Geometry optimizations and semiempirical Hamiltonians
Contents
Geometry optimizations and semiempirical Hamiltonians¶
Objectives
Learn how to run geometry optimization using the semiempirical xTB method.
Keypoints
Run a geometry optimization calculation.
Visualize the change of geometry during optimization.
(Optional) Try geometry optimization using a different coordinate system
Introduction¶
In this exercise we will use the semiempirical extended tight-binding (xTB) method [BCE+21], combined with the geomeTRIC optimization code [WS16], to optimize the geometry of the zinc tetraphenylporphyrin dimer.
Geometry optimization is the procedure to find local minimum on the potential energy surface. A coordinate system is therefore necessary for describing the geometry of the system of interest. The Cartesian coordinate system is the simplest; however, it is very inefficient due to the complexity of the potential energy surface. In practice, it is common to employ the so-called internal coordinates that describes the collective motion of atoms in a more efficient way. A displacement in the internal coordinate \(\Delta \mathbf{q}\) is related to the displacement in Cartesian coordinates \(\Delta \mathbf{x}\):
Here \(\mathbf{B}\) is the Wilson B-matrix, with elements:
and \(\mathbf{G} = \mathbf{B} \mathbf{B}^T\).
In the geomeTRIC optimization code, the translation-rotation internal coordinate (TRIC) system is employed. This coordinate system treats intra- and intermolecular coordinates separately by introducing translation and rotation coordinates for the individual molecules in the system.
Efficient geometry optimizations demand good prediction of the next step in the conformation space. This can be done based on a quadratic approximation for the local shape of the potential energy, where an apprximate evaluation of the Hessian can be provided by, for example, the Broyden-Fletcher-Goldfarb-Shanno (BFGS) method.
The gradient, or the first derivative of the energy with respect to nuclear displacements, is provided by the semiempirical xTB method, which is an efficient tight-binding model that covers almost the entire periodic table (\(Z \le 86\)).
System: zinc tetraphenylporphyrin dimer¶
Input file¶
Below is the input file for the geometry optimization of the zinc tetraphenylporphyrin dimer. You can read more about the VeloxChem input keywords in this page.
@jobs
task: optimize
@end
@method settings
xtb: gfn2
@end
@optimize
coordsys: tric
@end
@molecule
charge: 0
multiplicity: 1
xyz:
C 61.02000 57.63000 26.81000
C 60.13000 58.56000 27.35000
H 59.66000 59.27000 26.67000
C 60.00000 58.63000 28.74000
H 59.41000 59.43000 29.18000
C 61.69000 56.68000 27.61000
H 62.19000 55.82000 27.18000
C 61.51000 56.81000 28.98000
H 62.08000 56.16000 29.64000
C 60.59000 57.69000 29.57000
C 60.37000 57.79000 31.03000
C 59.85000 56.56000 31.60000
N 59.49000 56.52000 32.87000
C 59.10000 55.22000 33.10000
C 59.19000 54.43000 31.92000
C 59.70000 55.29000 30.97000
H 59.80000 55.11000 29.91000
H 58.72000 53.46000 31.74000
C 60.82000 58.94000 31.61000
N 60.45000 59.24000 32.89000
C 61.63000 59.93000 30.98000
H 62.03000 60.07000 29.98000
C 61.65000 60.89000 31.97000
H 62.09000 61.87000 31.81000
C 60.90000 60.46000 33.11000
C 60.57000 61.25000 34.28000
C 61.20000 62.59000 34.20000
C 62.50000 62.80000 34.66000
C 63.08000 64.07000 34.69000
C 62.43000 65.19000 34.15000
C 61.08000 64.95000 33.88000
C 60.42000 63.73000 33.94000
H 59.35000 63.68000 33.83000
H 60.46000 65.84000 33.79000
H 64.12000 64.24000 34.93000
H 63.10000 61.94000 34.94000
C 60.13000 60.69000 35.45000
N 59.62000 59.44000 35.68000
C 60.02000 61.48000 36.63000
H 60.32000 62.52000 36.71000
C 59.45000 60.64000 37.54000
H 59.14000 60.85000 38.55000
C 59.07000 59.44000 36.87000
C 58.27000 58.37000 37.47000
C 57.95000 58.61000 38.88000
C 56.62000 58.49000 39.31000
H 55.76000 58.37000 38.65000
C 56.29000 58.46000 40.67000
H 55.24000 58.39000 40.91000
C 57.32000 58.67000 41.60000
C 58.65000 58.67000 41.17000
H 59.41000 58.80000 41.93000
C 58.98000 58.61000 39.82000
H 60.03000 58.43000 39.59000
C 58.14000 57.18000 36.80000
N 58.54000 56.82000 35.54000
C 57.52000 56.11000 37.50000
H 57.13000 56.21000 38.50000
C 57.64000 55.06000 36.64000
H 57.25000 54.07000 36.85000
C 58.31000 55.52000 35.46000
C 58.48000 54.77000 34.23000
C 57.72000 53.51000 34.33000
C 58.36000 52.27000 34.33000
H 59.43000 52.22000 34.14000
C 57.69000 51.08000 34.62000
H 58.24000 50.15000 34.70000
C 56.30000 51.10000 34.76000
C 55.62000 52.30000 34.59000
H 54.54000 52.23000 34.46000
C 56.32000 53.50000 34.49000
H 55.79000 54.43000 34.42000
Zn 59.32000 58.09000 34.16000
C 61.11500 57.37900 25.29400
H 62.11800 57.10600 25.04000
H 60.45000 56.58600 25.02100
H 60.84400 58.27000 24.76700
C 63.05900 66.57900 33.93200
H 62.86400 67.19700 34.78300
H 64.11600 66.47500 33.80100
H 62.63400 67.02900 33.05900
C 56.98100 58.53100 43.09600
H 55.98500 58.88200 43.27000
H 57.05200 57.50300 43.38300
H 57.67000 59.11100 43.67300
C 55.51800 49.77900 34.88200
H 55.35500 49.37000 33.90600
H 56.08000 49.08400 35.47000
H 54.57500 49.96500 35.35300
C 51.90685 54.01054 27.22931
C 51.08826 55.04635 26.75625
H 50.63137 54.97974 25.75855
C 50.85509 56.17646 27.52709
H 50.16044 56.95120 27.21364
C 52.43436 54.16073 28.50813
H 53.07729 53.35934 28.89585
C 52.24520 55.31614 29.27427
H 52.83384 55.39049 30.18606
C 51.41554 56.33346 28.78956
C 51.33770 57.58639 29.56986
C 50.29095 57.44320 30.56834
N 50.23192 58.24238 31.61367
C 49.14509 57.72138 32.28848
C 48.58769 56.53405 31.74108
C 49.29854 56.42902 30.57993
H 49.18752 55.65041 29.81806
H 47.80098 55.86766 32.10413
C 52.22597 58.63368 29.52727
N 52.15765 59.80755 30.22661
C 53.34680 58.65385 28.64531
H 53.60257 57.91295 27.90461
C 53.96035 59.87727 28.80717
H 54.82908 60.22741 28.27602
C 53.18605 60.51770 29.83074
C 53.53974 61.80807 30.40792
C 54.25378 62.66374 29.42664
C 55.60300 62.95809 29.54126
C 56.27367 63.68836 28.54271
C 55.59029 64.02614 27.36676
C 54.29840 63.54640 27.17441
C 53.59645 62.93900 28.22217
H 52.56662 62.63989 28.05223
H 53.78787 63.75629 26.22642
H 57.27868 64.08228 28.67150
H 56.12443 62.72773 30.45988
C 53.25154 62.17278 31.69125
N 52.19464 61.71645 32.44105
C 54.06370 63.13581 32.35307
H 54.99243 63.65131 32.10343
C 53.38562 63.20580 33.54735
H 53.76259 63.81070 34.37553
C 52.20650 62.41438 33.56272
C 51.16392 62.22037 34.56067
C 51.08203 63.30535 35.56874
C 49.90980 64.05988 35.71530
H 49.04323 63.93837 35.07375
C 49.77985 64.95739 36.77483
H 48.86230 65.46814 37.01529
C 50.81683 65.14126 37.68799
C 52.02339 64.45505 37.48616
H 52.74371 64.51766 38.29154
C 52.12549 63.46800 36.49229
H 53.02731 62.87378 36.39942
C 50.27029 61.20423 34.59321
N 50.09230 60.17540 33.70843
C 49.45803 60.96836 35.75671
H 49.36640 61.59538 36.63413
C 48.66956 59.90166 35.41752
H 47.86239 59.57121 36.05649
C 49.07159 59.46371 34.12524
C 48.63160 58.26794 33.41959
C 47.55852 57.63075 34.21443
C 47.74741 56.42903 34.89642
H 48.75643 55.99974 34.92928
C 46.71433 55.65391 35.45153
H 46.96803 54.70387 35.90402
C 45.40565 56.08167 35.28487
C 45.17826 57.26877 34.56816
H 44.20226 57.71751 34.43869
C 46.22569 58.06008 34.08539
H 46.05336 59.04010 33.66259
Zn 51.32929 59.90367 32.08904
C 52.27990 52.78969 26.36754
H 53.30327 52.86701 26.06458
H 52.14439 51.89471 26.93907
H 51.65292 52.75858 25.50165
C 56.35220 64.88676 26.34155
H 56.62834 65.81747 26.79255
H 57.23252 64.36862 26.02540
H 55.72443 65.07263 25.49586
C 50.67441 66.04556 38.92639
H 50.65214 65.44182 39.80888
H 51.50547 66.71789 38.97389
H 49.76618 66.60651 38.85488
C 44.20161 55.21778 35.70364
H 43.49410 55.82310 36.23077
H 43.73866 54.80444 34.83142
H 44.53612 54.42480 36.33918
@end
Results¶
Submit a job
Runs the above example on 1 node. On Beskow this will take around 10 minutes so please make sure that you specify a proper walltime limit in the job script.
Visualize the result
The change of energy during optimization is printed at the end of the output file.
We can visualize the process of the optimization in a Jupyter notebook on MyBinder.
(Optional) Rerun the optimization using another coordinate system
You can find the input keyword for other coordinate systems in this page.