# How to generate accurate displacements along normal modes?

How can i displace my structure along a particular normal mode, without coupling to other modes ? Rather than a exact mathematical procedure, I am more interested in a software/script/package that can help me accomplish it.

For the kind of computations I am doing just displacing along modes in cartesians isn't accurate because modes involving bending and angles lead to bond stretching. For example,the descriptin of rotational mode of methyl group in cartesian cant be used for displacements as it leads to stretching of CH bonds

I have a pseudo-process in my mind. A frequency computation in Gaussian gives me the normal modes in both cartesian displacements and redundant internals. My aim is to displacement along modes in redundant internals and then back-transform to cartesian coordinates. I beleive this should be possible as Gaussain must store the transforming matrixes somewhere( after all, it does this during optimizations), but I have not been able to accomplish this even after rummagging through all iops.

More importantly, I think this kind of task is quite standard (for decades !) and there surely must be an efficient way to do this.

So, If anyone here can advise me or point me towards the right direction.

• Comments are not for extended discussion; this conversation has been moved to chat.
– Tyberius
Commented Apr 13, 2021 at 14:32
• I know I’m late to the party, but what would be the purpose of this? Are you looking to generate a potential energy surface? Because if that’s what you are after, there’s a way to calculate the PES along a normal mode using ORCA (I think it’ll give you the resulting geometries for each point along the coordinate, too) Commented Oct 26, 2023 at 15:30
• If I have understood correctly, you can find the tools here, or in modified fork repo, here.
– Pro
Commented May 29 at 13:19

## 2 Answers

Well, I found a dirty way to do with Gaussian itself. I make the computtaion print the normal modes in redundant internals with IntModes option.

To displace the structure along the normal modes in redundant internals, I use the GIC section and manually specify the values of the redundant internals. Then I submit a pseudo-computaion(hf/sto-3G) to gaussian.

Before doing the computtaion gaussian prints the displaced structure in Cartesians.

I still feel this is quite ugly, and there must be a proper way to accomplish this.

The normal mode direction at the stationary point, i.e. the tangent, is independent on which coordinates are used to perform the vibrational analysis, and Cartesians are here preferred due to simplicity. However, any finite displacement along the normal coordinate depends on the choice of coordinates. Cartesian here leads to the problem that e.g. bond lengths change when moving along a torsional mode normal coordinate. Doing the analysis in internal coordinates, where e.g. the torsional coordinate is one of them, leads to the expected 'pure' rotation. The transformation from internal to Cartesian is iterative and requires the Wilson B-matrix, and it thus slightly non-trivial. And the finite displacements will depend on exactly which set of non-redundant (internal) coordinates that have been chosen. You may find this paper useful: J. Chem. Theory Comp. 7 (2011) 223-230