Recently, a panel of experts, nominated by IUPAC, proposed the following tentative definition for the hydrogen bond: “The hydrogen bond is an attractive interaction between a group X-H and an atom or group of atoms Y in the same or different molecule(s), where there is evidence of bond formation” (Arunan, 2007). The energy of H-bond (~5 Kcal/mole of H-bonds) is intermediate between those of Van der Waals interaction (~0.3 Kcal/mole) and covalent (~100 Kcal/mole) chemical bonds (Stillinger, 1980). Since the energy of H-bond is of the order of a few KTs, thermal energy constantly acts to disrupt H-bonds. One can thus consider the energetics to drive formation of H-bonds, and entropic factors arising from thermal energy to break H-bonds. The result is a time-varying distribution of H-bonds among the different donor-acceptor pairs in the system. Combination of femtosecond 2D IR spectroscopy and molecular dynamics simulations demonstrated that the vast majority of average numbers of H-bonds are part of a H-bonded well of attraction and virtually all molecules return to a H-bonding partner within 200 fs (Eaves et al., 2005). Despite this continuous dynamics, fluctuation in the total number of H-bonds in a system containing a large number of molecules is quite small. Most simulation models suggest that a given H atom in water is H-bonded for 85-90% of the time (Bakker & Skinner, 2010).
H-bonds have been a subject of intense research over several decades owing to the enormous role they play on several physico-chemical properties of interest. As quoted by Buckingham et al., “The concept of the H-bond is a century old but youthful because of its vital role in so many branches of science and because of continued advances in experiment, theory and simulation” (Buckingham et al., 2008). The significance of H-bonds can be best understood by comparing the physical state of water and methane, both of similar size; at room temperature, while methane is supercritical, water exists in liquid state, making it possible for life to sustain on earth. The anomalous expansion of water at 4 C makes it possible for marine life to exist. The high dielectric constant of water opens up the entire field of electrochemistry. The internal structure of water is largely responsible for self-assembly of surfactants, leading to a wide array of liquid crystalline phases. H-bonds are largely responsible for preserving the structure/conformation of several life-supporting biological molecules such as DNA, RNA and proteins in aqueous solutions.
Despite the vast advances made in the recent past, H-bonding in liquid water continues to be one of the most challenging topics to understand. Each water molecule possesses two proton donors and two proton acceptors (lone pairs of electrons). X-ray and neutron diffraction studies reveal a three-dimensional network of H-bonds with a local preference for tetrahedral geometry (Narten & Levy, 1971).
In the absence of a universally agreed mathematical definition for the H-bond, it is not surprising to note that H-bonding between water molecules under the influence of an external field is an even less understood topic. This is nevertheless an extremely important topic given that we commonly observe water being subject to external fields such as that imposed by an uncharged solid wall, a liquid-liquid interface, an electrode surface, a nano-pore or an ion. In-fact, a detailed understanding of this topic probably holds the key in resolving some of the most difficult problems in Chemical Physics, such as: What is the origin of Hofmeister Series? What is the mechanism of gating of ion channels in biological membranes? What is the role played by interfacial water on electrochemical reaction pathways?
The present Chapter aims to elucidate our current understanding of H-bonding in liquid water, and is organized as follows. We start with a description of H-bonding in liquid water in the absence of any external field (Section 2), and then proceed to understand the influence of external fields generated near an electrode surface (Section 3) and around an ion (Section 4).
2. Structure of bulk water
We start with a qualitative discussion on the internal structure of water, followed by a compilation of literature data on a specific quantitative feature of the H-bond, namely the average number of H-bonds per water molecule.
Bernal and Fowler (Bernal & Fowler, 1933) suggested that molecules in liquid water are arranged in a tetrahedral manner, with each water molecule forming approximately four H-bonds with its nearest neighbors. Wall and Horing (Wall & Hornig, 1965) observed the Raman-scattering motions of the HDO molecules in H2O or D2O and concluded that liquid water does not have any significant fraction of unbonded molecules. Narten and Levy (Narten & Levy, 1969) supported the viewpoint that water molecules in liquid state are arranged in a predominantly tetrahedral geometry based on the observation that the mean separation between nearest neighbor molecules in ice and water are only marginally different. Stillinger and Rahman (Stillinger & Rahman, 1974) also suggested a similar structure for liquid water and additionally concluded that it contained a large proportion of broken H-bonds. Narten et al. (Narten et al., 1982) showed that most water molecules are connected to their nearest neighbors through nearly straight H-bonds. Gorbaty and Demianets (Gorbaty & Demianets, 1983) and Hoffmann and Conradi (Hoffmann & Conradi, 1997) showed, through independent studies, that the disorder in H-bond structure in liquid water increases with increasing temperature. Schwegler et al. (Schwegler et al., 2000) showed that the application of external pressure on pure water weakens H-bonds. Lee and Tuckerman (Lee & Tuckerman, 2006) studied the structural property of liquid water using a Car-Parrinello ab initio molecular dynamics (CPAIMD) simulations combined with Kohn-Sham density functional theory and BLYP exchange correlation functional for electronic structure, and found that more than 50% of water molecules are bonded in a tetrahedral geometry. Leetmaa et al. (Leetmaa et al., 2008) confirmed the tetrahedral arrangement with 74% double H-bond donors (DD) and 21% single donors (SD). Lehmann et al. (Lehmann et al., 2009) used quantum cluster theory and found dominance (75%) of two-bonded water molecules at room temperature.
Figure 1 shows the temperature variation of the average number of H-bonds per water molecule,. Two points are worth noting. One, irrespective of the source of literature, is seen to decrease with increasing temperature. Two, there is a large scatter in data points; for example, at room temperature varies from 2 to 4. This scatter can be attributed to a number of factors, such as differences in the definition of the H-bond, limitations in experimental/simulation techniques, and ambiguities in the interpretation of experimental data in relation to H-bond stoichiometry. Such an in-depth analysis of the factors involved is not within the scope of the present Section. However, in order to provide an appreciation of the ongoing debate in this area of research, we will bring out the key features of two landmark papers published in
We first start with a discussion on the paper published by Smith et al. (Smith et al., 2004) which concluded that ~3.3. The authors used oxygen K-edge X-ray absorption technique, wherein a core electron was excited to an unoccupied electronic state. The electronic character of the unoccupied states is known to be sensitive to the local geometric structure. The authors recorded area-normalized spectra of water at 254 K and 288 K. The intensity of pre-edge region (~535 eV), which is a signature of distorted H-bonds configurations, increased with increasing temperature. On the other hand, the intensity of post-edge region (~541 eV), which is a signature of stronger and fully coordinated ice-like bonds, decreased. The authors assumed the relative populations of post-edge (Ipost) and pre-edge (Ipre) intensities to be a function of absolute temperature only, and proposed that a plot of ln(Ipost/Ipre) versus 1/T would yield a straight line with a slope that is proportional to the average difference in energy between the two classes, and determined the rearrangement energy between two classes of H-bonding distributions to be 1.5 ± 0.5 kcal/mol. This small energy difference indicates that molecules contributing to pre-edge intensity are only slightly distorted compared to those contributing to post-edge intensity. The average energy of a fully formed ice-like H bond is known to be ~5.5 kcal/mol (Kuo & Mundy, 2004; Stillinger, 1980). Therefore, the authors attributed the difference in energy (1.5 kcal/mol) between the two H-bonding distributions to a loss of 27 ± 9% of average H-bond energy. Later, Nilsson et al. (Nilsson et al., 2005) questioned the quality of the temperature dependent X-ray spectra presented by Smith et al. (Smith et al., 2004). They pointed that three different sets of measurements displayed an energy difference of approximately 1.2, 1.5 and 1.8 kcal/mol between the two different species, and attributed this lack of reproducibility to energy dependent nonlinear effects in X-ray absorption spectrum measurements. In response to Nilsson comments, Smith et al. (Smith et al., 2005) showed that under constant conditions (e.g., jet size, collection geometry), the X-ray absorption spectrum is highly reproducible.
We now focus our attention on another paper which suggested a different value for. Wernet et al. (Wernet et al., 2004) employed X-ray absorption (XAS) and X-ray Raman (XRS) spectroscopic techniques to understand the H-bond configurations in bulk ice, ice surface, NH3 terminated ice surface and bulk liquid water. The spectra were divided into three regions: pre-edge (~535 eV), main edge (537-538 eV), and post-edge (540-541 eV). The bulk ice spectrum was dominated by the intensity in post-edge region and showed a weak main edge structure. Both the surface ice and liquid water spectra had a peak in the pre-edge region, a dominant main edge, and lesser intensity compared with bulk ice in the post-edge region. Termination of ice surface with NH3 entails a coordination of free O-H groups and caused the pre-edge peak to vanish. It was observed that liquid water spectra closely resembles that of ice surface, which consists of one strong and one non-bonded or weakly-bonded O-H group, but is very different from that of bulk ice. On the basis of these findings, the authors concluded that liquid water consists of two structural species, one with two H-bonded (at one acceptor and one donor site) and another tetrahedrally coordinated. A theoretical analysis of XAS and XRS spectra, based on density functional theory (DFT) with a small model cluster of 11 molecules, revealed that each molecule has on average 2.2 ± 0.5 H-bonds at 25 C and 2.1 ± 0.5 at 90 C temperature.
3. Structure of water near electrode surfaces
Structure and orientation of water molecules adjacent to charged surfaces play an important role in surface science, electrochemistry, geochemistry and biology (Thiel & Madey, 1987; Henderson, 2002; Guidelli & Schmickler, 2000). Several force fields are operational in such situations. Molecular dynamic simulations (Segura et al., 1997) reveal entropy driven piling-up effect near even an uncharged wall. Additional presence of charge on surface polarizes water molecules. The presence of ions (H+, OH-) in the liquid phase further induces formation of an electrical double layer within which the electric field decays with distance from the surface. Advanced experimental and molecular simulation techniques are just beginning to shed light on the influence of a charged electrode surface on the various aspects of the internal structure of water, such as H-bonding, density and dipolar alignment. It is the purpose of this Section to discuss the current understanding of this topic. More specifically, we focus on studies revealing two opposing viewpoints; one suggesting that the H-bond structure of water near a charged surface is significantly disrupted, and the other concluding the opposite, namely that the H-bond network near the surface is largely intact.
Toney et al. (Toney et al., 1994) studied the distribution of water molecules perpendicular to a charged silver (111) electrode interface in NaF solution using X-ray scattering technique. An interface at a single crystal creates additional scattering to the Bragg peaks of crystal, which permits the determination of surface structure and water distribution. Figure 2 shows the distribution of oxygen atoms with distance from the electrode surface. Using Gaussian functions to fit the oxygen distribution function, the first layer density was calculated to be 1.1 and 1.8 water molecules per Ag atom, corresponding to an applied voltage of -0.23 V and +0.52 V, respectively. In contrast, bulk water had a density of ~0.8 water molecules per Ag atom. The conclusion that water density is significantly altered near a charged electrode was confirmed by Danielewicz-Ferchmin (Danielewicz-Ferchmin & Ferchmin, 1996) as well, albeit using a different approach. A simulation study (Zhu & Robinson, 1991) with SPC-FP water model (simple point charge model with flexible bonds and polarization) also showed that water density near a charged surface is higher than that in bulk and increases with field intensity. Moreover, they found that the length of O-H bond (of water) near the electrode surface is smaller than in bulk, indicating weaker H-bonds. Suresh (Suresh, 2007) arrived at a similar conclusion using a statistical thermodynamic model, and showed that the average number of H-bond per molecule near the charged surface decreases from 2.8 at zero electric field to 2 at E = 2109 V/m.
We now focus our attention on another set of papers (Schweighofer et al., 1996; Torrie et al., 1988; Yeh & Berkowitz, 2000) that reached a different conclusion, namely that the H-bond structure of water near a charged electrode surface is largely intact. Schweighofer et al. (Schweighofer et al., 1996) performed molecular simulations with SPC/E water molecules
contained between two parallel Ag(111) surfaces with charge densities fixed at 0.0, 8.85, and 26.55 μC/cm2. They did not observe increase in water density near the electrode even with the highest charge density (+26.5 μC/cm2); rather, it was found to decrease. Authors explained this observation to strong polarization of water molecules due to the applied electric field resulting in some of the oxygen atoms associated with water molecules to desorb from the surface and move into subsequent layers in order to keep intact the H-bond network. Torrie et al. (Torrie et al., 1988) showed that the H-bond structure near the electrode is resistant to surface charges as high as 17.5 μC/cm2, apparently because such a strong field can not compete with the stronger intermolecular forces of water-like models. Yeh (Yeh & Berkowitz, 2000) studied water density near a charged silver electrode surface using polarizable point charge model and found that water density near the surface was not affected by surface charge. Xia and Berkowitz (Xia & Berkowitz, 1995) performed molecular simulations with SPC/E modeled water lamina embedded between two Pt (100) walls, charged with 0, 8.85, 26.55 and 35.40 μC/cm2 on the left wall and values opposite in sign on the right wall. Figure 3 shows the density profile of O and H atoms of water as varying from positively charged electrode to negatively charged electrode.
There was no significant change in density profile up to 8.85 μC/cm2 surface charge. When the surface charge density was increased to 26.66 μC/cm2, which is close to the surface charge density in experiments performed by Toney et al. (Toney et al., 1994) four distinct water layers were observed near the positively charged surface. When the charge density on electrode was increased to 35.4 μC/cm2, water restructured itself in order to adapt to the new environment and eventually crystallized into domains of cubic ice. In other words, the H-bond network not only survives in electric field, but is also responsible for the observed structural changes. Otani et al. (Otani et al., 2008) performed
4. Structure of water near ions
Hofmeister first established that different ions have different efficiency at salting-out egg-white protein (Hofmeister, 1888). The sequence of ions, based on their effectiveness towards enhancing or diminishing the solubility of proteins, is termed as Hofmeister series. This series is generally written as (Marcus, 2009).
Kosmotrope (Structure maker) Chaotrope (Structure breaker)
Kosmotrope (Structure maker) Chaotrope (Structure breaker)
The molecular origin of salting-out or salting-in effects is not fully understood. But broadly, the current view is that addition of salts alters the internal structure and hence the solubility power of water. In this context, ions are classified in two groups, namely “structure makers” and “structure breakers” (Cox & Wolfenden, 1934). Implicit in this conjecture is that ions influence the long-range structure of water. Whether this conjecture is indeed borne out in experiments is one of the topics of debate in the literature. In this Section, we discuss key aspects of papers on both sides of this debate.
Leberman and Soper (Leberman & Soper, 1995) showed that ions can induce a change in water structure equivalent to that caused by the application of high pressure, and that the extent of this effect is ion-specific. Based on neutron diffraction patterns, the authors determined distribution distances between water protons in aqueous solutions of salts (NH4)2SO4, NH4Cl, Na2SO4, and NaCl), and in pure water at high pressure. Figure 4 shows that the in all these cases are of qualitatively similar shape. The general trend is a negative region near r = 2 Å, a positive region near r = 3.2 Å and a set of oscillations with a period of ~3 Å. Under ambient conditions, the intermolecular HH pair correlation function for pure water consists of two peaks, one at ~2 Å and another at ~3.8 Å, with a minimum between them at r = 3.0 Å. In ionic solutions under normal pressure and pure water at high pressure, peaks at ~2.4 Å and 3.8 Å are apparently diminished and a minimum at ~3.0 Å fills in. These results strongly suggest that ions disrupt the water structure comparable in extent to that caused by the application of high pressure to pure water. The possibility of pressure and salt leading to similar effects on the structure of water has also been investigated using molecular simulation techniques. Holzmann et al. performed molecular dynamics simulations of aqueous NaCl solutions, and arrived at three broad conclusions (Holzmann et al., 2007). One, the H-bond network is modified well beyond the first hydration shell. Two, an analysis of free water distribution showed that the effect of salt and pressure might be considered as “two sides of the same coin”. Three, the authors cautioned against using the pressure/salt equivalence as a sole factor influencing solubility of biomolecules; adsorption/desorption of ions might also have to be accounted for.
Chandra (Chandra, 2000) investigated the specific role of ions on H-bonds between water molecules using molecular dynamics. The systems chosen were NaCl and KCl in water at various concentrations (from 0M to 3.35M). Water molecules were modeled by the extended simple point charge (SPC/E) potential and ions were modeled as charged Lennard-Jones particles. For analyzing the hydrogen bond breaking dynamics, the author calculated the time correlation functions
Hribar et al. (Hribar et al., 2002) employed a two-dimensional MB model, in which each water molecule was represented as a two-dimensional disk that interacted with other water molecules through a Lennard-Jones (LJ) interaction and an orientation-dependent H-bond interaction. Figure 6A shows that the average number of H-bonds per water molecule around the first shell of smaller cations such as Li+ and Na+ (kosmotropes) is lesser than that in bulk water, while the corresponding number for molecules around larger ions such as K+, Rb+ and Cs+ are higher. The molecular picture giving rise to this conclusion is shown in Figure 6B. The number of H-bonds per water molecule in the first shell around an ion is governed by two competing ordering effects, one induced by electrostatic interaction with the ion and the other by water-water H-bond interaction. For small ions, the former effect dominates, while for large ions the later effect dominates.
We now turn out attention to papers that concluded the opposite, namely that the presence of ions do not lead to an enhancement or a breakdown of H-bond network in liquid water. This viewpoint, which was originally initiated by Omta et al. (Omta et al., 2003), has profound implications, one of which is that the conjecture of ions being classified as being “structure-makers” and “structure breakers” does not have a molecular basis. The authors
measured the orientational correlation time of water molecules in Mg(ClO4)2 solution by using femtosecond pump-probe spectroscopy. The technique was based on measuring the anisotropy parameter (R), which was defined as [(Δα║(τ) - Δα┴(τ))/ (Δα║(τ) + 2Δα┴(τ))], wherein (Δα║) and (Δα┴) are absorption changes measured parallel and perpendicular to the pump polarization, and τ is the time delay between pump and probe pulses. To measure R, OH groups in the liquid were anisotropically excited by a linearly polarized pump pulse. The decay time of R represents the orientational correlation time of water molecules, a measure for the stiffness of the H-bond network. The decay of
We now mention two other recent studies whose conclusions are broadly in line with those of Omta et al. (Omta et al., 2003). Guardia et al. (Guardia et al., 2006) carried out extensive molecular dynamics simulations of aqueous alkali metal and halides at ambient and supercritical conditions to explore the effects of ions on the intermolecular connectivity of water in the close vicinity of solutes. From a dynamical perspective, the most relevant feature was that the lifetimes of hydrogen bond do not seem to be affected in an appreciable manner by the presence of ions. More recently, in 2007, Smith et al. (Smith et al., 2007) compared experimental Raman spectral measurements with classical Monte Carlo simulations and concluded that the change in vibrational spectrum of water by the addition of potassium halides is a direct result of the electric fields that anions exert on adjacent H atoms, and that the halide ions induce only minor HB distortions beyond the adjacent shell of coordinating OH groups.
Given the ongoing debates in our current understanding of liquid structure of water even in the absence of external fields, it is not surprising that there is lack of consensus in the literature on even some of the fundamental aspects of H-bond interactions in the presence of an external field. For example, it is not yet clear whether the H-bond structure near a charged electrode surface is disrupted or not. Similarly, E-fields are generally considered to align water dipoles in the direction of the field; however, a recent study (Suresh et al., 2006) has reported the additional presence of H-bond stabilized water molecules with their dipoles lying perpendicular to that of field. The fraction of such molecules is relatively small; for every thousand molecules with their dipoles aligned in the direction of field, roughly one was found aligned perpendicular to that of the field. Nevertheless, the role of these “defects” on the transport or solvation properties of water remains to be investigated. Whether ions induce long-range changes in the structure of water is still an open question (Bakker, 2008). The study of confined water molecules is equally, if not more interesting. The thermodynamic properties of confined water are generally considered to be different from those of bulk water; however, what gives rise to these differences is still an open question. A recent study (Han et al., 2009) showed reduced extent of H-bonding in a quasi-two-dimensional hydrophobic nanopore slit as compared to that in bulk water, partly due to geometric constraints imposed by confined geometries on the tetrahedral bonding patterns in water; however, the characteristics of H-bond dynamics, such as the Arrhenius dependence of the average H-bond lifetime, have been reported to be largely preserved.
In the above context, it is clear that the structure of water in external fields is a topic that requires much more detailed investigations before unambiguous conclusions can be reached. While this endeavor would require the development of advanced techniques, it is equally if not more important that the scientific community agrees on a single mathematical definition of what constitutes a H-bond. It is hoped that this clarity will help in reducing the confusion prevailing today in relation to design, implementation and interpretation of experimental/simulation data related to the internal structure of water.
Arunan E. 2007 92 17 18
Bakker H. J. 2008, 108 1456 1473
Bakker H. J. Skinner J. L. 2010, 110 1498 1517
Bernal J. D. Fowler R. H. 1933, Vol. l, 515 548
Bondarenko G. V. Gorbaty Yu. E. 1991 74 639 647
Buckingham A. D. Bane J. E. D. Mc Dowell S. A. C. 2008, 463 1 10
Chandra A. 2000, 85 768 771
Cox W. M. Wolfenden J. H. 1934, 145 475 488
Danielewicz-Ferchmin I. Ferchmin A. R. 1996, 100 17281 17286
Eaves J. D. Loparo J. J. Fecko C. J. Roberts S. T. Tokmakoff A. Geissler P. L. 2005, 102 13019 13022
Gorbaty Yu. E. Demianets Yu. N. 1983 100 450 454
Guardia E. Laria D. Marti J. 2006, 110 6332 6338
Guidelli R. Schmickler W. 2000, 45 2317 2338
Haggis G. H. Hasted J. B. Buchanan T. J. 1952, 20 1452 1465
Han S. Kumar P. Stanley H. 20092009 , 79 0412021-5
He C. Lian J. S. Jiang Q. 2007, 437 45 49
Henderson M. A. 2002 46 1 308
Hetenyi B. Angelis F. D. Giannozzi P. Car R. 2004, 120 8632 8637
Hoffmann M. M. Conradi M. S. 1997, 119 3811 3817
Hofmeister F. 1888, 24 247 260
Holzmann J. Ludwig R. Geiger A. Paschek D. 2007, 46 8907 8911
Hribar B. Southall N. T. Vlachy V. Dill K. A. 2002, 124 12302 12311
Kalinichev A. G. Bass J. D. 1997, 101 9720 9727
Kumar R. Schmidt J. R. Skinner J. L. 2007, 126 2041071-12
Kuo-F I. W. Mundy C. J. 2004, 303 658 660
Leberman R. Soper A. K. 1995, 378 364 366
Lee H. S. Tuckerman M. E. 2006, 125 1545071-14
Leetmaa M. Wikfeldt K. T. Ljungberg M. P. Odelius M. Swenson J. Nilsson A. Pettersson L. G. M. 2008 129 0845021-13
Lehmann S. B. C. Spickermann C. Kirchner B. 2009, 5 1650 1656
Luck W. A. P. 1967, 43 115 127
Marcus Y. 2009 109 1346 1370
Morokuma K. Pedersen L. 1968, 48 3275 3282
Morokuma K. Winick J. R. 1970, 52 1301 1306
Myneni S. Luo Y. Naslund L. A. Cavalleri M. Ojamae L. Ogasawara H. Pelmanschikov A. Wernet Ph. Vaterlein P. Heske C. Hussain Z. Pettersson L. G. M. Nilsson A. 2002, 14 L213 L219
Narten A. H. Levy H. A. 1969, 165 447 454
Narten A. H. Levy H. A. 1971, 55 2263 2269
Narten A. H. Thiessen W. E. Blum L. 1982, 217 1033 1034
Nieto-Draghi C. Avalos J. B. Rousseau B. 2003, 118 7954 7964
Nilsson A. Wernet Ph. Bergmann U. Nordlund D. Cavalleri M. Odelius M. Ogasawara H. Nasulund L. A. Hirsch T. K. Ojamae L. 2005, 308 793a
Omta A. W. Kropman M. F. Woutersen S. 2003& Bakker, H. J. 301 347 349
Otani M. Hamada I. Sugino O. Morikawa Y. Okamoto Y. Ikeshoji T. 2008, 10 3609 3612
Prendergast D. Galli G. 2006, 96 2155021-4
Schwegler E. Galli G. Gygi F. 2000, 84 2429 2432
Schweighofer K. J. Xia X. Berkowitz M. L. 1996, 12 3747 3752
Segura C. J. Chapman W. G. Shukla K. S. 1997 90 759 772
Smith J. D. Cappa C. D. Wilson K. R. Messer B. M. Cohen R. C. Saykally R. J. 2004, 306 851 853
Smith J. D. Cappa C. D. Messer B. M. Cohen R. C. Saykally R. J. 2005, 308 793b
Smith J. D. Saykally R. J. Geissler P. L. 2007 129 13847 13856
Soper A. K. Bruni F. Ricci M. A. 1997, 106 247 254
Stillinger F. H. Rahman A. 1974, 60 1545 1557
Stillinger F. H. 1980, 209 451 457
Suresh S. J. Naik V. M. 2000, 113 9727 9732
Suresh S. J. Satish A. V. Choudhary A. 2006 124 0745061-9
Suresh S. J. 2007, 126 2047051-8
Thiel P. A. Madey T. E. 2007, 71987, 211 385
Toney M. F. Howard J. N. Richer J. Borges G. L. Gordon J. G. Melroy O. R. Wiesler D. G. Yee D. Sorensen L. B. 1994, 368 444 446
Torrie G. M. Kusalik P. G. Patey G. N. 1988, 88 7826 7840
Wall T. T. Hornig D. F. 1965, 43 2079 2087
Wernet P. Nordlund D. Bergmann U. Cavalleri M. Odelius M. Ogasawara H. Naslund L. A. Hirsch T. K. Ojamae L. Glatzel P. Pettersson L. G. M. Nilsson A. 2004, 304 995 999
Xenides D. Randolf B. R. Rode B. M. 2006 123 61 67
Xia X. Berkowitz M. L. 1995, 74 3193 3196
Yamabe S. Morokuma K. 1975, 97 4458 4465
Yeh I. C. Berkowitz M. L. 2000, 112 10491 10495
Zhu S. B. Robinson G. W. 1991, 94 1403 1410