Ab-initio Molecular Electronics: are we reaching the limit? Yamila.García Applied Physics Department, Alicante University, Spain

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1 Ab-initio Molecular Electronics: are we reaching the limit? Yamila.García Applied Physics Department, Alicante University, Spain

2 To be, or not to be: that is the question: Whether tis nobler in mind to suffer The slings and arrows of outrageous fortune, Or to take arms against a sea of troubles, And by opposing end them. To die: to sleep; No more! (...) Castle of Elsinore, Denmark, 1600 Ab-initio Molecular Electronics: are we reaching the limit? Niels Bohr Summer Institute, Denmark, 2005

3 Remarks 1. The ab-initio calculation does not exist. To attain this limit SCF methods must be improved. We have devised a code to achieve this within the mean-field approach. The code is distribution free :

4 It is a profoundly erroneous truism... that we should cultivate the habit of thinking of what we are doing. The perfect opposite is the case. Civilization advances by extending the number of important operations which we can perform without thinking about them. -Alfred North Whitehead Our method 1. Theoretical background. 2. The present theory. 3. Numerical vs. Experimental results: H 2 in Pt nanocontacts.

5 Theoretical background Why? 0. Ab-initio Molecular Electronics 1. Landauer I G = = V T 2 e h [ ] ε ε ε ε ( ε ) = Tr Γ ( ) g + ( ) Γ ( ) g ( ) left 2 T ( ε ) Fermi right 5. The SCF Method : g ± ( ε )

6 Theoretical background Mathematical fact: g ± [ ] I 1 ( ε ) ( ε ± iδ ) = H mean field One-electron molecular orbitals are the poles of the Green Function

7 Left electrode Bulk + Nanojunction Right electrode + Bulk Microscopical picture of energetic alignment at the contact

8 Fermi level LUMO GAP HOMO Fermi level t>>0 t=0 Bulk + Left electrode Nanojunction atoms/molecules + Bulk Right electrode Microscopical picture of energetic alignment at the contact

9 Theoretical background 1. Key Message: Alignmentat the neck will determine electronic measurements: HOMO-LUMO gap is the quantity to examine.

10 Present Theory: H mean field H mean field i r ( r ) ϕ ( r ) ϕ = ε i i i r i V ext + V xc r ϕ = ε i i i ( r ) ( r ) ϕ ( r ) i r i r i How can we compute the exchange-corrrelation potential?

11 Present Theory: H mean field two extreme options currently in use: WF and DFT methods: V HF xc = V HF [ ϕ ( r )] V DFT = V DFT [ ρ( r )] x i r i dynamic correlations local correlations non-locality=pauli... xc xc r HF DFT xc OUR SUGGESTION: HF x ( 1 a) V DFT V DFT V = a V + + x c a HF exchange

12 Numerical vs. Experimental results A benchmark system: A single Hydrogen molecule bridging Platinum nanocontacts:

13 Experimental results R.H.M. Smit,Y.Noat,C.Untiedt,N.D.Lang,M.van Hemert,J.M.vanRuitenbeek, Nature 419, 906 (2002) Number of counts Pt/H 2 Pt G [2 e 2 / h] A Hydrogen molecule: The smallest molecular bridge?

14 Numerical results: The HOMO-LUMO gap strongly depends on the SCF method. one-electron Kohn-Sham orbitals [ev] GAP HOMO 0 a HF exchange a = ε ε HF exchange LUMO 1

15 Numerical results: Conductance strongly depends on the SCF method. 1 G [2 e 2 / h] a HF exchange

16 Numerical results. The doubts: Which is the right HOMO-LUMO gap? Which is the right method? Which is the right conductance value?

17 Numerical results: the right HOMO-LUMO gap HOMO-LUMO GAP [ev] from ground state calculations GAP ( N ) E ( N 1) E ( 1) = 2 E N + HF MP2 MP3 MP4 ccsd ccsd(t) LSDA GGA MGGA Quantum Chemistry Methods in use

18 Numerical results 2. Key Message: Ab-initio molecular electronics will suffer from the shortcomings of DFT-based approaches (LSDA,GGA,MGGA). To remain within mean-field methods we must go beyond DFT.

19 Numerical results:the HOMO-LUMO gap strongly depends on of the SCF method. one-electron Kohn-Sham orbitals [ev] GAP = ε HOMO ε 0 a HF exchange a HF exchange LUMO 1

20 Numerical results: Conductance strongly depends on the SCF method. 1 G [2 e 2 / h] a HF exchange

21 Numerical results: DFT vs HF-DFT. G [2 e 2 / h] DFT = 0 %HF exchange hdft = 60 % HF exchange [E E Fermi ] ev

22 Experimental results R.H.M. Smit,Y.Noat,C.Untiedt,N.D.Lang,M.van Hemert,J.M.vanRuitenbeek, Nature 419, 906 (2002) Number of counts Pt/H 2 Pt G [2 e 2 / h] DFT groups HF+DFT= Alicante s group A Hydrogen molecule: The smallest molecular bridge?

23 Numerical vs. experimental results 3. Key Message: The experimental measurement of the perfect quantum of conductance may not be associated with the smallest molecular bridge. Yamila.García, J.J.Palacios, E. SanFabián, J.A. Vergés, A.J.Pérez-Giménez, and E.Louis, Phys. Rev. B.67, (2003)

24 Future Work Inelastic scattering events Large size molecules Finite bias Finite temperature.. Ab-initio molecular electronics

25 In collaboration with: J.J. Palacios E. Louis Applied Physics Department,Alicante University,Spain Applied Physics Department,Alicante University,Spain J.C. Sancho-García E. SanFabián Physical-Chemistry Department,Alicante University,Spain Physical-Chemistry Department,Alicante University,Spain J. A. Vergés Materials Science Institute of Madrid, Spain

26 To be, or not to be: that is the question: Whether tis nobler in mind to suffer The slings and arrows of outrageous fortune, Or to take arms against a sea of troubles, And by opposing end them. To die: to sleep; No more! (...) Castle of Elsinore, Denmark, 1600 Ab-initio Molecular Electronics: are we reaching the limit? The doubt remains Niels Bohr Summer Institute,Denmark, 2005

An ab initio approach to electrical transport in molecular devices

INSTITUTE OF PHYSICSPUBLISHING Nanotechnology 13 (00) 1 4 An ab initio approach to electrical transport in molecular devices NANOTECHNOLOGY PII: S0957-4484(0)31500-9 JJPalacios 1,ELouis 1,AJPérez-Jiménez,ESanFabián