(4 K)$^{b,}$[@Lee11]                     120         25
                 Tight binding (300 K)$^{,}$[@Ryu11]                  $\sim$150   $\sim$17
                                                                         40           7
                                                                         80           6
                DFT, SZP basis set $^{a,}$[@Carter11]                    120          6
                                                                         160          6
                                                                         200          6
                   ordered $^{b,}$[@Carter09]                            40          120
                     random disorder $^{b,}$[@Carter09]                  40       $\sim$70
                     $[110]$ direction alignment $^{b,}$[@Carter11]      40       $\sim$270
       DFT, SZP: dimers $^{b,}$[@Carter11]                               40       $\sim$85
                     random disorder $^{b,}$[@Carter11]                  40       $\sim$80
                   clusters $^{b,}$[@Carter11]                           40       $\sim$65
                     $[100]$ direction alignment $^{b,}$[@Carter11]      40       $\sim$50
                ordered, $M$=4$^{b,}$[^3]$^{,}$[@Carter11]               80          153
      DFT, SZP: ordered, $M$=6$^{b,}$$^{,}$[@Carter11]                   80          147
                   ordered, $M$=10$^{b,}$$^{,}$[@Carter11]               80          147
                                                                         40         145.1
                                                                         60         144.7
                   SZP, $M$=9 (this work)$^{b,c,}$                       80         144.8
                                                                         120        144.7
                                                                         160        144.7
                                                                         200        144.7
                                                                         16         118.6
                                                                         32         94.1
                   PW, $M$=9 (this work)$^{b,}$[^4]                      40         93.5
                                                                         60         93.3
                                                                         80         93.2
                                                                         40          100
                                                                         60         99.5
                    DZP, $M$=9 (this work)$^{b,c}$                       80         99.5
                                                                         120        99.3
                                                                         160        99.6
  ------------------------------------------------------------------ ----------- -----------

  : Valley splitting values of 1/4 ML P-doped silicon obtained using different techniques. Techniques are grouped by similarity.[]{data-label="tab:valley"}

Our results show that valley splitting is highly sensitive to the choice of basis set. Due to the nature of PW basis set, it is straightforward to improve its completeness by increasing the plane wave cutoff energy. In this way, we establish the most accurate valley splitting value within the context of density functional theory. Using this benchmark value, we 