J. Phys. Chem. C 2007, 111, 13879-13885
13879
Adsorption of Organic Molecules on Gold Electrodes Gilberto Teobaldi† and Francesco Zerbetto* Dipartimento di Chimica “G. Ciamician”, UniVersita` di Bologna, V. F. Selmi 2, 40126 Bologna, Italy ReceiVed: May 24, 2007; In Final Form: July 12, 2007
We develop a simple approach to investigate the stability of an organic adlayer on a gold surface in the presence of an external voltage. All atoms are treated explicitly, and there is no predefined bond connectivity between the metal and the organic phase so that molecules are able to slide on the surface. Three applications are discussed: the first considers the structure and energetics of the deposition of citric acid on Au(111). The second is the similar deposition of a porphyrin derivative. The third is the voltage dependent desorption of thiolate chains in self-assembled monolayers. Consistently, the energetics of the systems are driven by the stabilization of the organic adlayer through the bias-dependent charge transfer between metal and molecules. Comparison with experimental results is encouraging. For case 1, the experimental formation of ordered structures between 0.5 and 0.8 V is explained by an increased stability of the cell of 4 molecules and 512 gold atoms. Analogously, the formation in case 2 of a well-ordered adlayer coincides with a region of high stability of a cell of 2 porphyrins and 672 gold atoms. Finally, in case 3, the estimated experimental slope of the activation energy of desorption, 10.8 kcal mol-1 V-1, is bracketed by those calculated for the desorption of a thiolate chain from a half-packed and from a fully packed thiolate monolayer and has the opposite sign of the slope for the desorption of an isolated chain. In all cases, the driving force for electroadsorption is the decrease of the molecular charge with voltage, which, in turn, decreases the Coulombic interactions in the organic adlayer.
Introduction Control over a variety of physical and chemical phenomena that range from catalysis to electron transfer to self assembly is often achieved through the extensive use of modified surfaces. Electrodes are a physical modification of a metal surface with an electric potential that can drive the adsorption of molecules from a solution phase and ultimately lead to their electrodeposition and self assembly into new chemical structures.1-6 Voltage can also modify the dynamics of the molecules7-9 and plays a major role in transistors, in general, and organic transistors, in particular.10-14 The understanding of the effect of voltage on molecules has greatly advanced over the past few years because of the possibility of performing single molecule experiments.15-19 The progress of the theoretical understanding of the electrodeposition and self-assembly processes driven by an electrostatic potential has been relatively minor despite their widespread use.20-22 One of the difficulties lies, perhaps, in the relative scarcity of approaches that are able to investigate the interactions between an organic substrate and a metal surface in the presence of voltage. Both ab initio and density functional theory (DFT) based models can of course add a voltage component to their Hamiltonians; however, they tend to be limited in the number of atoms they can handle, and the comprehension of deposition requires them to include both a sizable number of metal atoms and at least a couple of molecules (plus periodic boundary conditions). Molecular dynamics and Monte Carlo methods based on classical potential energy functions can model association and aggregation processes.23-26 However, the simulation of organic molecules adsorbed on * Corresponding author. E-mail:
[email protected]. † Present address: Surface Science Research Centre, Department of Chemistry, University of Liverpool, L69 3BX, Liverpool, United Kingdom. E-mail:
[email protected].
metals is still a matter of ongoing research, and the effect of an electrostatic potential usually enters only as a Coulomb force experienced by the local partial charges of the atoms. On an electrode, the effects of voltage are manifold: (1) it shifts the orbital energy levels of the molecules that are either adsorbed on it or in its vicinity; (2) if positive, it stabilizes the orbitals, with respect to the energies of either the free electron or the hole, and electrons can more easily be injected into the molecule, while it is more difficult to extract an electron from it; (3) if negative, it destabilizes the orbitals, with respect to the energies of the free electron or hole, and electrons can more easily be extracted from the molecule, while it is more difficult to inject an electron into it; (4) voltage-induced variation of the energy levels affects the atomic chemical potentials and therefore can induce charge redistribution inside the molecule; (5) variation of the orbital energies also varies the polarizability of the molecules and its atoms; and (6) local atomic charges of the molecules interact with the electrostatic potential and consequently the deposition pattern may differ from that occurring on the pure metal surface. Apart from the additional force experienced by the local atomic charges, the other effects are mainly caused by the shift of the energy levels with respect to the energy of the free electron. Here, we propose a simple approach to account for the effect of voltage based on the shift of the atomic ionization potentials (IPs) and the electron affinities (EAs) and apply it to three cases where experimental data of good quality are available for comparison. The Model The gold surface and its bulk phase are described by a formulation of the Embedded Atom model called “glue model”,27 which contains an atomic density-dependent many-body term
10.1021/jp074017g CCC: $37.00 © 2007 American Chemical Society Published on Web 08/18/2007
13880 J. Phys. Chem. C, Vol. 111, No. 37, 2007
Teobaldi and Zerbetto
SCHEME 1: Voltage Dependence of Ionization Potential and Electron Affinity in a Closed Shell System
TABLE 1: Simulation Cell Parameters # of citrates # of Au layers
4 512 (256 free, 256 frozen) 4+4
# of porphyrin derivatives
2
# of Au atoms
672 (336 free, 336 frozen) 4+4
# of Au atoms
# of Au layers # of thiolates # of Au atoms # of Au layers
1 or 12 or 24 576 (288 free, 288 frozen) 4+4
a (Å) b (Å)
23.08 19.992
R β
90° 90°
c (Å)
100.
γ
90°
a (Å)
34.986
R
90°
19.992
β
90°
c (Å)
100.
γ
120°
a (Å) b (Å)
19.992 25.965
R β
90° 90°
b (Å)
c (Å)
100.
γ
can reconstruct. Its relative simplicity (which, however, requires the inversion of large matrices) has allowed us to investigate rather large unit cells (with hundreds or even thousands of atoms) and to perform long-time molecular dynamics simulations (of the order of the nanosecond). Under the same conditions, the use of modern density functional theory or ab initio programs would be too demanding for the present computer hardware, especially for applications where large unit cells are necessary in conjunction with long dynamics runs. Voltage is introduced directly in the charge equilibration method of Rappe´ and Goddard,28 which calculates atomic charges in chemical systems starting from a power series expansion of the energy, EA, of isolated atoms for charges of 0, +1, and -1:
EA(0) ) EA0 EA(+1) ) EA0 +
EA(-1) ) EA0 -
() ( )
+ ...
() ( )
+ ...
∂E ∂q ∂E ∂q
+
A0
+
A0
1 ∂2E 2 ∂q2 1 ∂2E 2 ∂q2
A0
(1)
A0
90°
The first and second derivatives of the energy are defined in terms of atomic IPs and EAs: in addition to the usual two-body interactions. The former mimics the “gluing” character of the atoms cohesion due to the conduction electrons in the metal, where the exact position of neighboring ions is relatively unimportant. The potential has a short-range “atomic density function” component so that, for each atom, one calculates an effective coordination given by the sum of the density contributions of neighboring atoms. The energy of an atom then depends nonlinearly on this effective coordination. The metal-organics interactions are the sum of long-distance and short-distance terms. The former are obtained as Coulomb interactions, with the charges calculated on-thefly as a function of the interatomic distances by the charge equilibration (QEq) scheme of Rappe and Goddard.28 Here, QEq is slightly modified to include the effect of the applied voltage. The latter interactions are given by the short-range Born-Mayer potential, which is necessary in order to tune the long-distance contribution, to account for higher order terms such as van der Waals, polarizability, and multipole interactions, and to balance attractive Coulombic metal-molecule attraction. The organic molecules are simulated by a standard force field.29 In the absence of voltage, this model was previously used to investigate a variety of processes such as (i) the different reconstruction patterns induced by C60 on Au(110) surface,30 (ii) the adsorption of alkanes and 1-alkenes on Au(111),31 where the adsorption energies of short chains, up to C10, were reproduced with an average deviation from the experiments of less than 1 kcal mol-1 and the unexpected transition to disorder that occurs for the deposition of alkyl chains between 18 and 26 carbon atoms was explained, (iii) the apparent symmetry breaking of a macrocyle on the Au surface,32 (iv) the substitution kinetics and dynamics of thiols in self-assembled monolayers,33,34 (v) the mechanochemistry of a polymer on the Au surface,35 and (vi) the adsorption and dynamics of DNA bases on Au(111) where the energies of adsorption were also within 1 kcal mol-1 from the experimental values.36 The approach does not require an a priori definition of bonds between the atoms of the molecules and those of the metal. The molecules are free to drift on the surface, which, in turn,
(∂E∂q)
A0
( ) ∂ 2E ∂q2
1 ) (IP + EA) ) χ0A 2 ) IP - EA ) J0AA
(2)
A0
where χ0A refers to the atomic electronegativity and the idempotential, J0AA, is the Colulomb repulsion between two electrons occupying the same orbital. For a system of N atoms, the total energy reads: N
EA(q1‚‚‚qN) )
(
1
EA0 + χ0AqA + J0AAq2A ∑ 2 A)1
)
+
N
∑
qAqBJAB
(3)
A,B)1 A
