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I am trying to reproduce the cyclooctatetraene isometrization process pulished here. In figure 3 of the paper, it shows the potential energy surface as a variable of the polar angle using the CAS(8,8) method. I am new to this field and I already learnt how to optimize the molecular geometry with simple control of degrees of freedom, like fix the bond dimension for certain atoms. However, generating the molecular geometry for system that complex seems challenging. Can someone tell me how to do this?

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I'm not 100% sure I know what you want. But let's walk through creating rough geometries for the different structures in the paper.

I'm going to use Avogadro, but it should be possible to do this in most editors.

  1. First off, I created the planar $D_{4h}$ geometry.

planar cyclooctatetraene

I drew this planar, then optimized with a constraint that only the X and Y positions could change and Z was constrained.

If you're optimizing this in a quantum program, you probably want to use a z-matrix and constrain the angles and dihedrals, see below.

  1. Next, there's the fully planar $D_{8h}$ starting point. This is not stable.

Going from the planar $D_{4h}$ geometry, you can tweak the z-matrix input to ensure there's only one average C-C bond length, one C-C angle, one C-H length, C-H angle, etc., e.g.

C  
C   1 B1
C   2 B1 1 A2
C   3 B1 2 A2 1 D3
C   4 B1 3 A2 2 D4
C   5 B1 4 A2 3 D5
C   6 B1 5 A2 4 D6
C   1 B1 2 A2 3 D7
Variables:
B1        1.40
A2      135.0
  1. Finally, you need to create one of the $D_{2d}$ "tub" geometries. I find these the easiest to make. If you just nudge some atoms up and down in the Z-direction, this will optimize fully. (In the z-matrix, just make the dihedral angles individual variables.)

"tub" cyclooctatetraene

In principal, you should restrict some of the dihedral angle variables for the $D_{2d}$ geometry so they're identical. My experience is that with modern codes, if you break the plane and start to optimize, you should end up with the $D_{2d}$ geometry or very close to it (such that you can run a symmetry-broken optimization, then enforce symmetry and re-run).

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    $\begingroup$ I'll mention that generally for enforcing particular symmetry, use of a symbolic z-matrix is really critical because you can constrain particular bond lengths and angles to be identical, but optimize to find the appropriate minima. $\endgroup$ Apr 29 at 18:28
  • $\begingroup$ Thanks for the helpful answer. I still have one question, though. Fig 3 in the paper used a spherical coordinate and change the polar angle to form the isometrizaton process. As I implement the geometry optimization for different polar angles in PySCF, the constraints of the dihedral angles do not seem to meet the requirement in Cartesian coordinate. This is because for the 𝐷2𝑑 geometry as the polar angles vary, constraint the dihedral angle between two pairs of adjoint carbon atoms will still change the polar angle. $\endgroup$ May 3 at 7:11
  • $\begingroup$ The aim here is to fix the angle between the each of the carbon atom and the center of mass of the molecule. Could you help me with this? $\endgroup$ May 3 at 7:12

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