Presentation on theme: "Application of DFTB in molecular electronics"— Presentation transcript:
1 Application of DFTB in molecular electronics Jeffrey R Reimers, Gemma C. Solomon, Zheng-Li Cai, Noel S. Hush,School of Chemistry, The University of Sydney, AustraliaAlessio Gagliardi, Thomas Frauenheim,Department of Theoretical Physics, Paderborn University, Germany,Theoretical Physics Department, University of Bremen, GermanyAlessandro Pecchia, and Aldo Di CarloDepartment of Electronic Engineering, University of Rome "Tor Vergata", Italy
2 Summary What is Molecular Electronics The “gDFTB” method for molecular electronics applicationsWhy use DFTB ?Problems with standard DFTDoes DTFB offer any intrinsic advantages ?Is DFTB accurate enough ?Use of gDFTB in interpreting experimentImplementing Symmetry in DFTBNature of molecular conduction channels
3 Molecular Electronics: Measuring single molecule conduction Wang et al.PRB 68 (2003)NanoporeKushmerick et al. PRL 89 (2002)Cross-wireSTM Break JunctionB. Xu & N. J. Tao Science (2003) 301, 1221Scanning ProbeCui et al.Science 294(2001) 571ElectromigrationH. S. J. van der Zant et al.Faraday Discuss. (2006)131, 347NanoclusterMechanical Break JunctionDadosh et al. Nature436 (2005) 677Reichert et al. PRL
4 Single-Molecule Conductivity L ELECTRODER ELECTRODEMOLECULE
5 Single-Molecule Conductivity L ELECTRODER ELECTRODEMOLECULEMolecular OrbitalsFermi energy
6 Single-Molecule Conductivity L ELECTRODER ELECTRODEMOLECULEMolecular OrbitalseVVI
7 Finding a true molecular signature: Inelastic Electron Tunnelling Spectroscopy (IETS) h/eVElasticVh/edI/dVInelastich/eVd2I/dV2h/eV
8 Application to molecules J. GKushmerick, J. Lazorcik, C. H. Patterson & R. ShashidharNano Lett. (2004) 4(4) 639W. Wang, T. Lee, I. Kretzschmar & M. Reed Nano Lett. (2004) 4(4) 643
9 Shot noise measurements Garcia et al. Phys. Rev. B (2004) 69,Thygesen & JacobsenPhys. Rev. Lett. (2005) 94,Djukic & Van Ruitenbeek Nano Lett. (2006) 6(4), 789Smit et al. Nature (2002) 419, 906
10 “gDFTB” Method for Calculating the Current Non-Equilibrium Green’s Function (NEGF) formalismImplementation developed at Tor VergataReduces to Landauer Formalism in some instances (eg., coherent current but not for IETS)DFTB implementation developed at Paderborn / Dresdencalled “gDFTB”calculates the system Hamiltionain H for electrode-molecule-electrode systemrequires an optimized geometryrequires vibrational analysis for IETSSee Poster COMP 300 by Gagliardi et al.
11 Diagonal blocks are the energies of each part Partitioning the Electrode-Molecule-Electrode Hamiltonian Operator for the System EnergyLMRDiagonal blocks are the energies of each partMujica, Kemp, Ratner, J. Chem. Phys. 101 (1994) 6849.
12 Off- Diagonal blocks are the interaction energies Partitioning the Electrode-Molecule-Electrode Hamiltonian Operator for the System EnergyLMROff- Diagonal blocks are the interaction energiesMujica, Kemp, Ratner, J. Chem. Phys. 101 (1994) 6849.
14 Why DFTB? General Serious Failures of DFT DispersionCovalent bond breakagePartial electron removal/addition (long range electron-transfer processes)Extended conjugationALL RELEVANTTO PHOTONICS ANDMOLECULAR ELECTRONICS !Can DFTB do better ???Reimers, Cai, Bilić, Hush, Ann. N.Y. Acad. Sci (2003) 235.
15 DFT Failure (1): Dispersion error leads to poor adsorption energies MoleculeSurfaceObservedPW91 CalculatedNH3Au(111)7.5-108Benzene92Cu(111)141Cu(110)236kcal/molkcal/molDFT calculations for benzene on a Cu13 model cluster for (110) = 19 kcal/molCASPT2 dispersion energy error for DFT = 15 kcal/molBilić, Reimers, Hush & Hafner J. Chem. Phys. 116 (2002) 8981Bilić, Reimers, Hoft, Ford & Hush J. Theor. Comput. Chem (2006).
16 DFT Failure (2): Covalent Bond Breakage H2: Source of long-range correlationSingle bonds break properly if and electrons have different orbitalsCai & Reimers J. Chem. Phys. 112 (2000) 527
17 Time-Dependent DFT (TDDFT) collapses for excited states The triplet instability has a profound effect for TDDFT and its analogue RPA (use H0 + H1 + H2 )CIS is OK (uses H0 + H1 )Cai & Reimers J. Chem. Phys. 112 (2000) 527
18 Electrode cluster – molecule – Electrode cluster MODEL SYSTEM Application to the weak electrode-electrode through molecule bonds that drive single-molecule conductivity experimentsElectrode cluster – molecule – Electrode clusterMODEL SYSTEMTypical pair of weakly coupled orbitalsActually there are 2 such pairs !Solomon, Reimers and Hush J. Chem. Phys. 112 (2000) 527
19 Fermi Level of system is OPEN SHELL Solomon, Reimers and Hush J. Chem. Phys. 112 (2000) 527
20 Closed-Shell treatments lead to split orbitals Closed-Shell GGA density functionals have incorrect asymptotes but maintain double degeneracy … results in additional weak conduction channels … is usefulClosed-shell hybrid density fucntionals gives asymptotically very poor result … perceived as strong coupling, resultant currents x 100 too high … uselessOpen-shell calculation gives asymptotically correct answerSolomon, Reimers and Hush J. Chem. Phys. 112 (2000) 527
21 DFT Failure (3): Partial Electron Removal All modern functionals have an incorrect asymptotic potentialShould beIsVx as a function of nuclear - electron distance r for the H atomTaken from Tozer et al. J. Chem. Phys. 112 (2000) P3507
22 DFT band lineup error for phenylthiol (RSH) on gold(111) RSH RS• RS– Adsorbate Gold (111)Obs PW PW PW Bridge FCC PW Obs.Band-gap error 5.6 eVBand lineup error 3.4 eVBilić, Reimers and Hush J. Chem. Phys. 122 (2005)
23 DFT Failure (4): Conjugated Systems Examples …. overestimation of metallic-like propertiesCollapse of band-gap in oligoporphyrin molecular wiresAppearance of charge-transfer bands in porphyrins and chlorophyllsLoss of band gap in polyacetylene, very high NLO properties
24 OligoporphyrinsSendt, Johnston, Hough, Crossley, Hush & Reimers J. Am. Chem. Soc. 124 (2002) 9299Cai, Sendt & Reimers J. Chem. Phys. 117 (2002) 5543
25 Can DFTB be better ? Dispersion – yes, via empirical corrections Covalent bond breakage – yes, no singlet/triplet thus no triplet instability !Partial electron removal/addition (long range electron-transfer processes) ???Extended conjugation ???
26 SCC-DFTB errors for properties of 63 Mg complexes PropertyB3LYPSCC-DFTBAM1PM3MNDO-dPM5Bond length / ÅAve.00.02-.03-.10-.05-.06.06.11.18.10.09Bond Ang. / °-1-2-9141425153IP / eV.20-.188.8.131.52.184.108.40.206.65.44.50Hf / kcal mol-1149-4-67246191823Incr. Ligand8166Binding / kcal mol-12117Deprotonation-72-17Energy / kcal mol-1101192722Comp. to either experiment or else CBS or else QCISDCai, Lopez, Reimers, Cui, Elstner in prep.
27 SCC-DFTB geometries of thiols on Au(111) Alkane chainS head groupp(5 5) Au surface celloptimized geometry has S on a top siteDFT calculations predict either FCC or bridge-distorted FCC siteexperiments indicate top site but may involve Au adatom insteadSolomon,Gagliardi, Pecchia, Frauenheim, Di Carlo, Reimers, Hush J.C.P. (2006) 124,
28 Observed and gDFTB-calculated IETS Reed’s experimentCalculations match and enhance experimental assignmentW. Wang, T. Lee, I. Kretzschmar & M. Reed Nano Lett. (2004) 4(4)Binding siteSolomon,Gagliardi, Pecchia, Frauenheim, Di Carlo, Reimers, Hush J.C.P. (2006) 124,
29 Effect of the binding site on CH intensity Wang, Lee, Kretzschmar & Reed Nano Lett. (2004) 4 643Opt structure Calculated IETSlower energyhigher energyJ. Kushmerick, Lazorcik, Patterson & Shashidhar Nano Lett. (2004) 4 639Solomon,Gagliardi, Pecchia, Frauenheim, Di Carlo, Reimers, Hush J.C.P. (2006) 124,
30 Importance of molecular symmetry Vibrations are characterized by their symmetry.What are the selection rules for IETS?What is the nature of the conduction channels through the molecule?How many are there?What is the role of the junction region?What is the role of the molecule and its molecular orbitals
31 Implementing symmetry in SCC-DFTB Find all atoms related by the Albelian symmetry operators C2 (two-fold rotation), (reflection plane), and i (inversion)Construct the transformation S that forces all atomic orbitals (AO), Cartesian tensor components, etc., to be eigenfunctions of these operatorsTransform the Kohn-Sham matrix H, force vector, Hessian matrix of second derivatives, etc. from AO basis and Cartesian coordinates into symmetry adapted representations:H = ST H SDiagonalize H to get symmetry-adapted molecular orbitals CBack transformation to get molecular orbitals in AO basisC = S CSolomon,Gagliardi, Pecchia, Frauenheim, Di Carlo, Reimers, Hush J.C.P. (2006) submitted
32 Numerical AdvantagesNumerical error is removed (numbers that should be zero ARE zero)Force optimization of transition states and saddle pointsBlock diagonalization gives speedup (eg, 4 for C2v)eg. Say that H has transforms according to the C2v point groupsymmetry operators C2z, xz, yz, and Eirreducible representations a1, a2, b1, and b2a1a2b1b2a1 a b1 b2H =
33 What is the point group in gDFTB calculations? Symmetry of entire system H is C2h (operators are C2z, xy, and i)Symmetry of molecular component HM is C2hSymmetry of individual molecule- electrode couplings JL and JR is Cs onlygDFTB equations use JL and JR explicitly hence there a new quantity is needed, theMOLECULAR CONDUCANCE POINT GROUPSolomon,Gagliardi, Pecchia, Frauenheim, Di Carlo, Reimers, Hush J.C.P. (2006) submitted
34 Determining the Molecular Conductance Point Group Eg., for chemisorbed 1,4-benzenedithiol S- C6H4-SAll symmetry operators that enforce end-to-end symmetry are lostAll other symmetry operators are retainedIn this case, D2h C2vSolomon,Gagliardi, Pecchia, Frauenheim, Di Carlo, Reimers, Hush J.C.P. (2006) submitted
35 Conduction split into symmetry channels Total transmissionA2 componentEf = Fermi energy of Au, controls low-voltage conductivity … its B1 !Solomon,Gagliardi, Pecchia, Frauenheim, Di Carlo, Reimers, Hush J.C.P. (2006) submitted
36 The transmission through each symmetry block can then be partitioned in other ways: 1. Büttiker eigenchannels (shot noise)2. Junction eignchannels coupled by the molecule3. Interference between Molecular Conductance Orbitals coupled through the junctionSolomon,Gagliardi, Pecchia, Frauenheim, Di Carlo, Reimers, Hush Nano Letts (2006) in press
37 Harnessing the power of DFTB Au atoms per electrode:Black- 3Red- 25Solomon,Gagliardi, Pecchia, Frauenheim, Di Carlo, Reimers, Hush J.C.P. (2006) submitted
38 ConclusionsgDFTB formalism provides powerful application areas to molecules coupled to solid-state devicesimplementation of symmetry into SCC-DFTB codeprovides faster and more stable central algorithmprovides key information for understanding molecular systemsmust be careful to use DFTB only for suitable propertiesinitial applications in molecular electronics encouragingconduction channelsIETS vibrational spectroscopybasic behaviour of method not yet fully characterizedready for testing on large systems
40 ACS Abstract Application of DFTB in molecular electronics Jeffrey R Reimers, Gemma C. Solomon, Zheng-Li Cai, Noel S. Hush, Alessio Gagliardi, Thomas Frauenheim, Alessandro Pecchia5, and Aldo Di Carlo, (1) School of Chemistry, The University of Sydney, Sydney, 2006, Australia, (2) School of Molecular and Microbial Biosciences, The University of Sydney, Sydney, 2006, Australia, (3) Theoretical Physics Department, University of Bremen, Germany, Vogeliusweg , Paderborn, , Germany, (4) Bremen Center for Computational Materials Science, Bremen University, Bibliothekstrasse 1, Bremen, 28359, Germany, (5) Department of Electronic Engeneering, University of Rome "Tor Vergata", Rome, ItalyMolecular electronics involves the passing of current between two electrodes through a single conducting molecule. Calculations in this area require not only the ability to handle large systems including metal-electrode fragments but also require accurate positioning of molecular and metallic energy bands and must treat occupied and virtual orbitals on an equivalent footing. Each of these requirements presents difficulties for standard DFT calculations, making DFTB an attractive alternative proposition. We present enhancements to the SCC-DFTB program that allow it to diagnose and utilize molecular symmetry, increasing computational speed and accuracy whilst providing important information concerning molecular orbitals and molecular vibrations. Optimized geometries are then obtained for molecules sandwiched between gold electrodes, leading to Green's-function based calculations of steady-state through-molecule electrical conductivity and incoherent inelastic tunnelling spectroscopy (IETS) arising from electrical current activation of molecular vibrational modes.
41 When the junction symmetry is less than that of the Molecular Conductance Point Group Black- 3 Au, exactGreen- 3 Au, using higher symmetryRed- 25 Au, exactSolomon,Gagliardi, Pecchia, Frauenheim, Di Carlo, Reimers, Hush J.C.P. (2006) submitted