Interaction between benzenedithiolate and gold: Classical force field for chemical bonding

Transcription

1 THE JOURNAL OF CHEMICAL PHYSICS 122, Interaction between benzenedithiolate and gold: Classical force field for chemical bonding Yongsheng Leng a Department of Chemical Engineering, Vanderbilt University, Nashville, Tennessee Predrag S. Krstić Physics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee Jack C. Wells Computer Science and Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee Peter T. Cummings Department of Chemical Engineering, Vanderbilt University, Nashville, Tennessee and Chemical Sciences Division and Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee David J. Dean Physics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee Received 4 April 2005; accepted 4 May 2005; published online 6 July 2005 We have constructed a group of classical potentials based on ab initio density-functional theory DFT calculations to describe the chemical bonding between benzenedithiolate BDT molecule and gold atoms, including bond stretching, bond angle bending, and dihedral angle torsion involved at the interface between the molecule and gold clusters. Three DFT functionals, local-density approximation LDA, PBE0, and X3LYP, have been implemented to calculate single point energies SPE for a large number of molecular configurations of BDT 1, 2 Au complexes. The three DFT methods yield similar bonding curves. The variations of atomic charges from Mulliken population analysis within the molecule/metal complex versus different molecular configurations have been investigated in detail. We found that, except for bonded atoms in BDT 1, 2 Au complexes, the Mulliken partial charges of other atoms in BDT are quite stable, which significantly reduces the uncertainty in partial charge selections in classical molecular simulations. Molecular-dynamics MD simulations are performed to investigate the structure of BDT self-assembled monolayer SAM and the adsorption geometry of S adatoms on Au 111 surface. We found that the bond-stretching potential is the most dominant part in chemical bonding. Whereas the local bonding geometry of BDT molecular configuration may depend on the DFT functional used, the global packing structure of BDT SAM is quite independent of DFT functional, even though the uncertainty of some force-field parameters for chemical bonding can be as large as 100%. This indicates that the intermolecular interactions play a dominant role in determining the BDT SAMs global packing structure American Institute of Physics. DOI: / I. INTRODUCTION The geometry of molecular bonding and packing of selfassembled monolayers SAMs at an organometallic interface is a fundamental issue in the development of molecular electronic devices. 1 While extensive experimental efforts have been invested in calibrating the transport properties of a single-molecule bridge between metal leads, 2,3 theoretical and experimental investigations also indicate that the conductance of metal-molecule-metal junctions depends on the molecular conformations, 4,5 the temperature, 5,6 the packing density, 7 and the contact nature between organic molecules and electrodes. 8 Understanding the equilibrium structure of a Author to whom correspondence should be addressed. Electronic mail: yongsheng.leng@vanderbilt.edu SAMs under zero bias should be a starting point to the subsequent transport calculations, though an actual electric current may affect the SAMs structure. 1,9 Recent ab initio density-functional theory DFT calculations of thiolate molecules on the Au 111 surface, either at full or low coverage, show that S head groups prefer to bond at bridge or bridgelike binding sites with a strong chemical bonding, instead of the fcc hollow sites. 15 The DFT calculations for the binding between thiolate molecules and gold clusters also find that sulphur forms strong chemical bonds with only one or two gold atoms, 9,16 18 corresponding to the on-top or on-bridge or on-bridgelike bonding on an extended gold surface. Indeed, the strong Au S covalent bonding is indicated by the larger concentration of electron density between S and bonded Au atoms 11,12,18 and by the distinctly directional Au S C bond whose bond angle is close to Given the evidence of the very local /2005/ /244721/12/$ , American Institute of Physics

2 Leng et al. J. Chem. Phys. 122, chemical bonding between S and Au atoms, we can safely assume that the interactions between thiolate molecules and gold clusters or bulk surfaces can be separated into two parts: the bonded interaction involving S and one or two Au atoms and the nonbonded interaction between thiolate molecule and other gold atoms. Whereas the far-field van der Waals interactions can be approximately described by a general universal force field UFF, 19 characterization of the locally bonded interactions by classical potentials is a real challenge. This is because the electronic structure and energetics of individual gold clusters may differ from those of the same clusters embedded in the bulk metal surfaces. 16,17 These differences may lead to different bonding geometries particularly the bond lengths. However, there is at least a quantitative way to calibrate this difference by increasing the cluster sizes, and in the present study we first focus on individual small clusters. In fact, mechanically pulling a thiolate molecule from a stepped gold surface already suggested that the final rupture is governed by the interaction between the molecule and 1 3 Au atoms. 20 We develop a set of classical potentials representing the local bonding behaviors of benzenedithiolate BDT molecule a prototypical molecular bridge well investigated in experimental measurements 2 and theoretical work 7,21 with only one or two Au atom clusters. These potentials can be used in large-scale molecular-dynamics MD simulations of molecular electronic devices. We note that a more complete treatment 14 of thiolate molecules on Au 111 surface employs the hybrid quantum mechanical with molecular mechanics QM/MM approach, 22 in which the QM subsystem involves the metal surface and thiol head groups and the remaining chain subsystem is dealt with the MM empirical potentials. However, the computational time is still quite demanding. In general, hybrid QM/MM methods can give better descriptions of vibrational spectra of molecules compared with crude MM force field. But in view of statistical structure properties, which are the main concerns in large-scale molecular simulations, the MM method particularly the classical force field derived from ab initio quantummechanical calculations for chemical bonding implemented in MD simulations is much more valuable. 22 In our early work 23 of the MD simulations of BDT monolayers on Au 111 surfaces, a primary force field for Au BDT chemical bonding was developed. However, the functional forms of bond stretching and angle bending were harmonic. We feel that these potentials cannot correctly describe the dynamics of BDT molecules, particularly at large deformations, and higher-order anharmonic terms should be included. Moreover, only the local-density approximation LDA in DFT was used to calibrate BDT Au bonded interactions. The present study explores other DFT methods see below to gain insight into the uncertainty of parameters in classical potentials and molecular packing structure to the choice of the DFT exchange-correlation XC functionals. We will also investigate the effect of molecular conformation on the Mulliken charge distributions in BDT 1, 2 Au complexes, one of the key components in determining the packing structure of SAMs. 24 Using the newly developed classical potentials for BDT/Au chemical bonding, we perform FIG. 1. Molecular models for BDT 1, 2 Au complexes. MD simulations to investigate the BDT SAM structure on Au 111 surfaces. Our main findings show that whereas the local bonding geometry at BDT/Au interface is directly related to the chemical bonding potentials particularly the bond-stretching terms derived from different DFT XC functionals, the global packing structure of BDT SAM is largely determined by the nonbonded intermolecular interactions, thus quite independent of XC functional used. The paper is constructed as follows: Sec. II briefly describes the molecular models for BDT/gold complexes and computational method. In Sec. III, we present in detail the derivations of the chemical bonding potentials for the interaction between BDT molecules and gold atoms based on the DFT energy calculations, followed by the investigations of the atomic charge variations with the changes of BDT 1, 2 Au molecular geometries. Section IV gives detailed MD simulations for the adsorption structure of BDT monolayer on Au 111 surface based on the developed force field for the BDT 1, 2 Au chemical bonding. Our conclusions are shown in Sec. V. II. MODELS AND METHOD A. BDT 1, 2 Au cluster models Based on recent DFT calculations for the binding between thiolate molecules and gold clusters, which showed that sulphur forms strong chemical bonds with only one or two gold atoms, 9,16 18 we construct two BDT/gold molecular models: BDT 1 Au and BDT 2 Au complexes, as shown in Figs. 1 a and 1 b. The geometry of the BDT molecule was obtained through the optimization of the molecular geometry by the UFF. 25 The top S H bond is perpendicular to the benzene ring. A recent, rather accurate MP2 calculation favored this perpendicular structure over the planar one by 2.1 kj/mol, which is comparable to kt at T=298 K. 26 In Fig. 1 a, the bond stretching, bond angle bending, and bond torsion correspond to Au14 S8, Au14 S8 C4, and Au14 S8 C4 C3 torsion Au14 S8 C4 C5 is also considered by

3 Interaction between benzenedithiolate and gold J. Chem. Phys. 122, dividing the force constant by a factor of 2. For the BDT 2 Au complex Fig. 1 b, we introduce a geometric point as the starting bonded atom marked by a dot X that represents the midpoint of 2-Au cluster. The bond stretching, bond angle bending, and bond torsion correspond to X S8, X S8 C4, and X S8 C4 C3. We notice that there should be a constraint barrier for the BDT molecule to move along the Au Au direction see Sec. III B. This barrier is the complement to the bonded interaction between the BDT and 2-Au clusters. We assume that the Au Au distance in Fig. 1 b is fixed and takes the bulk value of 2.88 Å, and omit the relaxation of Au Au distance induced by the chemical bonding with S. 9 B. Computational method FIG. 2. The BDT 1 Au bond-stretching curves from the LDA, PBE0, and X3LYP density functionals. The isotropic Morse potential from Ref. 37 and LJ repulsion part from UFF Ref. 19 are also shown for comparisons. All the calculations were performed within the framework of the DFT using the NWCHEM package. 27 The Gaussian valence triple zeta basis set 6-311G Ref. 28 is used for S, C, and H in BDT molecule and the effective core potential CRENBL-ECP and associated basis set 29 is used for the Au atoms. The 60 core electrons of Au are represented by ECP and the 19 remaining active electrons are represented by 44 basis functions. 30 For the open shell systems BDT 2 Au complex, we use spin-polarized wave functions. Since the optimal form of the DFT functional for such organometallic clusters is not known, three separate calculations of the force parameters were done, employing various DFT functionals: 1 standard local-density approximation LDA with Slater exchange and Vosko Wilk Nusair VWN-V correlation, 31 2 the PBE0, 32 often used for transition metals, a hybrid, parameter-free approximation for exchange-correlation combining a generalized gradient functional LDA-GGA 25% Hartree Fock exact exchange, 75% PBE exchange functional, Perdew91 LDA local correlation functional, and PBE nonlocal correlation functional, and 3 the X3LYP, 33 often used for hydrocarbons improvement of the conventional B3LYP, an extended hybrid, generalized gradient functional combined with Lee Yang Parr correlation functional 21.8% Hartree Fock exact exchange, 78.2% local Slater exchange functional, 54.2% nonlocal Becke 1988 exchange functional, 87.1% Lee Yang Parr correlation functional, 16.7% Perdew91 nonlocal correlation functional, and 12.9% VWN-I RPA local correlation functional. We investigate the sensitivity of the force-field parameters to the DFT functionals from these three calculations, which enables us to set the relevant uncertainty for each parameter. Since we are not interested in the global energy minimum for BDT 1, 2 Au complexes but rather in local energy changes due to the geometry variation of BDT and gold, all the energy curves are obtained from the total DFT energy while keeping the BDT molecule rigid. Moreover, we do not consider the cross or coupling between different bonding terms. Thus, when dealing with the higher-order bonded interactions e.g., Au14 S8 C4 C3 torsion term, the lowerorder bond geometry parameters e.g., Au14 S8 bond length and Au14 S8 C4 bond angle are fixed to the localoptimized equilibrium values. The partial charge distributions within the molecule are obtained simultaneously from Mulliken population analysis. 34 We note that the continuous and lowest-energy curve while varying stretching distance is obtained by the total singlet spin state in the case of BDT 1 Au complex, and by the total quartet spin pairing for the BDT 2 Au complex. This is an artifact of the simplified model of the gold surface, containing only one and two Au atoms. It is expected that the spin dependence is suppressed with an increase of the number of Au atoms in the model, and eventually disappears for the bulk of Au substrate. Our test comparison of the BDT 1 Au singlet and triplet stretching curves with the ones using BDT 10 Au complex not shown in this paper support this conclusion. III. RESULTS AND DISCUSSION For the chemical bonding between the S atom in BDT and 1, 2 Au atoms, the total force-field energy is written as a sum of several individual bonding terms E tot = E str + E bend + E tors + E constr, 1 where E str, E bend, and E tors are the bond-stretching, anglebending, and bond-torsion energies, and E constr is the constraint potential for BDT molecule sliding along the Au Au direction in the case of BDT 2 Au complex. Below we describe the development of these individual terms from the DFT energy calculations. A. BDT 1 Au complex 1. Bond stretching We first investigate a very simple case where the S atom of BDT molecule bonds to one gold atom. Figure 2 shows the bond-stretching curves for the BDT 1 Au interaction from the three DFT methods, the LDA, PBE0, and X3LYP functionals. For the convenience of comparison, all the energy minimums are shifted to zeros. In the bond dissociation region r 2.3 Å, LDA shows a slower increase in bonding energy compared with PBE0 and X3LYP. The equilibrium Au S bond lengths see Table I are consistent with other calculated results reported in the literature Ref. 16

4 Leng et al. J. Chem. Phys. 122, TABLE I. BDT 1 Au bond-stretching potentials. The units of parameters are kcal/mol, Å 1, Å, and kcal/mol Å 2, respectively. Parameter LDA PBE0 X3LYP Average Variation % Iso-Morse E a r E a The fitted values are slightly different from the DFT results. and Å, 17 both using the CPMD package with planewave basis sets and BP86 or PBE functional, see the related references for thiol molecule bonded to single gold atoms, but are less than recent experimental values of methylthiolate at atop site on bulk Au 111 surface 2.42 Ref. 35 and 2.5 Å Ref. 36. The bond-stretching curves can be well fitted by a shifted Morse potential E str = E 0 e r r 0 e r r E 0, 2 where r is the distance between the S atom and Au atom, and E 0 the well-depth, and r 0 the equilibrium bond length are the parameters to be fitted, which are listed in Table I. It is interesting to note that previously the isotropic Morse Iso- Morse potential between Au and S has been developed based on temperature-programmed desorption TPD value of a methylthiolate on gold surface. 37 Parameters of this Iso- Morse potential are also listed in Table I for comparison. The force constants at equilibrium d 2 E/dr 2 r=r 0 =2 2 E 0, which are listed at the bottom row of Table I, show that values from the DFT are approximately five to ten times of that of Iso-Morse, suggesting that single BDT Au chemical bond is much stronger than the Iso-Morse bond. We believe that this is probably because in the development of the Iso- Morse potential, 37 the treatment of nondistinction between the bonded and nonbonded Au S interactions may smear out the very strong chemical bonding. Specifically, the data in the last two rows in Table I show that PBE0 and X3LYP functionals give mutually consistent Au S bond lengths and force constants compared with LDA results. These bond lengths are smaller than that given by the Iso-Morse potential. The average values and total variations defined as the difference between the largest and the smallest values divided by the average value of the fitted force-field parameters from the three DFT functionals are also show in Table I. Obviously, the larger uncertainties come from the bond-stretching parameters E 0 and. In the UFF, 19 the nonbonded van der Waals interactions are represented by the 12-6 Lennard-Jones potentials, where the repulsive interaction is proportional to the overlap between the squared wave functions of two species. For the S and Au nonbonded atomic pairs, this weak repulsion is used for the distances much larger than the Au S bond lengths. In Fig. 2, only the shifted LJ repulsion part beyond 2.5 Å is shown. It goes to zero at r LJ =3.65 Å not shown in the figure. 2. Bond angle bending From geometric consideration, the angle-bending Au14 S8 C4 should be out of the plane of benzene ring. The three DFT functionals, LDA, PBE0, and X3LYP, give very similar bending energy curves shown in the supplemental Fig. S1. 38 Similar to the UFF, 19 these bending curves can be approximately fitted by a harmonic cosine functional in a larger range of bending angle from 90 to 180 : k E bend = 2 sin 2 cos cos 0 2, 3 0 where k is the force constant k = 2 E bend / 2 0, and 0 is the bending angle at equilibrium. Values of the fitted force constants and equilibrium angles from the LDA, PBE0, and X3LYP functionals are listed in Table II. Equation 3 is equivalent to the following three-term Fourier expansion: E bend = k C 0 + C 1 cos + C 2 cos 2 with the three expansion coefficients defined as C 2 =1/ 4 sin 2 0, C 1 = 4C 2 cos 0, C 0 = C 2 2 cos Bond torsion Keeping Au S bond length and Au S C bond angle at equilibrium values and rotating the benzene ring along the S S axis, we obtain the variation of torsional energies versus the rotational angle see supplementary Fig. S2. 38 Following the general rules in UFF Ref. 19 and keeping in mind that the rotation of benzene ring has two-fold symmetry, we can write the torsional potential as TABLE II. BDT 1 Au bond angle-bending and torsion potential parameters. Parameter Units LDA PBE0 X3LYP Average Variation % k kcal/ mol rad degree E kcal/mol degree

5 Interaction between benzenedithiolate and gold J. Chem. Phys. 122, TABLE III. The constant Mulliken charges in BDT molecule unit=e. The partial charges on the symmetric atoms in BDT are omitted. DFT functional C1 C2 S7 H9 H10 H13 LDA PBE X3LYP E tors = 1/2E 1 cos 2 0 cos 2, where E is the rotational barrier and 0 the equilibrium rotation angle see Table II. Specifically, the preference of out-of-plane bending of benzene ring leads to 0 =90. The PBE0 and X3LYP give mutually consistent rotational barriers compared with the LDA result. However, these barriers are much less than the bond-stretching and bond anglebending energies. In Table II, the uncertainties of parameters from the three functionals are quite small, except for the rotational barrier. But we anticipate that the large uncertainty of this rotational barrier to the SAMs structure is small since the torsion potential is not the dominant part in chemical bonding. 4. Partial charges 4 The distribution of atomic partial charges within the BDT Au complex has a profound effect on molecular conformation and packing structure through the long-range Coulombic interactions. A detailed analysis of the variation of this charge distribution with the BDT Au bonding geometry is therefore necessary. Along with the calculations of single point DFT energies for each of BDT Au bonding geometries, we also computed atomic charges from Mulliken population analysis. 34 Our emphasis is on the charge variation when varying the BDT Au bonding geometry, though we know that the absolute value of an atomic charge in a molecule is not uniquely defined physically. 9,39 Since the X3LYP functional yields quite similar charge distributions as those given by PBE0 functional, either for BDT 1 Au or BDT 2 Au complexes, hereafter, we will concentrate on the results given by LDA and PBE0. Further, all the figures related to the discussion of atomic charge variations are put into a supplemental document 38 to avoid too many illustrations in this paper. Figure S3 Ref. 38 shows the variations of atomic partial charges versus the Au S bond lengths from the LDA and PBE0 functionals. These charges are for the atoms involved in chemical bonding between the BDT molecule and the Au atom. We found that the Mulliken charges on other atoms in BDT molecule remain almost constant, and only those atoms involved in chemical bonding, in particular, atoms Au14, S8, and C4, experience substantial charge transfer. Table III presents all other charges that remain constant. This phenomenon suggests that the electronic structure change due to metal/molecule chemical bonding is very localized, leaving the structure of the BDT molecule largely unchanged. In Fig. S3, atomic charges from PBE0 and LDA show somewhat different charge variations, but the same amount of charge transfer 0.3e from S8 to Au14 during the dissociation process from r Au S =2Åtor Au S 3.2 Å. Moreover, atom C4 has obtained more negative charge 0.2e trending toward the C1 partial charge due to molecular symmetry. In contrast, the partial charges on C3 C5 which are only involved in bond torsion have changed slightly 0.04e. Keeping the Au S bond length at equilibrium value r 0 and changing the bond angle Au14 S8 C4 from 180 to 90, we also found significant charge transfers between atoms involved in BDT Au chemical bonding, as shown in Fig. S4. 38 The Mulliken charges on bonded atoms change dramatically in the range of The LDA functional predicts that some 0.14e is transferred from the molecule to the gold atom, while the PBE0 shows that more charges are transferred 0.32e. The Mulliken charge on C4 atom, on the other hand, becomes more negative, and C3 C5 charge only changes slightly. The variations of Mulliken charges with the Au S C C dihedral angle are comparably small. All the three functionals predict very similar result Fig. S5. 38 This is consistent with the notion that the rotation of benzene ring does not change dramatically the electronic structure of the metal/ molecule complex. In molecular-dynamics MD simulations, fixed atomic charges should be assigned to particles a priori before the long-range Coulombic interactions can be calculated. Our detailed MD simulations see below show that for BDT molecules adsorbed on Au 111 surfaces at room temperature, the molecules only explore very limited regions of conformation space. These regions are marked in shaded areas in Figs. S3 and S4. This limited sampling of configuration space significantly reduces the uncertainty in the atomic partial charge determinations. B. BDT 2 Au complex For the chemical bonding between the S atom in BDT and the two Au atoms, in addition to bond-stretching, anglebending, and bond-torsion terms, the total force-field energy needs to add one more component, the constraint barrier for BDT molecule sliding along the Au Au direction, E constr,as described in Eq. 1. Below we describe these individual terms from the DFT energy calculations. 1. Bond stretching Similar to the BDT 1 Au complex, the shifted bond X S bond, see Fig. 1 stretching curve for BDT 2 Au interaction from the three DFT functionals can be well fitted by the Morse potential given by Eq. 2. All the parameters in the fitted Morse potentials are listed in Table IV. The force constants of the fitted Morse potentials are four to five times

6 Leng et al. J. Chem. Phys. 122, TABLE IV. BDT 2 Au bond-stretching potentials. The units of parameters are kcal/mol, Å 1, Å, kcal/mol Å 2. The parameters in parentheses are for the single bond Au S Morse potentials. Parameter LDA PBE0 X3LYP Average Variation % Iso-Morse E a r E a The fitted values are slightly different from the DFT results. of that of the Iso-Morse potential. Since there are two Au S bonds involved in chemical bonding, the Au S bond lengths shown in parentheses in Table IV are already close to d Au S of thiolate bonded to bridge or bridgelike sites on bulk gold surfaces 2.55, depending on the coverage, 11,13 and 2.5 Å Refs. 14 and 40. These numbers are also consistent with other results for small thiolate gold clusters Å. 9 Assuming that the bonding energy of individual BDT Au bond is equal to the half of the total DFT energy and refitting the bonding curves, we still get a very strong Morse potential the corresponding parameters are shown in parentheses in Table IV. Interestingly, the well depths of the newly fitted individual BDT Au Morse potential decrease drastically, but are still larger than that of the Iso-Morse. The force constants decrease slightly due to the increase of parameter. As for the BDT 1 Au complex, we also calculate the average values and total variations of the fitted force-field parameters, as shown in Table IV. Obviously, the larger uncertainties come from the bond-stretching parameters E 0 and. 2. Bond angle bending and torsion As in the BDT 1 Au case, the bond angle-bending and torsional potentials can be well fitted by Eqs. 3 and 4, which have sound mathematical forms due to the Fourier cosine expansion in or. However, the magnitudes of bending force constants and rotational barriers decrease substantially due to the two Au S bonds involved in chemical bonding. These numbers are listed in Table V. Specifically, the rotational barriers from the three DFT functionals are comparable to kt 0.6 kcal/mol. This suggests that torsional constraint forces are less dominant than the bondstretching and angle-bending forces, as observed by other DFT research on thiolate Au 111 systems Constraint potential along Au Au direction Keeping the distance between the S atom in BDT and the line Au Au at the equilibrium bond length r 0, there should be a constraint barrier to centralize BDT over the midpoint X between the two Au atoms. This potential can be described by a small cosine Fourier expansion in the distance R away from one Au atom E constr = 0.5E C 1 + cos R/R 0, 5 where E C is the constraint barrier and R 0 the half distance between the two Au atoms, i.e., R 0 =1.44 Å. All the three DFT methods predict almost the same constraint barriers E C, which are significantly larger than the rotational barriers see supplementary Fig. S6. 38 Values of these barriers from the LDA, PBE0, and X3LYP functionals are also included in Table V. Table V also shows that the uncertainties of parameters in bond angle-bending, torsion, and constraint potentials from the three functionals are quite small for BDT 2 Au complex. 4. Partial charges Following the same procedure as in the BDT 1 Au case, we investigate the atomic charge variations in BDT 2 Au complex. Similar to the case in BDT 1 Au complex, the Mulliken charges of nonbonded atoms in BDT molecule remain almost constant and take the values of those in BDT 1 Au complex see Table III. In particular, the LDA predicts that about 0.14e has been transferred from the molecule to the gold atoms, and S8 becomes more positive charged during dissociation. The PBE0 predicts that about 0.1e has been transferred from each of the Au atoms to the molecule, resulting in S8 and C4 having more negative charges see supplemental Fig. S7. However, as we mentioned before and will see later, X S bond length only explores very lim- TABLE V. BDT 2 Au bond angle-bending, torsion, and constraint potential parameters. Parameters units LDA PBE0 X3LYP Average Variation % k kcal/ mol rad degree E kcal/mol degree E C kcal/mol

7 Interaction between benzenedithiolate and gold J. Chem. Phys. 122, ited region where variations of Mulliken charges are quite small. In fact, for BDT 2 Au complex, the magnitudes of partial charges on bonded atoms, S8 and Au14 Au15, are comparably small compared with those in the BDT 1 Au complex. This is probably due to the weaker chemical bonding in the BDT 2 Au complex. Bending the BDT molecule relative to the Au atoms from the straight-up configuration also yields charge transfers from the BDT molecule to the gold atoms. All the three DFT functionals predict the same phenomenon: when the bending angle changes from 180 to tilt, about 0.1e charge has been transferred locally from the sulphur atom to the two-gold cluster. This can be seen from the LDA and PBE0 results shown in Fig. S8, 38 which are consistent with other investigations for benzenethiolate bonded on the bridge sites of small gold clusters. 39 Our results show that the variations of Mulliken charges due to the rotation of benzene ring are quite small, as they are in the BDT 1 Au case. All the three DFT functionals give very similar charge variations see the LDA result in Fig. S9. 38 The partial charges on gold atoms Au14 and Au15 switch back and forth symmetrically around a very low mean value of 0.04e in the range of =0 180, and no significant charge variations are observed for C4, C3 C5, and S8 in this range. We note that these Mulliken charges are calculated based on the molecular configuration where the X S bond length and X S C bond angle take the equilibrium values. We believe that adding all the components of molecular interactions does not change dramatically the molecular configurations, as we have previously observed. 23 Variation of the Mulliken charge within the BDT 2 Au complex is also a concern when the BDT molecule shifts away from the center X of Au Au cluster due to the thermal motion along the Au Au direction. We demonstrate in Fig. S10 Ref. 38 that the BDT molecular shift does not change significantly the charge distribution within the molecule, except for a very small dipole induced between the two gold atoms. Since this induced dipole is parallel to the Au Au direction and the thermal shifts of the BDT molecule are symmetric about the midpoint X on average, the effect of the induced dipole on the molecular conformation should be small. IV. MOLECULAR-DYNAMICS SIMULATIONS We consider the BDT monolayer adsorbed on Au 111 surface. Molecular system is the same as that in the previous TABLE VI. Mulliken partial charges for bonded atoms. BDT 1 Au/BDT 2 Au, unit=electron. Atoms LDA PBE0 X3LYP C3 C5 0.08/ / / 0.10 C4 0.43/ / / 0.32 S8 0.10/ / /0.11 Au 0.04/ / / work. 23 The simulation box is rhombic in two-dimension 2D whereas the unit cell takes the R13.9 structure with one BDT molecule on the top site and the other three BDT molecules on the bridge sites. This fullcoverage adsorption structure had been observed in early scanning tunneling microscope STM experiment for benzenethiolate BT monolayer on Au 111 surface. 42 The intra- and intermolecular interactions within and between BDT molecules and between BDT molecules and nonbonded gold atoms are described by UFF, 19 and these force-field parameters are given in Tables I and II in Ref. 23. For the bonded interactions between the BDT and Au atoms, the force-field parameters, together with constant atomic charges directly come from Tables I V. Atomic charges for the bonded atoms are determined based on the most possible BDT 1, 2 Au configurations. Initially, we assume that these partial charges correspond to equilibrium configuration r 0, 0, 0 and perform MD runs at 298 K. We find that BDT molecules in SAMs actually explore a limited configuration space as shown in the shaded areas in Figs. S3, S4, S7, S8, and S10 Ref. 38. We then reselect these atomic charges as the averages in these shaded areas and conduct MD runs again to obtain the final SAMs packing structure this is equivalent to an iteration procedure. Table VI lists all the bonded atomic charges from the LDA, PBE0, and X3LYP functionals. The double RESPA algorithm 23 based on the original work of Tuckerman et al. 43 is employed in MD simulations. To correctly calculate the long-range electrostatic interactions, we use the three-dimensional 3D Ewald summation with a correction term 44 EW3DC for the 2D rhombic slab geometry. The initial molecular configuration of BDT monolayer was assumed to be normal to the Au 111 surface. This configuration corresponds to =180 of Au S C bond angle large molecular deformation, and the bending force can only be calculated correctly through Eq. 3, rather than the FIG. 3. Normalized probability distributions of Au S bond stretching for a BDT 1 Au and b BDT 2 Au complexes from MD simulations and from the Boltzmann results obtained from individual bond-stretching potentials.

8 Leng et al. J. Chem. Phys. 122, FIG. 4. Normalized probability distributions of Au S C bond angle bending for a BDT 1 Au and b BDT 2 Au complexes from MD simulations and from the Boltzmann results obtained from individual bond anglebending potentials. harmonic potential used in our previous work. 23 To avoid any metastable states, we first increase the temperature to K and run MD for a substantially long time usually a few hundreds of picoseconds, then gradually decrease the temperature to 298 K. At high temperatures, to avoid desorption of BDT molecules from Au 111 surface, we increase the well depth of Morse potential by 50% 100%. This does not influence the packing structure of BDT SAM at 298 K. The time step in MD runs is 2 fs, and the three-layer gold substrate is kept rigid, though we realize that significant relaxation of Au substrate may be possible. 12 A. BDT 1, 2 Au local bonding geometry In order to understand how the BDT 1, 2 Au bonded interaction potentials dominate the local bonding geometry in SAMs, we plot the probability distributions for all of the bonding geometric parameters from MD simulations, and the corresponding normalized Boltzmann factor distributions which are solely determined by the specific potentials. Figures 3 and 4 show the BDT 1, 2 Au bond-stretching and angle-bending distributions from the LDA, PBE0, and X3LYP functionals. We see that at 298 K BDT molecules in SAM structure only explore very limited molecular configuration space. The possible regions of bond stretching and angle bending are also marked by the shaded areas in supplemental Figs. S3, S4, S7, and S8 Ref. 38 for atomic charge variations. Obviously, there are somewhat shifts of the MD curves relative to the Boltzmann distributions due to the effect of intermolecular interactions. These shifts are more evident for the angle-bending curves compared with the bondstretching curves, implying that bond-stretching potential is the most dominant part in chemical bonding. This conclusion was also obtained in the previous studies 23 concentrating on different DFT basis sets. At the highest end, Fig. 5 shows that the bond-torsion distributions from MD simulations are dramatically different from the Boltzmann distributions, suggesting that torsional forces are not the main constraint forces in determining the SAMs structure. The universal two peaks around 50 and 150, instead of a single peak around 90, are directly related to the global packing structure of BDT monolayer on Au 111 surface see below. In the previous work, 23 the torsional barrier at bridge site was incorrectly too high, resulting in a single peak around 90. In Fig. 5 b, the bond-torsion distributions for BDT 2 Au show more divergence compared with those for BDT 1 Au in Fig. 5 a. This is due to the very small rotational barrier in BDT 2 Au complex which has two Au S bonds involved in chemical bonding. Likewise, in comparison with BDT 1 Au in Fig. 4 a, the angle-bending distributions from MD simulations for BDT 2 Au Fig. 4 b also show more divergence and more shifts relative to the Boltzmann distributions. As we have seen in Tables I, II, and IV, larger uncertainties of the force-field parameters for different DFT functionals come from E 0,, and E. These uncertainties are reflected in Figs. 3 and 5 a that present fairly different distribution curves. Figure 6 shows the PBE0 results of probability distributions of BDT molecular shift along the Au Au direction in BDT 2 Au complex. The LDA and X3LYP functionals give the quite similar results and are not shown in the figure. The central point r=0 corresponds to 1.44 Å distance away from one Au atom. We see that MD curve is a little wider than the FIG. 5. Normalized probability distributions of Au S C C bond torsion for a BDT 1 Au and b BDT 2 Au complexes from MD simulations and from the Boltzmann results obtained from individual bond-torsion potentials.

9 Interaction between benzenedithiolate and gold J. Chem. Phys. 122, FIG. 6. The PBE0 results of normalized probability distributions of BDT molecule shift along Au Au direction in BDT 2 Au complex. The solid line corresponds to the MD simulation result. The dashed line is for the Boltzmann distribution obtained from individual constraint potential along Au Au direction. Boltzmann distribution but with no relative deviation. This indicates that intermolecular interactions do not bias the bridge S atom away from the bridge or bridgelike bonding site. The region explored by BDT molecules in Fig. 6 is also marked by a shaded area in Fig. S10 Ref. 38. B. Global packing structure and S adsorption site The above results and discussions on the BDT 1, 2 Au local bonding geometry show that the intermolecular interaction also plays an important role in determining the BDT SAM structure. This is particularly true when looking at the probability distributions in Figs. 4 and 5. Following the same definitions as in the previous work, 23 we consider three angles describing the global packing structure of BDT monolayer on Au 111 surface: the tilt angle, the azimuthal angle, and twist angle see Fig. 7. Figures 8 10 show the probability distributions of the three angles. The distributions of tilt angle Fig. 8 from the three DFT functionals have the same peak at =32. This global tilt angle is a little larger than the previous result The twist angle distributions shown in Fig. 10 have two peaks around =40 50 and = , depending on the DFT functional used. Very interestingly, Fig. 9 FIG. 8. The normalized probability distributions of global tilt angle from the LDA, PBE0, and X3LYP functionals. shows that the three DFT functionals yield very similar azimuthal angle distributions but with a relative shift of 60 in turn. These distributions have two distinct peaks separated by 40. Evidently, Figs. 9 and 10 indicate that the global packing structure of BDT SAM adopts a herringbone structure, as shown in Fig. 11. These three herringbone structures are actually the same structure, but being viewed along different directions: 120, 60, and 0 for the LDA, PBE0, and X3LYP, respectively. To give a clear picture of the adsorption sites of S atoms on Au 111 surface, Fig. 12 shows the PBE0 result of the adsorbed S adatoms and the first two gold layers. The adsorption structures predicted by the LDA and X3LYP functionals are quite similar and will not be shown here. In general, about one half of the bridge S atoms B are located at the bridge sites slightly shifted to the fcc-hollow sites fcc bridge, and another half of the bridge S atoms are located at the bridge sites slightly shifted to the hcp-hollow sites hcp bridge. This equal partition between the fcc-bridge and hcpbridge adsorption sites seems reasonable since the difference of adsorption energies between the two is comparable to kt. 12 The atop S atoms T are not right above the top sites, instead, there is always a slight shift due to the Au S C angle bending. Figure 13 shows the Au S distance distributions between the S adatoms and the first-layer gold atoms. The results from the PBE0 and X3LYP functionals show the first small peak at 2.28 Å and the second larger peak at FIG. 7. Global orientation of BDT molecule described by three geometric angles. FIG. 9. The normalized probability distributions of global azimuthal angle from the LDA, PBE0, and X3LYP functionals.

10 Leng et al. J. Chem. Phys. 122, FIG. 10. The normalized probability distributions of global twist angle from the LDA, PBE0, and X3LYP functionals. 2.5 Å, which correspond to the atop Au S and bridge Au S bond lengths, separately. The third peak at 2.78 Å corresponds to the nonbonded Au S distance between the bridge S atom and the third-nearest Au atom around the hollow site. Compared with the PBE0 and X3LYP results, the LDA does not show the first small peak. This may be because the bondstretching force constant from LDA is too low compared with those of PBE0 and X3LYP see Table I. The second and third peaks correspond to the Au S distances of 2.42 and 2.76 Å, respectively, which are slightly shorter than the PBE0 and X3LYP results. Looking back at the data in Table IV, we see that when two Au S bonds are involved in chemical bonding, the Au S bond length is already increased substantially. When all the components of intermolecular interactions are considered, the Au S bond length on the bridge or bridgelike site approaches the universal value of 2.5 Å but this seems unfortunate for the atop case, which needs further investigation. We believe that this is largely due to the LJ repulsions from the nonbonded Au atoms nearby. The clear cut at 2.7 Å to distinguish between the bonded and nonbonded Au S distances seems reasonable since mechanically pulling a thiolate molecule away from a stepped gold surface 20 found that the bond rupture usually happened at this distance. V. SUMMARY AND CONCLUSIONS FIG. 11. BDT SAM herringbone packing structures from the three DFT functionals: a LDA 120 view, b PBE0 60 view, and c X3LYP 0 view. The present study develops a classical force field for the chemical bonding between gold atoms and BDT molecules that can be used for large-scale molecular simulations for the self-assembly on either extended gold surfaces or gold clusters. The bond-stretching and angle-bending potentials are represented by the Morse potential and harmonic cosine terms, respectively, allowing the BDT molecule to explore larger range of deformations. In the current study, the effect of the functional forms of bond stretching Morse or harmonic on SAM structure both interfacial and global packing should be small since the BDT molecules are already assumed to be anchored on the top or bridge sites based on experimental observations. However, we anticipate that in self-assembly simulations the Morse potential is more suitable to search for chemical bonds than harmonic potential. Moreover, the Morse potential for bond stretching is suitable to describe the bond dissociation process. The harmonic cosine term for the bond angle-bending potential can yield correctly the bending forces even at =180, which is crucial in determining correct packing structures in MD runs. We employ DFT as an efficient, practical approach to the quantum many-body problem, but its main drawback is somewhat ad hoc choice of exchange-correlation functionals when used to describe new systems, especially organometallic complexes. To quantitatively describe and stress the importance of this issue we utilize three well-known approximations to the XC functional, LDA, PBE0, and X3LYP, to investigate the sensitivity of the force-field parameters to the choice of the XC approximation. In general, they yield similar bonding curves, whereas PBE0 and X3LYP give more mutually consistent results compared with LDA. The largest variations in the derived force-field parameters come from the well depth of Morse potential for bond stretching, E 0, for which LDA has predicted a significantly different as large as 95.5% for BDT 2 Au result for the bond dissociation curve.

11 Interaction between benzenedithiolate and gold J. Chem. Phys. 122, FIG. 12. The PBE0 result of the adsorption structure of S adatoms on Au 111 surface. The black dots are S adatoms, the large and small empty circles represent the first and second gold layers. FIG. 13. The normalized probability distributions of the Au S distance between the S adatoms and the first-layer gold atoms from the LDA, PBE0, and X3LYP functionals. The main contributions to the force field for chemical bonding are the bond-stretching and angle-bending terms. However, for the BDT 2 Au complex, the constraint barrier along the Au Au direction is also significant. A complete investigation of the atomic charge distribution, a key component in determining SAMs structure, versus the molecular geometry is given. The Mulliken partial charge distribution within the molecule/metal complex is found to be quite stable for the molecular conformation space that BDT molecule samples in SAMs structure. The partial charge variation due to the change of molecular geometry is consistent with other investigations. 39 For the current study, we do not consider the polarization effects due to intermolecular charge interactions, which is an interesting issue in the future work. Our MD simulations on the adsorption of BDT SAM on Au 111 surface using the developed force field for BDT/Au chemical bonding, combined with the UFF 19 for nonbonded intermolecular interactions, show that the local bonding geometry at BDT/Au interface does depend to some extent on the DFT XC functional used, and the bond-stretching potential is the most dominant part in chemical bonding, whereas the torsional potential is the weakest part. The global packing structures of BDT SAMs from the three XC functionals are basically the same herringbone structures. In other words, the SAM packing structure largely depends on the intermolecular interactions, instead of the XC functional. However, as we mentioned before, XC functional does influence the interfacial bonding properties, which plays equally an important role in determining the organometallic structure. As shown in the bond-stretching curves in Fig. 2 and Morse parameters in Tables I and IV, the bonded interaction between S and Au is much stronger than the isotropic Morse potential. The convergence of the DFT energy usually becomes more difficult at larger bond lengths around 3Å, where we keep in mind that the BDT-Au interaction in this case should be switched to nonbonded interaction, and our choice of localized Gaussian basis set becomes inadequate for the disassociation process. Moreover, the current study does not consider the relaxation of gold substrate upon the adsorption of BDT molecules. Some DFT investigations show that this relaxation is significant even at ground state. 12,15 This fundamental issue is very interesting and will be investigated in our future work. The methodology of force-field development in the present study is general and applicable to other organometallic complexes, which is beneficial to the large-scale molecular simulations for a variety of organometallic nanostructures and molecular electronic devices. ACKNOWLEDGMENTS Our research was sponsored by the Office of Science of the US Department of Energy Computational Nanoscience Project YSL, PTC, the Office of Fusion Energy Sciences PK, Division of Materials Sciences and Engineering JCW, and used resources of the Center for Computational Sciences at Oak Ridge National Laboratory, all under Contract No. DE-AC05-00OR22725 with UT-Battelle, LLC. 1 A. Nitzan and M. A. Ratner, Science 300, M. A. Reed, C. Zhou, C. J. Muller, T. P. Burgin, and J. M. Tour, Science 278, ; X. Y. Xiao, B. Q. Xu, and N. J. Tao, Nano Lett. 4, X. D. Cui, A. Primak, X. Zarate et al., Science 294, ; B.Q. Xu and N. J. J. Tao, ibid. 301, C. Joachim, J. K. Gimzewski, and A. Aviram, Nature London 408, ; J. Chen, M. A. Reed, A. M. Rawlett, and J. M. Tour, Science 286, ; P. E. Kornilovitch and A. M. Bratkovsky, Phys. Rev. B 64, ; E. G. Emberly and G. Kirczenow, Phys. Rev. Lett. 87, E. G. Emberly and G. Kirczenow, Phys. Rev. Lett. 91, M. Di Ventra, S. G. Kim, S. T. Pantelides, and N. D. Lang, Phys. Rev. Lett. 86, J. Tomfohr and O. F. Sankey, J. Chem. Phys. 120, S. N. Yaliraki, M. Kemp, and M. A. Ratner, J. Am. Chem. Soc. 121, ; K. W. Hipps, Science 294, ; J. Nara, W. T. Geng, H. Kino, N. Kobayashi, and T. Ohno, J. Chem. Phys. 121, H. Basch and M. A. Ratner, J. Chem. Phys. 119, J. Gottschalck and B. Hammer, J. Chem. Phys. 116, Y. Yourdshahyan and A. M. Rappe, J. Chem. Phys. 117, J. Nara, S. Higai, Y. Morikawa, and T. Ohno, J. Chem. Phys. 120, M. C. Vargas, P. Giannozzi, A. Selloni, and G. Scoles, J. Phys. Chem. B 105,