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Article

Nuclear Magnetic Resonance (NMR) and Density Functional Theory (DFT) Study of Water Clusters of Hydrogen-Rich Water (HRW)

by
Nikolay Vassilev
1,
Ignat Ignatov
2,*,
Teodora P. Popova
3,
Fabio Huether
4,
Alexander I. Ignatov
2,
Mario T. Iliev
5 and
Yordan Marinov
6
1
Institute of Organic Chemistry with Centre of Phytochemistry, Bulgarian Academy of Sciences, Acad. G. Bontchev Str. Bl. 9, 1113 Sofia, Bulgaria
2
Scientific Research Center of Medical Biophysics (SRCMB), 1111 Sofia, Bulgaria
3
Faculty of Veterinary Medicine, University of Forestry, 10 Kl. Ohridski Blvd., 1756 Sofia, Bulgaria
4
EVODROP AG, 8306 Brüttisellen, Switzerland
5
Faculty of Physics, Sofia University, St. Kliment Ohridski, 1000 Sofia, Bulgaria
6
Georgi Nadjakov Institute of Solid State Physics, Bulgarian Academy of Sciences, 72 Tzarigradsko Chaussee Blvd., 1784 Sofia, Bulgaria
*
Author to whom correspondence should be addressed.
Water 2024, 16(22), 3261; https://doi.org/10.3390/w16223261
Submission received: 23 September 2024 / Revised: 9 November 2024 / Accepted: 11 November 2024 / Published: 13 November 2024
(This article belongs to the Section Water and One Health)
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Versions Notes

Abstract

:
The present study investigated the 1H Nuclear Magnetic Resonance (NMR) spectra of hydrogen-rich water (HRW) produced using the EVObooster device. The analyzed HRW has pH = 7.1 ± 0.11, oxidation–reduction potential (ORP) of (−450 ± 11) mV, and a dissolved hydrogen concentration of 1.2 ppm. The control sample was tap water filtered by patented technology. A 600 NMR spectrometer was used to measure NMR spectra. Isotropic 1H nuclear magnetic shielding constants of the most stable clusters (H2O)n with n from 3 to 28 have been calculated by employing the gauge-including-atomic-orbital (GIAO) method at the MPW1PW91/6-311+G(2d,p) density function level of theory (DFT). The HRW chemical shift is downfield (higher chemical shifts) due to increased hydrogen bonding. More extensive formations were formed in HRW than in control filtered tap water. The exchange of protons between water molecules is rapid in HRW, and the 1H NMR spectra are in fast exchange mode. Therefore, we averaged the calculated chemical shifts of the investigated water clusters. As the size of the clusters increases, the number of hydrogen bonds increases, which leads to an increase in the chemical shift. The dependence is an exponential saturation that occurs at about N = 10. The modeled clusters in HRW are structurally stabilized, suggesting well-ordered hydrogen bonds. In the article, different processes are described for the transport of water molecules and clusters. These processes are with aquaporins, fusion pores, gap-junction channels, and WAT FOUR model. The exponential trend of saturation shows the dynamics of water molecules in clusters. In our research, the chemical shift of 4.257 ppm indicates stable water clusters of 4–5 water molecules. The pentagonal rings in dodecahedron cage H3O+(H2O)20 allow for an optimal arrangement of hydrogen bonds that minimizes the potential energy.

1. Introduction

It is important to note that hydrogen as a gas and dissolved in water has no known toxic effects [1]. This safety profile and hydrogen’s potential in medical applications remained relatively unexplored in direct medical applications until 2007. In 2007, Ohsawa et al. reported that inhaling 1–4% hydrogen gas could significantly reduce hydroxyl radicals and peroxynitrite [2]. This discovery marked a significant turning point in the field, opening up new possibilities for medical applications of hydrogen [3,4,5].
NMR studies are influenced by various changes in water’s properties, one of which is its solvency. A team of German scientists conducted a study to determine the minimum number of water molecules required to dissolve another substance. Five water molecules bind to four HCl molecules, which dissociate, resulting in two ion pairs [6], forming a cluster with the formula H+Cl−((H2O)5).
The result serves as a valuable model for understanding the minimum number of water molecules needed to act as a solvent, specifically for acids. In hydrogen-rich water (HRW), neutral clusters with the formula (H2O)n and protonated clusters such as (H3O+(H2O)20 are anticipated. Characteristic NMR spectra for proton transfer in protonated water clusters were studied for H+(H2O)n, where n = 2–5 [7]. Many studies of water clusters involve hydrophobic environments [8]. NMR studies involving zeolite yield clusters with formula H+(H2O)8 [9]. An exciting model for fundamental studies of water clusters of the type [H+(H2O)nm(H2)] has been obtained through the association of water clusters with hydrogen gas [10]. Hydrogen-rich water (HRW) can be produced through a proton exchange membrane (PEM) during the process of electrolysis [11]. The effects of hydrogen bonding had been studied for neutral water clusters with formula (H2O)n. The results were achieved for n = 2–6 [12]. With the application of 1H-NMR and DFT, clusters were investigated with the formula (MSA)m(H2O)n(m = 1–2, n = 1–5). MSA is methane sulfonic acid [13]. The most indicative experiment is in a hydrophobic environment with slower hydrogen ion (H+) interactions between water molecules in clusters. A signal from the water clusters is obtained within three days [14]. Studies on hydrogen bond strength and vibrational spectroscopy were performed [15]. Density functional theory has applications for researching water clusters with different numbers of water molecules. For example, the structure of water clusters in the wide range of n = 2 to n = 34 was modeled at HF/6-31G(d) level of theory [16]. It was found that hexagonal water clusters have been theoretically proposed to include combinations of 21 and 22 water molecules with the formula H+(H2O)n [17]. The hexagonal structures (H2O)6 and dodecahedron clusters of (H2O)20 have been well established [18,19]. Mehandjiev and co-authors have shown that the most stable clusters, based on the Gaussian distribution of hydrogen bond energies, include 12 or 13 water molecules [20].
According to charge, water clusters can be categorized as neutral, positively, and negatively charged. The formula of neutral water clusters is (H2O)n [21]. Clusters with a positive charge have a general formula, H+(H2O)n, and with a negative charge, OH−(H2O)n [17].
The studies of water clusters were performed with Nuclear Magnetic Resonance (NMR) [22].
Many articles discussed the effects of hydrogen bonds on the structuring of water clusters. Hydrogen bonds have cooperative effects within water clusters [23].
Density functional theory (DFT) was applied to examine the role of hydrogen bonding in evaluating the stability of water clusters [24]. The Quantum Theory of Atoms in Molecules (QTAIM) and different DFT functionals have been applied to explore the non-covalent bonding in water clusters with the formula (H2O)n, considering n = 2–7 [25]. The formation of hexagonal water clusters is discussed in the context of hydrogen bonding [26], as these structures allow for an optimal arrangement of hydrogen bonds [19], which minimizes potential energy [27]. This process is intensified during freezing, high pressure, hydrophobic surfaces, and filtration.
Aquaporins, discovered by Agre, are essential for transporting water molecules across cell membranes [28,29]. Water molecules affect the structure and function of biological membranes, contributing to processes like membrane fusion. Pores in the fusion process ranging in size from 1 to 7 nm can be formed in lipid bilayer membranes. One realistic model for the fusion of two membranes assumes a proteinaceous initial fusion pore, since biological “fusion pores” can be as small as ion channels or gap junctions. The investigation has found pore opening and flickering during the fusion of protein-free phospholipid vesicles with planar phospholipid bilayers. Fusion pore formation appears to follow the coalescence of contacting monolayers to create a zone of hemifusion where continuity between the two adherent membranes is lipidic but not aqueous [28,29]. Although controlled and mediated by specialized proteins, the authors suggest that biological fusion proceeds through lipid-dependent steps that involve the same membrane lipid rearrangement as the fusion of pure lipid bilayers. The water molecules in the hydrocarbon region of the phospholipid bilayers are organized into single files of H-bonded molecules. These water molecules interact with the phospholipid molecules through their chemical potential, whereby the thermodynamic state of the phospholipid molecules changes. New types of phase transitions occurring at specific values of this activity have been identified. The chemical potential of water molecules in membranes likely regulates their thermodynamic state, affecting membrane proteins’ activity [30]. Water molecules are transported through gap-junction channels of 1.5–2.0 nm [31].
The WAT FOUR model, utilized in this study, is a coarse computational approach in which four beads represent each water molecule. This model is designed to simplify the simulation, such as hydrogen bonding. It allows for a more efficient analysis of large systems, though it did not capture the fine quantum mechanical details of rigorous methods like DFT. The model lumps approximately 11 WATer molecules into FOUR tetrahedrally interconnected beads, hence the name WAT FOUR [32].
Our study has water clusters with sizes from 3 to 23 water molecules and a saturation of 10 water molecules. Our DFT results also correspond to the WAT FOUR model.
Heine et al. 2017 showed that the primary frequency of hydrogen bonds in hexagonal structures is 1117 cm−1 [33]. The hexagonal clusters are formed near the freezing point and lower temperatures, high pressure, hydrophobic surfaces, and filtration. The results with filtered water in hexagonal structures of 1117 cm−1 were published [19].
Additional electrons from the device’s cathode for HRW increase the energies of the hydrogen bonds, making the water clusters more compact. This leads to more vital chemical shifts in NMR.
The specific property of HRW is the oxidation–reduction potential (ORP), which measures the solution’s capacity to act as a reducer or oxidizer [34]. The negative ORP indicates its ability to donate electrons, thereby neutralizing free radicals.
The present research used NMR and DFT methods to analyze the possibility that water clusters tend to stabilize around 10 water molecules. Still, larger clusters of up to 23 molecules were also modeled.

2. Materials and Methods

2.1. Hydrogen-Rich Water (HRW)

The experiments for chemical reaction for hydrogen-rich water were conducted in the Georgi Nadjakov Institute of Solid State Physics, Bulgarian Academy of Sciences.
The chemical reaction for hydrogen-rich water is [35]:
Mg + 2H2O → Mg (OH)2 + H2
Hydrogen-rich water (HRW) is also obtained through a chemical process using a Proton Exchange Membrane (PEM) [36]. With PEM, there are anode and cathode chambers.
At the anode chamber, oxygen (O2) and protons (H+) are formed:
2H2O → 4H+ + O2 + 4e−
At the cathode chamber, hydrogen gas and water are generated:
2H+ + 2e−→ H2
As a result, the hydrogen-rich water has a neutral pH and negative oxidation redox potential (ORP).
The experiments for NMR and DFT were performed in the Institute of Organic Chemistry with Centre of Phytochemistry, Bulgarian Academy of Sciences.
Figure 1 illustrates the scheme for hydrogen-rich EVOdrop water (HEW).
In our research for HRW, we applied the EVObooster device to obtain hydrogen-rich water (Figure 2). The principal scheme is shown in [37].
The device standard is a hydrogen concentration of 0.9–1.2 ppm, an ORP of (−450~−580) mV, and a pH of 7.1–7.3 [37].
The control sample was tap water filtered using patented technology [38,39]. The control sample has a certificate from European Drinking Water Directive 2020/2184 with certificate No. 13100/02.02.2023.

2.2. NMR Spectroscopy

The nuclear magnetic resonance (NMR) spectra were measured on Bruker Avance II+ 600 NMR spectrometer using a 5 mm direct detection dual broadband probe. The experiments were performed at a temperature of 298 K. 1H NMR spectra were acquired with 128 K time domain points, spectrum width of 9600 Hz, 16 scans, and a relaxation delay of 60 s. The chemical shifts were referenced to the residual dmso-d6 resonance used as an external reference (2.5 ppm). The dmso-d6 was placed in a coaxial capillary in the sample tube and used as a lock signal.

2.3. Theoretical Calculations

The water sample results from NMR were calculated using the Gaussian 16 [40] software. The optimization of the structure of water clusters was performed by MP2/CBS-e [41], by M06-2X/aug-cc-pVDZ [42], by B3LYP/6-31++G** [43], or by MP2/aug-cc-pVTZ [44]. We have used MPW1PW91 hybrid density functional theory (DFT) in combination with the 6-311+G(2d, p) basis set. The set has yielded reliable NMR and geometrical results for moderately sized hydrogen-bonded systems, which have been subjected to realistic computational expenses [45,46].
The Gaussian method analyzed the chemical shielding tensors of NMR, including atomic orbitals (GIAO). GIAO was developed and implemented for DFT and Gaussian software 16 [16] based on the methods of Ditchfield and Hameka [47]. The SMD optimization implicitly included the solvent effect with the built-in water parameters [48].

2.4. Water Clusters

The water clusters were studied using NMR and DFT. The following types were the objects of the investigations: (i) the water trimer in the form of a cooperative ring; (ii) tetramer consisting of a ring (S4); (iii) pentamer in the form of a cooperative ring; hexamer in the form of a hexagonal ring. The selected tetramer and hexamer are the best-structuring energy clusters [19,28]. In addition, the structures of heptamer CH1, octamer D2d, nonamer D2dDDh, and decamer PP1 were studied to include stable clusters with 7 to 10 water molecules [42,49].
The papers demonstrate the optimized structures of the dodecahedral water cage (H2O)20, tetrakaidecahedral water cage (H2O)24, and hexakaidecahedral water cage (H2O)28, which were investigated [42]. Our study also researched the structure of the pentagonal dodecahedron cage and H3O+(H2O)20 [43], in which the hydronium ion resides on the surface of the cage.

2.5. Research of pH and Oxidation–Reduction Potential (ORP)

The research on pH was performed in a licensed laboratory, Eurotest control, Sofia, Bulgaria, from European Drinking Water Directive 2020/2184 with certificate No. 13100/02.02.2023. The oxidation–reduction potential (ORP) was measured with Redox Potential Sensor ORP XT1 (Senect GmbH&Go. KG, Landau, Germany) in the Bulgarian Academy of Sciences laboratory.

3. Results and Discussion

The results with HRW were achieved with hydrogen concentrations of 0.9–1.0 ppm [50], 0.9 ppm [51].
The results of water clusters with hydrogen-rich water (HRW) were achieved using NMR and DFT. EVObooster was applied as an experimental device with hydrogen concentration for the sample of 1.2 ppm, pH = 7.1 ± 0.11, ORP = (−450 ± 11) mV.
Table 1 illustrates the chemical shifts of filtered tap water (control sample) and Hydrogen Evodrop Water (HEW).
Results of hydrogen-rich water with 1H NMR.
NMR is a physical phenomenon in which the nuclei of certain isotopes resonate when placed in a strong magnetic field and exposed to a radiofrequency pulse. The magnetic field strength at the nuclei results in an electromagnetic signal.
The electrons of nuclei shield them from the magnetic field. Therefore, different types of nuclei (1H, 13C, etc.) resonate at different frequencies (difference in MHz). Every type of nuclei, hydrogen nuclei, for example, is surrounded by different electron densities, and therefore, they resonate at different frequencies (difference from Hz to kHz; in practice, the ppm scale is used).
Bruker Avance II+ 600 NMR is used to measure 1H NMR spectra. The device uses a 5 mm direct-direction dual broadband probe [52]. The experimental temperature is 293 K. The 1H NMR spectra have the following parameters: 128 time domain points, spectrum width 9600 Hz, 15 scans, and 60 s relaxation delay. The chemical shifts were connected to the DMSO-d6 resonance used as an external reference of 2.5 ppm. The DMSO-d6 was placed in a coaxial capillarity in the sample tube and used as a lock signal.
The results of HEW and control samples with 1H NMR are shown in Table 1 and Figure 3.
The chemical shift of water HEW is shifted to a lower field (higher chemical shifts), which can be explained by the shifting of dynamic equilibrium with clusters [53,54]. The data illustrate that the more extensive sets are in HEW, according to the control sample, which has filtered tap water. The signal area determines the number of nuclei of hydrogen atoms and ions [22].
The signal area determines the number of hydrogen atoms and ions. The NMR spectra show the following dependencies. If there are more hydrogen bonds, the proton nuclei are strongly deshielded, and they appear in the NMR spectrum at higher chemical shifts; hydrogen bonding decreases the electron density of hydrogen, which leads to higher chemical shifts.
Hydrogen bonding reduces the electron density around the hydrogen nucleus, causing deshielding, which results in a downfield shift (higher chemical shift) in the NMR spectrum.
The authors obtained metastable clusters in hydrophobic solvents and studied them by standard 1H NMR spectra. Under these conditions, separate signals are observed for water clusters, dissolved water, and water aggregates. Comparing the experimental and theoretically calculated chemical shifts, the signal for 5.26 ppm is attributed to the cubic octamer D2d structure.
In our HEW sample conditions, proton exchange between water molecules is very fast on the NMR time scale, and an average signal of all water protons is observed. Therefore, we averaged the calculated chemical shifts of the investigated water clusters.
A more extensive width line ν1/2 is connected with faster relaxation of the hydrogen nuclei. The increased relaxation rate with NMR is observable in natural waters.
The number of water molecules was calculated based on chemical shifts using the GIAO/SMD/MPW1PW91/6-311+G-(2d,p)//MP2/aug-cc-pVTZ method, with optimization performed at MP2/aug-cc-pVTZ geometries.
Table 2 illustrates the average chemical shifts of modeled water clusters under fast exchange conditions calculated using the GIAO/SMD/MPW1PW91/6-311+G-(2d,p) method combined with MP2/aug-cc-pVTZ geometries.
Table 3 illustrates the computed averaged (fast exchange) chemical shifts of modeled water clusters at GIAO/SMD/MPW1PW91/6-311+G-(2d,p)//MP2/CBS-e level of theory (MP2/CBS-e geometries are taken from [41]).
The article by Ojha et al. emphasizes hydrogen bonds as the strength of the structure and dynamic of water molecules [15]. In the data in Table 2, it can be seen that as the number of water molecules in the cluster increases, the number of hydrogen bonds grows in a non-linear fashion, indicating the formation of bigger water clusters. For larger clusters in the table, the chemical shift approaches a stable value, potentially indicating saturation in the structure stability of hydrogen bonds. The Ojna et al. study discusses how hydrogen bonds can lead to a limited increase in frequencies within a stable network, explaining δ/Δδ for large clusters stabilizing specific values [15].
To understand this trend deeply, we modeled the most stable clusters (H2O)n (n = 3–23) and the solvated hydronium ion H3O+·(H2O)20. The calculated GIAO/SMD/MPW1PW91/6-311+G-(2d,p)//MP2/CBS-e proton chemical shifts were averaged (fast exchange) and are presented in Table 2. It can be seen from the table that with the increase in the size of clusters, the number of hydrogen bonds increases, and the chemical shift increases as well.
Figure 4 illustrates the dependence of all DFT computed averaged NMR chemical shifts on the size of the modeled clusters.
Figure 4 illustrates the dependence between the number of water molecules and the chemical shift (δ). The geometries were optimized using various levels of theory, including MP2/CBS-e, B3LYP/6-31++G**, for modeling of water clusters.
The graph demonstrates that the chemical shift in the NMR spectrum of water clusters increases rapidly to about 10 water molecules after an exponential saturation occurs. The measured chemical shift of 4.257 ppm is evidence for stable water clusters with 4–5 molecules. Once stabilized, these clusters reach their energetically optimal state. It causes minimal changes in the chemical shift as the number of molecules increases.
Figure 4 presents neutral clusters with the formula (H2O)n achieved with density functional MPZ/aug-cc-pVTZ for n = 3–23 and MPZ/CBS-e for n = 3–10.
Table 4 shows the average chemical shifts of modeled H3O+(H2O)x clusters under fast exchange conditions calculated using GIAO/SMD/MPW1PW91/6-311+G-(2d,p) method combined with B3LYP/6-31++G** optimized geometries.
We have paid particular attention from DFT to the dodecahedron cage H3O+(H2O)20 [44], the structure shown in Figure 5.
The cluster with the formula H3O+(H2O)20 has pentagonal rings arranged in a three-dimensional network. The results with filtered water were achieved in [19].
Geometries were obtained from various theoretical approaches. Careful comparison ensured consistency across different models, though slight variations in calculated shifts are expected due to methodological differences.
The image from Figure 5 shows water molecules connected by hydrogen bonds, forming a three-dimensional network. This structure likely contains a combination of pentameric rings. They are typical for water clusters with cage-like structures. These cycles are essential for the cluster’s stability and demonstrate the hydrogen-bonded network’s complexity. Hexameric rings are generally more common in ice structure, while a combination of tetramers and pentamers is characteristic of amorphous and cluster forms of water.
Figure 4 shows an exponential saturation dependence of chemical shift from a number of water molecules. At N = 10, saturation occurs, and the clusters in HRW stabilize structurally. The chemical shifts at N = 10 begin to stabilize, indicating well-ordered hydrogen bonds.
This result agrees with the cell cage research of water clusters with n = 8–20 [47] and n = 3–6 and n = 8–20 [48].
Ab initio calculations have been performed using the 6-31G(d,p) and 6-311++G(2d,2p) basis sets for (H2O)n, where n = 8–20 [54,55,56]. The most stable geometries arise from the fusion of tetrameric or pentameric rings. This result corresponds to our findings for stable clusters and rings with tetrameric and pentameric structures.
The studies with HEW had effects with blood serum of hamsters [57].
The most indicative experiment is in a hydrophobic environment with slower hydrogen ions (H+) or proton interactions between water molecules in clusters. A signal from the water clusters is obtained within three days [22].
Density functional theory (DFT) was used to analyze the stability of water clusters depending on the number of hydrogen bonds and the intermolecular interactions of the water clusters [58]. Using Nuclear Magnetic Resonance and Fourier Transform Infrared spectroscopy methods, dimer, tetramer, and hexamer water clusters have been studied with medical applications [59].
Water can be considered as a convenient yet complex model for investigating cooperative interactions and structural organization of molecular clusters sized over the nano- and mezzo-scales. NMR-based parameters demonstrate the number of water molecules and hydrogen bonds in water clusters [42,43]. In addition to enriching fundamental scientific knowledge, the mathematical modeling of water clusters with analyses of the hydrogen bond parameters and, respectively, the hexagonal structures enhance the students’ educational level and laboratory experience [19].

4. Conclusions

1H Nuclear Magnetic Resonance (NMR) spectra of hydrogen-rich water (HRW) produced by a proton exchange membrane (PEM) chemical process were measured on a 600 MHz NMR spectrometer. The chemical shift of water in the tested water sample was slightly shifted to a lower field (higher chemical shifts). The more significant structuring of the HRW can explain this shift produced with the EVOdrop device compared to the control filtered tap water samples. By modeling different water clusters (H2O)n with a range of n from 3 to 23, it was shown that as the size of the clusters increases, the number of hydrogen bonds increases, and the average chemical shift of the hydrogen atoms in the clusters also increases. The pentagonal dodecahedron cage H3O+(H2O)20 structure was investigated. The present research used NMR and DFT methods to analyze the possibility that water clusters tend to stabilize around 10 water molecules. The exponential trend of saturation shows the dynamics of water molecules in clusters. In our research, the chemical shift of 4.257 ppm indicates stable water clusters of 4–5 water molecules. The pentagonal rings in dodecahedron cage H3O+(H2O)20 allow for an optimal arrangement of hydrogen bonds that minimizes the potential energy.

Author Contributions

Methodology, N.V., I.I. and F.H.; Software, M.T.I.; Validation, M.T.I.; Formal analysis, A.I.I.; Investigation, N.V., F.H. and Y.M.; Resources, T.P.P.; Data curation, I.I. All authors have read and agreed to the published version of the manuscript.

Funding

This research received no external funding.

Data Availability Statement

Data is contained within the article.

Acknowledgments

This investigation used research equipment from Distributed Research Infrastructure INFRAMAT, part of the Bulgarian National Roadmap for Research Infrastructures, supported by the Bulgarian Ministry of Education and Science.

Conflicts of Interest

Author Fabio Huether is co-inventor of the Patent CH Patent WO2020169852A1. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

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Water 16 03261 g001
Figure 1. Scheme for hydrogen-rich EVOdrop water (HEW).
Figure 1. Scheme for hydrogen-rich EVOdrop water (HEW).
Water 16 03261 g001
Water 16 03261 g002
Figure 2. EVObooster for hydrogen-rich water.
Figure 2. EVObooster for hydrogen-rich water.
Water 16 03261 g002
Water 16 03261 g003
Figure 3. 1H NMR spectra of EVOdrop hydrogen-rich water (top) and control sample of tap water (bottom).
Figure 3. 1H NMR spectra of EVOdrop hydrogen-rich water (top) and control sample of tap water (bottom).
Water 16 03261 g003
Water 16 03261 g004
Figure 4. The origin of geometries is given in the inset: MP2/aug-cc-pVTZ geometries (black squares), MP2/6-31G* geometries (red circles), M06-2X/aug-cc-pVTZ geometries (blue triangles) and B3LYP/6-31++G** optimized geometries of H3O+(H2O)x clusters (green triangles). The (*) refers to basis function used in quantum chemistry and indicates that the basis set is supplemented with polarization function for a better description of the electronic structure.
Figure 4. The origin of geometries is given in the inset: MP2/aug-cc-pVTZ geometries (black squares), MP2/6-31G* geometries (red circles), M06-2X/aug-cc-pVTZ geometries (blue triangles) and B3LYP/6-31++G** optimized geometries of H3O+(H2O)x clusters (green triangles). The (*) refers to basis function used in quantum chemistry and indicates that the basis set is supplemented with polarization function for a better description of the electronic structure.
Water 16 03261 g004
Water 16 03261 g005
Figure 5. The structure of dodecahedron cage H3O+(H2O)20 (the coordinates taken from [42]).
Figure 5. The structure of dodecahedron cage H3O+(H2O)20 (the coordinates taken from [42]).
Water 16 03261 g005
Table 1. Chemical shifts of a control sample of filtered tap water and hydrogen-rich water (HRW).
Table 1. Chemical shifts of a control sample of filtered tap water and hydrogen-rich water (HRW).
Sampleδ, ppmΔν1/2, HzComment
14.1736.50A control sample of filtered tap water
24.2578.77Sample of HEW
Table 2. Average chemical shifts of modeled water clusters under fast exchange conditions were calculated using the GIAO/SMD/MPW1PW91/6-311+G-(2d,p) method combined with MP2/aug-cc-pVTZ geometries.
Table 2. Average chemical shifts of modeled water clusters under fast exchange conditions were calculated using the GIAO/SMD/MPW1PW91/6-311+G-(2d,p) method combined with MP2/aug-cc-pVTZ geometries.
Number of Water Molecules in ClusterNumber of Hydrogen Bondsδ, ppm
332.38
444.16
554.39
684.28
7104.54
8124.97
9135.03
10155.19
11175.03
12205.12
13215.19
14235.30
16285.20
17285.50
18315.27
19315.57
20345.52
21345.72
22385.51
23395.60
Table 3. The computed averaged (fast exchange) chemical shifts of modeled water clusters at GIAO/SMD/MPW1PW91/6-311+G-(2d,p)//MP2/CBS-e level of theory (MP2/CBS-e geometries).
Table 3. The computed averaged (fast exchange) chemical shifts of modeled water clusters at GIAO/SMD/MPW1PW91/6-311+G-(2d,p)//MP2/CBS-e level of theory (MP2/CBS-e geometries).
ClusterNumber of Hydrogen Bondsδ, ppmComment
H2O01.83
(H2O)212.56
(H2O)333.69Cyclic
(H2O)444.38Cyclic
(H2O)554.60Cyclic
(H2O)664.58Cyclic
(H2O)784.83CH1
(H2O)8125.42D2d
(H2O)9135.45D2dDDh
(H2O)10155.57PP1
(H2O)20305.60[42]
(H2O)24365.29[42]
(H2O)28425.33[42]
H3O+(H2O)20346.02[43]
Table 4. Average chemical shifts of modeled H3O+(H2O)x clusters under fast exchange conditions calculated using GIAO/SMD/MPW1PW91/6-311+G-(2d,p) method combined with B3LYP/6-31++G** optimized geometries (starting geometries are taken from https://www-wales.ch.cam.ac.uk/~wales/CCD/H3O+..H2ON/gmin.html, accessed on 26 February 2018).
Table 4. Average chemical shifts of modeled H3O+(H2O)x clusters under fast exchange conditions calculated using GIAO/SMD/MPW1PW91/6-311+G-(2d,p) method combined with B3LYP/6-31++G** optimized geometries (starting geometries are taken from https://www-wales.ch.cam.ac.uk/~wales/CCD/H3O+..H2ON/gmin.html, accessed on 26 February 2018).
Number of Water Molecules in ClusterNumber of Hydrogen Bondsδ, ppm
336.14
446.14
556.14
686.01
7106.16
8126.16
9136.15
10156.15
11176.15
12205.93
13215.94
14235.93
16285.91
17285.92
18315.90
19315.96
20346.00
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Vassilev, N.; Ignatov, I.; Popova, T.P.; Huether, F.; Ignatov, A.I.; Iliev, M.T.; Marinov, Y. Nuclear Magnetic Resonance (NMR) and Density Functional Theory (DFT) Study of Water Clusters of Hydrogen-Rich Water (HRW). Water 2024, 16, 3261. https://doi.org/10.3390/w16223261

AMA Style

Vassilev N, Ignatov I, Popova TP, Huether F, Ignatov AI, Iliev MT, Marinov Y. Nuclear Magnetic Resonance (NMR) and Density Functional Theory (DFT) Study of Water Clusters of Hydrogen-Rich Water (HRW). Water. 2024; 16(22):3261. https://doi.org/10.3390/w16223261

Chicago/Turabian Style

Vassilev, Nikolay, Ignat Ignatov, Teodora P. Popova, Fabio Huether, Alexander I. Ignatov, Mario T. Iliev, and Yordan Marinov. 2024. "Nuclear Magnetic Resonance (NMR) and Density Functional Theory (DFT) Study of Water Clusters of Hydrogen-Rich Water (HRW)" Water 16, no. 22: 3261. https://doi.org/10.3390/w16223261

APA Style

Vassilev, N., Ignatov, I., Popova, T. P., Huether, F., Ignatov, A. I., Iliev, M. T., & Marinov, Y. (2024). Nuclear Magnetic Resonance (NMR) and Density Functional Theory (DFT) Study of Water Clusters of Hydrogen-Rich Water (HRW). Water, 16(22), 3261. https://doi.org/10.3390/w16223261

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