Water is an indispensable substance in life，carrying out essential functions necessary for sustaining life activities ^［1-5］. It actively participates in many biological activities，such as metabolism，maintaining internal environmental stability，and protein structure maintenance ^［6-10］. Therefore，a deep understanding of the physical properties of water molecules is crucial.

In nature，most water exists in the form of free state bulk water（BW）. However，in biochemical reactions and macromolecular biological functions，water often exists in the form of confined water within inorganic pores and certain protein structures，playing a key role. For example，the water channel protein Aquaporin-1 in biological organisms has been proven to efficiently transport water molecules across membranes while preventing ions from passing through ^［11］. In water protein channels，water molecules are arranged in a one-dimensional manner to form one-dimensional confined water（1DCW） ^［12］. Studies by Hummer et al. observed similar 1DCW structures and characteristics in（6，6） single-walled carbon nanotubes（SWNT） ^［13］. Due to being confined to specific one-dimensional nanochannels，water molecules are connected through H-bonds in a front-to-back manner，achieving overall coordinated and orderly movement. This structure endows 1DCW with unique dynamic properties ^［14-16］. These studies further suggest that SWNT materials are simple to manufacture，structurally stable，and uniform，also possessing transport properties similar to biological channels. Therefore，simple nanochannels mimic complex biological channels，making artificial SWNT an ideal choice for studying biomimetic nano-confinement ^［17-19］.

In recent years，with the capabilities of high-performance computing and large-scale data processing，scientists have conducted more precise and complex simulations and calculations of the water structure inside SWNT，discovering novel behaviors not observed on a macroscopic scale. These findings have propelled SWNT into new application prospects，such as precise water molecule control ^［20］，seawater desalination ^［21］，etc. Although understanding of 1DCW has increased ^{［13，15-17］}，current experimental technology limitations mean that a complete understanding of its dynamic properties is still to be deepened. Infrared spectroscopy（IR） technology plays an important role in analyzing the structure and properties of materials ^［22-27］. In terms of analyzing the microstructure of water，IR technology provides important information on the internal structure and configuration of water molecules. By analyzing the vibrational and rotational modes of water molecules，the formation，breaking，and dynamic characteristics of H-bonds in water molecules can be inferred. Furthermore，IR technology can also be used to study the dynamic properties of water molecules，such as the rates of vibration and rotation，and interaction strength. Recent studies indicate that confined water exhibits significantly different absorption characteristics compared to bulk water in the infrared and far-infrared ranges ^［28-32］. Studies also show that the infrared spectrum of water molecules presents three significant absorption peaks in these infrared and far-infrared ranges. The different frequency ranges of these peaks reflect the different motion modes of water molecules. The high-frequency absorption peaks primarily originate from the stretching vibrations of the oxygen-hydrogen（O-H） bonds within water molecules ^［33］. Since the stretching vibrations of O-H bonds are extremely sensitive to changes in the local environment，they are often used as effective probes for detecting and analyzing the state of water molecules ^［34］. Additionally，the H-bond network structure between water molecules also significantly impacts the motion characteristics of water ^［35］. Therefore，using molecular dynamics（MD） simulation methods to further study the H-bond network and motion characteristics of 1DCW and BW，especially focusing on the high-frequency stretching vibrations of O-H bonds，is crucial for a deep understanding of the dynamic properties of water molecules in different environments.

This paper utilizes the SPC/E water model based on the MD simulation method to study the infrared spectroscopy and motion characteristics of 1DCW in（6，6） SWNT. The results indicate significant differences in the O-H bond stretching vibration infrared spectra between 1DCW and BW. Subsequent analysis of the O-H bond length stretching changes，H-bonds，and motion trajectory diagrams reveals the fundamental reasons for the spectral differences.

First，we establish a cubic simulation box with dimensions of 3.00 nm × 5.11 nm × 7.00 nm，as shown in Fig 1. The system contains a capless（6，6） SWNT of 2.33 nm in length and 0.81 nm in diameter，horizontally positioned between two parallel open graphite sheets. Both the SWNT and graphite sheets are maintained in a rigid state，with the ends of the graphite forming a water-filled reservoir. We employed the flexible SPC/E water molecule model ^［36］ and filled the system with 2524 water molecules under standard temperature and pressure conditions. The interactions between water molecules are represented by a potential energy function：

The first term represents long-range electrostatic interactions，while the second term involves short-range Lennard-Jones（L-J） interactions. Here，$k=\mathrm{1}/(\mathrm{4}\pi {\epsilon }_{\mathrm{0}})$ represents the dielectric constant in vacuum； $r_{ij}$ is the distance between atoms $i$ and $j$； $q_i$ is the charge on atom $i$； and the parameters ${\epsilon }_{ij}$ and ${\sigma }_{ij}$ represent the values for L-J interactions. The force field parameters for our flexible SPC/E water model are detailed in Table 1. We conducted simulations using GROMACS 5.1.4 simulation software and treated interatomic interactions with the OPLS/AA force field，calculating the L-J parameters between different atoms using the geometric averaging method. The leapfrog integration algorithm was used to solve the equations of motion for the particles，and periodic boundary conditions were employed to eliminate boundary effects. The simulation system operated under constant temperature and pressure conditions，with the system temperature maintained at 300 K using a Nose-Hoover thermostat and a temperature relaxation time set at 0.2 ps. The particle mesh Ewald method was used to handle electrostatic interactions，and the cutoff radius for electrostatic and van der Waals interactions was set at 1 nm. An initial pre-equilibration of 10 ns was conducted，followed by a 5 ns simulation. Data was collected at intervals of 1 fs，with the last 1 ns of trajectory data used for analyzing vibrational spectra and dynamic characteristics.

In studying the infrared spectra of the O-H bond stretching vibrations in water molecules within SWNT，the required infrared spectra are calculated by performing a Fourier transform on the time autocorrelation function of the O-H bond lengths in water molecules. The mathematical expression for this calculation is as follows：

In the above expression，$I$ represents the vibrational intensity，$f$ is the frequency，$t$ is the time variable，and $r_{O-H}$ is the length of the O-H bond in the water molecules.

Weak interaction analysis can reveal the non-covalent interactions among water molecules，such as electrostatic forces，H-bonds，and van der Waals forces. In this study，based on the initial configurations output from the MD simulations of infrared spectroscopy analysis，one water molecule is fixed while allowing other water molecules to move freely. A 1 ns MD simulation is conducted under the same conditions，yielding 1000 trajectory data frames. Utilizing these coordinate data，the average reduced density gradient（aRDG） among the water molecules is analyzed using the quantum chemical wave function analysis program Multiwfn ^［37］. The aRDG is calculated based on the average density gradient（$\overline{\nabla \rho \left(r\right)}$） and the average density（$\overline{\rho \left(r\right)}$） from the trajectory data，with the specific formula shown as follows：

Firstly，we calculated the time autocorrelation functions of the O-H bond lengths in 1DCW and BW using MD simulations，and then processed these autocorrelation functions with Fourier transform to obtain the infrared spectra of the stretching vibrations. As shown in Fig 2，the gray and red curves represent the variations in the spectral intensity of the stretching vibrations of water molecule's H₁ and H₂ atoms with the O atom across different vibration frequencies，with absorption peaks primarily distributed in the 90-100 THz range. Compared to the experimentally measured overall vibration infrared spectra of the O-H bonds in BW within the 90-110 THz range，our theoretical calculations are consistent with the actual values ^［38］. Fig 2（a） displays the stretching vibration spectra of the O-H₁ and O-H₂ bonds in 1DCW，where significant differences in the vibration frequency peaks of the two are evident. The main absorption peak of the O-H₁ bond is located at 95.0 THz，while that of the O-H₂ bond is around 98.2 THz，indicating that these two O-H bonds in 1DCW exhibit different stretching vibration modes. In contrast，in BW water（as shown in Fig 2b），both O-H₁ and O-H₂ bonds exhibit two major absorption peaks，with peak frequencies and intensities that largely coincide，indicating they are in the same stretching vibration mode. By comparing the infrared spectra of water in these two different environments，we find that in 1DCW，both O-H bonds have their specific vibration frequencies，whereas in BW，the vibration frequencies of the two O-H bonds vary between two peaks.

Typically，the vibrational frequency of water molecules is closely related to the internal constraints，which we liken to a spring in simple harmonic motion for the O-H bond stretching，where the force applied determines the stiffness coefficient k ^［39］. In simple terms，the strength of donor-acceptor interactions in the O-H bond is the main determinant of k，the interatomic distance（$R_{O-H}$）. Based on the expression for spring harmonic vibration frequency，$f=\sqrt[]{k/m}$，when the interaction energy of the O-H bond is high，the spring is more rigid，meaning the stiffness coefficient k is larger，and consequently，the vibration frequency also increases. Therefore，we have conducted a detailed analysis of the O-H bond lengths and their distribution. Fig 3a and 3b show the noticeable fluctuations in the O-H₁ and O-H₂ bond lengths observed in real-time in 1DCW and BW. In 1DCW，the fluctuations in O-H₁ and O-H₂ bond lengths are distinctly different，with H₁ showing greater stretching lengths. In contrast，the fluctuations of the two O-H bonds in BW are more consistent，displaying a mix of longer and shorter bonds. As shown in Fig 3c and 3d，our statistical analysis further reveals that in 1DCW，the O-H₂ bond is shorter than the O-H₁ bond，with peak distribution lengths of 0.1005 nm and 0.1035 nm，respectively. Using the flexible SPC/E water model，the O-H bond length is 0.1000 nm（see Table 1），indicating that the O-H₂ bond in 1DCW is not affected by external forces，maintaining its vibrational characteristics，while the O-H₁ bond length has increased by 0.003 nm. Consequently，its interaction strength is reduced，the spring's rigidity is weakened，leading to a relative decrease in peak frequency. On the other hand，the distribution of the two O-H bond lengths in BW is almost identical，with peaks at about 0.1024 nm，but their distribution range is broader than in 1DCW. This indicates that the stretching amplitude of BW’s O-H bonds fluctuates between longer and shorter bonds. This result further confirms that the differences in the infrared spectra of O-H bond stretching vibrations between 1DCW and BW are due to their different stretching amplitudes.

In infrared spectroscopy analysis，the high-frequency stretching vibration frequencies of the O-H bonds within water molecules exhibit a strong correlation with the H-bond network structure. To deeply understand the influence of the differences in O-H bond stretching amplitudes in 1DCW and BW on vibration frequencies，we analyzed the forces exerted by the H-bonds. Fig 4 displays a visual representation of H-bond interactions in these two different systems. Fig 4a shows that in SWNT，water molecules form a one-dimensional chain structure and are orderly connected to adjacent water molecules through H-bonds（indicated by blue discs）. In 1DCW，the O-H₁ bond forms an H-bond with the oxygen atom of a neighboring water molecule，while the O-H₂ bond does not participate in H-bond formation，exhibiting free vibrations. This phenomenon is reflected in the significantly lower main peak frequency of O-H₁ in the infrared spectrum. The fundamental reason for this difference is that the O-H₁ bond，acting as an H-bond donor and being attracted by the H-bond，experiences increased stretching amplitude，reduced interaction force，weaker spring stiffness，and consequently，a lower peak frequency. On the other hand，as shown in Fig 4b，BW molecules form a tetrahedral H-bond network structure in the bulk phase，where both O-H bonds can form significant H-bonds with adjacent water molecules，distinctly different from the situation inside SWNT. These two unique H-bond network structures create different constraint environments，not only affecting the extent of O-H bond stretching but also leading to significant differences in vibration frequency patterns. This phenomenon profoundly reveals the key impact of H-bond network structures on molecular vibrational characteristics. In 1DCW，the O-H₁ bond involved in H-bond formation shows a lower infrared spectroscopy frequency of stretching vibrations than the O-H₂ bond，which does not form H-bonds. Meanwhile，in BW，the O-H bonds participate in both the formation and breaking of H-bonds，but due to the rapid formation and breaking，their stretching vibration frequencies fluctuate between higher and lower frequencies.

Finally，we compared the motion trajectories of water molecules in different environments. Fig 5 visually illustrates the motion characteristics of H atoms and the differences induced by their environments through two-dimensional plane projections of H atom trajectories obtained from 8 ps of MD simulations. Fig 5a and 5b reveal the differences in the motion patterns of H₁ and H₂ atoms inside SWNT in 1DCW. Due to H₁ atom's participation in H-bonds，influenced by H-bond interactions and the spatial constraints of SWNT，its trajectory across all three planes is more concentrated，indicating its relatively slow and limited range of motion. In contrast，the H₂ atom，not involved in H-bonds，exhibits a more dispersed trajectory，especially showing a significant circular path on the XY plane，clearly indicating the free motion around the tube axis（Z-axis being the direction of the SWNT） for H atoms not involved in H-bonds inside SWNT. This phenomenon further illustrates how H-bond affects the vibrational characteristics of the O-H bonds，thereby causing differences in the spectra. Turning to Fig 5c and 5d，we observed no significant differences in the amplitude of motion between the two H atoms in BW. Further analysis reveals that the motion trajectories of H atoms in BW seem to be a composite of those of H₁ and H₂ atoms in 1DCW，with the amplitude between the constrained motion of H₁ and the free motion of H₂. However，the motion space for water molecules in the bulk environment far exceeds the narrow constraints of SWNT，thus allowing H atoms in the bulk to have a much larger range of activity. This finding suggests that in BW，the state of H atom motion continuously transitions between free and constrained motions，frequently undergoing the process of H-bond formation and breaking. In summary，we not only elucidate the differences in the stretching vibration infrared spectra of the O-H bonds in 1DCW and BW but also reveal the deeper mechanisms behind these differences. In 1DCW，a one-dimensional H-bond network structure is formed，while BW displays a tetrahedral H-bond network. The state of H atom motion shows clear differences due to different spatial constraints. These constraints and the interactions of H-bonds not only affect the amplitude of the O-H bond stretching vibrations but also produce unique characteristics in the infrared spectra.

In summary，this paper based on molecular dynamics simulations，analyzes the infrared spectroscopic characteristics of the O-H bonds of water in two different environments： SWNT and bulk phase. The study reveals that in 1DCW，the stretching vibration frequency of the O-H₁ bond involved in H-bond is lower than that of the O-H₂ bond which does not participate in H-bond. Conversely，in BW，the main peak frequencies of both O-H bonds are nearly identical. Further analysis showed that the stretching amplitude of the O-H₁ bond in 1DCW is significantly higher than that of the O-H₂ bond，resulting in a lower vibration frequency for O-H₁. In BW，both O-H bonds have consistent stretching amplitudes，displaying both long and short bonds，hence there are two main frequency absorption peaks. To understand more deeply the reasons for these differences in stretching amplitudes，we conducted a detailed analysis of the H-bond networks of the water molecules. In SWNT，water molecules form a one-dimensional chain structure，with only one H atom involved in H-bond，leading to differentiated stretching characteristics of the two O-H bonds. In contrast，the tetrahedral H-bond network structure in BW results in more uniform stretching amplitudes for both O-H bonds. Finally，by comparing the motion trajectories of water molecules in different environments，it was found that in 1DCW，the H₁ atom shows constrained dynamic behavior due to its participation in H-bond，while H₂，not involved in H-bond，exhibits greater freedom of movement. This dynamic difference indirectly reflects the vibrational modes of the water molecule's O-H bonds and forms specific characteristics in the infrared spectrum. However，in the tetrahedral H-bond network of BW，both H atoms are subject to similar constraints，thus their motion trajectories show no significant differences，but the state of motion continuously transitions between free and constrained，further displaying the dynamic equilibrium of H-bonds. These findings reveal the structure and dynamics of the H-bond networks of water molecules in different microenvironments and clarify how these characteristics influence the infrared spectrum of water molecules. This research deepens our understanding of the unique characteristics of molecules in diverse environments ^［40-41］ and the fluctuation in the confinement ^［42-43］. Additionally，this study also provides important theoretical support for precision water modulation technologies based on infrared spectral absorption peaks ^［44-45］，and has important implications for the study of nanofluids ^［46-47］.