Excited-State N2 Dissociation Pathway on Fe-Functionalized Au

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Excited-State N2 Dissociation Pathway on Fe-Functionalized Au John Mark P. Martirez, and Emily A. Carter J. Am. Chem. Soc., Just Accepted Manuscript • DOI: 10.1021/jacs.6b12301 • Publication Date (Web): 07 Mar 2017 Downloaded from http://pubs.acs.org on March 7, 2017

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Journal of the American Chemical Society

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Excited-State N2 Dissociation Pathway on Fe-

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Functionalized Au John Mark P. Martirez† and Emily A. Carter†,‡,*

3 †

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‡

Department of Mechanical and Aerospace Engineering and

School of Engineering and Applied Science, Princeton University, Princeton, New Jersey,

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08544-5263, United States

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Corresponding Author

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*[email protected]

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ABSTRACT

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Localized surface plasmon resonances (LSPRs) offer the possibility of light-activated chemical

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catalysis on surfaces of strongly plasmonic metal nanoparticles. This technology relies on lower-

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barrier bond formation and/or dissociation routes made available through energy transfer

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following the eventual decay of LSPRs. The coupling between these decay processes and a

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chemical trajectory (nuclear motion, charge-transfer, intersystem crossing, etc.) dictates the

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availability of these alternative (possibly lower barrier) excited-state channels. The Haber-Bosch

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method of NH3 synthesis from N2 and H2 is notoriously energy intensive. This is due to the

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difficulty of N2 dissociation despite the overall reaction being thermodynamically favorable at

ACS Paragon Plus Environment

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ambient temperatures and pressures. LSPRs may provide means to improve the kinetics of N2

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dissociation via induced resonance electronic excitation. In this work, we calculate, via

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embedded n-electron valence second-order perturbation theory within the density functional

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embedding theory, the excited-state potential energy surfaces for dissociation of N2 on an Fe-

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doped Au(111) surface. This metal alloy may take advantage simultaneously of the strong LSPR

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of Au and the catalytic activity of Fe towards N2 dissociation. We find the ground-state

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dissociation activation energy to be 4.74 eV/N2, with Fe as the active site on the surface.

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Consecutive resonance energy transfers (RETs) may be accessed due to the availability of many

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electronically excited states with intermediate energies arising from the metal surface that may

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couple to states induced by the Fe-dopant and the adsorbate molecule, and crossing between

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excited states may effectively lower the dissociation barrier to 1.33 eV. Our work illustrates that

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large energetic barriers, prohibitive towards chemical reaction, may be overcome through

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multiple RETs facilitating an otherwise difficult chemical process.

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INTRODUCTION

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Large-scale artificial N2 fixation to form ammonia is currently achieved via the Haber-Bosch

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(HB) process, where N2 and an H2 source (e.g., obtained from decomposition of hydrocarbons or

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the water-gas shift reaction: H2O+CO) are mixed together with an Fe-based catalyst.1-2 The

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synthetic process alone is very energy-intensive, as it requires high temperatures (~400-500 °C)

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and pressures (~200 atm) due to the reaction’s very slow kinetics.1 Although the HB process’

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discovery was already a giant leap in the mass production of ammonia, further optimization of

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existing catalysts and the search for chemically distinct new ones for the HB process continue.3

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Further tuning the process so that a less energy-dependent scheme is developed could have


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potential positive economic and environmental impact, and may also improve accessibility of

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this technology for developing countries.2-3

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Diazotrophic organisms carry out N2 fixation to produce ammonia at room temperature (e.g.,

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via the two-component nitrogenase enzyme with Fe- and FeMo-cofactors) at the cost of energy

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input in excess of the thermodynamic requirement and two reducing equivalents per N2.4-5 The

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complex mechanism of the catalytic action of nitrogenases is still being actively investigated.5

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However, despite the various mechanisms proposed for biological N2 fixation, it seems that these

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organisms have evolved to selectively break the N-N bond only after hydrogenation.4-5 These

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energy requirements and mechanistic steps attest to the inefficiency of nitrogen fixation and the

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prohibitive task of breaking N2 under mild conditions.

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Surface plasmon catalysis on plasmon-active metal nanoparticles has been demonstrated to be

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effective for room temperature H2 dissociation/desorption on Au,6-7 Al,8 and Al-Pd (antenna-

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reactor complexes),9-10 O2 activation on Ag,11 and dehydrogenation of formic acid on Au-Pd

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nanorods,12 to name a few. The physical mechanisms leading to the magnified chemical

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reactivity and/or enhanced optical response of adsorbed molecules on plasmonic materials

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include plasmon-induced generation of reactive energetic charge carriers (within the metal13 or

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directly between the metal and the molecule14), local heating,13 electric field or light intensity

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magnification,13 and modulation of or participation in non-radiative resonance energy transfer

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(RET).12, 14-18 The potential use of excited-state heterogeneous catalysis on much more energy

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demanding chemistries, such as N2 activation, at room temperature has yet to be realized. At this

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time, there are only a few stable and strongly surface plasmonic active metals (namely, Al, Cu,

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Ag, and Au).19 This short list limits the possible chemical reactions that may be directly

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catalyzed via plasmonics. Coupling two metallic components, one that is plasmonically active


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and one that is catalytically active, has been shown to be a promising route to take full advantage

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of this new paradigm in heterogeneous catalysis.9-10 Recently, we have shown computationally

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via density functional theory (DFT) that doping Au(111) surface with either Fe, Ni, Co, or Mo

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(the primary components of known high-temperature HB catalysts1) enhances the ground-state

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molecular and dissociative adsorption of N2 on this surface at the dopant sites.20 In this paper, we

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further explore through combined DFT and many-body ab initio quantum mechanical methods

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the possibility of using Fe-substituted Au(111) surface to catalyze N2 dissociation.

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exploration includes determination of excited-state pathways that couple absorption of incident

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light by surface plasmon resonances in Au to local surface excitations.

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RESULTS AND DISCUSSION

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Ground-state N2 dissociation pathway on Fe-doped Au(111) surface

This

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Previously,20 we studied the stability and reactivity towards N2 of M-doped Au(111) surfaces,

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where M= Fe, Ni, Co, and Mo, using DFT within the Perdew-Burke-Ernzerhof (PBE)

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generalized gradient approximation (GGA)21 to electron exchange-correlation (XC) with

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Grimme et al.’s D3 approximation of the dispersion interaction.22-23 We also calculated the free

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energy of dissociative adsorption of N2 at the dopant site, as well as the formation and oxidation

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energies of the transition metal lattice substitutions. We found that AuMo exhibits the best

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reactivity towards N2, while AuFe presents a balance between stability and reactivity. Here, we

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calculate the pathway and the associated energy barrier for N2 molecular adsorption and

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dissociation on the Fe-doped Au surface. From the previously found stationary structures,20 we

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calculated from DFT-GGA+D3 the minimum energy paths (MEPs) for the above-mentioned

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reactions on a 105-atom five-layer (√21×√21)R10.9° Au(111) slab doped with an Fe atom

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(Figure 1a).


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Figure 1. A, the (√21×√21)R10.9° five-layer Fe-substituted Au(111) periodic slab; grey atoms

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comprise the Au environment. B, the Au10Fe cluster carved out from the slab shown in A (sub-

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surface atoms are faded out), used in performing embedded correlated wavefunction

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calculations. The positions of the “ghost” atoms (light blue spheres), added to expand the

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cluster’s basis set at the cluster-environment interface,24 are also shown in the top view (left)

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panel. C, Isosurface plot of the embedding potential generated for the environment and the

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cluster fragments described in A and B (blue: +1 V, purple: -1 V). D, two-dimensional contour

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plots of the embedding potential as viewed from planes cutting through the first Au layer (left)

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and second Au layer (right). Blue lines: positive, red lines: negative, contour interval (topology):

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0.4 V (max: 5.4 V, min: -14.2 V). The red hexagonal boxes in A, B, and D correspond to the

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same region of the surface.

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Figure 2. Predicted structures along the MEP for adsorption and dissociation of N2 at the Fe site

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of an AuFe surface alloy. Numerical indices correspond to the points on the energy curves shown

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in Figure 3. Only the Au9Fe fragment of each slab and the molecule are shown; second-layer Au3

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atoms are faded out. See text for a description of the mechanism.

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A total of 25 structures or images were involved in the determination of the reaction pathway

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(see Computational Methods for details). In Figure 2, the stationary state structures (red, green,

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and purple boxes, numbered as 0, 11, and 24, respectively) and the transition-state structure (blue

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box, 22) are shown. The normal mode vibrational frequencies of the molecule and active site for

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these structures are plotted in Figure S1 of the Supporting Information (see section I there for

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details). Some of the intervening structures along the reaction trajectory (images 6, 8, 13, and 17)


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are also shown. In this mechanism, the N2 molecule starts about 6 Å away from the surface

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(image 0) and is arbitrarily oriented horizontally. The molecule then rotates (images 0-11) as it

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approaches the surface until one of the N atoms is adsorbed on top of the Fe and the molecule is

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oriented vertically (image 11). The final configuration in the molecular adsorption process,

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image 11 (green box), depicts the most stable adsorption configuration of N2 and is referred to as

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an “end-on” (η1-N2) interaction.20 This adsorption configuration has been observed

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experimentally on other transition metals, e.g., W,25 Ni,26-27 Rh,28 and Fe,29-30 via infrared active

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N-N stretch vibration modes measured upon adsorption (dipole forbidden in all other

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configurations). This configuration is calculated to have an N-N bond length of 1.130 Å and a

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stretch mode frequency of 2180 cm-1, consistent with the end-on N2 frequencies measured, e.g.,

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on Ni(110): 2194 cm-1,26 and Fe(111): 2100 cm-1.29 Note that the calculated gas phase N2

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vibrational stretch frequency is significantly higher at 2416 cm-1, indicating an already

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significant π-backbonding interaction between N2 and Fe that begins to weaken the N-N bond.

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The Fe-N bond length was calculated to be 1.878 Å with an associated stretch frequency of 1004

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cm-1. From this configuration, N2 dissociation may proceed once bound to the surface. However,

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the molecule first has to rotate until it lies parallel to the surface and both N atoms are

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coordinated with Fe (images 11-17). Image 17 depicts a π-bonded or “side-on” bonded N2 (η2-

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N2) on Fe. This type of bonding has been shown experimentally to be the precursor for N2

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dissociation on Fe(111).29-31 Elongation of the N-N bond progresses with the N atoms creeping

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over to occupy Au-Fe bridge sites and eventually onto the two adjacent hollow sites (images 17-

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24). The transition state (blue box, image 22) has an elongated N-N bond length (1.810 Å), and

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short Fe-N bond lengths (1.766 Å) with associated symmetric and anti-symmetric N-Fe-N

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stretches of 682 and 575 cm-1, respectively (see Supporting Information Figure S1 for the


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vibrational spectrum and Figure S2 for the associated changes in the structural parameters along

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the reaction trajectory). The N-N stretch mode (associated with the transition-state vector) has an

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imaginary frequency of 596i cm-1. At the dissociated state (image 24), the Fe-N bond lengths

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further decrease to 1.659 Å, and the symmetric and anti-symmetric N-Fe-N stretch frequencies

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increase to 871 and 854 cm-1, respectively (see Figures S1 and S2), suggesting stronger Fe-N

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bonding.

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Figure 3A illustrates the ground-state DFT-predicted MEP, black curve, and free energy

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at 298 K and 1 atm of N2, red dashed line, for N2 adsorption and dissociation. The figure

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illustrates that it is energetically downhill with no barrier for the N2 molecule to molecularly

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adsorb on top of the Fe site, with ∆E = −0.61 eV (−0.53 eV with zero point energy correction),

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and ∆G = −0.07 eV;20 the loss of translational entropy of the gas phase molecule upon adsorption

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is largely responsible for the very small driving force. Rotation of the molecule leading to η2-N2

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bonding with Fe and its eventual dissociation are energetically unfavorable processes, with ∆E =

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1.76 eV (1.81 eV with zero point energy correction), and ∆G = 2.29 eV relative to gas phase

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N2,20 with an energy barrier of ∆E‡ = 3.79 eV (3.18 eV measured relative to the gas phase

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molecule, which would be the effective barrier of the dissociation). The calculated effective

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barrier is larger than the barriers predicted for flat surfaces of the best high-temperature HB

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catalysts, e.g. 1.90 eV/N2 on hexagonal-close-packed Ru(0001)32and 1.11 eV on body-centered-

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cubic Fe(110).33 These were calculated from DFT using the revised-PBE (RPBE) XC functional,

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which is comparable to what is used here. The barrier for AuFe is, however, much smaller than

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the DFT-calculated thermodynamic dissociation energies of N2 on pure Au(111), 4.98 eV (4.99

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eV zero point energy, ZPE, corrected),20 and in the gas phase, 10.41 eV (10.26 eV ZPE-

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corrected,

20

9.76 eV from experiment at 0 K)34. Therefore, while barrier is reduced on the Fe-


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doped Au, additional energy needs to be supplied to promote N2 dissociation, thus the

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importance of electronic excitation through plasmon resonance and energy transfer is evident (to

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be discussed further below).

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Note that the magnetic moment (grey curve) is quenched from 3 µB to ~2 µB when N2 is

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molecularly adsorbed (image 11) and to ~0 µB when it is completely dissociated (image 24).

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This is consistent with magnetic quenching experimentally observed when sputtering Fe together

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with N2(g) in the synthesis of Fe-N films, where eventually a paramagnetic Fe2N phase prevails

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at high N2 doses.35 It was previously shown by DFT that the reduction in the magnetic moment

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in Fe as the fraction of N in FexN compounds increases is a consequence of the hybridization of

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the Fe 3d with N 2p orbitals to form strong Fe-N σ bonds. The strongly hybridized Fe 3d orbitals

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are thus no longer subject to large exchange splitting.36 We therefore also investigated the non-

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adiabatic curves for the entire reaction with Sz=2 and 1 and Sz =0 near and at the transition and

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product states (Figure 3B). This was done to map out the individual energies of the different spin

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manifolds as a function of the reaction coordinate. We assume that the hopping between spin

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surfaces, between or among the ground and excited states, could only happen when they are

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degenerate, otherwise the reaction occurs along a single spin manifold. Quantification of the

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hopping probability requires quantum dynamics simulations that are beyond the scope of this

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work. It is clear in the lower panel of Figure 3B, where the relative energies of the different spin

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manifolds are shown, that a high-spin Fe is favored when the molecule is away from the surface.

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However, as the molecule approaches the surface, the magnetization transitions from S=2 to Sz=1

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(starting at image 10) and finally Sz=0 when the molecule is completely dissociated (image 24).


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Figure 3. Ground-state energetics of N2 adsorption and dissociation. A, spin-polarized DFT-

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GGA+D3 adiabatic minimum energy path (black line) with residual electronic spin (grey) as

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functions of the reaction coordinate (RC; defined in Section II of the Supporting Information).

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Red dashed line corresponds to the free energy of the stationary points (relative to gas phase N2)

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at 298 K and 1 atm of N2. Upper panel B, spin-polarized DFT-D3 ground-state potential energy

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curves along the RC for spin diabats: Sz=2 (4 μB), 1 (2 μB), and 0 (0 μB). Upper panel C and D,

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emb-CASPT2 and emb-NEVPT2 ground-state potential energy curves for spin diabats: S=2, 1,

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and 0. Lower panel in B (C and D) shows the energies of the Sz(S)=2 and Sz(S)=0 relative to


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Sz(S)=1. In these plots, a positive value means Sz(S)=1 is the more stable spin. Numerical indices

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within the panel correspond to structures shown in Figure 2.

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Embedded correlated wavefunction (ECW) correction to the ground-state reaction energy

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curve

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We employed ECW calculations within the density functional embedding theory (DFET)

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formalism to correct the DFT ground-state energies and calculate electronically excited state

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energies.37-38 We carved out an Au10Fe cluster (Figure 1B) from the slab model (Figure 1A). The

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cluster size is chosen according to Ref.

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surface Au atom to accommodate an even number of cluster electrons so as to not induce any

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artificial spin polarization. This cluster size also allows for a complete saturation of the Fe atom

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with its nearest-neighbor Au atoms. Completing the Fe atom’s coordination is deemed important

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since it is the primary reactive site. Embedding potentials were constructed following the Huang-

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Pavone-Carter DFET scheme37-38 to reproduce the slab density from the sum of the densities of

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the cluster and its environment (see Computational Methods for details regarding construction of

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the embedding potential). Figures 1C and 1D show the real space visualization of the embedding

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potential. The embedding potential is characterized by negative (attractive) regions at the nuclei

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and at the cluster-environment interface, while positive (repulsive) regions immediately surround

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the atoms. Both the attractive potential regions at the cluster-environment interface, and the

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repulsive potential regions surrounding the atoms facing this interface, delocalize the electrons

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and “soften” the valence electronic wavefunctions between the nuclei in the cluster and the

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environment to simulate bonding. We use this embedding potential as an additional term in the

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for top site adsorption, but with an additional sub-


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one-electron Hamiltonians in both cluster DFT and correlated wavefunction (CW) calculations.

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The inclusion of the embedding energy term was found to be important in stabilizing the

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adsorption of the molecule onto the cluster, which is otherwise very unfavorable in the absence

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of this term (see Figure S3 in the Supporting Information). The method employed has been

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demonstrated to successfully predict both ground-state and excited-state PESs for reactions

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involving small molecules on metallic surfaces.6, 8, 37-42 Embedded complete active space self-

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consistent field43-45 (emb-CASSCF) calculations were then conducted, from which the zeroth

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order wavefunctions were derived and subsequently used to perform both embedded CAS

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second-order perturbation theory46-47 (emb-CASPT2) and embedded n-electron valence second-

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order perturbation theory48 (emb-NEVPT2) calculations.

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For a select set of molecular configurations along the MEP, different spin multiplicities,

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namely singlet (S=0), triplet (S=1), and quintet (S=2), were also considered for emb-CASPT2

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and emb-NEVPT2 calculations as shown in Figures 3C and 3D (see Computational Methods for

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the expression for the energy correction). Both CW methods predict barriers higher than

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predicted by DFT, by about 1 eV (compare Figures 3C and 3D to Figure 3B), increasing to 4.63

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and 4.74 eV, within the CASPT2 and NEVPT2 levels, respectively, using double zeta basis sets

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(see Table S1 of the Supporting Information). Similarly, the reaction energy increased to 3.19

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and 3.62 eV from 2.37 eV. The CASPT2 and NEVPT2 gas phase dissociation energies were

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determined to be 9.64 and 9.53 eV, respectively, using a quadruple zeta basis set (9.91 eV from

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experiment after removing ZPE correction at 0 K;34 see also Table S2 in the Supporting

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Information). We estimate corrections to the emb-NEVPT2 calculated barrier and reaction

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energy of up to +0.26 and +0.45 eV, respectively, due to basis set incompleteness error incurred

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by using double zeta basis sets. This approximates the correction needed to make the results on


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par with using a quadruple basis set on N (see section III and Figure S4 in the Supporting

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Information).

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correction, remains to be significantly smaller compared to the gas phase dissociation energy.

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Note that although there is a large disagreement between DFT- and ECW-predicted barriers, both

236

theories predict the spin to be quenched from S=1 to S=0 at the transition state. In Figure 4, it is

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clear from the DFT-predicted residual Bader charge49 – a real-space charge partitioning that is

238

weakly basis-set dependent – on N2 that charge transfer begins even prior to the molecule’s bond

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elongation. Most notably at ~6 Å, where N2 is adsorbed in an η1-N2 configuration on Fe, a more

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significant partial charge transfer is predicted by DFT associated with the π-backbonding

241

interaction between N2 and Fe. In emb-CASSCF (from which the zeroth order wavefunctions are

242

derived for both the emb-CASPT2 and emb-NEVPT2), the charge on the molecule is subtler

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prior to dissociation (even when the molecule is proximal to the surface), consistent with the π-

244

backbonding noted earlier. However, a more drastic charge transfer occurs at the point where the

245

bond begins to stretch (image 21, see also Figure S2), and a nearly integer negative charge

246

(higher than in DFT) is predicted once the molecular bond has completely broken (~1 electron

247

on each N atom at image 24). The higher barrier therefore can be easily rationalized by DFT’s

248

tendency to delocalize electrons, leading to a smooth and artificial early onset of charge transfer

249

from the surface to the molecule, which tends to lower dissociation barriers on metal surfaces.39-

250

40

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DFT’s XC functional is a major cause of artificial charge delocalization and more favorable

252

prediction for dissociative adsorption of the molecule.39-40 The lack of a derivative discontinuity

253

in DFT can lead to unphysical minima associated with fractional occupations of the orbitals.50-51

254

By contrast, the presence of exact, nonlocal exchange and static correlation in CASSCF

The predicted barrier for N2 dissociation at the Fe site, despite the ECW

The absence of a derivative discontinuity in energy as a function of orbital occupation in


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effectively restores the derivative discontinuity, thus favoring either full or no electron transfer at

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all between the surface and molecule. The larger, closer to integer, charge transfer at the

257

transition state for emb-CASSCF thus leads to larger Coulomb repulsion between the N atoms at

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the transition state (image 22), contributing to the higher energy barrier. Attempts to correct for

259

these shortcomings in DFT can be made through the use of hybrid XC functionals (introducing a

260

fraction of exact exchange that relieves to some degree the self-interaction error, e.g., PBE0,52

261

B3LYP,53 and HSE54-55) or the introduction of a Hubbard-like on-site “U” term (commonly

262

referred to as DFT+U, which reintroduces derivative discontinuity via an averaged Hartree-Fock-

263

like on-site term)56-57 for molecules and semiconductors. However, these attempts unsurprisingly

264

are less successful when applied in metals,51,

265

metals.62 Thus such methods subsequently have questionable applicability for our current

266

investigation. We therefore have not utilized the above-mentioned methods and instead utilize

267

higher levels of post-Hartree-Fock theory to better describe the physical properties. Multi-

268

reference methods such as CASSCF and NEVPT2, when utilized properly, are more accurate in

269

describing the important aspects of the types of behavior studied here, including bond breaking

270

and bond formation, charge-transfer processes, and the description of PESs around conical

271

intersections.

58-61

because Hartree-Fock theory diverges for

272


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Figure 4. Bader charge analysis. Net charge on the N2 molecule along the reaction pathway

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relative to gas phase N2, calculated from electron densities obtained from emb-DFT and emb-

276

CASSCF for different spin manifolds. Some of the adsorption configurations along the pathway

277

are annotated (Figures 2 and 3).

278 279

Excited-state reaction energy landscape

280

Incident light typically in the range of visible to UV is absorbed by metallic nanoparticles such

281

as Au with high absorption cross sections and can result in concomitant generation of a surface

282

plasmon. These waves have narrower spatial confinement and higher local field intensity than

283

the incident photon, which are suspected to contribute to reaction enhancement on the surface of

284

plasmonic nanoparticles. Among the many mechanisms of enhancement discussed in the

285

literature, we consider energy transfer via plasmon-induced RET14, 18 an extension of the Förster

286

RET (FRET) to the interaction of plasmonic particles with semiconductors18 or molecules.14

287

Figure 5A illustrates the non-radiative RET mechanism between the LSPR states in the


15


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nanoparticle, generated after photon absorption, and defect- or adsorbate-induced local states at

289

the surface. By virtue of this mechanism, we calculate the excited states at the reactive site with

290

the N2 molecule along the reaction pathway to determine the feasibility of local resonance

291

excitation, which may lower the reaction barrier of N2 dissociation.

292

Figure 5B shows the calculated ground-state and some of the low-lying excited-state energy

293

curves along the dissociation pathway. Here, S=2 and S=1 curves are constructed to investigate

294

both the effect of local excitation on the reaction energetics and the possibility of intersystem

295

crossing between different spin manifolds in the excited state. Note that the ground-state energy

296

curve in Figure 5B is slightly changed by the state-averaging procedure in emb-CASSCF used to

297

generate the zeroth order wavefunctions that are subsequently used in state-specific emb-

298

NEVPT2 calculations (compare with Figure 3D that is based on ground-state only CASSCF).

299

Nonetheless, it is clear from the results of our calculations that there is a significant barrier,

300

requiring very high temperatures to obtain the necessary activation energy for N2 dissociative

301

adsorption on Fe-doped Au in the ground state.

302

From the excited-state energy curve, we trace out possible channels with the lowest associated

303

thermal energy requirement to cause the dissociation of the molecule. In Figure 5B, electronic

304

excitation when N2 is molecularly adsorbed vertically (image 10) can facilitate the molecule’s

305

rotation to lie parallel to the surface (image 17). Assuming a RET mechanism, this may be

306

achieved via excitation at image 10 from the ground state to the 6th excited state at S=1, which is

307

incidentally nearly degenerate with the 4th excited state of the S=2 state. This excitation requires

308

a plasmon with 2.7 eV (~460 nm, blue light) of energy, with a predicted transition oscillator

309

strength, f0,6, of 2.5x10-4. Among the many pathways available for relaxation, this state can

310

evolve and decay to the lower-lying S=2 state at image 11, e.g., the 2nd and 3rd excited states,


16

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311

where a low-barrier molecular rotation to reach η2-N2 bonding with Fe can be achieved (image

312

17). From this precursor state, a second RET with energy of 2.4 eV (~520 nm, green light), with

313

a predicted oscillator strength of f0,4=6.3x10-4, may facilitate excitation from the ground state to

314

the 4th excited state of S=2, at which point an effective barrier of 1.33 eV (much lower than the

315

ground-state barrier of 4.74 eV) needs to be overcome to completely dissociate the molecule

316

(e.g., provided thermally).

317

We note that the time scale between two RETs described is much longer than the time scale of

318

an electronic excitation or relaxation, and thus should be considered as separate events. The first

319

RET increases the probability of forming N2 molecules that are bonded to Fe in a side-on (η2-N2)

320

configuration, such as in structure 17, by providing the energy needed to rotate the molecule

321

from an end-on configuration (η1-N2), structures 10 and 11. The second RET will provide part of

322

the energy needed for dissociation from an η2-N2 configuration, thus leading to an effectively

323

reduced barrier. Mechanisms involving multiple photons driving chemical reactions have been

324

demonstrated experimentally. In particular, plasmon-induced reactions sometimes require

325

multiple photon scattering events per reactant molecule or reaction site. In these reactions, non-

326

linear (super-linear) dependencies of the reaction rate on incident light intensity are observed.9,

327

63-64

328

hydrogenation towards ethene on Pd-Al nanoparticle complexes.9

Examples include ethene epoxidation on Ag,63 and H2 desorption and selective acetylene

329

Au nanoparticles would be capable of providing LSPRs with the right energy to induce the

330

aforementioned excitations to occur. Au nanorods, for example, have a broad visible absorption

331

band at 520 nm that spans from ~450 nm to ~570 nm, corresponding to the rod’s transverse

332

plasmon mode,65 while Au nanospheres that are 26 ± 10 nm in diameter have broad resonance


17


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Page 18 of 28

333

that peaks at 526 nm (slightly blue shifted with increasing Fe concentration for lightly doped

334

cases, e.g., to 504 nm).66

335

Although the lower than average transition oscillator strength in the aforementioned

336

excitations suggest low probability of energy transfer, the transfer rate is also proportional to the

337

transition dipole moment of the donor (plasmon in the metal nanoparticle). Thus considering the

338

large extinction cross-section of Au nanoparticles at the plasmon resonance peak,66 coupled with

339

the field enhancement at the surface (enhanced67-68 as ~|E|2, leading for example to surface

340

enhanced Raman scattering, SERS, enhancement of about ~102 for isolated Au spherical

341

nanoparticles, and as much as ~107 at dimer junctions or hot spots66), the desired excitations may

342

occur. Local field enhancement at the surface and large optical extinction coefficients of the

343

plasmonic nanoparticles are precisely the draw of this new phenomenon in the field of light-

344

induced heterogeneous catalysis.14

345

346 347

Figure 5. A, RET mechanism where the metal nanoparticle’s (NP’s) plasmonic response yields

348

donor states, while the local surface states, which may originate from a surface defect or


18

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349

molecular adsorbate, serve as acceptor states. The purple vertical arrow represents the collective

350

plasmonic excitation in the NP leading to the broad LSPR energy distribution (yellow curve)

351

above the Fermi level (EF). B, Excited-state energetics of N2 adsorption and dissociation on Fe-

352

doped Au(111). Emb-NEVPT2 predicted curves for the ground (g.s.) and of some of the low-

353

energy excited states (e.s.) for spin diabats, S=2 (broken lines) and S=1 (solid lines). Arrows

354

annotate a possible excited-state N2 dissociation pathway. Red arrows mean excitation (solid)

355

and excited-state decay (broken). Orange curvy arrows denote thermally driven nuclear

356

rearrangement.

357 358

CONCLUSIONS AND OUTLOOK

359

Implication of excited-state kinetics in low-temperature NH3 synthesis, and design goals for

360

future plasmonic Haber-Bosch (HB) catalysts.

361

The main driving force for the improvement of the HB process is a reduction of the

362

present, substantial energy costs, limiting the accessibility of the process to the most affluent

363

nations in world.2 Massive energy input has to be spent thermally and mechanically in order to

364

enable N2 dissociation. Here, we present an idea of using light to overcome the high activation

365

barrier for this reaction. To potentially be able to deliver energy of more than 2 eV to a reaction

366

without increasing the temperature of the system is at the core of the advantage of utilizing

367

plasmons to facilitate catalysis. Sequential RETs are found to be key in supplying the large

368

energy required to break the N2 molecule’s triple bond. The AuFe catalyst is however far from

369

optimal in providing the necessary ground- and excited-state pathways for room temperature N2

370

dissociation (1.33 eV is still large for the dissociation to occur at room temperature), and a study

371

of N-H bond formation on this type of catalyst (another piece of the puzzle) has yet to be


19


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Page 20 of 28

372

conducted. We have, on the other hand, illustrated here a feasible mode for light to make

373

possible N2 activation, which constitutes a significant bottleneck in NH3 synthesis. This study

374

brings us a step closer to the long-term vision of optimizing a catalyst that will eventually not

375

require high temperatures and pressures to facilitate the N2 dissociation reaction. We therefore

376

are starting to explore the more reactive Mo-doped Au(111) surface, which may have the

377

potential to achieve room temperature N2 activation.20 A tandem antenna-reactor complex

378

proposed recently by Swearer et al.9 and Zheng et al.,12 is also a promising direction to pursue.

379

Note that room temperature H2 dissociation on plasmonic nanoparticles such as Au will also be a

380

necessary step in NH3 production and has already been demonstrated under ambient conditions.6-

381

7

382

COMPUTATIONAL METHODS

383

Density Functional Theory (DFT)

384

A five-layer thick √21 × √21 Au(111) slab was used to simulate the surface, with

385

approximately 15 Å of vacuum normal to the surface in the periodic cell. The in-plane lattice

386

constants of the slabs were fixed to the simulated equilibrium bulk fcc Au lattice constant

387

a=4.168 Å. A surface Au atom was substituted with a Fe atom. Spin-polarized Kohn-Sham (KS)

388

DFT calculations with the projector augmented-wave (PAW) method69 and periodic boundary

389

conditions were carried out using the Vienna Ab-initio Simulation Package (VASP) version

390

5.3.5.70 The PBE-GGA was used as the XC functional.21 van der Waals interactions were taken

391

into account by using the D3 energy correction with Becke-Johnson damping.22-23 A dipole field

392

correction was also used to further remove spurious field interactions within the vacuum.71-72 The

393

2s and 2p orbitals of N; 3s, 3p, 4s, and 3d orbitals of Fe; and 6s and 5d orbitals of Au were


20

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394

explicitly treated as valence electrons solved for self-consistently. A planewave (PW) basis set

395

was used with a kinetic energy cutoff of 500 eV for force evaluation and structural relaxation.

396

All atoms were relaxed until the atomic forces are converged to values ≤ 0.01 eV/Å. The

397

minimum energy path for adsorption and dissociation of N2 on the surface was determined via

398

the nudged elastic band (NEB) method.73-74 Subsequently, the energies and vibrational

399

frequencies were evaluated using a PW cutoff of 660 eV for the total energy refinement with an

400

energy convergence threshold of ≤1.0×10-3 eV/atom. Brillouin zone integration was carried out

401

using the Methfessel-Paxton method,75 with a smearing width of 0.09 eV and k-point meshes of

402

4×4×1 via Γ-point-centered Monkhorst-Pack sampling.76

403

Density Functional Embedding Theory (DFET)

404

DFET is a method to (locally) correct for the self-interaction error inherent in DFT, the

405

approximate nature of the XC functional designed for DFT, and to account for (non-empirically

406

fitted) van der Waals dispersion. This is done to, e.g., achieve more accurate reaction energies on

407

surfaces and calculate for excited-state energies in the framework of many-body theories that

408

would be otherwise intractable to calculate for systems composed of ≳300 electrons. Using this

409

method, we partition the system into two subsystems, namely, the cluster (cl) and environment

410

(env). The cluster is composed of the reactive site on the surface, as described above. The DFET

411

energy37 is then evaluated via the following equation:

, = , + , − ,

412

, , , , and , are respectively the energies of the periodic slab from DFT (removing

413

the D3 dispersion energy to avoid double counting of the dispersion interaction) and of the

414

embedded cluster from a CW method and from DFT, for the ith image. The slab, cluster, and


21


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Page 22 of 28

415

environment are defined in Figure 1. Embedded energies , and , were calculated

416

using a modified Hamiltonian = ° +

417 418 419 420

where ° is the usual zeroth order Hamiltonian defined for the cluster (or environment) subsystem, and is a local electronic potential constructed from DFT in the PW basis.

is determined such that the of both the cluster and environment generate ground-state electron

densities ( and ) whose sum gives the ground-state density of the total system (!" , here

421

the clean metal slab is designated as the reference). is determined from an in-house

422

modified VASP 5.3.3 24 code by maximizing the functional ( !" + − & ' ) *+ #( , ) = (

423

with the gradient defined as (# ( ( ( !" = + − ≈ + − !" ( ( ( (

424

The gradient therefore vanishes by construction, which results to + = !" .24

425

The , is calculated using MOLPRO77-78 from either a contracted space CASPT246-47

426

(via the “rs2c” implementation in MOLPRO) or partially contracted (PC) NEVPT248 using

427

orbitals obtained from ground-state (Figure 3) or state-averaged (over 8 states, Figure 5)

428

CASSCF calculations. Gaussian-type basis sets were used (all at the double zeta level for a

429

balanced description of each component), where a relativistic effective core potential was used

430

for Au. The basis set is summarized in Table S1 of the Supporting Information. The


22

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431

appropriateness of the basis set used is discussed in the Supporting Information sections III and

432

IV (see also Table S2 and Figures S4 and S5 there). The active space in the CASSCF

433

calculations is defined by the four singly-occupied Fe 3d-derived orbitals, a pair of empty and

434

filled Au 6s-derived orbitals, and six N2 3σ, 1π, 4σ*, 2π*-derived orbitals, for a total of 12

435

orbitals with 12 electrons. These orbitals were chosen to define a consistent active space of

436

reasonable size along the reaction (see Supporting Information Figures S6-S10 for the evolution

437

of the CAS natural orbitals along the reaction). Convergence of the barrier and dissociation

438

energy with respect to the CAS size is also investigated (see Supporting Information Section V

439

and Table S3 there). The modified zeroth order one-electron Hamiltonian for the CASSCF

440

calculations that contains was introduced via the matrix manipulation feature in MOLPRO.

441

The embedding integral matrices - ,. = / 0 ∗ (+) 0. (+)*+ in the primitive Gaussian basis

442

0 (+) were constructed using an in-house, stand-alone embedding integral generation code and

443

were added to the respective Hamiltonians. The CASPT2 and NEVPT2 calculations included

444

additional (dynamic) correlation from almost all of the orbitals, with the exception of some of the

445

inner core orbitals, namely: N 1s, Fe 1s, 2s, 2p, and 3s, and Au 5s. For CASPT2, modification of

446

the zeroth order Hamiltonian were implemented via an “ionization potential electron affinity”

447

(IPEA) shift79 of 0.25 a.u. together with a level shift80 of 0.3 a.u. to eliminate intruder states,

448

which therefore facilitate electronic convergence. The , were calculated using the same

449

basis sets as above and KS-DFT with the PBE XC functional.

450 451

Transition oscillator strengths for an excitation from state n to m are calculated from CASSCF as follows: 2, =

2 7 ( − )(|(56 |7 +8(59 8 +|(5: |7 ) 3


23


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 24 of 28

452

where − is the energy of excitation (in atomic units, a.u.) and 5s are the transition dipole

453

moments of the excitation (in a.u.).81

454

ASSOCIATED CONTENT

455

Supporting Information. Method for computing vibrational frequencies, definition of the

456

reaction coordinate, vibrational spectra of the stationary and transition states, structural

457

parameters as a function of the reaction coordinate, relative embedded cluster DFT energies with

458

and without embedding, table of basis sets used, benchmark calculations for the dissociation of

459

the gas phase N2, a survey of the basis set incompleteness error and counterpoise correction,

460

CAS natural orbitals, CAS-size-dependence of the barrier and reaction energy, and ground- and

461

excited-state absolute energies of all the structures calculated with different methods. (PDF)

462

Compressed cif and xyz structure files (ZIP)

463

AUTHOR INFORMATION

464

Corresponding Author

465

*[email protected]

466

Notes

467

The authors declare no competing financial interests.

468

ACKNOWLEDGMENT

469

EAC acknowledges financial support from the Air Force Office of Scientific Research via the

470

Department of Defense Multidisciplinary University Research Initiative, under Award FA9550-

471

15-1-0022. The High Performance Computing Modernization Program (HPCMP) of the U.S.


24

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472

Department of Defense and Princeton University’s Terascale Infrastructure for Groundbreaking

473

Research in Engineering and Science (TIGRESS) provided the computational resources. We

474

would also like to thank Dr. Kuang Yu for his assistance in using the embedding implementation

475

in VASP and Dr. Caroline M. Krauter for her assistance in conducting and implementing

476

embedding calculations in MOLPRO. Additionally, we thank Dr. Vincent A. Spata and Dr.

477

Caroline M. Krauter for their suggestions for improving the manuscript.

478

REFERENCES

479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509

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Excited-State N2 Dissociation Pathway on Fe-Functionalized Au

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