The inductive effect in nitridosilicates and oxysilicates and its effects on 5d energy levels of Ce 3+

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The inductive effect in nitridosilicates and oxysilicates and its effects on 5d energy levels of Ce 3+ Yuwei Kong, Zhen Song, Shuxin Wang, Zhiguo Xia and Quanlin Liu* The Beijing Municipal Key Laboratory of New Energy Materials and Technologies, School of Materials Sciences and Engineering, University of Science and Technology Beijing, Beijing 100083, China Supporting information All the following results of statistical analysis of established models is calculated and output by SPSS software. Table S1 The statistical analytical results of equation (6) (a) /Removed a 1 µ χ b. Enter (b) Summary b R R Std. Error of the Estimate 1.898 a.807.800.0070153 b. Dependent Variable: WeightedAverageBondLength Sum of s df Mean F Sig. 1 Regression.005 1.005 104.684.000 b Residual.001 25.000 Total.006 26 (d) a 1 (Constant) 1.731.002 910.458.000 1.727 1.735 S1

µ χ.017.002.898 10.232.000.013.020 Table S2 The statistical analytical results of equation (7) (a) /Removed a 1 WeightedAverag ebondlength b Removed Method. Enter (b) Summary b R R Std. Error of the Estimate 1.998 a.995.995.0114276 a. Predictors: (Constant), WeightedAverageBondLength Sum of s df Mean F Sig. 1 Regression.771 1.771 5901.057.000 b Residual.004 27.000 Total.774 28 b. Predictors: (Constant), WeightedAverageBondLength (d) a 95.0% Confidence Interval B Std. Error Beta t Sig. Lower Upper 1 (Constant) 21.077.225 93.768.000 20.616 21.538 WeightedAverageBondLength -9.902.129 -.998-76.818.000-10.167-9.638 Table S3 The statistical analytical results of equation (9) (a) /Removed a S2

1 µ χ b. Enter (b) Summary b R R Std. Error of the Estimate 1.924 a.854.847.0624921 Sum of s df Mean F Sig. 1 Regression.523 1.523 134.030.000 b Residual.090 23.004 Total.613 24 (d) a 1 (Constant) 3.931.017 227.325.000 3.896 3.967 µ χ -.169.015 -.924-11.577.000 -.199 -.139 Table S4 The statistical analytical results of equation (11) (a) /Removed a 1 µ χ b. Enter (b) Summary b Std. Error of the R R Estimate 1.510 a.260.240.00573 S3

b. Dependent Variable: WeightedAverageBondLength Sum of s df Mean F Sig. 1 Regression.000 1.000 13.327.001 b Residual.001 38.000 Total.002 39 (d) a 1 (Constant) 1.622.002 839.378.000 1.618 1.626 µ χ.004.001.510 3.651.001.002.005 Table S5 The statistical analytical results of equation (12) (a) /Removed a 1 WeightedAvera gebondlength b Removed. Enter Method (b) Summary b R R Std. Error of the Estimate 1.996 a.992.992.00737 a. Predictors: (Constant), WeightedAverageBondLength Sum of s df Mean F Sig. 1 Regression.264 1.264 4852.230.000 b Residual.002 40.000 Total.266 41 S4

b. Predictors: (Constant), WeightedAverageBondLength (d) a 95.0% Confidence Interval B Std. Error Beta t Sig. Lower Upper 1 (Constant) 21.221.248 85.689.000 20.720 21.721 WeightedAverageBondLength -10.600.152 -.996-69.658.000-10.907-10.292 Table S6 The statistical analytical results of equation (13) (a) /Removed a 1 µ χ b. Enter (b) Summary b R R Std. Error of the Estimate 1.509 a.259.240.06113 Sum of s df Mean F Sig. 1 Regression.051 1.051 13.619.001 b Residual.146 39.004 Total.197 40 (d) a 1 (Constant) 4.025.020 197.671.000 3.984 4.067 S5

µ χ -.038.010 -.509-3.690.001 -.058 -.017 S6

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