Brian K. Kendrick, Ph.D.

Technical Staff Member phone: (505) 667-0856 Office: TA-3 Bldg 471 Room 111
Theoretical Division FAX: (505) 665-3909
Group T12, Mail Stop B268 email: bkendric@lanl.gov
Los Alamos National Laboratory
Los Alamos, NM 87545

Research Interests


Quantum Reactive Scattering and Molecular Spectra:

During the past 20 years, our group has developed the capability to perform numerically exact, full (six) dimensional quantum reactive scattering calculations for three-body systems. The methodology is based on body-frame hyperspherical coordinates. The scattering or bound-state solutions are obtained by propagating a set of coupled-channels with respect to the hyperradius. The coupled channels are obtained by diagonalizing the angular part of the Hamiltonian using an Implicitly Restarted Lanczos Algorithm (ARPACK) with respect to a primitive basis set consisting of a hybrid DVR (discrete variable representation) and FBR (finite basis (polynomial) respresentation). The methodology is numerically exact. That is, no dynamical approximations are used and all coupling between the various degrees of freedom are included. By making use of both fine and coarse grain parallel algorithms, our computer codes have been parallelized to run efficiently on a variety of computing platforms: a single workstation, clusters of workstions, and massively parallel supercomputers. Some of our calculations on an Origin 2000 have utilized over 1000 processors running simultaneously for days at a time. This work was supported by several LDRD grants and the supercomputer support was provided by grants from the Ohio Supercomputer Center, the Pittsburgh Supercomputer Center, the San Diego Supercomputer Center, and the High Performance Computing Initiative at LANL.

Applications of this methodology include several fundamental chemical reactions and triatomic spectra:
  1. H + O2(v,j) → OH(v',j') + O (rate limiting step in combustion, astrophysics, atmospheric chemistry)
  2. H + O2(v,j) → H + O2(v',j') (inelastic scattering, collision induced vibrational relaxation, cold and ultra cold collisions)
  3. H + H2(v,j) → H2(v',j') + H (most fundamental chemical reaction - allows detailed comparison with experiment,
  4. H + D2(v,j) → HD(v',j') + D applications include: astrophysics, control, plasmas (ionic variants))
  5. D + H2(v,j) → HD(v',j') + H
  6. O + O2(v,j) → O2(v',j') + O (key reaction in the anomalous isotope effect in ozone formation in upper atmosphere)
  7. H + Ne2 ↔ H + Ne + Ne (first full dimensional collision induced dissociation calculation - important for BEC)
  8. Na3 (correct ordering of vibrational spectra must include geometric phase effects)
  9. N3 (correct ordering of vibrational spectra must include geometric phase effects - even for fundamentals!)
  10. HO2 (correct identification of physically allowed states must account for the geometric phase)
  11. O3 (the ozone molecule)

n3.jpg Our investigations of fundamental chemical reactivity and spectra has focused on the effects of the geometric (Berry) phase. In particular, the scattering calculations for systems 2-5 and the spectra for systems 8-10 listed above were done both with and without the geometric phase. The geometric phase was included by using single-valued boundary conditions on the primitive basis set and solving a generalized Born-Oppenheimer equation for the nuclear motion for which the momentum operator p goes to p - A where A is the relevant vector potential. The geometric phase effectively alters the symmetry of the nuclear motion wave function causing it to exhibit (simultaneously) symmetric and anti-symmetric properties. This change in symmetry behavior can lead to shifts or a reordering of the ro-vibrational energy levels (relative to the spectrum which ignores geometric phase effects, see figure at right). In regards to scattering, the geometric phase can significantly alter the state-to-state reaction probabilities and resonance spectrum for individual values of total angular momentum (J). However, when the contributions from even and odd values of J are added together to compute integral cross sections for the H + H2 system (and its isotopic variants) ALL geometric phase effects vanish! The cancellation is not entirely complete for the differential cross sections and some small interference effects do survive the sum over J (unfortunately these interference effects are probably too small to be detected experimentally). These surprising results explain why high-resolution crossed-molecular beam experiments were unable to detect any effects in this system (i.e., the experimental results are in excellent agreement with calculations which ignore the geometric phase). An exception is the para-para and ortho-ortho transitions in the H + H2 system. For these transitions, significant geometric phase effects are predicted (but have not yet been measured experimentally) in both the integral and differential cross sections due to the interference between the reactive and non-reactive contributions to the cross sections. The geometric phase alters the sign of the interference term for these transitions.








dcs.jpg In collaboration with Professor Miranda (University of Leeds, UK) and Professor Aoiz (Universidad Complutense, Madrid, Spain), our scattering results for the H + D2 and D + H2 systems have been used to investigate the effects of reactant polarization (i.e., the alignment of the diatomic internuclear axis with respect to the incoming atom's momentum vector). Significant polarization effects on the differential and integral cross sections were found relative to the standard isotopic case which includes contributions from all reactant polarizations. These effects could be observed experimentally with existing technology. Since the reactant polarization can be controlled experimentally, the outcome of the reaction can be ``controlled'' using this approach. Reactant polarization provides unique insight into the mechanisms and control possibilities of fundamental collisions and reactivity.




In recent years, our scattering methodology has also been applied to acurately treat collision induced dissociation an important loss mechanism in the evaporative cooling of a BEC. We are currently studying these and other important loss mechanisms such as collision induced vibrational relaxation. A good understanding of vibrational relaxation is crucial to obtaining a molecular BEC and then exploiting its possible applications. Cold and ultra-cold collision dynamics present a unique and difficult theoretical challenge which we are currently pursuing in collaboration with Professor Balakrishnan at UNLV.

The Quantum Many-Body Problem:

qtraj.jpg The computational cost associated with a standard quantum mechanical treatment of the nuclear motion in a molecular system increases exponentially with respect to the number of atoms. This well known "exponential scaling" severly limits the number of atoms that we can treat quantum mechanically (typically just 3 or 4 even using massively parallel supercomputers). In order to overcome this scaling problem, we have to look for new ways to solve the problem. A promising new approach is based on the de Broglie-Bohm description of quantum mechanics. In this approach, the nuclear motion wave function is written in polar form (magnitude times a phase). Upon substituting the polar form into the time-dependent Schrodinger equation a set of quantum hydrodynamics equations of motion are obtained. These fluid-type equations describe the flow of probability and the flow lines are the well-defined "quantum trajectories" (see figure at right). The equation of motion is given by F=ma where F=-∇V -∇Q and -∇V is the well-known classical force and -∇Q is the quantum force. The quantum potential Q and its associated force give rise to all quantum effects such as tunneling, zero point energy, and resonances. 2d.jpg



The quantum hydrodynamic approach is intuitively appealing since the quantum potential and force appear on equal footing with the classical potential and force. Approximations to Q and its associated force give rise to an approximate quantum treatment somewhat analogous to a semi-classical theory. However, unlike classical trajectories which are decoupled, quantum trajectories are coupled due to the non-local nature of Q and cannot be propagated separately. Futhermore, the quantum potential and force can become singular. Our research in this area has focused on addressing these two shortcommings. In recent work, we have shown that by introducing artificial viscosity into the equations of motion, the singularities can be avoided and the propagation of a stable solution for long times becomes possible (see figure at right). We have also shown that by invoking a vibrational decoupling approximation, the quantum trajectories can be decoupled and linear scaling with respect to the dimensionality of the problem becomes possible (see figure lower right). Important applications under study include enzyeme catalysis and other proton transfer reactions, hydrogen diffusion in metals, and complex reactions in polymer, atmospheric and combustion chemistry. This work was supported by an LDRD grant. vds.jpg




An international workshop on this topic is currently being organized:

"LANL/CNLS Workshop on Quantum Trajectories", July 28-30, 2008
Organizers: Brian Kendrick (LANL) and Bill Poirier (Texas Tech University)
Workshop on Quantum Trajectories Home Page






Coupling Chemical Kinetics to Macroscopic Transport

Many important applications involve the coupling of microscopic and macroscopic length scales. At the microscopic level, fundamental physical and chemical processes take place. These fundamental processes depend upon but also affect the macroscopic variables such as flow, diffusion, surface topology, and material properties. Coupling these two length scales is crucial for a complete understanding and the development of realistic predictive models. Our group has experience in coupling different length scales in a variety of applications including: chemical vapor deposition, alumina precipitation in the Bayer process for aluminum production, hydrolysis of Estane (a polyester-urethane) in plastic bonded explosives, and hydrogen adsorption/desorption in metal foams. In a typical application, the chemical rate coefficients and other fundamental constants are not all known a priori. In some cases, these parameters can be calculated from first principles using electronic structure theory and molecular dynamics calculations. In more complicated cases, these parameters are determined empirically by fitting the model's predicted macroscopic behavior to a set of well-controlled experiments.

cvd.gif At right is a three-dimensional simulation of the chemical vapor deposition on a multi-layer surface with a square hole "skylight" overlaying a larger square void. The macroscopic variable in this case is the surface topology which changes as material is deposited. The sticking coefficient at each location on the surfaces depends upon the concentration of the incident chemical species, their reaction rate coefficients, and the surface topology (i.e., the angle between the normal to the surface and the incident velocity vectors of the various chemical species). The chemical kinetics was modeled using the CHEMKIN package and the three-dimensional mesh was generated using the LANL tessellated grid code X3D/LaGriT. This work was supported by a CRADA between LANL and a consortium of semi-conductor manufacturers.



psd.jpg The particle size distribution of alumina particles in a saturated solution of caustic soda (NaOH) and buaxite ore is plotted as a function of time. The solution is contained in a large stirred reactor with a residency time of several days. Once the alumina particle size is large enough, they are collected and heated to burn off excess water, and then sent to the electrolysis stage for extracting the pure aluminum. This process is known as the Bayer process for aluminum production invented in 1887. The goal of this work was to couple the fundamental physical and chemical processes of precipitation: (1) nucleation, (2) surface growth, (3) agglomeration, and (4) break-up, with the fluid flow of the reactor. A coupled predictive model might provide insight for a more efficient reactor design (reducing the residency time for example). From the particle size distrubtion, moments can be computed. The 0th-moment represents the number of particles, the 1st-moment represents an effective average length scale, the 2nd-moment represents the effective average surface area, and so on. The 2nd-moment can be used to compute a local "drag coefficient" which then couples to and alters the fluid flow. The local flow velocity also couples to the microscopic processes by increasing or decreasing agglomeration and break-up depending upon the details of the flow. This work was supported by a small LDRD grant. The interested industrial partner was ALCOA the world's leading producer of aluminum.





mw.jpg The molecular weight of the Estane binder in a square sample of plastic bonded explosive undergoing hydrolysis is plotted. Hydrolysis occurs when a water monomer attacks the C-O bond in the soft segment of the Estane polymer chain. The hydrolysis reaction cuts the polymer in two which reduces the Estane molecular weight. The hydrolysis mechanism is in fact acid catalyzed. That is, the presence of acid ended polymers leads to an enhancement of the hydrolysis reaction which can result in auto-catalytic behavior or run-away degradation. During the past 10 years, we have developed a detailed chemical kinetics model for the hydrolysis reaction and have recently coupled it to the macroscopic diffusion of water within the material. The fundamental rate coefficients have been determined by fitting the predicted Estane molecular weight to well controlled experiments. The model can now be used to predict the molecular weight within a sample of material once the temperature and water concentration on the boundaries of the sample are specified. The molecular weight of the Estane binder can be related to important material properties such as strength. This work was supported by the Enhanced Surveillance Campaign at LANL.




pdfoam.jpg At right the mass gain due to hydrogen (H) uptake in a palladium metal foam is plotted as the pressure of the hydrogen gas (H2) is increased. A chemical kinetics model is being developed which includes the adsorption and desorption of hydrogen on the surface of the metal, diffusion of the hydrogen into the metal, and its subsequent hydrogenation reaction with the metal. Due to the porous nature of the metal foam, we also expect to couple the model to the macroscopic transport (flow) of the hydrogen into the pores of the metal foam. Preliminary results of the model are encouraging. This work is supported by an LDRD grant is being done in collaboration with Erik Luther (MST-6).









Selected Publications

  1. Geometric Phase Effects in H + O2 Scattering. I. Surface Function Solutions in the Presence of a Conical Intersection, Brian Kendrick and Russell T Pack, The Journal of Chemical Physics, 104, 7475 (1996).
  2. Geometric Phase Effects in H + O2 Scattering. II. Recombination Resonances and State-to-State Transition Probabilities at Thermal Energies, Brian Kendrick and Russell T Pack, The Journal of Chemical Physics, 104, 7502 (1996).
  3. Geometric Phase Effects in the Vibrational Spectrum of Na3(X), Brian Kendrick, Physical Review Letters, 79, 2431 (1997).
  4. Quantum Reactive Scattering Calculations for the D + H2 → HD + H Reaction, Brian K. Kendrick, The Journal of Chemical Physics 118, 10502 (2003).
  5. Geometric Phase Effects in Chemical Reaction Dynamics and Molecular Spectra, Brian K. Kendrick, Feature Article in The Journal of Physical Chemistry A107, 6739 (2003).
  6. Quantum hydrodynamics: Application to N-dimensional reactive scattering, Brian K. Kendrick, The Journal of Chemical Physics 121, 2471-2482 (2004).
  7. Quantum hydrodynamics: Capturing a reactive scattering resonance, S. W. Derrickson, E. R. Bittner, and B. K. Kendrick, The Journal of Chemical Physics 123, 054107 (2005).
  8. How Reactants polarization can be used to change and unravel chemical reactivity, J. Aldegunde, M. P de Miranda, J. M. Haigh, B. K. Kendrick, V. Saez-Rabanos, and F. J. Aoiz, The Journal of Physical Chemistry A109, 6200-6217 (2005).
  9. Analysis of the H + D2 reaction mechanism through consideration of the intrinsic reactant polarization, J. Aldegunde, J. M Alvarino, B. K. Kendrick, V. Saez-Rabanos, M. P. de Miranda, and F. J. Aoiz, Physical Chemistry Chemical Physics 8, 1, (2006).