HERSCHEL A. RABITZ
Current Research Interests

Dr. Rabitz's group research focuses on molecular dynamics at both the microscopic and macroscopic scales. The ultimate goal is the prediction and correlation of observable dynamics phenomena. The studies are also being used in a novel fashion to design experiments and provide the theoretical foundations to analyze the resultant data. The following descriptions outline the current projects of Dr. Rabitz's research group:

• Control of Molecular Motion
• Biomolecular Design
• High Dimensional Model Representation (HDMR)
• Inverse Dynamics: Extracting the Information Content from Laboratory Data
• Quantum Theory of Chemical Reactions
• How Do Intermolecular Forces Affect Dynamical Observations?

Control of Molecular Motion. The purpose of this research is to study the degree to which we can use specially designed optical fields to control molecular motion, including the prospect of achieving site-specific chemistry and intramolecular rearrangements. The aim of using specially designed lasers to manipulate molecular motion and chemical reactions has been a long sought-after, frustrating goal in chemistry. We recently recognized that this problem should be approached by carefully designing laser fields, rather than using traditional, intuitively-based approaches. The problem becomes one of designing the laser fields for their action at the molecular scale. The tools of control theory familiar in engineering are being adapted for this purpose. These new tools are helping us assess the feasibility of achieving particular chemical objectives, as well as helping us design the optical fields that will reach the objectives. We are assessing a wide variety of theoretical designs, and collaborative experimental research is under way to verify and implement these designs in the laboratory. Back to the Top

Biomolecular Design. New approaches to the quantitative design of molecular structures are being undertaken, based on advanced techniques of molecular dynamics and especially, new analysis tools. Particular emphasis is being given to applications in the area of biochemistry, where the structure of biomolecules is associated with their actual function. Until now, the "design" of bioactive molecules has largely been based on intuition, and our research is concerned with the development of new quantitative theoretical tools to investigate molecular structural relationships. These tools allow us to determine how a localized functional modification in a molecule influences its overall molecular structure. This research has broad practical, as well as fundamental, significance for molecular design; it is being carried out in collaboration with several pharmaceutical companies for the purpose of applying it to realistic problems of biomolecular structure and drug design. Back to the Top

High Dimensional Model Representation (HDMR). In this research, a novel technique is being developed for the determination of critical variables and features of physical/chemical models and large data bases, where there is a multitude of variables. The overall goal includes the identification of cooperative relationships amongst the variables for their impact on laboratory observations. Problems of this type have been commonly viewed as plagued with the "curse of dimensionality", by growing exponentially in difficulty as the number of variables increase. The new HDMR technique promises to dramatically reduce the laboratory effort to deduce the critical variables, so that the labor now only scales polynomically in complexity with the number of variables. The technique can work with existing experimental data bases, as well as provide specific guidance on how to generate optimal experimental runs, to yield the maximum information upon the underlying physical variables. HDMR can identify which variables are important, acting either alone or collectively, thereby leading to the ability to make physical assessments and to perform product optimization. Back to the Top

Inverse Dynamics: Extracting the Information Content from Laboratory Data. Laboratory spectroscopic, dynamics, and kinetics data are known to be rich in information about the underlying forces between atoms and molecules. Knowledge of these forces is fundamental for all physical-chemical processes. Until now there has been no systematic means to extract the desired information from the laboratory data. The operation involved is referred to as an inverse problem, whereby one uses the laboratory data as input and passes it through the Schrödinger equation in the inverse direction to extract information about the underlying Hamiltonian. The solution of such inverse problems has stood for many years as a major challenge in chemistry. We are developing algorithms for this purpose, based on the introduction of new conceptual and mathematical tools. First, it is necessary to quantitatively determine how much information resides in a particular body of laboratory data, and second, devise reliable algorithms to extract the information. Finally, the extracted Hamiltonian must be represented in a form that can be efficiently utilized for subsequent applications. Back to the Top

Quantum Theory of Chemical Reactions. Collisions between molecules can lead to chemical reactions under appropriate conditions. A detailed understanding of such reactive collisions lies at the foundation of modern chemical kinetics. Techniques are being developed for the quantum mechanical treatment of chemical reactions. Back to the Top

How Do Intermolecular Forces Affect Dynamical Observables? The interaction of molecules is a fundamental dynamical event in chemistry. The results of such interactions are expressed in terms of laboratory-measurable collision cross-sections and rate constants. A basic issue is how these laboratory observables draw on different features in the underlying Hamiltonian or potential surface. We are obtaining this valuable information by calculating the sensitivity of the observables to the structure in the Hamiltonian. Quantitative sensitivity coefficients may be computed to answer several physical questions, including the interrelationship between different portions of a system Hamiltonian and their effect on particular observables. Ultimately, this research at the molecular scale interfaces with chemical kinetics to explore the influence that very intimate atomic-scale events have on processes at the macroscopic, bench-top level. Back to the Top