<table><caption>**Table A5.** B3LYP set of optimized S222 cell parameters per SIC. As in Table A3, SICs are ordered by increasing energy and labelled (L<sub>SIC</sub>). In a given SIC, the parameters can permute depending on the considered configuration.</caption><thead><tr><th>L<sub>SIC</sub></th><th>CEC</th><th>a</th><th>b</th><th>c</th><th>L<sub>SIC</sub></th><th>CEC</th><th>a</th><th>b</th><th>c</th><th>L<sub>SIC</sub></th><th>CEC</th><th>a</th><th>b</th><th>c</th></tr></thead><tbody><tr><td>1</td><td>(0,4,4)</td><td>8.4343</td><td>8.3081</td><td>8.3082</td><td>55</td><td>(2,3,3)</td><td>8.3685</td><td>8.3375</td><td>8.3386</td><td>109</td><td>(2,2,4)</td><td>8.3671</td><td>8.3707</td><td>8.3058</td></tr><tr><td>2</td><td>(0,4,4)</td><td>8.4398</td><td>8.3068</td><td>8.3068</td><td>56</td><td>(1,3,4)</td><td>8.4003</td><td>8.3417</td><td>8.3051</td><td>110</td><td>(1,2,5)</td><td>8.3990</td><td>8.3700</td><td>8.2780</td></tr><tr><td>3</td><td>(2,2,4)</td><td>8.3710</td><td>8.3710</td><td>8.3079</td><td>57</td><td>(2,3,3)</td><td>8.3677</td><td>8.3382</td><td>8.3419</td><td>111</td><td>(0,1,7)</td><td>8.4320</td><td>8.4000</td><td>8.2170</td></tr><tr><td>4</td><td>(1,3,4)</td><td>8.4020</td><td>8.3391</td><td>8.3083</td><td>58</td><td>(1,3,4)</td><td>8.4024</td><td>8.3379</td><td>8.3070</td><td>112</td><td>(1,2,5)</td><td>8.4000</td><td>8.3680</td><td>8.2770</td></tr><tr><td>5</td><td>(1,3,4)</td><td>8.4067</td><td>8.3383</td><td>8.3067</td><td>59</td><td>(2,2,4)</td><td>8.3710</td><td>8.3714</td><td>8.3063</td><td>113</td><td>(1,2,5)</td><td>8.4010</td><td>8.3670</td><td>8.2780</td></tr><tr><td>6</td><td>(2,2,4)</td><td>8.3702</td><td>8.3701</td><td>8.3083</td><td>60</td><td>(2,3,3)</td><td>8.3697</td><td>8.3360</td><td>8.3418</td><td>114</td><td>(0,3,5)</td><td>8.4340</td><td>8.3390</td><td>8.2740</td></tr><tr><td>7</td><td>(2,3,3)</td><td>8.3708</td><td>8.3407</td><td>8.3385</td><td>61</td><td>(1,3,4)</td><td>8.4013</td><td>8.3379</td><td>8.3088</td><td>115</td><td>(2,3,3)</td><td>8.3684</td><td>8.3406</td><td>8.3356</td></tr><tr><td>8</td><td>(2,3,3)</td><td>8.3700</td><td>8.3392</td><td>8.3392</td><td>62</td><td>(2,3,3)</td><td>8.3688</td><td>8.3405</td><td>8.3366</td><td>116</td><td>(1,3,4)</td><td>8.4012</td><td>8.3384</td><td>8.3057</td></tr><tr><td>9</td><td>(2,3,3)</td><td>8.3738</td><td>8.3383</td><td>8.3385</td><td>63</td><td>(1,3,4)</td><td>8.4016</td><td>8.3377</td><td>8.3087</td><td>117</td><td>(0,3,5)</td><td>8.4340</td><td>8.3360</td><td>8.2770</td></tr><tr><td>10</td><td>(1,3,4)</td><td>8.4033</td><td>8.3406</td><td>8.3069</td><td>64</td><td>(2,3,3)</td><td>8.3681</td><td>8.3390</td><td>8.3383</td><td>118</td><td>(1,2,5)</td><td>8.4010</td><td>8.3680</td><td>8.2760</td></tr><tr><td>11</td><td>(1,3,4)</td><td>8.4048</td><td>8.3395</td><td>8.3070</td><td>65</td><td>(2,3,3)</td><td>8.3697</td><td>8.3383</td><td>8.3381</td><td>119</td><td>(2,2,4)</td><td>8.3682</td><td>8.3696</td><td>8.3064</td></tr><tr><td>12</td><td>(2,2,4)</td><td>8.3707</td><td>8.3732</td><td>8.3067</td><td>66</td><td>(1,3,4)</td><td>8.4026</td><td>8.3378</td><td>8.3081</td><td>120</td><td>(2,2,4)</td><td>8.3694</td><td>8.3726</td><td>8.3043</td></tr><tr><td>13</td><td>(2,3,3)</td><td>8.3697</td><td>8.3390</td><td>8.3406</td><td>67</td><td>(1,3,4)</td><td>8.4009</td><td>8.3396</td><td>8.3052</td><td>121</td><td>(2,2,4)</td><td>8.3662</td><td>8.3701</td><td>8.3080</td></tr><tr><td>14</td><td>(2,2,4)</td><td>8.3719</td><td>8.3716</td><td>8.3071</td><td>68</td><td>(2,2,4)</td><td>8.3685</td><td>8.3694</td><td>8.3074</td><td>122</td><td>(1,3,4)</td><td>8.3993</td><td>8.3382</td><td>8.3079</td></tr><tr><td>15</td><td>(2,2,4)</td><td>8.3705</td><td>8.3730</td><td>8.3069</td><td>69</td><td>(1,2,5)</td><td>8.4040</td><td>8.3700</td><td>8.2760</td><td>123</td><td>(2,3,3)</td><td>8.3712</td><td>8.3371</td><td>8.3371</td></tr><tr><td>16</td><td>(2,2,4)</td><td>8.3733</td><td>8.3710</td><td>8.3069</td><td>70</td><td>(2,3,3)</td><td>8.3713</td><td>8.3395</td><td>8.3362</td><td>124</td><td>(0,4,4)</td><td>8.4300</td><td>8.3034</td><td>8.3108</td></tr><tr><td>17</td><td>(2,3,3)</td><td>8.3717</td><td>8.3383</td><td>8.3399</td><td>71</td><td>(2,3,3)</td><td>8.3696</td><td>8.3386</td><td>8.3366</td><td>125</td><td>(2,3,3)</td><td>8.3719</td><td>8.3371</td><td>8.3349</td></tr><tr><td>18</td><td>(2,3,3)</td><td>8.3704</td><td>8.3399</td><td>8.3399</td><td>72</td><td>(2,2,4)</td><td>8.3696</td><td>8.3696</td><td>8.3069</td><td>126</td><td>(1,3,4)</td><td>8.3997</td><td>8.3387</td><td>8.3056</td></tr><tr><td>19</td><td>(2,3,3)</td><td>8.3728</td><td>8.3380</td><td>8.3399</td><td>73</td><td>(1,1,6)</td><td>8.4010</td><td>8.4010</td><td>8.2460</td><td>127</td><td>(2,3,3)</td><td>8.3661</td><td>8.3390</td><td>8.3390</td></tr><tr><td>20</td><td>(2,3,3)</td><td>8.3717</td><td>8.3391</td><td>8.3380</td><td>74</td><td>(1,3,4)</td><td>8.4022</td><td>8.3360</td><td>8.3084</td><td>128</td><td>(1,2,5)</td><td>8.4000</td><td>8.3680</td><td>8.2770</td></tr><tr><td>21</td><td>(2,3,3)</td><td>8.3714</td><td>8.3406</td><td>8.3379</td><td>75</td><td>(2,2,4)</td><td>8.3697</td><td>8.3701</td><td>8.3064</td><td>129</td><td>(2,3,3)</td><td>8.3679</td><td>8.3364</td><td>8.3406</td></tr><tr><td>22</td><td>(0,3,5)</td><td>8.4340</td><td>8.3390</td><td>8.2760</td><td>76</td><td>(2,2,4)</td><td>8.3695</td><td>8.3708</td><td>8.3052</td><td>130</td><td>(1,3,4)</td><td>8.4011</td><td>8.3380</td><td>8.3054</td></tr><tr><td>23</td><td>(2,3,3)</td><td>8.3718</td><td>8.3394</td><td>8.3395</td><td>77</td><td>(0,2,6)</td><td>8.4328</td><td>8.3692</td><td>8.2463</td><td>131</td><td>(1,3,4)</td><td>8.3990</td><td>8.3383</td><td>8.3075</td></tr><tr><td>24</td><td>(0,3,5)</td><td>8.4370</td><td>8.3380</td><td>8.2760</td><td>78</td><td>(2,2,4)</td><td>8.3695</td><td>8.3674</td><td>8.3087</td><td>132</td><td>(1,3,4)</td><td>8.4010</td><td>8.3384</td><td>8.3053</td></tr><tr><td>25</td><td>(1,2,5)</td><td>8.4020</td><td>8.3700</td><td>8.2770</td><td>79</td><td>(0,2,6)</td><td>8.4335</td><td>8.3689</td><td>8.2456</td><td>133</td><td>(0,4,4)</td><td>8.4324</td><td>8.3066</td><td>8.3067</td></tr><tr><td>26</td><td>(1,2,5)</td><td>8.4020</td><td>8.3700</td><td>8.2770</td><td>80</td><td>(2,2,4)</td><td>8.3690</td><td>8.3711</td><td>8.3065</td><td>134</td><td>(2,2,4)</td><td>8.3654</td><td>8.3695</td><td>8.3111</td></tr><tr><td>27</td><td>(2,2,4)</td><td>8.3707</td><td>8.3706</td><td>8.3075</td><td>81</td><td>(0,2,6)</td><td>8.4327</td><td>8.3692</td><td>8.2461</td><td>135</td><td>(1,3,4)</td><td>8.3980</td><td>8.3386</td><td>8.3059</td></tr><tr><td>28</td><td>(2,2,4)</td><td>8.3727</td><td>8.3727</td><td>8.3063</td><td>82</td><td>(2,2,4)</td><td>8.3709</td><td>8.3691</td><td>8.3067</td><td>136</td><td>(2,3,3)</td><td>8.3686</td><td>8.3367</td><td>8.3371</td></tr><tr><td>29</td><td>(1,2,5)</td><td>8.4030</td><td>8.3700</td><td>8.2760</td><td>83</td><td>(1,3,4)</td><td>8.4020</td><td>8.3374</td><td>8.3085</td><td>137</td><td>(1,2,5)</td><td>8.4000</td><td>8.3680</td><td>8.2780</td></tr><tr><td>30</td><td>(0,4,4)</td><td>8.4347</td><td>8.3053</td><td>8.3088</td><td>84</td><td>(2,3,3)</td><td>8.3677</td><td>8.3396</td><td>8.3379</td><td>138</td><td>(1,2,5)</td><td>8.4010</td><td>8.3710</td><td>8.2740</td></tr><tr><td>31</td><td>(1,2,5)</td><td>8.4030</td><td>8.3700</td><td>8.2760</td><td>85</td><td>(1,1,6)</td><td>8.4010</td><td>8.4010</td><td>8.2460</td><td>139</td><td>(2,2,4)</td><td>8.3668</td><td>8.3669</td><td>8.3076</td></tr><tr><td>32</td><td>(1,3,4)</td><td>8.4017</td><td>8.3373</td><td>8.3077</td><td>86</td><td>(2,3,3)</td><td>8.3707</td><td>8.3396</td><td>8.3360</td><td>140</td><td>(1,3,4)</td><td>8.4024</td><td>8.3342</td><td>8.3087</td></tr><tr><td>33</td><td>(2,3,3)</td><td>8.3705</td><td>8.3373</td><td>8.3391</td><td>87</td><td>(2,3,3)</td><td>8.3722</td><td>8.3375</td><td>8.3362</td><td>141</td><td>(0,0,8)</td><td><b>8.4315</b></td><td><b>8.4315</b></td><td><b>8.1876</b></td></tr><tr><td>34</td><td>(1,2,5)</td><td>8.4020</td><td>8.3710</td><td>8.2760</td><td>88</td><td>(2,2,4)</td><td>8.3689</td><td>8.3706</td><td>8.3079</td><td>142</td><td>(0,4,4)</td><td>8.4346</td><td>8.3027</td><td>8.3096</td></tr><tr><td>35</td><td>(1,3,4)</td><td>8.4034</td><td>8.3383</td><td>8.3072</td><td>89</td><td>(0,2,6)</td><td>8.4353</td><td>8.3687</td><td>8.2456</td><td>143</td><td>(2,2,4)</td><td>8.3679</td><td>8.3700</td><td>8.3052</td></tr><tr><td>36</td><td>(1,3,4)</td><td>8.4000</td><td>8.3391</td><td>8.3075</td><td>90</td><td>(1,1,6)</td><td>8.4010</td><td>8.4020</td><td>8.2460</td><td>144</td><td>(2,3,3)</td><td>8.3683</td><td>8.3387</td><td>8.3349</td></tr><tr><td>37</td><td>(1,3,4)</td><td>8.4032</td><td>8.3366</td><td>8.3076</td><td>91</td><td>(2,3,3)</td><td>8.3684</td><td>8.3397</td><td>8.3361</td><td>145</td><td>(1,3,4)</td><td>8.3979</td><td>8.3347</td><td>8.3092</td></tr><tr><td>38</td><td>(1,2,5)</td><td>8.4040</td><td>8.3700</td><td>8.2750</td><td>92</td><td>(1,2,5)</td><td>8.4000</td><td>8.3700</td><td>8.2770</td><td>146</td><td>(2,3,3)</td><td>8.3661</td><td>8.3364</td><td>8.3403</td></tr><tr><td>39</td><td>(1,3,4)</td><td>8.4013</td><td>8.3388</td><td>8.3076</td><td>93</td><td>(1,3,4)</td><td>8.4018</td><td>8.3373</td><td>8.3079</td><td>147</td><td>(2,2,4)</td><td>8.3689</td><td>8.3675</td><td>8.3073</td></tr><tr><td>40</td><td>(2,2,4)</td><td>8.3682</td><td>8.3707</td><td>8.3075</td><td>94</td><td>(2,3,3)</td><td>8.3704</td><td>8.3390</td><td>8.3375</td><td>148</td><td>(0,2,6)</td><td>8.4307</td><td>8.3706</td><td>8.2448</td></tr><tr><td>41</td><td>(1,2,5)</td><td>8.4010</td><td>8.3700</td><td>8.2760</td><td>95</td><td>(2,3,3)</td><td>8.3684</td><td>8.3409</td><td>8.3376</td><td>149</td><td>(1,3,4)</td><td>8.3992</td><td>8.3378</td><td>8.3055</td></tr><tr><td>42</td><td>(1,3,4)</td><td>8.4003</td><td>8.3383</td><td>8.3093</td><td>96</td><td>(0,4,4)</td><td>8.4302</td><td>8.3077</td><td>8.3078</td><td>150</td><td>(1,1,6)</td><td>8.3990</td><td>8.3990</td><td>8.2470</td></tr><tr><td>43</td><td>(2,3,3)</td><td>8.3701</td><td>8.3375</td><td>8.3375</td><td>97</td><td>(1,1,6)</td><td>8.4000</td><td>8.4000</td><td>8.2460</td><td>151</td><td>(0,2,6)</td><td>8.4306</td><td>8.3673</td><td>8.2484</td></tr><tr><td>44</td><td>(1,3,4)</td><td>8.4019</td><td>8.3364</td><td>8.3092</td><td>98</td><td>(1,3,4)</td><td>8.4031</td><td>8.3402</td><td>8.3044</td><td>152</td><td>(0,3,5)</td><td>8.4300</td><td>8.3390</td><td>8.2770</td></tr><tr><td>45</td><td>(2,2,4)</td><td>8.3685</td><td>8.3696</td><td>8.3096</td><td>99</td><td>(2,3,3)</td><td>8.3709</td><td>8.3391</td><td>8.3356</td><td>153</td><td>(2,2,4)</td><td>8.3662</td><td>8.3662</td><td>8.3077</td></tr><tr><td>46</td><td>(2,2,4)</td><td>8.3681</td><td>8.3721</td><td>8.3069</td><td>100</td><td>(0,4,4)</td><td>8.4327</td><td>8.3072</td><td>8.3071</td><td>154</td><td>(2,3,3)</td><td>8.3662</td><td>8.3369</td><td>8.3369</td></tr><tr><td>47</td><td>(2,2,4)</td><td>8.3697</td><td>8.3705</td><td>8.3074</td><td>101</td><td>(0,4,4)</td><td>8.4325</td><td>8.3072</td><td>8.3073</td><td>155</td><td>(2,2,4)</td><td>8.3655</td><td>8.3655</td><td>8.3106</td></tr><tr><td>48</td><td>(1,3,4)</td><td>8.4032</td><td>8.3398</td><td>8.3052</td><td>102</td><td>(0,3,5)</td><td>8.4320</td><td>8.3360</td><td>8.2780</td><td>156</td><td>(1,2,5)</td><td>8.3980</td><td>8.3700</td><td>8.2750</td></tr><tr><td>49</td><td>(1,2,5)</td><td>8.4010</td><td>8.3720</td><td>8.2760</td><td>103</td><td>(0,3,5)</td><td>8.4320</td><td>8.3400</td><td>8.2740</td><td>157</td><td>(1,3,4)</td><td>8.3961</td><td>8.3392</td><td>8.3083</td></tr><tr><td>50</td><td>(0,2,6)</td><td>8.4337</td><td>8.3699</td><td>8.2461</td><td>104</td><td>(1,3,4)</td><td>8.4000</td><td>8.3387</td><td>8.3077</td><td>158</td><td>(2,2,4)</td><td>8.3685</td><td>8.3685</td><td>8.3045</td></tr><tr><td>51</td><td>(2,2,4)</td><td>8.3695</td><td>8.3696</td><td>8.3090</td><td>105</td><td>(1,2,5)</td><td>8.4000</td><td>8.3710</td><td>8.2750</td><td>159</td><td>(2,2,4)</td><td>8.3643</td><td>8.3719</td><td>8.3061</td></tr><tr><td>52</td><td>(2,2,4)</td><td>8.3683</td><td>8.3748</td><td>8.3047</td><td>106</td><td>(1,2,5)</td><td>8.4030</td><td>8.3680</td><td>8.2760</td><td>160</td><td>(2,3,3)</td><td>8.3705</td><td>8.3354</td><td>8.3354</td></tr><tr><td>53</td><td>(1,2,5)</td><td>8.4030</td><td>8.3710</td><td>8.2760</td><td>107</td><td>(2,3,3)</td><td>8.3666</td><td>8.3391</td><td>8.3393</td><td>161</td><td>(2,3,3)</td><td>8.3663</td><td>8.3375</td><td>8.3375</td></tr><tr><td>54</td><td>(2,2,4)</td><td>8.3699</td><td>8.3694</td><td>8.3091</td><td>108</td><td>(1,3,4)</td><td>8.3980</td><td>8.3388</td><td>8.3081</td><td>162</td><td>(0,4,4)</td><td>8.4261</td><td>8.3087</td><td>8.3087</td></tr></tbody></table>
<table><caption>**Table A5.** B3LYP set of optimized S222 cell parameters per SIC. As in Table A3, SICs are ordered by increasing energy and labelled (L<sub>SIC</sub>). In a given SIC, the parameters can permute depending on the considered configuration.</caption><thead><tr><th>L<sub>SIC</sub></th><th>CEC</th><th>a</th><th>b</th><th>c</th><th>L<sub>SIC</sub></th><th>CEC</th><th>a</th><th>b</th><th>c</th><th>L<sub>SIC</sub></th><th>CEC</th><th>a</th><th>b</th><th>c</th></tr></thead><tbody><tr><td>1</td><td>(0,4,4)</td><td>8.4343</td><td>8.3081</td><td>8.3082</td><td>55</td><td>(2,3,3)</td><td>8.3685</td><td>8.3375</td><td>8.3386</td><td>109</td><td>(2,2,4)</td><td>8.3671</td><td>8.3707</td><td>8.3058</td></tr><tr><td>2</td><td>(0,4,4)</td><td>8.4398</td><td>8.3068</td><td>8.3068</td><td>56</td><td>(1,3,4)</td><td>8.4003</td><td>8.3417</td><td>8.3051</td><td>110</td><td>(1,2,5)</td><td>8.3990</td><td>8.3700</td><td>8.2780</td></tr><tr><td>3</td><td>(2,2,4)</td><td>8.3710</td><td>8.3710</td><td>8.3079</td><td>57</td><td>(2,3,3)</td><td>8.3677</td><td>8.3382</td><td>8.3419</td><td>111</td><td>(0,1,7)</td><td>8.4320</td><td>8.4000</td><td>8.2170</td></tr><tr><td>4</td><td>(1,3,4)</td><td>8.4020</td><td>8.3391</td><td>8.3083</td><td>58</td><td>(1,3,4)</td><td>8.4024</td><td>8.3379</td><td>8.3070</td><td>112</td><td>(1,2,5)</td><td>8.4000</td><td>8.3680</td><td>8.2770</td></tr><tr><td>5</td><td>(1,3,4)</td><td>8.4067</td><td>8.3383</td><td>8.3067</td><td>59</td><td>(2,2,4)</td><td>8.3710</td><td>8.3714</td><td>8.3063</td><td>113</td><td>(1,2,5)</td><td>8.4010</td><td>8.3670</td><td>8.2780</td></tr><tr><td>6</td><td>(2,2,4)</td><td>8.3702</td><td>8.3701</td><td>8.3083</td><td>60</td><td>(2,3,3)</td><td>8.3697</td><td>8.3360</td><td>8.3418</td><td>114</td><td>(0,3,5)</td><td>8.4340</td><td>8.3390</td><td>8.2740</td></tr><tr><td>7</td><td>(2,3,3)</td><td>8.3708</td><td>8.3407</td><td>8.3385</td><td>61</td><td>(1,3,4)</td><td>8.4013</td><td>8.3379</td><td>8.3088</td><td>115</td><td>(2,3,3)</td><td>8.3684</td><td>8.3406</td><td>8.3356</td></tr><tr><td>8</td><td>(2,3,3)</td><td>8.3700</td><td>8.3392</td><td>8.3392</td><td>62</td><td>(2,3,3)</td><td>8.3688</td><td>8.3405</td><td>8.3366</td><td>116</td><td>(1,3,4)</td><td>8.4012</td><td>8.3384</td><td>8.3057</td></tr><tr><td>9</td><td>(2,3,3)</td><td>8.3738</td><td>8.3383</td><td>8.3385</td><td>63</td><td>(1,3,4)</td><td>8.4016</td><td>8.3377</td><td>8.3087</td><td>117</td><td>(0,3,5)</td><td>8.4340</td><td>8.3360</td><td>8.2770</td></tr><tr><td>10</td><td>(1,3,4)</td><td>8.4033</td><td>8.3406</td><td>8.3069</td><td>64</td><td>(2,3,3)</td><td>8.3681</td><td>8.3390</td><td>8.3383</td><td>118</td><td>(1,2,5)</td><td>8.4010</td><td>8.3680</td><td>8.2760</td></tr><tr><td>11</td><td>(1,3,4)</td><td>8.4048</td><td>8.3395</td><td>8.3070</td><td>65</td><td>(2,3,3)</td><td>8.3697</td><td>8.3383</td><td>8.3381</td><td>119</td><td>(2,2,4)</td><td>8.3682</td><td>8.3696</td><td>8.3064</td></tr><tr><td>12</td><td>(2,2,4)</td><td>8.3707</td><td>8.3732</td><td>8.3067</td><td>66</td><td>(1,3,4)</td><td>8.4026</td><td>8.3378</td><td>8.3081</td><td>120</td><td>(2,2,4)</td><td>8.3694</td><td>8.3726</td><td>8.3043</td></tr><tr><td>13</td><td>(2,3,3)</td><td>8.3697</td><td>8.3390</td><td>8.3406</td><td>67</td><td>(1,3,4)</td><td>8.4009</td><td>8.3396</td><td>8.3052</td><td>121</td><td>(2,2,4)</td><td>8.3662</td><td>8.3701</td><td>8.3080</td></tr><tr><td>14</td><td>(2,2,4)</td><td>8.3719</td><td>8.3716</td><td>8.3071</td><td>68</td><td>(2,2,4)</td><td>8.3685</td><td>8.3694</td><td>8.3074</td><td>122</td><td>(1,3,4)</td><td>8.3993</td><td>8.3382</td><td>8.3079</td></tr><tr><td>15</td><td>(2,2,4)</td><td>8.3705</td><td>8.3730</td><td>8.3069</td><td>69</td><td>(1,2,5)</td><td>8.4040</td><td>8.3700</td><td>8.2760</td><td>123</td><td>(2,3,3)</td><td>8.3712</td><td>8.3371</td><td>8.3371</td></tr><tr><td>16</td><td>(2,2,4)</td><td>8.3733</td><td>8.3710</td><td>8.3069</td><td>70</td><td>(2,3,3)</td><td>8.3713</td><td>8.3395</td><td>8.3362</td><td>124</td><td>(0,4,4)</td><td>8.4300</td><td>8.3034</td><td>8.3108</td></tr><tr><td>17</td><td>(2,3,3)</td><td>8.3717</td><td>8.3383</td><td>8.3399</td><td>71</td><td>(2,3,3)</td><td>8.3696</td><td>8.3386</td><td>8.3366</td><td>125</td><td>(2,3,3)</td><td>8.3719</td><td>8.3371</td><td>8.3349</td></tr><tr><td>18</td><td>(2,3,3)</td><td>8.3704</td><td>8.3399</td><td>8.3399</td><td>72</td><td>(2,2,4)</td><td>8.3696</td><td>8.3696</td><td>8.3069</td><td>126</td><td>(1,3,4)</td><td>8.3997</td><td>8.3387</td><td>8.3056</td></tr><tr><td>19</td><td>(2,3,3)</td><td>8.3728</td><td>8.3380</td><td>8.3399</td><td>73</td><td>(1,1,6)</td><td>8.4010</td><td>8.4010</td><td>8.2460</td><td>127</td><td>(2,3,3)</td><td>8.3661</td><td>8.3390</td><td>8.3390</td></tr><tr><td>20</td><td>(2,3,3)</td><td>8.3717</td><td>8.3391</td><td>8.3380</td><td>74</td><td>(1,3,4)</td><td>8.4022</td><td>8.3360</td><td>8.3084</td><td>128</td><td>(1,2,5)</td><td>8.4000</td><td>8.3680</td><td>8.2770</td></tr><tr><td>21</td><td>(2,3,3)</td><td>8.3714</td><td>8.3406</td><td>8.3379</td><td>75</td><td>(2,2,4)</td><td>8.3697</td><td>8.3701</td><td>8.3064</td><td>129</td><td>(2,3,3)</td><td>8.3679</td><td>8.3364</td><td>8.3406</td></tr><tr><td>22</td><td>(0,3,5)</td><td>8.4340</td><td>8.3390</td><td>8.2760</td><td>76</td><td>(2,2,4)</td><td>8.3695</td><td>8.3708</td><td>8.3052</td><td>130</td><td>(1,3,4)</td><td>8.4011</td><td>8.3380</td><td>8.3054</td></tr><tr><td>23</td><td>(2,3,3)</td><td>8.3718</td><td>8.3394</td><td>8.3395</td><td>77</td><td>(0,2,6)</td><td>8.4328</td><td>8.3692</td><td>8.2463</td><td>131</td><td>(1,3,4)</td><td>8.3990</td><td>8.3383</td><td>8.3075</td></tr><tr><td>24</td><td>(0,3,5)</td><td>8.4370</td><td>8.3380</td><td>8.2760</td><td>78</td><td>(2,2,4)</td><td>8.3695</td><td>8.3674</td><td>8.3087</td><td>132</td><td>(1,3,4)</td><td>8.4010</td><td>8.3384</td><td>8.3053</td></tr><tr><td>25</td><td>(1,2,5)</td><td>8.4020</td><td>8.3700</td><td>8.2770</td><td>79</td><td>(0,2,6)</td><td>8.4335</td><td>8.3689</td><td>8.2456</td><td>133</td><td>(0,4,4)</td><td>8.4324</td><td>8.3066</td><td>8.3067</td></tr><tr><td>26</td><td>(1,2,5)</td><td>8.4020</td><td>8.3700</td><td>8.2770</td><td>80</td><td>(2,2,4)</td><td>8.3690</td><td>8.3711</td><td>8.3065</td><td>134</td><td>(2,2,4)</td><td>8.3654</td><td>8.3695</td><td>8.3111</td></tr><tr><td>27</td><td>(2,2,4)</td><td>8.3707</td><td>8.3706</td><td>8.3075</td><td>81</td><td>(0,2,6)</td><td>8.4327</td><td>8.3692</td><td>8.2461</td><td>135</td><td>(1,3,4)</td><td>8.3980</td><td>8.3386</td><td>8.3059</td></tr><tr><td>28</td><td>(2,2,4)</td><td>8.3727</td><td>8.3727</td><td>8.3063</td><td>82</td><td>(2,2,4)</td><td>8.3709</td><td>8.3691</td><td>8.3067</td><td>136</td><td>(2,3,3)</td><td>8.3686</td><td>8.3367</td><td>8.3371</td></tr><tr><td>29</td><td>(1,2,5)</td><td>8.4030</td><td>8.3700</td><td>8.2760</td><td>83</td><td>(1,3,4)</td><td>8.4020</td><td>8.3374</td><td>8.3085</td><td>137</td><td>(1,2,5)</td><td>8.4000</td><td>8.3680</td><td>8.2780</td></tr><tr><td>30</td><td>(0,4,4)</td><td>8.4347</td><td>8.3053</td><td>8.3088</td><td>84</td><td>(2,3,3)</td><td>8.3677</td><td>8.3396</td><td>8.3379</td><td>138</td><td>(1,2,5)</td><td>8.4010</td><td>8.3710</td><td>8.2740</td></tr><tr><td>31</td><td>(1,2,5)</td><td>8.4030</td><td>8.3700</td><td>8.2760</td><td>85</td><td>(1,1,6)</td><td>8.4010</td><td>8.4010</td><td>8.2460</td><td>139</td><td>(2,2,4)</td><td>8.3668</td><td>8.3669</td><td>8.3076</td></tr><tr><td>32</td><td>(1,3,4)</td><td>8.4017</td><td>8.3373</td><td>8.3077</td><td>86</td><td>(2,3,3)</td><td>8.3707</td><td>8.3396</td><td>8.3360</td><td>140</td><td>(1,3,4)</td><td>8.4024</td><td>8.3342</td><td>8.3087</td></tr><tr><td>33</td><td>(2,3,3)</td><td>8.3705</td><td>8.3373</td><td>8.3391</td><td>87</td><td>(2,3,3)</td><td>8.3722</td><td>8.3375</td><td>8.3362</td><td>141</td><td>(0,0,8)</td><td><b>8.4315</b></td><td><b>8.4315</b></td><td><b>8.1876</b></td></tr><tr><td>34</td><td>(1,2,5)</td><td>8.4020</td><td>8.3710</td><td>8.2760</td><td>88</td><td>(2,2,4)</td><td>8.3689</td><td>8.3706</td><td>8.3079</td><td>142</td><td>(0,4,4)</td><td>8.4346</td><td>8.3027</td><td>8.3096</td></tr><tr><td>35</td><td>(1,3,4)</td><td>8.4034</td><td>8.3383</td><td>8.3072</td><td>89</td><td>(0,2,6)</td><td>8.4353</td><td>8.3687</td><td>8.2456</td><td>143</td><td>(2,2,4)</td><td>8.3679</td><td>8.3700</td><td>8.3052</td></tr><tr><td>36</td><td>(1,3,4)</td><td>8.4000</td><td>8.3391</td><td>8.3075</td><td>90</td><td>(1,1,6)</td><td>8.4010</td><td>8.4020</td><td>8.2460</td><td>144</td><td>(2,3,3)</td><td>8.3683</td><td>8.3387</td><td>8.3349</td></tr><tr><td>37</td><td>(1,3,4)</td><td>8.4032</td><td>8.3366</td><td>8.3076</td><td>91</td><td>(2,3,3)</td><td>8.3684</td><td>8.3397</td><td>8.3361</td><td>145</td><td>(1,3,4)</td><td>8.3979</td><td>8.3347</td><td>8.3092</td></tr><tr><td>38</td><td>(1,2,5)</td><td>8.4040</td><td>8.3700</td><td>8.2750</td><td>92</td><td>(1,2,5)</td><td>8.4000</td><td>8.3700</td><td>8.2770</td><td>146</td><td>(2,3,3)</td><td>8.3661</td><td>8.3364</td><td>8.3403</td></tr><tr><td>39</td><td>(1,3,4)</td><td>8.4013</td><td>8.3388</td><td>8.3076</td><td>93</td><td>(1,3,4)</td><td>8.4018</td><td>8.3373</td><td>8.3079</td><td>147</td><td>(2,2,4)</td><td>8.3689</td><td>8.3675</td><td>8.3073</td></tr><tr><td>40</td><td>(2,2,4)</td><td>8.3682</td><td>8.3707</td><td>8.3075</td><td>94</td><td>(2,3,3)</td><td>8.3704</td><td>8.3390</td><td>8.3375</td><td>148</td><td>(0,2,6)</td><td>8.4307</td><td>8.3706</td><td>8.2448</td></tr><tr><td>41</td><td>(1,2,5)</td><td>8.4010</td><td>8.3700</td><td>8.2760</td><td>95</td><td>(2,3,3)</td><td>8.3684</td><td>8.3409</td><td>8.3376</td><td>149</td><td>(1,3,4)</td><td>8.3992</td><td>8.3378</td><td>8.3055</td></tr><tr><td>42</td><td>(1,3,4)</td><td>8.4003</td><td>8.3383</td><td>8.3093</td><td>96</td><td>(0,4,4)</td><td>8.4302</td><td>8.3077</td><td>8.3078</td><td>150</td><td>(1,1,6)</td><td>8.3990</td><td>8.3990</td><td>8.2470</td></tr><tr><td>43</td><td>(2,3,3)</td><td>8.3701</td><td>8.3375</td><td>8.3375</td><td>97</td><td>(1,1,6)</td><td>8.4000</td><td>8.4000</td><td>8.2460</td><td>151</td><td>(0,2,6)</td><td>8.4306</td><td>8.3673</td><td>8.2484</td></tr><tr><td>44</td><td>(1,3,4)</td><td>8.4019</td><td>8.3364</td><td>8.3092</td><td>98</td><td>(1,3,4)</td><td>8.4031</td><td>8.3402</td><td>8.3044</td><td>152</td><td>(0,3,5)</td><td>8.4300</td><td>8.3390</td><td>8.2770</td></tr><tr><td>45</td><td>(2,2,4)</td><td>8.3685</td><td>8.3696</td><td>8.3096</td><td>99</td><td>(2,3,3)</td><td>8.3709</td><td>8.3391</td><td>8.3356</td><td>153</td><td>(2,2,4)</td><td>8.3662</td><td>8.3662</td><td>8.3077</td></tr><tr><td>46</td><td>(2,2,4)</td><td>8.3681</td><td>8.3721</td><td>8.3069</td><td>100</td><td>(0,4,4)</td><td>8.4327</td><td>8.3072</td><td>8.3071</td><td>154</td><td>(2,3,3)</td><td>8.3662</td><td>8.3369</td><td>8.3369</td></tr><tr><td>47</td><td>(2,2,4)</td><td>8.3697</td><td>8.3705</td><td>8.3074</td><td>101</td><td>(0,4,4)</td><td>8.4325</td><td>8.3072</td><td>8.3073</td><td>155</td><td>(2,2,4)</td><td>8.3655</td><td>8.3655</td><td>8.3106</td></tr><tr><td>48</td><td>(1,3,4)</td><td>8.4032</td><td>8.3398</td><td>8.3052</td><td>102</td><td>(0,3,5)</td><td>8.4320</td><td>8.3360</td><td>8.2780</td><td>156</td><td>(1,2,5)</td><td>8.3980</td><td>8.3700</td><td>8.2750</td></tr><tr><td>49</td><td>(1,2,5)</td><td>8.4010</td><td>8.3720</td><td>8.2760</td><td>103</td><td>(0,3,5)</td><td>8.4320</td><td>8.3400</td><td>8.2740</td><td>157</td><td>(1,3,4)</td><td>8.3961</td><td>8.3392</td><td>8.3083</td></tr><tr><td>50</td><td>(0,2,6)</td><td>8.4337</td><td>8.3699</td><td>8.2461</td><td>104</td><td>(1,3,4)</td><td>8.4000</td><td>8.3387</td><td>8.3077</td><td>158</td><td>(2,2,4)</td><td>8.3685</td><td>8.3685</td><td>8.3045</td></tr><tr><td>51</td><td>(2,2,4)</td><td>8.3695</td><td>8.3696</td><td>8.3090</td><td>105</td><td>(1,2,5)</td><td>8.4000</td><td>8.3710</td><td>8.2750</td><td>159</td><td>(2,2,4)</td><td>8.3643</td><td>8.3719</td><td>8.3061</td></tr><tr><td>52</td><td>(2,2,4)</td><td>8.3683</td><td>8.3748</td><td>8.3047</td><td>106</td><td>(1,2,5)</td><td>8.4030</td><td>8.3680</td><td>8.2760</td><td>160</td><td>(2,3,3)</td><td>8.3705</td><td>8.3354</td><td>8.3354</td></tr><tr><td>53</td><td>(1,2,5)</td><td>8.4030</td><td>8.3710</td><td>8.2760</td><td>107</td><td>(2,3,3)</td><td>8.3666</td><td>8.3391</td><td>8.3393</td><td>161</td><td>(2,3,3)</td><td>8.3663</td><td>8.3375</td><td>8.3375</td></tr><tr><td>54</td><td>(2,2,4)</td><td>8.3699</td><td>8.3694</td><td>8.3091</td><td>108</td><td>(1,3,4)</td><td>8.3980</td><td>8.3388</td><td>8.3081</td><td>162</td><td>(0,4,4)</td><td>8.4261</td><td>8.3087</td><td>8.3087</td></tr></tbody></table>
<table><caption>**Table A6.** Total energy $E_T$ (in $E_h$) and volume $V$ (in Å³) for the 39 SICs of the (2,3,3) CEC of the 2 × 2 × 2 supercell (S222) at PBE0 level for the FM solution and for 2 formula units of KFeF₃. The SIC multiplicity is given by the M column. ΔE (in μ$E_h$) and ΔV (in mÅ³) are the energy and volume differences (or relative energy or volume) with respect to the REF case. In the last three columns the lattice parameters of the S222 supercell (40 atoms) are shown.</caption><thead><tr><th>I</th><th>E<sub>T</sub></th><th>ΔE</th><th>M</th><th>VOL</th><th>ΔV</th><th>a</th><th>b</th><th>c</th></tr></thead><tbody><tr><td></td><td>-4325.748339</td><td>0.0</td><td>1</td><td>142.8361</td><td>0.0</td><td>8.1502</td><td>8.3727</td><td>8.3727</td></tr><tr><td>1</td><td>-4325.749389</td><td>-1049.6</td><td>48</td><td>142.8489</td><td>12.8</td><td>8.3169</td><td>8.2896</td><td>8.2879</td></tr><tr><td>2</td><td>-4325.749358</td><td>-1018.9</td><td>48</td><td>142.8582</td><td>22.0</td><td>8.3194</td><td>8.2877</td><td>8.2878</td></tr><tr><td>3</td><td>-4325.749352</td><td>-1013.4</td><td>24</td><td>142.8255</td><td>-10.6</td><td>8.3164</td><td>8.2883</td><td>8.2883</td></tr><tr><td>4</td><td>-4325.749318</td><td>-979.2</td><td>48</td><td>142.8404</td><td>4.3</td><td>8.3165</td><td>8.2879</td><td>8.2895</td></tr><tr><td>5</td><td>-4325.749280</td><td>-940.7</td><td>24</td><td>142.8517</td><td>15.6</td><td>8.3164</td><td>8.2891</td><td>8.2891</td></tr><tr><td>6</td><td>-4325.749276</td><td>-937.4</td><td>48</td><td>142.8495</td><td>13.4</td><td>8.3177</td><td>8.2876</td><td>8.2891</td></tr><tr><td>7</td><td>-4325.749253</td><td>-913.7</td><td>48</td><td>142.8622</td><td>26.1</td><td>8.3190</td><td>8.2873</td><td>8.2889</td></tr><tr><td>8</td><td>-4325.749252</td><td>-912.6</td><td>48</td><td>142.8323</td><td>-3.9</td><td>8.3179</td><td>8.2880</td><td>8.2875</td></tr><tr><td>9</td><td>-4325.749213</td><td>-874.2</td><td>48</td><td>142.8475</td><td>11.4</td><td>8.3175</td><td>8.2892</td><td>8.2876</td></tr><tr><td>10</td><td>-4325.749177</td><td>-838.2</td><td>48</td><td>142.8595</td><td>23.4</td><td>8.3175</td><td>8.2886</td><td>8.2888</td></tr><tr><td>11</td><td>-4325.748950</td><td>-611.0</td><td>48</td><td>142.8081</td><td>-28.0</td><td>8.3168</td><td>8.2867</td><td>8.2885</td></tr><tr><td>12</td><td>-4325.748895</td><td>-556.3</td><td>24</td><td>142.7824</td><td>-53.7</td><td>8.3170</td><td>8.2868</td><td>8.2868</td></tr><tr><td>13</td><td>-4325.748824</td><td>-485.4</td><td>48</td><td>142.7752</td><td>-61.0</td><td>8.3152</td><td>8.2868</td><td>8.2881</td></tr><tr><td>14</td><td>-4325.748808</td><td>-468.8</td><td>48</td><td>142.8251</td><td>-11.0</td><td>8.3146</td><td>8.2875</td><td>8.2909</td></tr><tr><td>15</td><td>-4325.748802</td><td>-463.5</td><td>48</td><td>142.7911</td><td>-45.0</td><td>8.3151</td><td>8.2897</td><td>8.2862</td></tr><tr><td>16</td><td>-4325.748796</td><td>-457.1</td><td>48</td><td>142.8214</td><td>-14.8</td><td>8.3162</td><td>8.2858</td><td>8.2908</td></tr><tr><td>17</td><td>-4325.748782</td><td>-443.1</td><td>48</td><td>142.7892</td><td>-46.9</td><td>8.3149</td><td>8.2880</td><td>8.2880</td></tr><tr><td>18</td><td>-4325.748758</td><td>-419.0</td><td>48</td><td>142.8007</td><td>-35.4</td><td>8.3161</td><td>8.2880</td><td>8.2875</td></tr><tr><td>19</td><td>-4325.748727</td><td>-388.2</td><td>48</td><td>142.8155</td><td>-20.6</td><td>8.3175</td><td>8.2890</td><td>8.2859</td></tr><tr><td>20</td><td>-4325.748723</td><td>-383.8</td><td>48</td><td>142.7786</td><td>-57.6</td><td>8.3161</td><td>8.2880</td><td>8.2862</td></tr><tr><td>21</td><td>-4325.748665</td><td>-326.2</td><td>48</td><td>142.7891</td><td>-47.0</td><td>8.3146</td><td>8.2890</td><td>8.2873</td></tr><tr><td>22</td><td>-4325.748652</td><td>-313.5</td><td>48</td><td>142.8060</td><td>-30.1</td><td>8.3170</td><td>8.2891</td><td>8.2858</td></tr><tr><td>23</td><td>-4325.748641</td><td>-302.0</td><td>48</td><td>142.8011</td><td>-35.0</td><td>8.3187</td><td>8.2870</td><td>8.2859</td></tr><tr><td>24</td><td>-4325.748633</td><td>-293.8</td><td>48</td><td>142.7710</td><td>-65.1</td><td>8.3148</td><td>8.2891</td><td>8.2859</td></tr><tr><td>25</td><td>-4325.748606</td><td>-266.9</td><td>48</td><td>142.8158</td><td>-20.3</td><td>8.3169</td><td>8.2885</td><td>8.2870</td></tr><tr><td>26</td><td>-4325.748602</td><td>-263.5</td><td>48</td><td>142.8154</td><td>-20.7</td><td>8.3153</td><td>8.2900</td><td>8.2870</td></tr><tr><td>27</td><td>-4325.748564</td><td>-224.9</td><td>48</td><td>142.7953</td><td>-40.9</td><td>8.3171</td><td>8.2886</td><td>8.2856</td></tr><tr><td>28</td><td>-4325.748488</td><td>-148.5</td><td>48</td><td>142.7836</td><td>-52.5</td><td>8.3135</td><td>8.2886</td><td>8.2884</td></tr><tr><td>29</td><td>-4325.748474</td><td>-135.4</td><td>48</td><td>142.7823</td><td>-53.8</td><td>8.3153</td><td>8.2898</td><td>8.2855</td></tr><tr><td>30</td><td>-4325.748445</td><td>-106.5</td><td>24</td><td>142.7945</td><td>-41.6</td><td>8.3179</td><td>8.2867</td><td>8.2867</td></tr><tr><td>31</td><td>-4325.748412</td><td>-72.7</td><td>48</td><td>142.7701</td><td>-66.1</td><td>8.3183</td><td>8.2868</td><td>8.2848</td></tr><tr><td>32</td><td>-4325.748402</td><td>-63.2</td><td>24</td><td>142.7709</td><td>-65.2</td><td>8.3132</td><td>8.2883</td><td>8.2883</td></tr><tr><td>33</td><td>-4325.748367</td><td>-28.3</td><td>48</td><td>142.7847</td><td>-51.4</td><td>8.3147</td><td>8.2863</td><td>8.2897</td></tr><tr><td>34</td><td>-4325.748351</td><td>-12.1</td><td>48</td><td>142.7483</td><td>-87.9</td><td>8.3151</td><td>8.2865</td><td>8.2869</td></tr><tr><td>35</td><td>-4325.748279</td><td>60.0</td><td>48</td><td>142.7415</td><td>-94.6</td><td>8.3153</td><td>8.2881</td><td>8.2848</td></tr><tr><td>36</td><td>-4325.748249</td><td>89.9</td><td>48</td><td>142.7558</td><td>-80.3</td><td>8.3131</td><td>8.2895</td><td>8.2864</td></tr><tr><td>37</td><td>-4325.748165</td><td>173.5</td><td>24</td><td>142.7112</td><td>-124.9</td><td>8.3131</td><td>8.2866</td><td>8.2866</td></tr><tr><td>38</td><td>-4325.747976</td><td>363.2</td><td>24</td><td>142.7349</td><td>-101.2</td><td>8.3170</td><td>8.2854</td><td>8.2854</td></tr><tr><td>39</td><td>-4325.747968</td><td>370.8</td><td>24</td><td>142.7340</td><td>-102.1</td><td>8.3136</td><td>8.2870</td><td>8.2870</td></tr></tbody></table>

<figure><img src="image_13.png" /><figcaption>**Figure A3.** The configuration indicated as *columnar* by Varignon et al., see Table III of Reference [14] of the main text.</figcaption></figure>
<table><caption>**Table A6.** Total energy $E_T$ (in $E_h$) and volume $V$ (in Å³) for the 39 SICs of the (2,3,3) CEC of the 2 × 2 × 2 supercell (S222) at PBE0 level for the FM solution and for 2 formula units of KFeF₃. The SIC multiplicity is given by the M column. $ΔE$ (in $μE_h$) and $ΔV$ (in mÅ³) are the energy and volume differences (or relative energy or volume) with respect to the REF case. In the last three columns the lattice parameters of the S222 supercell (40 atoms) are shown.</caption><thead><tr><th>I</th><th>E<sub>T</sub></th><th>ΔE</th><th>M</th><th>VOL</th><th>ΔV</th><th>a</th><th>b</th><th>c</th></tr></thead><tbody><tr><td></td><td>-4325.748339</td><td>0.0</td><td>1</td><td>142.8361</td><td>0.0</td><td>8.1502</td><td>8.3727</td><td>8.3727</td></tr><tr><td>1</td><td>-4325.749389</td><td>-1049.6</td><td>48</td><td>142.8489</td><td>12.8</td><td>8.3169</td><td>8.2896</td><td>8.2879</td></tr><tr><td>2</td><td>-4325.749358</td><td>-1018.9</td><td>48</td><td>142.8582</td><td>22.0</td><td>8.3194</td><td>8.2877</td><td>8.2878</td></tr><tr><td>3</td><td>-4325.749352</td><td>-1013.4</td><td>24</td><td>142.8255</td><td>-10.6</td><td>8.3164</td><td>8.2883</td><td>8.2883</td></tr><tr><td>4</td><td>-4325.749318</td><td>-979.2</td><td>48</td><td>142.8404</td><td>4.3</td><td>8.3165</td><td>8.2879</td><td>8.2895</td></tr><tr><td>5</td><td>-4325.749280</td><td>-940.7</td><td>24</td><td>142.8517</td><td>15.6</td><td>8.3164</td><td>8.2891</td><td>8.2891</td></tr><tr><td>6</td><td>-4325.749276</td><td>-937.4</td><td>48</td><td>142.8495</td><td>13.4</td><td>8.3177</td><td>8.2876</td><td>8.2891</td></tr><tr><td>7</td><td>-4325.749253</td><td>-913.7</td><td>48</td><td>142.8622</td><td>26.1</td><td>8.3190</td><td>8.2873</td><td>8.2889</td></tr><tr><td>8</td><td>-4325.749252</td><td>-912.6</td><td>48</td><td>142.8323</td><td>-3.9</td><td>8.3179</td><td>8.2880</td><td>8.2875</td></tr><tr><td>9</td><td>-4325.749213</td><td>-874.2</td><td>48</td><td>142.8475</td><td>11.4</td><td>8.3175</td><td>8.2892</td><td>8.2876</td></tr><tr><td>10</td><td>-4325.749177</td><td>-838.2</td><td>48</td><td>142.8595</td><td>23.4</td><td>8.3175</td><td>8.2886</td><td>8.2888</td></tr><tr><td>11</td><td>-4325.748950</td><td>-611.0</td><td>48</td><td>142.8081</td><td>-28.0</td><td>8.3168</td><td>8.2867</td><td>8.2885</td></tr><tr><td>12</td><td>-4325.748895</td><td>-556.3</td><td>24</td><td>142.7824</td><td>-53.7</td><td>8.3170</td><td>8.2868</td><td>8.2868</td></tr><tr><td>13</td><td>-4325.748824</td><td>-485.4</td><td>48</td><td>142.7752</td><td>-61.0</td><td>8.3152</td><td>8.2868</td><td>8.2881</td></tr><tr><td>14</td><td>-4325.748808</td><td>-468.8</td><td>48</td><td>142.8251</td><td>-11.0</td><td>8.3146</td><td>8.2875</td><td>8.2909</td></tr><tr><td>15</td><td>-4325.748802</td><td>-463.5</td><td>48</td><td>142.7911</td><td>-45.0</td><td>8.3151</td><td>8.2897</td><td>8.2862</td></tr><tr><td>16</td><td>-4325.748796</td><td>-457.1</td><td>48</td><td>142.8214</td><td>-14.8</td><td>8.3162</td><td>8.2858</td><td>8.2908</td></tr><tr><td>17</td><td>-4325.748782</td><td>-443.1</td><td>48</td><td>142.7892</td><td>-46.9</td><td>8.3149</td><td>8.2880</td><td>8.2880</td></tr><tr><td>18</td><td>-4325.748758</td><td>-419.0</td><td>48</td><td>142.8007</td><td>-35.4</td><td>8.3161</td><td>8.2880</td><td>8.2875</td></tr><tr><td>19</td><td>-4325.748727</td><td>-388.2</td><td>48</td><td>142.8155</td><td>-20.6</td><td>8.3175</td><td>8.2890</td><td>8.2859</td></tr><tr><td>20</td><td>-4325.748723</td><td>-383.8</td><td>48</td><td>142.7786</td><td>-57.6</td><td>8.3161</td><td>8.2880</td><td>8.2862</td></tr><tr><td>21</td><td>-4325.748665</td><td>-326.2</td><td>48</td><td>142.7891</td><td>-47.0</td><td>8.3146</td><td>8.2890</td><td>8.2873</td></tr><tr><td>22</td><td>-4325.748652</td><td>-313.5</td><td>48</td><td>142.8060</td><td>-30.1</td><td>8.3170</td><td>8.2891</td><td>8.2858</td></tr><tr><td>23</td><td>-4325.748641</td><td>-302.0</td><td>48</td><td>142.8011</td><td>-35.0</td><td>8.3187</td><td>8.2870</td><td>8.2859</td></tr><tr><td>24</td><td>-4325.748633</td><td>-293.8</td><td>48</td><td>142.7710</td><td>-65.1</td><td>8.3148</td><td>8.2891</td><td>8.2859</td></tr><tr><td>25</td><td>-4325.748606</td><td>-266.9</td><td>48</td><td>142.8158</td><td>-20.3</td><td>8.3169</td><td>8.2885</td><td>8.2870</td></tr><tr><td>26</td><td>-4325.748602</td><td>-263.5</td><td>48</td><td>142.8154</td><td>-20.7</td><td>8.3153</td><td>8.2900</td><td>8.2870</td></tr><tr><td>27</td><td>-4325.748564</td><td>-224.9</td><td>48</td><td>142.7953</td><td>-40.9</td><td>8.3171</td><td>8.2886</td><td>8.2856</td></tr><tr><td>28</td><td>-4325.748488</td><td>-148.5</td><td>48</td><td>142.7836</td><td>-52.5</td><td>8.3135</td><td>8.2886</td><td>8.2884</td></tr><tr><td>29</td><td>-4325.748474</td><td>-135.4</td><td>48</td><td>142.7823</td><td>-53.8</td><td>8.3153</td><td>8.2898</td><td>8.2855</td></tr><tr><td>30</td><td>-4325.748445</td><td>-106.5</td><td>24</td><td>142.7945</td><td>-41.6</td><td>8.3179</td><td>8.2867</td><td>8.2867</td></tr><tr><td>31</td><td>-4325.748412</td><td>-72.7</td><td>48</td><td>142.7701</td><td>-66.1</td><td>8.3183</td><td>8.2868</td><td>8.2848</td></tr><tr><td>32</td><td>-4325.748402</td><td>-63.2</td><td>24</td><td>142.7709</td><td>-65.2</td><td>8.3132</td><td>8.2883</td><td>8.2883</td></tr><tr><td>33</td><td>-4325.748367</td><td>-28.3</td><td>48</td><td>142.7847</td><td>-51.4</td><td>8.3147</td><td>8.2863</td><td>8.2897</td></tr><tr><td>34</td><td>-4325.748351</td><td>-12.1</td><td>48</td><td>142.7483</td><td>-87.9</td><td>8.3151</td><td>8.2865</td><td>8.2869</td></tr><tr><td>35</td><td>-4325.748279</td><td>60.0</td><td>48</td><td>142.7415</td><td>-94.6</td><td>8.3153</td><td>8.2881</td><td>8.2848</td></tr><tr><td>36</td><td>-4325.748249</td><td>89.9</td><td>48</td><td>142.7558</td><td>-80.3</td><td>8.3131</td><td>8.2895</td><td>8.2864</td></tr><tr><td>37</td><td>-4325.748165</td><td>173.5</td><td>24</td><td>142.7112</td><td>-124.9</td><td>8.3131</td><td>8.2866</td><td>8.2866</td></tr><tr><td>38</td><td>-4325.747976</td><td>363.2</td><td>24</td><td>142.7349</td><td>-101.2</td><td>8.3170</td><td>8.2854</td><td>8.2854</td></tr><tr><td>39</td><td>-4325.747968</td><td>370.8</td><td>24</td><td>142.7340</td><td>-102.1</td><td>8.3136</td><td>8.2870</td><td>8.2870</td></tr></tbody></table>

<figure><img src="image_13.png" /><figcaption>**Figure A3.** The configuration indicated as *columnar* by Varignon et al., see Table III of Reference [14] of the main text.</figcaption></figure>
<table><caption>Table A7. As Table A6, for HSE06.</caption><thead><tr><th>I</th><th>E<sub>T</sub></th><th>ΔE</th><th>M</th><th>VOL</th><th>ΔV</th><th>a</th><th>b</th><th>c</th></tr></thead><tbody><tr><td></td><td>-4325.741347</td><td>0.0</td><td>1</td><td>142.8354</td><td>0.0</td><td>8.1489</td><td>8.3733</td><td>8.3733</td></tr><tr><td>1</td><td>-4325.742425</td><td>-1077.7</td><td>48</td><td>142.8448</td><td>9.4</td><td>8.3169</td><td>8.2877</td><td>8.2895</td></tr><tr><td>2</td><td>-4325.742392</td><td>-1044.5</td><td>48</td><td>142.8545</td><td>19.1</td><td>8.3197</td><td>8.2874</td><td>8.2876</td></tr><tr><td>3</td><td>-4325.742390</td><td>-1042.4</td><td>24</td><td>142.8201</td><td>-15.3</td><td>8.3165</td><td>8.2881</td><td>8.2881</td></tr><tr><td>4</td><td>-4325.742352</td><td>-1004.4</td><td>48</td><td>142.8361</td><td>0.7</td><td>8.3165</td><td>8.2877</td><td>8.2894</td></tr><tr><td>5</td><td>-4325.742317</td><td>-969.7</td><td>24</td><td>142.8468</td><td>11.4</td><td>8.3163</td><td>8.2890</td><td>8.2890</td></tr><tr><td>6</td><td>-4325.742309</td><td>-961.5</td><td>48</td><td>142.8461</td><td>10.7</td><td>8.3178</td><td>8.2874</td><td>8.2890</td></tr><tr><td>7</td><td>-4325.742284</td><td>-936.9</td><td>48</td><td>142.8278</td><td>-7.6</td><td>8.3180</td><td>8.2878</td><td>8.2874</td></tr><tr><td>8</td><td>-4325.742282</td><td>-934.9</td><td>48</td><td>142.8599</td><td>24.5</td><td>8.3192</td><td>8.2870</td><td>8.2888</td></tr><tr><td>9</td><td>-4325.742242</td><td>-895.1</td><td>48</td><td>142.8434</td><td>8.0</td><td>8.3176</td><td>8.2891</td><td>8.2873</td></tr><tr><td>10</td><td>-4325.742205</td><td>-857.4</td><td>48</td><td>142.8572</td><td>21.8</td><td>8.3176</td><td>8.2885</td><td>8.2888</td></tr><tr><td>11</td><td>-4325.741986</td><td>-638.6</td><td>48</td><td>142.8025</td><td>-32.8</td><td>8.3170</td><td>8.2864</td><td>8.2883</td></tr><tr><td>12</td><td>-4325.741931</td><td>-583.8</td><td>24</td><td>142.7752</td><td>-60.2</td><td>8.3170</td><td>8.2866</td><td>8.2866</td></tr><tr><td>13</td><td>-4325.741861</td><td>-513.8</td><td>48</td><td>142.7682</td><td>-67.2</td><td>8.3152</td><td>8.2866</td><td>8.2879</td></tr><tr><td>14</td><td>-4325.741837</td><td>-489.9</td><td>48</td><td>142.8212</td><td>-14.2</td><td>8.3145</td><td>8.2873</td><td>8.2909</td></tr><tr><td>15</td><td>-4325.741835</td><td>-488.1</td><td>48</td><td>142.7849</td><td>-50.5</td><td>8.3151</td><td>8.2896</td><td>8.2860</td></tr><tr><td>16</td><td>-4325.741824</td><td>-476.5</td><td>48</td><td>142.8171</td><td>-18.3</td><td>8.3163</td><td>8.2854</td><td>8.2908</td></tr><tr><td>17</td><td>-4325.741814</td><td>-466.9</td><td>48</td><td>142.7832</td><td>-52.1</td><td>8.3148</td><td>8.2879</td><td>8.2878</td></tr><tr><td>18</td><td>-4325.741788</td><td>-440.3</td><td>48</td><td>142.7957</td><td>-39.7</td><td>8.3163</td><td>8.2877</td><td>8.2873</td></tr><tr><td>19</td><td>-4325.741755</td><td>-407.4</td><td>48</td><td>142.7723</td><td>-63.1</td><td>8.3162</td><td>8.2878</td><td>8.2859</td></tr><tr><td>20</td><td>-4325.741753</td><td>-406.1</td><td>48</td><td>142.8112</td><td>-24.1</td><td>8.3177</td><td>8.2889</td><td>8.2856</td></tr><tr><td>21</td><td>-4325.741695</td><td>-348.0</td><td>48</td><td>142.7819</td><td>-53.4</td><td>8.3145</td><td>8.2888</td><td>8.2872</td></tr><tr><td>22</td><td>-4325.741678</td><td>-330.8</td><td>48</td><td>142.8016</td><td>-33.8</td><td>8.3172</td><td>8.2889</td><td>8.2855</td></tr><tr><td>23</td><td>-4325.741667</td><td>-320.0</td><td>48</td><td>142.7965</td><td>-38.9</td><td>8.3189</td><td>8.2868</td><td>8.2856</td></tr><tr><td>24</td><td>-4325.741665</td><td>-317.9</td><td>48</td><td>142.7643</td><td>-71.1</td><td>8.3147</td><td>8.2890</td><td>8.2857</td></tr><tr><td>25</td><td>-4325.741628</td><td>-280.9</td><td>48</td><td>142.8126</td><td>-22.8</td><td>8.3170</td><td>8.2883</td><td>8.2869</td></tr><tr><td>26</td><td>-4325.741626</td><td>-278.6</td><td>48</td><td>142.8121</td><td>-23.3</td><td>8.3153</td><td>8.2900</td><td>8.2869</td></tr><tr><td>27</td><td>-4325.741589</td><td>-241.4</td><td>48</td><td>142.7909</td><td>-44.5</td><td>8.3172</td><td>8.2885</td><td>8.2853</td></tr><tr><td>28</td><td>-4325.741518</td><td>-170.8</td><td>48</td><td>142.7782</td><td>-57.2</td><td>8.3134</td><td>8.2883</td><td>8.2885</td></tr><tr><td>29</td><td>-4325.741501</td><td>-153.5</td><td>48</td><td>142.7776</td><td>-57.7</td><td>8.3153</td><td>8.2897</td><td>8.2852</td></tr><tr><td>30</td><td>-4325.741467</td><td>-120.1</td><td>24</td><td>142.7907</td><td>-44.7</td><td>8.3180</td><td>8.2865</td><td>8.2865</td></tr><tr><td>31</td><td>-4325.741442</td><td>-95.0</td><td>48</td><td>142.7632</td><td>-72.2</td><td>8.3185</td><td>8.2865</td><td>8.2845</td></tr><tr><td>32</td><td>-4325.741432</td><td>-84.4</td><td>24</td><td>142.7649</td><td>-70.5</td><td>8.3131</td><td>8.2882</td><td>8.2882</td></tr><tr><td>33</td><td>-4325.741394</td><td>-46.7</td><td>48</td><td>142.7791</td><td>-56.3</td><td>8.3147</td><td>8.2859</td><td>8.2897</td></tr><tr><td>34</td><td>-4325.741385</td><td>-37.3</td><td>48</td><td>142.7404</td><td>-95.0</td><td>8.3152</td><td>8.2862</td><td>8.2866</td></tr><tr><td>35</td><td>-4325.741311</td><td>36.0</td><td>48</td><td>142.7342</td><td>-101.2</td><td>8.3152</td><td>8.2880</td><td>8.2845</td></tr><tr><td>36</td><td>-4325.741278</td><td>69.6</td><td>48</td><td>142.7494</td><td>-86.0</td><td>8.3130</td><td>8.2861</td><td>8.2895</td></tr><tr><td>37</td><td>-4325.741200</td><td>147.6</td><td>24</td><td>142.7030</td><td>-132.4</td><td>8.3131</td><td>8.2864</td><td>8.2864</td></tr><tr><td>38</td><td>-4325.741006</td><td>341.3</td><td>24</td><td>142.7276</td><td>-107.8</td><td>8.3172</td><td>8.2851</td><td>8.2851</td></tr><tr><td>39</td><td>-4325.740999</td><td>348.2</td><td>24</td><td>142.7261</td><td>-109.3</td><td>8.3135</td><td>8.2869</td><td>8.2869</td></tr></tbody></table>

<figure><img src="image_14.png" /><figcaption>Figure A4. Comparison between the B3LYP relative energies (ΔE<sub>calc</sub>) and the relative energies predicted according to the 12 interaction model described in the text (ΔE<sub>pred</sub>) for the 162 SICs. Energies refer to 2 f.u. Top: E<sub>pred</sub> as a function of E<sub>calc</sub>. The even distribution with respect to the perfect agreement straight line (dashed line) confirms the good quality of the model. Bottom: Deviation (ΔE<sub>pred</sub>-ΔE<sub>calc</sub>) as a function of ΔE<sub>calc</sub>. The two panels share the horizontal scale. The energy differences are a small fraction of the energy interval covered by the set of SICs; only 4 exceed 10% of the energy interval.</figcaption></figure>
<table><caption>Table A7. As Table A6, for HSE06.</caption><thead><tr><th>I</th><th>E<sub>T</sub></th><th>ΔE</th><th>M</th><th>VOL</th><th>ΔV</th><th>a</th><th>b</th><th>c</th></tr></thead><tbody><tr><td></td><td>-4325.741347</td><td>0.0</td><td>1</td><td>142.8354</td><td>0.0</td><td>8.1489</td><td>8.3733</td><td>8.3733</td></tr><tr><td>1</td><td>-4325.742425</td><td>-1077.7</td><td>48</td><td>142.8448</td><td>9.4</td><td>8.3169</td><td>8.2877</td><td>8.2895</td></tr><tr><td>2</td><td>-4325.742392</td><td>-1044.5</td><td>48</td><td>142.8545</td><td>19.1</td><td>8.3197</td><td>8.2874</td><td>8.2876</td></tr><tr><td>3</td><td>-4325.742390</td><td>-1042.4</td><td>24</td><td>142.8201</td><td>-15.3</td><td>8.3165</td><td>8.2881</td><td>8.2881</td></tr><tr><td>4</td><td>-4325.742352</td><td>-1004.4</td><td>48</td><td>142.8361</td><td>0.7</td><td>8.3165</td><td>8.2877</td><td>8.2894</td></tr><tr><td>5</td><td>-4325.742317</td><td>-969.7</td><td>24</td><td>142.8468</td><td>11.4</td><td>8.3163</td><td>8.2890</td><td>8.2890</td></tr><tr><td>6</td><td>-4325.742309</td><td>-961.5</td><td>48</td><td>142.8461</td><td>10.7</td><td>8.3178</td><td>8.2874</td><td>8.2890</td></tr><tr><td>7</td><td>-4325.742284</td><td>-936.9</td><td>48</td><td>142.8278</td><td>-7.6</td><td>8.3180</td><td>8.2878</td><td>8.2874</td></tr><tr><td>8</td><td>-4325.742282</td><td>-934.9</td><td>48</td><td>142.8599</td><td>24.5</td><td>8.3192</td><td>8.2870</td><td>8.2888</td></tr><tr><td>9</td><td>-4325.742242</td><td>-895.1</td><td>48</td><td>142.8434</td><td>8.0</td><td>8.3176</td><td>8.2891</td><td>8.2873</td></tr><tr><td>10</td><td>-4325.742205</td><td>-857.4</td><td>48</td><td>142.8572</td><td>21.8</td><td>8.3176</td><td>8.2885</td><td>8.2888</td></tr><tr><td>11</td><td>-4325.741986</td><td>-638.6</td><td>48</td><td>142.8025</td><td>-32.8</td><td>8.3170</td><td>8.2864</td><td>8.2883</td></tr><tr><td>12</td><td>-4325.741931</td><td>-583.8</td><td>24</td><td>142.7752</td><td>-60.2</td><td>8.3170</td><td>8.2866</td><td>8.2866</td></tr><tr><td>13</td><td>-4325.741861</td><td>-513.8</td><td>48</td><td>142.7682</td><td>-67.2</td><td>8.3152</td><td>8.2866</td><td>8.2879</td></tr><tr><td>14</td><td>-4325.741837</td><td>-489.9</td><td>48</td><td>142.8212</td><td>-14.2</td><td>8.3145</td><td>8.2873</td><td>8.2909</td></tr><tr><td>15</td><td>-4325.741835</td><td>-488.1</td><td>48</td><td>142.7849</td><td>-50.5</td><td>8.3151</td><td>8.2896</td><td>8.2860</td></tr><tr><td>16</td><td>-4325.741824</td><td>-476.5</td><td>48</td><td>142.8171</td><td>-18.3</td><td>8.3163</td><td>8.2854</td><td>8.2908</td></tr><tr><td>17</td><td>-4325.741814</td><td>-466.9</td><td>48</td><td>142.7832</td><td>-52.1</td><td>8.3148</td><td>8.2879</td><td>8.2878</td></tr><tr><td>18</td><td>-4325.741788</td><td>-440.3</td><td>48</td><td>142.7957</td><td>-39.7</td><td>8.3163</td><td>8.2877</td><td>8.2873</td></tr><tr><td>19</td><td>-4325.741755</td><td>-407.4</td><td>48</td><td>142.7723</td><td>-63.1</td><td>8.3162</td><td>8.2878</td><td>8.2859</td></tr><tr><td>20</td><td>-4325.741753</td><td>-406.1</td><td>48</td><td>142.8112</td><td>-24.1</td><td>8.3177</td><td>8.2889</td><td>8.2856</td></tr><tr><td>21</td><td>-4325.741695</td><td>-348.0</td><td>48</td><td>142.7819</td><td>-53.4</td><td>8.3145</td><td>8.2888</td><td>8.2872</td></tr><tr><td>22</td><td>-4325.741678</td><td>-330.8</td><td>48</td><td>142.8016</td><td>-33.8</td><td>8.3172</td><td>8.2889</td><td>8.2855</td></tr><tr><td>23</td><td>-4325.741667</td><td>-320.0</td><td>48</td><td>142.7965</td><td>-38.9</td><td>8.3189</td><td>8.2868</td><td>8.2856</td></tr><tr><td>24</td><td>-4325.741665</td><td>-317.9</td><td>48</td><td>142.7643</td><td>-71.1</td><td>8.3147</td><td>8.2890</td><td>8.2857</td></tr><tr><td>25</td><td>-4325.741628</td><td>-280.9</td><td>48</td><td>142.8126</td><td>-22.8</td><td>8.3170</td><td>8.2883</td><td>8.2869</td></tr><tr><td>26</td><td>-4325.741626</td><td>-278.6</td><td>48</td><td>142.8121</td><td>-23.3</td><td>8.3153</td><td>8.2900</td><td>8.2869</td></tr><tr><td>27</td><td>-4325.741589</td><td>-241.4</td><td>48</td><td>142.7909</td><td>-44.5</td><td>8.3172</td><td>8.2885</td><td>8.2853</td></tr><tr><td>28</td><td>-4325.741518</td><td>-170.8</td><td>48</td><td>142.7782</td><td>-57.2</td><td>8.3134</td><td>8.2883</td><td>8.2885</td></tr><tr><td>29</td><td>-4325.741501</td><td>-153.5</td><td>48</td><td>142.7776</td><td>-57.7</td><td>8.3153</td><td>8.2897</td><td>8.2852</td></tr><tr><td>30</td><td>-4325.741467</td><td>-120.1</td><td>24</td><td>142.7907</td><td>-44.7</td><td>8.3180</td><td>8.2865</td><td>8.2865</td></tr><tr><td>31</td><td>-4325.741442</td><td>-95.0</td><td>48</td><td>142.7632</td><td>-72.2</td><td>8.3185</td><td>8.2865</td><td>8.2845</td></tr><tr><td>32</td><td>-4325.741432</td><td>-84.4</td><td>24</td><td>142.7649</td><td>-70.5</td><td>8.3131</td><td>8.2882</td><td>8.2882</td></tr><tr><td>33</td><td>-4325.741394</td><td>-46.7</td><td>48</td><td>142.7791</td><td>-56.3</td><td>8.3147</td><td>8.2859</td><td>8.2897</td></tr><tr><td>34</td><td>-4325.741385</td><td>-37.3</td><td>48</td><td>142.7404</td><td>-95.0</td><td>8.3152</td><td>8.2862</td><td>8.2866</td></tr><tr><td>35</td><td>-4325.741311</td><td>36.0</td><td>48</td><td>142.7342</td><td>-101.2</td><td>8.3152</td><td>8.2880</td><td>8.2845</td></tr><tr><td>36</td><td>-4325.741278</td><td>69.6</td><td>48</td><td>142.7494</td><td>-86.0</td><td>8.3130</td><td>8.2861</td><td>8.2895</td></tr><tr><td>37</td><td>-4325.741200</td><td>147.6</td><td>24</td><td>142.7030</td><td>-132.4</td><td>8.3131</td><td>8.2864</td><td>8.2864</td></tr><tr><td>38</td><td>-4325.741006</td><td>341.3</td><td>24</td><td>142.7276</td><td>-107.8</td><td>8.3172</td><td>8.2851</td><td>8.2851</td></tr><tr><td>39</td><td>-4325.740999</td><td>348.2</td><td>24</td><td>142.7261</td><td>-109.3</td><td>8.3135</td><td>8.2869</td><td>8.2869</td></tr></tbody></table>

<figure><img src="image_14.png" /><figcaption>**Figure A4.** Comparison between the B3LYP relative energies (ΔE<sub>calc</sub>) and the relative energies predicted according to the 12 interaction model described in the text (ΔE<sub>pred</sub>) for the 162 SICs. Energies refer to 2 f.u. Top: E<sub>pred</sub> as a function of E<sub>calc</sub>. The even distribution with respect to the perfect agreement straight line (dashed line) confirms the good quality of the model. Bottom: Deviation (ΔE<sub>pred</sub>-ΔE<sub>calc</sub>) as a function of ΔE<sub>calc</sub>. The two panels share the horizontal scale. The energy differences are a small fraction of the energy interval covered by the set of SICs; only 4 exceed 10% of the energy interval.</figcaption></figure>
<table><caption>Table A8. As Table A6, for UHF.</caption><thead><tr><th>I</th><th>E<sub>T</sub></th><th>ΔE</th><th>M</th><th>VOL</th><th>ΔV</th><th>a</th><th>b</th><th>c</th></tr></thead><tbody><tr><td></td><td>-4320.657779</td><td>0.0</td><td>1</td><td>148.3826</td><td>0.0</td><td>8.2509</td><td>8.4815</td><td>8.4815</td></tr><tr><td>1</td><td>-4320.658161</td><td>-381.9</td><td>48</td><td>148.4167</td><td>34.1</td><td>8.4235</td><td>8.3956</td><td>8.3946</td></tr><tr><td>2</td><td>-4320.658154</td><td>-375.3</td><td>48</td><td>148.4207</td><td>38.1</td><td>8.4240</td><td>8.3955</td><td>8.3944</td></tr><tr><td>3</td><td>-4320.658142</td><td>-362.8</td><td>48</td><td>148.4322</td><td>49.6</td><td>8.4264</td><td>8.3944</td><td>8.3937</td></tr><tr><td>4</td><td>-4320.658135</td><td>-356.5</td><td>24</td><td>148.4331</td><td>50.5</td><td>8.4253</td><td>8.3941</td><td>8.3953</td></tr><tr><td>5</td><td>-4320.658135</td><td>-350.1</td><td>24</td><td>148.4331</td><td>50.5</td><td>8.4251</td><td>8.3940</td><td>8.3950</td></tr><tr><td>6</td><td>-4320.658082</td><td>-303.6</td><td>48</td><td>148.4274</td><td>44.7</td><td>8.4265</td><td>8.3939</td><td>8.3939</td></tr><tr><td>7</td><td>-4320.658042</td><td>-263.5</td><td>48</td><td>148.4240</td><td>41.3</td><td>8.4251</td><td>8.3956</td><td>8.3934</td></tr><tr><td>8</td><td>-4320.658041</td><td>-262.3</td><td>48</td><td>148.4278</td><td>45.2</td><td>8.4266</td><td>8.3940</td><td>8.3937</td></tr><tr><td>9</td><td>-4320.658006</td><td>-227.4</td><td>48</td><td>148.4342</td><td>51.6</td><td>8.4260</td><td>8.3950</td><td>8.3937</td></tr><tr><td>10</td><td>-4320.657965</td><td>-186.5</td><td>48</td><td>148.4276</td><td>45.0</td><td>8.4248</td><td>8.3963</td><td>8.3932</td></tr><tr><td>11</td><td>-4320.657868</td><td>-89.1</td><td>24</td><td>148.3641</td><td>-18.5</td><td>8.4235</td><td>8.3936</td><td>8.3936</td></tr><tr><td>12</td><td>-4320.657859</td><td>-80.7</td><td>48</td><td>148.3874</td><td>4.8</td><td>8.4245</td><td>8.3937</td><td>8.3938</td></tr><tr><td>13</td><td>-4320.657817</td><td>-38.0</td><td>48</td><td>148.3627</td><td>-19.9</td><td>8.4232</td><td>8.3938</td><td>8.3936</td></tr><tr><td>14</td><td>-4320.657803</td><td>-23.8</td><td>48</td><td>148.3883</td><td>5.6</td><td>8.4244</td><td>8.3935</td><td>8.3942</td></tr><tr><td>15</td><td>-4320.657797</td><td>-18.6</td><td>48</td><td>148.3855</td><td>2.9</td><td>8.4245</td><td>8.3933</td><td>8.3941</td></tr><tr><td>16</td><td>-4320.657764</td><td>15.2</td><td>48</td><td>148.3655</td><td>-17.1</td><td>8.4232</td><td>8.3942</td><td>8.3933</td></tr><tr><td>17</td><td>-4320.657763</td><td>15.5</td><td>48</td><td>148.3629</td><td>-19.8</td><td>8.4233</td><td>8.3942</td><td>8.3932</td></tr><tr><td>18</td><td>-4320.657762</td><td>17.2</td><td>48</td><td>148.3656</td><td>-17.0</td><td>8.4231</td><td>8.3942</td><td>8.3935</td></tr><tr><td>19</td><td>-4320.657757</td><td>21.8</td><td>48</td><td>148.3596</td><td>-23.1</td><td>8.4239</td><td>8.3932</td><td>8.3934</td></tr><tr><td>20</td><td>-4320.657752</td><td>26.4</td><td>48</td><td>148.3810</td><td>-1.7</td><td>8.4246</td><td>8.3939</td><td>8.3932</td></tr><tr><td>21</td><td>-4320.657745</td><td>33.6</td><td>48</td><td>148.3733</td><td>-9.3</td><td>8.4244</td><td>8.3940</td><td>8.3928</td></tr><tr><td>22</td><td>-4320.657743</td><td>35.8</td><td>48</td><td>148.3748</td><td>-7.8</td><td>8.4244</td><td>8.3940</td><td>8.3929</td></tr><tr><td>23</td><td>-4320.657739</td><td>39.8</td><td>48</td><td>148.3673</td><td>-15.4</td><td>8.4228</td><td>8.3946</td><td>8.3935</td></tr><tr><td>24</td><td>-4320.657709</td><td>69.3</td><td>48</td><td>148.3551</td><td>-27.5</td><td>8.4235</td><td>8.3938</td><td>8.3929</td></tr><tr><td>25</td><td>-4320.657681</td><td>97.9</td><td>48</td><td>148.3612</td><td>-21.4</td><td>8.4226</td><td>8.3951</td><td>8.3928</td></tr><tr><td>26</td><td>-4320.657680</td><td>98.5</td><td>48</td><td>148.3647</td><td>-18.0</td><td>8.4240</td><td>8.3939</td><td>8.3929</td></tr><tr><td>27</td><td>-4320.657653</td><td>126.0</td><td>24</td><td>148.3484</td><td>-34.2</td><td>8.4237</td><td>8.3930</td><td>8.3930</td></tr><tr><td>28</td><td>-4320.657646</td><td>132.9</td><td>48</td><td>148.3443</td><td>-38.4</td><td>8.4226</td><td>8.3939</td><td>8.3929</td></tr><tr><td>29</td><td>-4320.657632</td><td>147.1</td><td>48</td><td>148.3563</td><td>-26.3</td><td>8.4243</td><td>8.3935</td><td>8.3925</td></tr><tr><td>30</td><td>-4320.657523</td><td>256.1</td><td>48</td><td>148.3436</td><td>-39.1</td><td>8.4225</td><td>8.3934</td><td>8.3936</td></tr><tr><td>31</td><td>-4320.657517</td><td>261.6</td><td>48</td><td>148.3377</td><td>-45.0</td><td>8.4233</td><td>8.3935</td><td>8.3924</td></tr><tr><td>32</td><td>-4320.657514</td><td>264.4</td><td>24</td><td>148.3389</td><td>-43.8</td><td>8.4223</td><td>8.3935</td><td>8.3935</td></tr><tr><td>33</td><td>-4320.657509</td><td>270.1</td><td>48</td><td>148.3579</td><td>-24.7</td><td>8.4236</td><td>8.3933</td><td>8.3935</td></tr><tr><td>34</td><td>-4320.657456</td><td>322.6</td><td>48</td><td>148.3264</td><td>-56.2</td><td>8.4224</td><td>8.3930</td><td>8.3931</td></tr><tr><td>35</td><td>-4320.657411</td><td>367.9</td><td>48</td><td>148.3247</td><td>-57.9</td><td>8.4219</td><td>8.3931</td><td>8.3935</td></tr><tr><td>36</td><td>-4320.657402</td><td>376.7</td><td>48</td><td>148.3188</td><td>-63.8</td><td>8.4230</td><td>8.3931</td><td>8.3920</td></tr><tr><td>37</td><td>-4320.657290</td><td>488.3</td><td>24</td><td>148.3002</td><td>-82.1</td><td>8.4215</td><td>8.3928</td><td>8.3928</td></tr><tr><td>38</td><td>-4320.657173</td><td>605.8</td><td>24</td><td>148.3049</td><td>-77.7</td><td>8.4225</td><td>8.3924</td><td>8.3924</td></tr><tr><td>39</td><td>-4320.657169</td><td>609.9</td><td>24</td><td>148.3051</td><td>-77.5</td><td>8.4222</td><td>8.3926</td><td>8.3926</td></tr></tbody></table>

<figure><img src="image_15.png" /><figcaption>Figure A5. As in previous Figure A4, for the AFM solutions.</figcaption></figure>
<table><caption>Table A8. As Table A6, for UHF.</caption><thead><tr><th>I</th><th>E<sub>T</sub></th><th>ΔE</th><th>M</th><th>VOL</th><th>ΔV</th><th>a</th><th>b</th><th>c</th></tr></thead><tbody><tr><td></td><td>-4320.657779</td><td>0.0</td><td>1</td><td>148.3826</td><td>0.0</td><td>8.2509</td><td>8.4815</td><td>8.4815</td></tr><tr><td>1</td><td>-4320.658161</td><td>-381.9</td><td>48</td><td>148.4167</td><td>34.1</td><td>8.4235</td><td>8.3956</td><td>8.3946</td></tr><tr><td>2</td><td>-4320.658154</td><td>-375.3</td><td>48</td><td>148.4207</td><td>38.1</td><td>8.4240</td><td>8.3955</td><td>8.3944</td></tr><tr><td>3</td><td>-4320.658142</td><td>-362.8</td><td>48</td><td>148.4322</td><td>49.6</td><td>8.4264</td><td>8.3944</td><td>8.3937</td></tr><tr><td>4</td><td>-4320.658135</td><td>-356.5</td><td>24</td><td>148.4331</td><td>50.5</td><td>8.4253</td><td>8.3941</td><td>8.3953</td></tr><tr><td>5</td><td>-4320.658135</td><td>-350.1</td><td>24</td><td>148.4331</td><td>50.5</td><td>8.4251</td><td>8.3940</td><td>8.3950</td></tr><tr><td>6</td><td>-4320.658082</td><td>-303.6</td><td>48</td><td>148.4274</td><td>44.7</td><td>8.4265</td><td>8.3939</td><td>8.3939</td></tr><tr><td>7</td><td>-4320.658042</td><td>-263.5</td><td>48</td><td>148.4240</td><td>41.3</td><td>8.4251</td><td>8.3956</td><td>8.3934</td></tr><tr><td>8</td><td>-4320.658041</td><td>-262.3</td><td>48</td><td>148.4278</td><td>45.2</td><td>8.4266</td><td>8.3940</td><td>8.3937</td></tr><tr><td>9</td><td>-4320.658006</td><td>-227.4</td><td>48</td><td>148.4342</td><td>51.6</td><td>8.4260</td><td>8.3950</td><td>8.3937</td></tr><tr><td>10</td><td>-4320.657965</td><td>-186.5</td><td>48</td><td>148.4276</td><td>45.0</td><td>8.4248</td><td>8.3963</td><td>8.3932</td></tr><tr><td>11</td><td>-4320.657868</td><td>-89.1</td><td>24</td><td>148.3641</td><td>-18.5</td><td>8.4235</td><td>8.3936</td><td>8.3936</td></tr><tr><td>12</td><td>-4320.657859</td><td>-80.7</td><td>48</td><td>148.3874</td><td>4.8</td><td>8.4245</td><td>8.3937</td><td>8.3938</td></tr><tr><td>13</td><td>-4320.657817</td><td>-38.0</td><td>48</td><td>148.3627</td><td>-19.9</td><td>8.4232</td><td>8.3938</td><td>8.3936</td></tr><tr><td>14</td><td>-4320.657803</td><td>-23.8</td><td>48</td><td>148.3883</td><td>5.6</td><td>8.4244</td><td>8.3935</td><td>8.3942</td></tr><tr><td>15</td><td>-4320.657797</td><td>-18.6</td><td>48</td><td>148.3855</td><td>2.9</td><td>8.4245</td><td>8.3933</td><td>8.3941</td></tr><tr><td>16</td><td>-4320.657764</td><td>15.2</td><td>48</td><td>148.3655</td><td>-17.1</td><td>8.4232</td><td>8.3942</td><td>8.3933</td></tr><tr><td>17</td><td>-4320.657763</td><td>15.5</td><td>48</td><td>148.3629</td><td>-19.8</td><td>8.4233</td><td>8.3942</td><td>8.3932</td></tr><tr><td>18</td><td>-4320.657762</td><td>17.2</td><td>48</td><td>148.3656</td><td>-17.0</td><td>8.4231</td><td>8.3942</td><td>8.3935</td></tr><tr><td>19</td><td>-4320.657757</td><td>21.8</td><td>48</td><td>148.3596</td><td>-23.1</td><td>8.4239</td><td>8.3932</td><td>8.3934</td></tr><tr><td>20</td><td>-4320.657752</td><td>26.4</td><td>48</td><td>148.3810</td><td>-1.7</td><td>8.4246</td><td>8.3939</td><td>8.3932</td></tr><tr><td>21</td><td>-4320.657745</td><td>33.6</td><td>48</td><td>148.3733</td><td>-9.3</td><td>8.4244</td><td>8.3940</td><td>8.3928</td></tr><tr><td>22</td><td>-4320.657743</td><td>35.8</td><td>48</td><td>148.3748</td><td>-7.8</td><td>8.4244</td><td>8.3940</td><td>8.3929</td></tr><tr><td>23</td><td>-4320.657739</td><td>39.8</td><td>48</td><td>148.3673</td><td>-15.4</td><td>8.4228</td><td>8.3946</td><td>8.3935</td></tr><tr><td>24</td><td>-4320.657709</td><td>69.3</td><td>48</td><td>148.3551</td><td>-27.5</td><td>8.4235</td><td>8.3938</td><td>8.3929</td></tr><tr><td>25</td><td>-4320.657681</td><td>97.9</td><td>48</td><td>148.3612</td><td>-21.4</td><td>8.4226</td><td>8.3951</td><td>8.3928</td></tr><tr><td>26</td><td>-4320.657680</td><td>98.5</td><td>48</td><td>148.3647</td><td>-18.0</td><td>8.4240</td><td>8.3939</td><td>8.3929</td></tr><tr><td>27</td><td>-4320.657653</td><td>126.0</td><td>24</td><td>148.3484</td><td>-34.2</td><td>8.4237</td><td>8.3930</td><td>8.3930</td></tr><tr><td>28</td><td>-4320.657646</td><td>132.9</td><td>48</td><td>148.3443</td><td>-38.4</td><td>8.4226</td><td>8.3939</td><td>8.3929</td></tr><tr><td>29</td><td>-4320.657632</td><td>147.1</td><td>48</td><td>148.3563</td><td>-26.3</td><td>8.4243</td><td>8.3935</td><td>8.3925</td></tr><tr><td>30</td><td>-4320.657523</td><td>256.1</td><td>48</td><td>148.3436</td><td>-39.1</td><td>8.4225</td><td>8.3934</td><td>8.3936</td></tr><tr><td>31</td><td>-4320.657517</td><td>261.6</td><td>48</td><td>148.3377</td><td>-45.0</td><td>8.4233</td><td>8.3935</td><td>8.3924</td></tr><tr><td>32</td><td>-4320.657514</td><td>264.4</td><td>24</td><td>148.3389</td><td>-43.8</td><td>8.4223</td><td>8.3935</td><td>8.3935</td></tr><tr><td>33</td><td>-4320.657509</td><td>270.1</td><td>48</td><td>148.3579</td><td>-24.7</td><td>8.4236</td><td>8.3933</td><td>8.3935</td></tr><tr><td>34</td><td>-4320.657456</td><td>322.6</td><td>48</td><td>148.3264</td><td>-56.2</td><td>8.4224</td><td>8.3930</td><td>8.3931</td></tr><tr><td>35</td><td>-4320.657411</td><td>367.9</td><td>48</td><td>148.3247</td><td>-57.9</td><td>8.4219</td><td>8.3931</td><td>8.3935</td></tr><tr><td>36</td><td>-4320.657402</td><td>376.7</td><td>48</td><td>148.3188</td><td>-63.8</td><td>8.4230</td><td>8.3931</td><td>8.3920</td></tr><tr><td>37</td><td>-4320.657290</td><td>488.3</td><td>24</td><td>148.3002</td><td>-82.1</td><td>8.4215</td><td>8.3928</td><td>8.3928</td></tr><tr><td>38</td><td>-4320.657173</td><td>605.8</td><td>24</td><td>148.3049</td><td>-77.7</td><td>8.4225</td><td>8.3924</td><td>8.3924</td></tr><tr><td>39</td><td>-4320.657169</td><td>609.9</td><td>24</td><td>148.3051</td><td>-77.5</td><td>8.4222</td><td>8.3926</td><td>8.3926</td></tr></tbody></table>

<figure><img src="image_15.png" /><figcaption>Figure A5. As in previous Figure A4, for the AFM solutions.</figcaption></figure>
## References

1. Glazer, A.M. The classification of tilted octahedra in perovskites. *Acta Crystallogr. Sect. B* **1972**, *28*, 3384–3392. [CrossRef]

2. Glazer, A.M. Simple ways of determining perovskite structures. *Acta Crystallogr. Sect. A* **1975**, *31*, 756–762. [CrossRef]

3. Knight, K.S.; Khalyavin, D.D.; Manuel, P.; Bull, C.L.; McIntyre, P. Nuclear and magnetic structures of KMnF3 perovskite in the temperature interval 10 K–105 K. *J. Alloy Compd.* **2020**, *842*, 155935. [CrossRef]

4. Jahn, H.A.; Teller, E.; Donnan, F.G. Stability of polyatomic molecules in degenerate electronic states I—Orbital degeneracy. *Proc. R. Soc. Lond. Ser. A—Math. Phys. Sci.* **1937**, *161*, 220–235.

5. Jahn, H.A.; Bragg, W.H. Stability of polyatomic molecules in degenerate electronic states II—Spin degeneracy. *Proc. R. Soc. Lond. Ser. A—Math. Phys. Sci.* **1938**, *164*, 117–131.

6. Englman, R. *The Jahn-Teller Effect in Molecules and Crystals*; Interscience Monographs and Texts in Physics and Astronomy; Wiley-Interscience: Hoboken, NJ, USA, 1972.

7. Bersuker, I.B. Four modifications of the Jahn-Teller effects. The problem of observables: Spin-orbit interaction, tunneling splitting, and orientational polarization of solids. *Phys. Chem. Chem. Phys.* **2023**, *25*, 1556–1564. [CrossRef] [PubMed]

8. Margadonna, S.; Karotsis, G. High temperature orbital order melting in KCrF₃ perovskite. *J. Mater. Chem.* **2007**, *17*, 2013–2020. [CrossRef]

9. Okazaki, A.; Suemune, Y. The Crystal Structures of KCuF3. *J. Phys. Soc. Jpn.* **1961**, *16*, 176–183. [CrossRef]

10. Paolasini, L.; Caciuffo, R.; Sollier, A.; Ghigna, P.; Altarelli, M. Coupling between Spin and Orbital Degrees of Freedom in KCuF₃. *Phys. Rev. Lett.* **2002**, *88*, 106403. [CrossRef]

11. Knox, K. Perovskite-like fluorides. I. Structures of KMnF3, KFeF3, KNiF3 and KZnF3. Crystal field effects in the series and in KCrF3 and KCuF3. *Acta Crystallogr.* **1961**, *14*, 583–585. [CrossRef]

12. Okazaki, A.; Suemune, Y. The Crystal Structures of KMnF3, KFeF3, KCoF3, KNiF3 and KCuF3 above and below their Néel Temperatures. *J. Phys. Soc. Jpn.* **1961**, *16*, 671–675. [CrossRef]

13. Scatturin, V.; Corliss, L.; Elliott, N.; Hastings, J. Magnetic structures of 3d transition metal double fluorides, KMeF₃. *Acta Crystallogr.* **1961**, *14*, 19–26. [CrossRef]

14. Varignon, J.; Bibes, M.; Zunger, A. Origins versus fingerprints of the Jahn-Teller effect in *d*-electron ABX₃ perovskites. *Phys. Rev. Res.* **2019**, *1*, 033131. [CrossRef]

15. Becke, A. Density-Functional Thermochemistry. III. The Role of Exact Exchange. *J. Chem. Phys.* **1993**, *98*, 5648. [CrossRef]

16. Lee, C.; Yang, W.; Parr, R. Development of the Colle-Salvetti Correlation-Energy Formula into a Functional of the Electron Density. *Phys. Rev. B* **1988**, *37*, 785. [CrossRef]

17. Adamo, C.; Barone, V. Toward Reliable Density Functional Methods Without Adjustable Parameters: The PBE0 Model. *J. Chem. Phys.* **1999**, *110*, 6158. [CrossRef]

18. Heyd, J.; Scuseria, G.E.; Ernzerhof, M. Hybrid functionals based on a screened Coulomb potential. *J. Chem. Phys.* **2003**, *118*, 8207–8215. [CrossRef]

19. Heyd, J.; Scuseria, G.E.; Ernzerhof, M. Erratum: "Hybrid functionals based on a screened Coulomb potential" [J. Chem. Phys. 118, 8207 (2003)]. *J. Chem. Phys.* **2006**, *124*, 219906. [CrossRef]

20. Dovesi, R.; Saunders, V.R.; Roetti, C.; Orlando, R.; Zicovich-Wilson, C.M.; Pascale, F.; Civalleri, B.; Doll, K.; Harrison, N.M.; Bush, I.J.; et al. CRYSTAL17 User's Manual; Università di Torino: Torino, Italy, 2017. Available online: http://www.crystal.unito.it (accessed on 10 February 2023).

21. Dovesi, R.; Erba, A.; Orlando, R.; Zicovich-Wilson, C.M.; Civalleri, B.; Maschio, L.; Rérat, M.; Casassa, S.; Baima, J.; Salustro, S.; et al. Quantum-Mechanical Condensed Matter Simulations with CRYSTAL. *Wires* **2018**, *8*, e1360. [CrossRef]

22. Dovesi, R.; Pascale, F.; Civalleri, B.; Doll, K.; Harrison, N.; Bush, I.; D'Arco, P.; Noël, Y.; Rérat, M.; Carbonnière, P.; et al. The CRYSTAL code, 1976–2020 and beyond, a long story. *J. Chem. Phys.* **2020**, *152*, 204111. [CrossRef]

23. Dovesi, R.; Freyria-Fava, F.; Roetti, C.; Saunders, V.R. Structural, electronic and magnetic properties of KMF₃ (M=Mn, Fe, Co, Ni). *Farad. Disc.* **1997**, *106*, 173. [CrossRef]

24. Dovesi, R.; Saunders, V.R.; Roetti, C.; Orlando, R.; Zicovich-Wilson, C.M.; Pascale, F.; Civalleri, B.; Doll, K.; Harrison, N.M.; Bush, I.J.; et al. CRYSTAL 2014 User's Manual; University of Torino: Torino, Italy, 2013.

25. Dovesi, R.; Pisani, C.; Roetti, C.; Saunders, V.R. Treatment of Coulomb Interactions in Hartree-Fock Calculations of Periodic Systems. *Phys. Rev. B* **1983**, *28*, 5781–5792. [CrossRef]

26. Causà, M.; Dovesi, R.; Orlando, R.; Pisani, C.; Saunders, V.R. Treatment of the Exchange Interactions in Hartree-Fock LCAO Calculations of Periodic Systems. *J. Phys. Chem.* **1988**, *92*, 909–913. [CrossRef]

27. Shanno, D.F. Conditioning of quasi-Newton methods for function minimization. *Math. Comput.* **1970**, *24*, 647–647. [CrossRef]

28. Broyden, C.G. The Convergence of a Class of Double-rank Minimization Algorithms 1. General Considerations. *IMA J. App. Math.* **1970**, *6*, 76–90. [CrossRef]

29. Broyden, C.G. The Convergence of a Class of Double-rank Minimization Algorithms. *IMA J. App. Math.* **1970**, *6*, 222–231. [CrossRef]

30. Fletcher, R. A new approach to variable metric algorithms. *Comput. J.* **1970**, *13*, 317–322. [CrossRef]

31. Goldfarb, D. A family of variable-metric methods derived by variational means. *Math. Comput.* **1970**, *24*, 23. [CrossRef]

32. Togo, A.; Tanaka, I. Spglib: A software library for crystal symmetry search. *arXiv* **2018**, arXiv:1808.01590.
References

1. Glazer, A.M. The classification of tilted octahedra in perovskites. *Acta Crystallogr. Sect. B* **1972**, *28*, 3384–3392. [CrossRef]

2. Glazer, A.M. Simple ways of determining perovskite structures. *Acta Crystallogr. Sect. A* **1975**, *31*, 756–762. [CrossRef]

3. Knight, K.S.; Khalyavin, D.D.; Manuel, P.; Bull, C.L.; McIntyre, P. Nuclear and magnetic structures of KMnF3 perovskite in the temperature interval 10 K–105 K. *J. Alloy Compd.* **2020**, *842*, 155935. [CrossRef]

4. Jahn, H.A.; Teller, E.; Donnan, F.G. Stability of polyatomic molecules in degenerate electronic states I—Orbital degeneracy. *Proc. R. Soc. Lond. Ser. A—Math. Phys. Sci.* **1937**, *161*, 220–235.

5. Jahn, H.A.; Bragg, W.H. Stability of polyatomic molecules in degenerate electronic states II—Spin degeneracy. *Proc. R. Soc. Lond. Ser. A—Math. Phys. Sci.* **1938**, *164*, 117–131.

6. Englman, R. *The Jahn-Teller Effect in Molecules and Crystals*; Interscience Monographs and Texts in Physics and Astronomy; Wiley-Interscience: Hoboken, NJ, USA, 1972.

7. Bersuker, I.B. Four modifications of the Jahn-Teller effects. The problem of observables: Spin-orbit interaction, tunneling splitting, and orientational polarization of solids. *Phys. Chem. Chem. Phys.* **2023**, *25*, 1556–1564. [CrossRef] [PubMed]

8. Margadonna, S.; Karotsis, G. High temperature orbital order melting in KCrF₃ perovskite. *J. Mater. Chem.* **2007**, *17*, 2013–2020. [CrossRef]

9. Okazaki, A.; Suemune, Y. The Crystal Structures of KCuF3. *J. Phys. Soc. Jpn.* **1961**, *16*, 176–183. [CrossRef]

10. Paolasini, L.; Caciuffo, R.; Sollier, A.; Ghigna, P.; Altarelli, M. Coupling between Spin and Orbital Degrees of Freedom in KCuF₃. *Phys. Rev. Lett.* **2002**, *88*, 106403. [CrossRef]

11. Knox, K. Perovskite-like fluorides. I. Structures of KMnF3, KFeF3, KNiF3 and KZnF3. Crystal field effects in the series and in KCrF3 and KCuF3. *Acta Crystallogr.* **1961**, *14*, 583–585. [CrossRef]

12. Okazaki, A.; Suemune, Y. The Crystal Structures of KMnF3, KFeF3, KCoF3, KNiF3 and KCuF3 above and below their Néel Temperatures. *J. Phys. Soc. Jpn.* **1961**, *16*, 671–675. [CrossRef]

13. Scatturin, V.; Corliss, L.; Elliott, N.; Hastings, J. Magnetic structures of 3d transition metal double fluorides, KMeF₃. *Acta Crystallogr.* **1961**, *14*, 19–26. [CrossRef]

14. Varignon, J.; Bibes, M.; Zunger, A. Origins versus fingerprints of the Jahn-Teller effect in *d*-electron ABX₃ perovskites. *Phys. Rev. Res.* **2019**, *1*, 033131. [CrossRef]

15. Becke, A. Density-Functional Thermochemistry. III. The Role of Exact Exchange. *J. Chem. Phys.* **1993**, *98*, 5648. [CrossRef]

16. Lee, C.; Yang, W.; Parr, R. Development of the Colle-Salvetti Correlation-Energy Formula into a Functional of the Electron Density. *Phys. Rev. B* **1988**, *37*, 785. [CrossRef]

17. Adamo, C.; Barone, V. Toward Reliable Density Functional Methods Without Adjustable Parameters: The PBE0 Model. *J. Chem. Phys.* **1999**, *110*, 6158. [CrossRef]

18. Heyd, J.; Scuseria, G.E.; Ernzerhof, M. Hybrid functionals based on a screened Coulomb potential. *J. Chem. Phys.* **2003**, *118*, 8207–8215. [CrossRef]

19. Heyd, J.; Scuseria, G.E.; Ernzerhof, M. Erratum: "Hybrid functionals based on a screened Coulomb potential" [J. Chem. Phys. 118, 8207 (2003)]. *J. Chem. Phys.* **2006**, *124*, 219906. [CrossRef]

20. Dovesi, R.; Saunders, V.R.; Roetti, C.; Orlando, R.; Zicovich-Wilson, C.M.; Pascale, F.; Civalleri, B.; Doll, K.; Harrison, N.M.; Bush, I.J.; et al. CRYSTAL17 User's Manual; Università di Torino: Torino, Italy, 2017. Available online: http://www.crystal.unito.it (accessed on 10 February 2023).

21. Dovesi, R.; Erba, A.; Orlando, R.; Zicovich-Wilson, C.M.; Civalleri, B.; Maschio, L.; Rérat, M.; Casassa, S.; Baima, J.; Salustro, S.; et al. Quantum-Mechanical Condensed Matter Simulations with CRYSTAL. *Wires* **2018**, *8*, e1360. [CrossRef]

22. Dovesi, R.; Pascale, F.; Civalleri, B.; Doll, K.; Harrison, N.; Bush, I.; D'Arco, P.; Noël, Y.; Rérat, M.; Carbonnière, P.; et al. The CRYSTAL code, 1976–2020 and beyond, a long story. *J. Chem. Phys.* **2020**, *152*, 204111. [CrossRef]

23. Dovesi, R.; Freyria-Fava, F.; Roetti, C.; Saunders, V.R. Structural, electronic and magnetic properties of KMF₃ (M=Mn, Fe, Co, Ni). *Farad. Disc.* **1997**, *106*, 173. [CrossRef]

24. Dovesi, R.; Saunders, V.R.; Roetti, C.; Orlando, R.; Zicovich-Wilson, C.M.; Pascale, F.; Civalleri, B.; Doll, K.; Harrison, N.M.; Bush, I.J.; et al. CRYSTAL 2014 User's Manual; University of Torino: Torino, Italy, 2013.

25. Dovesi, R.; Pisani, C.; Roetti, C.; Saunders, V.R. Treatment of Coulomb Interactions in Hartree-Fock Calculations of Periodic Systems. *Phys. Rev. B* **1983**, *28*, 5781–5792. [CrossRef]

26. Causà, M.; Dovesi, R.; Orlando, R.; Pisani, C.; Saunders, V.R. Treatment of the Exchange Interactions in Hartree-Fock LCAO Calculations of Periodic Systems. *J. Phys. Chem.* **1988**, *92*, 909–913. [CrossRef]

27. Shanno, D.F. Conditioning of quasi-Newton methods for function minimization. *Math. Comput.* **1970**, *24*, 647–647. [CrossRef]

28. Broyden, C.G. The Convergence of a Class of Double-rank Minimization Algorithms 1. General Considerations. *IMA J. App. Math.* **1970**, *6*, 76–90. [CrossRef]

29. Broyden, C.G. The Convergence of a Class of Double-rank Minimization Algorithms. *IMA J. App. Math.* **1970**, *6*, 222–231. [CrossRef]

30. Fletcher, R. A new approach to variable metric algorithms. *Comput. J.* **1970**, *13*, 317–322. [CrossRef]

31. Goldfarb, D. A family of variable-metric methods derived by variational means. *Math. Comput.* **1970**, *24*, 23. [CrossRef]

32. Togo, A.; Tanaka, I. Spglib: A software library for crystal symmetry search. *arXiv* **2018**, arXiv:1808.01590.
33. Mustapha, S.; D'Arco, Ph.; De La Pierre, M.; Noël, Y.; Ferrabone, M.; Dovesi, R. On the use of symmetry in configurational analysis for the simulation of disordered solids. *J. Phys. Condens. Matters* **2013**, *25*, 105401. [CrossRef]

34. D'Arco, Ph.; Mustapha, S.; Ferrabone, M.; Noël, Y.; De La Pierre, M.; Dovesi, R. Symmetry and random sampling of symmetry independent configurations for the simulation of disordered solids. *J. Phys. Condens. Matters* **2013**, *25*, 355401. [CrossRef] [PubMed]

35. Rutherford, J.S. The enumeration and symmetry-significant properties of derivative lattices. *Acta Crystallogr. Sect. A* **1992**, *48*, 500–508. [CrossRef]

36. Rutherford, J.S. The enumeration and symmetry-significant properties of derivative lattices. II. Classification by colour lattice group. *Acta Crystallogr. Sect. A* **1993**, *49*, 293–300. [CrossRef]

37. Rutherford, J.S. The enumeration and symmetry-significant properties of derivative lattices. III. Periodic colourings of a lattice. *Acta Crystallogr. Sect. A* **1995**, *51*, 672–679. [CrossRef]

38. Grau-Crespo, R.; Hamad, S.; Catlow, C.R.A.; de Leeuw, N.H. Symmetry-adapted configurational modelling of fractional site occupancy in solids. *J. Phys. Condens. Matter* **2007**, *19*, 256201. [CrossRef]

39. Hart, G.L.W.; Forcade, R.W. Algorithm for generating derivative structures. *Phys. Rev. B* **2008**, *77*, 224115. [CrossRef]

40. D'Arco, Ph.; Mustapha, S.; Pascale, F.; Dovesi, R. Symmetry independent configurations for the simulation of Jahn-Teller distorted crystalline systems. 2022, in preparation.

41. Williams, J.H. The molecular electric quadrupole moment and solid-state architecture. *Accounts Chem. Res.* **1993**, *26*, 593–598. [CrossRef]

**Disclaimer/Publisher's Note:** The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.
33. Mustapha, S.; D'Arco, Ph.; De La Pierre, M.; Noël, Y.; Ferrabone, M.; Dovesi, R. On the use of symmetry in configurational analysis for the simulation of disordered solids. *J. Phys. Condens. Matters* **2013**, *25*, 105401. [CrossRef]

34. D'Arco, Ph.; Mustapha, S.; Ferrabone, M.; Noël, Y.; De La Pierre, M.; Dovesi, R. Symmetry and random sampling of symmetry independent configurations for the simulation of disordered solids. *J. Phys. Condens. Matters* **2013**, *25*, 355401. [CrossRef] [PubMed]

35. Rutherford, J.S. The enumeration and symmetry-significant properties of derivative lattices. *Acta Crystallogr. Sect. A* **1992**, *48*, 500–508. [CrossRef]

36. Rutherford, J.S. The enumeration and symmetry-significant properties of derivative lattices. II. Classification by colour lattice group. *Acta Crystallogr. Sect. A* **1993**, *49*, 293–300. [CrossRef]

37. Rutherford, J.S. The enumeration and symmetry-significant properties of derivative lattices. III. Periodic colourings of a lattice. *Acta Crystallogr. Sect. A* **1995**, *51*, 672–679. [CrossRef]

38. Grau-Crespo, R.; Hamad, S.; Catlow, C.R.A.; de Leeuw, N.H. Symmetry-adapted configurational modelling of fractional site occupancy in solids. *J. Phys. Condens. Matter* **2007**, *19*, 256201. [CrossRef]

39. Hart, G.L.W.; Forcade, R.W. Algorithm for generating derivative structures. *Phys. Rev. B* **2008**, *77*, 224115. [CrossRef]

40. D'Arco, Ph.; Mustapha, S.; Pascale, F.; Dovesi, R. Symmetry independent configurations for the simulation of Jahn-Teller distorted crystalline systems. 2022, in preparation.

41. Williams, J.H. The molecular electric quadrupole moment and solid-state architecture. *Accounts Chem. Res.* **1993**, *26*, 593–598. [CrossRef]

**Disclaimer/Publisher's Note:** The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.