SciDAC Review 17 - SCALABLE MOLECULAR SIMULATION: Toward an Understanding of Complex Chemical Systems

SCALABLE MOLECULAR SIMULATION

Toward an Understanding of Complex Chemical Systems

Energy production and security are among the major challenges facing the nation. To extend performance levels beyond what is now possible for the production, storage, and use of energy, technological breakthroughs must occur. Only with these breakthroughs will energy independence, environmental sustainability, and continued economic opportunities be ensured.

Accomplishing these tasks requires the ability to design and control matter at the level of the electron and nucleus. A detailed molecular knowledge provided by theory and computation is thus becoming increasingly important in a world where materials can now be engineered with specific chemical properties. To enable the creation of these new materials with novel properties, an understanding at the molecular level of the interactions and transformations will be imperative. Quantum mechanics provides an understanding of the chemical, electrical, and physical properties of materials, and computational chemistry allows the examination of questions that are not possible or are very difficult to examine in the laboratory, thus paving the way for highly efficient energy technologies needed for the future. These increasingly powerful computational capabilities allow for simulating realistic chemistry of (large) systems in the bulk and at the interfaces of materials.

A detailed molecular knowledge provided by theory and computation is becoming increasingly important in a world where materials can now be engineered with specific chemical properties.

Scientists at the Pacific Northwest National Laboratory (PNNL) and the University of Zurich are conducting research and developing state-of-the-art molecular simulation tools, combined with increasingly powerful supercomputers, to further understand the dynamics of atoms and nuclei interacting under the laws of quantum mechanics. Their research focuses on the chemical reactions in solutions and at interfaces. Understanding the basic chemistry of water in different environments (for example, in bulk and at interfaces) will be important for energy production, especially as the environments apply to the development of practical hydrogen storage materials and design catalysts.

Both hydrogen storage and catalysis directly relate to energy in two ways: how it is stored, and how it is efficiently used. Our whole energy economy relies heavily on the ability to remove hydrogen from carbon and replace it with oxygen. Hydrocarbon or fossil fuels are saturated with hydrogen, and through the process of combustion produce carbon dioxide and energy. The challenge to alleviate our dependence on fossil fuels relies on our ability to control both the removal and addition of hydrogen at will. This manipulation of hydrogen can only be done through controlling specific chemical reactions and transformations – the essence of catalysis science. The science of hydrogen storage is the substitution of carbon with another element (perhaps nitrogen or boron) that may enable better control of the extraction and addition of hydrogen through a catalytic process. Moreover, in some solar cells, energy is produced in the form of hydrogen by electrochemical processes that cleave water. The chemistry involves various radical species and the well known charged defects, hydronium cation (H₃O⁺) and hydroxide anion (OH^–). Thus, understanding the basic chemistry and structure of water in different environments will be important for energy storage and production, and the insights gained from these studies will enable technological advances capable of addressing the U.S. Department of Energy’s (DOE) energy mission and keeping the nation at the forefront of technology development.

A Molecular World View
Controlling material at the molecular level has foreseen and still-to-be-learned benefits. Molecular modeling will be fundamental to the creation and control of new materials with novel properties.

Molecular modeling will be fundamental to the creation and control of new materials with novel properties.

The foundation for molecular interactions and chemical bonding requires solving the quantum mechanical problem for electrons in the presence of nuclei. Two essential ingredients in the theoretical treatment of electrons are: (1) the precise whereabouts of all other electrons in the molecule (called correlation), and (2) the numerical description needed to represent the wave nature of the electron (basis set). Conventional quantum chemical methods that include both a high level of electron correlation and large basis sets are presently suitable only for gas-phase clusters ranging from 10–100 atoms without temperature (that is, 0 K, or -273°C). The systems of interest to energy applications are comprised of novel condensed phase materials that contain a large number of atoms. These collections of molecules are moving, colliding, and reacting on a catalytic surface (figure 1; sidebar “Molecular Science and Simulation”). Moreover, these condensed phase systems are likely to be composed of several complex interfaces between different states of matter under a variety of conditions, both ambient and extreme.

Illustration: A. Tovey

Figure 1. The fundamentals of molecular science and simulation.

Ultimately, linking computational models with observation is a key step to progress toward understanding complex chemical processes. Taking appropriate averages over the collection of molecules, namely statistical mechanics, provides the essential bridge between quantum mechanics and observables. Through statistical mechanics, molecular scale insights are obtained about the underlying complex chemical processes at the temperatures, pressures, and concentrations relevant to DOE’s mission.

The highest level of electron correlation for predicting the collective response of molecules in a condensed phase is computationally intractable. Thus, an accurate and computationally efficient theory of the electron with sufficient level of electron correlation is required to perform relevant size calculations and the appropriate statistical mechanical sampling that is essential to understanding novel materials.

Computational Approach
Perdew et al. (2005, J. Chem. Phys. 123, 062201) has characterized the hierarchy of treatments of electron correlation within a “Jacob’s Ladder” of approximations, where the goal is to obtain the true electronic density at the final rung (sidebar “Jacob’s Ladder: The Heaven of Chemical Accuracy”). The underlying quantum mechanical theory that is described by the second and fourth rungs is known as the Kohn–Sham (KS) density functional theory (DFT). With efficient integration of KS-DFT and statistical mechanics, the fundamental understanding needed to control matter at the molecular scale can be obtained.

There has been rapid progress in the past few years in developing fast and accurate electronic structure methods based on KS-DFT and for understanding the statistical mechanics of condensed phases. KS-DFT can now be used to characterize the thermodynamic landscapes essential to advance our understanding of matter at ever-finer scales. To this end, PNNL and Zurich researchers use and develop the publicly available CP2K (cp2k.berlios.de) code in order to perform ab initio molecular dynamics.

CP2K provides a novel and scalable solution to the quantum mechanical equations, which yields an accurate and efficient approximation to the electron density. For the level of electron correlation represented by the second and third rungs of Jacob’s Ladder, CP2K uses an implementation of KS-DFT that is a result of mixing methodologies from quantum chemistry and solid state physics. Achieving this sweet spot between two well-developed disciplines is a unique quality of our computational approach and enables the solution of the electronic structure problem with speed and accuracy (sidebar “The CP2K Project” p13).

Using the power provided by DOE’s leadership-class computing facilities, the CP2K code was used for all applications discussed below in a regime where it exhibits good to excellent weak scaling, and time-to-solution was of interest. For moderate system sizes, 100–1,000 atoms give the best overall real-time performance, but the parallel efficiency drops from nearly 70% for 64 water molecules (96 atoms) to nearly 50% for up to 512 water molecules (1,536 atoms). Excellent weak scaling is once again recovered (approximately 70%) for 1,024 water molecules (3,076 atoms). It is important to note that these moderate-sized systems comprise the current state-of-the-art for KS-DFT in conjunction with statistical mechanical sampling. Because of the ensemble nature of the calculations, 10,000 cores were easily utilized. The key to scaling up to that many cores relies on the perfect scaling that is afforded by statistical mechanical sampling. This idea, which can be attributed to J.W. Gibbs (one of the founding fathers of statistical mechanics), is the need to sample replicas of the system under different initial conditions or constraints. Thus, the idea of the statistical ensemble can be used in conjunction with KS-DFT to effectively utilize large numbers of cores, which is imperative to making contact with observation.

Molecular Simulation in the Condensed Phase
The presented applications use quantum mechanics in conjunction with statistical mechanical sampling to go beyond traditional quantum chemical simulation methodologies to advance our understanding of matter in the condensed phase. The condensed phase environment has a unique influence on chemical reactions by: (1) providing an efficient route for energy transfer, (2) initiating chemical reactions that would not occur in the gas phase, (3) stabilizing reaction intermediates, (4) facilitating the transfer of electrons, (5) limiting the mass transfer of reacting species, (6) stabilizing transition states and thus modifying reaction barriers, and (7) moderating collision dynamics.

Using the power provided by DOE’s leadership-class computing facilities, the CP2K code was used for applications in a regime where it exhibits good to excellent weak scaling, and time-to-solution was of interest.

Interfaces, such as those associated with the liquid–air or solid–liquid boundary, provide an additional unique (but poorly understood) environment where novel chemistry occurs. Our understanding of these interfacial processes is still in its infancy, but understanding interfacial structure, transport to and across interfaces, and subtle surface chemistry provides the crucial foundation for chemical control of many important processes, including catalysis. CP2K provides a powerful computational tool for examining complex molecular systems in the condensed phase and their interfaces.

Modeling Complex Chemical Processes
The accurate treatment of condensed phase reactions presents many challenges. Chemical reactions in solution and at interfaces can require long time scales (10^-6–10 seconds) relative to the duration of the most efficient molecular dynamics trajectories (10^-12–10^-9 seconds). Thus, these reactions are often identified as rare events, because it is uncommon to “see” a reaction occur in a molecular simulation. To bring the reactive event into focus during reasonable simulation times and to overcome the bottleneck associated with long trajectories will require novel statistical mechanical methods.

PNNL–Zurich Collarboration

Figure 4. A schematic illustration of a reaction coordinate for proton transfer. Proton transfer is defined as moving a hydrogen, H^*, from oxygen O_a on the “reactant” water to O_b on the “product” water. The statistical sampling of this process is related to the observable reaction kinetics and thermodynamics through the free energy, depicted as the green curve juxtaposed onto the actual molecular process.

The concept of a reaction coordinate is introduced in figure 4. The reaction coordinate provides a reduced representation of the reactive processes that allows us to focus on the crucial reactive event. The illustration’s salient point is that a complex chemical process in the condensed phase is reduced to examining the motion of a few key atoms that participate in the chemistry. These participating atoms, and their concomitant motion, define a reaction coordinate. Reaction coordinates will represent a chemical transformation from the reactant, through a transition state, and finally the product state. Observed reaction thermodynamics (or free energies) can be rigorously determined through statistical mechanical sampling of a reaction coordinate and thus plays a vital role in a molecular understanding of fundamental processes in the condensed phase. Moreover, because of the ensemble nature of the calculation, the sampling of reaction coordinates generally exhibit perfect scaling. Thus, the 1,000 cores at Oak Ridge National Laboratory’s (ORNL) Cray XT4 and XT5 and Argonne National Laboratory’s (ANL) Blue Gene/P can be accessed to directly probe chemical transformations in the condensed phase. These concepts will become imperative to furthering our understanding of chemistry, which is at the center of energy storage and production.

Molecular Processes at Interfaces

Reactions at the Air–Water Interface
Many essential processes occur at the boundaries between solid, liquid, and gas phases. For example, understanding collective motions and chemical reactions of water’s interfaces has implications for catalysis and hydrogen transport that are essential in energy production and storage. Moreover, understanding water’s structure in the vicinity of interfaces goes beyond energy applications and enhances our ability to understand protein folding, the structure of living cells.

Although water is ubiquitous, scientists are still trying to understand and predict properties of aqueous systems and their interfaces. Water’s large dipole moment, polarizability, hydrogen bonding, and ability to auto-ionize (which defines the pH scale) make this substance one of the most difficult to understand via molecular simulation. An experimental and theoretical consensus has not yet been achieved regarding the precise concentration of hydroxide anion and hydronium cation in the vicinity of the air–water interface. The question of whether water’s liquid–air interface is more acidic or basic is still not answered. Understanding the basic chemistry of water could have profound consequences on what chemical processes can occur at the ubiquitous air–water interface.

The use of Leadership Computing Facilities afforded to PNNL and the University of Zurich by a 2008–2010 Innovative and Novel Computational Impact on Theory and Experiment (INCITE) award is the first step toward providing chemical insight through the simultaneous statistical mechanical sampling of the reaction coordinate for proton transfer as well as determining the propensity of the hydroxide anion to be present at the air–water interface. The INCITE program, established by DOE’s Office of Science, enables researchers to conduct large-scale, computationally intensive research projects at America’s premier computing centers.

The PNNL–Zurich calculations were performed on the Cray XT4 and Blue Gene/P using 216 water molecules (648 atoms) of a water slab containing two free interfaces. Simultaneously sampling both the reaction coordinate, as depicted in figure 4 , as well as the hydroxide anion as a function of the interfacial coordinate, the researchers were able to use nearly 6,000 cores. Typical calculations usually require approximately 200,000 evaluations of the KS-DFT energy. The results allow the examination of how complex chemical processes can differ approaching the air–water interface.

Illustration: A. Tovey

Figure 5. An illustration of the hydrogen bonding network of water. The hydrogen bond is the interaction of the positively charged hydrogen (white) atom with negative electron density present on oxygen (red) atom. The two hydrogen atoms on the water molecule are called donors (D1 and D2), and electron density on the oxygen atom allows water to accept two hydrogen bonds (A1 and A2). It is the ability of water to form these hydrogen bond networks that gives rise to its unique properties.

Findings on the hydroxide anion have provided a picture where there is a weak propensity for the anion to be at the air–water interface, a prediction that is exactly the opposite of that deduced from classical empirical potentials (2009, Chem. Phys. Lett. 481, 2–8). The reason for this can be found in the hydroxide anions’ unique electronic structure. Water both donates and accepts two hydrogen bonds as shown in figure 5. The hydroxide anion, through subtle quantum mechanical effects, can accept four hydrogen bonds and donate one (figure 6). This peculiar electronic structure persists in the vicinity of the air–water interface, but now the hydroxide anion is only accepting three hydrogen bonds and donating zero. The change in structural moieties facilitated by the unique electronic structure of the anion promotes its presence at the air–water interface with little free energy penalty. These important findings reinforce the notion that novel chemistry can occur in the vicinity of the air–water interface and emphasize the necessity of large-scale quantum mechanical modeling to understand it.

PNNL–Zurich Collarboration

Figure 6. An illustration of the peculiar electronic structure of the hydroxide anion (OH^–, depicted in yellow) surrounded by neighboring water molecules (depicted in red) in configurations extracted from bulk (upper panel) and interfacial solvation (lower panel). The salient feature is the ring-like or inner tube arrangement electron density (rendered in gray) that encircles the OH^–. This allows the OH^– under bulk solvation to accept four hydrogen bonds and donate one, forming the so-called “hypercoordinated” complex. This peculiar electronic structure persists at configurations in the vicinity of the air–water interface (lower panel) where it is clear that OH^– is now only accepting three hydrogen bonds. It is very difficult to parameterize the subtle differences of bulk and interfacial solvation into classical empirical potentials.


PNNL–Zurich Collarboration
Figure 7. The 216 water system comprising the air–water interface with a hydrated proton (H₃O⁺). Oxygen is rendered in red, hydrogen in white, and the hydrogen bonds between water molecules are denoted in yellow. The large sphere rendering of water denotes the periodic image yielding an infinite interface in the horizontal direction. In (a), the hydronium is located in the so-called eigen form where the hydronium core is easily identified as H₃O⁺ using a ball-and-stick rendering. The blue waters are highlighted as the hydrogen bond partners of the eigen core. In (b), the so-called zundel form is isolated at the interface. It is clear from the ball-and-stick rendering that this charged complex has the chemical formula H₅O₂ ⁺, and is involved in four hydrogen bonds.

The PNNL–Zurich studies of hydronium cations will continue to provide a microscopic picture of the interfacial propensity and novel chemistry of these important ions in the vicinity of the ubiquitous air–water interface. Specifically, they continue to use the proton transfer coordinate to quantify the difference in stabilization of two different charged moieties (eigen versus zundel) under bulk and interfacial solvation, as depicted in figure 7. Because of the better scaling of CP2K on the Cray XT5, approximately 10,000 cores were effectively used. With the results from the hydroxide anion, they will be one step closer to a molecular depiction of how interfaces can alter the important chemistry that hydrogen participates in for energy applications.

The Prediction and Observation of Novel Meta-Stable Phases of Water
A further important step toward controlling interfacial chemistry is the ability to create and characterize novel phases of matter in the laboratory. The study of thin films of water on substrates having both an affinity to (hydrophilic) and against (hydrophobic) water yields insight into water’s properties near interfaces. Although it is easy to imagine a strong hydrophilic interface may alter water’s structure, strongly hydrophobic interfaces are also known to have a profound influence on the structure of water and thus control important biological process through the so-called hydrophobic effect. The PNNL–Zurich team used infrared spectroscopy and found signatures of a novel two-layer structure on hydrophobic substrates (graphene).

Illustration: A. Tovey

Figure 8. A simulated two-dimensional ice structure with oxygen rendered in red and hydrogen in white. The atoms on the bottom (or behind) are rendered in gray, and the blue dashed line represents hydrogen bonds. (a) A top view. The two-dimensional ice has clear hexagonal symmetry that can be experimentally verified. (b) A side view, showing the flat bilayers of water molecules with interconnecting hydrogen bonds. (c) Experimental (solid lines) and theoretical (dashed lines) of infrared (IR) absorbance spectra.

Using KS-DFT theory, a model two-layer water structure was constructed and simulated at the experimentally determined temperatures (2009, J. Am. Chem. Soc. 131, 12838). Specifically, calculations were performed on 48 water molecules (144 atoms) on the 1,500 CPU Linux cluster comprised of 2.33 GHz Clovertown chips housed in the Environmental Molecular Science Laboratory (EMSL) at PNNL. The bilayer structure is such that every water molecule forms three hydrogen bonds in-plane, and a fourth hydrogen bond is formed between the layers (figure 8, p18). These strained geometries of the novel bilayer phase of water differ dramatically from well-characterized, ice-like structures (figure 5) where all hydrogen bonds are nearly equivalent. Indeed, as seen with the hydroxide anion, it is the ability of water to bend and contort in unimaginable ways that is likely responsible for its unique properties. Thus, a phase of water was found that is composed of two flat layers of fully saturated hydrogen bonded structures (that is, each water donates and accepts two hydrogen bonds). To sample two different ensembles of the bilayer structure, 256 cores were used to achieve the appropriate statistical averaging over electronic properties. As a result of this averaging, the infrared spectra was simulated and directly compared to experiment. The near quantitative agreement between computed and measured spectra provides proof of the molecular picture of this novel phase (figure 8) and is further evidence that unusual meta-stable phases of water can exist near hydrophobic interfaces. This discovery highlights the role of molecular simulation in providing a microscopic picture of the hydrophobic effect and, through close collaboration with experiment, a step toward controlling matter at interfaces.

Breaking the Technological Barriers

Hydrogen Storage Materials
Hydrogen storage is one of the most challenging technical barriers in the implementation of a hydrogen-based energy economy. In the pursuit of practical hydrogen storage materials, the chemical and physical properties of many complex hydrides – for example, metal-amides, alanates, and boronates with high hydrogen content – have been re-examined during the past decade. New breakthroughs in the development of complex hydrides as practical hydrogen storage materials will benefit from knowledge of the thermodynamic, kinetic, and structural properties of the reactants, products, and key intermediates formed in the dehydrogenation reaction pathways.

Hydrogen storage is one of the most challenging technical barriers in the implementation of a hydrogen-based energy economy.

Molecular simulation is an effective tool to better understand the characteristic slow motions that influence the material properties and are responsible for the initial stages of hydrogen release. A proper statistical mechanical analysis involving adequate sampling of relevant dynamics and physical states is required to have a molecular understanding of hydrogen storage.

Illustration: A. Tovey

Figure 9. Hydrogen storage materials. In the left panel, atoms are depicted in the following colors: hydrogen in white, nitrogen in blue, and boron in pink. The examples in the left panel show ZB (left) and RS (right) structures of NH₄ ⁺BH₄ ^–. The ZB set shows the 0 K geometry optimized structures, the RS set shows the CP2K dynamics at 300 K, and the graph in the right panel shows the thermal corrections as computed from the CP2K trajectory to make the thermodynamic prediction on the relative stability of RS over ZB.

An important hydrogen storage compound with the highest gravimetric hydrogen density is ammonium borohydride, ca. 24 wt% hydrogen. A recent study predicted NH₄⁺BH₄^- should be energetically stable in the zinc blende structure rather than the rock salt structure (figure 9). However, these conclusions were based on ground state electronic energies only (again, 0 K or -273°C with no statistical mechanical sampling). Furthermore, there were no experimental data that provided insight into the solid phase structure of NH₄⁺BH₄^- or the reaction energies for hydrogen release that would provide a benchmark for the calculations. In order to estimate the relative thermodynamics, or free energy difference, between the rock salt and zinc blende structures, the thermal correction to the energy was computed, which reflects the true disorder in a system due to temperature and pressure from a CP2K trajectory (figure 9). From this analysis it was found that the rock salt structure is thermodynamically more stable than the zinc blende structure, which is consistent with the measured X-ray diffraction pattern of NH₄⁺BH₄^-. Figure 9 shows the X-ray diffraction pattern for the rock salt and the zinc blende structures at 300 K (room temperature). Using statistical sampling afforded by CP2K at the experimentally relevant temperature, 16 NH₄⁺BH₄^- pairs (160 atoms) of both zinc blende and rock salt were simulated using 128 cores at the National Energy Research Scientific Computing Center (NERSC). These provided the theoretical evidence that NH₄⁺BH₄^- crystallizes at ambient conditions in a rock salt structure and not in a zinc blende structure as previously proposed. Moreover, this finding was verified by experiment that also demonstrated that NH₄⁺BH₄^- in the rock salt structure releases more than 20 wt% hydrogen in three steps at temperatures less than 160°C.

Applications to Catalysis
As discussed in the introduction, chemical bonds are one of the best means to store energy because of the high energy density of chemical fuels. Catalysis is an essential process to enable control of the needed chemical transformations for the clean and efficient production and use of fuels. A recent report, Basic Research Needs: Catalysis for Energy (http://www.science.doe.gov) emphasized the need for advancement of theory and computation to understand and design catalysts that provide activity (namely, accelerate rates of reactions) and selectivity, such as direct molecular processes to produce desired products. A critical element for computational studies of these catalytic materials is the chemical complexity of the actual materials being studied experimentally.

Catalysis is an essential process to enable control of the needed chemical transformations for the clean and efficient production and use of fuels.

Statistical mechanical methods can provide insight into the chemical species and processes occurring under the real thermodynamic conditions of a catalytic reaction by allowing us to make direct contact with operando spectroscopic measurements. For example, it was reported that the addition of rhodium-based coordination compounds to aminoboranes in solution could lead to the catalytic release of hydrogen, a condition favorable for practical applications of the hydrogen storage materials discussed above. Although it was first assumed this process occurred by the formation of Rh-nanoparticles, subsequent operando extended X-ray absorption fine structure (EXAFS) measurements (2007, J. Am. Chem. Soc. 129, 11936) found that the active species was in fact an Rh4 cluster species that formed during the reaction in solution. Unfortunately, EXAFS was unable to definitively assign a structure to the observed species, a fact that precludes the inference of a catalytic mechanism.

The PNNL–Zurich team recently deployed KS-DFT molecular dynamics simulations, combined with statistical sampling, to compute EXAFS spectra. Using approximately 500 cores afforded by NERSC, the ensemble averaged approximately 40 possible structures comprised of nearly 100 atoms that were compatible with the EXAFS measurements (2009, J. Am. Chem. Soc. 131, 10516).

Illustration: A. Tovey

Figure 10. Identification of catalytic intermediates observed by operando XAFS measurements. An Rh₄(BH₂N(CH₃)₂)₈ ²⁺ cluster was identified as the catalyst resting state during the hydrogen release from dimethylaminoborane by the detailed comparison of KS-DFT simulations and experimental EXAFS spectra. The molecular diagram on the left shows two MD snapshots approximately 75 ps apart in time, showing the large amplitude fluxional motion of the cluster; methyl groups have been removed for clarity. The graph on the right is the ensemble-averaged simulated EXAFS spectrum (red) compared with experiment (blue).

From these simulations, the species were identified that were consistent with the EXAFS measurements (figure 10, p20), as well as many of the faster processes such as boron to rhodium hydride transfer of the catalytic cycle. In addition to significantly augmenting the information obtained from these operando measurements, a catalytic mechanism was inferred for the H₂ release process. This result is an important step toward a molecular understanding of controlling hydrogen release in model hydrogen storage materials such as aminoborane.

Future Research
Future pursuits will focus on sampling different reaction coordinates to model photovoltaic cells vital to energy production. These applications harness the inexhaustible resource of our Sun to initiate the appropriate chemical reactions to produce energy. Here, the energetic process is described by a reaction coordinate describing the localization of an electron (for example, charge transfer) from one site to another. In order to describe complex phenomena such as electron transfer, a higher level of electron correlation is used, represented by the fourth rung of Jacob’s Ladder. The fourth rung, the so-called hyper functionals, has a profound effect on the quality of simulations in cases where the exact location of electrons is truly essential. Future applications of KS-DFT will use the fourth rung of Jacob’s Ladder together with statistical methods, which will ultimately pave the way to the use of exascale hardware to provide molecular depictions of complex processes describing the harvesting of light.

J. VandeVondele, U. Zurich

Figure 11. A realistic model of the N3 sensitized anatase(101)/acetonitrile interface, which is key in dye sensitized solar cells. Calculations based on hybrid functionals (fourth rung of Jacob’s Ladder) allow for an accurate prediction of the electronic levels in this system, and are an essential ingredient to quantitatively predict the electron transfer rates across the interface.

A quantum mechanical description of the interaction between molecules is imperative to meet the challenges of energy production and energy security facing DOE and the nation.

In the modeling of typical photovoltaic cells, electrons will generally be localized in product and reactant states and delocalized in a transition state. Only the fourth rung of Jacob’s Ladder can capture the detailed energetics of this balance between localization and delocalization. For a new class of photovoltaic devices, dye-sensitized solar cells, also known as Graetzel cells (2001, Nature 414, 338), getting these properties right is essential for a realistic model. A detailed atomistic model has been constructed for the active interface in dye-sensitized solar cells. This model (figure 11) explicitly takes the oxide, the solvent, and the dye into account and employs a quantum mechanical description for approximately 1,500 atoms. Using this model, the key question of light adsorption and electron injection can be addressed to initiate the chemistry to produce and store energy from the Sun.

Future research using leadership-class computers will create a sharper molecular-scale picture of the processes governing complex systems, which, in turn, will lead to a greater ability to control them.

Conclusion
In summary, a quantum mechanical description of the interaction between molecules is imperative to meet the challenges of energy production and energy security facing DOE and the nation. It is through the use of statistical mechanical methods and a quantum mechanical treatment of the electron that we will meet these goals. Future research using leadership-class computers will create a sharper molecular-scale picture of the processes governing complex systems, which, in turn, will lead to a greater ability to control them. The insights gained from the PNNL–Zurich calculations will enable technological advances capable of addressing DOE’s energy mission and keeping the United States at the forefront of technology development.

Contributors Christopher J. Mundy, Shawn M. Kathmann, Roger Rousseau, and Gregory K. Schenter, all at Chemical and Materials Sciences Division, PNNL; Joost VandeVondele and Juerg Hutter, Physical Chemistry Institute, University of Zurich

Acknowledgements
his work is supported by the DOE Office of Basic Energy Sciences Chemical Sciences, Geosciences, and Biosciences program. Calculations presented herein were performed at NERSC on the Cray XT4 (Franklin) and through resources afforded by the 2008–2009 INCITE award, namely the Cray XT4 and XT5 (Jaguar) at ORNL and the IBM Blue Gene/P (Intrepid) at ANL. The authors are also grateful for an Early Use award on ORNL’s Cray XT5. They also would like to acknowledge the state-of-the-art facilities at PNNL, namely the 1500 CPU Linux cluster comprised of 2.33 GHz Clovertown chips (NWice) housed in EMSL. EMSL is a national scientific user facility sponsored by DOE’s Office of Biological and Environmental Research and located at PNNL.