Spectroscopic probe on N–H⋯N, N–H⋯O and controversial C–H⋯O contact in A–T base pair: A DFT study

Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 120 (2014) 542–547

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Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy journal homepage: www.elsevier.com/locate/saa

Spectroscopic probe on N–H  N, N–H  O and controversial C–H  O contact in A–T base pair: A DFT study Venkatesan Srinivasadesikan a, Prabhat K. Sahu b, Shyi-Long Lee a,⇑ a b

Department of Chemistry and Biochemistry, National Chung Cheng University, Chia-Yi, Taiwan Department of Chemistry, National Institute of Science and Technology, Berhampur 761008, India

h i g h l i g h t s

g r a p h i c a l a b s t r a c t

 Experimental spectroscopic results

serve as a benchmark for computational study.  Computational results help in interpreting and guiding experiments.  C–H  O contact in A–T base pair as a hydrogen bond?  IR and NMR spectroscopic results for A–T base pair using DFT functional.

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Article history: Received 21 May 2013 Received in revised form 1 November 2013 Accepted 29 November 2013 Available online 8 December 2013 Keywords: A–T base pair Spectroscopy Hydrogen bond Van der Waals interaction C–H  O interaction DFT

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a b s t r a c t DNA base pair A–T has been investigated by IR and NMR spectroscopy using DFT methods. The results have been analyzed in terms of infrared vibrational frequencies and 1H NMR chemical shifts. Different types of interactions N–H  N, N–H  O and C–H  O types have been investigated in DNA base pairs. Although, previous reports argued about the third C–H  O type interaction in A–T base pair, such typical interaction has been analyzed thoroughly by IR and NMR spectroscopy using DFT methods. Our results show that the CH  O interaction in the A–T base pair is a weak interaction compared to normal hydrogen bond interactions. Ó 2013 Elsevier B.V. All rights reserved.

Introduction Intermolecular interactions play a vital role in bio-macromolecules and are significant for the conformation and stability [1,2]. Hydrogen bonding and van der Waals interactions are the two most important intermolecular interactions and play a key role in DNA, RNA, protein etc. Number of experimental [3] and theoret⇑ Corresponding author. Address: Department of Chemistry and Biochemistry, National Chung Cheng University, Chia-Yi 621, Taiwan. Tel.: +886 5 2428305; fax: +886 5 2721040. E-mail address: [email protected] (S.-L. Lee). 1386-1425/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.saa.2013.11.110

ical studies on DNA base pair with the different view of analysis on interactions in hydrogen-bonds [4,5], stacking [5], water interaction [6] and proton transfer [7] have been reported. Recent progress of computational modeling has shown that the sequence of DNA virtually can be framed and converted into real system through DNA synthesizer. A large number of computational studies are proficient to characterize the hydrogen bonding and van der Waals interactions between nucleic acids [8]. Spectroscopy is a tool to investigate the individuals and complexes of the components. In general, IR [9,10] and NMR [11,12] are the two major spectral tools to elucidate the polyatomic and

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bio-molecules in order to provide insights into fundamental interactions of clusters. Number of theoretical reports on the spectroscopic studies has been reported for the DNA base pairs. Bickelhaupt et al. [13] investigated the hydrogen bonds strength between RNA and DNA using theoretical spectroscopy which revealed that the RNA A:U base pair is strongly bound than the A:T base pair. Such results have also been experimentally proved as shown that the N1  N3 hydrogen bonds are stronger in A:U base pair than the A–T base pair using NMR coupling constant values by Vakonakis and LiWang [14] Vries and Hobza [15] reviewed and investigated the reports on bio-molecular building blocks using gas-phase spectroscopy. The major motivation of such gasphase spectroscopy analysis is helpful to distinguish between intrinsic molecular properties and fundamental molecular interactions. The experimental spectroscopy results serve as a benchmark for computational algorithms and force fields, while computational results help in interpreting and guiding experiments. Recently, scientists [16,17] have plunged into the study of interactions of C–H  O in A–T base pair in question [18–24]. Bickelhaupt et al. [13] reported that they did not find any donor – acceptor orbital interaction corresponding to C–H  O bond in A–T base pair and is not a hydrogen bond. Most recently Leszczynski et al. [16] and Zhou and Qiu [17] reported that the C–H  O contact on A–T base pair can be considered as van der Waals interaction rather than a hydrogen-bonding interaction. Leszczynski et al. [16] have concluded it as van der Waals interaction using the electron density (q) and laplacian parameter (r2qr) obtained from ‘‘quantum theory of atoms in molecules’’ (QTAIM) analysis for the C–H  O interaction. Zhao et al. [17] conducted the study of C–H  O contact in A–T base pair using the AIM and NBO analysis and suggested a blue shifted van der Waals contact rather than red shifted hydrogen-bonding for N–H  N and N–H  O type in A–T base pair. Despite the recent progress in computational chemistry [25–27], recently developed DFT level such as hybrid-GGA, hyper-GGA and dispersion corrected DFT level have not yet been applied for the spectroscopic investigation. Particularly the investigation on hypothetical C–H  O interaction in A–T base pair through the IR and NMR spectroscopy using DFT level has not been reported. Therefore, we have investigated the C–H  O interaction in A–T base pair using IR vibrational frequency and NMR chemical shifts using different DFT levels.

1.911 (1.907) 1.896 (1.899) 1.934 (1.936) 1.93 (1.932) 1.927 (1.924) 61

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6 1.818 (1.859) 30) 1.788 (1.8 ) 1.81 (1.859 ) 63 .8 (1 2 1.83 25) 1.869 (1.9

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Fig. 1. Optimized structure of Watson–Crick adenine–thymine with hydrogen bonding lengths at different DFT levels in gas phase and solvent phase (B3LYPblack; M06-Red; M062X-Pink; B97D-Blue; wB97XD-Green). Solvent phase values are in brackets. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

and solvent phase. The heavy atom distances have also been shown in Table 1. The geometrical parameters at M06-2X level in gas phase show the close agreement with experimental findings [39,40]. Though, the solvent phase calculation using CPCM model has not shown well agreement with the experimental findings. The computed hydrogen bond lengths have revealed the discrepancy with experimental values. The divergence arises from the molecular environment of water, sugar hydroxyl groups, and counter ions of the base pairs in the crystals studied experimentally were missing in the current investigation for the model study. The stretching vibrational frequencies of A–T base pair and its monomers are shown in Figs. 2–6 and their values are listed in Tables S3–S9 (See Supporting Information). The NMR chemical shifts of A–T base pair and its monomers are shown in Figs. 7-9 and their values are listed in Tables S10–S15 (see Supporting Information). A question has been raised [18–24,41] for the interaction of C2–H2  O2 contact as a hydrogen bond? in A–T base pair. Here, we have clarified this question by using the IR and NMR theoretical spectroscopic results calculated by DFT levels in the subsequent sections.

Computational details

IR frequency for monomers and base pair

All computations have been performed using Gaussian 09 program [28]. The hybrid-GGA B3LYP [29–33], hyper-GGA M06 [34] and M062X, [34] dispersion corrected B97D [35] and wB97XD [36] levels at 6-31+G* are adopted to compute geometries, IR frequencies and NMR chemical shifts of the A–T base pair and monomers, in which the sugar and phosphate groups are modeled by hydrogen [37] (Fig. 1). Aforementioned DFT levels are taken into account and the performance of these DFT levels has been evaluated in our study. The shielding tensors are evaluated at all computational levels using gauge-independent atomic orbital (GIAO) on DFT-optimized geometries. The NMR chemical shift of methyl group in thymine monomer and base pair are utilized to calculate the average value and is listed in Tables S11 and S15. The continuum model CPCM-UAKS (polarisable conductor calculation model along with United Atom Topological Model) [38] using DMSO as a solvent that accounts for the overall polarizability of the solvent has been employed (e = 46.826).

Stepanian et al. [42] and later on Nowak et al. [43,44] studied the infrared spectra of adenine isolated in low-temperature Ar, Ne and N2 matrices. The IR spectra of adenine in gas phase are reported by Colarusso et al. [45] Vibrational frequencies for adenine have also been calculated at various level of theory [43,44,46–54]. Hobza et al. [55] reassigned some of the contradictory bands for adenine monomer. Here we have calculated the vibrational frequencies for adenine monomer at different DFT levels. As is seen from Table S3 vibrational frequencies calculated at M06 and B97D levels seems promising and is approaching to the experimental results. The calculated N–H stretching frequencies 3743, 3649, 3604 at M06 and 3662, 3559, 3522 at B97D, approaches to the experimental frequencies of 3569, 3508, 3452 cm1 determined for the N9–H tautomer of adenine in a supersonic jet [56]. The C8–H8 and C2–H2 stretching vibrations of adenine in an Ar matrix [44] are previously assigned at 3057 and 3041 cm1, respectively, whereas the former vibration has been assigned at 3061 cm1 in gas phase spectrum [45]. According to Hobza et al. [55] these assignments are incorrect due to the predicted IR intensity, which is zero for this particular stretching vibration. So, they have reassigned the above mentioned stretching vibrations. Calculated anharmonic frequency assigned at 3102 cm1 for C8–H8

Results and discussions Fig. 1 shows the optimized structure of A–T base pair with hydrogen bonding lengths at different DFT levels at gas phase

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Table 1 Geometrical parameters of heavy atom distances in A–T base pair at different DFT levels/6-31+G in gas phase and solvent phase (in bracket) (Å).

C2–O2 N1–N3 N6–O4

B3LYP

M06

M062X

B97D

wB97XD

3.748 (3.812) 2.913 (2.965) 2.946 (2.945)

3.66 (3.680) 2.877 (2.905) 2.95 (2.953)

3.629 (3.680) 2.856 (2.900) 2.951 (2.954)

3.632 (3.667) 2.846 (2.883) 2.924 (2.927)

3.658 (3.698) 2.862 (2.899) 2.929 (2.927)

X-ray results: [39,40] N1–N3 (2.835); N6–O4 (2.94).

3700

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3500 Complex Monomer

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Fig. 2. IR frequency of N6–H61 in adenine monomer and its A–T base pair complex in gas phase at different DFT levels.

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Fig. 5. IR frequency of C2–O2 in thymine monomer and its A–T base pair complex in gas phase at different DFT levels.

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Fig. 3. IR frequency of C2–H2 in adenine monomer and its A–T base pair complex in gas phase at different DFT levels.

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Fig. 6. IR frequency of C4–O4 in thymine monomer and its A–T base pair complex in gas phase at different DFT levels.

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Fig. 4. IR frequency of N3–H3 in thymine monomer and its A–T base pair complex in gas phase at different DFT levels.

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Fig. 7a. NMR chemical shifts of N6–H61 in adenine monomer and its A–T base pair complex in gas phase at different DFT levels.

vibration with the infrared intensity is almost zero. As seen from Table S3, our results are read as 3244 and 3191 cm1 at M06 and B97D levels for C8–H8 vibrations, respectively. In our results B3LYP and wB97XD levels show the overestimated infra-red stretching vibrations whereas M06 and B97D approach the experimental results. The C2–H2 vibration has been observed at 3163

and 3122 cm1 at M06 and B97D, respectively, whereas 3057, 3061 and 3049 cm1 observed at matrix [44], gas phase emission spectrum [45] and anharmonic vibration [55], respectively. The band at 1229 cm1 in an Ar matrix (and 1234 cm1 in the

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gas-phase) corresponds to the computed stretching mode on B3LYP, M06 revealed at 1248, 1250 cm1, respectively, whereas M062X, wB97XD overestimate (1268, 1269 cm1) and B97D underestimate (1213 cm1) the stretching frequency. The vibration mode for NH2 rocking, is coupled with N1–C6 stretching vibration which has been observed at 1015 cm1 in M06 level corresponding to 1017 cm1 in matrix calculation (1018 cm1 in the gas-phase) whereas other DFT levels B3LYP and wB97XD overestimate the stretching vibrations and B97D underestimate (993 cm1) the vibration mode. For this particular mode of vibration the DFT–GGA methods [48] with ultrasoft pseudopotential and a plane wave basis have been reported at 95 cm1 showing a large underestimation compared to experimental results.

15 14 13 12 11

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Fig. 9a. NMR chemical shifts of N3–H3 in thymine monomer and its A–T base pair in gas phase at different DFT levels.

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Fig. 7b. NMR chemical shifts of N6–H61 in adenine monomer and its A–T base pair complex in solvent phase at different DFT levels.

9.2 9 8.8 8.6 Complex 8.4

Monomer

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M06

M062X

B97D

wB97XD

Fig. 8a. NMR chemical shifts of C2–H2 in adenine monomer and its A–T base pair complex in gas phase at different DFT levels.

9 8.8 8.6 8.4 Complex 8.2

Monomer

8 7.8 7.6 B3LYP

M06

M062X

B97D

wB97XD

Fig. 8b. NMR chemical shifts of C2–H2 in adenine monomer and its A–T base pair complex in solvent phase at different DFT levels.

M06

M062X

B97D

wB97XD

Fig. 9b. NMR chemical shifts of N3–H3 in thymine monomer and in A–T base pair in solvent phase at different DFT levels.

For NH2 vibration mode, number of discrepancies have been found between the theoretical results reported [43,44,47–49,52]. Our results are in good agreement with Hobza et al.’s NH2 rocking and inversion vibration. We have observed the vibration mode at 162 cm1 at M06 level which supports the gas-phase emission spectrum results (162 cm1). The results show that the M06 level can substantially reproduce the experimental IR frequencies. A coupled vibration at 210 cm1 on M06 level represents the butterfly motion of adenine rings, NH2 inversion and torsion vibration of 6-membered ring. This assignment is close agreement with the gas-phase emission spectrum which results at 208 cm1 [46]. As seen from Table S4 (Supporting Information), the calculated frequencies of thymine monomer at different DFT levels are in good agreement with experiment [44]. It has enabled us to provide an unambiguous vibrational assignment for thymine. Number of bands assigned at theoretical levels is not identified in experiment due to their complicated pattern; therefore, their detailed assignment is difficult by experiment. The two computed N–H stretching vibrations at B97D revealed close agreement with the experimental results. The other DFT methods simply overestimate the stretching frequencies. The other C–H stretching vibration in C6– H and C–H vibration in methyl group can be assigned clearly at DFT levels. At C–H vibration mode all the DFT levels have been observed as close vibrational frequencies. Stretching vibration C5–C along with the plane bending has been observed for N1–H, N3–H at 1402 by B97D level, in close agreement with gas-phase and matrix level experiments. Deformation of the six member ring has been observed at 460 cm1 by M06 level which is corresponding to 462 cm1 by gas-phase emission spectrum. As seen from Figs. 2–6 and Table S5 (Supporting Information), the vibrational frequency for N3–H3 stretching of thymine monomer is revealed at 3518–3650 cm1 at different DFT levels. The

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same N3–H3 stretching vibrational frequency is revealed for the thymine in A–T base pair at 2816–3090 cm1. The decrease of N3–H3 stretching vibrational frequencies is indicate the existence of hydrogen bonding between N3–H3  N1 in A–T base pair. The stretching frequency values vary among the different DFT levels due to the % of HF level and the dispersion corrected is included in the different levels. Similar to N3–H3 case of thymine, red shift is also observed in N6–H6 stretching vibrational frequency (see Table S8) of adenine in A–T base pair at 3420–3475 cm1. The anti-symmetric vibrational frequency has not been observed for adenine in A–T base pair complex due to the hydrogen bond formation between N6–H6 of adenine and O4 of thymine. In addition, we also have observed the frequency for C2–H2 of adenine and C2–O2 of thymine monomers and their base pair listed in Tables S6 and S9. As is seen from Fig. 3 the C2–H2 stretching frequency of adenine monomer is observed at 3160–3235 cm1 and the C2–H2 stretching frequency in complex is observed at 3135–3230 cm1 and no deviation has been observed between monomer and base pair at different DFT levels. The C2–O2 stretching frequency for thymine monomer and for thymine in the A–T base pair complex is at 1760–1855 cm1 and at 1730–1845 cm1, respectively at different DFT levels. From Figs. 3 and 5, no significant deviation has been observed in C2–H2 and C2–O2 case between thymine monomer and thymine in A–T base pair. The results clearly indicate that there is no frequency shifting in C2–H2 and C2–O2 stretching of the monomer and its components in base pair. The results also demonstrate the absence of hydrogen bond, along with miniature frequency difference which implies that the electrostatic interaction might be van der Waals interaction and should not be considered as a hydrogen bond interaction. 1

H NMR chemical shifts for base pair and monomers

GIAO 1H chemical shift calculations have been carried out using different DFT level with 6-31+G(d) basis set for the optimized geometry. The results are shown in Figs. 7-9 and are tabulated in Tables S10–S15. As experimental 1H chemical shift values are not available for individual hydrogen atoms of methyl group of thymine, we have presented the average of the computed values. NMR chemical shifts at five theoretical levels for adenine monomer have been observed from Table S12, which reproduces the essential features of experimental 1H NMR chemical shifts. To compare among the DFT results with the experiment 1H NMR results, M06 gives the better performance. Only in the case of C2–H2 proton, the computed chemical shift of 8.0 ppm at B3LYP and B97D are in close agreement with the experimental results at 7.9 ppm. For N6–H61 and H62 protons in adenine monomer, the NMR chemical shifts have been observed at different position due to its free rotation. The average chemical shifts are shown in Tables S13 and 14. The NMR results at the solvent phase calculations have shown the down field than the gas phase. Moreover, implicit solvation model are parameterized for the purpose of energy, and not NMR, calculations. For the thymine monomer the results are shown in Table S15 at different DFT levels. The N–H protons in the monomer have been observed at 5.6–6.6 ppm at different DFT levels depending on the neighboring atoms in the structure. The 1H NMR results for adenine and thymine monomer and its complex, are very helpful to investigate the hydrogen bonding as well as van der Waals interaction between N–H  N, N–H  O and C–H  O in A–T base pair. The H3 of thymine chemical shift can be observed from Fig. 9 for the monomer and its complex. The H3 proton of thymine monomer chemical shift is observed at 6–7 ppm at different DFT levels. The same proton in complex is observed at 13–14 ppm at different DFT levels. The large deviation from 6 to 13 ppm clearly demonstrates the presence of strong interaction is hydrogen bonding. Similarly, difference in chemical

shift of H61 proton of adenine monomer and its complex have also shown the deviation. The H61 proton of adenine monomer is observed at 4.2–4.6 ppm and the same proton in the complex is observed at 8 ppm at different DFT levels (see Fig. 7a). The chemical shifting from 4 ppm of up field to 8 ppm of down field suggests the presence of strong interaction between N6–H61 of adenine and O4 of the thymine which is hydrogen bonding. In the itinerary the aforementioned interaction has also been investigated using NMR signals for C2–H2  O2 in A–T base pair. From Figs. 8a and 8b, the chemical shift for the H2 of adenine monomer and its complex of A–T base pair is observed at 8–9 ppm. It is revealed that, not much variation between monomer and its complex at C2–H2 proton. Yet only small variation is observed as 0.3 ppm in the chemical shift of H2 proton between monomer and its complex of adenine. It explains that the existence of weak interaction may be a van der Waals interaction rather than hydrogen bond. To account for the solvent effect we have considered CPCM model and perform the spectroscopic calculation in aqueous phase. Inconsiderable variation has been observed between the gas phase and the solvent phase calculation for the 1H NMR chemical shifts. However, the solvation model has reported lower energetic values than the gas phase [57], the gas phase spectroscopic results are not far from the solvent phase. Moreover, the gas phase calculations for the large species can avoid the problem of convergence and large computational time. In general, an interaction of infrared waves with matter is expressed in terms of changes in molecular electric dipoles associated with vibrations and rotations [58]. The presence of interaction between N1 and H3–N3 reflects on the shifts in the spectral frequencies. The difference between the monomers (A and T) and its complex (A–T base pair) of IR frequency 500– 700 cm1 is due to the strong interaction. Therefore these spectral changes indicate the presence of hydrogen bonding. Similarly two stretching modes (symmetric as well as anti-symmetric) for adenine monomer has become a single stretching mode of vibration in A–T base pair and the difference has been observed 300 cm1. The stretching mode of vibrational frequency difference indicates the strong interaction between N6–H61 of adenine and O4 of thymine. While considering the C2–H2 of adenine and O2 of thymine, large difference has not been notified between monomer and its complex due to the weak interaction such as van der Waals interaction. The NMR chemical shifts for hydrogen bond in complex typically include proton deshielding in X–H  Y (X,Y = N,O), through hydrogen bond spin–spin couplings between heavy atom of X and Y [59]. The NMR results for C–H  O interaction show only 0.3 ppm difference between monomer of adenine and its A–T base pair whereas large difference has been observed for N6–H61(adenine) and N3–H3(thymine). The strong electro negativity Y (Y = O,N) and the positive H atom of A–T base pair may also be a reason for the stretching mode of frequency shifting in IR spectra and down field chemical shift in NMR between monomer and complex. Thus, theoretical spectroscopic results has revealed weak interaction to be van der Waals interaction of C2– H2  O2 contact in A–T base pair and cannot be considered as hydrogen bond.

Conclusion The controversial interaction on C–H  O contact in A–T base pair [18–24,41] has been addressed through theoretical IR and NMR spectroscopic results. Different DFT levels, including hybridGGA, hyper-GGA and dispersion corrected level have been selected for the optimization of the base pair and the monomers as well to obtain the IR and NMR spectra. Among the DFT levels, strikingly, only B97D theoretical spectroscopic results are found to be

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deviated from the other DFT results. Particularly, B97D underestimates the vibrational stretching mode and 1H NMR chemical shift values. Hydrogen bonds N–H  O and N–H  N in the A–T base pair are well identified and is accompanied by red-shift in N–H  N and N–H  O stretching mode while C–H  O contact has been observed to be the weak interaction known as blue shift. From the above mentioned view the interaction can be concluded as the C–H  O contact in A–T base pair is a van der Waals interaction and cannot be considered as a hydrogen bond. Acknowledgements This research was supported by the National Science Council (NSC) of Taiwan and the computational resource is partially supported by National Center for High-Performance Computing (NCHC), Hsin-Chu, Taiwan. Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.saa.2013.11.110. References [1] T. Kubarˇ, M. Hanus, F. Ryjácˇek, P. Hobza, Chem. Eur. J. 12 (2006) 280–290. [2] I. Dabkowska, H.V. Gonzales, P. Jurecˇka, P. Hobza, J. Phys. Chem. A 109 (2005) 1131–1136. [3] J.D. Watson, F.H.C. Crick, Nature 171 (1953) 737–738. [4] (a) C.F. Guerra, F.M. Bickelhaupt, J.G. Snijders, E.J. Baerends, J. Am. Chem. Soc. 122 (2000) 4117–4128; (b) J.M. Rosenberg, N.C. Seeman, R.O. Day, A. Rich, Biochem. Biophys. Res. Commun. 69 (1976) 979–987; (c) J.M. Rosenberg, N.C. Seeman, R.O. Day, A. Rich, J. Mol. Biol. 104 (1976) 145– 167. [5] (a) P. Jurecka, P. Nachtigal, P. Hobza, Phys. Chem. Chem. Phys. 3 (2001) 4578– 4582; (b) P. Jurecka, P. Hobza, J. Am. Chem. Soc. 125 (2003) 1560815613; (c) J. Sponer, K.E. Riley, P. Hobza, Phys. Chem. Chem. Phys. 10 (2008) 2595– 2610. [6] (a) M. Wolter, M. Elstner, T. Kubarˇ, J. Phys. Chem. A 115 (2011) 11238–11247; (b) D. Sivanesan, K. Babu, S.R. Gadre, V. Subramanian, T. Ramasami, J. Phys. Chem. A 104 (2000) 10887–10894. [7] (a) J. Florián, J. Leszczynski, J. Am. Chem. Soc. 118 (1996) 3010–3017; (b) J.P. Cerón-Carrasco, A. Requena, E.A. Perpète, C. Michaux, D. Jacquemin, Chem. Phys. Lett. 484 (2009) 64–68; (c) L. Gorb, Y. Podolyan, P. Dziekonski, W.A. Sokalski, J. Leszczynski, J. Am. Chem. Soc. 126 (2004) 10119–10129. [8] J. šponer, K.E. Riley, P. Hobza, Phys. Chem. Chem. Phys. 10 (2008) 2595–2610. [9] P. Colarusso, K. Zhang, B. Guo, P.E. Bernath, Chem. Phys. Lett. 269 (1997) 39– 48. [10] A.M. Lifschitz, J.M. Rodgers, C. Samet, J. Phys. Chem. B 116 (2012) 211–220. [11] R. Ishikawa, C. Kojima, A. Ono, M. Kainosho, Magn. Reson. Chem. 39 (2001) S159–S165. [12] I.A. Konstantinov, L.J. Broadbelt, J. Phys. Chem. A 115 (2011) 12364–12372. [13] M. Swart, F.C. Guerra, F.M. Bickelhaupt, J. Am. Chem. Soc. 126 (2004) 16718– 16719. [14] I. Vakonakis, A.C. LiWang, J. Am. Chem. Soc. 126 (2004) 5688–5689. [15] M.S. Vries, P. Hobza, Annu. Rev. Phys. Chem. 58 (2007) 585–612.

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