Introduction to DFTB+

1. Introduction to DFTB+ Martin Persson Accelrys, Cambridge

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

3. Why DFTB+

4. 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

5. 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

6. Examples of what can be done with DFTB+ Diamond nucleation Novel SiCN ceramics Si cluster growth Magnetic Fe clusters WS2 nanotubes

7. Basic DFTB Theory

8. 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

9. DFTB basis set • Minimal basis set • Pseudo atomic orbitals • Slater orbitals • Spherical harmonics

10. Pseudo atomic orbitals Silicon sp3d5orbitals S P1 P2 P3 D1 D2 D3 D4 D5 For Silicon the d-orbitals are un-occupied but needed to properly model the conduction band.

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

12. 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

13. 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

14. 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

15. 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

16. DFTB+ Performance

17. 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

18. DFTB+ in Materials Studio 6.0

19. 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

20. 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

21. 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

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

23. Materials Studio 6.0 Parameterization tool

24. 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)

25. 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

26. 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...

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

28. 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

29. Evaluating the result benzene ------- DMol3 C3-C2 = 1.39838 C3-H9 = 1.09097 DFTB+ C3-C2 = 1.41171 C3-H9 = 1.10386 Diff C3-C2 = 0.01333 C3-H9 = 0.01289 DMol3 C2-C7-C6 = 120.00000 H12-C7-C6 = 120.00000 DFTB+ C2-C7-C6 = 119.99783 H12-C7-C6 = 120.00930 Diff C2-C7-C6 = -0.00217 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 H4-C1-H3 = 116.69702 DFTB+ C1-C2-H6 = 121.55765 H4-C1-H3 = 116.88453 Diff C1-C2-H6 = -0.09384 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 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.

30. 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

31. 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, 3.590 (3.544) Å Average bond difference: 0.0096 Å Average angle difference: 1.16 degrees Accuracy is comparative to that of the Mio library.

32. CHNO: Larger molecules CNT-6x6 • Successfully tested for: • CNT • C60 • Caffeine • Glucose • Porphine • N-Acetylneuraminic acid Caffeine N-AA

33. Thanks for your attention Other contributors: Paddy Bennett (Cambridge, Accelrys) Bálint Aradi (Bremen, CCMS) ZoltanBodrog (Bremen, CCMS)

34. 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

35. 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

36. 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

37. 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

38. 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

39. 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

40. 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

41. 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

42. Performance figures N2.9 N1.5 • 10x10 CNT • 32 atoms/unitcell • Run on single core • Intel(R) Xeon(TM) CPU 3.00GHz OpenMP • Small systems (<300 atoms) O(N) processes dominate • Large systems (>300) eigenvalue solver dominates

43. DMol3 vs. DFTB+ • 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

44. 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.

45. 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

46. 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

47. 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

48. 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

49. DFTB+ Result files Visible files Hidden files • <>.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

50. Zn compounds using DFTB+