Comparative investigation of uridine and Hachimoji RNA base interaction with single-walled carbon nanotube

Abstract

Context

Single-walled carbon nanotubes (SWCNTs) are promising platforms for biosensing because their electronic properties are sensitive to molecular adsorption. While canonical nucleic acid bases have been extensively studied, little is known about how synthetic Hachimoji bases interact with nanotube surfaces. In this study, we investigate the adsorption of uridine (rU) and the Hachimoji base S (rS) on a finite (5,5) SWCNT fragment. The study aims to compare binding strength and electronic effects between canonical and synthetic bases within a finite gas-phase SWCNT model and to examine whether the two bases show distinguishable local adsorption behavior.

Methods

All geometries of the isolated molecules and the SWCNT+rU and SWCNT+rS complexes were fully optimized using density functional theory (DFT) with the PBEh-3c composite method in ORCA. The adsorption complexes were analyzed on an 8 Å hydrogen-terminated (5,5) SWCNT fragment, with the bases initially placed approximately parallel to the nanotube sidewall at ~ 3.1 Å. HOMO-LUMO gaps were calculated for each system: rU (~ 7.5 eV), rS (~ 7.7 eV), SWCNT (~ 3.21 eV), SWCNT + rU (~ 3.19 eV), and SWCNT + rS (~ 3.20 eV). Interaction energies of the optimized complexes were computed using the supermolecule approach, yielding − 0.43364 eV for SWCNT+rU and − 0.55405 eV for SWCNT + rS. Mulliken population analysis was performed to quantify fragment charge redistribution, showing only minor net charge transfer.

Supplementary Information

The online version contains supplementary material available at 10.1007/s00894-026-06726-3.

Introduction

Single-walled carbon nanotubes (SWCNTs) have attracted wide attention as building blocks for nanoscale electronics and biosensors due to their electronic and photonic properties [1–5]. Multiple studies have shown that SWCNTs interact with nucleobases mainly through π-π stacking [6–8]. The strength and nature of these interactions depend sensitively on several factors such as the chirality of the nanotube [9], on whether the tube is pristine or functionalized [10], and on the sequence of the nucleobase [11]. Understanding how individual bases interact with carbon nanotubes is therefore a key step toward rational design of nanotube-based biomolecular devices.

Most previous theoretical work has focused on the four natural DNA/RNA bases: adenine (A), guanine (G), cytosine (C), and thymine (T)/uracil (U). Several DFT studies on the interaction between nucleobases and SWCNTs have found that dispersion and π-π stacking are the main driving forces, with binding energies of about 0.2–0.6 eV [11–13]. Multiple studies have shown that non-canonical DNA/RNA interacts differently with materials than canonical counterparts [14, 15]. These findings suggest that artificial or non-canonical nucleobases may provide additional ways to tune nanotube-nucleic-acid interactions.

Synthetic biology has introduced expanded genetic alphabets such as the Hachimoji DNA/RNA system, which uses eight letters (A, T/U, G, C, B, S, P, and Z) forming four orthogonal base pairs while preserving a double-helical structure [16]. Hachimoji nucleic acids have been proposed for applications ranging from information storage [17, 18] and drug design [19–21] to nanobioelectronics [22–24]. However, very little is known about how these synthetic bases interact with nanostructured materials such as carbon nanotubes.

Recent work has begun to explore the interfacial behavior of Hachimoji DNA. Babar et al. analyzed how different Hachimoji bases influence the optical response of MoS₂ monolayers and demonstrated that the B and P bases can be distinguished by their adsorption-induced changes in electronic structure [22]. Quantum-chemical studies have also examined the ionization potentials and charge-transport characteristics of isolated Hachimoji nucleobases, highlighting systematic differences from the natural bases that could influence their interactions with conductive substrates [25]. To our knowledge, no previous DFT study has compared the adsorption of a canonical base and its Hachimoji counterpart on a carbon nanotube.

From the computational side, realistic modeling of nucleobase-nanotube complexes requires methods that can describe dispersion, polarization, and charge transfer at moderate cost. Conventional hybrid functionals with large basis sets are often too expensive for systems containing tens to hundreds of atoms, while pure generalized-gradient approximations may underestimate binding energies and gaps. Composite “3c” approaches such as PBEh-3c, which combines a modified hybrid functional with a small tailored basis, an atom-pairwise dispersion correction and a geometric counterpoise term, have been developed to provide reliable structures and noncovalent interaction energies for large molecules at low cost [26]. Benchmark studies show that PBEh-3c yields interaction energies and equilibrium geometries for molecular complexes that are comparable to larger-basis hybrid DFT or MP2 calculations, while remaining largely free of basis-set superposition error [26]. This makes it a suitable choice for exploring noncovalent adsorption of nucleobases on carbon nanotubes.

In this work, we use DFT with the PBEh-3c composite method to investigate the interaction of a finite (5,5) SWCNT fragment with uridine (rU) and its Hachimoji analog S (rS). We analyze optimized geometries, HOMO-LUMO gaps, interaction energies, and Mulliken charge distributions to assess how replacing a natural RNA base by a Hachimoji base affects the strength and character of adsorption. By comparing rU and rS on the same nanotube model, we aim to provide a quantitative picture of how expanded-alphabet bases interact with carbon nanostructures, and to test whether the S base perturbs the electronic structure of the SWCNT more strongly than its canonical counterpart. The present study is intended as a system-specific comparison of rU and rS adsorption on a finite (5,5) SWCNT fragment. The results provide a first model-level picture of how a Hachimoji base and its canonical counterpart interact with the same curved carbon surface and may help guide future studies that include solvent and more realistic device environments.

Computational methods

All electronic structure calculations were carried out with the ORCA software [27]. All calculations were carried out in the gas phase, and no implicit or explicit solvent model was included. The present work therefore focuses on intrinsic adsorption trends within the chosen finite-fragment model. The systems studied were a finite segment of a (5,5) single-walled carbon nanotube (SWCNT) and two methyl-capped nucleobase models derived from uracil/uridine and the Hachimoji base S. The uracil-based model was obtained from the Avogadro RNA library and truncated at N1, which was then capped with a methyl group. The corresponding rS model was generated from the same scaffold by replacing the oxygen atom at the C2 position with nitrogen.

The SWCNT adsorption model used in the present work was built in Avogadro as a hydrogen-terminated (5,5) tube with an approximate length of 8 Å along the tube axis. Additional bare-tube models of 4 Å and 12 Å were also considered to evaluate the finite-size dependence of the HOMO-LUMO gap [28]. A finite hydrogen-terminated (5,5) armchair SWCNT fragment was selected as a representative curved π-conjugated carbon surface that remains computationally tractable for geometry optimization, configurational sampling, and benchmark calculations. The purpose of this model was to compare rU and rS on the same nanotube surface, not to provide a systematic survey of chirality or diameter effects. Initial geometries of rU and rS were also generated in Avogadro. Because finite armchair nanotube segments are known to exhibit length-dependent frontier-orbital gaps, an additional hydrogen-terminated (5,5) SWCNT fragment with an approximate length of 12 Å was calculated as a benchmark to evaluate the finite-size dependence of the HOMO-LUMO gap.

Geometry optimizations were carried out using the PBEh-3c composite method. Tight self-consistent-field convergence criteria were employed for all optimizations. The same level of theory was used to optimize the isolated SWCNT fragment, rU, and rS. For each adsorbate, several initial adsorption geometries were generated by varying the lateral position and rotational alignment of the base relative to the SWCNT surface. These starting structures were first screened by single-point calculations, and the lowest-energy configuration for each adsorbate was then selected for full optimization and further analysis. The optimized isolated structures were then used as references when computing interaction energies. For the complexes, the final optimized geometries were inspected visually in Avogadro to confirm reasonable stacking distances and the absence of artificial strain in the tube or the bases. The adsorption height, shortest heavy-atom intermolecular distance, and relative base-tube orientation were extracted from the optimized 8 Å benchmark complexes using Avogadro. The optimized geometries of the isolated systems and adsorption complexes are provided in the Supplementary Information, together with the corresponding Cartesian coordinates in xyz format.

Single-point calculations at the optimized geometries provided the total electronic energies, orbital energies, and Mulliken populations. HOMO-LUMO gaps were calculated as the difference between the lowest unoccupied and highest occupied orbital energies and reported in electron volts. To validate both the frontier-orbital analysis and the adsorption energetics, additional single-point calculations were carried out with the PBE0 hybrid functional and the def2-SVP basis set on the PBEh-3c optimized geometries of the isolated 8 Å SWCNT fragment, the isolated rU and rS models, and the SWCNT+rU and SWCNT+rS complexes. These benchmark calculations were used to assess the sensitivity of the HOMO-LUMO gap and interaction energies to the level of theory.

Interaction energies between the SWCNT and the bases were evaluated with the supermolecule approach. For each base X (X = rU, rS), the interaction energy was obtained as

$$\begin{array}{c}{E}_{\mathit{int}}\left(S,W,C,N,T,+,X\right)=E_{\left(S,W,C,N,T,+,X\right)}-E_{\mathit{SWCNT}}-E_X\end{array}$$ 1

where $E_{\mathit{int}}\left(S,W,C,N,T,+,X\right)$ is the total energy of the optimized complex, and $E_{(SWCNT+X)}$ and $E_X$ are the energies of the isolated SWCNT fragment and isolated base in their own optimized geometries. Interaction energies were evaluated with the supermolecule approach at the PBEh-3c level. This composite method includes a built-in damped geometrical counterpoise (gCP) correction that explicitly accounts for basis set superposition error (BSSE). Therefore, the reported adsorption energies already contain a BSSE treatment within the native PBEh-3c framework, and no additional Boys–Bernardi counterpoise correction was applied [29].

All adsorption energies reported in this work are electronic interaction energies obtained from optimized structures. No zero-point, thermal, or entropic corrections were included. Full harmonic frequency calculations were not performed for the SWCNT-base complexes because the present work focuses on electronic adsorption energies of weakly adsorbed finite-fragment models. In such systems, the lowest vibrational modes are dominated by very soft intermolecular motions, so harmonic frequency calculations would be computationally demanding and of limited value for the main comparative conclusions of this study. Accordingly, the optimized SWCNT-base complexes discussed in this work are treated as lowest-energy optimized structures within the sampled configurational space, rather than formally verified minima from vibrational analysis.

Mulliken atomic charges were extracted from the population analysis section of the output. To quantify charge redistribution upon adsorption, we grouped atoms into two fragments: the SWCNT and the base. Fragment charges were obtained by summing the Mulliken atomic charges over all atoms belonging to each fragment. For each complex, the change in charge on fragment Y (Y = SWCNT, base) was defined as

$$\begin{array}{c}{\mathrm{\Delta }q}_Y=q_Y^{\left(c,o,m,p,l,e,x\right)}-q_Y^{\left(i,s,o,l,a,t,e,d\right)}\end{array}$$ 2

where $q_Y^{(complex)}$ is the Mulliken charge of fragment Y in the complex and $q_Y^{(isolated)}$ is the corresponding charge in the isolated molecule. Since the isolated systems are neutral, $q_Y^{(isolated)}$ is close to zero and ${\mathrm{\Delta }q}_Y$ is essentially the net Mulliken charge carried by that fragment in the complex. To support the charge-transfer analysis, Löwdin population analysis was also carried out for the optimized 8 Å SWCNT+rU and SWCNT+rS complexes. To further characterize the adsorption mechanism, non-covalent interaction (NCI) analysis based on the reduced density gradient (RDG) was carried out for the optimized 8 Å SWCNT+rU and SWCNT+rS complexes. The wavefunctions were converted to Molden format from ORCA output files, and the RDG/NCI analysis was performed using Multiwfn [30]. The resulting isosurfaces were visualized in VMD and colored according to sign (${\lambda }_2$)ρ to distinguish weak attractive interaction regions.

Results and discussion

Figure 1 shows the HOMO-LUMO gaps obtained for the isolated bases (rU and rS), the 8 Å hydrogen-terminated (5,5) SWCNT fragment, and the two adsorption complexes. The isolated bases show large gaps of 7.50 eV for rU and 7.69 eV for rS. The bare SWCNT fragment has a much smaller gap of 3.214 eV. This value should not be interpreted as the intrinsic electronic structure of an infinite periodic (5,5) nanotube, which is known to be metallic. Instead, it reflects the finite length and hydrogen termination of the fragment model used in this work. To verify this point, an additional calculation was carried out on a 12 Å hydrogen-terminated (5,5) SWCNT fragment. The HOMO-LUMO gap decreases to 2.589 eV for the longer model. This trend is consistent with the expected reduction of the finite-size gap with increasing tube length [31, 32]. Within the 8 Å fragment model, adsorption of rU and rS changes the gap only slightly, to 3.194 eV and 3.199 eV, respectively. These values are therefore used here only as comparative frontier-orbital descriptors for the same finite adsorption model.

Fig. 1.

The HOMO-LUMO energy gaps for isolated rU, rS, SWCNT, SWCNT+rU and SWCNT+rS complexes

This indicates that the smaller gap of the SWCNT is essentially preserved upon adsorption of the bases. To test the robustness of this interpretation, an additional single-point PBE0 calculation was performed on the optimized SWCNT+rS complex. The PBE0 frontier orbital energies are HOMO = − 4.980 eV and LUMO = − 2.540 eV, which gives a HOMO-LUMO gap of 2.44 eV. Although this value is lower than the PBEh-3c result, it still confirms that the adsorbed system remains a finite-gap complex. This comparison suggests that the qualitative electronic picture is preserved, while the absolute gap value depends on the level of theory.

The optimized geometries of the adsorption complexes show that both bases adopt a nearly parallel-displaced arrangement relative to the SWCNT surface, consistent with a π-stacking motif. The corresponding structural descriptors are summarized in Table 1. For SWCNT+rU, the adsorption height is 3.30 Å and the shortest heavy-atom intermolecular distance is 3.20 Å. For SWCNT+rS, the corresponding values are 3.17 Å and 3.10 Å. These values are typical of weak noncovalent π–π interactions on curved carbon surfaces.

Table 1.

Key structural parameters of the optimized 8 Å SWCNT adsorption complexes

Complex	Adsorption height, $h(\mathrm{A})$	Shortest heavy-atom distance, $d_{\mathit{min}}(\mathrm{A})$	Relative orientation
SWCNT+rS	3.17	3.10	Parallel
SWCNT+rU	3.30	3.19	Parallel

This behavior is in line with the weak, mainly physiosorbed nature of the complexes. The bases interact with the tube through π-π stacking at a distance of about 3.1–3.3 Å, so the overlap between their frontier orbitals and the delocalized π system of the SWCNT is limited. As a result, the tube retains its electronic character, and the bases behave more like external perturbations than strongly coupled dopants. Within the present gas-phase model, these results suggest that any distinction between rU and rS is more likely to arise from local energetic and electronic differences than from a large global change in the frontier-orbital gap. The similarity of the gaps for SWCNT+rU and SWCNT+rS also suggests that differences in detection between the two bases will not come from global band-gap modulation, but from more detailed features of the interaction, which we examine through the binding energies and charge analysis in the following sections.

Figure 2 compares the interaction energies of rU and rS with the (5,5) SWCNT fragment. Because π-π stacking interactions depend on orientation and lateral displacement, three initial adsorption poses were considered for each base on the 8 Å hydrogen-terminated (5,5) SWCNT fragment: a parallel arrangement aligned approximately with the tube axis, a parallel arrangement rotated by about 90°, and a laterally shifted parallel arrangement. For rU, the shifted and 90° poses were higher in energy than the parallel pose by 0.035 and 0.180 eV, respectively. For rS, the corresponding energy differences were 0.160 and 0.260 eV. In both systems, the parallel pose was the lowest-energy starting geometry and was therefore used for full optimization. The interaction energies discussed below correspond to the lowest-energy optimized structures obtained from this configurational search and should be interpreted as electronic adsorption energies. The values are − 0.43364 eV for SWCNT+rU and − 0.55405 eV for SWCNT+rS. A benchmark of the adsorption energies was also carried out at the PBE0/def2-SVP level using the optimized 8 Å geometries. The resulting interaction energies are − 0.144 eV for SWCNT+rU and − 0.211 eV for SWCNT+rS. Although these values are smaller in magnitude than the corresponding PBEh-3c results, they preserve the same qualitative ordering and again indicate stronger adsorption of rS than rU. This cross-validation supports the conclusion that the relative interaction trend is robust, even though the absolute adsorption energies remain method-dependent. Both numbers are negative, which confirms that adsorption is thermodynamically favorable in each case and that the complexes are stabilized by noncovalent forces. The magnitude of these energies is typical for π-π stacking of nucleobases on carbon nanostructures and is consistent with a physisorption regime rather than chemisorption [13]. The rS base binds more strongly to the nanotube than rU by about 0.120 eV. This difference is meaningful for a noncovalent interaction and suggests that the rS base interacts more efficiently with the nanotube π system. Even though the HOMO-LUMO gaps of the two complexes are very similar, the stronger interaction of rS suggests that, within the present gas-phase finite-fragment model, the Hachimoji base interacts more favorably with the nanotube surface than the canonical base. To assess the reversibility of adsorption in a sensing context, approximate recovery times were estimated [33]. The resulting recovery times are $2.16\times {10}^{-5}\mathrm{s}$ for SWCNT+rU and $2.34\times {10}^{-3}\mathrm{s}$ for SWCNT+rS, which are both short and therefore consistent with reversible physisorption [34]. The longer recovery time of rS agrees with its stronger interaction energy. This trend may be relevant for future nanotube-based sensing designs, but additional work on larger tubes, other diameters, different chiralities and explicit environmental effects would be needed before making broader device-level conclusions.

Fig. 2.

Interaction energies of the SWCNT+rU and SWCNT+rS complexes

Figure 3 shows the Mulliken charge redistribution upon adsorption, expressed as the fragment charge change Δq for the SWCNT and the adsorbed bases. In the SWCNT+rU complex, the SWCNT carries − 0.017 e and the adsorbed base carries 0.017 e. In the SWCNT+rS complex, the corresponding values are − 0.021 e for the SWCNT and 0.021 e for the base. These values indicate only small charge redistribution upon adsorption. In both complexes, the SWCNT becomes slightly negative while the adsorbed base carries the corresponding positive charge, showing that overall charge conservation is maintained. Although some polarization occurs, the magnitude of charge transfer remains very small. The rS complex shows slightly larger charge redistribution than the rU complex, which is consistent with its stronger binding, although the overall magnitude remains small. Taken together with the NCI/RDG analysis in Fig. 4, these results indicate that adsorption of rU and rS on the SWCNT is dominated by weak noncovalent π-π interaction with only minor charge redistribution, rather than strong charge-transfer doping. Löwdin population analysis gives the same qualitative trend, with charge changes of − 0.00622 e/+ 0.006217 e for SWCNT+rU and − 0.00898 e/+ 0.008982 e for SWCNT+rS, confirming that charge transfer remains very small and is slightly larger in the rS complex.

Fig. 3.

Charge change, Δq(e), of the SWCNT and adsorbed bases in the optimized SWCNT+rU and SWCNT+rS complexes

Fig. 4.

Reduced density gradient (RDG)/non-covalent interaction (NCI) isosurfaces for the optimized 8 Å SWCNT+rS (left panel) and SWCNT+rU (right panel) complexes. The broad green interfacial regions between the nucleobase and the SWCNT indicate weak attractive non-covalent interactions characteristic of dispersion-dominated π-π stacking

To complement the Mulliken charge analysis, the adsorption mechanism was further examined by NCI/RDG analysis. The corresponding isosurfaces for the optimized 8 Å SWCNT+rU and SWCNT+rS complexes are shown in Fig. 4. In both cases, a broad green region appears between the nucleobase ring and the nanotube wall, which is characteristic of weak attractive noncovalent interaction. This pattern is consistent with dispersion-dominated π-π stacking rather than covalent bonding or strong donor-acceptor interaction. The NCI analysis therefore supports the physisorbed nature of both complexes. The green interfacial region is slightly more extended in the rS complex, in agreement with its somewhat stronger adsorption energy.

Conclusion

We used DFT with the PBEh-3c composite method to study adsorption of uridine (rU) and the Hachimoji base S (rS) on a (5,5) SWCNT. The isolated bases show large HOMO-LUMO gaps, while the nanotube has a smaller gap. The reported HOMO-LUMO gaps should be understood as frontier-orbital properties of finite hydrogen-terminated SWCNT fragments rather than as the intrinsic band structure of an infinite metallic (5,5) nanotube. After adsorption, the gaps of SWCNT+rU and SWCNT+rS complexes remain close to that of the bare tube, indicating that the nanotube continues to dominate the frontier electronic structure and that a single base does not strongly perturb the band gap. The reported adsorption energies should therefore be understood as electronic energies of optimized finite-fragment models rather than fully vibrationally corrected thermodynamic quantities. An additional PBE0/def2-SVP benchmark preserves the same qualitative trend, with rS remaining more strongly adsorbed than rU, which supports the robustness of the comparative conclusion despite the method dependence of the absolute adsorption energies.

Interaction energies of − 0.43364 eV for SWCNT+rU and − 0.55405 eV for SWCNT+rS place both complexes in the physisorption regime. The rS base binds more strongly, showing that the Hachimoji base interacts more favorably with the tube than its natural counterpart. The optimized adsorption heights of 3.30 Å for SWCNT+rU and 3.17 Å for SWCNT+rS, together with the shortest heavy-atom distances of 3.20 and 3.10 Å, confirm a stable nearly parallel-displaced π-π stacking motif on the longer nanotube fragment. The estimated recovery times are short for both complexes, supporting the reversible nature of adsorption. Mulliken analysis shows small net charge redistribution in both complexes, with the SWCNT carrying about − 0.017e in SWCNT+rU and − 0.021e in SWCNT+rS, balanced by corresponding positive charge on the adsorbed bases. This conclusion is also supported by Löwdin analysis, which reproduces the same qualitative charge-redistribution trend with smaller absolute values. Adsorption therefore involves weak charge rearrangement and is governed mainly by dispersion and π-π stacking. This interpretation is further supported by the NCI/RDG isosurfaces, which show broad weakly attractive interfacial regions between the base rings and the SWCNT surface. Overall, within the present gas-phase finite-fragment model, rS shows stronger local adsorption than rU through modest energetic and electronic differences rather than through strong doping or large gap changes. Future work should test whether this trend remains valid for larger diameters and different nanotube chiralities and include solvent and environmental effects to assess their relevance to realistic biosensing conditions. Calculations of density of states and simple transport properties could link the present electronic signatures more directly to measurable conductance changes in CNT devices.

Supplementary Information

Below is the link to the electronic supplementary material.

Author contribution

M.A. designed the study, ran the simulations, prepared the figures, and wrote the main manuscript text.

Funding

The author declares that no funds, grants, or other support were received during the preparation of this manuscript.

Data availability

No datasets were generated or analysed during the current study.

Declarations

Competing interests

The authors declare no competing interests.