Visualization of ab initio molecular

dynamics trajectories near two-

state conical intersectionsLooking for where quantum mechanical effects

greatly influence the motions of molecules

Jiahao ChenDept. of Chemistry

CS 519, 1 May 2007

Classical mechanics

• Things move according to Newton’s 2nd law,

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

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

- r V = F = ma

Classical mechanics

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

• Dynamics = rolling around on multiple potential energy surfaces (PESs)

Quantum

H ª = i~@ª@t

Choice of forces!?

spawn point

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.

PopulationProbability of becoming child or parent

65%

35%

1. Start 95%

5%

2. Spawn

2CI

100%

Need for visualization

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

Help answer fundamental questions like:• How do trajectories behave near 2CIs?• How far from 2CIs dos spawning occur?• What influences population transfer?

summarize

cis-trans isomerization of C2H4

• Prototype chemical reaction for human vision and photosynthesis

instanceof

Implementation: Python, NumPy, VTK

Molecule

simulation parametersFMSTrajectory

PopulationvtkDoubleArray

ConicalIntersectionModelCone

ModelCone

ConfigurationMolecule

instanceof

Trajectorynumpy.array

Energiesnumpy.array

attributedata in

g vectornumpy.array

h vectornumpy.array

Energyfloat

Structurenumpy.array

ProjectedTrajectoryvtkPoints

InputDatavtkPolyData

ProjectedMomentavtkDoubleArray[3]

used to calculate

props in

GlyphActorvtkConeSource

vtkGlyph3DvtkPolyData

vtkPolyDataMappervtkActor

SparkActorvtkSphereSource

vtkPolyDataMappervtkActor

OutlinevtkOutlineSource

vtkPolyDataMappervtkActor

Main DisplayvtkRenderer

vtkRenderWindowvtkRenderWindowInteractor

vtkPNGWriter

ConeActorvtkQuadric

vtkSampleFunctionvtkContourFilter

vtkPolyDataMappervtkActor

AxesvtkAxesActor

CouplingvtkDoubleArray

Plot: 1 parent and 1 child

Spawnpoint

child

parentOrigin = 2CI

GlyphActorvtkSphereSource

vtkGlyph3DvtkPolyData

vtkPolyDataMappervtkActor

TubeActorvtkPolyDatavtkTubeFilter

vtkPolyDataMappervtkActor

ProjectedTrajectoryvtkPoints

InputDatavtkPolyData

no attribute data

X