1.
Tight Binding Simulation of Finite Temperature Electronic
Structure in Methylammonium Lead Iodide (MAPbI3)
David Abramovitch1 and Liang Tan2
1Department of Physics, University of California Berkeley
and 2Molecular Foundry, Lawrence Berkeley National Lab

2.
Motivation
Halide Perovskite electronic structure is
connected to nonlinear lattice dynamics
on length and time scales too large for
DFT A. Poglitsch and D. Weber J. Chem. Phys. 87, 6373 (1987)
Atomic orbital Tight Binding Models:
Previous: Boyer-Richard et al J. Phys. Chem. Lett. 2016,
7, 19, 3833-3840, Zheng et al Energy Environ.
Sci.,2019,12,1219
Our model modifies original finite temperature
model by Mayers et al Nano Lett. 2018, 18, 12, 8041-
8046
→ Better prediction of transverse modes and
charge fluctuations
→ Thorough benchmarking against DFT shows
improvements

3.
Methods
Orbitals: Wannier90 projections of
Pb s, Pb p, and I p orbitals
Atom positions from classical MD
↓
DFT electronic structure and Wannier90
projection onto atomic orbitals
↓
Fit onsite and hopping parameters from
distances, potentials, etc.
↓
Model Hamiltonian
↓
Tight Binding Electronic Structure

4.
Onsite Energies
Onsite Energies:
Fit: E = E0 + aV(0) + b d2V/dx2
Symmetry based Spin Orbit Coupling between p
orbitals on same atom as in Mayers et al Nano Lett. 2018,
18, 12, 8041-8046

5.
Hopping Parameters

6.
Tests - Bandgap and Fluctuations
The new model predicts
fluctuations in the gap gap
much more accurately, across a
range of temperatures and
phases
For 300 K:
DFT Bandgap = 0.44 eV
TB Bandgap = 0.54 eV

7.
Tests - Band Edge

8.
Urbach Tail
Density of states calculations show a
small (5 - 20 meV) temperature
dependent Urbach tail.
30 8x8x8 structures with 10x10x10 kpoint
grid and 2 meV Gaussian smoothing

9.
Low Temperature Carrier Mobility
Collaboration with McClintock et al
(J. Phys. Chem. Lett 2020, 11, 3)
found dramatically increased
transport at low temperatures
Our TB model indicates temperature
effects on free carrier mass and
scattering are too small, supporting
excitonic explanation

10.
Conclusion and Outlook
Quantitatively accurate tight binding
allows for new calculations
Applicable to nanostructures,
surfaces, etc.
General procedure is transferable to
other perovskites and likely beyond Mayers et al Nano Lett. 2018, 18, 12, 8041-8046

11.
Acknowledgements
This research was supported by the Computational
Materials Sciences Program funded by the US
Department of Energy, Office of Science, Basic Energy
Sciences, Materials Sciences and Engineering Division.
This research used resources of the National Energy
Research Scientific Computing Center, a DOE Office of
Science User Facility supported by the Office of Science
of the U.S. Department of Energy under Contract No. DE-
AC02-05CH11231.
Travel costs were supported in part by the National
Society of Physics Students

12.
References
[1] M. Z. Mayers, L. Z. Tan, D. A. Egger, A. M.Rappe, and D. R. Reichman, How lattice and charge fluctuations control carrier dynamics in halide
perovskites, Nano Letters 18, 8041 (2018), pMID: 30387614,https://doi.org/10.1021/acs.nanolett.8b04276.
[2] A. Mattoni, A. Filippetti, M. I. Saba, and P. Delugas,Methylammonium rotational dynamics in lead halide perovskite by classical molecular
dynamics: The role of temperature, The Journal of Physical Chemistry C119, 17421(2015), https://doi.org/10.1021/acs.jpcc.5b04283.
[3] M. T. Weller, O. J. Weber, P. F. Henry, A. M. Di Pumpo,and T. C. Hansen, Complete structure and cation orientation in the perovskite photovoltaic
methylammonium lead iodide between 100 and 352 k, Chem. Commun.51, 4180(2015).
[4] T. Baikie, Y. Fang, J. M. Kadro, M. Schreyer, F. Wei,S. G. Mhaisalkar, M. Graetzel, and T. J. White, Synthesis and crystal chemistry of the hybrid
perovskite(ch3nh3)pbi3 for solid-state sensitised solar cell applications, J. Mater. Chem. A1, 5628 (2013).
[5] S. Boyer-Richard, C. Katan, B. Traor ́e, R. Scholz, J.-M. Jancu, and J. Even, Symmetry-based tight binding modeling of halide perovskite
semiconductors, The Journal of Physical Chemistry Letters 7, 3833 (2016), pMID:27623678, https://doi.org/10.1021/acs.jpclett.6b01749.
[6] L. McClintock, R. Xiao, Y. Hou, C. Gibson, H. C.Travaglini, D. Abramovitch, L. Z. Tan, R. T. Senger,Y. Fu, S. Jin, and D. Yu, Temperature and
gate dependence of carrier diffusion in single crystal methylammonium lead iodide perovskite microstructures, The Journal of Physical Chemistry
Letters 11, 1000 (2020), pMID:31958953, https://doi.org/10.1021/acs.jpclett.9b03643.
[7]A.Poglitsch and D.Weber, Dynamic disorder in methylammonium trihalogenoplumbates (ii) observed by millimeter - wave spectroscopy ,The
Journal of Chemical Physics 87,6373 (1987),https://doi.org/10.1063/1.453467.
[8] F. Zheng and L.-w. Wang, Large polaron formation and its effect on electron transport in hybrid perovskites, EnergyEnviron. Sci.12, 1219 (2019)

13.
Supporting Slides

14.
Other Hopping Parameters
Next nearest neighbors: Spin orbit coupling occurs between p
orbitals on the same atom, as follows:
With 𝛾 = 0.31 eV for I and 𝛾 = 0.56 eV for Pb, as in
Mayers et al.
Nano Letters 2018 18 (12), 8041-8046
Mean (eV) 0.139 0.160
Standard
Deviation (eV)
0.0209 0.0349
Best Fit Error (eV) -- 0.0114

15.
Methods
Atom positions from classical MD
↓
Parameterize model by computing
DFT electronic structure and using
Wannier90 to project to atomic
orbitals.
↓
Fit onsite and neighbor hopping
parameters based on structure,
potentials, etc.
Calculation Details:
MD: Force field from Mattoni et al2, use
experimental lattice ratios3,4 and equilibrate volume
on 6x6x6 orthorhombic supercell. Ran NVT
trajectories on 2x2x2 stoichiometric (MAPbI3)
supercells and stoichiometric 8x8x8 supercells.
2x2x2 supercells are used for parameterizing tight
binding.
DFT: Quantum Espresso, PBE GGA functional,
OPIUM norm-conserving non-local
pseudopotentials, 4x4x4 𝚪 centered k-point grid, 50
Rydberg energy cutoff, non-collinear spin orbit.

16.
Atomic Orbitals
Orbitals: Wannier90 projections
of Pb s, Pb p, and I p orbitals
Atomic Orbital Wannier Hamiltonian shows
very good prediction of band structure

17.
Onsite Energies
Orbital Mean
(eV)
Standard
Deviation (eV)
Fit Error
(eV)
Pb s -2.45 0.119 0.0583
Pb p 5.93 0.129 0.0598
I p 2.51 0.204 0.0942
Onsite energies are fitted linearly using
coulomb potential, second derivative, and
unit cell volume.
Onsite Energies:
Fit: E = E0 + aV(0) + b d2V/dx2

18.
Hopping - Sigma Bonds
Mean 1.029 eV (geometry determines sign) 1.663 eV
Standard Deviation 0.192 eV 0.178 eV
Best Fit Error 0.0146 eV 0.0351 eV

19.
Hopping - Pi Bonds and Junctions
Mean -0.373 eV 0.0 eV (sign from displacement and geometry)
Standard Deviation 0.0852 eV 0.227 eV
Best Fit Error 0.0239 eV 0.0247 eV

20.
Tests - Bandgap and Fluctuations
The new model predicts
fluctuations in the gap gap
much more accurately, across a
range of temperatures and
phases
Tempe
rature
(K)
DFT Bandgap
mean (SD)
(eV)
New Model
Bandgap mean
(SD) (eV)
Model 8x8x8
Bandgap mean
(SD) (eV)
150 0.574 (0.036) 0.737 (0.034) 0.869 (0.0059)
220 0.422 (0.050) 0.546 (0.061) 0.725 (0.014)
300 0.440 (0.049) 0.535 (0.060) 0.643 (0.0072)

21.
Tests - Original Model Band Structure

22.
Tests - New Model Band Structure

23.
Thing Explained
Better Computer Way to Understand Tight Waves and Excited Stuff in Warm Sun
Catching Rock
These new sun catching rocks are good, but hard to understand even on a computer when
warm and moving. Using tight waves is easier for the computer, but it is hard to guess how
the waves touch when they move because they are warm. We have a new set of tight
pieces which can be turned into waves if you know where the pieces are. It is pretty good,
close to using a computer to get the full waves, even with pieces out of order. Since it is
much easier than finding full waves, the computer can understand the waves in big, warm
pieces of rock and how they change and move. This allows us to understand how to move
light power through the rock.