Density Functional Theory Applications in Chemistry

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Density functional theory for electron transport
through molecules and related problems
Matthias Ernzerhof
Department of Chemistry, University of Montreal
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Hamiltonian for open systems
stationary states
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Continuity equation
stationary state

meta-stable state
stable state
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Bound state
Muga et al., Phys. Rep. 395 (2004) Santra,
Cederbaum, Phys. Rep. 368 (2002) Moiseyev, Phys.
Rep. 302 (1998)
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Systems with a finite lifetime
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Density of states
bound
meta stable
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Siegert state
Siegert, Phys. Rev. 56 750 (1939)
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Siegert state
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Complex absorbing potentials
Riss, Meyer, J. Phys. B 26, 4503 (1993)
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Molecular electronics
Break junction technique
Reed, Zhou, Muller et al.,
Science 278, 252 (1997) Reichert, Ochs, Beckman
et al., PRL, 88, 176804 (2002)
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Landauer formula (non-interacting electrons)
molecule
E
E
left contact
right contact
0
T(E)
1
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The scattering wave function from a finite model
system

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Diatomic molecule in the Hückel approximation
source
sink
Goyer, Ernzerhof, Zhuang, JCP, 126,144104 (2007).
Ernzerhof, JCP, to appear.
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Simple formula for the reflection coefficient
Ernzerhof, JCP, to appear.
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MED containing a diatomic
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The reflection coefficientGeneralization of the
Siegert-state approach
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Impact of the position of the anchor group on
molecular conductance
Mayor, Weber, Reichert, Elbing, von Hänisch,
Beckmann, Fischer, Ang. Chemie Int. Ed., 42,
5834-5838 (2003)
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Para-connected molecule to first-order
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Meta-connected molecule to first-order
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Current distribution in benzene
Para
Ortho
Ernzerhof, Bahmann, Goyer, Zhuang, Rocheleau, J.
Chem. Theory Comput., 2, 1291 (2006)
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Molecular version of the double-slit experiment
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Wires attached to Coronene
Ernzerhof, Bahmann, Goyer, Zhuang, Rocheleau, J.
Chem. Theory Comput., 2, 1291 (2006)
ortho
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Conductance of para coronene
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Conductance of ortho coronene
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Magnetic moment produced by ortho coronene
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Molecules with side groups
Ernzerhof, Zhuang, Rocheleau, JCP 123, 134704,
(2005)
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Molecules with side groups
Re(j)
Im(j)
Re(j)
Im(j)
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Molecules with side groups
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Molecules with side groups
Greens function-DFT method
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Fano resonance
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Fano resonance
Greens function-DFT method
Goyer, Ernzerhof, Zhuang, JCP, 126,144104 (2007).
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Interacting transport theory
Use values of r on a grid, and fit r(E) to
obtain r for real energy values
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Complex symmetric Hamiltonians


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Complex-density functional theory
(Stationarity principle)
M. Ernzerhof, JCP, 125, 124104 (2006)
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Energy as a functional of the potential
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Legendre transformation of E
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Series representation of density functionals
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Potential response functions
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Series representation of density functionals
Potential response functions
Ernzerhof, PRA 50, 4593 (1994)
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Locally defined density functionals
i)
ii)
iii)
iv)
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Continuation of F into the complex plane
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Kohn-Sham-type equation

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Illustration

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Illustration

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Exchange-correlation effectson the imaginary
part of the energy
Exchange-correlation hole at full coupling
strength
Adiabatic connection
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Relation between complex and Hermitian density
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Acknowledgments

• Min Zhuang
• Philippe Rocheleau
• Hilke Bahmann
• Francois Goyer
• Paul Boulanger
• - Sergey Maximoff

Funding and other support NSERC, CFI, GAUSSIAN
Inc.