Visualization of ab initio molecular dynamics trajectories near two-state conical intersections Looking for where quantum mechanical effects greatly influence the motions of molecules Jiahao Chen Dept. of Chemistry CS 519, 1 May 2007

Classical mechanics Things move according to Newton’s 2 nd law, Dynamics = rolling around on a potential energy surface (PES) PES for N particles is (3N-6)-dimensional - r V = F = m a

Things move according to Newton’s 2 nd law,

Dynamics = rolling around on a potential energy surface (PES)

PES for N particles is (3N-6)-dimensional

Classical mechanics Things move according to Newton’s 2 nd law, Schrödinger’s equation Dynamics = rolling around on multiple potential energy surface s (PES s ) Quantum Choice of forces!? H ª = i ~ @ ª @ t

Things move according to Newton’s 2 nd law, Schrödinger’s equation

Dynamics = rolling around on multiple potential energy surface s (PES s )

Solution: spawning Choice concentrated at special points, e.g. two-state conical intersections (2CI) At 2CI, only 2 dimensions of PES (called g and h ) are important M. Ben-Nun and T. J. Martínez, Adv. Chem. Phys. 121 , 2002, 439-512. Population Probability of becoming child or parent 2CI 100% spawn point 65% 35% 1. Start 95% 5% 2. Spawn

Choice concentrated at special points, e.g. two-state conical intersections (2CI)

At 2CI, only 2 dimensions of PES (called g and h ) are important

Need for visualization Help answer fundamental questions like: How do trajectories behave near 2CIs? How far from 2CIs dos spawning occur? What influences population transfer? Plots in (g, h, E) space 9150.00 0.210 0.387 1.576 -0.094 -0.078 -1.337 0.616 -2.078 -0.703 -0.789 -1.184 2.404 -1.981 -0.684 -1.582 0.767 0.241 -2.987 -9.334 8.961 3.075 7.298 5.084 -14.247 -6.508 -8.510 1.336 2.157 -8.886 7.438 9.073 2.633 7.285 -2.686 0.719 -4.886 1.619 -0.004 -0.073 0.005 2.000 9160.00 0.206 0.391 1.577 -0.091 -0.076 -1.343 0.581 -2.124 -0.697 -0.777 -1.233 2.446 -1.932 -0.669 -1.542 0.754 0.246 -3.015 -9.602 9.008 2.604 7.458 4.043 -13.050 -6.511 -8.255 0.888 2.288 -8.715 7.759 8.642 2.793 7.173 -2.274 1.126 -5.374 3.874 -0.004 -0.073 0.005 2.000 9170.00 0.201 0.396 1.578 -0.088 -0.075 -1.349 0.545 -2.169 -0.694 -0.764 -1.280 2.490 -1.886 -0.653 -1.503 0.742 0.253 -3.046 -9.903 8.931 2.209 7.850 3.018 -11.848 -6.494 -7.933 0.425 2.485 -8.416 7.982 7.959 2.897 7.017 -1.897 1.504 -5.786 6.072 -0.004 -0.073 0.005 2.000 9180.00 0.197 0.400 1.579 -0.084 -0.074 -1.354 0.509 -2.212 -0.692 -0.750 -1.325 2.534 -1.845 -0.637 -1.465 0.733 0.262 -3.078 -10.218 8.748 1.885 8.495 2.025 -10.673 -6.453 -7.556 -0.048 2.732 -8.009 8.116 7.010 2.940 6.824 -1.565 1.851 -6.104 1.887 -0.004 -0.073 0.005 2.000 9190.00 0.192 0.404 1.580 -0.080 -0.073 -1.359 0.474 -2.252 -0.694 -0.734 -1.368 2.579 -1.809 -0.621 -1.428 0.725 0.273 -3.113 -10.535 8.476 1.624 9.394 1.076 -9.551 -6.389 -7.132 -0.527 3.013 -7.509 8.169 5.799 2.924 6.603 -1.282 2.164 -6.318 3.852 -0.004 -0.073 0.005 2.000 9200.00 0.187 0.407 1.581 -0.075 -0.073 -1.363 0.439 -2.290 -0.698 -0.717 -1.407 2.624 -1.781 -0.605 -1.393 0.719 0.286 -3.148 -10.840 8.131 1.420 10.525 0.173 -8.504 -6.302 -6.668 -1.008 3.317 -6.935 8.150 4.350 2.855 6.365 -1.050 2.443 -6.422 5.661 -0.004 -0.073 0.005 2.000 9210.00 0.182 0.411 1.581 -0.070 -0.073 -1.366 0.405 -2.325 -0.705 -0.698 -1.444 2.668 -1.762 -0.590 -1.358 0.714 0.300 -3.183 -11.124 7.727 1.267 11.838 -0.693 -7.546 -6.191 -6.171 -1.487 3.634 -6.301 8.066 2.714 2.751 6.117 -0.870 2.688 -6.417 1.026 -0.004 -0.073 0.005 2.000 9220.00 0.177 0.414 1.582 -0.064 -0.073 -1.370 0.371 -2.358 -0.715 -0.677 -1.477 2.712 -1.751 -0.575 -1.325 0.709 0.315 -3.218 -11.380 7.274 1.158 13.261 -1.540 -6.685 -6.059 -5.646 -1.962 3.957 -5.619 7.925 0.960 2.631 5.867 -0.739 2.899 -6.304 2.524 -0.004 -0.073 0.005 2.000 9230.00 0.171 0.418 1.582 -0.058 -0.074 -1.373 0.338 -2.387 -0.727 -0.654 -1.506 2.755 -1.751 -0.561 -1.294 0.705 0.332 -3.252 -11.602 6.784 1.090 14.703 -2.388 -5.919 -5.906 -5.096 -2.429 4.278 -4.900 7.734 -0.823 2.523 5.616 -0.650 3.077 -6.092 3.896 -0.004 -0.073 0.005 2.000 9240.00 0.166 0.421 1.583 -0.051 -0.075 -1.375 0.307 -2.413 -0.741 -0.630 -1.530 2.797 -1.761 -0.547 -1.264 0.702 0.349 -3.285 -11.786 6.263 1.057 16.071 -3.257 -5.239 -5.733 -4.525 -2.888 4.595 -4.153 7.497 -2.547 2.449 5.361 -0.601 3.224 -5.789 5.179 -0.004 -0.073 0.005 2.000 11 GB of numbers summarize

Help answer fundamental questions like:

How do trajectories behave near 2CIs?

How far from 2CIs dos spawning occur?

What influences population transfer?

cis-trans isomerization of C 2 H 4 Prototype chemical reaction for human vision and photosynthesis

Prototype chemical reaction for human vision and photosynthesis

Implementation : Python, NumPy, VTK instance of simulation parameters FMSTrajectory Population vtkDoubleArray ConicalIntersection ModelCone instance of Trajectory numpy.array Energies numpy.array attribute data in g vector numpy.array h vector numpy.array Energy float Structure numpy.array Coupling vtkDoubleArray Molecule ModelCone Configuration Molecule ProjectedTrajectory vtkPoints InputData vtkPolyData ProjectedMomenta vtkDoubleArray[3] used to calculate props in GlyphActor vtkConeSource vtkGlyph3D vtkPolyData vtkPolyDataMapper vtkActor SparkActor vtkSphereSource vtkPolyDataMapper vtkActor Outline vtkOutlineSource vtkPolyDataMapper vtkActor Main Display vtkRenderer vtkRenderWindow vtkRenderWindowInteractor vtkPNGWriter ConeActor vtkQuadric vtkSampleFunction vtkContourFilter vtkPolyDataMapper vtkActor Axes vtkAxesActor

Plot: 1 parent and 1 child Spawn point child parent Origin = 2CI GlyphActor vtkSphereSource vtkGlyph3D vtkPolyData vtkPolyDataMapper vtkActor TubeActor vtkPolyData vtkTubeFilter vtkPolyDataMapper vtkActor ProjectedTrajectory vtkPoints InputData vtk PolyData no attribute data X