**3. Results**

The influence of the interaction in the nucleotide-metal nanoparticle system is numerically modelled in the MD system. The validation of the model was performed twofold: first, to obtain a spectral resolution sufficient to register changes due to the LJ interaction, and secondly, to evaluate the corresponding variations in the vibrational spectra of the nucleotide-nanoparticle system.

#### *3.1. Resolution of Nucleotide Spectra*

First, we evaluated the variations in the nucleotide–graphene system at translocation. Spectral variations which were examined due to interaction force in the nucleobase– graphene nanopore system pointed to the influence of the conformation on the nucleotide spectral maps [55,56]. The transient vibrational frequencies of all passing nucleotides were calculated at the same initial incident angle and shift distance from pore edge. To separate decay in the calculated data from the proper spectrum, we have extracte decay components out of calculated spectral data. The calculation of the transient autocorrelation function includes relatively short interaction time during which the correlation data are accumulated. As a result of the transience of the correlation signal, the exponential function of time decay is converted by the Fourier transfer into a decaying spectral map. In order to separate decay components from the spectra itself, we propose the two-parametric exponential fitting, as follows:

$$\begin{array}{lcl}\boldsymbol{\chi}\_{\exp ft} & = \boldsymbol{a} \times \exp(b\boldsymbol{\chi}\_{1}),\\\boldsymbol{\chi}\_{\exp ft} & = \boldsymbol{\chi}\_{amp} - \boldsymbol{\chi}\_{\exp ft} \end{array} \tag{2}$$

The introduced exponential function was fitted by parameters *a*, *b* either to the function's low-frequency region (head) or high-frequency (tail) region. The exponential decay component *<sup>x</sup>*exp *fit* was then subtracted from the calculated *xamp* spectra. The lowfrequency fitting produced better-resolved spectra above 5 THz compared with the highfrequency fitting. All calculated spectra of nucleotides that are discussed were obtained in the low-frequency fitting. The initial spectral resolution Δ *f* of Fourier transform that was tested was 40 cm<sup>−</sup>1.

In contrast with quantum density functional theory (DFT) calculations of IR and Raman spectra, transient MD calculations are sensitive to the duration of correlation time and relative interaction of the structures studied. Therefore, obtained spectra should be compared with the other available calculations and experimental data. The spectral maps of nucleotides that we calculated were highly sensitive to interactions in the system. Since all nucleotide spectral maps were calculated in identical conditions of nanopore translocation, the obtained transient frequencies could be used as reference values to distinguish nucleotides from each other. Comparison with results of 2D-IR experiments and DFT calculations [57] shows a 50–80 cm<sup>−</sup><sup>1</sup> discrepancy between corresponding stretching C-C and C-N frequencies calculated in the MD model at 40 cm<sup>−</sup><sup>1</sup> resolution. The SERS data on the breathing mode [35] of nucleotides with the full width at half maximum of the peak wavenumber being 13 and 20 cm<sup>−</sup><sup>1</sup> show the presence of the mode in the 660–800 cm<sup>−</sup><sup>1</sup> interval for nucleotides. Our single bond spectra in Appendix A exhibit the presence of the bending type of mode in the above interval, different for each nucleotide; however, our resolution in the case is limited by 40 cm<sup>−</sup>1. For guanine, we obtained a bending peak at 655 cm<sup>−</sup><sup>1</sup> as compared to the measured [35] peak at 661 cm<sup>−</sup>1; thymine exhibited the calculated 860 cm<sup>−</sup><sup>1</sup> peak vs. the measured 795 cm<sup>−</sup>1. All measurements were held in the aqueous solution with nucleotides in proximity to the gold nanoslits or nanoparticles for enhancement of the signal. To improve our model, the resolution was improved and the metal nanoparticle was introduced.

The employed spectral resolution in our MD calculations has been sufficient/enough to register structural dependence of the molecular spectral map on a bond-to-bond basis. However, the 2000 cm<sup>−</sup><sup>1</sup> upper limit excludes the C-H and N-H bonds from the calculated frequency region. With the increased resolution of IR and SERS/TERS SM spectroscopy [35,58] and ab initio MD (AIMD) calculations of the chemical bonding effect in SERS [59,60], the information on vibrational mode variations due to interaction with environment, which could be hydration changes or a Van der Waals interaction with graphene pore, should be available in MD calculations as well. The approximation of the MM2/MM3 potential used for nucleotides cannot allow the estimation of dipole moment and polarizability changes with the environment that are calculated in DFT and AIMD spectra. However, transient dynamics sample a sufficient number of states that constitute several periods of vibrations. The coupled anharmonic bonding is also present in the MD potentials which are used. Therefore, a partial reproduction of the changes of dipole moments and polarizabilities with interaction has a cumulative presence in velocity correlation data calculated in MD. To extend the spectral range up to 4000 cm<sup>−</sup>1, we considered the sampling resolution in real space over the interaction potential *<sup>U</sup>*(*r*(<sup>Δ</sup>*t*)) by decreasing Δ*t,* and in reciprocal space by extending the number of time steps [61]. The testing of the proposed spectral resolution was carried out for the hydroxymethylcytosine (HMC) nucleotide that has H-X bonding sites to X=C and O atoms in hydroxymethyl group (marked in Figure 4).

**Figure 4.** The spectra of a single bond marked as C(10)-C(3) in internal atom numbering of the hydroxymethylcytosine (HMC) nucleotide. The C(10) atom belongs to the hydroxymethyl group and exhibits high frequencies of the C-H bond. The spectra are collected outside of graphene pore interaction (vz = 0) at a different propagation time step (2.0 ÷ 0.5 × 10−<sup>16</sup> s) and total simulation time (in step number) in two frequency domains: 0–2000 cm<sup>−</sup><sup>1</sup> at the left and 2000–4000cm−<sup>1</sup> at the right. The base part of the HMC nucleotide with the marked bond adjacent to H-X (C, O) is shown in the center.

As shown in Figure 4, the time step of 0.05 fs and 32,768 steps has given the resolution of vibrational modes at Δ*f* = 20 cm<sup>−</sup><sup>1</sup> and up to 4000 cm<sup>−</sup>1. The Δ*f* = 20 cm<sup>−</sup><sup>1</sup> spectral resolution is comparable to the 15 cm<sup>−</sup><sup>1</sup> half-width of the Lorentzian function that is used to broaden Raman spectral lines in the DFT calculation [54]. To further confirm our resolution of the Raman spectra of nucleotides, HMC was calculated at the DFT level with the 20 Å size of the supercell for the methylated nucleotide using the Quantum Espresso package [62]. Some of the H-X stretching modes in the hydroxymethylcytosine are shown in Figure 5. The C(10)-C(3) and C(10)-O(16) bonds of hydroxymethyl group are scanned for highest intensity vibration frequencies, which are compared with the Raman frequencies obtained in the DFT calculations. Correspondence, where it was obtained between the MD and DFT frequency modes, is within 10 cm<sup>−</sup>1. Not all MD vibrational modes with high amplitudes correspond to the DFT normal modes. Some of the modes that have high intensity in the MD calculation (2524 and 2605 cm<sup>−</sup>1) can be Raman inactive in the DFT calculation but exhibit IR activity. This relation should be further clarified. The MD calculations with 20 cm<sup>−</sup><sup>1</sup> spectral resolution have been carried out in equilibrium conditions without interaction with graphene.

As compared to the typical sampling timescale of the SERS and TERS techniques being a few microseconds, the typical time scale of the plasmon excitation of the metal enhancer system relates to the scale of 100 fs, and the coupling between the electronic and vibrational degrees of freedom is on the time scale of 0.1–0.5 ps. Therefore, interaction and conformation-dependent single molecule measurements and calculations should concentrate on the time scale of few vibrational periods that we presently cover with a 1.64 ps

time interval. Experimentally, nanophotonic probing of the acoustic phonon propagation has been achieved now at the ps timescale [63]. Only the highest peaks in the spectrum are considered as modes in our case. In spectral calculations, the increase in the spectral range resolution simultaneously causes a noise connected to the time step reduction as a consequence of Fourier transfer. The source of the noise is twofold at short time step: (1) the velocity projection on the bond vectors starts to resolve traces of vibrations related to nearest bonds connected by the atom and (2) the FFT procedure in spectra calculations can produce low intensity side lobes of the signal peaks that are not smoothed out with window functions in order not to lose spectral information on essential modes.

**Figure 5.** Spectral frequencies of the C(10)-C(3) and C(10)-O(16) bonds of hydroxymethylcytosine (HMC) (see Figure 3) calculated by MD outside of graphene pore (vz = 0) for the 2000–4000 cm<sup>−</sup><sup>1</sup> frequency region. Comparison to the density functional theory (DFT) calculations of Raman frequencies.

#### *3.2. Interaction between Metal Clusters and Nucleotides*

In order to confirm the effect of the LJ interaction on the vibration spectra of in the nucleotide–Au20 nanoparticle system, the Au20 NP was placed into an already-tested graphene-nucleotide system close to initial nucleotide position as shown in Figure 6a. Cytosine nucleotides' vibrational spectra have been estimated for base bonds circled in Figure 3 in red. To exclude the interaction with the graphene sheet at the initial stage, the distance from the graphene was out of range of the LJ interaction. The initial orientation of the NP relative to the cytosine nucleotide at the 4 Å distance between the tip of NP and the atoms of the nucleotide was selected to keep the LJ interaction at a relatively weak level. Figure 7 compares vibrational spectra of the bonds C(2)–C(3), C(2)–N(5), C(3)–H(10), and C(1)–O(12) in the absence and presence of Au20 NP. Explicit changes in modes due to interaction are shown with vertical arrows ↓ in each case.

**Figure 6.** (**a**) System of Au20 nanoparticle and cytosine nucleotide vs. graphene sheet in initial Au20 NP orientation where interaction is localized primarily within the tip atom of the Au20 pyramid; (**b**) rotated NP with the upper plane of the pyramid parallel to the graphene (*x,y*) plane and interaction with the edge atoms of the Au20 pyramid enhanced; (**c**) interaction direction of nucleotide with NP changes during nucleotide conformation and alignment at the vibration time. Calculations were first carried out with the initial vcom = 0 in x,y,z directions for cytosine and NP.

**Figure 7.** Vibrational spectra of the cytosine (CYT) bonds (**a**) C(2)–C(3), (**b**) C(2)–N(5), (**c**) C(3)–H(10), and (**d**) C(1)–O(12) in the absence and presence of interaction with the Au20 NP. Changes in spectra such as mode shifts and large amplitude changes are marked by vertical arrows.

In the C(2)–C(3) case, there were changes in bending and twisting at the 500–1000 cm<sup>−</sup><sup>1</sup> frequency range. On the 1300–2000 cm<sup>−</sup><sup>1</sup> interval, the stretch mode is blue shifted due to interaction with NP, so it is attributed to the breathing mode of the nucleotide base. In the C(2)–N(5) bond, the changes in modes related to bending and twisting can be also seen: the amplitude of the breathing mode was very weak, and the C-N stretching mode had no shift but only an increase in amplitude. The C(3)–H(10) bond had changes in C-H bending and stretching modes at the 1000–2000 cm<sup>−</sup><sup>1</sup> interval. For the C(1)–O(12) bond, the largest changes were in breathing and the stretching modes at the 1300–2000 cm<sup>−</sup><sup>1</sup> range. Interaction with the nanoparticle modified transient vibrational frequencies of cytosine at the ps interval in our MD simulation.

For the Au20 NP, the vibrational spectra were also estimated for individual atoms in Cartesian coordinates. Figure 8 exhibits the spectra of the tip atoms in the pyramid in the absence of interaction in x, y, and z coordinates with the basic 188 cm<sup>−</sup><sup>1</sup> cluster mode for all tip atoms that can be a mode characterising the whole Au20 nanoparticle. Comparing results in Figure 8, it can be seen that the closer to the nucleotide, the stronger the influence. In addition, it can be seen that there is an even greater effect between atoms 4190 and 4196. Obtained spectra relate to a single orientation of the NP vs. nucleotide. A change in NP orientation would lead to variation in LJ interaction strength and subsequent changes in vibration spectrum.

**Figure 8.** Vibrational spectra of the tip atoms of Au20 nanoparticle numbered 4190, 4193, 4196, and 4200 in *x, y*, and *z* coordinates without interaction with the cytosine.

The Au NP was then rotated as seen in Figure 6b,c. The upper plane of the pyramid was moved to be in the (*x,y*) plane and *z*-axis rotation placed the four atoms of the edge of the pyramid into LJ interaction proximity to the nucleotide. Figure 6c shows the animation snapshot after rotation, and Figure 9 shows the spectral change in 4196 atom's modes after rotation. The vibrational spectra of the interaction with the cytosine single atom (4196) of Au20 nanoparticle tip contrast with the spectra of the rotated NP with edge interaction (Figure 9a,b). The basic 188 cm<sup>−</sup><sup>1</sup> frequency of the NP remains intact after rotation. A strong amplitude enhancement is seen for frequencies 76 and 81 cm<sup>−</sup><sup>1</sup> in y and z-direction due to the change in the LJ interaction. The interaction with the nucleotide initiates a slight movement of the NP, which can be reflected in the appearance of the low-frequency modes. For relatively large spherically shaped Au nanoparticles, a typical Raman band over the range of 300–900 cm<sup>−</sup><sup>1</sup> was observed experimentally. For the pyramid-shaped Au20 NP, we obtained lower basic frequency that remains stable at different strength of Van der Waals interactions with the nucleotide.

The sensor's design often suggests a fixed attachment of the enhancer nanoparticle and transport of the molecules in the measurement process. To measure transient vibrational spectra of the nucleotides, a scope of molecule's passing velocity vz has been tested in MD simulations. For the given spectral resolution, a cytosine's c.o.m. velocity in the range vz = 0.25 m/s = 25 Å/ps has been selected by interaction time being approximately half of the nucleotide's total propagation time. Passing of the nucleotide limits interaction duration with the NP and leads to changes in vibrational bands. To reveal the connection of the transient time with the changes in the spectrum, we compared spectra of the bond C(2)-C(3) from both end atoms for cytosine alone, a cytosine at 4 Å distance without transient velocity (vz = 0), and with vz = 0.025 m/s as shown in Figure 10. The C(2) atom of the ring is bound to the amino group NH2 and C(3) atom of the ring has a C-H bond. The spectra reflect the presence of the different set of bands for each atom in the bond and attachment to the amino group influences transient regime in Figure 10a not only by changes in band amplitude and frequency shifts, but by a velocity of DOS decay that becomes slower. The C(2) atom in Figure 10b exhibits smaller changes in the basic C-C ring vibration frequencies corresponding to ~1550 and 1690 cm<sup>−</sup><sup>1</sup> in present calculations (seen

in Figure 7a,c) in stationary and transient regimes. The velocity has been added to the c.o.m. motion of nucleotide at all durations of propagation. Such a simple model reproduces, in general, the motion of partially charged molecules in a uniform electric field. The present result connects the transient velocity of a molecule, size of NP, and interaction time with the molecule's vibrational spectra. The ring remains relatively stable in the transient regime while the amino group attached to the ring structure responds to the transient interaction.

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**Figure 9.** Vibrational spectra of the interacting tip atom (4196) of Au20 nanoparticle in x, y, and z coordinates at initial (**a**) and rotated (**b**) orientation relative to cytosine localization.

**Figure 10.** Vibrational spectra of the cytosine bonds (**a**) C(2)–C(3) and (**b**) C(3)–C(2), in the absence and presence of interaction with the Au20 NP. Transient velocity of the nucleotide was vz = 0.025 m/s.
