SciDAC Review - Q-SIMAN: Probing the Properties of Water through Advanced Computing

Q-SIMAN

Probing the Properties of Water through Advanced Computing

Exploiting the power of IBM Blue Gene supercomputers at the Argonne Leadership Computing Facility and IBM Blue Gene Watson Research Laboratory, a team of researchers is using first-principles simulations to investigate what happens at the microscopic level when water meets hydrophilic and hydrophobic surfaces and how the properties of this ubiquitous liquid are modified at the nanoscale. The findings can be applied to solve complex problems in both biology and materials science.

Unraveling the properties of water at organic and inorganic interfaces is a key step toward understanding the function of biological systems and the behavior of soft and hard materials in many natural environments. Probing such properties is a challenging task, from both an experimental and a theoretical standpoint. The challenge is even greater when water is confined in very small spaces (a few nanometers). Examples that illustrate this challenge are the surfaces of proteins, channels devised to transport matter at the nanoscale (nanofluidic devices), or natural rocks, such as zeolites or clays.

Seeking to Predict and Design
In ancient Greece, the so-called physicalists named water one of four basic elements, and water's properties have fascinated scientists ever since. Even today, the chemical bonding that keeps water molecules together in the liquid is not completely understood. This chemical bond is usually referred to as "hydrogen bonding," and it is one of the basic interactions in biological systems. Hydrogen bonds (figure 1) are responsible for the characteristic tetrahedral network of ice and the distorted tetrahedral arrangements that water molecules adopt in the liquid state.

G. Galli, UC-Davis, and E. Schwegler, LLNL

Figure 1. Top, a typical geometrical arrangement of two water molecules (H₂O) forms a so-called hydrogen bond. Oxygen (O) and hydrogen (H) atoms are represented as red and white spheres, respectively. In a hydrogen bonding configuration between two water molecules, a hydrogen of one molecule points toward the oxygen of the other one. The blue surface encompassing the two molecules represents the electronic charge density arising from the outermost electrons of each molecule. Bottom, together with a ball-and-stick representation of a given H₂O molecule in the liquid, a function (blue) is shown, representing the probability of finding neighboring water molecules of the chosen one. This indicates that at any given time, if one focuses on a specific water molecule and "looks" around it, one sees about four neighboring molecules arranged in a tetrahedral geometry.

Over decades, many studies have investigated the anomalous properties of pure water and the interaction of water with organic and inorganic surfaces. However, only in recent years have researchers focused on probing these interactions at the microscopic level. Among these researchers is a team conducting the Quantum Simulations of Materials and Nanostructures (Q-SIMAN) project. This effort is supported by U.S. Department of Energy (DOE) Scientific Discovery through Advanced Computing (SciDAC-2) Scientific Application Partnership (SAP) funding. The team seeks answers to the following questions: What happens at the molecular and atomic levels when water molecules meet with a surface? How is the liquid perturbed by the presence of a surface? And, in turn, how does the surface change? Does it react with or simply adjust to the presence of water? Understanding how a water interface—whether a solid material or a macro-molecule—looks at the atomistic level can help explain biological and environmental processes, and eventually may give insight on how to design materials with specific surfaces and target functions.

Understanding how a water interface--whether a solid material or a macromolecule--looks at the atomistic level can help explain biological and environmental processes, and eventually may give insight on how to design materials with specific surfaces and target functions.

Water, Water Everywhere!
In spite of water's ubiquitous presence on Earth in all living systems and many technological and industrial processes, much remains to be investigated and understood about the physical and chemical properties of water interfaces. Even the basic structural properties of water itself have recently been the subject of heated debate.

A paper by Stanford University researchers that appeared in Science (2004) has questioned the well-accepted quasi-tetrahedral model of water. This study stimulated ample discussions on whether the electronic properties of the liquid measured by the group were indicative of a microscopic, molecular structure that is less tetrahedral than previously thought (namely, different from the commonly accepted form shown in figure 1, p23). The initial interpretation of the experimental data hinted a ring structure may be present for liquid water , which differs from than the tetrahedral, geometrical arrangements found in ice. Several experimental and theoretical groups have since attempted to analyze and interpret the Stanford data, including Dr. Giulia Galli and collaborators. In a paper published in Physical Review Letters last year, Dr. David Prendergast and Dr. Galli argued that, based on their ab initio electronic structure calculations of X-ray absorption spectra, the Stanford results were not at all conclusive about the existence of a model different from the standard "old" one, adopted to describe water for the past 50 years. They concluded that no experimental evidence at present disproves that model, and they noted that thermodynamic data available so far are consistent with the so-called standard tetrahedral model of the liquid.

Controversies on water's structure and properties are intricate and encompass many areas of science; even the popular press has covered the topic, in addition to many articles in scientific journals. For instance, the Wall Street Journal featured an article titled, "The structure of water isn't certain after all."

To unravel the mysteries of the structure and properties of water in different environments, and especially at the nanoscale, is one of the objectives of the Q-SIMAN project. For several decades, scientists have used experimental techniques such as neutron and X-ray diffraction to characterize the properties of the bulk liquid. However, these techniques are more difficult to use at the nanoscale, and detailed information on water confined in spaces with nanometer dimensions is limited. Theoretical and computational studies of water at surfaces and the nanoscale have also been limited because such complex, multi-component systems require the derivation of very accurate interactions to be simulated in a realistic manner; when solving the equations, these interactions require the use of high-performance computers. Many past studies were restricted to computational models based on molecular dynamics (MD) with classical, empirical potentials (for instance, potentials fitted to a certain class of experimental data) that have limited predictive power and cannot directly probe the electronic properties of the liquid.

In spite of water's ubiquitous presence on Earth in all living systems and many technological and industrial processes, much remains to be investigated and understood about the physical and chemical properties of water interfaces.

A First-Principles Approach
Capitalizing on Advanced Computers
The SciDAC Q-SIMAN team has taken a rigorous approach using ab initio MD, where the potential between atoms is derived from sophisticated electronic structure calculations at each ionic move. In MD simulations with classical potentials, explains Dr. Galli, one describes the motion of atoms and molecules according to forces defined by empirical interactions, fitted to a given set of experimental or theoretical data. However, to be predictive and take into account detailed effects of water-water and water-surface interactions, one needs to resort to first-principles, or ab initio, simulations.

The development and use of ab initio simulation techniques to simulate materials and nanostructures is the overarching theme of the Q-SIMAN project. The study of water is one of the grand challenge applications of the quantum simulation (QS) tools used and developed by the Q-SIMAN team. Figure 2 and the sidebar, "Quantum Simulations of Materials and Nanostructures (Q-SIMAN)," summarize the project's main goals.

Source: G. Galli, UC-Davis, and E. Schwegler, LLNL Illustration: A. Tovey

Figure 2. Summary of the activity of the SciDAC-2 SAP Q-SIMAN project at a glance. Acronym definitions: ab initio molecular dynamics (AIMD); quantum Monte Carlo (QMC); high-performance computing (HPC).

Dr. Galli and her colleagues used the Qbox code developed by Dr. François Gygi (University of California–Davis), recipient of the 2006 Gordon Bell Award for best performance (sidebar "Qbox Offers Peak Performance" p26) to carry out their ab initio simulations of water at interfaces. Qbox calculates the electronic structure of a system by using methods based on density functional theory, which defines a system's energy and electronic structure in terms of its electron density.

Many of the researchers' calculations have been performed on the IBM Blue Gene/L (BG/L) machine at the Argonne Leadership Computing Facility (ALCF) at Argonne National Laboratory, taking advantage of a DOE Innovative and Novel Computational Impact on Theory and Experiment (INCITE) award that has provided extensive and dedicated use of the Argonne high-performance computer. Simulations of a liquid interacting with a surface are extremely demanding from a computational standpoint. Not only do these simulations involve electronic structure calculations for large systems (the team treated up to 466 atoms and 1,648 electrons in their study), but also these calculations need to be repeated at each ionic move (that is, every time the coordinates of all the atoms of the system are evolved in time), following Newtonian dynamics.

Controversies on water's structure and properties are intricate and encompass many areas of science.

For example, in order to run for 20 ps, which is the minimum amount of time required to derive a trajectory for the calculation of molecular diffusion or vibrational spectra, approximately 80,000 MD steps need to run. At each step, the optimization of about 10⁸ degrees of freedom is required (for example, for a CNT with diameter d = 1.5 nm filled with water). These requirements make the simulations extremely demanding in terms of central processing unit (CPU) cycles and data storage. "Of course, the use of codes such as Qbox, highly optimized for parallel architectures like BG/L, is of tremendous help, and it has made these difficult simulations possible," says Dr. Giancarlo Cicero, a postdoctoral researcher who worked with Dr. Galli and Dr. Gygi on water simulations. (Dr. Cicero is now a researcher at the University of Turin in Italy.) However, much work is required to improve the scaling of the algorithms employed today in ab initio MD simulations. This is another key goal of the Q-SIMAN team, and some team members are actively working at developing algorithms for ab initio MD with a scaling more favorable than the current one. Currently, the calculation workload is growing as the third power of the number of atoms (and electrons) in the system.

To unravel the mysteries of the structure and properties of water in different environments, and especially at the nanoscale, is one of the objectives of the Q-SIMAN project.

New Results, New Questions
To date, the researchers have studied both pure water and water at interfaces with graphite nanotubes, hydrogenated diamond surfaces, and biocompatible materials such as silicon carbide. Snapshots of several systems studied by the group are shown in figure 3.

G. Galli, UC-Davis, and E. Schwegler, LLNL

Figure 3. Snapshots from an ab initio simulation of water in contact with surfaces, clusters, and molecules, representative of state-of-the-art calculations of the interaction of liquid water with (from left to right) hydrophilic substrates (hydroxylated SiC), hydrophobic substrates (graphite and carbon nanotubes), and hydrophobic solutes such as benzene and small ions (for example, Mg and Ca ions and small silicon clusters).

There is a basic difference between water on nonpolar surfaces, such as graphene and hydrogenated diamond, and water on substrates such as silicon carbide. The former are so-called hydrophobic substrates; these surfaces do not engage in hydrogen bonding with water. Although this phenomenon is sometimes explained by noting these surfaces repel water, there is no physical repulsion between water and the surface. Stronger bonds are formed by the water molecules not engaged in interactions with the surface. Silicon carbide is a hydrophilic substrate, which is a surface that forms hydrogen bonds with water molecules. The way a water droplet behaves at the macroscopic level in contact with hydrophilic or hydrophobic substrates is well known. Everybody has experienced water apparently repelled by the hydrophobic surface of a Teflon pan, or simply by an oil droplet, and the sticking of water on the surface of sand (silicon dioxide). However, the microscopic origin determining this behavior, especially in the hydrophobic case, is still the subject of intense scientific debate. It is a problem of great interest to understand the underlying principles of hydrophobic interactions, as these interactions are believed to play a key role in determining the structure of proteins and the structural, electronic, and mechanical properties of many materials in natural environments. The SciDAC team attacked this problem using QS to look at what happens when water molecules encounter different types of surfaces to investigate water's structural and dynamical properties.

It is a problem of great interest to understand the underlying principles of hydrophobic interactions, as these interactions are believed to play a key role in determining the structure of proteins and the structural, electronic, and mechanical properties of many materials in natural environments.

The team identified the key role played by electrons in determining the arrangements of water molecules at the surface. They also computed vibrational spectra and provided predictions and interpretations of what should be seen experimentally when measuring how water molecules vibrate in contact with surfaces.

"The results were surprising," remarks Dr. Galli. "We found that hydrophobic surfaces tend to have a more pronounced effect on the structural properties of confined liquid water than do hydrophilic surfaces. In addition, we found intriguing vibrational properties that we think may be probed by infrared spectroscopy, and we have made predictions that we hope experimentalists will try to verify." Some results of this investigation are in press in the Journal of the American Chemical Society, and the results on spectra have just been submitted for publication. Predictions were made not only for water in carbon nanotubes and within graphene sheets but also for water in contact with hydrogenated diamond surfaces (surfaces of a diamond that have been terminated with hydrogen atoms), representing the most hydrophobic substrate studied by the team (figure 4).

G. Galli, UC-Davis, and E. Schwegler, LLNL

Figure 4. Snapshot of an ab initio molecular dynamics simulation of water confined in a hydrogenated diamond slab. Oxygen, carbon, and hydrogen atoms are represented as red, green, and white spheres, respectively

Even in the case of a hydrogenated diamond slab, subtle, electrodynamical interactions between the surface and water were detected in the simulations. Water certainly does not form hydrogen bonds with a hydrophobic surface (or, in other words, bonds as strong as those that two water molecules form with each other). However, interactions are present that depend on the specific substrate and are important in determining molecular and materials properties when in contact with water.

"Our results are perfectly consistent with the accepted concept of hydrophobicity; they just add an atomistic, microscopic interpretation to it, revealing the importance of electronic effects," says Dr. Galli. "The phobia (fear) of some apolar substances for aqueous (hydro) environments does not imply lack of attraction to water. Neither does it imply absence of interaction. Rather, it originates from the strength of this attraction, which, similar to that between the constituents of apolar substances, is smaller than the force between water molecules. And, of course, fear of those who dominate the scene (in this case, water hydrogen bonds) is hardly surprising."

G. Galli, UC-Davis, and E. Schwegler, LLNL

Figure 5. Snapshots of simulations of water at hydrophilic (silicon carbide, left) and hydrophobic (graphene, right) surfaces. Oxygen, carbon, silicon, and hydrogen atoms are represented as red, gray, light blue, and white spheres, respectively. The blue and yellow surfaces in proximity represent electronic charge densities.

The results obtained by Dr. Galli's team for all the surfaces studied underscored the importance of electronic effects (figure 5) in determining interfacial properties, along with the influence of the surface microscopic structure (figure 6) on the structural and dynamical properties of the liquid. "The atomic and electronic structure of the surface are extremely important in determining how the liquid molecules arrange themselves in contact with hydrophobic substrates," says Dr. Eric Schwegler from Lawrence Livermore National Laboratory, who is a member of the SciDAC-2 SAP team. "Our calculations show that you cannot really represent a hydrophobic surface as a simple hard wall and neglect its detailed atomic structure. This means simple, general models (as appealing as they may sound) are not up to the task of describing the intricate microscopic structure of water at hydrophobic interfaces." The effects probed by Dr. Galli's team are subtle and challenging to detect experimentally, and the use of sophisticated simulation techniques and advanced computational facilities has been key to unraveling them.

G. Galli, UC-Davis, and E. Schwegler, LLNL

Figure 6. Arrangement of water molecules on a graphene substrate. Graphite is composed of graphene sheets that consist of carbon atoms arranged in a hexagonal pattern. Oxygen, carbon, and hydrogen atoms are represented by red, gray, and white spheres, respectively. The blue and red spots (left) represent the region of space where it is the most probable to find oxygen (red) and hydrogen (blue) atoms belonging to water molecules, when liquid water confined at the nanoscale is in contact with a graphene sheet.

For both hydrophilic and hydrophobic substrates, the perturbation on water induced by the presence of the surface was found to be localized within a rather thin interfacial layer that can be probed by spectroscopic means (for example, by using infrared spectroscopy measurements). There have been some experimental claims about strong perturbation induced by the presence of a surface on the water structure, extending up to several nanometers from the substrate. The simulations carried out by the SciDAC team have shown that instead the molecular structure and hydrogen bonding network are really changed, with respect to those found in the bulk liquid, only within a thin layer of about half a nanometer wide.

The importance of using ab initio methods to understand solvation effects also has recently been highlighted in the case of small hydrophobic solutes by Dr. Galli and her collaborators and a research group led by Prof. Roberto Car at Princeton University. The group reported an investigation of hydrophobic association for a model system comprising two methane molecules in water and have computed the potential of mean force between the two methane molecules. Their results differ from those obtained by using empirical potentials. Similar discrepancies between empirical potentials and ab initio descriptions also have been reported in other work conducted by Dr. Galli's and Dr. Schwegler's groups, which studied isolated methane and silane and benzene and hexafluorobenzene molecules in water, respectively. The methane molecule, CH₄, has one carbon atom bonded to four hydrogens, while silane, SiH₄, has one silicon bonded to four hydrogens; benzene, C₆H₆, is composed of a hexagon of carbon atoms, each bonded to a hydrogen atom; in hexafluorobenzene, instead of hydrogen atoms, fluorine atoms are bonded to carbon. In the benzene and hexafluorobenzene cases (figure 7, p30), the results showed these molecules do not behave as ordinary hydrophobic solutes, but rather present two distinct regions, one equatorial and the other axial, that exhibit different solvation properties (that is, they have distinct regions that, at the microscopic level, interact differently with water molecules). As in the case of infinite surfaces, these results highlighted the importance of properly including electronic effects to accurately account for solute-solvent interactions.

G. Galli, UC-Davis, and E. Schwegler, LLNL

Figure 7. Snapshot of ab initio molecular dynamic simulations of benzene (left) and hexafluorobenzene (right) in liquid water, showing the electronic charge density (blue and red isosurfaces) and just one water molecule in close proximity with the solute.

A perspective on hydrophobic interactions by Dr. Galli recently appeared in the Proceedings of the National Academy of Science (2007), where a short historical perspective was given and it was noted that "whether in the case of mere reordering of water in contact with infinite hydrophobic substrate, or of breaking of hydrogen bonds (in the case of small solutes), the ability to understand the nature of hydrophobic interfaces at the microscopic level is crucial for building a molecular theory of hydrophobicity." Such a molecular theory will help further the understanding of fundamental biological processes such as protein folding, molecular recognition, and the formation of membranes.

The Next Step
The ab initio simulations of water at surfaces and in contact with small solutes carried out by the SciDAC team, as well as other research groups around the world, are just the first steps toward understanding aqueous environments at the microscopic level. "These are really complex, dynamical systems," says Dr. Schwegler. "The team will work on different fronts to tackle problems related to aqueous environments." One approach is to improve the theoretical tools available so far to describe water and water interactions with surfaces. The quantum mechanical theory used in the team's simulations is approximate, and much work is yet to be done to fully validate this theory and eventually improve it for the aqueous systems.

"We do not quite yet have a full understanding of how well the theory we are using performs to describe different aqueous environments, in spite of the coming of age of quantum simulation techniques and the fundamental progress brought about by their use in the fields of condensed matter physics and materials science," admits Dr. Galli.

"In addition to addressing theoretical issues, we need to address many important algorithmic and numerical problems," adds Prof. Gygi.

In ab initio calculations, only a small number of molecules can be simulated for a short time, compared to what is feasible when using empirical potentials. With empirical potentials, thousands of molecules can be simulated for nanoseconds; ab initio simulations are limited to a few hundred (usually around 100) picoseconds. For example, for an approximately 100-molecule solution of benzene in water, the longest simulation times reached to date are 150 ps, and these simulations have been performed by using rigid water models. In these models, water molecules are considered as fixed in a given, triangular configuration, where vibration leading to bond angle changes has been neglected during the simulation. However, the algorithmic and software developments of the type carried out within the Q-SIMAN SciDAC-2 project (sidebar "Quantum Simulations of Materials and Nanostructures") are expected to lead to substantial improvements in the simulation techniques and, thus, in the type of system sizes and time scales that can tackle aqueous environments.

The results for all the surfaces studied underscored the importance of electronic effects in determining interfacial properties, along with the influence of the surface microscopic structure on the structural and dynamical properties of the liquid.

Density functional theory, the first-principles theory used in the SciDAC team simulations, yields results that compare well with experiments for all the major structural properties of water, some of its electronic spectroscopic signatures (in a qualitative manner), and several dynamical properties. However, it is still unclear how well, compared to experiments, the theory can describe the phase diagram and the thermodynamic properties of water at and close to ambient conditions. In addition to hydrogen bonding, there are other interactions between molecules in liquid water, weaker than hydrogen bonds, that are not expected to be well described by density functional theory as implemented in ab initio MD simulations. These are usually referred to as dispersion forces or van der Waals forces. The incorporation of these "weak" forces in ab initio MD will take some time and is a subject of active research. Similarly, the inclusion of hydrogen quantum effects in the description of water and solvation properties is in its infancy. The dynamics are treated classically, using Newton's laws of motion, in ab initio MD. This approach includes the dynamics of hydrogen atoms that are very light compared to, for example, oxygen atoms (which are 16 times heavier) and should really be described as quantum particles. One of the Q-SIMAN SciDAC team's projects, led by Prof. David Ceperley at the University of Illinois–Urbana-Champaign, is aimed at understanding hydrogen quantum effects in water using sophisticated quantum Monte Carlo techniques.

"The theory we're using is not perfect, but if we are careful in interpreting our results and estimating theoretical error bars on our data, we can proceed with the tools we have in hand right now and attack problems involving more complex aqueous environments while we work at improving our theory," says Dr. Galli. "Our strategy has always been to work on different fronts at the same time: address theoretical issues, tackle the numerical problems required to efficiently 'implement' our theory, and carry out grand challenge applications," adds Prof. Gygi. "These goals may be pursued at the same time, and it is important to do so, as it is precisely the interplay between theoretical, algorithmic, and application results that usually leads to the most exciting progress."

One other grand challenge application the team has in mind in aqueous environments involves oxides and nanoclusters in water, and it is related to addressing energy and environmental issues. Processes at the molecular-, nano-, and macroscopic-scale control both the synthesis of ceramics by "green" low-temperature routes and their degradation in the environment. Thus, a detailed fundamental understanding of transformations from dissolved aqueous species to clusters, nanoparticles, and, finally, solids—and back again—is essential to devising efficient and environmentally benign materials synthesis and controlling and mitigating the effects of contamination. First-principles simulations may provide important contributions to understanding these processes, in collaboration with a variety of experimental techniques. One important goal of the SciDAC team's research is to integrate the simulation work as well as possible with that of experimental techniques and establish close connections with experiments, so as to devise novel, powerful tools to solve major problems, such as energy-related and environmental issues.

The algorithmic and software developments of the type carried out within the Q-SIMAN SciDAC-2 project are expected to lead to substantial improvements in the simulation techniques and, thus, in the type of system sizes and time scales that can tackle aqueous environments.

"We've a number of outstanding problems to solve. For some of them, we have a clear plan; for others, we are still in an exploratory phase. It truly is an exciting time for the application of quantum simulations to solving important scientific problems," says Dr. Galli. "And key to our success will be access to high-performance computing to carry out the large-scale simulations essential to simulations at the nanoscale."

Contributors Dr. Giulia Galli, Professor of Chemistry, Department of Chemistry, University of California–Davis; Cheryl Drugan, Coordinating Writer/Editor for the Argonne Leadership Computing Facility; and Dr. Gail Pieper, Senior Coordinator of Writing and Editing, Mathematics and Computer Science Division, Argonne

Further Reading
SAP Q-SIMAN
http://www.scidac.gov/matchem/design.html

Qbox
http://eslab.ucdavis.edu/