+1. Welcome to the site and thank you for contributing your question here! We hope to see much more of you in the future !!!

see my answer here, chemistry.stackexchange.com/a/134595/26815

@CodyAldaz My question is slightly different. I don't want to transform the hessian, but rather generate displacements along selected normal modes in internals and get the displaced structure back as cartesian coordinates

right... to convert cartesian hessian to internal coordinate hessian is in the same package, tho.

@vkj Transforming the hessian, and geometry, (same transformation matrix) to internal coordinates and doing displacement along the eigenvectors of the transformed hessian will do the displacements in internal coordinates. It sounds to me though like you actually want to transform your geometry along localized normal modes. Whether or not you use internal coordinates, the normal modes will probably involve movement of many atoms. Localized normal modes are somewhat standard now but not often used. What is your actual application? That would help a lot.

The formula you are looking for to obtain the Cartesian displacements of every atom for a given normal mode can be found in my answer here: mattermodeling.stackexchange.com/questions/1779/… I do not know how to extract this from Gaussian, but as you correctly say, it is not particuarly difficult to code up.

@vkj Do want to displace along a normal mode of an optimized structure ? If yes, then it is immaterial which coordinate system you use. The normal mode displacement vector is a coordinate system independent vector. Only it's coordinate representation changes when you change coordinate systems but it doesn't get more accurate due to this. Could it be, that your optimization was not done at a equilibrium structure ? If you calculate frequencies and modes at a non equilibrium structure you can get unexpected results for the displacement vectors, since the harmonic approximation fails.

@HansWurst I am indeed displacing along normal modes of a an optimized structure. The issue is for an a elementary example, a methyl group rotating normal mode. If I displace along the given normal mode direction printed in cartesians, it will also elongate the Carbon-Hydrogen bond lengths. But in an internal coordinate, this will be just angular rotation. I am facing this for all out of plane bendings, dihedral frequencies etc.

@jheindel I am just trying to compute various properties mainly energies (ground and excited) along various normal modes of ground-state optimized structure. The displacements are upto 3 or 4 in dimensionless units (delta_cartesian * sqrt(reduced_mass) * sqrt(frequency)) . The issues are when we displace by such significant amounts using normal modes in cartesian coordinates along bending or dihedral modes they also lead to stretching of various bonds. I want to displace in internal coords to reduce the error and get the cartesian coordinates of displaced geoms.

@vkj If the elongation is part of the normalmode vector then you must include it. What makes you believe that the rotation and elongation do not belong together ? Normal modes are in general not localized to a bond and include movement of all atoms. Without knowing the molecule and your computational details, i can't decide whether your normal calculation is faulty or if you have perhaps a misunderstanding to what a normal mode is. But having bonds stretching and parts of the molecule looking like they rotate is nothing out of the ordinary for a normal mode.

@HansWurst I have edited the original question with an image that hopefully conveys my question more clearly. I know that the displacements generated using Cartesian directions are erroneous as the energy of the ground state rises much more than expected along that mode precisely because stretchings dump more energy in the displaced structures. These erroneous potential energy surfaces thus also lead to wrong photophysics of the system along these modes.

@vkj The picture is helpful. The motion that you want to describe is not a pure normal mode motion. You would indeed get a mixing of normal coordinates to describe the rotational motion that you indicate in your figure. I am not familiar with normal mode analysis in internal coordinates but if you are interested in a reaction pathway or something akin, you might want to do a relaxed scan along the normal coordinate or apply the nudged elastic band method. A single normal coordinate displacement cannot describe such pathways except in special cases.

@ShoubhikRMaiti Displacing it with gaussview with lead to the second image in the picture, but what i want is third. Again this is just an elementray example. The real molecule will have more complicated breathing, bending and torsional modes

@vkj I see. Yes, then I agree with Hans that you could try a relaxed PES scan by varying the normal coordinate. If that does not work, you may have to write a python script to do what you want.

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