SUPPLEMENTARY INFORMATION. Multinuclear NMR of CaSiO3 Glass: Simulation from First-Principles

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1 Suemetary Materia (ESI) for PCCP This joura is the Ower Societies SUPPLEMENTARY INFORMATION Mutiucear NMR of CaSiO3 Gass: Simuatio from First-Pricies Afoso Pedoe,, * Thibaut Charetier 3 * ad Maria Cristia Meziai Diartimeto di Chimica, Uiversità di Modea e Reggio Emiia, Via G. Cami 83, 4 Modea, ITALIA Scuoa Normae Sueriore, Piazza dei Cavaieri 7, Pisa, ITALIA 3 CEA, IRAMIS, Service Iterdisciiaire sur es Systèmes Moécuaires et Matériaux, LSDRM F-99 Gif-sur-Yvette cedex, Frace

2 Suemetary Materia (ESI) for PCCP This joura is the Ower Societies SECTION. The NMR frequecy ν of the trasitio m m + of a ucear si I which is subjected to iteractios as rereseted by the Hamitoia H is give by ν m H m m + H () m + Cosiderig the quadruoar ad chemica shift iteractios, the tota Hamitoia H is () ( ) () H + H H () H + where () H, ( ) H are the first ad secod order quadruoar iteractio (iteractios are treated as erturbatio with resect to the domiat eema iteractio H γ N I ωi ) ad H is the (first order) chemica shift iteractio. Each iteractio is deedet uo the reative orietatio of its Pricia Axes System (PAS) with the aboratory frame (with axis aog the magetic fied). Itroducig the Wiger matrix rotatio eemets imα iγ D ( α β, γ ) e d ( β ) e where ( α β, γ ), (3), are the three Euer ages, deoted Ω for sae of simicity beow. The geera exressios of each iteractio are H () C, T V Dm I H ( ) ( I ) C ν I, m m ( I ) A,,4 ( Ω ) m 3 H, m () δiso + Vm Dm ( Ω ) I m ( η ) D ( Ω ) λ 3 λ λ η where V,, V, ± ad V λ, ± are the sherica comoets of λ ( λ, ) tesor i its ( ) PAS, 3 I( I ) T I +. 6 ( ) (4) (5) (6) Exressios of the A oerators ad m( η ) comoets are:

3 Suemetary Materia (ESI) for PCCP This joura is the Ower Societies A A A 4 4 ± 4 ± 4 ± 4 ( I( I + ) 3I ) I I I η η 3 4 η ( 8I( I + ) I 3) ( 8I( I + ) 34I 5) 3 η 7 3η 4 η 4 7 (8) (9) Itroducig the Euer ages Ω, that reates the chemica shift PAS to the quadruoar PAS ad taig advatage of the roerties of the Wiger rotatio eemet ( ) yieds the deedece of H with resect to Ω (over which the owder averagig is erformed) V m m D ( Ω ) Vm D ( Ω, ) D, ( Ω ) m V Vm D ( Ω, ) D, ( Ω ) m ( Ω ) D ( Ω ),, (7) Combiig a the revious exressios aows us to exad eemet as foows: ( Ω ) H i term of the Wiger rotatio H H D () m,,4 m + so that the NMR frequecy is

4 ν ν, ν,,4 +, m H D, m m + H ( Ω ) m + Suemetary Materia (ESI) for PCCP This joura is the Ower Societies This fia exressio aows the cacuatio of the NMR frequecy i term of the NMR arameters δ iso, δ A, η A, C, η ad Ω, as comuted from the outut of the GIPAW cacuatio. SECTION. Uder same rotatio, oe has to itroduce the Euer ages that reates the quadruoar (or chemica shift for I/) PAS to the rotor frame Ω. The atter is reated to the aboratory frame through the, R time-deedet Euer ages () t ( ω t,θ,) Ω R R where ωr πν R () is the siig frequecy ad θ the ages betwee the rotatio axis ad the magetic fied. Oce agai, taig advatage of the Wiger matrix rotatio eemets: D, ( Ω () t ) D ( Ω ) D ( ω t, θ,) D D,,,, R, R iωrt ( α, β, γ ) e d ( θ ) R i{ ωrt+ γ R } ( α, β,) e R R R R, d, ( θ ) () the time deedet NMR frequecy ca be writte as ν,( ),,4 +, ν D, ( αr, βr,) d,( θ ),,4 + ex{ i( ωrt + γ R )} ν ( αr, βr ) ex{ i( ωrt + γ R )}, () t ν D Ω () t (3)

5 Suemetary Materia (ESI) for PCCP This joura is the Ower Societies Tabe S. GIPAW ad exerimeta 9 Si NMR arameters for β-woastoite. Exerimeta data are tae from Ref. 3 δ iso Δ η Cac Ext Cac Ext Cac Ext Si() Si() Si(3)

6 Suemetary Materia (ESI) for PCCP This joura is the Ower Societies Tabe S. GIPAW ad exerimeta 7 O NMR arameters for β-woastoite. δ iso P Cac Ext 4 Cac Ext 4 OA ±. OA ±. OA ±. O ±. O ±. O ±. OC ±. OC ±. OC ±.

7 Suemetary Materia (ESI) for PCCP This joura is the Ower Societies Tabe S3. GIPAW ad Exerimeta 43 Ca NMR arameters for β-woastoite. δ iso C η Cac Ext 5 Cac Ext Cac Ext Ca() a..45.a. Ca() a..39.a. Ca(3) 34...a..5.a.

8 Suemetary Materia (ESI) for PCCP This joura is the Ower Societies Figure S.. View of the two CaSiO 3 gass modes after otimizatio at the GGA-PE eve of theory. Siico, oxyge ad cacium ios are rereseted i yeow, red ad gree sheres, resectivey.

9 Suemetary Materia (ESI) for PCCP This joura is the Ower Societies

10 Suemetary Materia (ESI) for PCCP This joura is the Ower Societies Figure S.. Theoretica 43 Ca 3MAS (simuated at 6.4T) sectrum for CaSiO 3. The ea maximum of the sectra of 5 (bue cross), 6 (bac cross) ad 7-fod (red cross) coordiated Ca ios are aso reorted.

11 Suemetary Materia (ESI) for PCCP This joura is the Ower Societies Refereces. () Scott, D. Mutivariate Desity Estimatio: Theory, Practice ad Visuaizatio; Wiey- Itersciece: New Yor, 99. () Rose, M. E. Eemetary Theory of Aguar Mometum; Wiey: New Yor, 957. (3) Hase, M. R.; Jaobse, H. J.; Sibsted, J. Iorg. Chem. 3, 4, 368. (4) Mueer, K. T.; atisberger, J. H.; Woote, E. W.; Pies, A. J. Phys. Chem. 99, 96, 7. (5) Duree, R.; Howes, A. P.; Koh, S. C. Chem. Phys. Lett. 997, 76, 399.