The focus of research in the Wyatt Research Group has been energy flow in molecules. All of the animations below represent trajectories that were calculated at the state of the art in computational chemistry at the time they were created.
Most of the animations were created to aid the research group in visualizing the motion represented by the calculations. Unless otherwise noted, all of the computations were performed by Todd J. Minehardt, Robert E. Wyatt, and J. David Adcock using various computing platforms, including lonestar, a Cray T3E Massively Parallel Computer system.
All of these animations were produced by J. David Adcock. The graphics were rendered using the POV Ray - The Persistence of Vision Raytracer program. The original animations were rendered using POV-Ray Version 3.0.1; as of this writing, the current release of POV-Ray is Version 3.7. In addition, the animations shown here are much smaller in dimension than the original animations, in order to reduce web bandwidth requirements.
[All of the animations that are linked below are reformatted copies of the original web animations, but each one has been enlarged on this page to provide a better viewer experience. Hence the resolution of the following animations is somewhat less than the original source animation. [By way of explanation, the original web-based animations were ALL rendered in a much smaller dimension due to the original bandwidth limitations of websites and internet connections at the time of their creation. As time allows, all of these animations will be re-rendered to provide a fully optimal viewer experience.]
Quasi-Classical Dynamics of the Benzene Molecule |
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This first set of animations was made to illustrate the vibrational
dynamics of the benzene molecule, C6H6.
All of the animations of these studies are based on computations using the
ab initio force field for a polyatomic molecule, which was
published by Maslen, Handy, Amos, and Jayatilaka1 in 1992.
The original force field contains terms through the fourth-order,
and these terms have been supplemented by fifth- and sixth-order terms
by Wyatt and Iung2.
The primitive direct product space has dimension 36.5 billion, which was
reduced to an active space of 16,000 by use of the Wave Operator Sorting
Algorithm3.
In each of the studies, we investigate the quasi-classical dynamics of benzene by computing many possible trajectories of the molecule under varying initial conditions and with various constraints. Each animation represents one possible trajectory of the molecule. Several different types of animations are shown below. More specifically, the study follows many possible trajectories of the molecule after excitation. (By the term trajectory, we refer to the (adiabatic) distribution of energy in a 21- or 30-dimensional space.) The trajectory of the molecule is determined by the initial conditions (potential and kinetic energy in each normal mode, corresponding to the position and momentum of each atom) and by various conditions imposed on the model. Each simulation begins by assigning a zero-point potential and kinetic energy value to each normal mode in the molecule; the proportion and phase are randomly selected. The next step is to add energy to the appropriate C-H stretch mode. From that point, the simulation follows the energetics of each mode of the 21- or 30-mode system. A large number of these cases are not physically viable (e.g. they lead to a negative energy in one of the modes or lead to energy in a mode that exceeds the bond energy), and these cases are discarded. The remaining trajectories represent physically significant configurations. Each animation follows the course of one such trajectory. The total duration of each of the full simulations is 2.4 picoseconds, though the short example animations shown here represent only small fractions of the complete interval of the study. The interval of each time step is 200 a.u. (4.8 fs) for the studies. In these animations, the small blue spheres represent the hydrogen atoms, and the red spheres represent the carbon atoms. In the animation on the right below, the trajectory of the molecule is constrained to a plane (i.e., 21-mode benzene4). In the other two animations, out-of-plane motion is allowed (i.e., 30-mode benzene5,6). The center animation (30 mode, First overtone) is a fine example of the versatility of the POV-Ray rendering engine. In this animation, the benzene molecule is contained inside a glass sphere, and the reflections and refractions appear exactly as a physical object of this design would appear in the background landscape. |
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A Carbon's Eye View of Molecular Dynamics in 21 mode Benzene
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Molecular Dynamics of Benzene, 30 mode First overtone
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Molecular Dynamics of Benzene, 30 mode Second overtone
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The C-H Chromophore in C6H |
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This set of animations was made to study the (quasi-classical)
dynamics of the C-H Chromophore in C6H.
This study7 is a (15-mode) subset of the full benzene
problem and was done to determine the scalability of certain
elements of the calculations within the full benzene problem.
Initially, the C-H chromophore is at a ground-level vibrational state. We then excite the molecule by adding the energy equivalent of a single photon in the C-H bond, and follow the distribution of this energy through the molecule. This is accomplished by computing the classical momentum and electrostatic force terms for each atom in the molecule at equally-spaced time intervals. The purpose of the study is to investigate the role of out-of-plane motion in the overall energy redistribution in the excited molecule. The total duration of the simulation is 2.4 picoseconds, though the short example animations below represent only small fractions of the entire simulation. In these animations, the molecule is oriented so that the C-H chormophore is located in the upper right corner of the molecule as viewed from the front. Only the C-H chromophore is shown, and the remaining carbon atoms in the molecule, i.e. the ones located beyond the range of the back reference grid, are omitted. The yellow sphere represents the hydrogen atom, and the blue sphere represents the carbon atom. In order to emphasize the motion of the hydrogen atom, it is shown at the successive locations of the hydrogen atom in the model, and preceeding locations of the atom are shown by an orange track. The shorter clips also include grids in the X, Y, and Z planes to help the viewer determine the orientation of the figure and the viewing angle. The first three clips below illustrate short examples of the three vibrational modes of the C-H chromophore: C-H stretch (increasing-decreasing C-H distance), C-H wag (in-plane side-to-side motion of H), and C-H bend (out-of-plane forward-and-backward motion of H). After time t = 0, the total vibrational energy of the C-H chromophore is never exclusively isolated in one particular mode, but is distributed among all three vibrational modes. Thus the electrostatic forces on the hydrogen atom cause it to move in complex combinations of the three vibrational modes. Of course, the same forces cause motion of the carbon atom, but since its mass is much greater than that of the hydrogen atom, the amplitude of motion of the carbon atom is much smaller than that of the hydrogen atom. The final clip is a segment of the full animation, and shows almost a third of the full simulation.
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C-H Stretch
The C-H stretch is the most energetic of the local modes of vibration of C6H. This motion occurs radially along the axis from the carbon to the hydrogen. This clip begins with a front-on view of the chromophore, and moves to a side view. Even though the stretch amplitude is very high in this particular interval, there is still a C-H Wag component of motion (see below). This wag component produces a wide "V" shape in the animation. The out-of-plane energy is very low at this time in the model, as can be seen from the fact that the "V" remains in the original plane of the molecule. This clip represents about 65 femtoseconds of the simulation. |
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C-H Wag
This front-on view of the C-H chromophore shows the side-to-side, in-plane wag motion of the hydrogen atom with respect to the carbon atom. At this point in the simulation, there is very little energy in the C-H stretch mode, as can be seen from the fact that the hydrogen atom remains at a relatively constant distance from the carbon atom. Also at this time, the carbon atom is also beginning to exhibit motion, as can be clearly seen in this short outtake. This clip represents about 35 femtoseconds of the simulation. |
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C-H Bend (Out-of-plane) motion
This edge-on view of the C-H chromophore shows a high-amplitude out-of-plane motion of the hydrogen atom with respect to the carbon ring. This motion, viewed as side-to-side movement by the hydrogen atom, is termed bend motion. In this clip, the bend is accompanied by a large component of wag motion (towards and away from the viewer) and a smaller amount of C-H stretch motion. This clip represents about 35 femtoseconds of the simulation. |
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C-H chromophore motion
This animation shows one possible trajectory of the hydrogen and carbon atoms from excitation (t = 0) until t = 0.72 picoseconds. In order to minimize the bandwidth requirement of this lengthy clip, only the lower grid is shown. |
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Quantum Dynamics of (30-mode) Benzene |
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This set of animations depicts a study of the quantum dynamics of the
benzene molecule8.
Since this is a quantum study, the Cartesian positions of the atoms in
the molecule are not readily available.
Instead, we illustrate the energy levels of the six classes of local
mode vibration: The study investigates the quantum dynamics of overtone relaxation in 30-mode benzene. The animation depicts the total energy in each of the six classes of local mode vibrations. For example, the energy in the six C-H stretch modes is collected into a single term in the graph labelled "C-H", the energy in the six C-H Wag modes is collected into a single term labelled "Wag", etc. At time t = 0, we choose the bright state to be one of the E1u symmetry states. We then propagate time through 1 picosecond and follow the energy flow through the other local modes. Clearly at very early time, virtually all energy is in the "C-H" stretch mode, and this component of the graph is off-scale. The in-plane C-H wag ("Wag"), out-of-plane C-H bend ("OOP"), and C-C stretch ("C-C") modes acquire energy early in the simulation, while the C-C-C bend mode ("C-C-C") and the C-C-C-C ring torsion mode ("Ring") acquire relatively little energy during the duration of this animation. Note especially that the out-of-plane C-H "Wag" mode acquires a considerable amount of energy after only a few femtoseconds into the simulation, and maintains this energy level for the duration of the animation. |
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Quantum Dynamics of 30-mode Benzene |
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Quantum Trajectory Method |
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The next class of animation depicts a sample application of the
Quantum Trajectory Method (QTM) that was originally
introduced by Bohm.
QTM treats regions of probability density as fluid "particles" and applies the principles of fluid dynamics to determine the motion of these "particles". This study follows the progress of a generic reaction of the form The reactant coordinate axis is oriented from left to right, and the product axis extends out of the screen towards the viewer. The vertical cylinders represent the probability of the state (and this vertical scale is exaggerated in the animation.) A grid in the original video has been removed from this web version to economize the bandwidth requirement of the animation. As the animation proceeds, most of the reactant moves rightward, towards the right-angle reaction/transition complex. As the "fluid" turns the corner of the reaction complex, it emerges as "product" along the axis that is oriented toward toward the viewer. Note that some of the "reactant" material does NOT pass through the reaction complex, but is reflected back along the reactant axis; this mimics acutal reaction dynamics. Near the end of the animation, reactant material can be seen to start retreating back toward the left, away from the transition complex; This phenomenon represents the "unreacted" reactant material. |
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Quantum Trajectory Method |
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Quasiclassical Trajectory (QCT) Calculations for O + HCl → OH + Cl |
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This animation depicts the a typical chemical reaction for
The computations were performed by Bala Ramachandran9 at Louisiana Tech University. In this animation, the yellow sphere represents the hydrogen atom, the green sphere represents the chlorine atom, and the blue sphere represents the oxygen atom. In order to highlight the trajectory of the various atoms, the preceding 200 locations of the center of each atom are shown by a track which has the same color as the atom. For the slower-moving chlorine and oxygen atoms, this track becomes a solid "tail", while the rapidly moving hydrogen atom is followed by a trail of spheres at the preceding atom center locations. The initial vibrational motion of the hydrogen atom with respect to the chlorine atom is shown to scale. Upon entering the reaction complex, the motion of the hydrogen atom is strongly influenced by the large electrostatic forces, and the entire complex can almost be considered an unstable triatomic molecule. Note how the track of the oxygen atom is also perturbed during this encounter. One of the principal areas of interest in this system is how the vibrational energy of the reactants is transferred into rotational energy in the products, and this model provides one explanation for this phenomenon. |
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| Quasi-Classical Trajectory Calculations for HCl + O → Cl + HO | |
For more information about any of these animations, please contact contact@lonestarbio.com.
Updated from the original Wyatt Research website: May 29, 2018