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

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

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 : http://www.dfa.ua.es

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.

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 )

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

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

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

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

Present Theory: H mean field H mean field i r ( r ) ϕ ( r ) ϕ = ε i i i r i 1 2 2 + 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?

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

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

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 0.8 0 Pt/H 2 Pt 0 1 2 3 4 5 G [2 e 2 / h] A Hydrogen molecule: The smallest molecular bridge?

Numerical results: The HOMO-LUMO gap strongly depends on the SCF method. one-electron Kohn-Sham orbitals [ev] 0-5 -10 GAP HOMO 0 a HF exchange a = ε ε HF exchange LUMO 1

Numerical results: Conductance strongly depends on the SCF method. 1 G [2 e 2 / h] 0 0 1 a HF exchange

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

Numerical results: the right HOMO-LUMO gap HOMO-LUMO GAP [ev] from ground state calculations 0-5 -10 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

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.

Numerical results:the HOMO-LUMO gap strongly depends on of the SCF method. one-electron Kohn-Sham orbitals [ev] 0-5 -10 GAP = ε HOMO ε 0 a HF exchange a HF exchange LUMO 1

Numerical results: Conductance strongly depends on the SCF method. 1 G [2 e 2 / h] 0 0 1 a HF exchange

Numerical results: DFT vs HF-DFT. G [2 e 2 / h] 5 4 3 2 1 0 DFT = 0 %HF exchange hdft = 60 % HF exchange -10 0 10 [E E Fermi ] ev

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 0.8 0 Pt/H 2 Pt 0 1 2 3 4 5 G [2 e 2 / h] DFT groups HF+DFT= Alicante s group A Hydrogen molecule: The smallest molecular bridge?

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, 055321 (2003)

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

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