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SUPPLEMENTARY MATERIAL

Topological Analysis of Tetraphosphorus Oxides

(P4O6+n (n=0-4))

Nancy Y. Acelas1, Diana López1, Fanor Mondragón1*, William Tiznado2 and Elizabeth Flórez3

1Institute of Chemistry, University of Antioquia, A.A. 1226, Medellín, Colombia 2Departamento de Ciencias Químicas, Facultad de Ciencias, Universidad Andres Bello, Av. República 275, Santiago, Chile. 3Department of Basic Sciences, University of Medellin, A.A 1226, Medellín, Colombia *Corresponding author: E-mail: [email protected] Table S1. Isomers and relative energies, the values in parentheses correspond to those obtained with the aug-cc-pcvtz basis set and the other values are the obtained with the aug- cc-pcvdz basis set. ∆ B3LYP is taken with reference to the most stable structure.

∆B3LYP Imaginary Electronic Molecule Structure Symmetry (eV) frequencies state 1 1 1 I C∞ 0.00 (0.00) 0 (0) ∑g ( ∑g) 1 1 1 II C2v 0.30 (0.47) 0 (0) A1 ( A’) 3 3 3 III C2v 0.48 (0.66) 0 (0) B2 ( B2) P2O 1 1 1 IV C2v (POP) 1.84 ( 2.23) 0 (1) A1 ( A1) 3 V C∞ 2.29 (2.32) 2 ( 2) nd (nd) 3 VI C∞ (POP) 2.49 (2.08) 1 (1) nd (nd) 3 3 3 I C2 0.00 (0.00) 0 (0) A ( A) 1 1 1 II C2 0.06 (0.11) 0 (0) A1 ( A) 3 3 3 III Cs 0.21(0.04) 0 (0) A” ( A”) 3 3 3 IV C2v 0.21 (0.04) 0 (0) A2 ( A2) 1 1 1 V Cs 0.62 (0.47) 0 (0) A’ ( A’) 1 1 1 P2O2 VI C2h 0.81 (0.75) 0 (1) Ag ( A) 3 3 3 + VII C∞ 0.84 (0.86) 2 (2) ∑g( ∑ g) 1 1 1 VIII C2v 0.88 (0.66) 1 (1) A1 ( A1) 1 IX C∞ 1.43 (1.46) 3 (3) nd (nd) 1 1 1 X C2v-b 1.90 (2.38) 0 (0) A1 ( A1) 3 3 3 XI C2v-b 3.58 (4.11) 1(1) B2 ( A2) 1 1 1 I C2 0.00 (0.00) 0 (0) A ( A) 1 1 1 II D3h 0.74 (1.00) 0 (0) A1’( A1) P2O3 3 3 3 III C2 2.51 (2.77) 1 (1) B ( B) 3 3 3 ” IV C2v 5.21 (5.51) 3 (3) A2 ( A ) 1 1 I 1 A ( A) C1-2 0.00 (0.00) 0(0) 1 1 II 1 A’( A) Cs 0.07 (0.08) 1(1) 1 1 III 1 A1( A) C3v 0.39 (0.49) 0(0) 1 1 IV 1 A1( A) D2d 1.14 (1.00) 0(0) 1 3 V 1 Ag ( B3u) D2h-2 1.20 (1.08) 1(2) 3 3 P2O4 VI 3 A( A) C1 2.89 (3.08 ) 0(0) 3 3 VII 3 A”( A”) Cs 2.89 (3.15) 0(1) 1 1 VIII 1 Ag( Ag) D2h 3.43 (3.62) 5(5) 3 3 IX 3 B2g( B2g) D2h 4.22 (4.46) 3(2) 3 3 X 3 B3u( B3u) D2h-2 4.49 (4.61) 2(3)

1 1 1 I D3h 0.00 (0.00) 0(0) A1’( A’) 1 1 1 II C2 3.10 (4.35) 0(0) A( A1) 3 3 III C2v 3.74 (13.53) 3 B1 3 3 1 P2O5 IV C2 4.49 (5.90) 1(0) A( A1) 1 1 1 V C2v 9.48 (10.94) 3(1) A1( A1’) 3 3 3 VI D2h 11.06(13.53) 1(1) B1u( B1u) 1 1 1 VII D2h 12.62 (14.77) 4(1) Ag( A1) Table S2. Geometric parameters of diphosphorus oxides obtained with the aug-cc-pcvdz basis set. Values in parentheses correspond to those obtained with the aug-cc-pcvtz basis set.

P2O P2O2 P2O3 P2O4 P2O5

Structure

1 C∞ 1 1 3 C2 C1 C2H

1 D3H Bond lengths (pm)R1 189 (189) 152 (148) 150 (146) 148 (145) 147 (144) R2 148 (147) 235 (233) 170 (165) 165 (160) 171 (167) R3 171 (166) 212 (207) R4 150 (146) Bond

angleA(P1-P2-O1) (Ả) 180.00 (180.00)

A(01-P1-P2) 108.35 (109.58)

A(O1-P1-O2) 109.98 (110.30) 135.72 (134.27) 128.48 (128.23)

A(P1-O3-P2) 124.93 (132.24) For the P2O3, P2O4 and P2O5, two, four and two structures of local minima were found respectively. In Table II other isomers are presented, however, these structures have negative frequencies and therefore correspond to activated complexes of n order (n=2,3,4, etc). It is important to observe that in some cases the change of the basis set can give raise to structures with imaginary frequencies. In the cases evaluated here the imaginary frequency can appear with either one of the basis sets. The formation of P2O4 corresponds to the addition of an oxygen atom to the structure of P2O3 and P2O5 is the molecule that has the highest structural

1 unit of the diphosphorus oxides and therefore a greater symmetry D3H. Figure S1. a) Ionization potential for diphosphorus oxides and b) HOMO-LUMO gap Table S3. Bond orders and charges for diphosphorus oxides, the values in parentheses correspond to those obtained with the aug-cc-pcvtz basis set and the other values are the obtained with the aug-cc-pcvdz basis set.

P2O P2O2 P2O3 P2O4 P2O5 PARAMETERS 3 1 1 1 C∞ C2h C2 C1 D3h

ATOM CHARGES NBO P1 -0.18 (-0.17) 0.87 (0.91) 1.55 (1.55) 2.46 (2.42) 2.39 (2.40)

P2 1.10 (1.11) 0.87 (0.91) 1.55 (1.55) 1.58 (1.57)

O1 -0.92 (-0.93) -0.87 (-0.91) -0.98 (-0.97) -0.97 (-0.96) -0.80 (-0.93) O2 -0.87 (-0.91) -1.15 (-1.15) -0.97 (-0.96) -0.73 (-0.98) O3 -0.98 (-0.97) -1.13 (-1.10) O4 -0.97(-0.97) CONNECTIVITY BOND ORDERS P1-P2 2.51 (2.53) 0.77 (0.77) 0.05(0.06) 0.03(0.03) 0.07 (0.08) P2-O1 1.35 (1.36) P1-O1 1.41 (1.40) 1.54 (1.57) 1.64 (1.52) P2-O2 1.57(1.58) 0.66(0.67) 0.61(0.67) P1-O2 0.66 (0.67) 1.41 (1.45) 0.61 (0.67) P2-O3 0.63 (0.65) P1-O3 0.67 (0.69) P2-O4 1.55 (1.57)

Table S3 presents the charges and bond orders calculated by population analysis (NBO) for diphosphorus oxides. It can be observed that the P-P bond varies from 2.53 for P2O to 0.08 for P2O5, indicating that the P2O bond is approximately triple, while in the P2O5 there is no bond formation, and as a consequence the P-P bond in the P2O is stronger than in the P2O2.

Structures with oxo-bridged bonds such as P2O3, P2O4, and P2O5 present values around 0.67, which could approximately correspond to a single bond. Besides, the P = O terminal bond orders are in the range from 1.35 for P2O to 1.64 for P2O5, which indicates greater strength in the P2O5 terminal bond. The negative charges are distributed mainly on the oxygen atoms due to the electronegativity of this element.