Molecular Science in the Environment

Molecular Theory Group, Theory Modeling and Simulation,
Environmental Molecular Sciences Laboratory,
Pacific Northwest National Laboratory

Recent technological breakthroughs in the development of high end computer architectures combined with new and novel approaches in high performance software methods, have provided the computational chemistry/physics community with the resources needed to address progressively more complex and difficult scientific problems. The presently available, and rapidly evolving, state-of-the-art hardware/software tools allows scientists to expand the scope and complexity of the systems and processes under investigation. In many cases, this has allowed us to tackle ``real world'' problems that were previously computationally intractable. It is now becoming possible to understand how molecular level events influence important processes in the environment, materials design, biological organisms, and many other systems. These technological breakthroughs require us to expand the vision of our scientific inquiry beyond traditional boundaries and present us with a tremendously exciting and scientifically challenging environment.

Scientific inquires must keep pace with the rapidly advancing computer industry. New scientific disciplines such as molecular environmental science and molecular biochemistry are, in part, products of the recent ``technological revolution.'' Major breakthroughs in these and related fields will be possible if we can understand the underlying molecular processes that control our world. In order to realize these goals, it is imperative that the scientific research community continues to forge strong links with computer developers and computer scientists. The crucial link between these areas is the development of high performance software that can utilize the hardware's full potential. A symbiotic relationship must exist between the theoretical chemical physics community and computer scientists and designers in order to continue to expand our scientific horizons.

Rapidly evolving high performance computer technologies allow us to probe complex problems in molecular chemistry/physics at many different levels. One approach is to use and develop these resources in order to examine the properties of ``large length scale'' systems - e.g. (10-1000+) atom clusters, nanoparticles, liquids, solids and homogeneous and heterogeneous interfaces. Understanding the underlying physics and chemistry of these systems provides us with insight into the behavior of many environmentally and industrially important processes including, the transport of contaminants through soils, the separation of heavy metals and radionuclides from liquid hazardous wastes, the development of efficient and more cost effective catalysts, the effect of heterogeneous reaction chemistry on atmospheric and terrestrial cycles, the development of bioremediation methods. These studies employ a range of methods from ab initio quantum mechanics to classical simulation techniques. The level of theory used to study a particular system depends on the nature of the problem, the size and complexity of the system, and the availability of sufficient computational resources (both hardware and software).

An alternate approach employs state-of-the-art computational resources to study complex electronic process (e.g. basis set development, reaction rate theory, electron-electron correlation effects, many body theories) in ``small length scale'' molecular or atomic systems. These scientific inquires are the basis for understanding the fundamental properties of molecules and their extended assemblages, including important information about interaction energies and reaction rates. This information is essential for developing quantitatively precise models that can predict the outcome of complex industrial and environmental processes. Highly accurate theoretical models (``computer experiments'') are often more cost effective and efficient than the corresponding laboratory or field studies and hence, are a fundamental component of research in fields ranging from environmental to biomedical to materials research.

Research in the Molecular Theory and Modeling program focuses on understanding the role that molecular processes play in condensed phases, characteristic of natural and contaminated environments. This research program integrates ab initio studies of fundamental molecular processes in model systems with modeling of the complex molecular systems found in the environment. This integrated approach is computationally demanding and relies heavily on the accessibility and utility of high-end computational resources.

Applications in this program focus on four overlapping research areas: cluster chemistry, solution-phase chemistry, separations chemistry, and chemistry at interfaces. A common element in each of these areas is the need to understand molecular interactions in aqueous solutions or at environmentally-important interfaces such as the interfaces between aqueous solutions and air, other liquids (e.g., organic solutions), minerals, and glasses. The development of new theoretical methods for treating these problems is concentrated in the areas of electronic structure method, reaction rate theory, and classical model development. The range and extent of these theoretical efforts are closely coupled to advances made in high-end computer architectures.

Examples from the four research areas - cluster chemistry, solution-phase chemistry, separations chemistry and interface chemistry - are described below. These examples are meant to illustrate the importance of high-end computing for solving complex problems in environmental molecular research.

Research in cluster chemistry is focused on the structure and properties of aqueous clusters and on the energetics and dynamics of molecular processes involving such clusters. Molecular clusters offer a unique opportunity to examine the transition from the gaseous phase to condensed phases and to enhance our understanding of the intermolecular interactions between solutes and water. In addition, to the extent that clusters model the solution phase, studies of molecular clusters provide an opportunity to ascertain the effects of solvation on chemical reactions: comparison of the pathways, energetics and dynamics of the ``solvated'' reaction with the gas-phase reaction will lead to insights into the detailed role that the solvent plays in altering the mechanism and rates of reactions in solution.

The methodologies developed to model gas-phase molecules and molecular processes are being applied to the study of the aqueous clusters. However, solution of the electronic and nuclear Schrödinger equation for aqueous clusters poses two challenges. First, the number of atoms involved in the calculations increases with the size of the cluster and accurate calculations rapidly become intractable. Second, the resulting potential energy surface possesses multiple minima that complicates the characterization and representation of the potential surface and subsequent dynamical studies. The primary focus of work in this area is the understanding of the structure and energetics of aqueous clusters and the development of improved interaction models for these systems.

Reliable theoretical data on the structure and energetics of small water clusters containing alkali or alkaline earth ions (Li⁺ through Cs⁺ and Mg²⁺ through Ra²⁺) are of interest due to the widespread appearance of such systems in nature and the difficulty of obtaining this information experimentally. Furthermore, the data is of interest because the observed binding preferences of crown ethers for particular cations in aqueous solution involves a competition between the binding of the ion to water and to 18-crown-6. The ion selectivity properties of crown ether complexes makes them unique materials for understanding enzyme chemistry and designing ion-separation techniques. This process can be modeled by calculating the energetics of the exchange reactions:

M⁺(H2O)_n + M $^{\prime{+}}$ (18-crown-6) $\Rightarrow$ M $^{\prime{+}}$ (H2O)_n + M+(18-crown-6)

M²⁺(H2O)_n + M $^{\prime{2+}}$ (18-crown-6) $\Rightarrow$ M $^{\prime{2+}}$ (H2O)_n + M²⁺(18-crown-6)

This competition between water-ion and crown ether-ion interactions is most easily determined theoretically because the synthesis of these materials is very complex.

Geometries, binding energies, and enthalpies of molecular clusters incorporating a single metal ion and up through 8 waters were determined using basis sets and levels of theory comparable to those employed in a parallel study of ion/18-crown-6 systems. Most calculations were done with the polarized 6-31+G* basis set and second order perturbation theory. In order to estimate the inherent accuracy in the MP2/6-31+G* level of theory, some of the same clusters were re-examined with more elaborate theoretical methods. This calibration study involved the use of the correlation consistent sequence of basis sets to estimate the complete basis set limit, coupled with higher order correlation methods (e.g. MP4 and CCSD(T)). Representative results for Li⁺(H2O) and Na⁺(H2O) are shown in Figure 12.

**Figure 12:** The binding energy (in kcal/mol) of Li⁺(H₂O) and Na⁺(H₂O) as a function of basis set size.
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Excellent agreement is observed between counterpoise (CP) corrected 6-31+G* results and the best theoretical values. Slightly poorer agreement is seen in the metal-oxygen distance because of the lack of a basis set superposition correction. In general the effects of correlation recovery on the basic cation-water distance and binding energy is small ( $\sim$ 0.03 Åand $\sim$ 2 kcal/mol, respectively). However, as the clusters increase in size and the potential for multiple water-water interactions increases, the importance of correlation effects also increase.

Due to the time consuming nature of large-basis-set, correlated calculations, we are limited in our ability to carry out the highest quality calculation to clusters containing no more than five or six waters. Such calculations require hundreds of hours on conventional supercomputers like the Cray C90. For example, a single point MP2 calculation on K⁺(H2O)₆ using a Dunning aug-cc-pVDZ basis set (277 functions) takes about 8 CPU hours using 30 Mwords of memory and 2 GB of scratch disk space on a C90. Improved algorithms for optimizing the structure of floppy systems and computationally cheaper theoretical methods are both needed, along with new computer architectures, such as massively parallel machines. We are currently investigating density functional theory with non-local gradient corrections and the ``Resolution of the Identify MP2'' method.

Solution-phase chemistry plays a central role in the Molecular Theory and Modeling program. The effort is focused on the structure, energetics and dynamics of molecular processes in aqueous solutions. This work is the basis for an enhanced understanding of molecular processes occurring in contaminated and natural ground-water and in complex waste solutions. This core program in solution chemistry is designed to further the understanding of the fundamental molecular processes occurring in solution (e.g., solvation and reaction), providing a basis for the development of accurate techniques for simulating the behavior of complex waste solutions. This work includes studies of ionic solvation, supercritical fluids, and solvent effects on chemical reactions.

Molecular dynamics simulations of liquid-liquid interface with polarizable potential models

An understanding of ion transport mechanisms across the interface of two immiscible liquids is fundamental to electrochemistry and surfactant chemistry. It is also closely related to environmental problems such as separations chemistry that is performed in binary solvent systems (i.e., organic and aqueous phases) and interactions of contaminated organic solvents with ground water. We begin our effort in this area by examining the equilibrium properties of the CCl₄/H₂O liquid-liquid interface using molecular dynamics (MD) simulation techniques. It is well known that some of the properties of H₂O and CCl₄ near the CCl₄/H₂O interface are significantly different from their respective bulk properties. For instance, differences in the hydrogen bonding network and/or orientation preferred by the water molecules at the liquid/vapor interface results in a change in the dipole moment from 2.6 - 2.8 D in the bulk to 2.2 - 2.3 D at the interface. Thus, it is instructive to include the non-additive effects in describing solvation properties at the interface.

Computer simulations of liquid-liquid interfaces have been reported by Benjamin and coworkers on the structure, dynamics and conformational equilibria at the water/1,2-dichloro-ethane liquid-liquid interface and subsequently the mechanism of ion transport across this interface. Work has also been done on the transport of water molecules through a lipid membrane and on the water/hexane liquid-liquid interface by Berendsen and coworkers, and on the problem of solute transfer across a liquid/liquid interface by Hayoun et al. All of these studies of the liquid-liquid interfaces employ pair-wise additive models. Thus, the effects of including polarization on the liquid-liquid interfacial equilibrium properties are not known. We report here a molecular dynamics study of the CCl₄/H₂O liquid-liquid interface using polarizable potential models. This particular interface is of great environmental importance. Due to its usage in the processing of the radioactive materials, CCl₄ contributes significantly to the problem of nuclear waste remediation. A detailed investigation of the CCl₄/H₂O liquid-liquid interface at a molecular level should aid in solving these environmental problems. In this work, we are able to describe the electrical properties (i.e. the induced and the total dipole moments) of the CCl₄ and H₂O molecules as a function of their distance normal to the interface. In Figure 13, we present the computed CCl₄/H₂O interface density profile averaged over a 100 ps simulation as a function of the z axis normal to the interface.

**Figure 13:** The density profiles of water and carbon tetrachloride at the room temperature from a 100 ps MD simulation.
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The density profiles are calculated using slab thickness of 1Å parallel to the XY plane. After closely examining the Figure 13, we observe that the interface is not molecularly sharp, and that the density profile of H₂O indicates no layering and it is similar to that obtained for the water liquid-vapor interface using our polarizable potential model. The individual density profiles of H and O atoms are also identical to the corresponding to that of H₂O. The density profile of CCl₄, on the other hand, exhibits some oscillations. This is maybe due to the small number of CCl₄ molecules used as compared to that of water. The simulations with a significantly longer trajectory and larger system size are in progress to evaluate the origin of these oscillations. During the dynamic simulation, the interfacial fluctuations are monitored by computing the interfacial width as a function of time (the results are not shown here). We find that the width is oscillating, which indicates that there are some penetrations and retreats by water and carbon tetrachloride molecules between the interface regions.

To understand the effect of the polarization effects on the electrical properties of water molecules near the interface, we calculate the total dipole moments of the water molecules as a function of Z axis normal to the interface, and the results are shown in Figure 14.

**Figure 14:** The total dipole moment of water molecules as a function of the Z-axis.
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The dipole moments are computed using slab thickness of 1Å parallel to the XY plane. Examining this figure, several observations are in order:

**Figure 15:** The induced dipole moments of water and carbon tetrachloride molecules as a function of the Z-axis normal to the interface.
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As expected, the average induced dipole moment of water molecules near the interface are rather small compared to water molecules in bulk-like regions. The induced dipole moment of carbon tetrachloride molecules near the interface regions significantly increase, which may be explained by the presence of the local electric field induced by the water molecules at the interface.The static orientations of the CCl₄ - H₂O near the interface are examined via the angular distribution functions as a function of C - O separation, and are presented in Figure 16.

**Figure 16:** Probability distributions for the angle between the intramolecular C - Cl bond and the vector pointing from C to the O atom as a function of the O - C separation. The data points correspond to O - C distances between 0-3 (filled circles), 3-4 (open circles), 4-5 (crosses), respectively. A uniform angular distribution function is described by a sine function.
$\begin{figure} \centerline{ \psfig {figure=gb_tms5.eps,height=100mm,width=100mm,silent=} }\end{figure}$

The angle is defined between the intramolecular C - Cl bond and the vector connecting the oxygen and carbon atom. When the C - O distance is around 3Å, the computed angular distribution functions show dramatic deviations from the sine curve that describes a uniform distribution. Two peaks centered at 72 $^{\circ}$ and 170 $^{\circ}$ are observed for a C - O distance less than 4Å, while the probability of finding CCl₄ in other orientations with respect to H₂O is almost vanished. Integrating over the area under these two peaks gives a ratio of magnitude of roughly 3:1.

This implies that each CCl₄ molecule has three of its chlorine atoms facing O, while the fourth chlorine atom sits on the opposite side of the central carbon atom away from O in an almost linear arrangement. This result suggests that water molecules induce a strong orientational order on the CCl₄ molecules near the interface, which is consistent with the increasing of the induced dipole moment of the CCl₄ molecules. As the C - O separation becomes larger (i.e., >5Å), the angular distribution curve behaves as a normal sine function, indicating the orientational order has been smeared out and the influences of water molecules on the carbon tetrachloride molecules have diminished. To our knowledge, this work is the first MD simulation on the liquid-liquid interfacial equilibrium properties that explicitly includes non-additive effects. As expected, the interface is not molecularly sharp. The density of water indicates a uniform distribution while that corresponding for the CCl₄ exhibits some oscillations. This oscillatory behavior deserves further investigation which is in progress.

Research in separations chemistry concentrates on the structure and energetics of ion-ligand complexes (such as crown ethers) and the dynamics of complex formation in aqueous solutions. The goal of this effort is to discover the factors that control the selectivity and efficiency of ligating species important in the pretreatment of nuclear and chemical wastes.

To date, this effort has focused on the crown ethers. Crown ethers have drawn much experimental and theoretical interest since they were first described by Pederson in 1967. These cyclic polyethers can form remarkably stable complexes with alkali- and alkaline-earth metal cations. Furthermore, the selectivity of this binding is sensitive to macrocycle ring size, ether-heteroatom, and macrocycle substituents. The ion specificity of crown-ethers makes them attractive as models for understanding enzyme chemistry as well as ligands useful to aid cleanup of mixed wastes that contain radionuclides such as cesium (Cs⁺) and strontium (Sr²⁺), and transuranic ions.

The only previous direct experimental measurement of the gas-phase binding energy of alkali metal cations and 18-crown-6 found values considerably smaller than our ab initio results. For example, their ion-cyclotron-resonance binding enthalpy for K⁺:18-crown-6 at 350 K was -40 $\pm$ 8 kcal/mol, compared to an MP2 value of -72 kcal/mol. To shed light on underlying sources of error in the theoretical numbers, a joint experimental/theoretical investigation was begun on the binding energies of alkali cations with small ethers (e.g., dimethyl ether, dimethoxy ethane and 12-crown-4). While the results of that study are still in a preliminary stage, to date there have been no instances of deviations greater than $\sim$ 2 kcal/mol. The theoretical approach employed the same basis sets and levels of theory which were used in the earlier crown ether study. As seen in Figure 17 the counterpoise corrected MP2/6-31+G* binding energy is in remarkable agreement with the apparent complete basis set limit.

**Figure 17:** Convergence of the Li⁺:dimethyl ether binding energy as a function of the basis set completeness and degree of correlation recovery. The dashed line represents the value obtained at the MP2/6-31+G* level, including counterpoint correction.
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Mechanism and Thermodynamics of Ion Selectivity in Aqueous Solutions of 18-Crown-6 Ether: A Molecular Dynamics Study

We have performed an extensive classical molecular dynamics simulation to examine the mechanism and thermodynamics for ion selectivity in aqueous solutions of 18-crown-6 ether. 18-crown-6 is one of the most extensive studied crown systems and the abundance of the experimental data for these systems provide a good prototype model to verify our approach. To the best of our knowledge, the present work is the first application of the potential of mean force approach to the evaluation of ion selectivity by crown ethers in aqueous solutions. Our simulations differ from previous work in that the free energies of complexation are computed as a function of the ion-crown separation, or potential of mean force (PMF). This makes the current study valuable for several reasons. First, the computed PMF allows us to examine the minima positions of the complexes and they can be related directly to the x-ray data. The second valuable aspect is that we can compute the absolute binding energies by integrating over the PMFs, the resultants can be directly compared with the corresponding experimental measurements. The third advantage of our approach is that we can examine the role of solvent effects along the reaction coordinate (i.e., contact pair or solvent separated pair).

The free energy profiles or PMF for M⁺:18-crown-6 (M⁺ = K⁺, Na⁺, Rb⁺, Cs⁺) complexation are computed via the free energy perturbation method. Counterion effects are considered and all long-range interactions are computed via the Ewald summation method. The resultant PMFs indicate that free-energy minima for the K⁺ and Na⁺ ions are located at the crown ether center-of-mass as shown in Figure 18(a). Potassium is selected over sodium because of the greater free energy penalty associated with displacing water molecules from sodium as it approaches the crown ether. This leads to a substantial increase in the activation free energy and a decrease in the binding free energy for Na⁺:18-crown-6 complexation as compared to K⁺:18-crown-6. The selection of potassium over rubidium and cesium is due to the cation-size relative to the crown-ether cavity. The calculated PMFs for all the ions are shown in Figure 18(a). We computed binding free energies by integrating over the PMFs and the results are summarized in Figure 18(b). They are slightly underestimated, although, they follow the sequence K⁺ > Rb⁺ > Cs⁺ > Na⁺ reported experimentally. The shortcoming in binding free energies can be overcome by improving the cation-crown ether interaction potential and/or taking to account the non-additive effects in these molecular systems. Studies on these and the related questions are in progress.

**Figure 18:** (a) The potential of mean force for the association of alkali cations to 18-crown-6 ether in water near 300 K. (b) Calculated binding energies of the cations to 18-crown-6 ether in water near 300 K.
$\begin{figure} \begin{center} (a)\end{center}\centerline{ \psfig {figure=gb_tms7.eps,height=150mm,width=110mm,silent=} } \begin{center} (b)\end{center}\end{figure}$

Research on the chemistry at interfaces includes studies of aqueous interfaces with air (or vapor), other liquids (e.g., carbon tetrachloride), crystalline solids (e.g., mineral oxides, clays, found in soils), and glasses. The studies of air-vapor interfaces are important to understanding heterogeneous processes that occur in the atmosphere. The studies of liquid-liquid interfaces is important to understanding the transport of molecules and ions between two immiscible liquids, which is relevant in a number of field such as electrochemistry, separations, and the interaction of contaminated organic solvents with ground water. The studies of aqueous-mineral interfaces is important to understanding the binding of contaminants to the soil. The studies of glass-water interfaces provides information on the dissolution and degradation of materials that are being proposed for long term storage of nuclear wastes.

Heterogeneous and interfacial systems are exceptionally challenging systems to study theoretically. The complex chemistry and physics occurring in these systems over large length and time scales requires extensive compute power to probe and predict experimental observables. To accomplish this task many new and inventive theoretical methodologies must be used and developed. Integrated methods that exploit the accuracy of ab initio quantum mechanical theories with the speed and time-dependent properties of classical mechanics are essential for examining complex interfacial phenomena. The development of efficient methods of this type is currently an area of active research that requires high end computer platforms. Future work in this field will utilize these compute resources to address more complex, ``real world'' problems.

The chemistry of naturally occurring and/or industrially important interfaces often involves dynamical processes of structurally and electronically complex materials. In particular, it is necessary to determine the properties of realistic surface sites (containing point defects, steps, kinks) to quantitatively predict surface chemistry. Magnesium oxide (MgO) is a structurally simple cubic oxide material whose interfaces play an important role in subsurface geochemistry, catalysis and materials design. The bulk, surface and interface properties of MgO are being studied to understand the behavior of MgO and to derive models that can be used to model processes involving more complex oxides. The composition (number of electrons) and structure (high symmetry) make this a ``computationally practical'' system that can be studied in detail using periodic ab initio electronic structure theory.

Research in this area probed several different problems. The electronic structure investigations of the MgO/water interface were extended to examine the effect of defect sites on the surface chemistry. Water is ever-present in the environment and can have a variety of interactions with exposed oxide surfaces, each of which will have a different effect on soil chemistry and on the transport of other chemicals through soils. Therefore, understanding the processes of water adsorption and chemical dissociation on oxide surfaces is fundamental to modeling subsurface transport phenomena. Ab initio periodic Hartree Fock (PHF) theory (including correlation corrections) was used to study the chemistry of water on clean, defected and strained MgO (001).

Structural defects were constructed containing both corner (3-coordinated) and edge (4-coordinated) sites. Isotropic distortions of the lattice probed the properties of strained MgO. The ab initio energetics revealed that molecular water binds weakly ( $\sim$ 10-15 kcal/mol) to flat MgO (100) and more strongly (17-25 kcal/mol) to the defected sites. Mulliken populations show that a fundamental change occurs in the surface oxygen sites as the coordination number of these sites decreases while the magnesium sites remain relatively unaffected by changes in their local environment. The reduction of the Madelung field surrounding the oxygen sites results in the migration of small amounts of charge from the surface oxygens to oxygens residing in the bulk material leaving the oxygen defect sites capable of forming more strongly covalent bonds than sites on the perfect surface. Chemidissociation - resulting in surface hydroxylation - is found only to occur on surface defect sites and not on the equilibrium structure flat surface. However, chemidissociation becomes more energetically favorable as the flat lattice is isotropically distorted (becoming exothermic with $\sim$ 5-8% dilation of the lattice constant). This data indicates that the surface chemistry of MgO could be adjusted if stable thin films of the material could be prepared under strained conditions. The dramatically different chemistry on defected, clean and strained surfaces illustrates, quantitatively, the importance of surface structure in regulating interfacial phenomena. Analytic expressions for the water/MgO (001) interaction potential were derived from the quantum mechanical data and are currently being used in classical simulations to examine the dynamical properties of the interface.

A new methodology was also developed to derive electrostatic models of oxide interfaces. These models are constructed from the energetics of an adsorbate - described by a multipolar expansion of the charge density - interacting with the quantum mechanical electric fields generated by the surface.

The terms on the right hand side of this expression represent the interaction of a charged species with the surface potential, a permanent dipole with the field, and a molecular quadrapole with the field gradient. The field generated by the surface and the moments of the adsorbate are computed quantum mechanically and the adsorbate-surface interaction is deduced from the classical electrostatic interaction (eq. 4). This electrostatic model produces a reliable computationally ``trivial'' method for examining the properties of a range of interfaces. The results have been validated by comparing the classical data to quantum mechanical calculations on several systems. Excellent agreement was found between the computed electrostatic energetics and the quantum mechanical values for HCl, H₂O and NH₃ on MgO (see Figure 19). This approach provides us with a quantitative interpretation of the interfacial bonding interactions that allow us to predict the properties of more complex, low symmetry materials.

**Figure 19:** Comparison of ab initio and electrostatic interaction energies for NH₃ on MgO (001). NH₃ is bound over the magnesium surface site with the nitrogen end pointing towards the surface. The repulsive potential (V12) is added to the purely electrostatic interaction potential (VME) to describe the classical electrostatic binding energetics. The surface oxygens are represented by bigger radii than the surface magnesiums.
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NERSC 3 Greenbook

Molecular Science in the Environment

NERSC 3 Greenbook