Supporting Information. Structure and electronic properties of a continuous random network model of amorphous zeolitic imidazolate framework (a-zif)

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1 Supporting Information Structure and electronic properties of a continuous random network model of amorphous zeolitic imidazolate framework () Puja Adhikari, Mo Xiong, Neng Li *, Xiujian Zhao, Paul Rulis, and Wai-Yim Ching * Department of Physics and Astronomy, University of Missouri-Kansas City, Kansas City, MO 64, USA. State Key Laboratory of Silicate Materials for Architectures, Wuhan University of Technology, No., Luoshi Road, Wuhan 437, P. R. China *Corresponding authors: Neng Li: lineng@whut.edu.cn; Wai-Yim Ching: Chingw@umkc.edu Construction and optimization of model It is well-known that ZIFs are closely related to zeolitic silica polymorphs by virtue of their analogous tetrahedral connectivity. However, the - distance of separation is approximately twice that of Si-Si in a-sio, which indicates that the volume of an analogous ZIF may be approximated by a supercell of a-sio with IM bridges that make a IM angle close to 45, similar to the Si-O-Si angle in a-sio. In converting the a-sio model to the model, we executed an in-house developed program to replace the Si with, the O with IM, and to keep the two atoms and IM in the same plane as shown in Fig. (a). Using a script that directly mapped the atoms in the -IM- plane to the Si-O-Si plane, we converted the enlarged a-sio model of 6 atoms to the initial model of 98 atoms retaining the same network topology. This initial structure was then force relaxed using the density functional theory (DFT)-based Vienna Ab Initio Simulation Package (VASP). We used the projector augmented wave (PAW) method with the Perdew-Burke-Ernzerhof (PBE) 3 potential for the exchange correlation functional within the generalized gradient approximation (GGA). For the electronic relaxation, a high energy cutoff of ev was used with the electronic convergence criterion set at -5 ev. For ionic relaxation, we set the force convergence criteria to be -3 ev/å. A single k-point at the zone center is sufficient for a large glassy model such. Fig. (c) - (f) depicts the final relaxed structures for,,, and. The relaxed cell parameters are listed in Table. The model converted from the a-sio model (space group P) has the same ring statistics, containing 5-, 6-, 7-, 8- and a few 9- membered rings and no 4-membered rings. Although crystalline and have identical chemical compositions [(C 3 H 3 N ) ], consisting of the divalent + and unsubstituted imidazole ligand S

2 [(C 3 H 3 N ) ], their structures and network topologies are quite different from. While contains the -methylimidazole ([(C 4 H 5 N ) ]) as the ligand. and are orthorhombic with space group Pbca and I4 cd respectively. Both of them contain 4-membered rings., however, has a cubic space group I43m and contains 6-membered rings and large pores. Electronic structure calculations of the model using OLCAO We used the first principles orthogonalized linear combination of atomic orbitals (OLCAO) method 4 for electronic structure and bonding calculations, based on the VASP-relaxed structure. The OLCAO method uses atomic orbitals for basis expansion, which is expedient and efficient for the calculation of electronic structure and optical properties. The combination of these two DFT-based methods has been demonstrated to be highly effective in the study of large, complex systems including noncrystalline solids 5-, liquids, large organic crystals, and biomolecules 3-4. More than years ago, the OLCAO method has already been used to calculate the structure and properties of a large-pore zeolite, microporous titanosilicate (ETS-) 5. In addition to the usual calculation of the density of states (DOS) and partial DOS (PDOS), the evaluation of effective charges Q α * at each atom and bond order (BO) values (overlap population) ρ αβ between any pair of atoms (α, β) based on Mulliken population analysis 6-7 are of central importance. () Q = C C S and ρ = C C S n* n * n n α iα jβ iα, jβ αβ iα jβ iα, jβ i n j, β n j, β occ occ Here i, j label the orbital quantum number and n the band index, are the eigenvector coefficients of the wave function and S α β is the overlap matrix between atomsα and β. The BO value αβ is a direct i, j quantitative measure of the strength of a bond between a pair of atoms. Although BO is not a quantum observable, it is far more accurate and precise than pure geometric criteria or other parameters such as coordination numbers. The Mulliken scheme is basis set-dependent and therefore its application must be confined to a specific method and a well-defined basis set. It is most effective when a more localized minimal basis set is used. In the present work, the BO is calculated using a minimal basis (MB) whereas for the self-consistent potential and electronic structure calculation, a full basis (FB) set is used (see reference 4 for details). Although there are other more elaborate methods for calculating BO values, they are usually limited to simpler molecules or crystals, are based on the numerical evaluation of a dense 3- dimensional mesh, and are therefore less efficient for analyzing multi-component complex structures such as. Fig. 3 shows the calculated TDOS, PDOS, and BO distributions of. Fig. S below shows n Cj β ρ S

3 the DOS and PDOS for the crystalline,, and. The BO distribution for the crystalline phases are similar to that of. (a) 8 (b) (c) PDOS(states/eV) Energy (ev) Energy (ev) Fig.S: and partial DOS of (a) (b) (c). The total bond order density (TBOD) is obtained by summing all the BO pairs and normalizing by the cell volume. TBOD is a single parameter from the electronic structure that reflects the internal cohesion of complex materials. The TBOD can be resolved into partial bond order density (PBOD) for any specific groups of atomic pairs. The use of TBOD and PBOD as a quantum mechanical metric for characterizing interatomic bonding in a variety of materials has been demonstrated recently 8-. Optical properties calculation for model For interband optical properties, the imaginary part of the dielectric function ε is evaluated first according to 4 : e v ( ) ( ) ( ) ( ) ( ) ( ( ) ( ) ) 3 v v v v v v v v ε hω = dk,, ψ n k r i ψ l k r fl k fn k δ En k El k ω πmω h BZ h () n, l Here E = ħω is the photon energy, l and n label the occupied and unoccupied states respectively, (, ) is the wave function for the n th state with energy ( ) at Brillouin zone point k, and ( ) is the Fermi distribution function. The momentum matrix elements (, ) (, ) are explicitly calculated from the ab initio wave functions. Only one k-point at the zone center (,,) is used in the S3

4 present calculation for. The real part of the dielectric function ε is obtained from the imaginary part ε via Kramers Kronig transformation : ( h ) π ( h ) sε ω ds s ω = + P ε ω From the complex dielectric function, the refractive index n can be estimated from the square root of ε at zero frequency, or = ε (). Also obtained is the energy loss function ELF (ħω). Peaks in the ELF are usually identified as plasmon peaks for the collective excitation of electrons in the solid. ε ( hω) ELF( hω) = IM{ } =. ε ( hω) [ ε ( hω) ε ( hω)] + In Fig. S, we compare the optical properties for the four ZIF systems:,,, and. The spectra look very similar because of the similarity in the short range order but minor differences in the peak positions can be clearly seen implying that accurate measurements could detect the variations in the optical properties due to sensitive dependence on their structures. (3) (4) ε (a) ε (b) ELF (c) Fig. S: Comparison of the optical properties of the 4 ZIFs-systems. (a), (b), (c) ELF. S4

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