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- 2019
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Journal article (peer-reviewed)
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| 2. |
- Kuo, Jer-Lai, et al.
(author)
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On the use of graph invariants for efficiently generating hydrogen bond topologies and predicting physical properties of water clusters and ice
- 2001
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In: Journal of Chemical Physics. - : AIP Publishing. - 0021-9606 .- 1089-7690. ; 114:6, s. 2527-2540
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Journal article (peer-reviewed)abstract
- Water clusters and some phases of ice are characterized by many isomers with similar oxygen positions, but which differ in direction of hydrogen bonds. A relationship between physical properties, like energy or magnitude of the dipole moment, and hydrogen bond arrangements has long been conjectured. The topology of the hydrogen bond network can be summarized by oriented graphs. Since scalar physical properties like the energy are invariant to symmetry operations, graphical invariants are the proper features of the hydrogen bond network which can be used to discover the correlation with physical properties. We demonstrate how graph invariants are generated and illustrate some of their formal properties. It is shown that invariants can be used to change the enumeration of symmetry-distinct hydrogen bond topologies, nominally a task whose computational cost scales like N2, where N is the number of configurations, into an N ln N process. The utility of graph invariants is confirmed by considering two water clusters, the (H2O)6 cage and (H2O)20 dodecahedron, which, respectively, possess 27 and 30 026 symmetry-distinct hydrogen bond topologies associated with roughly the same oxygen atom arrangements. Physical properties of these clusters are successfully fit to a handful of graph invariants. Using a small number of isomers as a training set, the energy of other isomers of the (H2O)20 dodecahedron can even be estimated well enough to locate phase transitions. Some preliminary results for unit cells of ice-Ih are given to illustrate the application of our results to periodic systems.
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| 3. |
- McDonald, S, et al.
(author)
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Graph theoretical generation and analysis of hydrogen-bonded structures with applications to the neutral and protonated water cube and dodecahedral clusters
- 1998
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In: Journal of Physical Chemistry A. - : American Chemical Society (ACS). - 1089-5639 .- 1520-5215. ; 102:17, s. 2824-2832
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Journal article (peer-reviewed)abstract
- Graph theoretical techniques are demonstrated to be of considerable use in the search for stable arrangements of water clusters. inspired by the so-called "ice rules" that govern which hydrogen-bond networks are physically possible in the condensed phase, we use graphical techniques to generate a multitude of local minima of neutral and protonated water clusters using oriented graph theory. Efficient techniques to precisely enumerate all possible hydrogen-bonding topologies are presented. Empirical rules regarding favorable water neighbor geometries are developed that indicate which of the multitude of hydrogen-bonding topologies available to large water clathrates (e.g., 30 026 for (H2O)(20)) are likely to be the most stable structures. The cubic (H2O)(8) and dodecahedral (H2O)(20) clusters and their protonated analogues are treated as examples. In these structures every molecule is hydrogen bonded to three others, which lends to hydrogen-bonding topology fixing the cluster geometry. Graphical techniques can also be applied to geometrically irregular structures as well. The enumerated oriented graphs are used to generate initial guesses for optimization using various potential models. The hydrogen-bonding topology was found to have a significant effect on cluster stability, even though the total number of hydrogen bonds is conserved. For neutral clusters, the relationship between oriented graphs and local minima of several potential models appears to be one-to-one. The stability of the different topologies is rationalized primarily in terms of the number of nearest neighbor pairs that both have a free OH bond. This lends to the identification of water dodecahedra of greatest stability.
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| 4. |
- Ojamäe, Lars, et al.
(author)
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POTENTIAL-ENERGY SURFACES AND VIBRATIONAL-SPECTRA OF H5O2+ AND LARGER HYDRATED PROTON COMPLEXES
- 1995
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In: International Journal of Quantum Chemistry. - : Wiley. - 0020-7608 .- 1097-461X. ; 56:29, s. 657-668
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Journal article (peer-reviewed)abstract
- This article presents calculations of the structure, binding energetics, potential energy surfaces, and vibrational spectra of the H5O ion. The 15-dimensional potential energy surface for the seven nuclei in the ionic complex was computed by pointwise ab initio Møller-Plesset second-order perturbation (MP2) calculations, using the correlation-consistent pVTZ basis set augmented with diffuse basis functions on oxygen. The potential energy surface for the proton-transfer mechanism was investigated, and the effects of surrounding water molecules on the proton-transfer potential energy curve was studied. Density functional calculations for the proton-transfer potential surface are compared to the MP2 results. Geometry-optimized structures, binding energies, and harmonic vibrational spectra of H5O and H9O are presented. The energy-minimum structure of H5O using the augmented pVTZ basis set is of C2 symmetry, whereas for H9O, using the TZ2P basis set, it is of C3 symmetry. The H-bonded OH stretching harmonic frequency of H5O is very low, 913 cm−1, whereas for H9O it is 2927 cm−1. The subspace spanned by the hydrogen-bonded OH distance and the OO distance were used in one- and two-dimensional calculations of the anharmonic vibrational spectrum using collocation methods. The coupling of the OH stretch with the OO vibration causes a redshift and the anharmonicity a blueshift of the OH frequency: the resulting fundamental frequency of the H-bonded OH vibration is 1275 cm−1. Zero-point energies of the proton vibration and pathways for exchange of protons within H5O are discussed. © 1995 John Wiley & Sons, Inc.
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| 5. |
- Ojamäe, Lars, et al.
(author)
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Potential models for simulations of the solvated proton in water
- 1998
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In: Journal of Chemical Physics. - : AIP Publishing. - 0021-9606 .- 1089-7690. ; 109:13, s. 5547-5564
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Journal article (peer-reviewed)abstract
- Analytical potential models are designed for simulations of water with excess protons. The potentials describe both intramolecular and intermolecular interactions, and allow dissociation and formation of the species (H 2 O) n H + . The potentials are parametrized in the form of interactions between H + and O 2− ions, with additional three-body (H–O–H) interaction terms and self-consistent treatment of the polarizability of the oxygen ions. The screening of electrostatic interactions caused by the overlap of the electron clouds in the real molecules is modeled by functions modifying the electric field at short distances. The model was derived by fitting to the potential surface of the H 5 O + 2 ion and other species, as obtained from ab initio MP2 calculations employing an extensive basis set. Emphasis was put on modeling the potential-energy surface for the proton-transfer reaction. Potential-surface profiles, geometry-optimizedstructures and formation energies of H 5 O + 2 , protonated water clusters [H + (H 2 O) n , n=2–4] and water clusters [(H 2 O) n , n=1–6] using these potentials are presented and compared to results using quantum-chemical calculations. The potential models can well reproduce ab initio results for the H 5 O + 2 ion, and can provide formation energies and structures of both protonated-water and water-only clusters that agree favorably with ab initio MP2 calculations.
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