# relaxed dihedral PES scan: symmetry of the system not reflected

Using G16 and performing a relaxed PES scan on a dihedral angle, I performed 72 steps where one phenyl group of a symmetric terphenyl is rotated about the C(aryl)-C(phenyl) bond by 5° in every step. I'm using the BP86 functional with the 6-31G basis set. I observe that -180° to 0° will not be the same as 0° to +180°.

In my opinion, rotation of a phenyl group (with a mirror plane which would be perpendicular to the C6 axis in benzene) should result in energies at x° being the exact same as for x°+180°. In the first graphics below, you can see one whole rotation (black dots, scan points 1 to 73) and the scan points 38 to 73 shifted by +180° (red dots). You can see that there is a shift on the abscissa, meaning that the first 180° of rotation about the aryl-phenyl bond are not the same as the second 180°. Interestingly, when rotating more than 360° (3-5 times 360°), the dots will be at the exact same position as 360° earlier - so x° and x°+360° will be the same in every case, while x° and x°+180° are not. Don't think that this is an issue related to convergence?

edit: @TAR86 suggested to have a look at the nuclear repulsion energies to check whether this is an issue related to the geometries produced. The respective image is added below.

edit2: @Martin - マーチン♦ requested an G16 input file to reproduce the problem. I've added the respective file below.

%chk=job.chk
%mem=8gb
%NProcShared=16
#p opt=(modredundant) BP86/6-31G geom=(gic)

dihedral pes scan

0 1
6        5.226229852      2.461878014      0.364189364
6        6.517648681      1.947188819      0.628146249
1        7.127277746      2.400165503      1.416350388
6        7.024836811      0.874189127     -0.119447737
6        6.252002950      0.287970075     -1.134646502
1        6.649922190     -0.550963401     -1.716497030
6        4.963870485      0.783187734     -1.399800460
6        4.455606763      1.856498426     -0.656174766
1        3.460115638      2.254235558     -0.885310716
1        8.028604788      0.493012088      0.098455632
1        4.355515157      0.336549951     -2.194552005
6        5.437910365      4.695855989      1.613350721
6        4.667674122      3.560511364      1.202847170
6        3.339228627      3.414455715      1.655493257
1        2.762287260      2.537249136      1.343693331
6        2.778852196      4.366478962      2.509604334
1        1.728615174      4.291477665      2.812827707
6        3.587531970      5.372572404      3.043834082
1        3.154198853      6.017546127      3.811431515
6        4.962035000      5.490387000      2.719069000
6        5.793408000      6.483337000      3.479780000
6        7.155794401      6.716767843      3.150348234
1        7.690505145      6.040409950      2.477397785
6        7.891233889      7.760301086      3.724625384
6        7.281499938      8.654025495      4.618188277
1        7.854319283      9.475639651      5.062586031
6        5.919284422      8.491819231      4.906055341
6        5.183645944      7.448680994      4.325851576
1        4.106339318      7.414359241      4.527417701
1        8.948095638      7.878562451      3.459649110
1        5.404779334      9.198550838      5.566858766
15       6.836613173      5.254444911      0.492426546
6        6.402468333      4.749060218     -1.232735776
1        5.331395678      4.884562656     -1.457090749
1        6.692781337      3.708789948     -1.428936030
1        6.992612351      5.408972053     -1.892849893
6        6.570730658      7.079097928      0.321764243
1        5.553588175      7.291894513     -0.050476225
1        7.307098080      7.438494888     -0.417840357
1        6.732539811      7.615443003      1.266231462
8        8.252395391      4.848887467      0.884390392

interplanar=Dihedral(22,21,20,12)
interplanar(NSteps=72, StepSize=5.00000)

• Could be a guess issue or something about the geometries. To detect the latter, examine the same plot based on nuclear repulsion energies. – TAR86 Mar 10 at 19:51
• @TAR86: I've added a plot showing the respective nuclear repulsion energies. The geometries are of x°+180° are not the exact same - which I don't understand. – user18258 Mar 11 at 10:26
• Relaxed PES scan should mean that some geometry optimization takes place before the evaluation of the final, plotted energy, right? There's all sorts of issues that can arise during that optimization and small differences in the input can be amplified. – TAR86 Mar 11 at 12:08
• This could very well be an issue due to the internal definition of the redundant coordinates; I'm not sure how Gaussian constructs them and if they are truly equivalent at these points. Could you add the input file, which you use to generate the energies, so that one could try to reproduce the problem. – Martin - マーチン Mar 11 at 21:07
• I've added the G16 input file above. – user18258 Mar 12 at 7:56