How Partial Atomic Charges and Bonding. Orbitals Affect the Reactivity of Aluminum

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Supporting Information for: How Partial Atomic Charges and Bonding Orbitals Affect the Reactivity of Aluminum Clusters with Water? Anthony M.S Pembere ξ, Xianhu Liu ξ, Weihua Ding, Zhixun Luo * State Key Laboratory for Structural Chemistry of Unstable and Stable Species, Institute of Chemistry, Chinese Academy of Sciences; and University of Chinese Academy of Sciences, Beijing 100090, China. * Correspondence. Email: zxluo@iccas.ac.cn ξ These authors contributed equally to this paper and share the first authorship. This paper is published to memorise A.W Castleman in the Pennsylvania State University. 1

S1. Energy Calculation Table S1. Binding energies (ev) calculated at B3LYP/ aug-cc-pvtz level of theory. Al 1 4H 2 O -1.52 Al 2 4H 2 O -1.45 Al 3 4H 2 O -1.02 Al 4 4H 2 O -1.01 Al 5 4H 2 O -1.03 Table S2. Relative energies for the reaction coordinates of Al 13 + H 2 O, Al 13 + H 2 O, Al 12 + H 2 O, Al 12 + H 2 O, Al 6 + H 2 O, Al 6 +H 2 O, Al 7 + H 2 O and Al 7 +H 2 O. Energies are in ev. Calculated at M06/CEP-31G* Level of theory. Path I 1 TS1 I 2 Al - 13 +H 2 O -0.19 0.29-0.83 Al 13 +H 2 O -0.64-0.11-1.43 Al - 12 +H 2 O -0.58-0.27-1.78 Al 12 +H 2 O -0.74-0.31-1.57 Al 6 +H 2 O -0.75-0.40-2.26 Al - 6 +H 2 O -0.32 0.16-1.80 Al 7 +H 2 O -0.47-0.01-1.72 Al - 7 +H 2 O -0.31 0.20-2.33 Table S3. Relative energies for the reaction coordinate of Al 6 +2H 2 O. Energies are in ev. Calculated at M06/CEP-31G* Level of theory. Path I1 TS1 I2 TS2 I3 TS3 I4 TS4 I5 Al 6 - +2H 2 0-0.75-0.72-2.24-1.53-1.62-1.51-3.75-3.31-3.32 Table S4. Relative energies for the reaction coordinate of Al 6 +4H 2 O. Energies are in ev. Calculated at M06/CEP-31G* Level of theory. Path I1 TS1 I2 TS2 I3 TS3 I4 TS4 I5 TS5 Al 6 - +4H 2 0-1.87-1.81-2.76-2.58-2.85-2.50-3.37-3.09-3.36-3.14 I6 TS6 I7 TS7 I8 TS8 I9 TS9 I10-3.43-3.27-5.12-4.65-4.67-4.48-4.82-4.75-5.01 2

S2. FMO Analysis Details of the FMO analysis performed at M06/CEP-31G* // B3LYP/ aug-ccpvtz level of theory are provided. The global electrophilicity index, ω, has been given by, ω= (µ 2 /2η), in terms of the electronic chemical potential µ and the chemical hardness η. Both quantities may be approached in terms of the one-electron energies of the frontier molecular orbitals HOMO and LUMO, εh and εl, as µ (εh + εl)/2 and η (εl - εh), respectively. Figure S1. The HOMOs, LUMOs, and HOMO LUMO gaps of water and Al 13 /Al 12 /Al 13 /Al 12 clusters. Atoms in purple, red, and white colors refer to Al, O, and H respectively. Figure S2. The HOMOs, LUMOs, and HOMO LUMO gaps of water and Al 6 /Al 6 /Al 7 /Al 7 clusters. Atoms in purple, red, and white colors represent Al, O, and H respectively. 3

Table S5. Energies of the frontier molecular orbitals and the global electrophilicity indexes of the Al clusters and H 2 O. Energies are in ev. εh εl HL gap(η) µ ω - Al 13-2.24 0.35 2.59-0.95 0.17 Al 13-5.34-2.93 2.41-4.14 3.56 - Al 12-1.65 0.03 1.68-0.81 0.48 Al 12-5.01-3.75 1.26-4.38 3.48 - Al 7-1.10 0.61 1.71-0.25 0.02 Al 7-4.91-3.01 1.90-3.96 4.13 - Al 6-1.01 1.06 2.07 0.03 0.0002 Al 6-4.91-3.91 1.00-4.41 9.72 H 2 O -8.82-0.68 8.14-4.75 1.39 S3. NPA Analysis As supplementary materials to the results in the main text, details of the natural population analysis (NPA) performed at M06/CEP-31G* level of theory are provided. Figure S3. Atom labels for all the following analysis. Atoms in purple, red, and white colors represent Al, O, and H respectively. 4

Table S6. Summary of Natural Population Analysis for H 2 O. Table S7. Summary of Natural Population Analysis for Al 12. 5

Table S8. Summary of Natural Population Analysis for Al 12 H 2 O complex. Table S9. Summary of Natural Population Analysis for Al 12. 6

Table S10. Summary of Natural Population Analysis for Al 12 H 2 O complex. Table S11. Summary of Natural Population Analysis for Al 13. 7

Table S12. Summary of Natural Population Analysis for Al 13 H 2 O complex. Table S13. Summary of Natural Population Analysis for Al 13 complex. 8

Table S14. Summary of Natural Population Analysis for Al 13 H 2 O complex. Table S15. Summary of Natural Population Analysis for Al 6. 9

Table S16. Summary of Natural Population Analysis for Al 6 H 2 O complex. Table S17. Summary of Natural Population Analysis for Al 6 -. Table S18. Summary of Natural Population Analysis for Al 6 - H 2 O complex. 10

Table S19. Summary of Natural Population Analysis for Al 6-2H 2 O complex. Table S20. Summary of Natural Population Analysis for Al 6-4H 2 O complex. 11

Table S21. Summary of Natural Population Analysis for Al 7 - Table S22. Summary of Natural Population Analysis for Al 7 - H 2 O complex. 12

Table S23. Summary of Natural Population Analysis for Al 7. Table S24. Summary of Natural Population Analysis for Al 7 H 2 O complex. 13

S4. NBO Analysis The second order perturbative energy provides a measure of the overlap integral between the lone-pair orbital of the acceptor and the antibonding orbital of the donor. For each donor NBO (i) and acceptor NBO (j), the stabilization energy E(2) associated with delocalization i j is estimated as; where q i is the donor orbital occupancy, e i, e j are diagonal elements (orbital energies) and F(i,j) is the off-diagonal NBO Fock matrix element. (s1) Table S25. Second order perturbation theory analysis of Fock matrix in NBO donor acceptor interactions in Al 13 - H 2 O. Energies are in ev. Table S26. Second order perturbation theory analysis of Fock matrix in NBO donor acceptor interactions in Al 13 H 2 O. Energies are in ev. 14

Table S27. Second order perturbation theory analysis of Fock matrix in NBO donor acceptor interactions in Al 12 - H 2 O. Energies are in ev. Table S28. Second order perturbation theory analysis of Fock matrix in NBO donor acceptor interactions in Al 12 H 2 O. Energies are in ev. Table S29. Second order perturbation theory analysis of Fock matrix in NBO donor acceptor interactions in Al 6 H 2 O. Energies are in ev. 15

Table S30. Second order perturbation theory analysis of Fock matrix in NBO donor acceptor interactions in Al 6 H 2 O. Energies are in ev. Table S31. Second order perturbation theory analysis of Fock matrix in NBO donor acceptor interactions in Al 7 H 2 O. Energies are in ev. Table S32. Second order perturbation theory analysis of Fock matrix in NBO donor acceptor interactions in Al 7 H 2 O. Energies are in ev. S5. Cartesian Coordinates for the Optimized Structures As supplementary materials to the results in the main text, XYZ coordinates for the optimized structures are provided below. Table S33. I1 for Al 13 - +H 2 O Pathway 16

Table S34. TS1 for Al 13 - +H 2 O Pathway Table S35. 12 for Al 13 - +H 2 O Pathway 17

Table S36. I1 for Al 13 +H 2 O Pathway Table S37. TS1 for Al 13 +H 2 O Pathway Table S38. I2 for Al 13 +H 2 O Pathway 18

Table S39. I1 for Al 12 - +H 2 O Pathway Table S40. TS1 for Al12 - +H2O Pathway Table S41. I2 for Al 12 - +H 2 O Pathway 19

Table S42. I1 for Al 12 +H 2 O Pathway Table S43. TS1 for Al 12 +H 2 O Pathway Table S44. I2 for Al 12 +H 2 O Pathway 20

Table S45. I1 for Al 6 + H 2 O Pathway Table S46. TS1 for Al 6 + H 2 O Pathway Table S47. I2 for Al 6 + H 2 O Pathway Table S48. I1 for Al 6 - + H 2 O Pathway 21

Table S49. TS1 for Al 6 - + H 2 O Pathway Table S50. 12 for Al 6 - + H 2 O Pathway Table S51. 11 for Al 7 + H 2 O Pathway Table S52. TS1 for Al 7 + H 2 O Pathway 22

Table S53. I2 for Al 7 + H 2 O Pathway Table S54. I1 for Al 7 - + H 2 O Pathway Table S55. TS1 for Al 7 - + H 2 O Pathway Table S56. 12 for Al 7 - + H 2 O Pathway 23

Table S57. 11a for Al 6 - + 2H 2 O Pathway Table S58. 11b for Al 6 - + 2H 2 O Pathway Table S59. 11c for Al 6 - + 2H 2 O Pathway Table S60. ts1 for Al 6 - + 2H 2 O Pathway 24

Table S61. 12 for Al 6 - + 2H 2 O Pathway Table S62. ts2 for Al 6 - + 2H 2 O Pathway Table S63. 13 for Al 6 - + 2H 2 O Pathway Table S64. TS3 for Al 6 - + 2H 2 O Pathway 25

Table S65. I4 for Al 6 - + 2H 2 O Pathway Table S66. TS4 for Al 6 - + 2H 2 O Pathway Table S67. I5 for Al 6 - + 2H 2 O Pathway 26

Table S68. I1a for Al 6 - + 4H 2 O Pathway Table S69. I1b for Al 6 - + 4H 2 O Pathway Table S70. TS1 for Al 6 - + 4H 2 O Pathway 27

Table S71. I2 for Al 6 - + 4H 2 O Pathway Table S72. TS2 for Al 6 - + 4H 2 O Pathway Table S73. I3 for Al 6 - + 4H 2 O Pathway 28

Table S74. TS3 for Al 6 - + 4H 2 O Pathway Table S75. I4 for Al 6 - + 4H 2 O Pathway Table S76. TS4 for Al 6 - + 4H 2 O Pathway 29

Table S77. I5 for Al 6 - + 4H 2 O Pathway Table S78. TS5 for Al 6 - + 4H 2 O Pathway Table S79. I6 for Al 6 - + 4H 2 O Pathway 30

Table S80. TS6 for Al 6 - + 4H 2 O Pathway Table S81. I7 for Al 6 - + 4H 2 O Pathway Table S82. TS7 for Al 6 - + 4H 2 O Pathway 31

Table S83. I8 for Al 6 - + 4H 2 O Pathway Table S84. TS8 for Al 6 - + 4H 2 O Pathway Table S85. I9 for Al 6 - + 4H 2 O Pathway 32

Table S86. TS9 for Al 6 - + 4H 2 O Pathway Table S87. I10 for Al 6 - + 4H 2 O Pathway 33

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