Organic Meets Inorganic In Silico

Chemistry in the "Virtual Laboratory"

By Mark Tuckerman, with Robin Hayes

Chemistry is often referred to as the central science, sharing common "boundaries" with biology, medicine, materials engineering, physics, neural science, geology, and numerous other fields. Diverse problems ranging from the design of novel materials, to the development of new drug compounds, to the construction of a quantum computer all embody at their core a basic chemical description—a specification of a system's constituent atoms and their interactions. The complexity of today's research questions, however, has caused the boundaries to blur, and progress on such problems requires an interdisciplinary approach that synthesizes knowledge from different scientific fields.

In this article, we will consider a particular problem in nanoscience that elegantly exemplifies this blurring, namely, the creation of hybrid materials from semiconductors—systems that usually lie within the purview of physics—and simple organic molecules. Such materials can be made sensitive to certain biological environments for sensing in medical applications. They can also be used in molecular electronics, wherein small molecules are sandwiched between source and drain electrodes to make tiny electronic devices. My group in NYU's Department of Chemistry seeks to understand and guide the design of these materials theoretically, using a computational approach that starts from a fundamental chemical description.

Designing a new material proceeds first via a "creation" phase, in which specific chemical processes are employed to generate the material's atomic/molecular structure. Following this, a "characterization" stage is needed to validate the final product. In both stages of this design protocol, chemical theory and high performance computing are playing increasingly important roles, providing the rational underpinnings of experimental findings and, with increasing frequency, pointing toward further experiments that lead to new molecular constructs and materials. As an example, the molecular electronics field alluded to above originated with theoretical ideas introduced by the American physicist Robert S. Mulliken and advanced in subsequent theoretical papers by Aviram and Ratner.¹ The development of new theoretical techniques, computational algorithms, and software modules is a driving force in my group that underlies and ultimately extends the complexity of the problems we can solve.

Before proceeding to a specific application, let us pause to answer the question: How is theoretical research in chemistry carried out? It is here that the "centrality" of chemistry must give way to the "fundamentality" of physics. A theoretician wants to know where every atom and its electron distribution are at each instant in time during a chemical reaction, so that the dynamical evolution of the chemical bonding pattern can be followed in the greatest possible detail. This can only be accomplished by solving the fundamental motion equations of physics that govern how each atom in the system moves in time from a given starting configuration. In principle, one universal theory—quantum theory—encodes this information for all chemical systems, and all we need to do is select from the periodic table the number of each type of atom to generate the specific system we wish to study.

Indeed, in 1929, the English physicist P. A. M. Dirac said about quantum theory, "The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known, and the difficulty is only that the exact solution of these laws leads to equations much too complicated to be soluble." By combining a few simplifying but well-controlled approximations with modern high performance computing architectures, Dirac's challenge can be met. The technique now known as ab initio molecular dynamics (AIMD)² was first introduced by R. Car and M. Parrinello in 1985³ and involves treating the relatively heavy atomic nuclei using the laws of classical Newtonian mechanics while retaining a quantum description of the electrons, which is necessary for an accurate description of chemical bonding. The term ab initio means "from the beginning" and, in this context, is taken to indicate an approach based on fundamental principles, as opposed to empirical models. In this way, we can create a "virtual laboratory" in silico—in the computer—for exploring a wide variety of chemical phenomena. The capabilities of the virtual lab are limited only by the computational resources available and the efficiency of the numerical algorithms.

AIMD calculations are computationally very intensive, requiring supercomputers with hundreds to thousands of processors. Exploiting the full potential of such a powerful computational resource requires specialized software that makes use of a programming technique called parallel programming. The underlying idea of this paradigm is to break down a computational task into many subtasks and farm these out to the large number of individual yet tightly coupled central processing units (CPUs) contained within the supercomputer. Although the need to perform some of the subtasks sequentially cannot be avoided, a large number of them can be executed simultaneously, i.e., in "parallel," by having each CPU perform computations locally and exchange data with other CPUs. The software encodes the algorithms for local computations and controls how and when messages are passed between the CPUs. The challenge in writing such software is to ensure that at each point in the calculation, every CPU has an equal amount of work to perform (called "dynamic load balancing") and that CPUs do not get bogged down in communicating with each other. Working in collaboration with Professor L. Kale in the Department of Computer Science at the University of Illinois at Urbana-Champaign and Dr. G. J. Martyna in the physical sciences division at the IBM T. J. Watson Research Center in Yorktown Heights, we have developed a software package⁴ for performing the requisite calculations efficiently on hundreds of processors available at NYU and ten thousand processors available using IBM's new BlueGene platform.

The specific application we will consider is a hybrid structure generated when an organic molecule forms chemical bonds with a silicon surface. Since these surfaces are produced by cleaving bulk silicon in particular ways, different surfaces are possible, and the chemical reactions that can occur on them will be affected by the choice of surface. For the class of organic molecules we have been investigating, the most useful surface is a simple "cut across the top," which, when allowed to relax, leaves long rows of silicon dimers⁵ (see Figure 1a). In fact, Figure 1a is an idealized structure that does not reflect the actual surface. The true surface structure is a disordered one as shown in Figure 1b.

This structure is characterized by a "buckled" pattern of the dimer rows, in which one silicon atom in each dimer dips below the surface and the other protrudes slightly. At room temperature, the buckling pattern is dynamic, with the dimers executing a kind of "rocking" motion or oscillation around the idealized structure of Figure 1a. The surface dimers are chemically reactive and can serve as receptors for certain types of organic molecules. For the latter, we have chosen two examples known as "conjugated dienes," which are small organic molecules containing two electron-rich carbon-carbon double bonds that react favorably with the surface dimers. (The reaction occurs via a component of the double bond known as a π-bond.) Unfortunately, it is often difficult to predict whether a particular bonding pattern will form exclusively or be one of several possible patterns. Understanding the detailed dynamical mechanism of the reactions can provide important clues as to how one can ultimately control and tailor the chemistry to select out specific final products. In this example, the surface chemistry is complicated by the fact that the buckling pattern, and thereby the distribution of electrons in the dimers, fluctuates thermally. Thus, in employing chemical theory and high performance computing, one of our aims is to elucidate the reaction mechanism, which involves "running the reaction" many times in the computer in order to garner a statistically meaningful picture of how the reaction occurs. All calculations described below were performed at NYU, on an SGI Altix 3700 Bx2 system purchased with funds from an NSF Major Research Instrumentation grant awarded to the Department of Chemistry and on the high performance computation cluster known as "Max," which is a 256-node IBM JS20 Blade Server.

From the calculations performed to date, we have learned several important things about how organic molecules react with the silicon surface shown in Figure 1b. First, we find that a variety of final products can be formed when the surface reaction is run numerous times with a cyclic organic molecule known as 1,3-cyclohexadiene. The products are shown in Figure 2.

The molecule is capable of forming products with a single dimer (A,D), with two dimers in one row (Ct,Cr,E,F) and with two dimers in neighboring rows (B). Except for F, all of the products are the result of the formation of two carbon-silicon bonds. Despite this common feature, these products all have rather different chemical and electronic products. From a technological standpoint, such a diverse distribution of products is disadvantageous since creating particular molecular patterns on the surface, such as organic "wires" along a row of silicon dimers, requires specific modes of reactivity.

As noted earlier, the first step in controlling and tailoring the surface chemistry is to understand how the chemistry works. What we have learned from our calculations is that the standard rules governing large classes of reactions in organic chemistry do not apply when semiconductor surfaces are involved. This is somewhat surprising, given that carbon and silicon lie in the same column of the periodic table, one row apart.^6,7 If the usual rules of organic chemistry applied, the two molecule-surface bonds would form synchronously, as would happen if the silicon surface were replaced by a purely organic molecule, such as ethylene (H2C=CH2). On the silicon surface, by contrast, the reaction proceeds asynchronously, with one carbon-silicon bond forming well in advance of the other, as shown in Figure 3 for product A.

This difference, although seemingly small, is actually quite profound. First, knowledge of this reaction path, which is understandably somewhat more complex than can be described here, allows the full product distribution to be rationalized and even predicted from a few basic principles.⁶ Second, the mechanism of Figure 3 involves a relatively stable intermediate (middle panel). Such an intermediate state can be exploited to tailor the reaction, by modifying the organic molecule, for example, so as to control where the second carbon-silicon bond forms and influence the final product. Finally, from an understanding of the reaction mechanism, it is possible to design in silico modified organic molecules that give rise to predictable changes in energetic and electronic properties along the reaction path and final products. We have, for example, created a designer molecule in the virtual laboratory in which a single hydrogen atom is replaced by a fluorine atom.⁷ This modification lowers the energy needed to detach the molecule from the surface, thereby rendering it potentially useful for chemical patterning, one of the major routes to surface preparation.

By increasing our understanding of how the surface chemistry works in this and other systems using the tools of the virtual laboratory and high performance computing platforms, we hope to predict new possibilities for molecule and substrate design. As the virtual laboratory concept matures, a key goal will be the algorithmic generation of increasingly novel chemical structures and materials in the computer with specific "tunable" properties—properties we can "dial in"⁸—that will drive new technological, biological, and biomedical applications.

Footnotes

1. A. Aviram and M. A. Ratner. Molecular rectifiers. Chem. Phys. Lett. 29, 277 (1974); A. Aviram. Molecules for memory, logic, and amplification. J. Am. Chem. Soc. 110, 5687 (1988).
2. M. E. Tuckerman. Ab initio molecular dynamics: Basic concepts, current trends, and novel applications. J. Phys. Condensed Matter 14, R1297 (2002).
3. R. Car and M. Parrinello. Unified approach for molecular dynamics and density functional theory. Phys. Rev. Lett. 55, 2471 (1985).
4. M. E. Tuckerman, D. A. Yarne, S. O. Samuelson, A. L. Hughes and G. J. Martyna. Exploiting multiple levels of parallelism in Molecular Dynamics based calculations via modern techniques and software paradigms on distributed memory computers. Comp. Phys. Comm. 128, 333 (2000); R. V. Vadali, Y. Shi, S. Kumar, L. V. Kale, M. E. Tuckerman and G. J. Martyna. Scalable fine-grained parallelization of plane-wave-based ab initio molecular dynamics for large supercomputers. J. Comp. Chem. 25, 2006 (2004).
5. A dimer is a special type of polymer made up of two linked subunits or monomers.
6. P. Minary and M. E. Tuckerman. Reaction Pathway of the [4+2] Diels-Alder adduct formation on Si(100)-2x1. J. Am. Chem. Soc. 126, 13920 (2004); Ibid. Reaction mechanism of cis-1,3-butadiene addition to the Si(100)-2 x 1 surface. J. Am. Chem. Soc. 127, 1110 (2005).
7. R. Iftimie, P. Minary and M. E. Tuckerman. Ab initio molecular dynamics: Concepts, recent developments, and future trends. Proc. Natl. Acad. Sci. 102, 6659 (2005).
8. O. A. von Lilienfeld and M. E. Tuckerman. Molecular grand-canonical ensemble density functional theory and exploration of chemical space. J. Chem. Phys. 125, 154104 (2006); O. A. von Lilienfeld and M. E. Tuckerman. Alchemical variationals of inter-molecular energies according to molecular grand-canonical ensemble density functional theory. J. Chem. Theor. Comput. (in press).

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Author Biographies

Mark Tuckerman is the Director of Graduate Studies and an Associate Professor of Chemistry and Mathematics in NYU's Department of Chemistry and the Courant Institute of Mathematical Sciences; Robin Hayes is a postdoctoral student in NYU's Dept. of Chemistry.

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