⇦Chinese Physics Letters, 2021, Vol. 38, No. 1, Article code 013101 Uncooperative Effect of Hydrogen Bond on Water Dimer Danhui Li (李丹慧)1, Zhiyuan Zhang (张志远)1, Wanrun Jiang (姜万润)1, Yu Zhu (朱瑜)1, Yi Gao (高嶷)2*, and Zhigang Wang (王志刚)1,3* Affiliations 1Institute of Atomic and Molecular Physics, Jilin University, Changchun 130012, China 2Shanghai Advanced Research Institute, Chinese Academy of Sciences, Shanghai 201210, China 3Institute of Theoretical Chemistry, Jilin University, Changchun 130012, China Received 16 November 2020; accepted 7 December 2020; published online 16 December 2020 Supported by the National Natural Science Foundation of China (Grant Nos. 11974136 and 11674123).
*Corresponding authors. Email: wangzg@jlu.edu.cn; gaoyi@zjlab.org.cn Citation Text: Li D H, Zhang Z Y, Jiang W R, Zhu Y, and Gao Y et al. 2021 Chin. Phys. Lett. 38 013101    Abstract The water dimer demonstrates a completely different protype in water systems, it prefers not forming larger clusters instead existing in vapor phase stably, which contracts the viewpoint of the cooperative effect of hydrogen bond (O–H$\cdots$O). It is well accepted that the cooperative effect is beneficial to forming more hydrogen bonds (O–H$\cdots$O), leading to stronger H-bond (H$\cdots$O) and increase in the O–H bond length with contraction of intermolecular distance. Herein, the high-precision ab initio methods of calculations applied on water dimer shows that the O–H bond length decreases and H-bond (H$\cdots$O) becomes weaker with decreasing H-bond length and O$\cdots$O distance, which can be considered as the uncooperative effect of hydrogen bond (O–H$\cdots$O). It is ascribed to the exchange repulsion of electrons, which results in decrease of the O–H bond length and prevents the decrease in the O$\cdots$O distance connected with the increasing scale of water clusters. Our findings highlight the uncooperative effect of hydrogen bond attributed to exchange repulsion of electrons as the mechanism for stabilizing water dimer in vapor phase, and open a new perspective for studies of hydrogen-bonded systems. DOI:10.1088/0256-307X/38/1/013101 © 2021 Chinese Physics Society Article Text As one of important issues worthy of paying attention and recognized in public views, peculiar and complicated water has been studied by many researchers.[1–4] Compared with most of the other properties, the phase diagram of water is extremely special and complex.[5] It has been reported that the phases of water involve the arrangement of molecules and hydrogen bonds, ice as well as liquid water were acquainted as the hexagonal and tetrahedral hydrogen-bonded systems respectively.[6,7] However, the water dimer exists in the supposed simple vapor phase stably, it does not prefer forming large clusters[8] instead serving a completely different protype in water systems.[9] It has been revealed that the water dimer cannot be the original model of bulk water and should be separated from other clusters. Although it can be observed experimentally,[10,11] it has never been explained, which captures our attention. Cooperative effect of hydrogen bond, proved to exist in water systems widely,[12–14] is known to play a critical role in the structures dominating the phases.[15–17] It was recognized that the existence of hydrogen bond between water monomers is beneficial to forming more hydrogen bonds (O–H$\cdots$O), accumulating the water monomers, and strengthening H-bond (H$\cdots$O) initially.[18–20] The subsequent researches have suggested a more intuitive conformation change reflected by the cooperative effect, the O–H bond length increases with simultaneous decreases of H-bond length and O$\cdots$O distance between any pairs of water molecules for water clusters and bulk water,[13,21,22] contributing to the structural formation of liquid water and ice.[13] In addition, the widely applied methods of density functional theory (DFT) and force field[23,24] can account for the structures and properties in liquid and solid phases of water.[25,26] Nevertheless, the influence of forming more hydrogen bonds and increasing scale of water clusters of cooperative effect is not exerted on the water dimer, it reminds that the cooperative effect does not originate from water dimer,[27] and a more precise approach applied on the special water dimer is needed. To explore the nature of water dimer's stable existence in vapor phase, we investigate the water dimer from the structural perspective with the ab initio wave function theory and other diverse methods, especially the properties with the compression of water dimer. Surprisingly, the results obtained with the ab initio methods reject those with other methods or even with generally admired DFT calculations. The O–H bond length decreases with the simultaneous decreases of H-bond distance and O$\cdots$O distance instead of its increase as reported in previous studies. It is also opposite with the conformational change when the scale of water clusters increases.[13,28] Moreover, the bond energy of H-bond is smaller, indicating the weaker H-bond. The decreasing O–H bond length and the weaker H-bond can be seen as the uncooperative effect on water dimer. Most importantly, we find that the uncooperative effect of hydrogen bond (O–H$\cdots$O) on the water dimer results from exchange repulsion of electrons, which tends to prevent the decrease of O$\cdots$O distance accompanied with the increasing scale of water clusters, leading to the stable existence of water dimer. Results and Discussion. The study was carried out with different methods: (1) coupled-cluster singles and doubles with perturbative triple excitations [CCSD(T)][29] and explicitly corrected coupled-cluster singles and doubles with perturbative triples method [CCSD(T)-F12][30] of ab initio methods, (2) DFT,[31] (3) tight-binding density function theory (DFTB)[32] with various dispersion, (4) methods of force field[33] containing SPC, SPCE, TIP3P and TIP4P water models [see Part 15 in the Supporting Information (SI) for details]. The stable structure optimized with CCSD(T) is shown in Fig. 1(a), and it conforms to the previous researches.[34,35] As it can be seen in Fig. 1(b), the O–H bond lengths of the water dimer calculated with the CCSD(T) and CCSD(T)-F12 methods keeps decreasing with the decreasing O$\cdots$O distance and H-bond length. However, results obtained with the DFT methods demonstrate that the O–H bond length increases and most of the $\Delta$O–H bond lengths are above zero. The different trends of the O–H bond length in the DFT methods are caused by the negligence of Coulomb repulsion of electrons with spin in opposite direction. Though Pauli repulsion of electrons with spin in the same direction has been considered in the DFT methods, electrons cannot occupy the same position because of Coulomb repulsion. On the contrary, the CCSD(T) method excites electrons from occupied orbitals to unoccupied orbitals, and more excited states reduce the probability of the same position occupied by electrons with opposite spin.[29] Obviously, such considerations are not capable to be implemented in classical simulations. This result is also clearly different from the previous compression results of water that the increasing O–H bond length keeps cooperative with the decreasing H-bond length and O$\cdots$O distance, which is related to the increasing scale of water clusters[13,20,21] (see Part 16 of the SI for details).
cpl-38-1-013101-fig1.png
Fig. 1. The structural parameters in the water dimer, the O–H distance and binding energies of O–H bond during the compression. (a) The stable structure of the water dimer optimized with the CCSD(T) method. (b) The O–H bond length (solid line) and the H-bond length (dotted line) in the water dimer scanned with the PEB0-D3, PBE-D3, B3PW91-D3, B3LYP-D3, HSE06-D3 methods of DFT as well as the ab initio CCSD(T) and CCSD(T)-F12 methods. (c) The binding energies without monomers' deformation energies of the O–H bond in the water dimer calculated with the PBE0-D3, PBE-D3, B3PW91-D3, B3LYP-D3, HSE06-D3, CCSD(T) methods as well as the CCSD(T)-F12 method. (d) The binding energies with monomers' deformation energies of the O–H bond in the water dimer calculated with the PBE0-D3, PBE-D3, B3PW91-D3, B3LYP-D3, HSE06-D3, CCSD(T) methods as well as the CCSD(T)-F12 method. (e) The deformation energies of monomers binding O–H bond in the water dimer calculated with the PBE0-D3, PBE-D3, B3PW91-D3, B3LYP-D3, HSE06-D3, CCSD(T) methods as well as the CCSD(T)-F12 method.
We also calculate the binding energies of the O–H bond with the ab initio CCSD(T), CCSD(T)-F12 and DFT methods. As shown in Figs. 1(c)–1(e), the binding energies of the O–H bond without and with monomers' deformation energies, as well as the deformation energies of monomers, are displayed, respectively. Without the deformation energies of monomers, the shorter the O–H bond length compared with the stable point is, the greater the released energies of bonded monomers calculated with CCSD(T) and CCSD(T)-F12 methods [see Fig. 1(c)] are. This indicates that more energies are needed to break the O–H bond and the bond energies of O–H bond are larger than the value 5.61 eV for the stable structure.[36] However, the relationship between the O–H bond length and the corresponding binding energies calculated with the DFT methods does not fit the linear relation obtained with the ab initio CCSD(T) and CCSD(T)-F12 methods. It reflects the inaccurate trend of the O–H bond during the compression with the DFT methods. The similar results are also obtained in the binding energies of the O–H bond with the deformation energies considered [see Fig. 1(d)], and there are less released energies compared with 5.43 eV for the stable structure [see Fig. 1(d) and Part 7 of the SI for details]. More clearly shown by Fig. 1(e), the deformation energies of ab initio methods become larger with further compression on the water dimer, while there is not an obvious connection between deformation energies and structures obtained with the DFT methods. All these consequences reveal that the DFT methods are improper for treating compression especially the water dimer. Furthermore, we calculate the binding energies of H-bond without monomers' deformation energies using the CCSD(T) and CCSD(T)-F12 methods. In contrast to the binding energies of the O–H bond, the value of $-0.20$ eV for H-bond in the stable structure is relatively smaller, which is consistent with the previous research.[37] As shown in Fig. 2(a), compared with the stable structure, there are less bond energies of H-bond with compression of water dimer. The weaker H-bond shows the uncooperative effect, which hinders to form more hydrogen bonds and to accumulate water monomers.
cpl-38-1-013101-fig2.png
Fig. 2. The related experimental properties and energy decomposition as well as the corresponding percentage of the four terms in the total interaction during the compression of the water dimer. (a) The binding energies of H-bond during compression of water dimer. (b) The NMR chemical shift of the O and H atoms connecting H-bond in water dimer scanned with the CCSD(T) method during the compression. The error bar respects the difference between the data of water dimer scanned with the CCSD(T) method and the CCSD(T)-F12 method. (c) The energy decomposition containing four parts $E_{\rm elec}$, $E_{\rm ex}$, $E_{\rm orb}$ and $E_{\rm disp}$ in Psi4 of the water dimer calculated with the CCSD(T) method. (d) The percentage of the four parts $E_{\rm elec}$, $E_{\rm ex}$, $E_{\rm orb}$ and $E_{\rm disp}$ in the energy decomposition corresponding to the structures of the water dimer at O$\cdots$O distances of 0 Å, $-0.12$ Å and $-0.24$ Å, corresponding O$\cdots$O distances of 2.91 Å, 2.79 Å and 2.67 Å.
For observation of experiment in the future, the nuclear magnetic resonance (NMR) chemical shift of the O and H atoms connecting H-bond is calculated with the CCSD(T) and CCSD(T)-F12 methods, as shown in Fig. 2(b). We can conclude that the chemical shift of the O and H atoms connecting the H-bond is decreasing under the compression, while the data of other atoms are almost unchanged compared with the stable structure (see Part 10 of the SI for details). This indicates that the H-bond becomes weaker because the formation of H-bond between free molecules would lead to the increase in the chemical shift.[38] For the fact that the variation of chemical shift shows the change of the electron density and the NMR reflects the shielding effect of electron density around H nuclei to external magnetic field, it points out a redistribution of the electron density upon H-bond formation.[39,40] The decrement of the NMR chemical shift shows the increment of the shielding effect and the electron density. In our work, the value of the O and H atoms in the H-bond calculated with the CCSD(T) and CCSD(T)-F12 methods decreases. This reveals the more delocalized electron density and less electronegative O atom as well as the weaker ability of the O atom to attract electrons, leading to the decreasing bond energies of H-bond with compression of water dimer.
Table 1. The percentage (%) of the four terms ($E_{\rm elec}$, $E_{\rm ex}$, $E_{\rm ind}$, $E_{\rm disp}$) in the energy composition for three points (in the beginning, middle and last) of the water dimer's scanning at different O$\cdots$O distances.
$\Delta$O$\cdots$O distance $E_{\rm elec}$ $E_{\rm ex}$ $E_{\rm ind}$ $E_{\rm disp}$
0 Å 38.36 38.09 11.63 11.91
$-0.12$ Å 35.11 41.58 12.19 11.11
$-0.24$ Å 32.40 44.67 12.58 10.35
To explain the uncooperative effect of hydrogen bond with compression of water dimer, we perform the symmetry-adapted perturbation theory (SAPT) calculation based on the quantum mechanics. The SAPT decomposes the interaction of two water monomers into four components: electrostatic interaction, exchange repulsion, induction, and dispersion simply and clearly [see Fig. 2(c) and Part 9 of the SI for details]. The decreasing O–H bond length can be explained by the exchange repulsion term in the energy decomposition, the $E_{\rm ex}$ increases with compression, and the percentage is the largest among the four terms, showing that the $E_{\rm ex}$ dominates the interaction between the water monomers [see Fig. 2(d)]. Considering that the exchange repulsion between water monomers mainly arises from the overlap of electrons' wavefunction, the physical basis of it can be seen as a pure quantum effect,[41] which leads to the decrease in the O–H bond length as well as the weaker H-bond (H$\cdots$O). What's more, the exchange repulsion of electrons prevents the decrease in the O$\cdots$O distance related to the increasing scale of water clusters and formation of more hydrogen bonds, resulting in the stable existence of water dimer in vapor phase. In summary, different from ice as well as liquid water known as the hexagonal and tetrahedral hydrogen-bonded systems respectively, the water dimer acts a quite special role in water systems, without forming large clusters and existing in vapor phase stably. It shows the uncooperative effect of hydrogen bond (O–H$\cdots$O) that the O–H bond length decreases and the H-bond (H$\cdots$O) becomes weaker with decreasing H-bond length and O$\cdots$O distance, which can be attributed to the exchange repulsion of electrons. More importantly, as the exchange repulsion of electrons between water monomers tends to prevent the decrease of O$\cdots$O distance, which is accompanied with the increasing scale of water clusters,[13,22] the mechanism of water dimer's stable existence in vapor phase is uncovered. In addition, our findings also reflect the limitations of DFT methods compared with ab initio methods and refresh the traditional perspective of hydrogen bond by investigating the unusual water dimer. It is of great significance for related study of water phase and electronic quantum effect of hydrogen-bonded systems in the future. Author Contributions. D. Li performed the theoretical simulations, Z. Wang initiated the work. Z. Wang and Y. Gao supervised the work. D. Li, Z. Zhang, W. Jiang and Y. Zhu discussed the results. D. Li, Y. Gao and Z. Wang wrote the article. We acknowledge D. Zhang, X. Yang and F. Yu for discussion. Z. Wang also acknowledges the High-Performance Computing Center of Jilin University and the National Supercomputing Center in Shanghai. 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