DFT Atomistic Thermodynamics Applied To Elucidate the Driving

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DFT Atomistic Thermodynamics Applied To Elucidate the Driving Force behind Glutamic Acid Self-Assemblies on Silver (100) Surface Dominique Costa,*,† Marco Smerieri,‡ Ionut Tranca,§ Letizia Savio,‡ Luca Vattuone,‡,∥ and Frederik Tielens*,⊥ †

Institut de Recherches de ChimieParis, ENSCP, Chimie ParisTech, 11 rue P. et M. Curie, F-75005 Paris, France IMEM-CNR, Via Dodecaneso 33, 16146 Genova, Italy § Dipartimento di Fisica dell’Università di Genova, Via Dodecaneso 33, I-16146 Genova, Italy ∥ Mulliken Center for Theoretical Chemistry Institut für Physikalische und Theoretische Chemie, Universität Bonn, Beringstraße 4, D-53115 Bonn, Germany ⊥ Sorbonne Universités, UPMC Univ Paris 06, UMR 7574, Laboratoire Chimie de la Matière Condensée, Collège de France, 11 place Marcellin Berthelot, 75231 Paris Cedex 05, France ‡

ABSTRACT: What is the driving force behind the self-assembly of molecules on a surface? Why can different organizations of an assembly coexist under the same conditions? The coexistence of two experimentally observed complex phases of glutamic acid on Ag(100) is discussed using a detailed atomistic thermodynamics approach based on periodic DFT electronic energies. The interplay between bond formation and loss of degrees of freedom, corresponding to the enthalpy−entropy balance, is used to explain in detail and quantitatively the subtle equilibrium between the two differently organized self-assemblies.

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INTRODUCTION The self-assembly of molecules is the spontaneous association of molecular building blocks under equilibrium conditions, occurring spontaneously at interfaces like gas/solid and liquid/ solid and in molecular crystals. Small biomolecules at surfaces represent a case of 2D-self-assembly with or without reminiscence of the molecular crystal structure. In this frame, the special case of biomolecules on metal surfaces is at the basis of the understanding of interface phenomena in biomaterials, such as biocompatibility and chiral recognition.1−3 For the last 20 years, adsorption of amino acids on metal surfaces has been studied by means of surface science techniques to unravel adsorption modes, 2D surface organization, and basic aspects of surface−biomolecule interactions.4−10 To build hybrid hard/ soft matter architectures, the formation of the assembly should be controlled, which is the main challenge in this field today. The amino acid−metal interaction has been investigated with a wide arsenal of experimental tools. In particular, the chemical state of the adsorbed layer has been mainly investigated by Xray photoemission spectroscopy (XPS),11,12 while selfassembled structures have been determined by scanning tunneling microscopy (STM).12,13 Recently, experimental techniques have been sided by computational tools such as molecular modeling.14−16 In particular, density functional theory (DFT) is indeed able to simulate the self-assembly of bioorganic molecules on metallic surfaces, especially when © 2014 American Chemical Society

detailed inputs are available from experimental data. This setup provides accurate information on the internal conformation of the molecules, on the driving mechanisms for self-organization, and on the molecule−surface interactions. Because of the complexity of these systems, a carefully chosen combination of experimental and computational techniques is mandatory for their complete characterization.4,15,17−25 One of the most complex assemblies of amino acids observed so far is the one of (S)-glutamic acid (Glu, C5H9NO4) on silver,12,26 for which unit cells formed by up to eight individual molecules are found. This amino acid consists of a five carbon atoms long chain; each end terminates with a carboxylic group, while the amino group is bonded to the fourth carbon atom, determining the chirality of the molecule. On Ag(100), Glu self-assembles in different geometries depending on deposition temperature.12 In particular, upon deposition at T = 350 K, we observed the coexistence of two structures12 (see Figure 1), named “Square” and “Flower” assemblies15,19 (see Figure 2). The geometry and electronic structure of both “Squares” and “Flowers” assemblies were elucidated in our previous works using density functional theory dispersion included (DFT-D) Received: September 12, 2014 Revised: November 24, 2014 Published: November 26, 2014 29874

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predictive trends that are helpful for the experience. In our team, we have applied this approach for different interfaces, for example, halide entry on nickel,37 water termination and amino acid organization at stainless steel,43 and amine self-assembling at TiO2.33 The atomistic thermodynamics approach is applied in the present study to discuss a fundamental question: What is the driving force behind the coexistence of very different structures under identical experimental conditions?

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METHODOLOGY All calculations are performed using an ab initio plane-wave pseudopotential approach as implemented in VASP.44,45 The Perdew−Burke−Ernzerhof (PBE) functional46,47 was chosen to perform the periodic DFT calculations with an accuracy on the overall convergence tested elsewhere. 48,49 The valence electrons are treated explicitly, and their interactions with the ionic cores are described by the projector augmented-wave method (PAW),50,51 which allows us to use a low-energy cut off equal to 400 eV for the plane-wave basis. The integration over the first Brillouin one is performed using the Γ oint. All thermodynamics values were calculated as explained in ref 33. In the thermodynamical approach used below the following approximations in the experimental conditions were considered: First, we neglect the constant drain (however small) of molecules from surface to gas phase (continuously emptied by the vacuum pumps). Second, we assume that H2, once formed and lost to the gas phase, will not adsorb, split, and react with the radicals again under the experimental conditions. The latter might prohibit transformation of the flower structure to the square structure and may lead to kinetically trapped systems that are observed in experiments, as discussed below. To calculate the Gibbs free-energy contributions of the adsorbed and gas phase molecules, a Born−Haber cycle has to be calculated, as expressed in Scheme 1.

Figure 1. STM images showing Glu molecules self-assembled in the “Flower” and “Square” assemblies. (a) Assemblies of different structure coexist on the same Ag(100) terrace. (b) Two geometries are mixed within a single assembly. V = −1.6 V, I = 0.3 nm, image size: 15.5 nm × 17.2 nm and 15.5 nm × 7.8 nm, respectively.

Figure 2. Molecular representations of the “Flower” assembly of density 1.95 × 1018 Glu molecule/m2 (mixture of neutral and radical species) and the “Square” assembly exposing 1.39 × 1018 Glu molecule/m2 (neutral species). (With permission from ref 19.)

Scheme 1. Born−Haber Cycle Relative to the Adsorption of Glu Molecules on the Ag(100) Surfacea

calculations.15,19 It was found that the squares are a physisorbed system, while the flowers are chemisorbed. These calculations, albeit giving precious information, do not include the freeenergy contributions to build a complete thermodynamical picture. Integration over the full potential energy surfaces (PES) is required to calculate properly the free energy of the system, which is computationally a very demanding task, especially when using first-principles calculations including temperature and when gas-phase compounds are used. Such an exhaustive search was out of the scope of the present study. However, to bridge the gap between “in silico” 0 K calculations and “laboratory conditions”, one can introduce a thermodynamical model including approximations. Atomistic thermodynamics allows us to bridge this “reality gap” between DFT calculations (at 0 K and under vacuum) and laboratory conditions (e.g., partial gas pressure and temperature) at relatively low cost. It has been applied successfully for numerous systems and validated by experimental data.27−42 This approach has been largely explained and reviewed recently concerning the adsorption of organic molecules on metal surfaces.32 Atomistic thermodynamics takes place in the now exponentially developing multiscale approach, which allows us to produce

a

n, number of Glu molecules; m, number of Glu radicals.

In the present system, two forms of Glu are possible: the Glu neutral molecules and the Glu radicals. Here both structures are considered. The particular cases that we will consider in the present work are m = 0 (square structure) and m = n (flower structure). Nevertheless, given the uncertainties, we would like to mention that the considered composition of the flower structure is solely based on our own theoretical work in ref 52. Finally, the reaction free energy defined from Scheme 1 is expressed as follows ΔG = (ΔG1 + (n + m)ΔG2 + ΔG3 − ΔG 4 − m /2ΔG5) (1)

All ΔG, except ΔG3, include explicitly the temperaturedependent terms of the reactants and products. However, some terms are neglected. Hereunder we detail which terms are 29875

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Table 1. Free Energy Terms (in eV) Calculated at T = 400 K for the Two Structures, Squares and Flowersa free-energy term

“flower” assembly (m = n)

formulas

ΔG3

ΔEads ΔEads + ΔZPE ΔG4 [G(Ag − (n + m)Glu)T − G(Ag − (n + m)Glu)0K] ΔFvib (400 K) ΔFrot (400 K) ΔFtrans (400) desorption temp. calculated for pGlu = 8 × 10−11 atm

“square” assembly (m = 0)

−1.24 −1.32

−1.29 −1.30

0.21 ΔFrot(400) = −Frotgasb = 0.68 ΔFtrans(400) =−Ftrans gasb = 0.48 410

0.06 ΔFrot(400) = −2/3Frotgasc = 0.46 ΔFtrans(400)d = 0 420

a Calculated desorption temperature is given for UHV conditions, that is, Glu and H2 of 8 × 10−11 atm. bTotal loss of degree of freedom. cPartial loss of degree of freedom. dNo loss of degree of freedom. The calculated ZPE values are ZPE(Ag-nGlu) − ZPE(Ag) = 1.2927 × 10−18 J/molecule (squares, m = 0), ZPE(Ag-(n + m)Glu) − ZPE(Ag) = 6.48974 × 10−19 J/molecule (flowers, n = m), ZPE(Glu) = 6.4764 × 10−19 J/molecule, ZPE (H2) = 4.33621 × 10−20 J/molecule.

Figure 3. Surface free energy (ΔΓ in J/m2, referred to the adsorbate-free Ag surface, T in K) of the two considered assemblies versus temperature. Dashed line, “Square” assembly; solid line, “Flower” assembly. When ΔΓ < 0, adsorption is thermodynamically favored, whereas desorption is predicted when ΔΓ > 0. The pressure is 8 × 10−11 atm for both Glu and H2 (pressures corresponding to the estimated experimental ones).

translation, and rotation). ΔG3 refers to the adsorption process occurring at 0 K, evaluated as following

neglected and which are taken into account.33 Each term can be expressed separately ΔG1 = [G(Ag)0K − G(Ag)T ]

ΔG3 = ΔEads + ΔZPE + Δ(pV)

(2)

refers to the temperature effects on the surface/gas interface free energy on the surface before the Glu adsorption. ΔG1 is not calculated here but is balanced by ΔG4, as detailed below. ΔG2 refers to the temperature (T) and pressure (p) effects on the Glu gas molecules. ΔG2 = [G(Glu)0K − G(Glu)T , p ]

where ΔZPE = ZPE(Ag‐(n + m)Glu) − (n + m)ZPE(Glu) − ZPE(Ag) + m /2ZPE(H 2)

(3)

ΔG2 = −(Fvib(mol)T , p + Ftrans(mol)T , p + Frot(mol)T , p ) (4)

in which Fvib, Frot, and Ftrans are the free-energy contributions emerging from temperature-dependent vibrational, rotational, and translational motions, respectively.53 Similarly, for H2

ΔG 4 = −[G(Ag‐nGlu)T − G(Ag‐nGlu)0K ]

(8)

The estimation of the free-energy variations due to vibrational, rotational, and translational degrees of freedom requires some assumptions. First, we considered the variation of free energy of the Ag surface itself without and with adsorbate, that is, G(AgnGlu)T ≈ G(Ag)T + G(nGluads)T, to be negligible. In consequence

ΔG5 = −(Fvib(mol)T , p + Ftrans(mol)T , p + Frot(mol)T , p ) (5)

ΔG and ΔG are calculated using the Gaussian software, and the equations of thermochemistry are applied considering the ideal gas approximation for each constituent (vibration, 5

(7)

is the zero point energy difference (temperature-dependent vibrational energy contribution not included) and ΔEads is the adsorption energy obtained from the electronic DFT energies of the products and reactants. Δ(pV) = 0 for this system. ΔG4 refers to the temperature effects on the surface/gas interface free energy of the surface after the Glu adsorption

or

2

(6)

54

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Figure 4. Phase diagrams as a function of the H2 and Glu partial pressure (pressure on a logarithmic scale). The structures are considered as coexisting when the difference in surface energy is 10−7 atm, only squares for PH2 < 10−11, and coexistence of both structures in between. In fact, the appearance of one single phase was observed experimentally in preliminary tests, showing that it is possible to go out of the isostability range. Increasing the temperature, desorption takes place; this is indicated by the smaller coexistence domain and by the larger dry Ag domain present at 400 K. This diagram suggests that, carefully controlling the Glu and H2 pressure at a given temperature, it is possible to tune the formation of a particular self-assembled

ΔG1 − ΔG 4 = [G(Ag)0K − G(Ag)T ] + [G(Ag‐nGlu)T − G(Ag‐nGlu)0K ] ≈ [G(Ag)0K − G(Ag)T ] + [G(Ag)T + G(nGluads)T − G(Ag)0K − G(nGluads)0K ] ≈ G(nGluads)T − G(nGluads)0K

Second, the vibrational entropy terms of the adsorbed species were estimated with a frequency calculation in the adsorbed state, and the standard formulas of the perfect gas approximation were applied to the frequencies of the adsorbed phase. (See more details in ref 29.) For the translational and rotational contributions, we calculated those values in the gas phase only, and we estimated the loss of degrees of freedom on the following basis: (a) In the dense chemisorbed “Flower” assembly, all Glu molecules, that is, both the chemisorbed “Flower-core” molecules and the physisorbed “Flower-leave” molecules, have lost all temperature-dependent translational and rotational degrees of freedom. This assumption is supported by STM measurements, showing that this structure is ordered until desorption. (b) In contrast, in the less dense, poorly bonded “Square” assembly, the molecules were supposed to remain free to rotate along the C−C backbone (in other words, 2/3 of the rotational degree of freedom is lost) and to conserve all translational degrees of freedom at the surface (i.e., no loss of translational degree of freedom). We considered that all translational degrees were maintained, including translation along the z axis. Note that assuming a loss of 1/3 of translational degrees for the physisorbed structure gave similar results as those shown here. We also verified in preliminary tests that it was necessary to take into account all of those contributions to reproduce the experimental data, as shown below. The values calculated for the present system are reported in Table 1.

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RESULTS AND DISCUSSION The free energy ΔG can be expressed as a function of the amount of Glu adsorbed (m + n), in eV, as done in Table 1, and also as a function of the surface area, as reported in Figure 3; writing the interfacial free energy Γ = θ G, where θ is the surface coverage of each assembly (θ = 1.95 × 1018 Glu molecules/m2 and 1.39 × 1018 Glu molecules/m2 for the “Flower” and the “Square” structures, respectively). This is simply done by dividing the ΔG values by the area of the unit cell for each structure. The Γ value includes now a new parameter, the surface coverage, which also influences the respective stability of the two phases, which differ in surface 29877

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geometry. Such a result may have relevant consequences for those applications, which aim at exploiting both the electronic (nanoelectronics) and the chemical (sensoristic) properties of organic layer films. Concerning the “Square” to “Flower” transition, the thermodynamics−kinetics competition can be quantified. To reach this goal, we calculated the adsorption of an individual “neutral Flower”, composed of four Glu molecules in a “Flower” geometry but without deprotonation. This structure, taken as an intermediate step for the transition from squares to flowers, was found to be exothermic by −1.6 eV (cf. ref 19). It is likely to be formed on the surface, certainly once weakly adsorbed Glu neutral molecules diffuse at the surface until they interact with another isolated adsorbed Glu molecule or another preexisting assembly. It appears that reorientation of the COOH group toward Ag surface yielding the formation of Ag−H bond and subsequent dehydrogenation of Glu is barrierless. The next step, H diffusion at the Ag surface and H−H bond formation and desorption, is likely to occur because the affinity of H to the Ag(100) surface is too poor to trap H at the surface.56−59 Thus, it appears that the transition from the physisorbed to the chemisorbed phase is kinetically possible thanks to the low reactivity of the Ag(100) surface. On this surface, experiments and calculations suggest that intermediary species such as isolated Glu and atomic H are poorly adsorbed15 and can diffuse without kinetically controlled barriers.

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CONCLUSIONS We have explored with an atomistic thermodynamics approach based on DFT calculations the coexistence and competition between two very different types of molecular assemblies of glutamic acid on Ag(100) at 350 K. The thermodynamical isostability of the two structures is explained by considering entropic factors that have a strong destabilizing impact on the chemisorbed “Flower” structure. In particular, taking into account the loss of translational and rotational degrees of freedom for the “Flower” structure is mandatory to reproduce the coexistence of the two structures and the temperature of desorption. The calculated temperatures at which the two structures are isoenergetic, T = 380 K, and of desorption, T = 420 K, are in close agreement with the experimental ones. Theoretical calculations using “atomistic thermodynamics” approaches have the potential to bridge the gap between observation and prediction.60 As illustrated in this work, in silico experiments are everyday closer to being used in place of difficult and costly experiments, especially for the study of complex molecular organizations on surfaces.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (D.C.). *E-mail: [email protected] (F.T.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was performed using HPC resources from GENCI[CCRT/CINES/IDRIS] (Grant 2014-[x2014082022]) and the CCRE of Université Pierre et Marie Curie. 29878

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