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**Martin Persson Accelrys, Cambridge**

Introduction to DFTB+ Martin Persson Accelrys, Cambridge

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**DFTB+ in Materials Studio**

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

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Why DFTB+

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**QM vs. CM 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

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**This is where DFTB+ comes in**

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

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**Examples of what can be done with DFTB+**

Diamond nucleation Novel SiCN ceramics Si cluster growth Magnetic Fe clusters WS2 nanotubes

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Basic DFTB Theory

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**DFTB theory in short DFTB Pseudo atomic orbital basis**

Non SCC Hamiltonian elements are parameterized 2nd 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

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**Pseudo atomic orbitals**

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

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**Pseudo atomic orbitals**

Silicon sp3d5 orbitals S P1 P2 P3 D5 D4 D3 D2 D1 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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DFT DFTB Expand the Kohn-Sham total energy expression of DFT to 2nd order in terms of electron and magnetization density fluctuations Represent the Hamiltonian elements in a minimal basis of pseudo-atomic orbitals Express the charge density in terms of Mulliken charges Expand the magnetization density in terms of non-overlapping spherically symmetric functions Replace the remaining terms with a short range repulsive energy

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

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

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

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DFTB+ Performance

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**Performance figures 10x10 CNT N2.9 N1.5 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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**DFTB+ in Materials Studio 6.0**

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

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Starting a DFTB+ job 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

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**Downloading parameters**

Need to register to get access. The downloaded parameters will contain many different Slater Koster files 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 <filename>] [End file <filename>], surrounds content of file. Will prevent accidental mixing of files between libraries and makes handling easier

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

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**Materials Studio 6.0 Parameterization tool**

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**The DFTB+ Parameterization Tool**

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 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, Erep, will be described using fitted repulsive pair potentials. Pair potentials The pair potentials are fitted against a basis of cutoff polynomials

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Systems 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...

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

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**Parameterization job results**

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

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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 Initial evaluation against small set of structures Final evaluation against larger set of structures Validation against larger structures Materials Studio supplies a MS Perl script which compares geometry and atomization energy for structures.

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**Si vacancy Formation energy**

SiGeH sp3d5 basis LDA(PWC) Fitted against Si, Ge and SiGe solids Si2H6, Si2H4 Ge2H6, Ge2H4 SiGeH6, SiGeH4 SiH4, GeH4 and H2 Tested against: Solids Nanowires Nanoclusters Si vacancy Si vacancy Formation energy Ef(eV) DFTB+ 2.6 DMol3 2.7

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**Tested against a large set (~60) of organic molecules **

CHNO 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 Bond type Average difference (Å) C-C 0.0108 C-N 0.0131 C-O 0.0105 C-H 0.0081 N-N 0.0070 N-O 0.0123 N-H 0.0087 Average bond difference: Å Average angle difference: 1.16 degrees Accuracy is comparative to that of the Mio library.

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**CHNO: Larger molecules**

CNT-6x6 Successfully tested for: CNT C60 Caffeine Glucose Porphine N-Acetylneuraminic acid Bond Diff (Å) C-C 0.005 Caffeine Bond Diff (Å) C-C 0.0095 C-N 0.0075 C-O 0.0078 C-H 0.0028 Bond Diff (Å) C-C 0.0148 C-N 0.0118 C-O 0.0100 C-H 0.0114 N-H 0.0127 O-H 0.0019 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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**Generating the orbitals**

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

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

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

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

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

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

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

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**Calculation time vs. structure size**

Most of DFTB+ is running with O(N) routines Two exceptions DFTB+ SCC Ewald-summation, O(N2) DFTB+ eigenvalue solvers LAPACK solvers, O(N3) Small systems (<300 atoms), the O(N) processes dominate Large systems (>300), the eigenvalue solver dominates

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**Performance figures 10x10 CNT N2.9 N1.5 32 atoms/unitcell**

Run on single core Intel(R) Xeon(TM) CPU 3.00GHz OpenMP #cpu Speedup Efficiency 1 1.0 2 0.87 3 0.80 4 0.72 Small systems (<300 atoms) O(N) processes dominate Large systems (>300) eigenvalue solver dominates

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**DMol3 vs. DFTB+ DFTB+ is significantly faster than a normal DFT code**

Atoms TimeDFTB+(s) TimeDMol3(s) TimeDMol3/TimeDFTB+ 32 4 233 58 64 8 632 79 96 17 872 51 128 26 1092 42 160 46 1501 33 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

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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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**Starting a DFTB+ job: Electronic**

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

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**Starting a DFTB+ job: Properties**

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

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**Starting a DFTB+ job: Job Control**

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

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During a DFTB+ job 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

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**Visible files Hidden files DFTB+ Result files *.tag *.cube *.bands**

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

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**Zn compounds using DFTB+**

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**Working with Zn containing compounds**

Zn-X (X = H, C, N, O, S, Zn) Can be downloaded at (znorg-0-1) Reference systems during fitting ZnH2, Zn(CH3)2, Zn(NH3)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, CO2 and NH3) Zn in biological systems N. H. Moreira, J. Chem. Theory Comput. 2009, 5 , 605

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**Zn Solids W-ZnO DFTB+ Method Ecoh a(Å) b(Å) B0(GPa) w-ZnO DFTB+ 9.77**

3.28 5.25 161 PBE 8.08 3.30 5.34 124 EXP 7.52 3.25 5.20 208 zb-ZnS 7.93 5.43 - 44.2 LDA 7.22 5.35 82 6.33 5.40 76.9 W-ZnO PBE Reasonable solid state properties N. H. Moreira, J. Chem. Theory Comput. 2009, 5 , 605

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**ZnO Surface stability DFTB+ DFT**

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

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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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**Small molecule surface interaction**

ZnO (1010)-CO2 ZnO (1010)-NH3 CO2 Bond difference 1-2% Binding too strong ~0.5 eV/CO2 Turn over point for monolayer well described NH3 Overall good agreement with experiments and DFT calculations N. H. Moreira, J. Chem. Theory Comput. 2009, 5 , 605

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**Electronic settings 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)

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**Polynomial fitting setup**

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

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**Possible future extensions to DFTB+**

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**DFTB+ features outside of Material Studio**

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

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