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Introduction to DFTB+ Martin Persson Accelrys, Cambridge Outline • DFTB – Why DFTB? – Basic theory DFTB – Performance • DFTB+ in Materials Studio – Energy, Geometry, Dynamics, Parameterization – Parameterization • Basic theory • Setting up a parameterization Why DFTB+ 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 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 Examples of what can be done with DFTB+ Diamond nucleation Novel SiCN ceramics Magnetic Fe clusters Si cluster growth WS2 nanotubes Basic DFTB Theory 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 DFTB basis set • Minimal basis set • Pseudo atomic orbitals – Slater orbitals – Spherical harmonics v r n , , l v , m v a n r lv n e r r lv m v r Pseudo atomic orbitals Silicon sp3d5 orbitals S D1 P1 D2 P2 D3 P3 D4 For Silicon the d-orbitals are un-occupied but needed to properly model the conduction band. D5 Hamiltonian elements • Diagonal elements use free atom energies • Two centre integrals • Tabulated values 0 H free atom if A B T V A V B if A B 0 otherwise DFT DFTB 1. Expand the Kohn-Sham total energy expression of DFT to 2nd order in terms of electron and magnetization density fluctuations 2. Represent the Hamiltonian elements in a minimal basis of pseudoatomic 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 occ E tot , i E xc n , 2 1 n i i v 2 2 1 2 N Z Z R R n ( r ) d r 3 r r i DFT DFTB 1. Expand the Kohn-Sham total energy expression of DFT to 2nd order in terms of electron and magnetization density fluctuations 2. Represent the Hamiltonian elements in a minimal basis of pseudoatomic 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 occ E tot , 1 2 1 2 i 2 1 n i i v 2 2 V xc n 0 , 0 i r r n d r 3 n n0 n 2 1 E xc 3 3 | n 0 , 0 n n d rd r r r nn E xc 2 | n 0 , 0 d rd r E xc n 0 , 0 3 V xc n 0 , 0 n 0 d r 3 1 2 3 n 0 n 0 r r d rd r 3 3 0 1 2 N Z Z R R DFT DFTB 1. Expand the Kohn-Sham total energy expression of DFT to 2nd order in terms of electron and magnetization density fluctuations 2. Represent the Hamiltonian elements in a minimal basis of pseudoatomic 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 occ E tot , 1 2 1 2 i n i 0 c i c i H q q N p l p l W l l E xc n 0 , 0 l l V xc n 0 , 0 n 0 d r 3 1 2 n 0 n 0 r r 1 2 d rd r 3 3 N Z Z R R DFT DFTB 1. Expand the Kohn-Sham total energy expression of DFT to 2nd order in terms of electron and magnetization density fluctuations 2. Represent the Hamiltonian elements in a minimal basis of pseudoatomic 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 occ E tot , 1 2 1 2 i n i 0 c i c i H q q N l l p l p l W l l E rep DFTB+ Performance Performance figures N2.9 N1.5 •10x10 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 DFTB+ in Materials Studio 6.0 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 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 www.dftb.org • • • mio, C-H-N-O-S-P pbc, Si-F-O-N-H|Fe matsci, various parameters – Make your own 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 DFTB+ Analysis • • • • • • • Band structure Density of states Electron density Fermi surface Orbitals Slater-Koster parameters Dynamics analysis is done using the Forcite analysis tools Materials Studio 6.0 Parameterization tool 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) Repulsive fitting occ E tot , 1 2 1 i n i 0 c i c i H q q The remaining terms, Erep, will be described using fitted repulsive pair potentials. N 2 p l p l W l l E rep l l pairs E rep E tot DFT E tot DFTB , bare U type ( ij ) ( rij ) i j Pair potentials The pair potentials are fitted against a basis of cutoff polynomials ( r rcutoff ) n if r rcutoff f n (r ) otherwise 0 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... Bond order fitting Use weight distributions to combine several bond orders into a single potential fit 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 Evaluating the result benzene ------DMol3 C3-C2 = 1.39838 DFTB+ C3-C2 = 1.41171 Diff C3-C2 = 0.01333 C3-H9 = 1.09097 C3-H9 = 1.10386 C3-H9 = 0.01289 DMol3 C2-C7-C6 = 120.00000 DFTB+ C2-C7-C6 = 119.99783 Diff C2-C7-C6 = -0.00217 H12-C7-C6 = 120.00000 H12-C7-C6 = 120.00930 H12-C7-C6 = 0.00930 Atomization Diff = -111.42032 ============================================== ethene -----DMol3 C2-C1 = 1.33543 C2-H5 = 1.09169 DFTB+ C2-C1 = 1.33114 C2-H5 = 1.09898 Diff C2-C1 = -0.00429 C2-H5 = 0.00729 DMol3 C1-C2-H6 = 121.65149 DFTB+ C1-C2-H6 = 121.55765 Diff C1-C2-H6 = -0.09384 H4-C1-H3 = 116.69702 H4-C1-H3 = 116.88453 H4-C1-H3 = 0.18751 Atomization Diff = -48.44673 ============================================== Bond Error Statistics: C-C = 8.81072e-03 C-H = 1.00915e-02 ================= Total Average = 9.45112e-03 Angle Error Statistics: HCH = 1.87511e-01 CCC = 2.16738e-03 HCC = 5.15662e-02 ================= Total Average = 7.32028e-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. SiGeH • sp3d5 basis • LDA(PWC) • Fitted against – – – – – Si, Ge and SiGe solids Si2H6, Si2H4 Ge2H6, Ge2H4 SiGeH6, SiGeH4 SiH4, GeH4 and H2 • Tested against: Si vacancy Formation energy E f E N 1 N 1 N EN Ef(eV) DFTB+ 2.6 DMol3 2.7 – – – – Solids Nanowires Nanoclusters Si vacancy CHNO 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: 0.0096 Å Average angle difference: 1.16 degrees Accuracy is comparative to that of the Mio library. • 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, 3.590 (3.544) Å CHNO: Larger molecules CNT-6x6 Bond Diff (Å) C-C 0.005 Caffeine N-AA 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 • Successfully tested for: – CNT – C60 – Caffeine – Glucose – Porphine – N-Acetylneuraminic acid Thanks for your attention Other contributors: Paddy Bennett (Cambridge, Accelrys) Bálint Aradi (Bremen, CCMS) Zoltan Bodrog (Bremen, CCMS) Generating the orbitals 2 r at ˆ T V eff ( r ) ( r ) ( r ) r 0 • The Kohn-Sham equation is solved for a single atom. • Using an added extra confining potential to better model molecules and solids DFT DFTB 1. Expand the Kohn-Sham total energy expression of DFT to 2nd order in terms of electron and magnetization density fluctuations 2. Represent the Hamiltonian elements in a minimal basis of pseudoatomic 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 occ E tot , i E xc n , 2 1 n i i v 2 2 1 2 N Z Z R R n ( r ) d r 3 r r i DFT DFTB 1. Expand the Kohn-Sham total energy expression of DFT to 2nd order in terms of electron and magnetization density fluctuations 2. Represent the Hamiltonian elements in a minimal basis of pseudoatomic 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 occ E tot , 1 2 1 2 i 2 1 n i i v 2 2 V xc n 0 , 0 i r r n d r 3 n n0 n 2 1 E xc 3 3 | n 0 , 0 n n d rd r r r nn E xc 2 | n 0 , 0 d rd r E xc n 0 , 0 3 V xc n 0 , 0 n 0 d r 3 1 2 3 n 0 n 0 r r d rd r 3 3 0 1 2 N Z Z R R DFT DFTB 1. Expand the Kohn-Sham total energy expression of DFT to 2nd order in terms of electron and magnetization density fluctuations 2. Represent the Hamiltonian elements in a minimal basis of pseudoatomic 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 occ E tot , 1 2 1 2 i n i * 0 c i c i H 2 1 E xc 3 3 | n 0 , 0 n n d rd r r r nn E xc 2 | d rd r E xc n 0 , 0 3 n0 ,0 V xc n 0 , 0 n 0 d r 3 1 2 3 n 0 n 0 r r d rd r 3 3 i c i 1 2 N Z Z R R 0 0 H i Hˆ i DFT DFTB 1. Expand the Kohn-Sham total energy expression of DFT to 2nd order in terms of electron and magnetization density fluctuations 2. Represent the Hamiltonian elements in a minimal basis of pseudoatomic 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 occ E tot , 0 c i c i H n q q 2 1 2 q q q 0 E xc 2 | n 0 , 0 r r E xc n 0 , 0 3 V xc n 0 , 0 n 0 r 3 1 2 n a 1 i n i 3 n 0 n 0 r r r r 3 3 1 2 N Z Z R R Hubbard U Coulomb interacion αβ αβ DFT DFTB 1. Expand the Kohn-Sham total energy expression of DFT to 2nd order in terms of electron and magnetization density fluctuations 2. Represent the Hamiltonian elements in a minimal basis of pseudoatomic 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 occ E tot , 1 2 1 2 i n i 0 c i c i H p al p l p l q q N p l p l W l l E xc n 0 , 0 l l V xc n 0 , 0 n 0 d r 3 1 2 n 0 n 0 r r 1 2 d rd r 3 3 N Z Z R R W ll spin interactio n DFT DFTB 1. Expand the Kohn-Sham total energy expression of DFT to 2nd order in terms of electron and magnetization density fluctuations 2. Represent the Hamiltonian elements in a minimal basis of pseudoatomic 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 occ E tot , 1 2 1 2 i n i 0 c i c i H q q N l l p l p l W l l E rep 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 Performance figures N2.9 N1.5 •10x10 CNT •32 atoms/unitcell •Run on single core •Intel(R) Xeon(TM) CPU 3.00GHz #cpu OpenMP Speedup Efficiency 1 1.0 2 0.87 •Small systems (<300 atoms) O(N) processes dominate 3 •Large systems (>300) eigenvalue solver dominates 4 0.80 0.72 DMol3 vs. DFTB+ 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 102-103 faster • DFTB+ compared to DMol3 is a factor of 30-80 faster 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. 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 www.dftb.org • • • mio, C-H-N-O-S-P pbc, Si-F-O-N-H|Fe matsci, various parameters – Make your own 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 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 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 DFTB+ Result files Visible files • <>.xsd – Final structure • <>.xtd (dynamics) – Dynamics trajectory • <>.txt – Compilation of the results • <>.dftb – The last output from DFTB+ • <>.skflib (parameterization) – Slater-Koster library Hidden files • *.tag – Final output data • *.cube – Density and orbital data • *.bands – Band structure data Zn compounds using DFTB+ Working with Zn containing compounds • Zn-X (X = H, C, N, O, S, Zn) • Can be downloaded at www.DFTB.org (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 Zn Solids W-ZnO DFTB+ w-ZnO zb-ZnS Method Ecoh a(Å) b(Å) B0(GPa) DFTB+ 9.77 3.28 5.25 161 PBE 8.08 3.30 5.34 124 EXP 7.52 3.25 5.20 208 DFTB+ 7.93 5.43 - 44.2 LDA 7.22 5.35 - 82 EXP 6.33 5.40 - 76.9 • Reasonable solid state properties N. H. Moreira, J. Chem. Theory Comput. 2009, 5 , 605 W-ZnO PBE 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, 15 139 N. H. Moreira, J. Chem. Theory Comput. 2009, 5 , 605 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 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 E abs ( E T E ZnO 10 1 0 n ) / 2 N. H. Moreira, J. Chem. Theory Comput. 2009, 5 , 605 • Overall good agreement with experiments and DFT calculations 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) Polynomial fitting setup • Each fitting is done using different polynomial orders • Fittings are done for a set of cutoff radius scale factors ( r rcutoff ) n if r rcutoff f n (r ) otherwise 0 Possible future extensions to DFTB+ 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.