Radicalized DNA Bases through Ring-Expansion Modification: An

Article pubs.acs.org/JPCC

Radicalized DNA Bases through Ring-Expansion Modification: An Intriguing Class of Building Blocks for the Magnetic DNA Nanowires Li Han, Hongfang Yang, Jing Zhao, and Yuxiang Bu* The Center for Modeling & Simulation Chemistry, Institute of Theoretical Chemistry, Shandong University, Jinan, 250100, P. R. China S Supporting Information *

ABSTRACT: In the present work, cyclopentadienyl radicals are introduced to nucleobases to gain the building blocks of DNA-based molecular wires with novel electromagnetic characteristics. Calculations reveal that the radicalized DNA bases exist stably because their extended π-conjugated structures are beneficial to spin delocalization, diradical base pairs possess open-shell singlet ground states, and magnetic coupling interactions of the multiradical systems are controlled by both intraand intermolecular interactions. For the designed base pairs, the intra-base-pair magnetic interactions are weak, especially in the diradical rA−rT base pair; as for the inter-basepair magnetic interactions, different cases are observed depending on the relative position of the radicalized bases. The overlap-stacking diradical helices manifest variable degrees of ferromagnetic and antiferromagnetic characteristics, whereas the magnetic coupling interactions in the cross-stacking diradical helices are generally weak. The latter is attributed to the long spatial distances between the two spin centers. Thus, for the tetraradical helices, their magnetic characteristics can be viewed as a combination of two overlap-stacking diradical base pairs, and mostly are antiferromagnetic. This work provides a reasonable strategy of designing magnetic building blocks for the magnetic DNA molecular wires or DNA molecular magnets.

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INTRODUCTION In the search for molecular materials with new interesting properties, DNA molecules have become an intensively studied topic in the past and recent years.1−10 The most important molecular characteristic that makes DNA both attractive and successful for designing a wide variety of structures and devices resides in its molecular and submolecular recognition capabilities.2−9 These capabilities enable the construction of many different architectures via self-assembly.10 In particular, DNA can form a well ordered and fully controllable stacking structure of π-aromatic compounds by means of π-stacking between the bases, i.e., purine and pyrimidine bases, and hydrogen bonding with their complementary bases. These characteristics are rather difficult subjects to realize for other artificial polymeric materials. Thus, finding potential applications of DNA to nanoscience and nanotechnology has been one of the fascinating subjects of DNA at the present time because the one-dimensional π-stacked aromatic array formed in DNA seems to be advantageous for charge conduction11,12 and magnetic exchange. However, though the four natural bases work well in natural biological systems, they have limitations in further applications in biological detections and nanostructure materials:13 there are only four kinds of DNA nucleobases, so that there are only four series of ionization energetics; there are only two types of structural units in DNA because of the fixed pairing mode; the electric conductivity of DNA is still under discussion; and natural nucleobases and base pairs are nonmagnetic and nearly © 2012 American Chemical Society

nonfluorescent. Thus, to expand applications of the DNA-based molecular wires or assembled nanostructures to various possible functional devices, many efforts have been devoted to nucleobase modification and structure assembly which mainly include (i) modifying nucleobases by ring-expansion or metallization of base pairs to assign DNA building blocks specific properties such as optical, magnetic, and conductive properties14−17 and (ii) developing novel assembled structures including hybridization, incorporation of other nanoparticles, for example, metal clusters, etc.14 On the other hand, organic molecules which possess high spin states have received extensive attention because of their remarkable electronic and magnetic properties during the past several decades.18−24 A large amount of multiradical molecules have been studied theoretically and experimentally to provide theoretical guidance for synthesis of magnetic materials,23,24 and to explore magnetic exchange mechanisms. Among the multiradicals, diradicals,25 which are characterized by two unpaired electrons upon two different atomic centers, form the basis of high-spin materials.26 Usually, magnetic properties of multiradical molecules are determined by both intra- and intermolecular magnetic couplings, and the latter largely depends on the intermolecular interaction in their crystal structures.22,24 Appropriate modulation of the strength or the Received: June 20, 2012 Revised: September 22, 2012 Published: October 23, 2012 23214

dx.doi.org/10.1021/jp306099m | J. Phys. Chem. C 2012, 116, 23214−23223

The Journal of Physical Chemistry C

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relative strength of these intra- and intermolecular interactions can not only lead to transitions among ferromagnetic (FM), antiferromagnetic (AFM), and nonmagnetic properties for the magnetic molecules or units but also realize interconversion among single-molecule magnets and single-chain magnets, and bulk magnets in the magnetic materials structures.21,27 It has been evidenced that single-molecule magnets and single-chain magnets exhibit quantum magnetism and magnetic relaxation phenomena in contrast to bulk magnets.28 Structurally, singlemolecule magnets are composed of magnetically isolated molecules with large spin ground states and uniaxial magnetic anisotropy29 linked via ligands, segments, or special interactions that can mediate the magnetism, causing a higher spin ground state, while single-chain magnets are generally made up of onedimensional chain complexes with magnetic coupling along the chain and noncancellation of the uniaxial anisotropic spins. The chains should be as magnetically isolated as possible so that the magnetic interchain interactions are too weak to form stable three-dimensional magnetic structures.30 Usually, large counterions and bulky molecules are used to prepare single-chain magnets.31 By virtue of their structural characteristics, DNA molecules seem particularly suitable to fulfill the requirements to construct or prepare single-molecule magnets and single-chain magnets if their base pair units are all or partly replaced by radicalized base pairs or radical analogues. Clearly, since purine bases have low ionization potentials, photoionization or photoexcitation can produce radicals of purine bases.32 However, the resulting radicals by such a way are likely to form the hydrazine-like (N−N) bonds,33 which makes the identification of their radical characteristics difficult and even their radical characteristics disappeared through the radical− radical interaction. Thus, we must expect and find other radical structures for these DNA base pairs to realize magnetization of DNA molecules. Recently, we are inspired by two aspects of works to design radicalized motifs as building blocks of DNA molecules. First, two radicals can be stabilized by forming diradicals with improved magnetic properties through introducing linkages (e.g., conjugated systems, hydrogen bonds, etc.) to mediate their spin−spin coupling interactions or expand spin delocalization.21,27 Second, aromatic rings such as benzene, furan, pyrrole, pyridine, and so on, can be introduced into DNA bases, forming a new molecular class of DNA base analogues, the expanded bases (x-bases) and expanded DNA (x-DNA), with enhanced fluorescent and conductive properties. More importantly, this ring-expansion scheme has been proved to be readily realized experimentally.14−17 Thus, it is conceivable that a radical-modified base can be obtained if a five-membered ring of cyclopentadienyl radical is introduced to the bases instead of the benzene ring via a similar way. The produced radical base (r-base) increases three extra sp2 hybridized carbon atoms to participate in expanding the π-conjugation, forming a large conjugated base. The resulting structures are expected to be stable, since the π-conjugations in nucleobases are conducive for spin delocalization. More importantly, their Watson−Crick hydrogen bonding faces hold and can form radicalized base pairs with their complementary bases which could be expected to be as stable as the natural base pairs. Thus, with the aim of designing stable radicalized DNA bases, we extend the ring-expansion scheme through introducing cyclopentadienyl radicals into nucleobases for forming radicalized bases (Figure 1).14−17 Structural and radical

Figure 1. Schematic diagram of the radicalized bases through radicalring expansion. Mulliken atomic spin densities are annotated on the corresponding atoms.

characteristics are examined by geometrical optimizations, molecular dynamics simulations, and calculations of energies and magnetic properties for these r-bases and their base pairs and DNA helices. As expected, the magnetic characteristics are controlled by both intra- and inter-base-pair interactions. The rbases can form stable radicalized base pairs with their complementary natural or radical bases. These base pairs are expected to possess the interbase magnetic couplings. Further double layer model examination indicates that interaction between adjacent radical base pairs could result in the layered diradical or tetraradical structures. Our calculations reveal that the radicalized base pairs possess open-shell ground states and the intra-base-pair magnetic interactions are weak. However, for multiradical model helices, the inter-base-pair magnetic coupling is stronger than the intra-base-pair one, exhibiting excellent characteristics for promising application in the magnetic DNA molecular wires or molecular magnets. The main objective of this work is to understand the magnetic characteristics of radicalized base pairs and helices, and then provide a theoretical basis for designing a new class of DNA building blocks with tunable magnetic properties.

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METHOD OF CALCULATIONS Calculations are performed on r-bases to obtain a comprehensive understanding of their structural, electronic, and magnetic properties using the Gaussian 09 package. 34 Geometry optimizations and energy calculations of r-bases and multiradical helices are performed at the unrestricted spin polarized theory level (UB3LYP) with a 6-311++G** basis set. The CASSCF approach is employed to determine the relative energies for comparison.27,41 The broken symmetry unrestricted formalism is introduced to reveal the magnetic interactions of them.35 Molecular dynamics (MD) simulations are performed to get the structural parameters of the radicalintroduced helices.36,37 The multiradical two-layer helices are rebuilt38 with the optimized r-bases according to these structural parameters. Considering the defect of the B3LYP method when dealing with π−π interaction,39 the M06-2x method40 which has been developed by Truhlar et al. is employed to investigate the multiradical introduced helices. The CASSCF calculations are performed on multiradical helices, too. All these calculations are performed with the CASSCF method at a 6-31+G* basis set level. More details of 23215



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Supporting Information), we can draw a conclusion that the spin density is delocalized and represents a trend to diffuse to the adjacent six-memberred ring in rG, while that is mainly localized on the extra five-membered ring in rA. This difference should be attributed to the fact that there are three hetero atoms which contribute to π-conjugation in the Watson−Crick (WC) face of rG, while there are only two hetero atoms in rA. Compared with the hydrogen atom in rA, the amino group which is connected to the C2 atom in rG is obviously more conducive to the spin delocalization. Another prerequisite for r-bases to assemble an electromagnetic wire is that they should form stable base pairs with their counterparts. Though an extra cyclopentadiene radical is introduced to each nucleobase, the WC face of it is hardly affected. It can be predicted that the pairing abilities of r-bases remain. This hypothesis is verified by binding energies. Binding energies of the natural and radical base pairs are shown in Figure 2 (see Table S2, Supporting Information, for details)

calculation and MD simulation can be found in the Supporting Information. Magnetic exchange interactions between two spin centers can be described by the Heisenberg−Dirac−van Vleck Hamiltonian

Ĥ = −2JSâ S b̂

(1)

where Sâ and Ŝb refer to the two spin operators of two magnetic centers a and b, respectively.42 The positive and negative values of the exchange coupling parameter (J) indicate ferromagnetic (FM) and antiferromagnetic (AFM) interaction between the two unpaired electrons. The J value can be determined by the energies of the singlet and high-spin (HS) state of magnetic molecules, since they are two eigenstates of the Heisenberg Hamiltonian. However, a pure open-shell singlet of diradical molecules is difficult to determine even with an unrestricted method. Thus, a broken symmetry (BS) unrestricted formalism has been developed by Noodleman to describe the weak coupling systems.35 In this work, a modified version of the BS formalism raised by Yamaguchi et al.43 has been introduced to estimate the J value. J=−

E HS − E BS 2 ⟨S ̂ ⟩HS − ⟨S ̂ ⟩BS 2

(2)

where EHS and EBS refer to energies of the high-spin and singlet state, respectively. ⟨Ŝ2⟩ refers to average spin square values for different spin states. The difference values are expected to be around 1.0 for diradical molecules, since the triplet state is the high-spin state.

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RESULTS AND DISCUSSION 1. Structural and Electronic Properties of RingExpanded Radical Bases. Schematic diagrams of four ringexpanded radical bases (r-bases) are shown in Figure 1. They are proved stable by the optimization and frequency calculation (Figure S1 and Table S1, Supporting Information). It can be seen that the most significant change brought by the introduction of cyclopentadienyl radical is an expansion of molecular size. Besides this, the structural character is hardly affected. The bond length differences between r-bases and the natural ones are no more than 0.02 Å. Excepting that the amino group on rG represents a trend of pyramid which led to slight nonplanarity of the whole molecule, the other three r-bases remained planar basically, and those are similar to structural characteristics of the corresponding natural bases. Bond lengths of the extra cyclopentadiene are shown in Table S1 (Supporting Information), too. We can seen that the bond lengths are around 1.40 Å, which are between those of C−C single bond (1.55 Å) and CC double bond (1.34 Å). That is, the extra cyclopentadiene demonstrates a certain degree of aromaticity and the conjugated system has been enlarged by the introduction of cyclopentadienyl radical. The dominating distribution of spin density on four r-bases is shown in Figure 1, too. In all four kinds of r-bases, the Mulliken atomic spin densities distribute mainly on the carbon atoms of the extra cyclopentadiene toward the major groove of bases. In r-purine bases, the spin density distributing on this carbon is more than 0.50, while the number is about 0.39 in r-pyrimidine base. The rest of the spin density distributes mainly on meta carbon and other atoms which have π−π conjugation with these carbon atoms. Taking the spin density distribution maps of rG and rA for comparison (see Figure 1 and Figure S1,

Figure 2. Binding energies of the natural and radicalized bases with their complementary bases. Binding energies of the natural G−C and A−T pairs are represented with the two horizontal dashes. The binding energies of both the natural bases and r-bases are obtained at the B3LYP/6-311++G** level of theory, while those for x-bases and nbases are obtained at the B3LYP/6-311++G**//B3LYP/6-311+G* level of theory.

together with those of x-base and hetero-ring-expanded bases (n-base). The binding energies of the natural G−C and A−T base pairs are −24.74 and −11.93 kcal mol−1, respectively. The binding energy differences between the natural base pairs and xbase pairs, which have been experimentally synthesized and proved stable, range from −1.58 to 0.27 kcal mol−1, indicating that the base pairs formed by the x-bases have almost equivalent binding energies with the natural base pairs. Similarly, the nbases reported in our previous work have also been proved to be able to pair with the corresponding natural counterparts and to form stable DNA-like helices. The binding energies between the n-bases and their natural counterparts are almost equivalent to those of natural pairs. In comparison, binding energies of rG−C, rA−T, and A−rT are −25.54, −12.05, and −12.03 kcal mol−1, respectively, which are larger than those of natural ones. For the G−rC pair, the binding energy is −24.11 kcal mol−1, which is 0.63 kcal mol−1 lower than that of G−C. Despite that, the rC base is still expected to combine with G to form a stable base pair, since the binding energy difference is smaller than that of xG−C, which has been proved stable by both theoretical and experimental approaches.14−16 In a word, all four r-bases 23216



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electronic structure. Either getting or losing an electron leads to an open-shell electronic structure with a single electron. However, for rG, the introduction of a five-membered ring radical into G not only leads to considerable energy level shifts of the HOMO and/or the LUMO, narrowing the HOMO− LUMO gap, but also, more importantly, yields an open-shell electronic structure with a singly occupied molecular orbital (SOMO). Both its cationic and anionic structures possess stable doubly occupied closed-shell electronic configurations which clearly favor the stabilization of the system. Further, the SOMO of rG is considerably higher than the HOMO of G but considerably lower than its LUMO. Clearly, such an alignment of the SOMO of rG relative to the HOMO and LUMO of G makes the rG base oxidized and electron-bound more easily than G. Similar trends for the other three bases are also observed. In short, expansion of these bases using a fivemembered-ring radical leads to a large change in the electronic structure. As a result, the energy levels of the HOMO and the LUMO considerably shift, while IPs are reduced and EAs are increased. 2. Spin States and Intra-Base-Pair Magnetic Interactions in Diradical Base Pairs. The optimized structures of open-shell singlet and triplet states of diradical base pairs are shown in Figure S2 (Supporting Information). It can be seen that the geometries of these two spin states are of little difference. The relative energies of singlet and triplet diradical base pairs, which are calculated by both DFT and CASSCF approaches, are given in Table 1. For rG−rC, the energy of a singlet is a bit lower than that of a triplet. The spin contamination is 1.0, which clearly indicates that the openshell singlet state is a mixture of the pure singlet (⟨S2⟩ = 0.0) and triplet state (⟨S2⟩ = 2.0). In summary, the rG−rC base pair possesses a ground state of open-shell singlet. For rA−rT, energies of open-shell singlet and triplet states are very close to each other according to both calculation methods. This shows that the spin states of the two unpaired electrons cause little effect on each other. In other words, the magnetic exchange interaction between the two radicals in the rA−rT pair is even weaker than that in the rG−rC pair, which is consistent with the fact that the spin density is more delocalized in the latter base pair. There is no doubt that the ground states of the natural base pairs are closed-shell singlet states, whereas, as is discussed above, both of the two diradical base pairs possess open-shell ground states. We present the geometric structures of these two states in Figure 5 for comparison. The covalent and hydrogen bond lengths of the natural base pairs are labeled here as a reference. The increase or reduction of these bond lengths in

are able to bind with their counterparts to form stable base pairs and then can act as the building blocks of DNA helices. Electronic properties of r-bases are determined by means of ionization potentials (IPs) and electron affinities (EAs). The IPs and EAs are calculated with the formula which is widely used to deal with nucleobases.44,45 The results are represented in Figure 3. The adiabatic IPs (AIPs) of four nucleobases are

Figure 3. The adiabatic and vertical ionization potentials (AIP, VIP) and electron affinities (AEA, VEA) of the natural and radical bases. The lengths of the arrows refer to the differences of the corresponding quantities.

about 7.68−8.81 eV with an order of G < A < C < T. These data are well consistent with previous theoretical and experimental studies.46,47 This shows that the theoretical method which has been employed in this work is credible. The vertical IPs (VIPs) of the four bases are 0.13−0.34 eV larger than AIPs, which appear to be reasonable, too. Figure 3 also reveals that both AIPs and VIPs are reduced by around 1.00 eV due to the introduction of the cyclopentadienyl radical. Meanwhile, it is noteworthy that the IP order of rG < rA < rC < rT is the same as that of the natural bases. The adiabatic electron affinity (AEA) values of the natural nucleobases range from −0.33 to 0.01 eV, which are basically consistent with the reported data, too.46 Both the AEA and VEA values are increased by about 2 eV thanks to the introduction of radicals. That is, r-bases can capture electrons more easily. Clearly, the changes of redox properties should be attributed to different electronic structures between the natural and radicalized bases. Taking the rG base as an example, its electronic structures together with those of the corresponding G base upon capturing and removing of an electron are given in Figure 4. As shown in Figure 4, G possesses a closed-shell

Figure 4. The frontier orbitals with the corresponding occupations of the neutral, cationic, and anionic G and rG bases. The subscript (v) denotes the vertical adding or removing of an electron. 23217



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Table 1. Calculated Relative Energies (ΔE, kcal mol−1) of Open-Shell Singlet (BS) and Triplet (T) States and the Magnetic Exchange Coupling Constants (J, cm−1) of the Diradicalized Base Pairs (BP)a

a

method

BP

ΔEBS

ΔET

J

BP

ΔEBS

ΔET

J

UB3LYP/6-311++G** CASSCF(8,8)/6-31+G*

rG−rC rG−rC

0 0

0.07 5.0 × 10−3

−24.39 −1.71

rA−rT rA−rT

0 0

1.4 × 10−4 −3.1 × 10−4

−0.04 0.11

Both the UB3LYP and CASSCF methods are employed for comparison.

Figure 5. Optimized geometries with the corresponding bond lengths (Å) for the natural base pairs (a and c). Optimized geometries of open-shell singlet diradical base pairs (b and d) with the corresponding bond length differences between the diradical and natural base pairs. The red numbers mean the increments, while the blue ones denote decrements compared with the bond lengths of the native base pairs in (a) and (c).

the diradical base pairs is distinguished with red or blue numbers, respectively. It is noteworthy that almost all the double bonds are elongated while the single ones are shortened. That is, the aromaticity of the base pair is enhanced and the conjugated system is enlarged by the cyclopentadienyl radical ring insertion. All three WC hydrogen bond lengths are reduced in rG−rC, while only one hydrogen bond length is reduced in rA−rT. This observation can explain the phenomenon that the interaction between the two radicals is stronger in rG−rC than that in rA−rT. Figure 5 also reveals that there are no qualitative changes on the spin density distribution of the diradical base pairs compared with r-bases. The spin distribution of diradical is still more delocalized in rG−rC than in rA−rT. Binding energies of rG−rC and rA−rT can be found in Figure 2, which are 0.20 and 0.21 kcal mol−1 larger than those of the natural base pairs, respectively. These ensure structural stabilities of the diradical base pairs. It is known that the hydrogen bonding interaction between nucleobases can be measured rapidly by determination of the inter-residue coupling constant (JNN). Considering that the coupling effect of hydrogen bond is very sensitive to electron distribution,48 the JNN value is bound to be affected by the introduction of a radical. Thus, the JNN values of rG−rC and rA−rT are calculated (Table 2). The calculated JNN of the natural A−T base pair is larger than that of the natural G−C by 0.8 Hz, which is consistent with previous investigation.49 The JNN values of xG−xC and xA−xT are larger than those of the natural base pairs, especially the latter. The situation is similar for diradicalized base pairs. The JNN value of rG−rC is enlarged much more than that of rA−rT, which is also consistent with the results of hydrogen bond length.

Table 2. The Spin−Spin Coupling Constants (JNN, Hz) of the N−H···N Hydrogen Bonds in the WC Hydrogen Bond Zones of the Base Pairs Obtained at the B3LYP/6-311+ +G** Level JNN hydrogen bonds G−C A−T

N−H···N N···H−N

natural BP

x-BP

r-BP

2.58 3.42

2.59 3.58

3.03 3.44

Once the open-shell states are demonstrated to be the ground states of rG−rC and rA−rT, the diradical character which may introduce novel electromagnetic properties should be clarified.50 The CASSCF (8, 8) calculations are preformed on the diradical base pairs to obtain the orbital occupation numbers, which are widely used as indices of diradical character. The occupation numbers of the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) are presented in Table S5 (Supporting Information). The LUMO occupation numbers of rG−rC and rA−rT are 0.984 (⟨S2⟩ = 1.006) and 0.998 (⟨S2⟩ = 1.023), which indicates that the amounts of diradical character are estimated to be 98.4 and 99.8%, respectively.27,41 These results verify the above conclusion that these base pairs possess significant diradical character. To gain an insight of diradical character, the frontier orbitals and spin density distributions of rG−rC and rA−rT are shown in Figure 6. The diradical character can be represented intuitively with the singly occupied molecular orbitals (SOMO) and spin density distribution. It can be seen that the two unpaired electrons are basically localized on the two cyclopentadienyl radical rings separately. The spin density 23218



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Figure 6. The SOMOs and spin density maps for the BS states of the diradical base pairs.

and rG−rC are closed-shell and open-shell singlet, respectively. The situation for the A−T pair is basically the same. The HOMO−LUMO gap reduces from 4.75 to 0.36 eV due to the introduction of radicals. One electron is excited from the HOMO to LUMO, and these two orbitals reorganize to form two lower SOMOs. The magnetic exchange coupling constant (J) was also determined to measure the intra-base-pair interaction of the two unpaired electrons. As shown in Table 1, for the rG−rC base pair, the energy of singlet is lower than that of triplet according to both calculation methods, which indicates slight AFM character. As for the rA−rT base pair, the energy differences between singlet and triplet are quite small, which demonstrates that the interaction between two spin centers is very weak. In short, the intra-base-pair magnetic coupling is relatively weak in both rG−rC and rA−rT, especially in rA−rT. 3. Inter-Base-Pair Magnetic Exchange Interactions in Multi-Radical Helices. Although the magnetic exchange interaction between the two r-bases in rG−rC and rA−rT, especially in the latter, is weak, the inter-base-pair interaction cannot be ignored. DNA possesses crystal structure of onedimensional chain, in which the base pairs are stacked via π−π conjugation. In that system, the intermolecular magnetic coupling is expected to be stronger than the intramolecular interaction. Therefore, the magnetic exchange interactions of two-layer structures, which are composed of radicalized base pairs, are discussed here. Since there are no relevant experimental data yet, the classical MD simulations are employed to gain the structural parameters of multiradicalized helices. The results of MD simulations indicate that the multiradicalized helices are stable, since the root-mean-square deviations (RMSD) tend to be constant in the latter part of simulations (Figure S3, Supporting Information). Average structures and the pairing/stacking parameters of these helices are given in the Supporting Information (Figure S4 and Table S6). The rise and twist parameters are two important ones which considerably affect the π−π interaction between the base pairs in DNA helices.41 The rises of r-DNA (3.19−3.37 Å) are smaller than that of the standard B-DNA (about 3.4 Å). And the twist angles of r-DNA range from 22.7 to 27.1°, which are considerably smaller than that of B-DNA (about 36°). Considerable variations of these two parameters implicate stronger interaction between the base pairs in r-DNA than in the natural ones. In addition, the differences of the C1−C1 distance between the r-base pairs and the natural ones are no more than 0.5 Å, which does not threaten the possibility for r-bases to form stable helices because of the flexibility of the DNA backbone.15e All of these two-layer multiradicalized helices discussed below are rebuilt with optimized r-bases according to these parameters. The 46

distributes on both fragments of diradical base pairs, and the spin orientations are opposite. These clearly indicate the diradical character of the open-shell singlet. To reveal the essence of the fact that the open-shell states are far more stable than the closed-shell states, the HOMO−LUMO gaps of the natural and diradical base pairs are determined and shown in Figure 7, the HOMO−LUMO gap of G−C is 3.80 eV, while

Figure 7. Molecular orbital energy levels of the natural and diradical G−C (a) and A−T (b) base pairs. The HOMO−LUMO gaps of the natural and closed-shell diradicals are labeled, and the frontier orbital contours are also represented here.

that of rG−rC sharply reduces to 0.44 eV. This induces a possibility for an electron to promote from HOMO to LUMO. The orbital shapes of the HOMO and LUMO of the CS state and the SOMOs of the open-shell state are shown in Figure 7, too. It indicates that the SOMOs, which originate from a mixture of HOMO and LUMO, obviously stabilized the system. This explains the fact that the ground states of G−C 23219



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centers, which are verified by the calculated energies and magnetic coupling constants. Helices in this group possess ground states of open-shell singlet. Also, the energy differences between singlet and triplet are very large, which indicates strong couplings between the two radicals. The calculated J values are very large, which indicates obvious AFM properties. In summary, r-purine-formed diradical helices possess slight FM character, since the ground states of these diradical structures are the triplet states. In contrast, three other series of overlap-stacking diradical helices possess open-shell singlet ground states, which lead to their AFM character. Among these groups, the magnetic exchange interactions in the 3′-rPu/5′-rPy mode are the weakest, while those in the 3′-rPy/5′-rPu mode are the strongest. As shown in Figure 9, the magnetic interactions strongly depend on the stacking mode of the two radicalized bases.

multiradical helices are divided into three series, and a schematic diagram is shown in Figure 8. Radical characteristics and energies of different spin states of these structures are discussed below.

Figure 8. Schematic diagram of the multiradical two-layer stacking model for a helix. Taking the overlap-stacking diradical (left one) as an example, it is named rB1-B2/rB3-B4, while B1−B4 refer to four nucleobases (natural or radical) in a two-layer stacking model.

3.1. Overlap-Stacking Diradical Helices. The overlapstacking helices can be divided into four groups according to the relative positions and types of the two r-bases in two adjacent layers of DNA helix as 3′-r-purine/5′-r-purine (3′-rPu/ 5′-rPu), 3′-r-pyrimidine/5′-r-pyrimidine (3′-rPy/5′-rPy), 3′-rpurine-5′-r-pyrimidine (3′-rPu/5′-rPy), and 3′-r-pyrimidine-5′r-purine (3′-rPy/5′-rPu). The common characteristic of these stacking modes is that two radical bases are in the same strand of a helix. 3′-rPu/5′-rPu Diradical Helices. For this type of stacking mode, the two spin centers are moderately spaced and have certain degrees of interaction. The energies of triplet states are lower than those of singlets, which result in ground states of open-shell triplet. According to the J values (Table S7, Supporting Information), the four structures in this group are ferromagnetic. However, because the energy differences between singlet and triplet are small, the J values are relatively small, which range from 16.38 to 108.33 cm−1. In a word, the overlap stacking r-purine diradical helices represent weak FM character. 3′-rPy/5′-rPy Diradical Helices. The situation is different when the radicalized pyrimidine bases are introduced to the helices. In this group, the ground states are open-shell singlets. The energy differences between singlet and triplet are 0.54− 0.96 kcal mol−1 according to DFT results and 0.38−0.94 kcal mol−1 according to CASSCF results. The magnetic coupling constants range from −184.8 to −326.4 cm−1 according to DFT results and −132.1 to −317.7 cm−1 according to CASSCF results, which clearly indicates the AFM character of these four helices. 3′-rPu/5′-rPy Diradical Helices. In this group, the energies of open-shell singlet are also lower than those of triplet state. However, the energy differences between these two open-shell states are no more than 0.05 kcal mol−1, which are smaller than those in the other three groups. Accordingly, the absolute values of J are the smallest, too. In other word, the magnetic interaction between the two unpaired electrons is very weak. This is due to large spatial separations between the two radical centers in these four helices. The two cyclopentadienyl radical rings are far apart from each other (Figure S7, Supporting Information) so that the interactions between them are weak. 3′-rPy/5′-rPu Diradical Helices. Interestingly, the cyclopentadienyl radicals in these four helices are well overlapped (Figure S8, Supporting Information). Thus, one can expect relatively strong magnetic interactions between the two spin

Figure 9. Calculated inter-base-pair magnetic exchange coupling constants (J) for the overlap stacking diradical two-layer helices. Both the UB3LYP and CASSCF results are given for comparison.

3.2. Cross-Stacking Diradical Helices. The cross-stacking diradical helices can be divided into six groups in the same way mentioned above, which include 3′-rPu/3′-rPu, 5′-rPu/5′-rPu, 3′-rPy/3′-rPy, 5′-rPy/5′-rPy, 3′-rPu/3′-rPy, and 5′-rPy/5′-rPu helices. The common structural characteristic is that the two radical centers are located at two strands of a helix. The relative energies of open-shell singlet and triplet states of all structures in this series and SOMO and spin density maps are given in the Supporting Information (Table S9, Figure S9−S14). 3′-rPu/3′-rPu Diradical Helices. In this group, the purine bases are radicalized, and they are crosswise stacked so that the interaction between the two spin centers is inhibited by a large spatial separation. The scanty interactions between the two spin electrons are attributed to the tendency of the spin density distribution to spread to the six-membered ring toward the Watson−Crick face. In this group, the energies of singlets are a little lower than those of triplet states, which indicate that the two electrons prefer to distribute separately with opposite spin directions (Figure S9, Supporting Information). The calculated spin contaminations and the occupation numbers of the HOMO and LUMO further confirm that these three helices possess ground states of open-shell singlet. Unfortunately, the energy differences between open-shell singlet and triplet are very small; thus, the interactions between the two radicals are relatively weak, as evidenced by small J values which range from 23220



Article

Figure 10. The SOMOs and spin density map for the BS state of the tetraradical rG−rC/rG−rC helix.

−5.2 to −24.3 cm−1 according to the DFT method and −3.5 to −60.8 cm−1 according to the CASSCF method. Other Five Series of Cross-Stacking Diradical Helices. In the remaining five groups, the orbital occupation numbers of HOMO and LUMO are very close to 1.00 according to the CASSCF calculations, which imply that the structures in these five groups exhibit significant diradical features. However, the energy differences between the two open-shell states are very small, which indicate that these two spin electrons basically have no effect on each other. Thus, the magnetic coupling constants are approximately equal to zero according to both the DFT and CASSCF method. In a word, owing to long special distances between the two spin centers, the magnetic interactions can be ignored in most cross-stacking diradical helices. 3.3. Tetraradical Helices. Structures which are built with four r-bases are expected to possess four spin centers (Figure 8), and their intermolecular magnetic interactions are expected to be more complicated. These tetraradical helices can be divided into three groups according to different stacking modes as the overlap-stacking (3′-rPu/5′-rPu versus 3′-rPy/5′-rPy), 3′-r-purine/5′-r-pyrimidine (3′-rPu/5′-rPy), and 3′-r-pyrimidine/5′-r-purine (3′-rPy/5′-rPu). As discussed above, the interactions between the two cross-stacked radicals can be neglected, and thus, the interaction in a tetraradical model can be viewed as a combination of the interactions of two overlapstacked diradicals. There are several possible spin states of tetraradical helices, which are open-shell singlet (BS), triplet (T), and quintet (Q). We determined spin characteristics and relative energies of these spin states for tetraradical helices. The relative energy results indicate that most tetraradical helices possess ground states of open-shell singlet (except that energies of singlet and triplet are of the same in several structures, Table S11, Supporting Information). Therefore, a representative tetraradical structure, rG−rC/rG−rC helix, is shown in Figure 10. It can be seen from the SOMOs and spin density map that the spin density localized on four r-bases separately. And the situations of other tetraradical helices are about the same. Overlap-Stacking Tetraradical Helices. In this group, the four helices exhibit different degrees of tetraradical character according to the CASSCF results (Table S12, Supporting Information). The tetraradical interaction can be viewed as a combination of diradical interactions of the r-purine and rpyrimidine diradical helices. The energy order for different spin states is EBS < ET < EQ (Table S13, Supporting Information). Thus, the open-shell singlet is the ground state for all the tetraradical helices in this group. 3′-rPu/5′-rPy Tetraradical Helices. The tetraradical structures in this group can be considered to be two overlap-stacked diradicals with the stacking mode of 3′-rPu/5′-rPy. According to the CASSCF calculational results, the orbital occupation

numbers of HOMO-1, HOMO, LUMO, and LUMO+1 of the relevant three structures are very close to 1.00 (Table S14, Supporting Information), which clearly indicates a perfect tetraradical character. Furthermore, the energy differences between open-shell singlet and high spin states are very small (EBS ∼ ET < EQ). This implies that the magnetic coupling between the four spin centers is very weak. This is well consistent with the results of 3′-rPu/5′-rPy diradical helices. 3′-rPy/5′-rPu Tetraradical Helices. The CASSCF calculational results (Table S12, Supporting Information) and spin density distributions (Figure S17, Supporting Information) indicate a tetraradical character of the relevant three structures in this group. The energy order of different spin states is BS < T < Q, and the energy differences between singlet and high spin states are relatively large. The ground states of these tetraradical structures are open-shell singlets, which is consistent with the results of the 3′-rPy/5′-rPu diradical helices. In a word, the two-layer base pairs which are composed of four r-bases exhibit different degrees of tetraradical character. The interaction of four radical centers (four r-bases) can be viewed as a combination of two overlap-stacked diradicals. Generally, the ground states of these tetraradical helices are open-shell singlet, which indicate AFM character. 3.4. Implications. The above results indicate that a cyclopentadienyl radical inserted into a purine base or fused to a pyrimidine base, leading to an r-base, can yield a corresponding nucleobase−based molecular magnet. Such magnetic nucleobase units possess two noticeable characteristics: delocalized π-type spin distribution and the Watson− Crick hydrogen-bond face, and thus are a class of promising magnetic units for applications. By virtue of the well-structured one-dimensional framework of DNA, one can utilize these rbases to assemble various magnetic DNA structures. As is known, in the assembly, if the interaction between two radicals is stronger, the radical moieties can effectively bind together, forming a stable closed-shell ground state even with a chemical bond between them, and thus the system does not exhibit any magnetic properties. Undoubtedly, mild interaction between the radicals may lead to tunable magnetic properties depending on their relative position. Thus, finding a suitable binding mode is the prerequisite to realize effective assembly of the magnetic materials and devices. Fortunately, DNA provides a promising structural framework for the magnetic material design. In DNA, two bases are hydrogen-bonded in a base pair with a considerable separation, while the separation between two adjacent layers is about 3.4 Å, a very suitable distance for yielding weak interaction between two adjacent base pairs. Our calculated results indicate that, if the r-bases, their base pairs, or even their two-layer stacks are put into the DNA helices, they can interact weakly with different degrees depending on the relative position of such r-bases in DNA. Thus, such r-base23221


The Journal of Physical Chemistry C assembled DNA helices could exhibit rich and tunable magnetic properties. According to the above results, we can expect the realization of the following possible magnetic assemblages:51 (1) If nonadjacent natural bases or base pairs are replaced by rbases or diradical base pairs, the produced mixed DNA helices certainly act as single molecular magnets. (2) For the monoradical base pairs, the mixed base pair formed by an rbase and a natural base, they can be used to assemble single molecular magnets via a complete cross-stacking mode, or single chain magnets via a complete overlap-stacking mode because the magnetic coupling interaction among the magnetic units is zero in the former while that has tunable nonzero values through changing the DNA sequence. (3) For the diradical base pairs, they could assemble the coupled double chain magnets. As an extension, the mixing assembly of different short monoradical/diradical DNA helices with the natural helices can yield various complicated magnetic assemblages. We believe these weakly interacted radical base pair structures have important implications. Certainly, the magnetic properties and magnetization mechanism of such DNA-based magnetic structures need further investigation.

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ASSOCIATED CONTENT

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AUTHOR INFORMATION

Article

S Supporting Information *

Computational detail and calculated data and figures including geometric parameters, binding energies, IPs and EAs of r-bases, frontier orbital energies and corresponding energy gaps of rbases; geometric parameters, energy order and CASSCF results of the diradicalized base pairs; energy order, CASSCF results and SOMOs and spin density map of multiradical helices and other. This material is available free of charge via the Internet at http://pubs.acs.org. Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by NSFC (20633060, 20973101), NCET, and Independent Innovation Foundation of Shandong University (2009JC020). A part of the calculations were carried out at Shanghai Supercomputer Center, High-Performance Supercomputer Center at SDU, and High-Performance Computational Platform at SDU-Chem.

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CONCLUSIONS In this work, the cyclopentadienyl radicals are introduced into nucleobases to get radicalized ones (r-bases) through a similar modification strategy of x-bases. The resulting r-bases are utilized as spin sources to form multiradical base pair systems. The r-bases are able to combine with their counterparts to form radicalized base pairs, which are as stable as natural ones. However, as is manifested by the variation of IPs and EAs, the r-bases appear to be more redox sensitive. The J−J couplings between two N atoms in a Watson−Crick hydrogen bond are slightly enhanced due to additional interbase interactions. It is proved by unrestricted DFT and CASSCF calculations that all the diradicalized base pairs possess ground states of open-shell states. Since the HOMO−LUMO gaps are drastically reduced due to the introduction of a cyclopentadienyl radical, the electrons are easily excited from HOMO to LUMO. Furthermore, these two orbitals tend to recombine to generate two lower SOMOs to reduce the energies of systems through possible structural reorganization. Thus, the open-shell states of the diradical base pairs are much more stable than the closedshell ones. However, the intra-base-pair magnetic interactions are relatively weak due to large spatial separations of the two spin centers, which are evidenced by their small magnetic coupling constants. For the inter-base-pair magnetic couplings, calculations on the radicalized two-layer models reveal different multiradical characteristics and magnetic properties. The overlap-stacking diradical helices manifest variable degrees of FM and AFM character. However, in the cross-stacking diradical helices, spatial distances of the two spin centers are too large to yield effective magnetic couplings. Since the magnetic interactions of the cross-stacking diradicals are negligible, the magnetic character of the tetraradical helices can be viewed as a combination of two overlap-stacking diradicals, and most of them exhibit AFM character. This work provides a theoretical basis for designing magnetic DNA molecular wires with tunable magnetic properties, and presents the impetus for further experimental tests and continued theoretical exploration.

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REFERENCES

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Radicalized DNA Bases through Ring-Expansion Modification: An

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