112
S. Yanagisawa and I. Hamada
4.2.2 Electronic Properties at Organic-Metal Interfaces:
Energy Level Alignment and Emergence of the Image
Potential-Like States
The important physical phenomenon crucially affecting the energy level alignment
at the interface and thus the charge transport properties [110] is the renormalization
of the HOMO-LUMO energy gap induced by the metal surface [111–113]. When a
molecule is close to the metal surface, electrons in the metal respond to and screen
charged excitations of the molecule. The molecular energy levels at the interface
are thus quasiparticle energy levels. As a result, when the molecule is located close
to the metal surface, the molecular HOMO and LUMO levels shift closer to the
metal Fermi level, and the HOMO-LUMO fundamental gap is narrowed [111–
113]. A rigorous theoretical treatment is the many-body perturbation theory within
the GW approximation for accurate treatment of the quasiparticle energies at the
organic-metal interface [112, 113]. However, the computationally demanding GW
treatment hampers its application to periodic systems with hundreds of atoms even
with present-day computational resources. That is also the case in treatment of an
organic-metal interface by employing a periodic slab model with a vacuum layer
along the direction normal to the slab [114]. In addition to the system size tractable,
the numerical convergence of the molecular quasiparticle energies and the metal
work function can be a problem [114, 115]. The DFT wave functions can be poor
approximations to the quasiparticle wave functions for hybridized interfaces, which
necessitate diagonalization of the self-energy matrix (E) for a better new starting
point for the perturbation beyond G 0 W 0 or another computational strategy such as
evaluation of the self-energy in the basis of the molecular orbitals, which is expected
to be diagonal [114].
To avoid the technical issues involved in the GW calculation of the overall
interface system, some efforts have been made, for instance, the DFT+ approach
[112, 116]. For physisorbed systems, with the assumption of weak coupling between
the molecule and the metal, the PDOS peaks of an isolated molecule could be
shifted by the quasiparticle self-energy correction to HOMO and LUMO energies,
along with the gap renormalization upon adsorption on the metal. With DFT+,
one adds two corrections denoted by to HOMO-/LUMO-derived levels obtained
with DFT within LDA or GGA. First, a difference between HOMO or LUMO
energy of an isolated molecule with DFT-LDA or DFT-GGA and that obtained at a
highly accurate level of theory such as GW is estimated. Second, the polarization
at the surface inducing gap renormalization is corrected based on the classical
image charge model 1/4[z − z 0 ], where z is the average height of the molecule
on the surface and z 0 is the image plane position. The DFT+ method has been
successfully employed to predict or elucidate the energy level alignment at organicmetal interfaces with physisorption [112, 117] and to explain the charge transport in
molecular junctions where the assumption of weak coupling is reasonable [116].
Overall, however, the representative theoretical works calculating the energy
level alignment at organic-metal interfaces within GW or DFT+, despite its
S. Yanagisawa and I. Hamada
4.2.2 Electronic Properties at Organic-Metal Interfaces:
Energy Level Alignment and Emergence of the Image
Potential-Like States
The important physical phenomenon crucially affecting the energy level alignment
at the interface and thus the charge transport properties [110] is the renormalization
of the HOMO-LUMO energy gap induced by the metal surface [111–113]. When a
molecule is close to the metal surface, electrons in the metal respond to and screen
charged excitations of the molecule. The molecular energy levels at the interface
are thus quasiparticle energy levels. As a result, when the molecule is located close
to the metal surface, the molecular HOMO and LUMO levels shift closer to the
metal Fermi level, and the HOMO-LUMO fundamental gap is narrowed [111–
113]. A rigorous theoretical treatment is the many-body perturbation theory within
the GW approximation for accurate treatment of the quasiparticle energies at the
organic-metal interface [112, 113]. However, the computationally demanding GW
treatment hampers its application to periodic systems with hundreds of atoms even
with present-day computational resources. That is also the case in treatment of an
organic-metal interface by employing a periodic slab model with a vacuum layer
along the direction normal to the slab [114]. In addition to the system size tractable,
the numerical convergence of the molecular quasiparticle energies and the metal
work function can be a problem [114, 115]. The DFT wave functions can be poor
approximations to the quasiparticle wave functions for hybridized interfaces, which
necessitate diagonalization of the self-energy matrix (E) for a better new starting
point for the perturbation beyond G 0 W 0 or another computational strategy such as
evaluation of the self-energy in the basis of the molecular orbitals, which is expected
to be diagonal [114].
To avoid the technical issues involved in the GW calculation of the overall
interface system, some efforts have been made, for instance, the DFT+ approach
[112, 116]. For physisorbed systems, with the assumption of weak coupling between
the molecule and the metal, the PDOS peaks of an isolated molecule could be
shifted by the quasiparticle self-energy correction to HOMO and LUMO energies,
along with the gap renormalization upon adsorption on the metal. With DFT+,
one adds two corrections denoted by to HOMO-/LUMO-derived levels obtained
with DFT within LDA or GGA. First, a difference between HOMO or LUMO
energy of an isolated molecule with DFT-LDA or DFT-GGA and that obtained at a
highly accurate level of theory such as GW is estimated. Second, the polarization
at the surface inducing gap renormalization is corrected based on the classical
image charge model 1/4[z − z 0 ], where z is the average height of the molecule
on the surface and z 0 is the image plane position. The DFT+ method has been
successfully employed to predict or elucidate the energy level alignment at organicmetal interfaces with physisorption [112, 117] and to explain the charge transport in
molecular junctions where the assumption of weak coupling is reasonable [116].
Overall, however, the representative theoretical works calculating the energy
level alignment at organic-metal interfaces within GW or DFT+, despite its