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How can one twist phenanthroline ligands in Cu(phen)2+ during PES scan?


Dear colleagues,
I'd like to find a solution for the following problem.
Say, we have a cationic complex of copper(I) chelated with two molecules of 1,10-phenanthroline (let name ligand just "phen"), with tetrahedral arrangement of nitrogens. This complex has S4 symmetry if one phen is perpendicular to the other, with axis going through the middle of C5-C6 bond and the middle of C1'-C10' bond of the first phen ligand, through copper atom and through the middle of C5-C6 bond and the middle of C1'-C10' bond of the second phen ligand. If we twist the complex along this axis, its symmetry will change to C2, and if we deflect one ligand by rotating it along axis through its nitrogen atoms, the symmetry wil be Cs.

The task it to explore PES of a series of bis(phenanthroline)copper(I) complexes with respect to this two distortions (apart) with varying substituent at 2 and/or 9 position(s) (ortho- to nitrogen atoms) of phen.
In other words, examine how rigidity of [Cu(phen)2]+ and its analogues depends on bulkiness of its ligands.

The problem is to describe these distortions for PES scan. There appear no atoms in positions which allow definition these distortions through bond angle or dihedral angle in general. Probably, one may describe twisting of the parent [Cu(phen)2]+ complex through, say, C5(1)-C6(1)-C6(2)-C5(2) (numbers in parentheses to describe first or second ligand) dihedral angle under C2-symmetry constraint, but this is just partial solution. First, this variable is close but not equal to the angle between two phen-planes, thus making somewhat questionable plotting energy vs this angle, say, for publication purpose. Second, this solution is not useful for substituted ligand since presence of substituent(s) may break C2-symmetry. Thus exploring a series of complexes is troublesome.

The use of higher-order (beyond dihedral angle) internal coordinates would solve the the problem. Unfortunately, they are not implemented in Firefly_8.2.0 ( ) despite they were considered for implementation more than a year ago. ( )

Very similar problem arises if one considers twisting of Cp rings in (substituted) ferrocene or for related systems like (C6H6)Cr(CO)3 and so on.

So, I will be grateful for any hint for solution based on current capabilities of Firefly code. Putting a ghost atom exactly in the middle of bond?
Next, I'd like to inspire and encourage Firefly team to add a possibility of operating higher-order internal coordinates. The above problem shows that there are very simple and natural tasks, nothing exotic, where they would be useful.

Thanks in advance.

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