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.


[![energy diagram showing energies at x° between -180° and 180° and energies x°+180° obtained from the original energies between -180° and 0° shifted by +180°.](https://i.stack.imgur.com/Rcaum.png)](https://i.stack.imgur.com/Rcaum.png)
[![energy diagram showing nuclear repulsion energies at x° between -180° and 180° and energies x°+180° obtained from the original energies between -180° and 0° shifted by +180°.](https://i.stack.imgur.com/giogn.png)](https://i.stack.imgur.com/giogn.png)



```
%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)


```

