Assessment of density functional theory to calculate the phase transition pressure of ice

To assess the accuracy of density functional theory (DFT) methods in describing hydrogen bonding in condensed phases, we benchmarked their performance in describing phase transitions among different phases of ice. We performed DFT calculations of ice for phases Ih, II, III, VI and VII using BLYP, PW91, PBE, PBE-D, PBEsol, B3LYP, PBE0, and PBE0-D, and compared the calculated phase transition pressures between Ih-II, Ih-III, II-VI, and VI-VII with the 0 K experimental values of Whalley [J. Chem. Phys., 1984, 81, 4087]. From the geometry optimization of many different candidates, we found that the most stable proton orientation as well as the phase transition pressure does not show much functional dependence for the generalized gradient approximation and hybrid functionals. Although all these methods overestimated the phase transition pressure, the addition of van der Waals (vdW) correction using PBE-D and PBE0-D reduced the transition pressure and improved the agreement for Ih-II. On the other hand, energy ordering between VI and VII reversed and gave an unphysical negative transition pressure. Binding energy profiles of a few conformations of water dimers were calculated to understand the improvement for certain transitions and failures for others with the vdW correction. We conclude that vdW dispersion forces must be considered to accurately describe the hydrogen bond in many different phases of ice, but the simple addition of the R(-6) term with a small basis set tends to over stabilize certain geometries giving unphysical ordering in the high density phases.     

The local and intermediate range structures of the five amorphous ices at 80 K and ambient pressure: a Faber-Ziman and Bhatia-Thornton analysis

Using isotope substitution neutron scattering data, we present a detailed structural analysis of the short and intermediate range structures of the five known forms of amorphous ice. Two of the lower density forms--amorphous solid water and hyperquenched glassy water--have a structure very similar to each other and to low density amorphous ice, a structure which closely resembles a disordered, tetrahedrally coordinated, fully hydrogen bonded network. High density and very high density amorphous ices retain this tetrahedral organization at short range, but show significant differences beyond about 3.1 A from a typical water oxygen. The first diffraction peak in all structures is seen to be solely a function of the intermolecular organization. The short range connectivity in the two higher density forms is more homogeneous, while the hydrogen site disorder in these forms is greater. The low Q behavior of the structure factors indicates no significant density or concentration fluctuations over the length scale probed. We conclude that these three latter forms of ice are structurally distinct. Finally, the x-ray structure factors for all five amorphous systems are calculated for comparison with other studies.     

Formation of high density amorphous ice by decompression of ice VII and ice VIII at 135 K

Monte Carlo computer simulations of ice VII and ice VIII phases have been undertaken using the four-point transferable intermolecular potential model of water. By following thermodynamic paths similar to those used experimentally, ice is decompressed resulting in an amorphous phase. These phases are compared to the high density amorphous phase formed upon compression of ice Ih and are found to have very similar structures. By cooling liquid water along the water/Ih melting line a high density amorphous phase was also generated.     

Transferable model of water with variable molecular size

By decreasing the steepness of the repulsive wing in the intermolecular potential, one can extend the applicability of a water model to the high pressure region. Exploiting this trivial possibility, we published a polarizable model of water which provided good estimations not only of gas clusters, ambient liquid, hexagonal ice, but ice VII at very high pressures as well [A. Baranyai and P. Kiss, J. Chem. Phys. 133, 144109 (2010)]. This straightforward method works well provided the closest O-O distance is reasonably shorter in the high pressure phase than in hexagonal ice. If these O-O distances are close to each other and we fit the interactions to obtain an accurate picture of hexagonal ice, we underestimate the density of the high-pressure phases. This can be overcome if models use contracted molecules under high external pressure.In this paper we present a method, which is capable to describe the contraction of water molecules under high pressure by using two simple repulsion-attraction functions. These functions represent the dispersion interaction under low pressure and high pressure. The switch function varies between 0 and 1 and portions the two repulsions among the individual particles. The argument of the switch function is a virial-type expression, which can be interpreted as a net force compressing the molecule. We calculated the properties of gas clusters, densities, and internal energies of ambient water, hexagonal ice, ice III, ice VI, and ice VII phases and obtained excellent match of experimental data.     

Proton ordering in cubic ice and hexagonal ice; a potential new ice phase--XIc

Ordinary water ice forms under ambient conditions and has two polytypes, hexagonal ice (Ih) and cubic ice (Ic). From a careful comparison of proton ordering arrangements in Ih and Ic using periodic density functional theory (DFT) and diffusion Monte Carlo (DMC) approaches, we find that the most stable arrangement of water molecules in cubic ice is isoenergetic with that of the proton ordered form of hexagonal ice (known as ice XI). We denote this potential new polytype of ice XI as XIc and discuss a possible route for preparing ice XIc.     

Structures of IV group elements and solid phases of water

The structures of solid phases of water and IV(b) group elements of the periodic table (carbon, silicon, germanium, and tin) are compared. Both water and mentioned elements are characterized by high polymorphism. All mentioned elements and ice have a modification with a diamond structure. For all substances considered, except tin, modifications with the structure of a hexagonal analogue of diamond (lonsdaleite) have been known. The modification with the β-Sn structure has not been known only for ice and carbon. One of the germanium modifications is isostructural to ice III. Tin has a modification with the α-Fe structure. The same structure is observed for ices VII, VIII, and X. Both water and IVb group elements can form clathrate compounds with cavities in the form of Allen’s polyhedra. In water clathrates these cavities contain noble gas atoms (Ar, Kr, Xe) and various molecules. Clathrates of IVb group elements contain metal atoms as well as noble gas atoms.     

Nearest-neighbor oxygen distances in liquid water and ice observed by x-ray Raman based extended x-ray absorption fine structure

We report the nearest-neighbor oxygen-oxygen radial distribution function (NN O-O RDF) of room temperature liquid water and polycrystalline ice Ih (-16.8 degrees C) obtained by x-ray Raman based extended x-ray absorption fine structure (EXAFS) spectroscopy. The spectra of the two systems were taken under identical experimental conditions using the same procedures to obtain the NN O-O RDFs. This protocol ensured a measurement of the relative distance distribution with very small systematic errors. The NN O-O RDF of water is found to be more asymmetric (tail extending to longer distances) with longer average distance (2.81 A for water and 2.76 A for ice) but a slightly shorter peak position (2.70 A for water and 2.71 A for ice). The refinement also showed a small but significant contribution from the linear O-H-O multiple scattering signal. The high sensitivity to short range distances of the EXAFS probe will set further restrictions to the range of possible models of liquid water.     

Radiation effects in water ice: a near-edge x-ray absorption fine structure study

The changes in the structure and composition of vapor-deposited ice films irradiated at 20 K with soft x-ray photons (3-900 eV) and their subsequent evolution with temperatures between 20 and 150 K have been investigated by near-edge x-ray absorption fine structure spectroscopy (NEXAFS) at the oxygen K edge. We observe the hydroxyl OH, the atomic oxygen O, and the hydroperoxyl HO(2) radicals, as well as the oxygen O(2) and hydrogen peroxide H(2)O(2) molecules in irradiated porous amorphous solid water (p-ASW) and crystalline (I(cryst)) ice films. The evolution of their concentrations with the temperature indicates that HO(2), O(2), and H(2)O(2) result from a simple step reaction fuelled by OH, where O(2) is a product of HO(2) and HO(2) a product of H(2)O(2). The local order of ice is also modified, whatever the initial structure is. The crystalline ice I(cryst) becomes amorphous. The high-density amorphous phase (I(a)h) of ice is observed after irradiation of the p-ASW film, whose initial structure is the normal low-density form of the amorphous ice (I(a)l). The phase I(a)h is thus peculiar to irradiated ice and does not exist in the as-deposited ice films. A new "very high density" amorphous phase-we call I(a)vh-is obtained after warming at 50 K the irradiated p-ASW ice. This phase is stable up to 90 K and partially transforms into crystalline ice at 150 K.     

Computer simulation study of metastable ice VII and amorphous phases obtained by its melting

Molecular dynamics simulations of metastable ice VII and cubic ice Ic are carried out in order to examine (1) the ability of commonly used water interaction potentials to reproduce the properties of ices, and (2) the possibility of generating low-density amorphous (LDA) structures by heating ice VII, which is known to transform to LDA at approximately 135 K at normal pressure [S. Klotz, J. M. Besson, G. Hamel, R. J. Nelmes, J. S. Loveday, and W. G. Marshall, Nature (London) 398, 681 (1999)]. We test four simple empirical interaction potentials of water: TIP4P [W. L. Jorgensen, J. Chandrasekhar, J. D. Madura, R. W. Impey, and M. L. Klein, J. Chem. Phys. 79, 926 (1983)], SPC/E [H. J. C. Berendsen, J. R. Grigera, and T. P. Straatsma, J. Phys. Chem. B 91, 6269 (1987)], TIP5P [M. W. Mahoney and W. L. Jorgensen, J. Chem. Phys. 112, 8910 (2000)], and ST2 [F. H. Stillinger and A. Rahman, J. Chem. Phys. 60, 1545 (1974)]. We have found that TIP5P ice VII melts at 210 K, TIP4P at 90 K, and SPC/E at 70 K. Only TIP5P water after transition has a structure similar to that of LDA. TIP4P and SPC/E have almost identical structures, dissimilar to any known water or amorphous phases, but upon heating both slowly evolve towards LDA-like structure. ST2 ice VII is remarkably stable up to 430 K. TIP4P and SPC/E predict correctly the cubic ice collapse into a high-density amorphous ice (HDA) at approximately 1 GPa whereas TIP5P remains stable up to approximately 5 GPa. The densities of the simulated ice phases differ significantly, depending on the potential used, and are generally higher than experimental values. The importance of proper treatment of long-range electrostatic interactions is also discussed.     

Structure of coexisting liquid phases of supercooled water: analogy with ice polymorphs

The structural changes occurring in supercooled liquid water upon moving from one coexisting liquid phase to the other have been investigated by computer simulation using a polarizable interaction potential model. The obtained results favorably compare with recent neutron scattering data of high and low density water. In order to assess the physical origin of the observed structural changes, computer simulation of several ice polymorphs has also been carried out. Our results show that there is a strict analogy between the structure of various disordered (supercooled) and ordered (ice) phases of water, suggesting that the occurrence of several different phases of supercooled water is rooted in the same physical origin that is responsible for ice polymorphism.     

Lattice- and network-structure in plastic ice

We have investigated structural and energetic characteristics of plastic ice, which was found in a high pressure region such as 10 GPa by molecular dynamics simulation and free energy calculation. It was predicted that plastic ice intervenes between ice VII and liquid water, in which diffusion is suppressed but rotation is allowed. In the present work, the structure in plastic ice is explored from both local and global view points and focus is placed on the local arrangement, the extent of deviation from the ideal lattice position, and the hydrogen-bonded patterns. The roles of the attractive interaction and the repulsive part of Lennard-Jones potential are also examined. It is found that the higher interaction energy in plastic ice induces a large dislocation of water molecules, which eventually conducts a facile rotation. There are a large amount of hydrogen-bonds which do not orient to the tetrahedral directions. These orientational defects give rise to fusion of the two interpenetrating sublattices of ice VII leading to a plastic phase rather than defect-containing ice VII, which results in a unique network structure of the plastic ice.     

Atomic force microscopy images of lyotropic lamellar phases

For the very first time, atomic force microscope images of lamellar phases were observed combined with a freeze fracture technique that does not involve the use of replicas. Samples are rapidly frozen, fractured, and scanned directly with atomic force microscopy, at liquid nitrogen temperature and in high vacuum. This procedure can be used to investigate micro-structured liquids. The lamellar phases in Sodium bis(2-ethylhexyl) sulfosuccinate (AOT)/water and in C12E5/water systems were used to asses this new technique. Our observations were compared with x-ray diffraction measurements and with other freeze fracture methods reported in the literature. Our results show that this technique is useful to image lyotropic lamellar phases and the estimated repeat distances for lamellar periodicity are consistent with those obtained by x-ray diffraction.     

A transferable classical potential for the water molecule

We developed a new model for the water molecule which contains only three Gaussian charges. Using the gas-phase geometry the dipole moment of the molecule matches, the quadrupole moment closely approximates the experimental values. The negative charge is connected by a harmonic spring to its gas-phase position. The polarized state is identified by the equality of the intermolecular electrostatic force and the spring force acting on the negative charge. In each timestep the instantaneous position of the massless negative charge is determined by iteration. Using the technique of Ewald summation, we derived expressions for the potential energy, the forces, and the pressure for Gaussian charges. The only properties to be fitted are the half-width values of the Gaussian charge distributions and the parameters of the nonelectrostatic repulsion-attraction potential. We determined the properties of gas-phase clusters up to six molecules, the internal energy and density of ambient water and hexagonal ice. We calculated the equilibrium density of ice VII as a function of pressure. As an additional test, we calculated the pair-correlation function, the isotherm compressibility, the heat capacity, and the self-diffusion coefficients for ambient water. As far as we know, this is the first classical model of water which is able to estimate both ends of the phase diagram, the high pressure ice VII, and the gas clusters of water with excellent accuracy.     

Microscopic observation and in-situ Raman scattering studies on high-pressure phase transformations of Kr hydrate

Direct observations through a microscope and in-situ Raman scattering measurements of synthesized single-crystalline Kr hydrate have been performed at pressures up to 5.2 GPa and 296 K. We have observed that the initial cubic structure II (sII) of Kr hydrate successively transforms to a cubic structure I (sI), a hexagonal structure, and an orthorhombic structure (sO) called "filled ice" at 0.45, 0.75, and 1.8 GPa, respectively. The sO phase exists at least up to 5.2 GPa. In addition to these transformations, we have also found the new phase behavior at 1.0 GPa, which is most likely caused by the change of cage occupancy of host water cages by guest Kr atoms without structural change. Raman scattering measurements for observed phases have shown that the lattice vibrational peak at around 130 cm(-1) disappears in the pressure region of sI, which enables us to distinguish the sI phase from sII and sH phases.     

Spectroscopic characterization of microscopic hydrogen-bonding disparities in supercritical water

The local hydrogen-bonding environment in supercritical water (380 degrees C, 300 bars, density 0.54 gcm3) was studied by x-ray Raman scattering at the oxygen K edge. The spectra are compared to those of the gas phase, liquid surface, bulk liquid, and bulk ice, as well as to calculated spectra. The experimental model systems are used to assign spectral features and to quantify specific local hydrogen-bonding situations in supercritical water. The first coordination shell of the molecules is characterized in more detail with the aid of the calculations. Our analysis suggests that approximately 65% of the molecules in supercritical water are hydrogen bonded in configurations that are distinctly different from those in liquid water and ice. In contrast to liquid water the bonded molecules in supercritical water have four intact hydrogen bonds and in contrast to ice large variations of bond angles and distances are observed. The remaining approximately 35% of the molecules exhibit two free O-H bonds and are thus either not involved in hydrogen bonding at all or have one or two hydrogen bonds on the oxygen side. We determine an average O-O distance of 3.1+/-0.1 A in supercritical water for the H bonded molecules at the conditions studied here. This and the corresponding hydrogen bond lengths are shown to agree with neutron- and x-ray-diffraction data at similar conditions. Our results on the local hydrogen-bonding environment with mainly two disparate hydrogen-bonding configurations are consistent with an extended structural model of supercritical water as a heterogeneous system with small patches of bonded molecules in various tetrahedral configurations and surrounding nonbonded gas-phase-like molecules.     

Combinatorial entropy and phase diagram of partially ordered ice phases

A close analytical estimate for the combinatorial entropy of partially ordered ice phases is presented. The expression obtained is very general, as it can be used for any ice phase obeying the Bernal-Fowler rules. The only input required is a number of crystallographic parameters, and the experimentally observed proton site occupancies. For fully disordered phases such as hexagonal ice, it recovers the result deduced by Pauling, while for fully ordered ice it is found to vanish. Although the space groups determined for ice I, VI, and VII require random proton site occupancies, it is found that such random allocation of protons does not necessarily imply random orientational disorder. The theoretical estimate for the combinatorial entropy is employed together with free energy calculations in order to obtain the phase diagram of ice from 0 to 10 GPa. Overall qualitative agreement with experiment is found for the TIP4P model of water. An accurate estimate of the combinatorial entropy is found to play an important role in determining the stability of partially ordered ice phases, such as ice III and ice V.     

X-ray and electron scattering factors for many-electron atomic system

Analytical expressions are developed for the x-ray and electron scattering factors for a many-electron atomic system when the single configuration wave function of the system is written as a sum of Slater determinants of spin orbitals. The radial part of the orbital is expanded in terms of Slater-type orbitals (STO 's). The expressions so developed have been used to calculate the coherent and incoherent x-ray and electron scattering factors and intensities for all the neutral atoms up to krypton (Z = 36) and for some positive and negative ions of chemical interest. The results obtained are used to test the value of Hartree–Fock wave functions for the evaluation of “one-electron properties” of many-electron atomic systems.     

Investigation of the hydrogen bonding in ice Ih by first-principles density function methods

It is a well recognized difficult task to simulate the vibrational dynamics of ices using the density functional theory (DFT), and there has thus been rather limited success in modelling the inelastic neutron scattering (INS) spectra for even the simplest structure of ice, ice Ih, particularly in the translational region below 400 cm(-1). The reason is partly due to the complex nature of hydrogen bonding (H-bond) among water-water molecules which require considerable improvement of the quantum mechanical simulation methods, and partly owing to the randomness of protons in ice structures which often requires simulation of large super-lattices. In this report, we present the first series of successful simulation results for ice Ih using DFT methods. On the basis of the recent advancement in the DFT programs, we have achieved for the first time theoretical outcomes that not only reproduce the rotational frequencies between 500 to 1200 cm(-1) for ice Ih, but also the two optic peaks at ～240 and 320 cm(-1) in the translational region of the INS spectra [J. C. Li, J. Chem. Phys 105, 6733 (1996)]. Besides, we have also investigated the impact of pairwise configurations of H(2)O molecules on the H-bond and found that different proton arrangements of pairwise H(2)O in the ice Ih crystal lattice could not alter the nature of H-bond as significantly as suggested in an early paper [J. C. Li and D. K. Ross, Nature (London) 365, 327 (1993)], i.e., reproducing the two experimental optic peaks do not need to invoke the two H-bonds as proposed in the previous model which led to considerable debates. The results of this work suggest that the observed optic peaks may be attributed to the coupling between the two bands of H-O stretching modes in H(2)O. The current computational work is expected to shed new light on the nature of the H-bonds in water, and in addition to offer a new approach towards probing the interaction between water and biomaterials for which H-bond is essential.     

Theoretical study of β- and γ-cyclodextrin complexes with ferrocene-containing azoles

The interaction between cyclodextrins (β- and γ-CD) and ferrocenyl azoles (i.e., pyrazole ferrocenes (I, III–V) and benzimidazole ferrocenes (VI, VII)), along with 1-ferrocenylethanol (II), each in the form of (R)- and (S)-enantiomers, in forming inclusion complexes is studied for the first time using detailed quantum chemical calculations. Compounds are calculated in terms of the density functional theory (DFT), using the Becke–Lee–Yang–Parr (B3LYP) approach in the 6-31G* basis sets. For the considered CD complexes with enantiomers of I–VII, structures in which a guest partially enters a host cavity from the side of the heterocyclic substituent (pyrazole or benzimidazole) are found to be energetically advantageous. It is shown that for successful resolution of (R,S)-enantiomers on chiral phases containing cyclodextrins, we must consider the interaction between outer hydroxyl groups on the CD cone’s surface, in addition to the correspondence of geometric dimensions. The calculated data correlate well with the data from the chromatographic separation of guest enantiomers on cyclodextrin sorbents.