On the Binding Strength Sequence for Nucleic Acid Bases and C₆₀ with Density Functional and Dispersion-corrected Density Functional Theories: Whether C₆₀ could protect nucleic acid bases from radiation-induced damage?

Abstract

The major objective of this paper is to address a controversial binding sequence between nucleic acid bases (NABs) and C₆₀ by investigating adsorptions of NABs and their cations on C₆₀ fullerene with a variety of density functional theories including two novel hybrid meta-GGA functionals, M05-2x and M06-2x, as well as a dispersion-corrected density functional, PBE-D. The M05-2x/6-311++G** provides the same binding sequence as previously reported, guanine(G) > cytosine(C) > adenine (A) > thymine (T); however, M06-2x switches the binding strengths of A and C, and PBE-D eventually results in the following sequence, G>A>T>C, which is the same as the widely accepted hierarchy for the stacking of NABs on other carbon nanomaterials such as single-walled carbon nanotube and graphite. The results indicate that the questionable relative binding strength is due to insufficient electron correlation treatment with the M05-2x or even the M06-2x method. The binding energy of G@C₆₀ obtained with the M06-2x/6-311++G(d,p) and the PBE-D/cc-pVDZ is −7.10 and −8.07 kcal/mol, respectively, and the latter is only slightly weaker than that predicted by the MP2/6-31G(d,p) (−8.10kca/mol). Thus, the PDE-D performs better than the M06-2x for the observed NAB@C₆₀ π-stacked complexes. To discuss whether C₆₀ could prevent NABs from radiation-induced damage, ionization potentials of NABs and C₆₀, and frontier molecular orbitals of the complexes NABs@C₆₀ and (NABs@C₆₀)⁺ are also extensively investigated. These results revealed that when an electron escapes from the complexes, a hole was preferentially created in C₆₀ for T and C complexes, while for G and A the hole delocalizes over the entire complex, rather than a localization on the C₆₀ moiety. The interesting finding might open a new strategy for protecting DNA from radiation-induced damage and offer a new idea for designing C₆₀-based antiradiation drugs.

1. Introduction

With a rapid development and wide application, the potential effect of nanoparticles on health and environment begins to be a hot topic in the nanotechnology field. A recent issue of Nano Today reported that manufacture and use of nanoparticles in medicine and other industries could pose a potential risk to human health.¹ As a typical nanoparticle, since its discovery C₆₀ has attracted considerable interest in the field of nanotechnology due to its unique properties. Because of its small size and poor solubility in polar solvents, it may penetrate through cellular membrane, resulting in adverse effects on biological systems, such as traveling through blood stream to heart and depositing on the targeted part of human body causing tissue hurt, lung disease and some toxic effects on human.² In spite of potential unfriendly to environment, a good deal of experiments have also established prospective applications for C₆₀ derivatives (water-soluble fullerene derivatives) in many fields such as antioxidants, neuroprotective agents, antiapoptotic activity, DNA photocleavage, enzyme inhibition, antimicrobial activity and anti-HIV activity.³ Various applications of C₆₀ derivatives have been reviewed by Nakamura et al.⁴ Particularly, C₆₀ fullerene is proposed to serve as a future antiradiation drug to protect against the side effects of cancer radiation therapy,⁵ which is a beneficial effect on biological systems. Understanding about the interaction mechanism between C₆₀ or C₆₀ derivatives and biomolecules can promote such kind of biomedical applications.

Oxidative DNA damage could cause several diseases, such as cancer⁶ and aging⁷. Radiation is one of the most general reasons for oxidative DNA damage.⁸ When the high-energy radiation interacts with DNA, an electron may be ejected from DNA, and a hole created in this way migrates over a long distance through a hopping mechanism,⁹ eventually ending on a guanine base of DNA because it has the lowest ionization potential among all DNA bases.¹⁰ The guanine radical cation (G^·+) is a harbinger of many pathological conditions in living cells as a result of its involvement in many multiform reactions.¹¹ As measured by photoionization yield, the adiabatic IP of C₆₀ fullerene molecule is close to 7.54eV,¹² which is lower than the adiabatic IP of guanine (7.77eV), the lowest one among four NABs.¹³ This trend is also confirmed by the PBE calculation (Table S1 in the Supporting Information). Consequently, a question is raised whether C₆₀ could protect guanine and other DNA bases from radiation-induced damage. Upon a high-energy radiation interacting with NAB@C₆₀ complexes, a hole will be created. If the hole localizes on the C₆₀ moiety rather than on the NAB moiety, it may demonstrate that C₆₀ can act as an antiradiation substance. This investigation is meaningful for the anticipative application of fullerenes in the antiradiation drug field. ⁵

To the best of our knowledge, there are few literatures about this issue. Shukla et al did useful pioneering research and trials in this topic, and located a stable geometry of C₆₀-guanine.^11a During the preparation of the paper, another closely relevant paper from Shukla et al was released on the website of Chem. Phys. Lett.^11b In the most recent paper, a novel hybrid meta-GGA DFT, M05-2X, was used to reveal the binding strength of NABs and C₆₀ molecules. Nevertheless, their binding energies and binding strength sequence may be questionable. The binding strength follows the order: G (−4.99kcal/mol) > C(−4.26) >A (−4.10) > T(−3.75), which is different from the well reported binding strength of DNA bases with single-walled carbon nanotube (SWNT) and graphite, G>A>T>C.¹⁴ In addition, the binding energy of G-C₆₀ is quite far from that obtained with MP2 method (−4.99 versus −8.10 kcal/mol).^11a Shukla et al ^11b claimed that the binding strength order predicted by the M05-2x/6-311++G(d,p) followed a recent experimental report, G>C>A>T. ¹⁵ However, the sequence is for poly-nucleotide/SWNT hybrids, specifically, 12-base-long single stranded DNA homopolymers consisting of poly d(A)₁₂, poly d(T)₁₂, poly d(C)₁₂ or poly d(G)₁₂, rather than for the single DNA base molecules. Because of quite different self-stacking of base molecules in ssDNA, the binding between the ssDNA and SWNT may be different from that of single base and SWNT. On the other hand, even for the poly-nucleotide, a different binding strength measured with spectroscopy is G>A>T>C.¹⁶ Although the HF level together with classical force field^14c and constraint optimizations with MPWB1K density functional ^14a predicted the binding order of G > A > T > C in the gas phase for the interaction of NABs with (5,5) SWCNT, the binding order based upon isothermal calorimetry experiments on much larger diameter nanotube was predicted to be T > A > C.^14c The solvent effects may be responsible for the diffidence.

The above deficiencies motivated us to revisit the system with more accurate methods dealing with “long range” electron correlation effects, such as, M06-2x and DFT-D methods. The results will allow us to get insights into whether the above strange strength order originates from the M05-2x method or it really is. As reported by Hobza et al,¹⁷ empirical dispersion-corrected density method functional (DFT-D, specifically TPSS-D) provides more accurate results for the π-stacked adenine dimers than M06-2x does. However, Sherrill et al’s assessment indicated that M06-2x performs somewhat better than PBE-D for the π-stacked NAB dimers.¹⁸ Thus, in addition to providing a benchmark binding strength for stacked complexes NABs@C₆₀, another objective of the paper is to assess performance of M05-2x, M06-2x and DFD-D on the π-stacked NABs@C₆₀. Furthermore, cationic systems (NABs@C₆₀)⁺ were also extensively investigated in order to explore whether fullerenes could protect NABs from radiation-induced damage.

2. Computational Methods

Full geometry optimizations and property calculations for DNA bases and C₆₀ were firstly performed with generalized gradient approximation (GGA) type of DFT, PW91 with a double numerical plus polarization function (DNP) basis sets, implemented in DMol³ package from Accelrys, Inc.¹⁹ The spin polarization scheme was utilized to deal with open-shell systems. The convergence threshold of energy was set as 10⁻⁷ a.u. Vibrational frequency analysis was also carried out at the level of geometry optimization. The optimized complexes were all minimum energy species along the potential energy surface. The less extensive method aims to extensively search for the π-stacked conformations for complexes NABs@C₆₀.

It is known that, in spite of great improvement over LDA, a typical GGA type of DFT like the above PW91 method still underestimates the binding for the systems mainly arising from van der Waals (vdW) interaction. Hybrid meta-GGA functionals, M05-2X and M06-2x, developed by Truhlar et al ²⁰ and implemented in Gaussian 09, ²¹ better describing the non-bonding interaction than PW91, were therefore also employed to fully optimize a few favorable structures for each NAB.

For an empirical dispersion-corrected density functional theory (DFT-D), Grimme’s scheme was adopted,²² where the vdw interaction term is well described by a damped interatomic potential, accounting for long-range dispersion effects in noncovalent systems. The total density functional energy can be written as follows:

$$E_{\mathit{DFT}-D}=E_{\mathit{DFT}}+E_{\mathit{vdw}}$$ (1)

where E_DFT is the normal self-consistent density functional energy, and E_vdw is the empirical dispersion correction term and is given by

$$E_{\mathit{vdw}}=-s_6\sum _{i=i}^{N-1}\sum _{j=i+1}^N\frac{C_6^{ij}}{R_{ij}^6}{f}_{\mathit{dmp}}(R_{ij})$$ (2)

Here, s₆ is a global scaling factor only depending on the applied density functional method. As usual, the combined dispersion coefficient for atom pair i and j, $C_6^{ij}$, was estimated with a geometric mean of individual C₆ coefficient, while R_ij, the interatomic distance between atoms i and j, is an arithmetic mean value of individual vdw radius. N is the number of atoms, and f_dmp (R_ij), a damping function, is expressed by the following equation

$$f_{\mathit{dmp}}(R_{ij})=\frac{1}{1+e^{-\alpha (R/R_0-1)}}$$ (3)

Where α is taken to be 20 in the exponent. Perdew-Burke-Ernzerhof (PBE) ²³ exchange-correlation functional in the DFT part was employed in the present work, and the DFT-D method was therefore referred to as PBE-D. The PBE-D calculations were conducted with the ORCA suite of programs.²⁴ Dunning’s correlation-consistent polarized valence basis sets of double-zeta (cc-pVDZ) and/or triple-zeta (cc-pVTZ) were used together with the PBE-D method, as usually applied to the other π-π stacking systems.¹⁸ All of the relevant systems were also fully optimized at the PBE-D levels.

3. Results and Discussion

3.1. Neutral Complexes (NABs@C₆₀) in the Gas Phase

With the PW91/DNP method, a variety of positions of NABs over C₆₀ were investigated. In C₆₀ fullerene, the hh C-C bond (the C-C bond shared by two hexagonal rings) has more π-bonding character than the hp C-C bond (the C-C bond shared by a hexagonal ring and a pentagonal ring).²⁵ There are three distinct symmetry sites in C₆₀ with respect to the hexagonal ring in NAB molecules: bridge, top and hollow. The adsorption on hollow site is less stable than on the other two sites. The hollow conformation therefore will not be discussed below. Various geometries and the relative energies at the PW91/DNP level are shown in Figure S1 and Table S2 in the Supporting Information.

For thymine (T), guanine (G), and cytosine (C), adsorption on the bridge site is the most stable, while for adenine the most stable one is on the top site. The fullerene molecule in these complexes does not undergo significant deformation. The binding energy E_b for the neutral complexes NAB@C₆₀ is defined as:

$$E_{\text{b}}=E(\text{NAB}@{\text{C}}_{60})-E(\text{NAB})-E({\text{C}}_{60})$$ (4)

where E(NAB-C₆₀), E(C₆₀), and E(NAB) are the total energies for the complex, isolated C₆₀, and NAB, respectively. It was widely accepted that the BSSE effect is nearly negligible when the numerical basis sets are employed.¹⁹ The basis set superposition error (BSSE) was therefore not included for the PW91/DNP level with Dmol³ code, and however, it was taken into account with counterpoise scheme at the M05-2x, M06-2x and PBE-D levels.²⁶

As shown in Table 1, the binding energies from the PW91/DNP for NAB@C₆₀ are quite small. Obviously, all NABs undergo physisorption processes when they interact with C₆₀. G@C₆₀ complex has the strongest binding (−2.63 kcal/mol), followed by C-C₆₀ (−2.30 kcal/mol) and A-C₆₀ (−2.12 kcal/mol), and T-C₆₀ complex has the lowest binding energy (−1.78 kcal/mol). This binding trend, G > C > A > T, is the same as that predicted by Shukla et al with M05-2X/6-311++G(d, p), although the binding is dramatically weaker than that obtained by M05-2X/6-311++G(d, p). The present full optimization with the M05-2x method generates the same binding energies for G@C₆₀ and C@C₆₀ complexes as reported by Shukla et al,^11b and those for T@C₆₀ and A@C₆₀ only slightly differ (−3.70 and −4.16 kcal/mol versus −3.75 and −4.10 kcal/mol). Although their detailed geometries for the NBA@C60 complexes are not available, because of rather similar binding energies the geometries from the present and Shukla’s work should be very similar as well. Except for the similar one for G@C₆₀ (3.031Å in the present work versus 3.041Å) the nearest distances between heavy (non-hydrogen) atom of NABs and carbon atoms of C₆₀ differ by 0.1–0.2Å different (3.001, 2.993, and 3.131Å versus 3.249, 3.245, and 3.220Å), which may arise from different definitions.

Table 1.

Binding energies (kcal/mol) for the neutral complexes with the PW91, M05, M06 and PBE-D methods. Basis sets A, B, and C are cc-pVDZ, 6-311++G(d,p), and cc-pVTZ, respectively.

Complex	PW91/DNP	M052x/A	M052x/B	M052x/Ba	M062x/A	M062x/Bb	PBE-D/A	PBE-D/C
A@C60	−2.12	−4.06	−4.16	−4.10	−6.24	−6.26(−6.40)	−7.36	−7.42
C@C60	−2.30	−3.78	−4.26	−4.26	−5.64	−6.01(−6.07)	−6.19	−6.34
G@C60	−2.63	−4.67	−5.00	−4.99	−6.80	−7.10(−7.55)	−8.07	−8.45 −8.10c
T@C60	−1.78	−3.54	−3.70	−3.75	−5.29	−5.46(−5.56)	−6.53	−6.69

^aRef. ^11b;

^bThe data in parenthesis are those without deformation correction;

^cRef. ^11a.

Table 1 also shows that both the M06-2x/cc-pVDZ and M06-2x/6-311++G(d,p) significantly enhance the binding between NABs and C₆₀ by 1–2 kcal/mol as compared with those from the M05-2x/6-311++G(d,p). It is interesting to note that the relative binding strength for C@C₆₀ and A@C₆₀ is opposite to that obtained by the M05-2X/6-311++G(d,p). The binding sequence for NBAs@C₆₀ is consequently changed to G>A>C>T. Although M06-2x is considerably improved in describing the non-covalent interaction over other GGAs,²⁰ there is still some deficiency compared with the dispersion-corrected density methods (DFT-D).¹⁷ As compared with the results from the M06-2x, the present PBE-D/cc-pVDZ does further strengthen the binding between NABs and C₆₀ so that the BSSE-corrected binding energy for G@C₆₀ complex (−8.07kcal/mol) is only slightly less negative than −8.10kcal/mol, obtained at the MP2/6-31G(d,p)//MP2/6-31G(d) level.^11a Thus, for the examined π-stacked dimers NAB@C₆₀, it seems that PDE-D performs better than M06 does. Since it is well known the MP2 method overestimates non-covalent interaction to some extent, the results obtained by PBE-D/cc-PVDZ method may be rather close to the real values of the binding energies. The PBE-D turns out that the binding strength between NABs@C₆₀ follows the sequence: G > A >T >C, which is the same as the binding sequence of NABs with (5, 5) as well as (10, 0) SWNTs 14a, 14c and the hierarchy of NABs with a graphene layer as well as graphite surface.^{14d, 27} PBE-D/cc-PVTZ further enhances the binding of NABs with C₆₀ by approximately 0.1kcal/mol for A, C, and T, yet by 0.35 kcal/mol for G. However, the binding strength remains the same as that from the PBE-D/cc-pVDZ. A variation of the binding strength for NABs@C₆₀ with theoretical methods is shown in Figure 2.

Figure 2.

Variation of binding strength for (NAB@C₆₀) with theoretical methods.

The displaced-stacked π-π interaction between NABs and C₆₀ is stabilized mainly by dispersion effect depending on the surface area of buried as well as on the polarizability of the moieties.²⁸ Since there are both five-membered imidazole ring and six-membered pyrimidine ring in guanine and adenine molecules, the π-π stacking interactions between adenine/guanine and C₆₀ should be generally stronger than thymine/cytosine with one only six-membered ring. London’s empirical formula may help understand the above binding sequence for the NABs@C₆₀ complexes. ²⁹

$$E_{AB}^{\mathit{disp}}=-\frac{3{\alpha }^A{\alpha }^B{I}_A{I}_B}{4(I_A+I_B)R^6}$$ (5)

where α and I are the polarizability and ionization potential for individual molecules, respectively, and R is the distance between molecules A and B. The polarizability of NABs, representing the deformability of the electronic charge distribution, is known to arise from the regions associated with the aromatic rings, lone electron pairs in nitrogen, and oxygen atoms. Guanine has the largest value of polarizability (120.8 au at the B3LYP/6-31G(d) level), followed by adenine (108.6 au), and thymine and cytosine have similar ones (94.7 and 90.5 au). This trend is the same as Gowtham’s report.²⁷ Based on London’s equation, the ratio of the dispersion forces of the four complexes is approximately as, 100% (G@C₆₀): 89%(A@C₆₀): 81%(T@C₆₀): 75%(C@C₆₀), which also supports that A@C₆₀ and T@C₆₀ should be stronger than C@C₆₀. Especially, the prediction confirms the binding sequence obtained by the PBE-D method.

To gain further insights into the electronic structures, Figure 3 illustrates the highest occupied molecular orbitals (HOMO) and the lowest unoccupied molecular orbitals (LUMO) of these complexes. LUMO of all these complexes localizes on C₆₀. Orbital energies for the HOMO of the five individual molecules are as follows: G(−0.208 a.u.) > A(−0.218)> C₆₀ (−0.220) > C(−0.227) > T(−0.240). As shown by the molecular orbitals in Figure 3 and the energy level diagrams in Figure 4, HOMOs from the NAB and C₆₀ make different contributions to the HOMO of complexes. For G@C₆₀ and A@C₆₀, the HOMO levels of the complexes are close to the HOMO of NAB, while the HOMO levels of complexes C@C₆₀ and T@C₆₀ are close to the HOMO level of C₆₀. According to Figure 3, HOMOs delocalize over both guanine/adenine moiety and C₆₀ for G/A@C₆₀ complexes, while they almost localize on C₆₀ in T/C@C₆₀ complexes. Accordingly, the presence of C₆₀ molecule may well protect thymine and cytosine from radiation damage. However, whether fullerene could protect guanine and adenine from radiation damage needs to be further investigated.

Figure 3.

Plots of the frontier orbitals of the NAB@C₆₀ complexes. The isovalue is 0.02 a.u.

Figure 4.

Molecular orbital energy level diagrams (au). The LUMO levels of NABs are significant higher than C₆₀. LUMO of NABs therefore has no contribution to the LUMO of complexes. For clarity NABs’ LUMO level are not shown in this picture. HOMO energies of A@C60 and C@C60 are too close to distinguish.

3.2. Cationic Complexes (NABs@C₆₀)⁺ in the Gas Phase

For the four (NABs@C₆₀)⁺ complexes (NAB=A, C, G and T), both the π-π stacked and the T-shaped σ-π conformations were optimized with the PW91/DNP, M05-2x/cc-pVDZ, M06-2x/cc-pVDZ, M06-2x/6-311++G**, and PBE-D/cc-pVDZ methods. The first ionization potentials of NAB and C₆₀ from the theoretical methods were summarized in Table 3 together with the experimental data. The M06-2x, PBE-D, and MPWB1K predicted that C₆₀ has lower adiabatic IP than T, C and A, yet higher aIP than G. At the M06-2x/cc-pVDZ level the aIPs for the NABs are lower by 0.1–0.2eV than the experimental data, while the M06-2x/6-311++G** yields higher ones by 0.1–2eV. Thus, because of higher aIP than C₆₀ for the ionic complexes of A, C, and T with C₆₀ the binding energy was defined for (NABs@C₆₀)⁺ as:

$${E_{\text{b}}}^{+}=E{(\text{NAB}@{\text{C}}_{60})}^{+}-E(\text{NAB})-E{({\text{C}}_{60})}^{+}$$ (6a)

Table 3.

The first adiabatic and vertical ionization potentials (aIP and vIP/eV) for nucleic acid bases and C₆₀ at various theoretical levels.

	Thymine	Cytosine	Adenine	Guanine	C60
aIP, M052x/cc-pVDZ	8.73	8.59	8.02	7.56	8.04
aIP, M062x/cc-pVDZ	8.71	8.58	8.02	7.56	7.96
aIP, M062x/6-311++G**	8.97	8.90	8.31	7.87	8.03
aIP, PBE-D/cc-pVDZ	8.34	8.14	7.68	7.23	7.25
vIP, PBE-D/cc-pVDZ	8.47	8.29	7.89	7.54	7.31
aIP, MPWB1K/cc-pVDZ	8.62	8.38	7.88	7.38	7.68
aIP, Exp.a/b	8.87/8.80	8.68/8.45	8.26/7.80	7.77/7.85
IP, Experimental rangec					7.54–8.1

^aPhotoionization mass spectroscopy in the gas phase. ¹³;

^bPhotoelectron spectra. ³¹

^cIonization energy determinations for C₆₀ at chemistry web book of NIST

Because of lower aIP than C₆₀ for the ionic complexes of G with C₆₀,

$${E_{\text{b}}}^{+}=E{(\text{NAB}@{\text{C}}_{60})}^{+}-E({\text{C}}_{60})-E{(\text{NAB})}^{+}$$ (6b)

The superscript “+” represents the cationic system, the other notations are the same as them in equation (4). In the cationic complexes, because of the predictable electrostatic force, the binding energies listed in Table 2 are higher negative than those of the neutral complexes NAB@C₆₀. Figure 5 shows the π-stacked as well as the T-shaped σ-π conformations for the complexes (NAB@C₆₀)⁺, together with the nearest distances. For the π-stacked conformations, consistent with stronger binding the nearest distances for the cationic complexes are shorter than those for the neutral counterparts, e.g., at the PBE-D/cc-pVDZ level, 2.805, 2.351, 2.812 and 3.034 Å versus 2.974, 3.129, 2.913 and 3.125 Å for adenine, cytosine, guanine, and thymine, respectively.

Table 2.

Binding energies (kcal/mol) for (NAB@C₆₀)⁺ at various calculation levels.

Complexes		PW91/DNP	M05-2x/cc-pVDZ	M06-2x/cc-pVDZa	M06-2x/6-311++G**	PBE-D/cc-pVDZa
(A@C60)+	stacking	−11.1	−16.4	−17.6 (−14.3)	−15.7	−22.2(−19.0)
(A@C60)+	σ-π	—	−9.7	−10.7	−7.1	—
(C@C60)+	stacking	—	—	−15.4	−14.5	−22.0(−17.6)
(C@C60)+	σ-π	−14.4	−31.5	−29.9 (−24.1)	−25.3	−26.8(−20.3)
(G@C60)+	stacking	—	−12.8	−14.5	−16.5	−26.1(−22.70)
(G@C60)+	σ-π	−18.7	−6.8	−10.7	−14.2	—
(T@C60)+	stacking	—	−8.3	−11.0	−11.2	−15.9(−13.5)
(T@C60)+	σ-π	−9.4	−9.1	−9.7	−9.7	−13.2(−10.6)

^aThe data in parentheses include BSSE correction.

Figure 5. π-stacked and T-shaped [NAB@C₆₀]⁺ complexes.

The dark, blue and red data are the nearest distance between non-hydrogen atom of NBA and C₆₀ with M05-2x/cc-PVDZ, M06-2x/cc-PVDZ, and PBE-D/cc-pVDZ methods, respectively.

At the PW91/DNP level, except for the π-stacked geometry of (A@C₆₀)⁺ that still maintains the favorable conformation similar to its neutral complex, for the other three complexes C₆₀⁺ binds with NABs through π and carbonyl oxygen, referred to as σ-π conformation. When electron correlation effects are well taken into account by the M05-2x, M06-2x and PBE-D methods, the located conformations are significant different from those obtained with the PW91/DNP method. At the M05-2x/cc-pVDZ level, for (C@C₆₀)⁺ the initial π-stacked conformations always converge to the σ-π conformation, while for other three cationic complexes (NAB@C₆₀)⁺ both the π-π stacked and T-shaped σ-π conformations were located. The stacked (T@C₆₀)⁺ is only 0.8 kcal/mol less stable than the T-shaped one. According to Table 2, however, the π-stacked conformation is more stable than the σ-π one by 6.7 and 6.0 kcal/mol for the (A@C₆₀)⁺ and (G@C₆₀)⁺ complexes, respectively.

As shown in Figure 5, as electron correlation is better included by the M06-2x/cc-pVDZ and M06-2x/6-311++G** methods, a rather tilted stacked conformation for (C@C₆₀)⁺ was also predicted, but it is considerably less stable than the T-shaped σ-π conformation by 14.5 and 10.8 kcal/mol. At the PBE-D/cc-pVDZ level, although the stacked conformation for (C@C₆₀)⁺ is still less stable than the T-shaped one, their binding energy difference is just 4.8 kcal/mol. The M06-2x/cc-pVDZ, M06-2x/6-311++G**, and PBE-D/cc-pVDZ also switch the relative binding for the (T@C₆₀)⁺ predicted by the M05-2x, e.g., the stacking is stronger than the σ-π interaction by approximately 1–2 kcal/mol. At the PBE/cc-pVDZ level, the binding strength including BSSE corrections decrease in the sequence, G (−22.7kcal/mol)> C(−20.3) >A(−19.0) >T (−13.6).

Obviously, favorable geometries of the cationic complexes are very sensitive to the applied theoretical methods. For the (NBAs@C₆₀)⁺ complexes, two principal forces, dispersion and electrostatic force, may determine the conformations of (NBAs@C₆₀)⁺. Because of possessing two aromatic rings, guanine and adenine interact more strongly with C₆₀⁺ via dispersion force than one-ring cytosine and thymine. When the high level methods are applied, such as M06-2x and PBE-D that can accurately deal with electron correlation inducing dispersion force, for adenine and guanine the favorable conformations are therefore the π-stacked ones. On the other hand, because of the positively charged surface in C₆₀⁺, electrostatic force in (NBAs@C₆₀)⁺ plays more important role on determining the conformation than in the neutral complexes. The unique oxygen atom in cytosine carries more negative charge (−0.362e) than carbonyl oxygen atoms (−0.338 and −0.354e) in thymine. The stronger electrostatic interaction between the oxygen of cytosine and C₆₀⁺ induces a favorable T-shaped σ-π conformation for (C@C₆₀)⁺ complex. Actually, as shown in Table 2 and Figure 5 only M06-2x and PBE-D predicts a rather tilted partially stacked conformation that is less stable than the T-shaped (C@C₆₀)⁺. For the (T@C₆₀)⁺ complex, the two major driving forces are well balanced, and both the stacked and T-shaped conformations are brought about at the M05-2x, M06-2x and PBE-D levels. Since the PW91 considerably underestimates dispersion force, at this level electrostatic force may determine the optimal complexes. Thus, for (C@C₆₀)⁺, (G@C₆₀)⁺, and (T@C₆₀)⁺ complexes the conformations obtained by PW91/DNP are T-shaped, which also supports the claim that the T-shaped configuration has more stabilizing electrostatic interaction than the displaced π-π stacking configuration due to favorable quadrupole-quadrupole interaction.³⁰

3.3 Hole Distribution and Its Biological Implication

To address the other objective whether fullerene can protect DNA bases from radiation damage, the spin densities for (NBAs@C₆₀)⁺ were illustrated in Figure 6 together with the atomic charge fitted from electrostatic potential and the total spin density on the C₆₀ moiety. The total atomic charges on the C₆₀ are +0.632e, +0.731e, +0.850e and +0.863e for the π-stacked complexes (G@C₆₀)⁺, (A@C₆₀)⁺, (T@C₆₀)⁺, and (C@C₆₀)⁺, respectively, while for the T-shaped (C@C₆₀)⁺ and (T@C₆₀)⁺ the charges are even larger (+0.888e and +0.975e). This shows that an electron can be dominantly ejected from the C₆₀ moiety for the (C@C₆₀) and (T@C₆₀) complexes upon photoionization or radiation. As a result, the trapped hole also mainly distributes over the C₆₀ portion in (C@C₆₀)⁺ and (T@C₆₀)⁺, which is further supported by the high spin density in the C₆₀ moiety ranging from 0.764 for the π-stacked (T@C₆₀)⁺ to 0.924 for the T-shaped (T@C₆₀)⁺. The above significant spin density localization over the C₆₀ moiety in the (C@C₆₀)⁺ and (T@C₆₀)⁺ complexes demonstrates that the presence of C₆₀ could well prevent C and T from radiation or photoionization. The spin density on the C₆₀ of (A@C₆₀)⁺ is lower than those of the π-stacked (C@C₆₀)⁺ and (T@C₆₀)⁺ by approximately 0.1, (0.670 versus 0.849 and 0.760). For (G@C₆₀)⁺, the spin density almost equivalently delocalizes over guanine and C₆₀ (0.461 versus 0.539). Thus, C₆₀ could only partially protect A and G from radiation damage by sharing the injected hole.

Figure 6.

The spin density surface of cationic complexes (NABs@C₆₀)⁺ with an isovalue of 0.004au. The numbers below each panel stand for the charge from ESP fitting and total spin density (in parentheses) in C₆₀ moiety.

The above spin density distribution scenario somehow agrees well with the IP difference between C₆₀ and NABs. The lager the IP difference, the higher the degree of the spin density delocalization over C₆₀. To obtain a more remarkable performance for NABs protection, it is therefore suggested to synthesize and utilize new fullerene derivatives that have a significant IP gap with guanine.

IP values for the complexes were also calculated, as defined below,

$$\text{IP}(\text{NAB}@{\text{C}}_{60})=E{(\text{NAB}@{\text{C}}_{60})}^{+}-E(\text{NAB}@{\text{C}}_{60})$$ (7)

Combination of equations (4), (6) and (7), results in,

$$\text{IP}(\text{NAB}@{\text{C}}_{60})=({E_{\text{b}}}^{+}-E_{\text{b}})+\text{IP}({\text{C}}_{60})$$ (8)

Binding energies of the cationic systems (E_b⁺) are much more negative than their corresponding neutral systems (E_b). Thus, IP of the complex is smaller than C₆₀ as well as NABs. As shown in Figure 7, the discrepancies between IPs of four NAB@C₆₀ complexes are smaller than those of four NABs. These observations indicate that the binding of NABs with C₆₀ can reduce the IP of whole system by sharing the hole as possible, leading NAB@C₆₀ to promising hole carriers or relays for the long-range charge migration. Further, the trend of IPs for NAB@C₆₀ is also different from that for the isolated NAB molecules. For the NAB@C₆₀ complexes, A@C₆₀ has larger IP than C@C₆₀, which is opposite to the isolated NAB (IP(C) > IP(A)). G@C₆₀ still has the lowest IP in the four complexes just as guanine in the four NABs. This implies that the NAB@C₆₀ carriers or relays of a hole are property-tunable via varying the base partners of C₆₀.

Figure 7.

Adiabatic IP values of the individual NABs and NABs@C₆₀ complexes in the gas phase at the PBE-D/cc-pVDZ level, while that of C₆₀ is 7.25eV.

Clearly, all above predictions are derived from the steady-state analysis on the properties of the NAB@C₆₀ complexes. However, some dynamics information are still unknown which hopefully provide the dynamic knowledge for a deep understanding of the interaction of the shortly-separated NABs and C₆₀ and their charge transfers. In addition, the protein surroundings and solvent molecules may yield considerable effects on the interaction modes between NABs and C₆₀, the charge transfer mechanism among them, and tunability of the carrier/relay properties of the NAB@C₆₀ complexes. Further investigations are certainly needed for a clarification of all these details.

4. Conclusions

In summary, geometric and electronic properties of NAB@C₆₀ and (NAB@C₆₀)⁺ were extensively investigated by the M05-2x, M06-2x and PBE-D methods. The binding strength sequence for the neutral complex NAB@C₆₀ varies with the applied theoretical methods. The M05-2x/6-311++G** provides the same binding sequence as previously reported by Shukla et al.,^11b guanine (G) > cytosine (C) > adenine (A) > thymine (T); however, the binding strengths of A and C are switched at the M06-2x level, resulting in the binding sequence, G > A > C > T. When dispersion force is explicitly included by the PBE-D method, the above sequence is further revised to, G>A>T>C, which is the same as the binding sequence of NABs with SWNTs, a graphene layer as well as a graphite surface,14a, 14c–d^{, 27} and also follows the sequence predicted by the London’s dispersion equation. The results indicate that the previous questionable relative binding strength is due to insufficient electron correlation treatment with the M05-2x. A comparison among the predicted binding energy with different methods for G@C₆₀ shows that PDE-D performs better than M06-2x. At both the M06-2x and PBE-D levels, the favorable conformation for (A@C₆₀)⁺, (G@C₆₀)⁺, and (T@C₆₀)⁺ is the π-stacked one; while for (C@C₆₀)⁺ the T-shaped σ-π conformation is more favorable. The frontier molecular orbital analysis reveals that when an electron escapes from the complexes, the hole dominantly localizes on C₆₀ for (C@C₆₀)⁺ and (T@C₆₀)⁺, while for (A@C₆₀)⁺ and (G@C₆₀)⁺ delocalizes over the entire complex. Thus, the presence of C₆₀ may well prevent C and T from radiation damage, while only partially protect A and G. It should be noted that protein surrounding and solvent effect could modify the binding modes and even the charge distributions, thus providing a possibility in regulating the interactions and charge exchange mechanism between the NABs and C₆₀ and competition among four NAB bases. This work is being expanded with great efforts in our co-laboratory.

Figure 1. Side- and top views of π-stacked NAB@C₆₀ complexes.

The dark, blue and red data are the nearest distance between non-hydrogen atom of NBA and C₆₀ with the M05-2x/6-311++G(d,p), M06-2x/6-311++G(d,p) and PBE-D/cc-pVDZ methods, respectively.