. For example, for uracil the differences are 0.63 eV at 6-31G*, 0.65 eV at MP2/6-31G*, 0.58 eV at
1062 J. Phys. Chem., Vol. 99, No. 3, 1995
Sevilla et al.
TABLE 4: Correlation Constants (Itz), Slopes (a), and Intercepts (b) for Fitting of the Theoretical EAs to the Experimental EAs Shown in Firmres 1 and 2a Koopmans vertical 6-31G* D95v 6-31+G(d) HF/6-3lG* MP2/6-31G* HF/6-31+G(d) MP2/6-31+G(d) R2 0.977 0.996 0.506 0.977 0.935 0.950 0.969 U 1.218 1.215 0.708 1.286 1.277 1.022 1.085 b -2.677 -2.134 -1.519 -1.941 -1.447 - 1.473 -0.790 a R2, a, and b were determined from the linear relationship, EA(theory) = u x EA(experiment) -I-b, obtained from the experimental EAs of uracil, naphthalene, pyridine, pyrimidine, and benzene.
TABLE 5: Predicted Vertical and Adiabatic Electron Affinities of the DNA Bases (eV) vertical" adiabaticb guanine -1.23 (-0.7)c adenine -0.74 (-0.3)' cytosine -0.40 0.2 thymine -0.32 0.3 uracil -0.19 0.4
_ I
-12
-10
-06
-08
-04
-02
00
Expenmental Vertical Electron Affimhea (ev)
Figure 1. Fit of the calculated vertical and Koopmans electron afthities with 6-31G* and D95v basis sets to the experimental EAs of uracil, naphthalene, pyridine, pyrimidine, and benzene, assuming the linear relationship EA(theory) = a x EA(experiment) b.
+
O'O I
1
-0.5{ MP2/6-31tC(d) Vertical
6.31+0(d) Kmpmans
B
5
-2.5
-1.2
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
Experimental Vertical Electron Afhities (ev)
Figure 2. Fit of the calculated Koopmans and vertical EAs to the experimental EAs of 5 model compounds. The diffuse functions make for the very poor fit of the Koopmans EAs, but give good fits for vertical HF/and MP2/6-31+G(d) calculations. 6-31+G(d), and 0.61 eV at MP2/6-31+G(d), whereas the corresponding differences for naphthalene are 0.25,0.27,0.22, and 0.26 eV, respectively. This suggests that scaling of adiabatic EAs from vertical EAs is reasonable. 3. Scaling of Electron Affinities. Each of the calculated vertical and Koopmans electron affinities for the model compounds were fit to the experimental EAs assuming a linear relationship between the two, EA(theory) = a x EA(experiment) b. The values a and b and the correlation constant are given for each calculation in Table 4, and the fits are shown in Figures 1 and 2. We note the best fit is found for the Koopmans EAs at the D95v//6-31G* level but that good fits (0.935 < RZ < 0.977) are found for all levels of calculation except for the Koopmans 6-31+G(d) EAs where an exceptionally poor fit is found (R2 = 0.506). In this regard, Staley and StmadZoreported earlier that the diffuse functions made for very poor fits of the Koopmans values. Inclusion of the M E correction for electron correlation on calculated vertical EAs does not improve the fit to experiment at the 6-31G* level but slightly improves the fit at the 6-31+G(d) level. The fact that a very poor fit is found
+
Obtained from the calculated D95v//6-31G* Koopmans EAs in Table 3 fitted to the parameters of Table 4. All predicted vertical EAs obtained from the 6-31G* Koopmans, the HF/or MP2/6-31G*vertical, the HF/or MP2/6-31+G(d) vertical EAs fitted to the parameters in Table 4 (R22 0.935) lie within 0.15 eV of those reported above (see text). Obtained by adding the average difference between adiabatic and vertical EAs (in Table 1) for each compound from the predicted vertical EAs shown in this table. For adenine, only the difference obtained at the HF level was considered. If the overall average difference between adiabatic and vertical EAs for all DNA bases is employed, then the resulting adiabatic EAs are -0.7, -0.2, 0.1, 0.2, and 0.4 eV, respectively. Negative adiabatic values for EAs usually cannot be measured experimentally due to the dissociation of the anion (before nuclear relaxation) to the electron and neutral molecules. We report them as reference energies toward stabilization in aqueous solution which should add ca. 3 eV to each value. for the Koopmans 6-31+G(d) EAs, but a good fit is found for the vertical HF and MP2 EAs using the same basis set clearly indicates that the differences between anion and neutral molecules track much better with experiment than the Koopmans value when the diffuse functions are added. As previously observed,17we note that the deviation of the vertical EAs from the experimental value becomes smaller as the basis set quality increases, Le., a = 1.085 and b = -0.790 for the MP2/6-31+G(d) calculation of the EAs (a = 1.0 and b = 0 for perfect agreement between calculated and experimental values). However, we note that we have performed calculations for cytosine adiabatic EA with an even larger basis set (6-311++G(2df,p)/ /6-3 1G*) at the HF and MP2 levels. The resulting EAs (- 1.21 and -0.85 eV, respectively) are not significantly improved over the 6-31+G(d)//6-31G* EAs (-1.27 and -0.83 eV, respectively). 4. Predicted Gas-Phase Vertical and Adiabatic EAs of DNA Bases. In Table 5 we present our predicted vertical EAs for the DNA bases from our best fit of the Koopmans EAs calculated at the D95v level in the relation EA(experiment) = l/a(EA(theory) - b). Any of the four other fits with RZ 2 0.95 yield EAs with a mean absolute deviation of only 0.1 eV from the values presented in Table 5 (the deviation ranges from 0.05 to 0.16 eV). Since the adiabatic EAs of the DNA bases are found to differ from the vertical values by a constant, we use this additive constant to estimate the adiabatic values for the DNA bases from the predicted vertical EAs. With this correction we find that thymine and cytosine are suggested to have positive adiabatic EAs of 0.3 and 0.2 eV, respectively. The adiabatic EAs of the purines remain negative, i.e., unstable to the dissociation into the electron and the neutral purines. The substantial body of experimental data used suggests only a small uncertainty in the vertical DNA base electron affinities (ca. 0.2
MO Calculations of DNA Radical Ions eV) with a somewhat larger uncertainty for the adiabatic values. The results in Table 5 clearly point to negative vertical EAs for all DNA bases. They also suggest positive adiabatic EAs for thymine, uracil, and cytosine and consequently predict stable anionic states in the gas phase for the pyrimidines but not for the purines. 5. DNA Base Anions in Aqueous Phase and DNA. In aqueous solution, the DNA base radical anions are further stabilized by ca. 3 eV.15 As a consequence all anions are stable toward dissociation (to neutral molecules and e(aq)-in this case). Solvation in H20 also allows for protonation of basic sites on the anion radicals which alters the relative stabilities of these species in solution." For example, cytosine and adenine anion radicals have sites which are likely to be fully protonated at pH = 7. The situation in dsDNA is somewhat more complex as proton transfer from base pairs must be considered. These processes have been studied in our previous
Acknowledgment. We thank the Office of Health and Environmental Research of the Department of Energy (Grant DEFG028ER60455) and the National Cancer Institute of the National Institute of Health (Grant ROlCA45424) for support of this work. We thank the DOE National Energy Research Supercomputer Center at Lawrence Livermore National Laboratory and the DOE Supercomputer Center at Florida State University for generous grants of computer time. We thank H. Bemhard Schlegel of Wayne State University for helpful discussions. Supplementary Material Available: Total energies of the DNA bases, uracil, and the model compounds considered in this work at various HF and MP2 levels (139 values) and x , y , z coordinates optimized at the 6-31G* basis set for 22 compounds (12 pages). Ordering information is given on any current masthead page. References and Notes (1) Orlov, V. M.; Smirnov, A. N.; Varshavsky, Y. M. Tetrahedron Lett. 1976, 48, 4377. (2) Hush, N. S.; Cheung, A. S. Chem. Phys. Lett. 1975, 34, 11. (3) Lias, S. G.; Bartmess, J. E.; Liebman, J. F.; Holmes, J. L.; Levin, R. D.; Mallard, W. G. J. Phys. Chem. Re& Data 1988, 17, Suppl.l. (4) 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. (5) Colson, A. 0.; Besler, B.; Close, D. M.; Sevilla, M. D. J. Phys. Chem. 1992, 96, 661. (6) Colson, A. 0.;Besler, B.; Sevilla, M. D. J. Phys. Chem. 1992, 96, 9787. (7) Younkin, J. M.; Smith, L. J.; Compton, R. N. Theor. Chim. Acta 1976, 41, 157.
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