In Gaussian (or rather, as displayed in the output/log file) what are my "Internal coordinates" called? Are they expressed as cartesian coordinates or as a z-matrix? I only notice "Standard orientation" and "Input orientation".
I'm not 100% sure about it, but if I remember correctly gaussian will always give you xyz coordinates (after each optimization step) dubbed as Standard Orientation. It will also give You z-matrix (after each optimization step) dubbed as Z-MATRIX, but only if you use opt(z-matrix).
Mind, however, that if you use simple opt, the optimization will be performed in redundant internal coordinates, a set of internally consistent, linearly maximally independent internal coordinates. These are chosen by gaussian in an automatic way (though you can influence it by using opt(addredundant) or opt(modredundant)) and are listed under Initial Parameters.
Thank you for that comment, Bartosz. It has certainly cleared up some confusion.
By any chance, do you know how to ask Gaussian to output the final internal coordinates and not only the standard orientation? I am trying to take the dot product between a unit vector of the internal coordinates of a displaced atom (from vibrational frequency calculations) with an eigen vector the the Hessian matching the displaced atom with an atom of interest (one that feels the force for the displacement).
Internal Coordinates in Guassian are of two types: XYZ and Z-Mat.
XYZ cordinates are the distance to origin of X, Y and Z axes, the most heavy atom preferably at the origin. A small change in XYZ coordinate will heavily change the potential energy, hence Z-Mat is used in Guassian for calculation.
Z mat is the bond length, bond angle and dihedral angle of the molecule. It is named Z mat as the first atom is taken at origin and the bond length is calculated to the second angle along the Z axis.
There are also internal redundant coordinates, which are the lengths of atoms which are not linked to each other. they are useful in ring systems. It has been proved that calculations are faster with the useof redundant coordinates.