micb25/rhOver

Random rotation of numerical grid adds noise in LF parameters

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The LFT part of rhOver adds numerical noise in case of a random rotation of the spherical Lebedev grids. This might be an issue for the higher rank (k = 4, 6) LFT parameters.

Grid 5 (with random rotation of the grid shells):

                        ------------------------------------------------------
                              k     q         A(k,q) / 1/cm       B(k,q) / 1/cm
                         ------------------------------------------------------
                              2    -2           -0.00324087      0.15813912E-04
                              2    -1            0.01623451     -0.79216700E-04
                              2     0         1395.12357557     -0.68075417E+01
                              2     1            0.75790389     -0.36982117E-02
                              2     2           -0.00489221      0.23871677E-04

                              4    -4            0.00202093     -0.17293780E-06
                              4    -3           -0.00065224      0.55813939E-07
                              4    -2           -0.00017142      0.14668831E-07
                              4    -1            0.01516587     -0.12977938E-05
                              4     0           26.69748848     -0.22845931E-02
                              4     1            0.59718395     -0.51103023E-04
                              4     2           -0.01164975      0.99690756E-06
                              4     3            0.00547354     -0.46838912E-06
                              4     4            0.00021365     -0.18282938E-07

                              6    -6           -0.00010462     -0.64103404E-09
                              6    -5            0.00288200      0.17658878E-07
                              6    -4           -0.00064805     -0.39707790E-08
                              6    -3           -0.00064955     -0.39799703E-08
                              6    -2            0.00073634      0.45117956E-08
                              6    -1            0.00538210      0.32977754E-07
                              6     0           -5.00915980     -0.30692637E-04
                              6     1            0.22004635      0.13482906E-05
                              6     2           -0.00487459     -0.29868070E-07
                              6     3            0.00175588      0.10758828E-07
                              6     4            0.00138185      0.84670285E-08
                              6     5            0.00045367      0.27797748E-08
                              6     6           -0.00000642     -0.39342856E-10
                         ------------------------------------------------------

Grid 5 + 'NoRandomRot':

                         ------------------------------------------------------
                              k     q         A(k,q) / 1/cm       B(k,q) / 1/cm
                         ------------------------------------------------------
                              2    -2           -0.00000000      0.20212125E-12
                              2    -1            0.00000000     -0.27705577E-13
                              2     0         1397.58435922     -0.68195491E+01
                              2     1            0.00000000     -0.32305824E-13
                              2     2           -0.00000001      0.26671850E-10

                              4    -4           -0.00000000      0.34183520E-14
                              4    -3            0.00000000     -0.49125719E-17
                              4    -2           -0.00000000      0.14146704E-14
                              4    -1            0.00000000     -0.54217029E-18
                              4     0           27.29701830     -0.23358969E-02
                              4     1           -0.00000000      0.42669259E-15
                              4     2           -0.00000000      0.89570968E-13
                              4     3           -0.00000000      0.41699498E-14
                              4     4            0.00369215     -0.31594990E-06

                              6    -6           -0.00000000     -0.88647347E-16
                              6    -5            0.00000000      0.15680617E-16
                              6    -4           -0.00000000     -0.45474788E-16
                              6    -3            0.00000000      0.58197668E-17
                              6    -2           -0.00000000     -0.12704705E-16
                              6    -1            0.00000000      0.51398134E-17
                              6     0           -4.90096227     -0.30029678E-04
                              6     1           -0.00000000     -0.52803393E-17
                              6     2            0.00000000      0.15749990E-15
                              6     3            0.00000000      0.62667197E-17
                              6     4           -0.00115062     -0.70501987E-08
                              6     5           -0.00000000     -0.74783583E-16
                              6     6            0.00000000      0.44937173E-15
                         ------------------------------------------------------

Known workaround:
Usage of 'NoRandomRot:'