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Introduction to DFTB+ Martin Persson Accelrys, Cambridge

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DFTB – Why DFTB? – Basic theory DFTB – Performance DFTB+ in Materials Studio – Energy, Geometry, Dynamics, Parameterization – Parameterization Basic theory Setting up a parameterization Outline

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Why DFTB+

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DFT codes are good for small systems Nano structures and bio molecules are often too large for DFT but their electronic properties are still of interest – hence quantum mechanical description is needed. Classical force field based codes can handle large systems but are missing the QM part Empirical TB has been applied to systems up to a few million atoms – No charge self consistency – Limited transferability – Using simplified energetic expressions QM vs. CM

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DFTB merges the reliability of DFT with the computational efficiency of TB – Parameters are based on an atomic basis – The parameters can be made transferable – Charge self consistent – Describes both electronic as well as energetic properties – Can handle thousands of atoms This is where DFTB+ comes in

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Examples of what can be done with DFTB+ Diamond nucleation Novel SiCN ceramicsSi cluster growth Magnetic Fe clustersWS2 nanotubes

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Basic DFTB Theory

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DFTB – Pseudo atomic orbital basis – Non SCC Hamiltonian elements are parameterized – 2 nd order charge self consistent theory – Charges are treated as Mulliken charges – Short range potential is used to correct the energetics – Hamiltonian matrix is sparse and can partly be treated with O(N) methods DFTB theory in short

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Minimal basis set Pseudo atomic orbitals – Slater orbitals – Spherical harmonics DFTB basis set

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Pseudo atomic orbitals SP1P1 P2P2 P3P3 D5D5 D4D4 D3D3 D2D2 D1D1 Silicon sp 3 d 5 orbitals For Silicon the d-orbitals are un-occupied but needed to properly model the conduction band.

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Hamiltonian elements Diagonal elements use free atom energies Two centre integrals Tabulated values

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1.Expand the Kohn-Sham total energy expression of DFT to 2 nd order in terms of electron and magnetization density fluctuations 2.Represent the Hamiltonian elements in a minimal basis of pseudo- atomic orbitals 3.Express the charge density in terms of Mulliken charges 4.Expand the magnetization density in terms of non-overlapping spherically symmetric functions 5.Replace the remaining terms with a short range repulsive energy DFT DFTB

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1.Expand the Kohn-Sham total energy expression of DFT to 2 nd order in terms of electron and magnetization density fluctuations 2.Represent the Hamiltonian elements in a minimal basis of pseudo- atomic orbitals 3.Express the charge density in terms of Mulliken charges 4.Expand the magnetization density in terms of non-overlapping spherically symmetric functions 5.Replace the remaining terms with a short range repulsive energy DFT DFTB

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1.Expand the Kohn-Sham total energy expression of DFT to 2 nd order in terms of electron and magnetization density fluctuations 2.Represent the Hamiltonian elements in a minimal basis of pseudo- atomic orbitals 3.Express the charge density in terms of Mulliken charges 4.Expand the magnetization density in terms of non-overlapping spherically symmetric functions 5.Replace the remaining terms with a short range repulsive energy DFT DFTB

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1.Expand the Kohn-Sham total energy expression of DFT to 2 nd order in terms of electron and magnetization density fluctuations 2.Represent the Hamiltonian elements in a minimal basis of pseudo- atomic orbitals 3.Express the charge density in terms of Mulliken charges 4.Expand the magnetization density in terms of non-overlapping spherically symmetric functions 5.Replace the remaining terms with a short range repulsive energy DFT DFTB

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DFTB+ Performance

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Performance figures N 2.9 N x10 CNT 32 atoms/unitcell Run on single core Intel(R) Xeon(TM) CPU 3.00GHz Small systems (<300 atoms) O(N) processes dominate Large systems (>300) O(n) eigenvalue solver dominates Around 100 times faster then normal DFT

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DFTB+ in Materials Studio 6.0

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First official release that includes the DFTB+ module Supported tasks – Energy – Geometry optimization – Dynamics – Parameterization Also support – Dispersion correction – Spin unrestricted calculations DFTB+ in Materials Studio 6.0

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Slater-Koster libraries instead of DFT Functionals – CH, CHNO and SiGeH What if I don’t have the needed library? – Download academic libraries at mio, C-H-N-O-S-P pbc, Si-F-O-N-H|Fe matsci, various parameters – Make your own Starting a DFTB+ job

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Need to register to get access. The downloaded parameters will contain many different Slater Koster files Downloading parameters To be used in MS-DFTB+ the parameters need to be packed up in a.skflib format. The.skflib file is just a tagged concatenation of the different files [Begin section] [End section], surrounds list of all files [Begin file ] [End file ], surrounds content of file. Will prevent accidental mixing of files between libraries and makes handling easier

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Band structure Density of states Electron density Fermi surface Orbitals Slater-Koster parameters Dynamics analysis is done using the Forcite analysis tools DFTB+ Analysis

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Materials Studio 6.0 Parameterization tool

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DFTB+ depends on parameters – Hamiltonian and overlap integrals – Hubbard terms (orbital resolved) – Spin constants – Wave function coefficients – Short range repulsive potential The DFTB+ Parameterization Tool The DFTB+ parameterization tool enables you to make your own parameterizations. It calculates all of the needed parameters. The result is packed up in a single file (.skflib)

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Repulsive fitting The remaining terms, E rep, will be described using fitted repulsive pair potentials. The pair potentials are fitted against a basis of cutoff polynomials Pair potentials

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Short range pair potentials are fitted against small molecules or solids Path generators – Stretch, Perturb, Scale, Trajectory Fitting against Energy and optionally forces Use of spin unrestricted calculations Steps, weights and width are set under Details... Systems

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Bond order fitting Use weight distributions to combine several bond orders into a single potential fit

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C-H.txt- Job summary Best fit (C-H.skflib) returned in the base folder Fits for alternative cutoff factors are returned in the Alternatives folder Parameterization job results

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Evaluating the result benzene DMol3 C3-C2 = C3-H9 = DFTB+ C3-C2 = C3-H9 = Diff C3-C2 = C3-H9 = DMol3 C2-C7-C6 = H12-C7-C6 = DFTB+ C2-C7-C6 = H12-C7-C6 = Diff C2-C7-C6 = H12-C7-C6 = Atomization Diff = ============================================== ethene DMol3 C2-C1 = C2-H5 = DFTB+ C2-C1 = C2-H5 = Diff C2-C1 = C2-H5 = DMol3 C1-C2-H6 = H4-C1-H3 = DFTB+ C1-C2-H6 = H4-C1-H3 = Diff C1-C2-H6 = H4-C1-H3 = Atomization Diff = ============================================== Bond Error Statistics: C-C = e-03 C-H = e-02 ================= Total Average = e-03 Angle Error Statistics: HCH = e-01 CCC = e-03 HCC = e-02 ================= Total Average = e-02 1.Initial evaluation against small set of structures 2.Final evaluation against larger set of structures 3.Validation against larger structures Materials Studio supplies a MS Perl script which compares geometry and atomization energy for structures.

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sp3d5 basis LDA(PWC) Fitted against – Si, Ge and SiGe solids – Si 2 H 6, Si 2 H 4 – Ge 2 H 6, Ge 2 H 4 – SiGeH 6, SiGeH 4 – SiH 4, GeH 4 and H 2 Tested against: – Solids – Nanowires – Nanoclusters – Si vacancy SiGeH Si vacancy Formation energy E f (eV) DFTB+2.6 DMol32.7

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sp3 basis GGA(PBE) Tested against a large set (~60) of organic molecules Also, validated against a smaller set of larger molecules Good diamond cell parameter, (3.544) Å CHNO Bond typeAverage difference (Å) C-C C-N C-O C-H N-N N-O N-H Average bond difference: Å Average angle difference: 1.16 degrees Accuracy is comparative to that of the Mio library.

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Successfully tested for: – CNT – C 60 – Caffeine – Glucose – Porphine – N-Acetylneuraminic acid CHNO: Larger molecules BondDiff (Å) C-C C-N C-O C-H BondDiff (Å) C-C0.005 BondDiff (Å) C-C C-N C-O C-H N-H O-H CNT-6x6 Caffeine N-AA

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Thanks for your attention Other contributors: Paddy Bennett (Cambridge, Accelrys) Bálint Aradi (Bremen, CCMS) Zoltan Bodrog (Bremen, CCMS)

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The Kohn-Sham equation is solved for a single atom. Using an added extra confining potential to better model molecules and solids Generating the orbitals

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1.Expand the Kohn-Sham total energy expression of DFT to 2 nd order in terms of electron and magnetization density fluctuations 2.Represent the Hamiltonian elements in a minimal basis of pseudo- atomic orbitals 3.Express the charge density in terms of Mulliken charges 4.Expand the magnetization density in terms of non-overlapping spherically symmetric functions 5.Replace the remaining terms with a short range repulsive energy DFT DFTB

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1.Expand the Kohn-Sham total energy expression of DFT to 2 nd order in terms of electron and magnetization density fluctuations 2.Represent the Hamiltonian elements in a minimal basis of pseudo- atomic orbitals 3.Express the charge density in terms of Mulliken charges 4.Expand the magnetization density in terms of non-overlapping spherically symmetric functions 5.Replace the remaining terms with a short range repulsive energy DFT DFTB

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1.Expand the Kohn-Sham total energy expression of DFT to 2 nd order in terms of electron and magnetization density fluctuations 2.Represent the Hamiltonian elements in a minimal basis of pseudo- atomic orbitals 3.Express the charge density in terms of Mulliken charges 4.Expand the magnetization density in terms of non-overlapping spherically symmetric functions 5.Replace the remaining terms with a short range repulsive energy DFT DFTB

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1.Expand the Kohn-Sham total energy expression of DFT to 2 nd order in terms of electron and magnetization density fluctuations 2.Represent the Hamiltonian elements in a minimal basis of pseudo- atomic orbitals 3.Express the charge density in terms of Mulliken charges 4.Expand the magnetization density in terms of non-overlapping spherically symmetric functions 5.Replace the remaining terms with a short range repulsive energy DFT DFTB

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1.Expand the Kohn-Sham total energy expression of DFT to 2 nd order in terms of electron and magnetization density fluctuations 2.Represent the Hamiltonian elements in a minimal basis of pseudo- atomic orbitals 3.Express the charge density in terms of Mulliken charges 4.Expand the magnetization density in terms of non-overlapping spherically symmetric functions 5.Replace the remaining terms with a short range repulsive energy DFT DFTB

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1.Expand the Kohn-Sham total energy expression of DFT to 2 nd order in terms of electron and magnetization density fluctuations 2.Represent the Hamiltonian elements in a minimal basis of pseudo- atomic orbitals 3.Express the charge density in terms of Mulliken charges 4.Expand the magnetization density in terms of non-overlapping spherically symmetric functions 5.Replace the remaining terms with a short range repulsive energy DFT DFTB

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Most of DFTB+ is running with O(N) routines Two exceptions – DFTB+ SCC Ewald-summation, O(N 2 ) – DFTB+ eigenvalue solvers LAPACK solvers, O(N 3 ) Small systems (<300 atoms), the O(N) processes dominate Large systems (>300), the eigenvalue solver dominates Calculation time vs. structure size

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Performance figures N 2.9 N x10 CNT 32 atoms/unitcell Run on single core Intel(R) Xeon(TM) CPU 3.00GHz Small systems (<300 atoms) O(N) processes dominate Large systems (>300) eigenvalue solver dominates #cpuSpeedup Efficiency OpenMP

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DFTB+ is significantly faster than a normal DFT code Depending on what DFT code we compare to its a factor faster DFTB+ compared to DMol3 is a factor of faster DMol3 vs. DFTB+ AtomsTime DFTB+ (s)Time DMol3 (s)Time DMol3 /Time DFTB

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Starting a DFTB+ job: Setup Available tasks Energy Geometry optimization Dynamics Parameterization Dispersion correction Spin unrestricted The parameterization dialogs are accessed through the More... Button.

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Select Slater-Koster library – CH, CHNO and SiGeH – Use Browse... to access local library What if I don’t have the needed library? – Download academic libraries at mio, C-H-N-O-S-P pbc, Si-F-O-N-H|Fe matsci, various parameters – Make your own Starting a DFTB+ job: Electronic

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Select any properties that should be calculated – Band structure – DOS – Electron density – Orbitals – Population analysis Properties will be calculated at the end of the job Starting a DFTB+ job: Properties

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Select server or run on local machine DFTB+ support OpenMP but not MPI On a cluster it will run on the cores available to it on the first node Parameterization is always run as a serial job Starting a DFTB+ job: Job Control

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The DFTB+ calculations are run by Materials Studio as an energy server Geometry optimization and Dynamics jobs are controlled by the same code that is used during a Forcite job During a DFTB+ job

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<>.xsd – Final structure <>.xtd (dynamics) – Dynamics trajectory <>.txt – Compilation of the results <>.dftb – The last output from DFTB+ <>.skflib (parameterization) – Slater-Koster library DFTB+ Result files *.tag – Final output data *.cube – Density and orbital data *.bands – Band structure data Visible filesHidden files

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Zn compounds using DFTB+

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Zn-X (X = H, C, N, O, S, Zn) Can be downloaded at (znorg-0-1)www.DFTB.org Reference systems during fitting – ZnH 2, Zn(CH 3 ) 2, Zn(NH 3 ) 2, Zn(SH) 2 – fcc-Zn, zb-ZnO Applied to: – Zinc solids, Zn, ZnO, ZnS – Surfaces, ZnO – Nanowires and Nanoribbons, ZnO – Small species interaction with ZnO surface (H, CO 2 and NH 3 ) – Zn in biological systems Working with Zn containing compounds N. H. Moreira, J. Chem. Theory Comput. 2009, 5, 605

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Zn Solids MethodE coh a(Å)b(Å)B 0 (GPa) w-ZnODFTB PBE EXP zb-ZnSDFTB LDA EXP W-ZnO DFTB+ W-ZnO PBE Reasonable solid state properties N. H. Moreira, J. Chem. Theory Comput. 2009, 5, 605

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ZnO Surface stability F. Claeyssens J. Mat. Chem. 2005, N. H. Moreira, J. Chem. Theory Comput. 2009, 5, 605 Predicts correct order and magnitude for the cleavage energy Bond and angle deviation ~1-2% DFTB+ DFT

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ZnO nanowires Good geometries and electronic structure Excellent agreement with DFT results Surface Zn atoms move inwards N. H. Moreira, J. Chem. Theory Comput. 2009, 5, 605

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CO 2 Bond difference 1-2% Binding too strong ~0.5 eV/CO 2 Turn over point for monolayer well described NH 3 Overall good agreement with experiments and DFT calculations Small molecule surface interaction ZnO (1010)-CO 2 ZnO (1010)-NH 3 N. H. Moreira, J. Chem. Theory Comput. 2009, 5, 605

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Choose functional (LDA(PWC) or GGA(PBE)) The electronic fitting can be done in two modes – Potential mode, confinement potential for wave function – Density mode, confinement potentials for wave function and electron density Each element will have its own settings – What basis to use – Electron configuration – Confinement potential(s) Electronic settings

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Each fitting is done using different polynomial orders Fittings are done for a set of cutoff radius scale factors Polynomial fitting setup

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Possible future extensions to DFTB+

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Optical Properties – LR-TD-DFTB Electronic transport – NEG-DFTB QM/MM Vibrational modes DFTB+ features outside of Material Studio Please let us know what extensions and enhancements you would like to see for DFTB+ in the future.

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