Exciton calculation
Contents
Exciton calculation¶
Objectives
Learn how to run an ab initio exciton model calculation.
Keypoints
Run an ab initio exciton model calculation.
Plot the UV-Vis absorption and ECD spectra.
Analyze the character of the excitations.
Introduction¶
In this exercise we will use an ab initio exciton model to compute the UV-Vis absorption and electronic ciruclar dichroism (ECD) of oligothiophene self-assembly.
The Frenkel exciton model describes the electronic structure of multi-chromophoric system by dividing the system into subgroups. It has been most successful in the weak-coupling limit where the excitons are localized on inidividual chromophores. The ab initio exciton model expands the Frenkel exciton model by taking into account charge-transfer between the chromophores, and is therefore more useful for studies of singly excited states. You may read more in this paper [LPL+17].
In the exciton model, the Hamiltonian adopts the following matrix form
where \(N\) is the total number of excited states, \(\phi_I\) is the \(I\)-th excitonic basis function, and \(E\) and \(V\) are the excitation energies and couplings, respectively. Diagonalization of the Hamiltonian gives the eigenvalues and eigenvectors for the excited states.
System: oligothiophene self-assembly¶
Input file¶
Below is the input file for ab initio exciton model calculation of oligothiophene self-assembly. You can read more about the input keywords in this page.
@jobs
task: exciton
@end
@method settings
basis: def2-svp
@end
@exciton
fragments: 6
atoms_per_fragment: 44
nstates: 5
ct_nocc: 1
ct_nvir: 1
@end
@molecule
charge: 0
multiplicity: 1
xyz:
H 118.845 123.055 249.799
C 119.154 123.082 250.844
S 118.107 122.412 252.061
C 120.464 123.254 251.169
H 121.231 123.434 250.415
C 120.649 122.832 252.511
H 121.507 123.114 253.122
C 119.493 122.392 253.145
C 119.359 121.952 254.521
S 120.401 122.690 255.732
C 119.573 121.848 257.038
C 118.485 121.141 256.539
H 117.654 120.912 257.207
C 118.363 121.193 255.126
H 117.717 120.537 254.543
C 119.943 122.005 258.420
S 119.037 121.231 259.716
C 120.261 121.681 260.898
C 121.217 122.520 260.340
H 121.876 123.153 260.934
C 121.033 122.684 258.951
H 121.792 123.146 258.320
C 120.032 121.220 262.243
S 121.062 121.625 263.613
C 120.146 120.545 264.657
C 119.017 120.049 264.015
H 118.290 119.390 264.489
C 118.964 120.434 262.659
H 118.183 120.141 261.956
C 120.562 120.194 265.990
S 122.227 120.526 266.452
C 121.783 120.110 268.103
C 120.429 119.815 268.219
H 119.881 119.920 269.156
C 119.714 119.745 266.996
H 118.730 119.308 266.823
C 122.808 120.275 269.117
C 124.072 120.828 268.951
H 124.275 121.519 268.131
C 124.684 120.733 270.229
H 125.732 120.974 270.407
C 123.956 120.278 271.284
H 124.088 120.503 272.341
S 122.392 119.743 270.742
H 127.712 115.074 271.928
C 127.450 115.156 270.873
S 126.874 116.712 270.349
C 127.625 114.299 269.832
H 128.033 113.294 269.940
C 127.241 114.826 268.570
H 127.034 114.302 267.636
C 126.843 116.153 268.680
C 126.306 116.998 267.630
S 126.211 116.315 266.010
C 125.817 117.933 265.440
C 125.631 118.884 266.436
H 125.231 119.888 266.298
C 126.042 118.361 267.691
H 126.258 118.842 268.646
C 125.657 117.928 264.010
S 124.725 119.204 263.234
C 125.201 118.552 261.671
C 125.861 117.331 261.750
H 126.375 116.862 260.911
C 126.148 117.006 263.091
H 126.642 116.077 263.376
C 124.928 119.306 260.475
S 125.040 118.329 259.016
C 124.644 119.732 258.029
C 124.581 120.914 258.759
H 124.547 121.965 258.470
C 124.639 120.623 260.136
H 124.625 121.387 260.914
C 124.471 119.638 256.604
S 124.043 121.158 255.826
C 124.219 120.306 254.297
C 124.545 118.957 254.375
H 124.617 118.339 253.480
C 124.668 118.570 255.737
H 124.929 117.585 256.122
C 124.297 121.089 253.079
C 124.393 122.471 252.956
H 124.556 123.113 253.820
C 124.187 122.838 251.600
H 124.615 123.786 251.274
C 123.936 121.850 250.699
H 123.724 121.925 249.632
S 123.940 120.325 251.535
H 120.598 119.084 247.493
C 120.650 119.035 248.580
S 121.311 117.733 249.527
C 120.100 120.048 249.303
H 119.459 120.796 248.838
C 120.233 119.841 250.701
H 120.426 120.635 251.423
C 120.820 118.611 250.970
C 120.988 117.871 252.206
S 120.404 118.638 253.679
C 120.949 117.227 254.579
C 121.449 116.225 253.755
H 121.839 115.296 254.171
C 121.572 116.624 252.397
H 122.334 116.298 251.689
C 121.053 117.352 256.010
S 121.716 115.971 256.877
C 121.511 116.916 258.347
C 121.086 118.226 258.158
H 121.144 119.011 258.913
C 120.794 118.465 256.799
H 120.189 119.282 256.405
C 121.841 116.263 259.587
S 121.780 117.373 260.952
C 122.192 115.991 261.960
C 122.305 114.754 261.335
H 122.461 113.786 261.812
C 122.137 114.954 259.951
H 121.802 114.109 259.348
C 122.108 116.376 263.345
S 122.610 115.155 264.510
C 122.300 116.216 265.880
C 121.780 117.410 265.392
H 121.596 118.211 266.109
C 121.738 117.555 263.980
H 121.204 118.385 263.517
C 122.620 115.679 267.188
C 122.318 116.134 268.466
H 122.042 117.177 268.616
C 122.783 115.291 269.510
H 122.233 115.292 270.452
C 123.520 114.267 269.003
H 124.328 113.733 269.503
S 123.414 114.110 267.273
H 123.715 111.237 269.393
C 124.457 111.278 270.190
S 124.085 112.034 271.712
C 125.747 110.854 270.106
H 126.191 110.451 269.195
C 126.526 111.307 271.203
H 127.480 110.862 271.485
C 125.771 111.910 272.202
C 125.969 111.962 273.638
S 124.560 111.311 274.467
C 125.406 111.462 276.003
C 126.648 112.058 275.820
H 127.317 112.265 276.655
C 126.996 112.372 274.478
H 127.731 113.094 274.122
C 124.954 110.914 277.256
S 126.130 110.951 278.564
C 125.036 110.098 279.648
C 123.896 109.713 278.951
H 123.096 109.114 279.384
C 123.792 110.265 277.657
H 122.880 110.482 277.102
C 125.495 109.942 281.003
S 124.372 109.324 282.209
C 125.671 109.250 283.394
C 126.839 109.817 282.897
H 127.660 110.113 283.550
C 126.757 110.177 281.536
H 127.636 110.214 280.894
C 125.459 108.595 284.659
S 126.744 108.564 285.862
C 125.607 107.875 287.016
C 124.316 107.851 286.500
H 123.509 107.665 287.209
C 124.210 108.208 285.130
H 123.286 108.008 284.587
C 126.084 107.722 288.375
C 125.238 107.836 289.471
H 124.243 108.274 289.388
C 125.969 107.523 290.648
H 125.437 107.247 291.559
C 127.314 107.395 290.491
H 128.026 107.536 291.303
S 127.761 107.411 288.810
H 130.198 109.180 271.826
C 129.217 109.162 272.300
S 129.140 109.513 274.004
C 128.144 108.541 271.740
H 128.159 108.125 270.733
C 127.108 108.369 272.697
H 126.232 107.721 272.719
C 127.545 108.771 273.953
C 126.975 108.328 275.212
S 128.053 108.280 276.603
C 126.764 107.608 277.594
C 125.582 107.430 276.884
H 124.657 107.259 277.432
C 125.713 107.843 275.530
H 124.855 107.990 274.875
C 127.061 107.075 278.897
S 125.784 106.086 279.598
C 126.623 106.147 281.143
C 127.831 106.834 281.122
H 128.483 106.723 281.990
C 128.057 107.346 279.828
H 128.943 107.950 279.630
C 125.801 105.626 282.204
S 126.672 105.044 283.618
C 125.146 104.844 284.473
C 124.072 105.238 283.682
H 123.013 105.097 283.898
C 124.427 105.708 282.400
H 123.823 106.415 281.831
C 125.149 104.527 285.876
S 126.701 104.475 286.704
C 125.978 103.898 288.202
C 124.614 103.712 288.008
H 124.113 103.273 288.871
C 124.136 104.099 286.728
H 123.154 103.876 286.311
C 126.764 103.708 289.405
C 128.118 103.413 289.508
H 128.838 103.622 288.715
C 128.506 103.238 290.861
H 129.414 102.666 291.052
C 127.473 103.398 291.732
H 127.503 103.239 292.810
S 125.973 103.845 290.971
H 125.720 113.779 294.384
C 125.769 113.277 293.417
S 125.804 114.175 291.927
C 125.809 111.927 293.260
H 125.468 111.219 294.016
C 126.044 111.550 291.911
H 126.073 110.534 291.516
C 125.887 112.642 291.066
C 125.684 112.552 289.634
S 125.054 113.952 288.771
C 125.384 113.099 287.267
C 125.819 111.790 287.439
H 125.876 111.141 286.565
C 126.059 111.500 288.807
H 125.901 110.482 289.164
C 125.132 113.746 286.005
S 125.089 112.763 284.546
C 124.836 114.255 283.647
C 124.737 115.408 284.417
H 124.336 116.357 284.060
C 124.963 115.107 285.775
H 124.700 115.770 286.599
C 124.742 114.244 282.211
S 124.147 115.699 281.418
C 123.936 114.740 279.958
C 124.258 113.395 280.089
H 124.388 112.705 279.255
C 124.750 113.127 281.383
H 125.099 112.164 281.755
C 123.562 115.408 278.738
S 123.972 114.549 277.258
C 123.534 115.992 276.352
C 123.063 117.045 277.128
H 122.306 117.664 276.646
C 123.163 116.719 278.505
H 122.708 117.376 279.246
C 123.770 116.102 274.924
C 124.202 115.075 274.094
H 124.663 114.134 274.391
C 124.118 115.418 272.719
H 124.230 114.710 271.898
C 123.663 116.687 272.534
H 123.516 117.249 271.610
S 123.359 117.550 274.013
@end
Exercise¶
Submit a job
Runs the above example. On Dardel this calculation takes around 10 minutes on 2 nodes. You can choose to run on more nodes.
Plot the spectrum
The excitation energies, oscillator strengths, and rotatory strengths will be printed at the end of the output file. You can plot the UV-Vis and ECD spectra by line broadening using e.g. Gaussian function.
import numpy as np import plotly.graph_objects as go def gaussian(x, y, xmin, xmax, xstep, sigma): """Gaussian broadening function Call: xi,yi = gaussian(energies, intensities, start energy, end energy, energy step, gamma) """ xi = np.arange(xmin, xmax, xstep) yi = np.zeros_like(xi) for _x, _y in zip(x, y): yi += _y * np.exp( -(xi - _x)**2 / (2 * sigma**2)) return xi, yi # insert your data! exc_ene = np.array([2.8, 3.0, 3.1, 3.15]) # insert your data! osc_str = np.array([0.3, 0.1, 1.0, 0.2]) x0, y0 = gaussian(exc_ene, osc_str, 2.5, 3.4, 0.01, 0.1) fig = go.Figure() fig.add_trace( go.Scatter( x=x0, y=y0, mode="lines", name="absorption", ) ) fig.update_layout( title="Absorption", xaxis_title="Excitation energy", yaxis_title="", height=500, width=600, ) fig.show()
Examine the character of the excitations
The character of the excitations will be printed at the end of the output file. Find out the characters of the important excitations.
Notation:
LE 5e(3)stands for the 3rd locally excited state (S3) on monomer 5.CT 3+(H0)4-(L0)stands for charge transfer from HOMO of monomer 3 to LUMO of monomer 4.