J. Phys. Chem. B 2007, 111, 9057-9061
9057
Electronic Structure of xDNA Miguel Fuentes-Cabrera,* Xiongce Zhao, P. R. C. Kent, and Bobby G. Sumpter Center for Nanophase Materials Sciences and Computer Science and Mathematics DiVision, Oak Ridge National Laboratory, P.O. Box 2008, Oak Ridge, Tennessee 37831-6494 ReceiVed: April 13, 2007; In Final Form: May 31, 2007
xDNA is an artificial duplex made of natural and benzo-homologated bases. The latter can be seen as a fusion between benzene and a natural base. We have used two different ab initio techniques, one based on B3LYP and a Gaussian expansion of the wave functions, and the other on GGA and plane-waves, to investigate the electronic properties of an xDNA duplex and a natural one with an analogous sequence. The calculations were performed in dry conditions, i.e., H atoms were used to neutralize the charge. It is found that the HOMOLUMO gap of xDNA is about 0.5 eV smaller than that of B-DNA, independent of the technique used. The π-π* gap of xDNA is 1.3 or 1.0 eV smaller than that of B-DNA, depending on whether one uses B3LYP/ 6-31G or GGA/plane-waves, respectively. An analysis of how saturation changes the electronic properties of the nucleotide pairs that make up these duplexes suggests that different saturation schemes significantly affect the HOMO-LUMO gap value of xDNA and B-DNA. The same is not true for the π-π* gap. That xDNA has a smaller π-π* gap than B-DNA suggests that xDNA could be a plausible candidate for molecular-wire applications.
I. Introduction The promise of using DNA as a molecular-wire in nanotechnological applications has fueled intensive research on its conductivity properties.1 Unfortunately, it is not yet clear whether DNA conducts and this has led to the investigation of alternative DNA-like molecules for which the conductivity is less controversial.2 In seeking other alternatives, we recently focused our attention on the field of Synthetic Biology. What attracted us is the fact that under the umbrella of this field, all the components of DNA, i.e., the sugar, the phosphate, and the bases, have been modified.3 Such modifications fulfill various purposes, e.g., from enabling the development of clinical assays for the diagnostic of HIV and hepatitis C viruses3 to probing the limit of the size in the DNA backbone4-6 and the DNA replication process.7 But we also wonder whether any of these modifications, particularly those concerning the geometrical extensions of the DNA bases by fusing them to aromatic rings, can lead to artificial DNAs with properties suitable for molecular-wire applications. Aromatic homologated bases created by fusing a natural base to an aromatic molecule, i.e., benzene and napthalene, have been used to synthesize a new type of artificial DNA known as sizeexpanded DNAs. There are three types of size-expanded DNAs. xDNA4 and yDNA5 are made of benzo-homologated bases (referred to here as x- and y-bases, respectively). yyDNA6 is made up of naptho-homologated bases (yy-bases). Our interest on size-expanded duplexes was motivated by the following. First, experimental studies have shown that these duplexes can self-assemble, which is a necessary requisite for creating DNAlike nanostructures.8 Second, size-expanded DNAs have higher melting points than natural DNAs, which is a consequence of the former having stronger π-π stacking interactions than the latter.4e,f,9,10 Since stronger π-π stacking interactions provide more efficient band conduction in G4 wires,11 size-expanded * Address correspondence to this author. E-mail:
[email protected].
DNAs should have more efficient band conduction than DNA. Third, benzo-homologated bases having smaller HOMOLUMO gaps than their natural analogues12,13 suggests that xDNAs and yDNAs will also have smaller HOMO-LUMO gaps than natural DNA; if this is true, it could also contribute to making these artificial duplexes better conductors than DNA. Here we wish to probe whether size-expanded DNAs have smaller HOMO-LUMO gaps than DNAs. For this purpose, we investigate the electronic structure of an xDNA duplex and its natural counterpart. II. Description of the Duplexes and Methodology xDNA is made of natural and x-bases. The former are Adenine, A, Cytosine, C, Guanine, G, and Thymine, T. The latter are benzo-Adenine, xA, benzo-Cytosine, xC, benzoGuanine, xG, and benzo-Thymine, xT. In an xDNA duplex, each base pair is made up of an x- and a complementary natural base. The complementarity is similar to that among natural bases. For example, whereas in DNA A pairs with T, in xDNA xA pairs with T, xT with A, etc. Parts a and b of Figure 1 show the base pairs T-A and T-xA, respectively. Due to the extra benzene ring, the x-bases are about 2.4 Å wider than the natural ones. The xDNA studied in this work was synthesized and analyzed with NMR by Kool and co-workers.4b The duplex contains 10 T-xA base pairs and its structure and sequence are shown in Figure 1, parts d and f, respectively. The natural duplex, referred to from now on as B-DNA, contains 10 T-A base pairs arranged in a sequence analogous to that of xDNA. The structure and sequence of B-DNA are shown in Figure 1, parts c and e, respectively. The natural duplex was generated with a 10 ns molecular dynamics simulations (MD) as follows. A duplex was built by using the package nucgen that is contained within the AMBER 8.0 suite of programs.14 The duplex was solvated with a TIP3P15 pre-equilibrated water box with at least 12 Å of water buffer over the three-dimensional periodic boundaries. Na + ions were added to neutralize the charge of the system. The DNA
10.1021/jp0729056 CCC: $37.00 © 2007 American Chemical Society Published on Web 07/26/2007
9058 J. Phys. Chem. B, Vol. 111, No. 30, 2007
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Figure 2. Energy level diagram of (a) B-DNA and (b) xDNA. The energies are given relative to the LUMO. The HL and π-π* gaps are denoted by arrows.
Figure 1. The B-DNA and xDNA duplexes studied in this work: (a) T-A Watson-Crick base pair that makes up B-DNA; (b) T-xA (proposed structure) base pair that makes up xDNA; (c) side (up) and top (down) view of B-DNA; (d) side (up) and top (down) view of xDNA; and (e and f) the sequences of B-DNA and xDNA, respectively. The top view of B-DNA and xDNA reveals the larger diameter of xDNA. Color code: oxygen, red; carbon, black; nitrogen, blue; hydrogen, maroon.
TABLE 1: Rise (in Å) and Twist Angle (in deg) Per Base Pair Step for Consecutive Base Pairs in B-DNA and xDNA (in parentheses) A(xA)-T T-A(xA) A(xA)-T A(xA)-T T-A(xA) A(xA)-T T-A(xA) T-A(xA) A(xA)-T T-A(xA)
rise
twist
0.0 (0.0) 3.21 (2.92) 3.51 (4.07) 3.07 (3.01) 3.10 (2.69) 3.65 (2.83) 3.23 (2.72) 3.45 (3.06) 3.37 (4.29) 3.28 (3.19)
0.0 (0.0) 31.76 (26.96) 36.29 (36.57) 31.30 (33.48) 26.67 (22.56) 46.45 (38.17) 33.70 (23.86) 39.98 (34.84) 29.00 (36.11) 32.40 (27.39)
molecule and the ions were modeled by the AMBER force field 1999 version.14 MD simulations were performed in the isothermal-isobaric ensemble at 1 bar16 and 300 K,17 using the NAMD18 package. A typical simulation includes 10 000 steps of energy minimization, heating from 0 to 300 K in 3 ps, solvent equilibration for 100 ps, and 10 ns production with a time step of 2 fs. Additional 2 ns runs, with a time step of 1 fs, were carried out for collecting DNA snapshots. An average DNA structure was subsequently obtained from the last 100 snapshots. The energetic minimization of this structure led to the configuration with the lowest potential energy, which was then used as the B-DNA structure for the electronic structure calculations. More details of the MD methodology are given in the Supporting Information. Table 1 contains the structural parameters known as rise and twist for B-DNA and xDNA (in parentheses) as calculated with the software X3DNA.19 Because the x-bases are wider than the natural bases, per base step the rise and twist of xDNA is, in general, smaller than that of B-DNA. This is better appreciated by reporting average values. The average rise for xDNA is 3.2 Å versus 3.3 Å for B-DNA. The average twist for xDNA is 31° versus 34.2° for B-DNA. (The Supporting Information contains the coordinates of xDNA and B-DNA and a complete list of the structural parameters per base step.) To study the electronic properties of these duplexes we made the following approximations. xDNA and B-DNA were studied in dry conditions, i.e., H atoms instead of solvent were used to
saturate the backbone. Each H atom was placed 1.48 Å from the phosphorus atom and equidistant to the oxygen atoms commonly denoted as O1P and O2P. In total, xDNA has 716 atoms, B-DNA has 656. The electronic properties were investigated with Density Functional Theory (DFT), which has been shown to give reasonably good qualitative results for the electronic structure of DNA duplexes.20-22 We calculated the electronic properties using two different techniques. In one, we approximated the exchange-correlation potential with the hybrid form B3LYP23 and expanded the electronic wave functions in the 6-31G Gaussian basis set. Larger basis sets, e.g., 6-31G**, are commonly used to investigate the DNA bases12 but the large size of the duplexes studied here imposes some computational restrictions.24 The calculations were performed with the NWChem25 suite of programs. In the second technique, we employed the plane-wave projector augmented wave technique as implemented in VASP.26 The exchange-correlation potential was approximated by the generalized gradient approximation (GGA)27 and the wave functions were expanded in plane-waves with a 400 eV energy cutoff. The duplexes were placed in large supercells, i.e., 44 × 41 × 49 and 39 × 52 × 39 Å3 for xDNA and B-DNA, respectively. The size of the cells ensured that consecutive molecules were separated by a vacuum of at least 16 Å. We sampled only the Γ point of the Brillouin zone, which is appropriate for an isolated molecule. In what follows we refer to these techniques as B3LYP/6-31G and GGA/plane-waves. III. Results The energy level diagram of B-DNA and xDNA as calculated with B3LYP/6-31G is shown in Figure 2. In B-DNA, the highest occupied molecular orbital (HOMO) resides on two A bases; this state is denoted in Figure 2a as πA. In xDNA, the HOMO resides on two xA bases, and is denoted in Figure 2b as πxA. In both duplexes, the lowest unoccupied molecular orbital (LUMO) is placed on the phosphate group and on the H atom that was used to saturate it. The 17 states immediately above the LUMO also reside on the phosphate groups. These states plus the LUMO form a set of 18 nearly degenerate molecular levels, denoted as H+/PO4-, that are spread over 0.9 and 0.2 eV in B-DNA and xDNA, respectively. Moving higher in energy one finds the π* state, which is placed on two T bases near the end of B-DNA (π*T in Figure 2a) and in one xA base at the end of xDNA (π*xA in Figure 2b). The π*xA state is extended over the whole base including the benzene moiety. (It should be noticed that in this analysis we are considering one snapshot of each duplex only, and that it remains to be seen how the positioning within each duplex of the π, LUMO, and π* states changes with thermal fluctuations.22b) In Figure 2, HL stands for the difference in energy between LUMO and HOMO, whereas π-π* stands for the difference in energy between the
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TABLE 2: HOMO-LUMO (HL) and π-π* Gaps (in eV) of B-DNA and xDNA Duplexes as Computed with B3LYP/ 6-31G (GGA/plane-waves)a B-DNA xDNA ∆HL ∆(π-π*)
HL
π-π*
2.18 (1.61) 1.68 (1.17) 0.50 (0.44) 1.28 (0.99)
4.34 (2.73) 3.06 (1.74)
a
∆HL is defined as the difference between the HL gap of B-DNA and xDNA. ∆(π-π*) is defined as the difference between the π-π* gap of B-DNA and xDNA.
π* and π states. Using GGA/plane-waves we obtain a similar energy level diagram. Table 2 contains the values for the HL and π-π* gaps of B-DNA and xDNA. The B3LYP/6-31G gap is larger than the GGA/plane-waves one, which is expected since B3LYP tends to overestimate the gap and GGA underestimates it. It is not possible to compare the HL and π-π* gaps obtained here to those obtained in previous theoretical studies, because the duplexes and the methodology are different. The variables ∆HL and ∆(π-π*) in Table 2 give the difference between the HL and π-π* gaps, respectively, of B-DNA and xDNA. B3LYP/ 6-31G and GGA/plane-waves find that the HL gap of xDNA is approximately 0.5 smaller than that of B-DNA. With B3LYP/ 6-31G, the π-π* gap of xDNA is 1.3 eV smaller than that of B-DNA; with GGA/plane-waves, this difference is 1.0 eV. That two different techniques are in qualitative agreement give confidence in the result that both the HL and π-π* gaps of xDNA are smaller than those of B-DNA. At this point we wish to discuss the presence of H+/PO4within the π-π* gap of B-DNA and xDNA. A literature review reveals that these states sometimes do appear within the gap, and sometimes do not. For example, Lewis et al.22b investigated an aperiodic polyA‚polyT duplex that was saturated with H equidistant to O1P and O2P, and found H+/PO4- within the π-π* gap. On the other hand, de Pablo et al.20 did not find these states within the gap of an infinite polyG‚polyC that was also investigated in dry conditions. Instead, the HOMO and LUMO of this duplex is made of πG and π*C states. These results prompted us to ask whether in calculations of duplexes in dry conditions it is possible to move the phosphate states in and out of the π-π* gap by changing the saturation procedure. This is an important question, as the presence or absence of phosphate states within the π-π* gap affects the HL gap of the duplex, which means it also affects the comparisons we have drawn between the electronic properties of B-DNA and xDNA. Unfortunately, checking how saturation changes the energy of the phosphate states is computationally expensive, for it involves calculating the electronic properties of the duplex for different saturation schemes. However, insights can be obtained by investigating the electronic properties of nucleotide pairs. A natural nucleotide is made of a natural DNA base, a sugar, and a phosphate group. Similarly, a benzene-homologated nucleotide contains an x-base, the sugar, and phosphate. The sugar and the x-base in the xA- and xG-nucleotides are connected by a N-C bond, as in the natural nucleotides; however, in the xC- and xT-nucleotides, sugar and base are connected by a C-C bond. A nucleotide pair is defined here as a Watson-Crick base pair (or the corresponding benzenehomologated counterpart) plus the sugar and phosphate motifs of each base. The nucleotide pairs investigated contain a T-A and T-xA base pair, and they were extracted from one end of the B-DNA and xDNA duplexes, respectively. (For simplicity, from now on we refer to these nucleotides as T-A and T-xA.)
Figure 3. T-A nucleotide pair with two different saturation schemes: (a) H is equidistant to O1P and O2P and (b) H is 1.0 Å from O2P. Color code: oxygen, red; carbon, black; nitrogen, blue; hydrogen, maroon; phosphorus, gray.
Figure 4. T-xA nucleotide pair with two different saturation schemes: (a) H is equidistant to O1P and O2P and (b) H is 1.0 Å from O2P.
Figure 5. Energy level diagram of (a) the T-A nucleotide pair and (b) the T-xA nucleotide pair, when H is equidistant to O1P and O2P.
Figures 3 and 4 show these nucleotide pairs with two different saturation schemes. In one scheme the H atom is equidistant to the oxygen atoms O1P and O2P (Figures 3a and 4a). In the other, the H atom is bonded to O2P with a bond length of about 1.0 Å (Figures 3b and 4b). The electronic properties of these four nucleotide pairs were investigated with B3LYP/6-31G. The energy level diagram of T-A and T-xA with H equidistant to O1P and O2P is shown in Figure 5. The nucleotide pairs have the same energy diagram as the corresponding duplexes,
9060 J. Phys. Chem. B, Vol. 111, No. 30, 2007
Figure 6. Energy level diagram of (a) the T-A nucleotide pair and (b) the T-xA nucleotide pair, when H is bonded to O2P.
Figure 7. Frontier molecular orbitals of the T-A nucleotide pair for different saturation schemes: (a and b) HOMO and LUMO when H is equidistant to O1P and O2P, respectively; and (c and d) HOMO and LUMO when H is 1.0 Å from O2P.
TABLE 3: π-π* Gap of T-A and T-xA Nucleotide Pairs As Computed with B3LYP/6-31G when H is Equidistant to O1P and O2Pa π-π* T-A T-xA
4.71 (4.75b) 3.93 (3.93)
a The π-π* gaps when H is bonded to O2P are given in parentheses. The difference between the π-π* gap of T-A with H equidistant to O1P and O2P,and H bonded to O2P is just 0.04 eV, which is probably within the precision limit.
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Figure 8. Frontier molecular orbitals of the T-xA nucleotide-pair for different saturation schemes: (a and b) HOMO and LUMO when H is equidistant to O1P and O2P, respectively; and (c and d) HOMO and LUMO when H is 1.0 Å from O2P.
saturation should not affect the π-π* gap of the duplexes since it does not affect the π-π* gap of the nucleotide pairs, and so the statement that xDNA has a smaller π-π* gap than B-DNA is valid. Finally, it is instructive to compare the π-π* gap of the duplexes to those of the corresponding nucleotide pairs. Then, one notices that in going from a T-A nucleotide pair to a B-DNA duplex the gap decreases by 0.37 eV, whereas in going from T-xA to xDNA the gap is reduced by 0.87 eV. In other words, in going from nucleotide pairs to duplexes the π-π* gap is reduced by 0.5 eV more when making an xDNA duplex than when making a B-DNA duplex. This could be an indication of much stronger stacking interactions between consecutive T-xA base pairs than between consecutive T-A base pairs. This result also brings up the question of how much the π-π* gap could be reduced if all the xA bases were occupying the same strand of xDNA, for in such a duplex one would expect to find even stronger stacking interactions than in the duplex we have studied here. It is interesting to notice that size-expanded DNAs with all the benzo-bases or naptho-bases occupying the same strand do indeed exist,6,28 and it will be interesting to examine the electronic properties of such duplexes.
b
including the presence of H+/PO4- states within the π-π* gap. However, when H is bonded to O2P the energy diagram changes and the phosphate states are no longer within the π-π* gap, as is shown in Figure 6. Table 3 contains the π-π* gaps of T-A and T-xA. As expected, the value of this gap is independent of the saturation scheme used. The effect that saturation has on the electronic properties on these nucleotide pairs is clearly seen in Figures 7 and 8, which show the frontier molecular orbitals of T-A and T-xA for the two saturation schemes. When H is equidistant to the O atoms the LUMO resides on the phosphate, but when H is bonded to O2P the LUMO resides on a base. The placement of the HOMO, on the other hand, is independent of the saturation used. It is plausible to assume that different saturation schemes affect the electronic properties of B-DNA and xDNA in a similar manner. For this reason, it is wiser to state that in calculations performed in dry conditions, the HL gap of xDNA is smaller than that of B-DNA as far as these duplexes are saturated in the same way. Interestingly, in calculations of natural duplexes in wet conditions counterions/phosphate states were found within the π-π* gap.1,21 This implies that caution should be exercised if one were to compare the electronic properties of xDNA and B-DNA in wet conditions, or the electronic properties of any two other duplexes in the same conditions. On the other hand,
IV. Conclusions Two different ab initio techniques, one based on B3LYP and a Gaussian expansion of the wave functions and the other on GGA and plane-waves, were used to investigate the electronic properties of an xDNA duplex and a B-DNA one with a counterpart sequence. The calculations were done in dry conditions, i.e., H atoms instead of solvent were used to saturate the duplexes. It was found that both techniques qualitatively agree in that the HOMO-LUMO and π-π* gaps of xDNA are smaller than those of B-DNA. After investigating how different saturation affects the electronic properties of the nucleotide pairs that make up xDNA and B-DNA, it was concluded that the HOMO-LUMO gap of these duplexes is likely to change significantly with the saturation scheme. As a consequence, it is advisable to only compare the π-π* gap of these duplexes, for this gap is independent of the saturation used. With B3LYP/6-31G, the π-π* of xDNA is 1.3 eV smaller than that of B-DNA, 1.0 eV smaller with GGA/plane-waves. These results, when added to the experimental and theoretical evidence that xDNA has stronger π-π stacking interactions than B-DNA, suggest that xDNA might be a plausible candidate for molecularwire applications. Of course, while we have shown that the electronic properties are favorable for such applications, this requires confirmation with calculations and/or measurements of the conductivity properties. We hope that our results will encourage such calculations and measurements.
Electronic Structure of xDNA Acknowledgment. The authors wish to thank Professor Eric T. Kool for insightful discussions and for providing the coordinates of xDNA. We also wish to thank Professor Javier Luque for inciting us to investigate how saturation affects the electronic properties. Work at Oak Ridge National Laboratory (ORNL) was supported by the Center for Nanophase Materials Sciences, sponsored by the Division of Scientific User Facilities, U.S. Department of Energy (USDOE) and used resources of the National Center for Computational Sciences, ORNL, supported by the Office of Science, USDOE. This research also used resources of the National Energy Research Scientific Computing Center, which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DEAC02-05CH11231. Supporting Information Available: Atomic coordinates for xDNA and B-DNA, details of the MD simulation, and complete refs 14 and 25a. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Endres, R. G.; Cox, D. L.; Singh, R. R. P. ReV. Mod. Phys. 2004, 76, 195-214. (2) (a) Tanaka, K.; Clever, G. H.; Takezawa, Y.; Yamada, Y.; Kaul, C.; Shionoya, M.; Carell, T. Nat. Nanotechnol. 2006, 1, 190-194. (b) Tanaka, K.; Tengeiji, A.; Kato, T.; Toyama, N.; Shionoya, M. Science 2003, 299, 1212-1213. (c) Clever, G. H.; Carell, T. Angew. Chem., Int. Ed. 2007, 46, 250-253. (d) Zhang, H. Y.; Calzolari, A.; Di Felice, R. J. Phys. Chem. B 2005, 109, 15345-15348. (e) Rakitin, A.; Aich, P.; Papadopoulus, C.; Kobzar, Yu.; Vedeneev, A. S.; Lee, J. S.; Xu, J. M. Phys. ReV. Lett. 2001, 86, 3670-3673. (f) Alexandre, S. S.; Soler, J. M.; Seijo, L.; Zamora, F. Phys. ReV. B 2006, 73, 205112-1, 205112-5. (3) Benner, S. A.; Sismour, A. M. Nat. ReV. 2005, 6, 533-543. (4) (a) Liu, H.; Gao, J.; Lynch, S. R.; Saito, Y. D.; Maynard, L.; Kool E. T. Science 2003, 302 868-871. (b) Liu, H.; Gao, J.; Lynch, S. R.; Kool, E. T. J. Am. Chem. Soc. 2004, 126, 6900-6905. (c) Liu, H.; Gao, J.; Kool, E. T. J. Am. Chem. Soc. 2005, 127, 1396-1402. (d) Gao, J.; Liu, H.; Kool, E. T. Angew. Chem., Int. Ed. 2005, 44, 3118-3122. (e) Liu, H.; Gao, J.; Kool, E. T. J. Org. Chem. 2005, 70, 639-647. (f) Gao, J.; Liu, H.; Kool, E. T. J. Am. Chem. Soc. 2004, 126, 11826-11831. (5) (a) Lu, H.; He, K.; Kool, E. T. Angew. Chem., Int. Ed. 2004, 43, 5834-5836. (b) Lee, A. H. F.; Kool, E. T. J. Org. Chem. 2005, 70, 132140. (c) Lee, A. H. F.; Kool, E. T. J. Am. Chem. Soc. 2005, 127, 33323338. (6) Lee, A. H. F.; Kool, E. T. J. Am. Chem. Soc. 2006, 128, 92199230. (7) Kim, T. W.; Delaney, J. C.; Essigmann, J. M.; Kool, E. T. Proc. Natl. Acad. Sci. 2005, 102, 15803-15808.
J. Phys. Chem. B, Vol. 111, No. 30, 2007 9061 (8) Rothemund, P. W. K. Nature 2006, 440, 297-302. (9) Huertas, O.; Blas, J. R.; Soteras, I.; Orozco, M.; Luque, F. J. J. Phys. Chem. A 2006, 110, 510-518. (10) McConnell, T. L.; Wetmore, S. D. J. Phys. Chem. B 2007, 111, 2999-3009. (11) Di Felice, R.; Calzolari, A.; Garbesi, A.; Alexandre, S. S.; Soler, J. M. J. Phys. Chem. B 2005, 109, 22301-22307. (12) (a) Fuentes-Cabrera, M.; Sumpter, B. G.; Wells, J. C. J. Phys. Chem. B 2005, 109, 21135-21139. (b) Huertas, O.; Poater, J.; Fuentes-Cabrera, M; Orozco, M.; Sola, M.; Luque, F. J. J. Phys. Chem. A 2006, 110, 1224912258. (13) Fuentes-Cabrera, M.; Sumpter, B. G.; Lipkowski, P.; Wells, J. C. J. Phys. Chem. B 2006, 110, 6379-6384. (14) Case, D. A.; et al. AMBER 8.0; University of California: San Francisco, CA, 2004. (15) Jorgensen, W. L. J. Am. Chem. Soc. 1981, 103, 335. (16) Martyna, G. J.; Tobias, D. J.; Klein, M. L. J. Chem. Phys. 1994, 101, 4177-4189. (17) Bru¨nger, A. T. X-PLOR, Version 3.1: A system for X-ray crystallography and NMR; Yale University: New Haven, CT, 1992. (18) Kale´, L.; Skeel, R.; Bhandarkar, M.; Brunner, R.; Grusoy, A.; Krawetz, N.; Phillips, J.; Shinozaki, A.; Varadarajan, K.; Schulten, K. J. Comp. Phys. 1999, 151, 283-312. (19) Lu, X.-J.; Olson W. K. Nucleic Acids. Res. 2003, 31, 5108-5121. (20) de Pablo, P.; Moreno-Herrero, F.; Colchero, J.; Go´mez-Herrero, J.; Herrero, P.; Baro, A. M.; Ordejo´n, P.; Soler, J. M.; Artacho, E. Phys. ReV. Lett. 2000, 85, 4992-4995. (21) Gervasio, F. L.; Carloni, P.; Parrinello, M. Phys. ReV. Lett. 2002, 89, 108102-1, 108102-4. (22) (a) Wang, H.; Lewis, J. P.; Sankey, O. F. Phys. ReV. Lett 2004, 93, 016401-1, 016401-4. (b) Lewis, J. P.; Cheatham, T. E.; Starikov, E. B.; Wang, H.; Sankey, O. F. J. Phys. Chem. B 2003, 107, 2581-2587. (23) (a) Becke, A. D. J. Chem. Phys. 1993, 98, 5648-5652. (b) Lee, C.; W. Yang, W.; Parr, R. G. Phys. ReV. B 1988, 37, 785. (24) For example, the 6-31G basis set led to 4612 and 4212 basis functions for xDNA and B-DNA, respectively, and adding just one set of polarization functions, e.g., 6-31G*, gives 7276 and 6232 basis functions. (25) (a) Apra`, E.; et al. NWChem, A Computational Chemistry Package for Parallel Computers, Version 4.7; Pacific Northwest National Laboratory: Richland, WA, 2005. (b) Kendall, R. A.; Apra`, E.; Bernholdt, D. E.; Bylaska, E. J.; Dupuis, M.; Fann, G. I.; Harrison, R. J.; Ju, J.; Nichols, J. A.; Nieplocha, J.; Straatsma, T. P.; Windus, T. L.; Wong, A. T. Comput. Phys. Commun. 2000, 128, 260-283. (26) (a) Kresse, G.; Hafner, J. Phys. ReV. B 1993, 37, 558. (b) Kresse G.; Furthmu¨ller, J. Comput. Mater. Sci. 1996, 6, 15. (c) Kresse, G.; Furthmu¨ller, J. Phys. ReV. B 54, 54, 11169. (d) Kresse, G.; Joubert D. Phys. ReV. B 1999, 59, 1758. (27) Perdew, J. P.; Chevary, J. A.; Vosko, S. H.; Jackson, K. A.; Pederson, M. R.; Singh, D. J.; Fiolhais, C. Phys. ReV. B 1992, 46, 6671. (28) Gao, J.; Liu, H.; Kool, E. T. Angew. Chem., Int. Ed. 2005, 44, 2-5.
