.. _science_calculators_mobility: Nanomatch Mobility Calculator ============================= .. list-table:: :header-rows: 1 :align: center * - Properties - Notes * - :ref:`science_properties_HOMOLUMO` - byproduct * - Dipole (property not yet described / available) - byproduct * - :ref:`science_properties_morphology` - byproduct * - :ref:`science_properties_mobility` - recommended Workflow -------- The **Nanomatch Mobility Calculator** is a multiscale simulations workflow designed to calculate the charge carrier mobility of organic semiconductors starting from the first-principles. The workflow progresses from the single molecular structure through atomic and electronic properties to the macroscopic hole and electron mobilities, ensuring an efficient and comprehensive computational protocol. The brief overview is given in the table below. .. list-table:: Mobility Workflow Overview :widths: 30 30 30 :header-rows: 1 * - **Nanomatch Software** - **Scientific Role** - **Illustration** * - `Parametrizer `_ - | Geometry optimization - .. image:: mobility/parametrizer.png :width: 300px :align: center * - `DihedralParametrizer `_ - | Computation of intramolecular | forcefields - .. image:: mobility/dhp.png :width: 300px :align: center * - `Deposit `_ - | Simulation of the physical | vapor deposition (PVD) | to obtain atomistic morphology - .. image:: mobility/deposit.png :width: 300px :align: center * - `QuantumPatch `_ - | Calculation of electronic properties | including charge transfer parameters - .. image:: mobility/quantumpatch.png :width: 300px :align: center * - `LightForge `_ - | Simulation of charge-carrier transport | using kMC protocol - .. image:: mobility/lightforge.png :width: 300px :align: center Implemented Scientific Methods ------------------------------ The following scientific methods are implemented in the **Nanomatch Mobility Calculator**: Molecular Structure Optimization ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ *obabel*, *xtb*, and *Density Functional Theory (DFT)* are used to generate initial 3D conformers, pre-optimize and optimize the geometry, and compute partial charges via an electrostatic potential (ESP) fit for single molecules in a vacuum. DFT optimization is performed with def2-TZVP/B3LYP level of theory. Morphology Generation ~~~~~~~~~~~~~~~~~~~~~ The *DEPOSIT protocol* [1]_ simulates physical vapor deposition to generate thin-film morphologies with atomistic resolution. This involves Monte Carlo (MC) based basin hopping with simulated annealing (SA) to model intermolecular interactions during deposition. In total, 1000 molecules are deposited into a box with a base size of 100x100 Å. After this, the top and bottom 7 Å are cut out, and periodic copies are added in the x and y axes to increase its base size to 300x300 Å. Electronic Structure Calculation ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Using the *QuantumPatch method* [2]_, energy disorder, electronic couplings, and reorganization energies are calculated by self-consistently equilibrating the charge densities of a subset of molecules in their unique environments. The shell structure is similar to those described in *Keiser et al* [3]_. In total, 200 molecules core molecules are considered, embedded in the generated morphology. For these 200 molecules the following is computed: - **HOMO/LUMO** levels of the embedded molecules, are self-consistently computed to yield the energy disorder, and their interactions are used to compute the overlap integral distribution across relevant distances. - **Electronic couplings** for every pair of 200 molecules if their distance is below a reasonable threshold. From HOMO/LUMO distributions, the energy disorder is deduced. The parameters of the *QuantumPatch* embedding scheme is as follows: - **Core molecule**: Self-consistent DFT def2-SVP/B3LYP - **First shell**: Self-consistent DFT shell def2-SVP/BP86, radius 15 Å - **Second shell**: Self-consistent DFTB, radius 25 Å - **Third shell**: Static DFTB, radius 60 Å Structure Expansion ~~~~~~~~~~~~~~~~~~~ To bridge the scales from atomistic resolution to the device level, a stochastic expansion scheme *EDCM* is used to expand the thin-film morphologies to the size of 40x40x40 nm\ :sup:`3`, drawing electronic couplings and site energies from distributions analyzed in the QuantumPatch method. Charge Transport Simulation ~~~~~~~~~~~~~~~~~~~~~~~~~~~ *Kinetic Monte Carlo (kMC) simulations* model charge transport in organic semiconductor thin films. The workflow uses the LightForge package to simulate field-dependent mobility, taking into account percolation and many-body effects [4]_. Zero-field mobility is extrapolated to the zero-field limit assuming Poole-Frenkel field dependence. Parameters of the kMC simulations: - **Fields**: three fields are applied: 0.02 0.03 0.04 eV/nm. - **Morphology** and **replicas**: for every field value, 10 independent morphologies are generated using the stochastic expansion scheme, including HOMO/LUMO/Js distributions derived from the *QuantumPatch* simulations. - **Temperature** is 300 K. - **Convergence criterion**: either the fluctuation parameter "iv_fluctuation" below 0.05, or "max_iterations" exceeds 5x10\ :sup:`6`. - **Number of Charge Carriers**: 30. In the expanded simulation box of 40x40x40 nm\ :sup:`3`, this results in a charge carrier concentration of 4.69x10\ :sup:`17` charges per cm\ :sup:`3`. Output ------ Displayed Results ~~~~~~~~~~~~~~~~~ The data below will be displayed as the workflow ends (backend name: `result.yml`): .. code-block:: yaml ZUOUZKKEUPVFJK-UHFFFAOYSA-N: HOMO: value: -6.304540838835274 LUMO: value: -0.9858224534777202 dipole: results: dipole_vector: - -1.3524802844422331e-05 - 3.1223022592016277e-06 - 1.662349335263646e-05 value: 2.1656629345848317e-05 electron_mobility: results: fields: units: V/nm values: - 0.2 - 0.3 - 0.4 mobilities: units: cm2/V*s values: - 0.12812247595879594 - 0.40451844574738705 - 0.6373425148883705 stderr: units: cm2/V*s values: - 0.006634144943223338 - 0.021912012246805144 - 0.020222231531951042 value: 0.0027914965621533006 hole_mobility: results: fields: units: V/nm values: - 0.2 - 0.3 - 0.4 mobilities: units: cm2/V*s values: - 0.023268197326548744 - 0.05054069044778844 - 0.08097590708969137 stderr: units: cm2/V*s values: - 0.0013433181652565155 - 0.003181913338943169 - 0.0027155426204215098 value: 0.0011653218988067668 morphology: results: average_neighbors: unit: Angstrom value: 17.6 mass_density: std: 0.01 unit: g/cm3 value: 1.14 molecular_volume: unit: nm3 value: 0.23 number_density: std: 9.9e+19 unit: 1/cm3 value: 4.36e+21 rdf_first_peak: unit: Angstrom value: 4.921630094043887 value: 'file: structure.cml' The hole and electron zero-field mobilities (in [cm2/V*s]) are: .. code-block:: yaml result['ZUOUZKKEUPVFJK-UHFFFAOYSA-N']['hole_mobility']['value'] result['ZUOUZKKEUPVFJK-UHFFFAOYSA-N']['electron_mobility']['value'] The value is derived from field-dependent mobilities, which are also provided in the output. Extrapolation is performed using linear regression in the log(mobility) vs. sqrt(field) plot. The extrapolation is shown in one of the output files, example: `mobility_vs_sqrt_field.png <../../../../../docs/build/html/_static/science/calculators/mobility/mobility_vs_sqrt_field.png>`_. Files ~~~~~ In addition to parsed output, the following files are available upon the workflow completion: .. list-table:: :header-rows: 1 :widths: 5 15 15 50 * - No. - File - Description - Example * - 1 - DeltaE.png - | Distribution of the HOMO/LUMO | levels, local and global, | values of computed disorder. - .. image:: mobility/DeltaE.png :width: 300px :align: center * - 2 - output_molecule.mol2 - | Molecule output file in MOL2 | format. - `output_molecule.mol2 <../../../../../docs/build/html/_static/science/calculators/mobility/output_molecule.mol2>`_ * - 3 - summary_RDF.png - | Radial distribution function | (RDF). - .. image:: mobility/summary_RDF.png :width: 300px :align: center * - 4 - | hole_mobility | _vs_sqrt_field.png - | Poole-Frenkel plot of the | hole mobility versus the | square root of the | electric field. - .. image:: mobility/hole_mobility_vs_sqrt_field.png :width: 300px :align: center * - 5 - | electron_mobility | _vs_sqrt_field.png - | Poole-Frenkel plot of the | electron mobility versus the | square root of the | electric field. - .. image:: mobility/electron_mobility_vs_sqrt_field.png :width: 300px :align: center * - 6 - structure.cml - | Molecular structure in | CML format. - `structure.cml <../../../../../docs/build/html/_static/science/calculators/mobility/structure.cml>`_ * - 7 - | visualization_2D | _and_3D.png - | 2D and 3D visualizations | of the molecules | (center of geometries) - .. image:: mobility/visualization_2D_and_3D.png :width: 300px :align: center Benchmark --------- Benchmark set ~~~~~~~~~~~~~~ The benchmark of the mobility workflow was performed against experimentally measured mobility of the materials consisting of the following molecules [3]_. .. image:: https://www.frontiersin.org/files/Articles/801589/fchem-09-801589-HTML/image_m/fchem-09-801589-g001.jpg :width: 600px :align: center :alt: Molecules Experimental verification ~~~~~~~~~~~~~~~~~~~~~~~~~ Excellent correlation with experimental data is observed for overwhelming majority of materials [3]_: .. image:: https://www.frontiersin.org/files/Articles/801589/fchem-09-801589-HTML/image_m/fchem-09-801589-g003.jpg :width: 600px :align: center :alt: Experiment vs Theory Superiority wrt Other Works ~~~~~~~~~~~~~~~~~~~~~~~~~~~ The table below compares simulated zero-field mobilities and material properties using present workflow to other theoretical works as reported in Keiser et al. [3]_ to prior works. .. list-table:: Electronic properties and zero-field mobility computed in this work and reported in literature. :widths: 20 20 20 20 20 20 :header-rows: 1 * - Molecule - σ/meV - 〈J²r²〉/eV² Ų - λ/meV - µ₀/cm² V⁻¹ s⁻¹ - Source * - Alq3p - 199 - 1.0 × 10⁻² - 195 - 2.6 × 10⁻⁹ - SK * - - 224 - 1.0 × 10⁻² - 296 - 1.0 × 10⁻¹⁰ - PF * - Alq3n - 182 - 8.6 × 10⁻³ - 215 - 1.7 × 10⁻⁷ - SK * - TPBin - 164 - 2.5 × 10⁻³ - 317 - 4.3 × 10⁻⁷ - SK * - BPBDn - 182 - 5.2 × 10⁻³ - 291 - 1.3 × 10⁻⁶ - SK * - DEPBp - 133 - 2.4 × 10⁻³ - 316 - 6.0 × 10⁻⁶ - SK * - - 130 - 1.4 × 10⁻³ - 266 - 2.1 × 10⁻⁵ - PF * - m-BPDp - 132 - 1.6 × 10⁻³ - 210 - 8.8 × 10⁻⁶ - SK * - - 110 - 1.5 × 10⁻³ - 143 - 7.4 × 10⁻⁴ - PF * - - - - 300 - 1.7 × 10⁻³ - DE * - BCPn - 139 - 3.2 × 10⁻³ - 314 - 1.4 × 10⁻⁵ - SK * - - - - - 1.8 × 10⁻² - PK * - NNPp - 124 - 1.6 × 10⁻³ - 281 - 1.2 × 10⁻⁵ - SK * - - 135 - 1.6 × 10⁻³ - 160 - 4.3 × 10⁻⁵ - PF * - spiroTADp - 105 - 1.7 × 10⁻³ - 139 - 8.7 × 10⁻⁵ - SK * - - 90 - - 250 - 1.6 × 10⁻³ - NK * - TCTAp - 107 - 1.7 × 10⁻³ - 206 - 1.3 × 10⁻⁴ - SK * - - 136 - - 257 - 7.2 × 10⁻⁷ - AM * - - 112 - - 260 - 1.0 × 10⁻⁴ - NK * - - - - 290 - 5.9 × 10⁻⁴ - DE * - NPBp - 104 - 1.4 × 10⁻³ - 205 - 1.8 × 10⁻⁴ - SK * - - 130 - - 203 - 6.9 × 10⁻⁷ - AM * - - 114 - - - 1.3 × 10⁻⁵ - PK * - - 144 - 2.0 × 10⁻³ - 158 - 1.8 × 10⁻⁵ - PF * - - 87 - - 310 - 1.1 × 10⁻³ - NK * - - - - 280 - 1.3 × 10⁻³ - DE * - o-BPDp - 96 - 1.8 × 10⁻³ - 213 - 3.2 × 10⁻⁴ - SK * - - - - 310 - 7.2 × 10⁻⁴ - DE * - TpPyPBn - 123 - 6.4 × 10⁻³ - 200 - 3.0 × 10⁻⁴ - SK * - TPDp - 96 - 1.7 × 10⁻³ - 208 - 7.9 × 10⁻⁴ - SK * - - 129 - 1.6 × 10⁻³ - 110 - 1.5 × 10⁻⁴ - PF * - - - - 310 - 8.3 × 10⁻⁴ - DE * - p-BPDp - 94 - 1.3 × 10⁻³ - 173 - 7.0 × 10⁻⁴ - SK * - - - - 230 - 3.8 × 10⁻⁴ - DE * - TPDIp - 82 - 4.8 × 10⁻³ - 145 - 1.0 × 10⁻³ - SK * - TAPCp - 74 - 1.4 × 10⁻³ - 89 - 4.6 × 10⁻³ - SK Abbreviations ~~~~~~~~~~~~~ * **SK**: Nanomatch Mobility Worflow (Keiser, S. et al., 2021 [3]_) * **AF**: A. Fuchs et al. (2012), "Molecular origin of differences in hole and electron mobility in amorphous Alq₃—a multiscale simulation study," *Phys. Chem. Chem. Phys.*, 14, 4259-4270. URL: https://doi.org/10.1039/C2CP23489K * **GA**: G. Aydin and I. Yavuz (2021), "Intrinsic Static/Dynamic Energetic Disorders of Amorphous Organic Semiconductors: Microscopic Simulations and Device Study," *J. Phys. Chem. C*, 125, 6862–6869. URL: https://doi.org/10.1021/acs.jpcc.0c11219 * **PK**: P. Kordt et al. (2015), "Modeling of Organic Light Emitting Diodes: From Molecular to Device Properties," *Adv. Funct. Mater.*, 25, 1955-1971. URL: https://doi.org/10.1002/adfm.201403004 * **AM**: A. Massé et al. (2016), "Ab initio charge-carrier mobility model for amorphous molecular semiconductors," *Phys. Rev. B*, 93, 195209. URL: https://doi.org/10.1103/PhysRevB.93.195209 * **DE**: D. Evans et al. (2016), "Estimation of charge carrier mobility in amorphous organic materials using percolation corrected random-walk model," *Org. Electron.*, 29, 50–56. URL: https://doi.org/10.1016/j.orgel.2015.11.021 * **PF**: P. Friederich et al. (2016), "Molecular Origin of the Charge Carrier Mobility in Small Molecule Organic Semiconductors," *Adv. Funct. Mater.*, 26, 5757–5763. URL: https://doi.org/10.1002/adfm.201601807 * **NK**: N. Kotadiya et al. (2018), "Rigorous Characterization and Predictive Modeling of Hole Transport in Amorphous Organic Semiconductors," *Adv. Electron. Mater.*, 4, 1800366. URL: https://doi.org/10.1002/aelm.201800366 References ---------- .. _ref1: .. [1] Neumann, T., Friederich, P., Symalla, F., Meded, V., Wenzel, W., "Simulating Charge Transport in Organic Semiconductors: From Quantum Chemistry to Device Simulation," Journal of Computational Chemistry, 34 (31), 2013, 2716-2725. URL: https://onlinelibrary.wiley.com/doi/abs/10.1002/jcc.23445. .. _ref2: .. [2] Friederich, P., Symalla, F., Meded, V., Neumann, T., Wenzel, W., "Ab Initio Treatment of Disorder Effects in Amorphous Organic Materials: Toward Parameter Free Materials Simulation," Journal of Chemical Theory and Computation, 10 (9), 2014, 3720-3725. URL: https://doi.org/10.1021/ct500418f. .. _ref3: .. [3] Keiser, S., et al., "De Novo Calculation of the Charge Carrier Mobility in Amorphous Small Molecule Organic Semiconductors," Frontiers in Chemistry, 9, 2021. URL: https://www.frontiersin.org/articles/10.3389/fchem.2021.801589. .. _ref4: .. [4] Symalla, F., Friederich, P., Massé, A., Meded, V., Coehoorn, R., Bobbert, P., Wenzel, W., "Charge Transport by Superexchange in Molecular Host-Guest Systems," Physical Review Letters, 2016, 117, 276803. URL: https://doi.org/10.1103/PhysRevLett.117.276803.