Supporting Information for. Predicting the Stability of Fullerene Allotropes Throughout the Periodic Table MA 02139

Size: px

Start display at page:

Download "Supporting Information for. Predicting the Stability of Fullerene Allotropes Throughout the Periodic Table MA 02139"

Gary Francis
5 years ago
Views:

1 Supporting Information for Predicting the Stability of Fullerene Allotropes Throughout the Periodic Table Qing Zhao 1, 2, Stanley S. H. Ng 1, and Heather J. Kulik 1, * 1 Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA Contents Table S1 Distance cutoffs for A-B bonds Table S2 Electronegativity differences Table S3 Bond distances of A 36 B 36 fullerenes Figure S1 A 36 B 36 nanoparticles Table S4 CN of A 36 B 36 nanoparticles Figure S2 Stability analysis of A 36 B 36 fullerenes Method S1 Build A 72 fullerenes Figure S3 HOMO-LUMO gaps of A 36 B 36 fullerenes Table S5 Experimental band gap of crystals Figure S4 HOMO, LUMO of A 36 B 36 fullerenes Table S6 CB, VB of A 36 B 36 fullerenes Figure S5 PDOS of A 36 B 36 fullerenes Figure S6 HOMO LUMO gaps of A and B atoms versus A 36 B 36 fullerenes Figure S7 Charge of A 36 B 36 fullerenes Figure S8 Charge analysis of A 36 B 36 fullerenes Table S7 Bond distances of A 28 B 28 fullerenes Table S8 Bond distances of A 30 B 30 fullerenes Table S9 Energy of A 28 B 28, A 30 B 30 fullerenes Method S2 Build A 60 fullerenes Text S3 Summary of acronyms Page S2 Page S2 Page S2 Page S3 Page S3 Page S4 Page S5 Page S6 Page S6 Page S7 Page S8 Page S9 Page S10 Page S10 Page S11 Page S11 Page S12 Page S13 Page S13 Page S14 Supporting Information for Fullerene allotropes Page S1

2 Table S1. Distances cutoffs for different A-B bonds in A. III-V N P As II-VI S Se B Zn Al Cd Ga In Table S2. Unitless Pauling electronegativity differences. III-V N P As II-VI S Se B Zn Al Cd Ga In Table S3. Comparisons of bond distances of A 36 B 36 fullerenes in A before and after geometry optimizations. BN AlN GaN InN BP AlP GaP InP Before After BAs AlAs GaAs InAs ZnS CdS ZnSe CdSe Before After Supporting Information for Fullerene allotropes Page S2

3 Figure S1. Symmetric nanoparticle models for nitrogen-containing III-V group compounds (left) and symmetric nanoparticle models for phosphorus-, arsenic-containing III-V group and II-VI group compounds (right). Table S4. Coordination number of geometry-optimized A 36 B 36 spherical nanoparticles. III-V N P As II-VI S Se B Zn Al Cd Ga In Supporting Information for Fullerene allotropes Page S3

4 Figure S2. Relationship between relative energy per pair of AB atoms in kcal/mol of A 36 B 36 fullerenes and materials properties: sum of A and B atoms atomic numbers or covalent radii, A- B bond distances of geometry-optimized A 36 B 36 fullerenes, and Pauling electronegativity differences between B and A atoms of III-V (green cycles) and II-VI (orange cycles) materials. Supporting Information for Fullerene allotropes Page S4

5 Method S1. Details of computing the relative stabilities of the homogeneous A 72 (A=C, Si, Ge) fullerenes. We also used the B 36 N 36 fullerene geometry obtained with the CRYSTAL14 package as a starting point to generate all A 72 fullerenes, and the only difference is replacing both B and N atoms by A atoms. The A 72 spherical nanoparticles (NP) are cut from their bulk face-centered diamond-cubic crystal structures. We conducted geometry optimizations on both A 72 fullerenes and A 72 nanoparticles to get the local minimum structures. We define a relative energy per A 2 atoms in optimized A 72 fullerenes (E(FL)) with respect to those in the optimized NP (E(NP)), for consistency with per pair of A, B atoms in A 36 B 36 fullerenes: E per A2 = E(FL) 36 E(NP) 36 (1) Supporting Information for Fullerene allotropes Page S5

6 Figure S3. Comparison of HOMO-LUMO gaps (in ev) of geometry-optimized A 36 B 36 fullerenes from III-V and II-VI materials obtained with ωpbeh (blue cycles) and B3LYP (red cycles). The default B3LYP definition in TeraChem uses the VWN1-RPA form for the local density approximation component of the correlation. Table S5: experimental band gaps of III-V and II-VI bulk crystal structures in ev. N P As S Se B Zn Al Cd Ga In Supporting Information for Fullerene allotropes Page S6

7 Figure S4: Cation (red) and anion (blue) element dependence of the individual HOMO and LUMO eigenvalues. The gray box represents the symbols from light to heavy atoms. Supporting Information for Fullerene allotropes Page S7

8 Table S6. Contributions of s, p, d orbitals of cation (A) and anion (B) atoms in valence band (VB) and conduction band (CB) of A 36 B 36 fullerenes. VB CB A-s A-p A-d B-s B-p A-s A-p A-d B-s B-p BN BP BAs AlN AlP AlAs GaN GaP GaAs InN InP InAs ZnS ZnSe CdS CdSe Supporting Information for Fullerene allotropes Page S8

9 Figure S5. Total density of states (TDOS) (black line) and orbital projected density of states (PDOS) of A atom s orbital (red solid line), A atom p orbital (red dashed line), A atom d orbital (red dashdot line), B atom s orbital (blue solid line) and B atom p orbital (blue dashed line) for (a) A=aluminum (b) A=indium (c) B=arsenic (d) II-VI fullerenes. The dominant orbitals in valence band and conduction band are indicated with light blue and light red shaded regions. The gray solid lines, green and orange dashed lines show the shifts of TDOS peaks and dominant orbitals peaks in PDOS of both the CB and VB. The brown dashed lines indicate the positions of the HOMO and LUMO. Supporting Information for Fullerene allotropes Page S9

Figure S6. Comparison of A 36 B 36 fullerene HOMO-LUMO gaps to the HOMO-LUMO gaps (all in ev) of individual A-type and B-type atoms following the same series as in Figure 5 in the main text.

10 Figure S6. Comparison of A 36 B 36 fullerene HOMO-LUMO gaps to the HOMO-LUMO gaps (all in ev) of individual A-type and B-type atoms following the same series as in Figure 5 in the main text. Figure S7. Charge on A (red) and B (blue) atoms from NBO analysis for A 36 B 36 fullerenes from III-V (dot) and II-VI (square) materials. Supporting Information for Fullerene allotropes Page S10

11 Figure S8. The relationship between the charge transfer from A atom to B atom of A 36 B 36 fullerenes given by NBO analysis from III-V (green dots) and II-VI (orange dots) materials. A linear best fit line (gray dashed) is also shown. Table S7. Comparisons of bond distances of A 28 B 28 fullerenes in A before and after geometry optimizations. BN AlN GaN InN BP AlP GaP InP Before After BAs AlAs GaAs InAs ZnS CdS ZnSe CdSe Before After Supporting Information for Fullerene allotropes Page S11

12 Table S8. Comparisons of bond distances of A 30 B 30 fullerenes in A before and after geometry optimizations. Before After A-B A-A B-B A-B BN BP BAs AlN AlP AlAs GaN GaP GaAs InN InP InAs ZnS ZnSe CdS CdSe Supporting Information for Fullerene allotropes Page S12

13 Table S9. Relative energy per pair of AB atoms in kcal/mol of geometry optimized A 28 B 28 fullerenes and A 30 B 30 fullerenes with respect to A 36 B 36 fullerenes from III-V and II-VI materials. BN BP BAs AlN AlP AlAs GaN GaP E(A 28 B 28 ) E(A 30 B 30 ) GaAs InN InP InAs ZnS ZnSe CdS CdSe E(A 28 B 28 ) E(A 30 B 30 ) Method S2. Details of obtaining the correlation between relative stabilities of the homogeneous A 60 (A=C, Si, Ge) fullerenes with respect to A 72 fullerenes and the ring-derived energy penalty differences. We used the C 60 fullerene geometry obtained from fullerene library as a starting point to generate all A 60 (A=C, Si, Ge) fullerenes, and screening the bond distances in the range of ±0.5 A around the experimental bond distances to get their optimal bond distances. We then conducted geometry optimizations on A 60 fullerenes to get the local minimum structures and defined a relative energy per A 2 atoms in optimized A 60 fullerenes (E(A 60 )) with respect to those in the optimized A 72 fullerenes we obtained before (E(A 72 )): E per A2 = E(A 60 ) 30 E(A 72 ) 36 (2) 4 The energy penalties of four-membered rings ( E penalty computed as follows: 5 ) and five-membered rings ( E penalty ) are 4 E penalty = 4 E(A H ) E(A 6 H 6 ) 6 (3), Supporting Information for Fullerene allotropes Page S13

14 5 E penalty = 5 E(A 5H 5 ) 5 E(A 6H 6 ) 6 (4) where E(A 4 H 4 ), E(A 5 H 5 ), and E(A 6 H 6 ) are the energies of optimized A 4 H 4 four-membered ring molecules, A 5 H 5 five-membered ring molecules, and A 6 H 6 six-membered ring molecules. The relative penalties for A 60 and A 72 fullerenes are calculated as a weighted difference in the number of unfavorable rings on a per-pair of atom basis: ΔE penalty = 12E 5 penalty 30 6E 4 penalty 36 (5) Method S3: Summary of acronyms A n B n : A is a cationic element (B, Al, Ga, or In in III-V materials), B is the anionic element (N, P, or As in III-V materials), and n is the number of atoms of each in materials described in this work. DFT: density functional theory LACVP*: A composite basis set from the Los Alamos LANLDZ effective core potential and the 6-31G* basis for lighter atoms. CNs: coordination numbers d cut (A B): cutoff for an A-b bond. A r cov : covalent (cov) radius of atom A. NBO: natural bond orbital NAO: natural atomic orbital PDOS: projected density of states σ: Gaussian broadening parameter in Hartrees (Ha). NPs: nanaoparticles Supporting Information for Fullerene allotropes Page S14

15 FL: fullerene E(FL): energy of a fullerene. Δχ B-A : unitless Pauling electronegativity difference. Δ-SCF: a method for computing band gaps from total energy differences after adding or removing an electron. HOMO: highest occupied molecular orbital LUMO: lowest unoccupied molecular orbital ω: range separation parameter in a hybrid functional ε HOMO : HOMO eigenvalue B3LYP: a hybrid exchange functional with Becke exchange and Lee-Yang-Parr correlation. ωpbeh: a range-separated hybrid with Perdew Burke Ernzerhof plus hybrid exchange PBE: Perdew Burke Ernzerhof functional 0D: isolated, not periodic system, e.g. a fullerene. CB: conduction band VB: valence band DOS: total density of states q A-B : charge transfer from A to B atoms. Bond A : extent of bonding character A atom contributes to A-B bonds. 4 E penalty : penalty for a four-membered ring model with respect to a six-membered ring model. n 4, n 5, n 6 are number of four-, five-, six-membered rings in the fullerenes. β: an overall descriptor (equation 11 main text). Supporting Information for Fullerene allotropes Page S15

Predicting the Stability of Fullerene Allotropes Throughout the Periodic Table

Predicting the Stability of Fullerene Allotropes Throughout the Periodic Table The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. Citation