Highlights of Research



Prof. David Tannor is a theoretical chemist, who studies quantum mechanics effects on the motion of molecules. His work currently has three main directions:  1) the design of specially tailored laser pulses to control breaking of chemical bonds and laser cooling of molecules; 2) the calculation of chemical reaction probabilities and rate constants, using quantum mechanical and semiclassical methods; 3) the development of concepts and methods for simulating quantum mechanical motion of molecules in a solvent. In all three of these areas Tannor uses time dependent quantum mechanics, where a moving wavepacket is the central dynamical object. This wavepacket is the closest analog there is in quantum mechanics to a classical trajectory, and thus this approach is conceptually simple, and often numerically advantageous as well. Below, each of these three research areas is described.

  1. Design of Femtosecond Pulse Sequences to Control Photochemical Reaction

    There has been spectacular progress in laser technology in recent years, so that it is now possible to make laser pulses which are much shorter than the characteristic time scale for chemical bond for mation and breaking. These pulses can be shaped in time and frequency with great precision, and sequences of such pulses can be orchestrated. How can these capabilities be used to break chemical bonds, cleanly, precisely, without unwanted by-products?
    Prof. Tannor's group has been at the forefront of the development of theoretical concepts and methods to address this question. They have developed pulse sequences to control chemical bond breakage, for shutting down multiphoton ionization, and for robust population transfer between quantum states in many-level systems. Current work focusses on pulse sequences for laser cooling of molecular internal and translational degrees of freedom, for control of electronic motion in atoms, and control of chemical bond breaking in the liquid phase.

    References:
    • V. S. Malinovsky and D. J. Tannor, Simple and Robust Extension of the Stimulated Raman Adiabatic Passage Technique to N-level Systems, Phys. Rev. A, 56, 4929 (1997).
    • A. Bartana, R. Kosloff and D. J. Tannor, Laser Cooling of Molecular Internal Degrees of Freedom by a Series of Shaped Pulses, J. Chem. Phys. 99, 196 (1993).
    • A. Bartana, R. Kosloff and D. J. Tannor, Laser Cooling of Molecular Internal Degrees of Freedom. II., J. Chem. Phys. 106, 1435 (1997).
    • A. Bartana, R. Kosloff and D. J. Tannor, Vibrationally Selective Coherent Population Trapping: Laser Cooling of Molecules by Dynamically Trapped States, Faraday Disc. 113, 365 (1999).
    • D.J. Tannor and A. Bartana, On the Interplay of Control Fields and Spontaneous Emision in Laser Cooling, J. Phys. Chem. 103, 10359 (1999)



  2. The Calculation of Reaction Probabilities and Rate Constants

    It is generally believed that all molecular processes are ultimately governed by the laws of quantum mechanics. This includes the central event in chemistry --- a chemical reaction --- in which reactants come together, exchange partners and separate into products. The quantum mechanical theory for chemical reactions is called "scattering theory", and it is the underlying theory behind all chemical transformations. Several years ago, Prof. Tannor's group developed a new mathematical expression for the scattering, or S- matrix, which is the central object in quantum scattering theory. The new expression is simple, conceptually appealing, and easily used for calculations. Recently, they have combined this formulation of the scattering matrix with a new semiclassical method, and have obtained excellent agreement with full quantum calculations for the benchmark system, collinear H+H2 -> H2 +H, fulfilling a dream which has eluded workers in the field since 1970. The group now is in the process of developing an analogous procedure which will allow to calculate directly the cumulative reaction probability, which is closely related to the thermal rate constant for the reaction.

    References:
    • S. Garashchuk and D. J. Tannor, Wave Packet Correlation Function Approach to H2(v) + H -> H + H2(v'): Semiclassical Implementation, Chem. Phys. Lett. 262, 477 (1996).
    • S. Garashchuk, F. Grossmann and D. J. Tannor, Semiclassical Approach to the Hydrogen Exchange Reaction: Reactive and Transition State Dynamics, J. Chem. Soc., Faraday Trans. 93, 781 (1997).
    • S. Garashchuk and D. J. Tannor, Correlation Function Formulation for the State Selected Total Reaction Probability, J. Chem. Phys. 109, 3028 (1998).
    • S. Garashchuk and D. J. Tannor, Cumulative Reaction Probabilities from Reactant-Product Wavepacket Correlation Functions, J. Chem. Phys. 110, 2761 (1999).
    • S. Garashchuk and D. J. Tannor Semiclassical Calculation of Cumulative Reaction Probabilities , Phys. Chem. Chem. Phys. 1 , 1081 (1999).
    • D. J. Tannor and S. Garashchuk, Annu. Rev. Phys. Chem., 51, 553(2000).



  3. Simulating Quantum Mechanical Motion of Molecules in a Solvent with Strong Laser Fields

    Most organic and inorganic chemistry is performed in solution, and it is a major challenge to theory to understand and predict the effect that the solvent has on the chemical reaction. In the last few years, the group has developed new phase space pictures which illuminate the role of the solvent on the reaction dynamics and are convenient for analyzing the extent of the correspondence between classical and quantum behavior in the presence of solvent. Recently, they have developed a novel set of equations of motion for the wavepacket density in the presence of the solvent which respects the three basic physical principles of positivity, translational invariance and approach to the correct equilibrium state. The method is convenient for numerical calculations, and is able to handle strong external laser fields in an elegant and efficient way. They are in process of applying the method to simulate femtosecond hole burning in the I2- ion. In the next stage, they intend to use this method to simulate electron transfer processes in solution, and their interrogation via nonlinear spectroscopies (e.g. multi-pulse echo spectroscopies). They also intend to use the approach to explore the limits of coherent control in the condensed phase, using strong laser fields.

    References: