Toward a Database of Chemically Accurate Barrier Heights for

Subscriber access provided by KUNGL TEKNISKA HOGSKOLAN

Perspective

Towards a Database of Chemically Accurate Barrier Heights for Reactions of Molecules with Metal Surfaces Geert-Jan Kroes J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.5b01344 • Publication Date (Web): 24 Sep 2015 Downloaded from http://pubs.acs.org on September 25, 2015

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

The Journal of Physical Chemistry Letters is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 45

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

The Journal of Physical Chemistry Letters

Towards a Database of Chemically Accurate Barrier Heights for Reactions of Molecules with Metal Surfaces Geert-Jan Kroes Leiden Institute of Chemistry, Gorlaeus Laboratories, Leiden University, P.O. Box 9502, 2300 RA Leiden, The Netherlands AUTHOR INFORMATION Corresponding Author * Geert-Jan Kroes, [email protected]

ABSTRACT Being able to calculate reaction barrier heights to within chemical accuracy (errors < 1 kcal/mol) is crucial to the accurate modeling of chemical reactions. Although accurate databases exist that can help theorists with benchmarking new electronic structure theories on gas phase chemical reactions, no such databases exist for reactions of molecules with metal surfaces. Nonetheless most chemicals are made in heterogeneously catalyzed processes, of which many take place over metal particles. Presently, barrier heights for molecule-metal surface reactions have been determined with chemical accuracy for only two systems, i.e., H2 + Cu(111) and H2 + Cu(100). This has been done with semi-empirically determined density functionals,

ACS Paragon Plus Environment

1


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 2 of 45

which were fitted through comparisons of dynamics results with molecular beam sticking probabilities. The prospects of extending the database with chemically accurate data for other molecule-metal reactions, either with the use of semi-empirical density functional theory or with first principles theory, are discussed.

TOC GRAPHICS

Gas phase chemical reactions involving three atoms (for instance, F + H2 → HF + H 1 and Cl + H2 → HCl + H 2) and four atoms (OH + HD → H2O + D 3) can now be modeled by theorists with unprecedented accuracy (of the order 0.1 kcal/mol), with the aid of potential energy surfaces (PESs) computed with high level ab initio methods. Theorists working on gas phase chemical reactions enjoy an important advantage in having available databases of accurate reaction barriers (geometries and barrier heights), on which they can benchmark the accuracy of new electronic structure theories. For instance, Peverati and Truhlar have recently benchmarked the accuracy of several density functionals (DFs) on a database of hydrogen transfer reactions (HTBH38/08) and of non-hydrogen transfer reactions (NHTBH38/08) 4. Because the data in these databases are based on a combination of accurate high-level ab initio methods and


2

Page 3 of 45

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


interpretations of experimental data 4, the mean unsigned errors (MUEs) computed for such databases allow conclusions regarding the accuracy of, for instance, new DFs for gas phase chemical reactions. Reactions of molecules with metal surfaces, such as the dissociative chemisorption reaction that is the topic of this paper, are arguably of much more practical relevance than gas phase reactions, as the majority of chemicals is produced in heterogeneously catalyzed reactions

5

of which many take place over metal particles. Nevertheless, similar

databases on reactions on metal surfaces, which would allow rigorous conclusions to be drawn regarding the accuracy of electronic structure methods for these systems, do not exist. Why is that so, and what can we do to change this? These are the questions we address in this Perspective paper. The construction of a database with chemically accurate barriers for elementary molecule-metal surface reactions can help pave the way to the chemically accurate modeling of all such reactions. This could eliminate an important source of error in kinetic simulations of heterogeneously catalyzed reactions6-7. The electronic structure problem. The first difficulty one encounters with the construction of the desired database (of barrier heights for reactions of molecules with metal surfaces) is what one may call the electronic structure problem. Because the system that needs to be modeled (a molecule interacting with a reasonably sized metal nano-particle, or with an extended metal surface) is large, an electronic structure method needs to be used of which the cost scales favorably with system size, to enable the convergence of calculations with system size. Up to now, in practice this has limited the application of electronic structure methods to the systems of interest to density functional theory (DFT) at the gradient approximation approximation

11

8-10

or meta-gradient

level. Unfortunately, tests on gas phase reactions suggest that DFT at these

levels should be of limited accuracy for reaction barrier heights: the MUE is 3.8 kcal/mol for the


3


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 4 of 45

best performing gradient approximation (MOHLYP2) and 1.8 kcal/mol for the best performing meta-gradient approximation (MN12-L) 4. This is still far removed from the goal one would like to set, of chemical accuracy (errors ≤ 1 kcal/mol). There is no reason to expect that the DFs tested for gas phase reactions will perform better for molecule-metal surface reactions and other, more accurate electronic structure methods are presently not available for these systems. It is therefore clear that the barrier height entries in the database we are after should be based on experimental results. Experiments for validation. The next question to be addressed is what type of experiments on which specific systems should be used in the construction of the database. One needs to address activated reactions if the goal is to determine barrier heights. But is it best to address experiments in which thermal rates are measured, or molecular beam sticking experiments in which reaction probabilities are measured as a function of the collision energy? As also noted by Klippenstein et al.12, it is best to validate theory through comparisons with experiments that measure the reaction probability of a molecule on a specific, well-defined (for instance, a low-index) metal surface as a function of the collision energy. The reason is that the surface geometry is well defined in these experiments, which is advantageous in benchmark calculations. In contrast, under thermal conditions rates of activated reactions are usually governed by reaction at defects, such as steps or kinks 13-14. The validation of electronic structure methods through comparison with molecular beam sticking experiments on activated dissociative chemisorption reactions can be performed as follows: One demands that the reaction probability curve computed with a suitable dynamics method on the basis of input from the electronic structure method shows little displacement along the collision energy axis from the measured reaction probability curve 15. This constitutes an accurate procedure for evaluating the accuracy of the electronic structure method, because to


4

Page 5 of 45

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


a good approximation (see for instance Ref.16) the reaction probability is equal to the fraction of configuration space perpendicular to the reaction coordinate for which the collision energy exceeds the barrier (as in the so-called hole model17). Which systems? The next question to address is then how to pick the systems, i.e., which molecules interacting with which metal surfaces. The choices to be made are governed by several considerations. It should be clear from the above that one should select a system for which suitable experimental results are available. To serve as a benchmark, it should be possible to model the system with a small enough number of atoms to allow testing of computationally expensive electronic structure methods. In the choice of the system one should also take into account that dynamics calculations are necessary to validate the electronic structure results, and that the comparison should not be hampered by defects of the dynamical model that can be used. Molecule-metal surface reactions may be affected by energy transfer involving the vibrational motion of the surface atoms (phonons) 18 and by electron-hole pair (ehp) excitation 19 or by other potentially non-adiabatic electronic effects, such as electron transfer

20-21

or the quenching of

electronic spin of the impinging molecule by the metal surface, which may be modeled inaccurately with an electronically adiabatic model as argued for O2 + Al(111) 22. These factors all lead to additional difficulties with performing accurate dynamics calculations. Rules of thumb that can be used to avoid complications in dynamics calculations are that lighter colliding molecules will transfer less energy to surface phonons

23-24

, electron transfer and ehp excitation

are less likely to occur for surfaces with a high work function and molecules with a low or negative electron affinity

25

, while complications with spin quenching can be avoided with the

use of closed-shell molecules. In addition, the need to describe motion in all molecular degrees of freedom may complicate the dynamical treatment of the reaction of polyatomic molecules


5


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 6 of 45

with metal surfaces, particularly if the use of a quantum dynamical (QD) method is preferred26-27. However, it is also desirable that the database contains results for a diversity of systems, so that the quality of novel electronic structure methods can be established for a variety of systems that is as much as possible representative of systems of interest to heterogeneous catalysis. Reactions of H2. Activated reactions of H2 with metal surfaces are typically viewed as ideal for benchmarking electronic structure methods, as under many conditions they are not, or hardly, affected by energy transfer involving phonons or e-h pair excitations

28-29

(but see below). This

means that modeling the motion in only the six degrees of freedom of the molecule is enough for achieving an accurate description of several observables related to the scattering of H2 from reactive metal surfaces

29

. This can be done with QD methods, but, remarkably, quite accurate

results can usually already be achieved with the aid of quasi-classical dynamics 30. An example of the level of agreement that can be achieved with reactive scattering experiments is shown in Fig. 1 for H2 + Cu(111)

31

. This level of agreement could be achieved

by adopting the so-called specific reaction parameter (SRP) approach to DFT implementation

15, 31

32

, in an

in which the mixing coefficient of a weighted average of two DFs at the

GGA level of theory was fitted to a molecular beam sticking experiment on D2 + Cu(111) in which high collision energies could be achieved

15, 31

. Not only did the measured and computed

reaction probability curve for D2 + Cu(111) agree to within better than chemical accuracy, the same level of agreement was also achieved for observables related to scattering of H2 from Cu(111) obtained in experiments to which the SRP density functional (SRP DF) was not fitted15, 31, 33

. Figure 1 provides an example of this, showing that the molecular beam sticking

probabilities measured for the H2 isotopologue by two different groups could also be reproduced with chemical accuracy. The difference between the measured sets of reaction probabilities


6

Page 7 of 45

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


illustrates that this was no trivial matter; the dynamics calculations were able to account for the hitherto unexplained difference in the reaction probabilities, which arose from large differences in the widths of the velocity distributions of the H2 beams. A crucial point conveyed by Fig.1 is that experimental measurements on H2 (and other molecules) reacting with metal surfaces can only be used to validate electronic structure theory if the properties of the molecular beams used (vibrational and rotational temperature, and, even more importantly, the velocity distribution) are known. As these details were usually not provided with the experimental results in the past, efforts to construct the desired database would benefit from new, well-documented molecular beam experiments on dissociative chemisorption on metal surfaces.

Figure 1. Computed reaction probabilities of H2 on Cu(111) are compared with experimentally measured molecular beam sticking probabilities for H2 + Cu(111) (Refs. 34-35). The empty circles represent experimental data from Ref. 35 and the empty squares experimental data from


7


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 8 of 45

Ref. 34. The dashed line shows the initial-state resolved reaction probability calculated for a specific incidence energy Ei, the full line the Boltzmann averaged reaction probability

for the nozzle-temperature Tn and energy Ei, and the full symbols the

molecular beam sticking probability

obtained with Boltzmann averaging over

rovibrational states and averaging over the translational energy distribution of the beam, with SRP-DFT (Ref.31). Taken from Ref. 31. An intriguing question is to what extent SRP DFs developed for one specific system are transferable to other systems. Calculations on H2 + Cu(100) using the SRP DF developed for H2 + Cu(111) suggest that SRP DFs for a specific molecule interacting with a specific metal should be transferable at least among the low index faces of that metal36. This was shown by establishing that molecular beam sticking experiments on H2 + Cu(100)37 could be reproduced with chemical accuracy using the SRP DF for H2 + Cu(111). This also suggest extensions to applications to defected surfaces of interest to heterogeneous catalysis: perhaps SRP DFs developed on the basis of surface science experiments on molecules reacting over low index metal surfaces can also be used to obtain accurate DFs for the same molecules reacting at stepped surfaces. We suggest that research be done to answer this question, and to determine whether the transferability among low index surfaces of the same metal observed for H2 + Cu also holds for other systems in which a specific molecule interacts with surfaces of one specific metal. In this context, systems for which the reaction is activated on one and non-activated on another low index surface, such as H2 + Ni38, could be of special interest. In contrast, calculations

39

on the weakly activated H2 + Ru(0001) dissociative chemisorption

reaction established that molecular beam sticking experiments on this system

40

could not be

reproduced with chemical accuracy using the semi-local SRP DF developed for H2 + Cu(111).


8

Page 9 of 45

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


This suggests that there should be limits on the transferability of these semi-empirically developed DFs. Additional calculations41 showed that the sticking experiments on H2 + Ru(0001) can be reproduced semi-empirically with functionals containing non-local correlation 42-43

. This makes sense as the H2 + Ru(0001) system exhibits an early minimum barrier that

occurs far away from the surface, where the van der Waals attraction simulated by the non-local correlation functionals42-43 should be important. It also raises the question of whether DFs containing non-local correlation might perhaps exhibit a greater degree of transferability among molecule-metal surface systems than semi-local functionals like the SRP DF for H2 + Cu(111). This can be investigated by testing SRP DFs developed for early barrier, weakly activated H2metal systems on late barrier, highly activated H2-metal systems. The brute force search for an SRP DF for H2 + Ru(0001) has also suggested a strategy for finding an SRP functional. The research revealed that the two DFs that worked well in reproducing molecular beam experiments on H2 and D2 + Ru(0001) exhibit not only a similar minimum barrier height for the reaction, but also a similar "energetic corrugation" of the PES, which can be operationally defined as the difference between the minimum barrier height and the barrier height obtained for another impact site and orientation of the molecule (see Fig.2) 44. The energetic corrugation of the PES is correlated with the "width" (inverse steepness) of the reaction probability vs. incidence energy curve. The above result suggests that monitoring the position of a DF in a plot of minimum barrier height vs. energetic corrugation (like Fig.2) while testing different DFs may guide the search for an SRP DF.


9


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 10 of 45

Figure 2. Energetic corrugation (operationally defined as the difference between the hcp and top site barrier heights) versus minimum barrier height of the PESs constructed with several DFs for H2 + Ru(0001) (Ref.44). The DFs are grouped (symbols) according to the type correlation functional used. The DFs providing good agreement with sticking experiments fall inside the red circle. Adapted with permission from [M. Wijzenbroek and G. J. Kroes, Journal of Chemical Physics, 140, 084702 (2014)]. Copyright 2014, AIP Publishing LLC. Meanwhile, research on H2-metal systems has established that the decision on whether or not to include phonons in the dynamical model to compute a specific observable should be taken with care. Molecular beam sticking experiments on activated dissociation are usually performed for a low surface temperature (room temperature or lower), and a comparison of Ab Initio Molecular Dynamics (AIMD) and static surface calculations has shown that under these conditions surface motion can be safely neglected (see fig.S1 of Ref.45). However, calculations on H2 + Cu(111) suggest that surface motion should be modeled when computing the so-called rotational quadrupole alignment parameter45, which provides information on whether specific orientations are preferred for reaction to occur, and when modeling vibrational excitation46.


10

Page 11 of 45

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


Interestingly, calculations on H2 dissociation on hot Cu(111)41,

47

and hot Cu(100)

48

surfaces

have revealed that the thermal expansion of the surface may have an important effect on the reaction. Also, the size of the effect may differ substantially among low index faces of the same metal, depending on which metal face exhibits the largest change in the distance between the top two surface layers with temperature

48

. This needs to be taken into account when testing

candidate SRP DFs fitted to molecular beam sticking experiments on cold surfaces by assessing their performance for observables extracted from associative desorption experiments done on hot surfaces. The observed effects of expansion also pose extra challenges to scientists aiming to develop DFs that accurately describe both chemical reactivity and bulk properties of metals, which remains difficult11, 49-50.


11


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 12 of 45

Figure 3. The dissociative sticking probability S0(Ei) is shown for H2 + Cu(110) for different angles of incidence ΘI (Ref.51). Full red and open black circles represent results obtained with and without consideration of ehp excitation, respectively. Reprinted figure with permission from [Juaristi, J. I.; Alducin, M.; Díez Muiño, R.; Busnengo, H. F.; Salin, A. Phys.Rev.Lett. 100, 116102, 2008]. Copyright (2008) by The American Physical Society. Calculations looking directly19,

51-52

or indirectly53 at the effect of ehp excitation on H2

dissociation at metal surfaces have typically found non-adiabatic effects to be minor. Nevertheless, a close inspection of results for H2 + Cu(110)51 (Fig.3) suggests that non-adiabatic effects are no longer negligible when chemical accuracy is sought. Specifically, for normal incidence the computed reaction probability curve shifts to higher incidence energies by up to 0.85 kcal/mol for H2, for reaction probabilities up to 0.4. One problem is that 0.85 kcal/mol is not negligible on the scale of chemical accuracy (1 kcal/mol). Another problem is that the way to compute the friction coefficients used in assessing the effect of ehp excitation in calculations using molecular dynamics with electronic friction (MDEF) is currently a topic of heated debate29, 52, 54-56

. The calculations used to produce Fig.3 where done using an independent atom

approximation to electronic friction, i.e., the friction force experienced by H2 is simply taken from the friction forces exerted on the H atoms considered separately51. Calculations on H2 + Cu(111)54 and Ru(0001)52 with tensorial friction theory, which takes the molecular electronic structure of H2 interacting with the surface into account when computing friction coefficients, find friction coefficients for motion along the H-H stretch coordinate that are three times larger at the transition state than the independent atom approximation would suggest. Fortunately, for H2 + Cu(111)15, 31 and Cu(100)36 the SRP DF would seem to err towards the "right side", i.e., adding the effect of friction would enhance the agreement with experiment if the effect is of the


12

Page 13 of 45

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


size suggested by Fig.3. However, the field would substantially benefit from the development of a reliable theory that would enable the accurate and efficient calculation of tensorial friction coefficients. On closing, we note that while ehp effects on most observables associated with H2 dissociation are minor, calculations suggest ehp excitation to be the dominant channel for energy dissipation of hot H atoms to metal surfaces57-58. Reactions of N2. Another class of reactions of closed-shell molecules interacting with metal surfaces is presented by N2-metal surface systems. Attempts to develop SRP DFs for such systems benefit from the fact that a diatomic molecule is selected with just six degrees of freedom, but problems with the dynamical treatment of surface phonons become more severe due to the larger mass of N2 compared to H2. This problem can now be addressed by using AIMD, which now allows the calculation of statistically converged reaction probabilities45,

59

while taking surface motion into account. The first application of AIMD to the benchmark problem N2 + W(110)60 lead to two important results (Fig.4). The first result is that comparison to static surface calculations shows that inclusion of surface motion leads to a substantial increase of the reaction probabilities at incidence energies smaller than 2 eV. This suggests that, in attempts to develop SRP DFs for N2-metal surface systems, phonons should be taken into account already at the stage when the performance of the DF is evaluated in the dynamics calculation. AIMD calculations are computationally expensive, so that it should be important to use efficient search strategies, like the one suggested by the work on H2 + Ru(0001) (see above). Earlier work had already suggested that the treatment of phonons should be essential to reproduce specific observables related to the scattering of N2 from W(110) back to the gas phase61. The second result is that treating the phonons does not yet seem to solve the problem that the use of neither the PW918 (or, almost equivalently9, the PBE functional9) nor the RPBE


13


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 14 of 45

functional10 is capable of reproducing measured62-63 sticking probabilities for normal and offnormal incidence64. Specifically, AIMD calculations with neither the PBE, nor the RPBE functional are capable of reproducing the experimental results for normal incidence (Fig.4)60.

Figure 4. The reaction probability is shown as a function of the collision energy, for normal incidence, for N2 + W(110). AIMD results for the "moving surface" (AIMD, diamonds, Ref.60 are compared to experimental data (Refs.62-63) (blue squares) measured for Ts = 800 K, and to previous static surface calculations (Ref.64). The AIMD-DF and AIMD-IF results are not relevant to the present discussion. The upper panel shows PBE-AIMD and PW91 static surface results, the lower panel only RPBE results. Reprinted with permission from [Nattino, F.; Costanzo, F.; Kroes, G. J. N2 J.Chem.Phys. 142, 104702, 2015]. Copyright (2015), AIP Publishing LLC.


14

Page 15 of 45

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


It is clearly desirable to develop an SRP DF for N2 + W(110), in order to be able to enter chemically accurate data for this system in the database. In exploring DFs for this system, one obvious idea is to test DFs containing non-local correlation, as has already been done in static surface calculations by Martin-Gondre et al.65. Developing an SRP DF for N2 + W(110) may be particularly challenging because the sticking is affected by molecular chemisorption wells, entrance barriers to these wells, and exit barriers to dissociative chemisorption60, 64. Achieving agreement with sticking experiments will require a DF that accurately describes the entrance barriers, the molecular chemisorption well depths, and the exit barriers. This represents a big challenge, as the finding that functionals that describe molecular binding energies well may not excel at the accurate description of reaction barriers for gas phase reactions66 suggests that it may be difficult to achieve a simultaneous accurate description of molecular chemisorption and reaction barriers. A problem with N2 + W(110) is that there is a substantial difference between the most recent results for sticking at normal incidence63 and older results62, which are also available for off-normal incidence62, which has not been explained in the literature. New and accurate sticking measurements employing well defined N2 beams might therefore provide a very useful benchmark. As discussed in Ref.29, experiments on scattering are available that would allow the validation of an SRP DF obtained from fitting to molecular beam sticking experiments. MDEF calculations suggest that ehp excitation has only a minor effect on dissociative51 and non-dissociative61 scattering of N2 from W(110), so that ehp excitation can be most likely neglected in the search of an SRP DF for this system. Another benchmark system for which both molecular beam sticking experiments and energy transfer scattering experiments are available is N2 + Ru(0001)29. Quasi-classical calculations modeling all six degrees of freedom (6D) of the molecule using the static surface approximation


15


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 16 of 45

and a PES computed with the RPBE10 functional have provided a quite reasonable description of the dissociative chemisorption67: the calculations reproduced the finding of a reaction probability of only a percent or so at a collision energy equal to roughly twice the height of the dissociation barrier. However, 6D calculations employing the same PES68 have totally failed at describing the vibrational distribution of N2 in associative desorption69 (see Fig.5), in agreement with earlier calculations of lower dimensionality69. These results68-69 and MDEF calculations on N2 + Ru(0001)

19

suggest that ehp excitation should be taken into account in dynamics calculations

aimed at developing an SRP DF for this system. The N2 + W(110) results60-61 suggest that the phonons should also be incorporated in the dynamics for N2 + Ru(0001). The best approach would probably employ the Ab Initio Molecular Dynamics with Electronic Friction (AIMDEF) method that was recently introduced, which allows a simultaneous description of the effect of surface atom motion and ehp excitation (through friction coefficients)57.

Figure 5. The flux D(ν,Ts) of N2 desorbing from Ru(0001) is shown as a function of the vibrational quantum number, comparing theoretical (Ref.68) to experimental results (Ref.69).


16

Page 17 of 45

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


Reprinted from Chem.Phys.Lett. 434, Díaz, C.; Perrier, A.; Kroes, G. J., Associative Desorption of N2 from Ru(0001): A Computational Study, pp. 231-236, Copyright (2007), with permission from Elsevier. Reactions of polyatomic molecules. Treating reactions of polyatomic molecules on metal surfaces carries with it the additional challenge of treating an increased amount of molecular degrees of freedom with sufficient accuracy to allow the extraction of chemically accurate reaction barriers for these systems. However, these systems also exhibit a wealth of additional phenomena that are of interest to physical chemistry, such as mode-selectivity (the efficiency of exciting a specific mode for promoting reaction depends on which mode is excited), bondselectivity, and orientational effects, as illustrated by experiments on dissociative chemisorption of methane70-73. A start has been made with developing an SRP DF for CH4 + Pt(111), through a comparison of AIMD calculations with molecular beam sticking experiments on hot CHD3 and ν1=1 CHD3, in which the CH-stretch mode is pre-excited with one quantum74. The preliminary results (Fig.6) show that the PBE functional underestimates the reaction barrier by about 0.1 eV,


17


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 18 of 45

Figure 6. Sticking probabilities computed with the AIMD method using the PBE functional are compared with results from molecular beam experiments on CHD3 + Pt(111) (Ref.74). Red symbols represent results for the ν1=1 excited state, the other symbols results for so-called laseroff experiments, for surface temperatures of 120 and 500 K. Reprinted from Ref. 74. Copyright (2014) American Chemical Society. which can be used in subsequent explorations of other candidate SRP DFs for this system. Note that the AIMD method allows the description of motion in all molecular degrees of freedom as well as motion in the surface atoms. Also, with the use of CHD3 artificial energy transfer from a pre-excited CH stretch to the other vibrations of the molecule (while the molecule flies through the gas phase) may be avoided on the time-scale of the collision in the classical dynamics74-75. An artifact of classical dynamics is that energy put in a particular vibrational mode is not constrained to stay in that mode even in the isolated molecule. However, this artificial intramolecular vibrational redistribution may be made slow by putting the energy in a mode with a high frequency that is distinctly different from the frequencies of the other modes75. AIMD calculations can also provide information on which dynamical approximations are likely to work well in QD simulations of the reaction dynamics. The results for CHD3 + Pt(111) suggest that sudden approximations will work well for motion of the molecule parallel to the surface, as well as for the molecule's rotations74. The former information is good news for the QD calculations performed with a reaction path formalism by Jackson and co-workers76-77, but the latter is not. These QD calculations treat all molecular vibrations explicitly and make a sudden approximation to the motion along the surface, but assume the rotational motion of the molecule (which becomes librational motion near the surface) to be rotationally adiabatic. Performing QD calculations on methane dissociation should be preferable at lower collision


18

Page 19 of 45

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


energies where tunneling might contribute importantly. Such calculations might also be preferable if the aim is to predict vibrational mode-selectivity of CH4, i.e., the efficacy of preexciting a specific vibrational mode for reaction. Figure 7 shows a comparison of QD results obtained with the method of Jackson and coworkers77 with results of molecular beam sticking experiments from two groups for two different initial vibrational states of CH4 colliding with Ni(111)71, 78. There is quite reasonable agreement with experiment for the ν3=1 state, but not for the so-called laser-off state (in which CH4 is in a vibrational state distribution determined by the nozzle temperature). In principle, good agreement can be obtained by fitting an SRP DF with AIMD calculations to molecular beam sticking experiments on CHD3 + Ni(111), and then following up with dynamics calculations on CH4 + Ni(111) using a suitably chosen QD method. Probably the best candidate for performing the dynamics while including all molecular degrees of freedom without approximations to molecular motion is the Multi-Configuration Time-Dependent Hartree (MCDTH) method. This method has already been used to compute initial-state selected79 and, most recently, state-tostate80 reaction probabilities for the CH4 + H → CH3 + H2 reaction for total angular momentum


19


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 20 of 45

Figure 7. Sticking probabilities are shown for methane in its ground vibrational state, and for the four different fundamental vibrational levels, for a surface temperature of 475 K. The lines represent results of QD calculations performed with a reaction path Hamiltonian method (Ref.77), the letters represent results of experiments ("A" from Ref.71 and "R" from Ref.78). Reprinted with permission from [Jackson, B.; Nave, S. J.Chem.Phys. 2013, 138, 174705.]. Copyright (2013), AIP Publishing LLC. J=0, while including all twelve degrees of freedom in the calculations. First principles methods. It would be desirable to base dynamics calculations on reactions of molecules with metal surfaces on a first principles electronic structure method that exhibits chemical accuracy for these systems. With the functionals currently available, DFT is not up to the job, and we do not see that change in the foreseeable future. The main reason for this pessimism is that the approach taken to improving DFT for molecules (i.e., mixing in exact


20

Page 21 of 45

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


exchange in the exchange functional) is unlikely to work for metals: this leads to an increased width of the highest metal band81-82, which can lead to a worse rather than better description of the molecule surface interaction energy82. Currently two other electronic structure approaches are being tested. The first uses correlated wave function approaches with DFT embedding21. This method has been applied to the dissociative chemisorption of O2 on Al(111)21 and of H2 on an idealized Au(111) surface83. Challenges to be overcome to compute converged barrier heights of chemical accuracy include making the embedded cluster large enough to ensure convergence with respect to cluster size21, and using a correlated wave function approach that ensures chemical accuracy (so far, the ab initio methods used include CASSCF, CASPT2, and the configuration interaction singles (CIS) methods21, 83). The second method is the Quantum Monte Carlo (QMC) method, which has been applied to the dissociative chemisorption of H2 on Mg(0001)84 and reactions of CO on Cu(100)85. Both of the two above methods will probably be too computationally expensive to map out PESs for molecule-metal surface reactions in the foreseeable future. However, if they could be demonstrated to possess chemical accuracy for the systems of interest, they could also be used to base the SRP-DFT approach on first principles29. For instance, the high accuracy method could be used to compute the molecule-surface interaction for a few representative geometries (for example, one asymptotic geometry, the minimum barrier geometry, and a few barrier geometries for other impact sites and molecular orientations). Next, the SRP DF could be fit to these high accuracy data, and the SRP DF could then be used to map out a PES or to perform AIMD calculations. Alternative experiments for validation. After addressing the challenges that one has to meet to derive reaction barrier heights with an approach in which dynamics calculations test electronic structure methods by comparison to molecular beam experiments, it is worthwhile to briefly


21


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 22 of 45

consider other avenues to obtaining entries for our database. In one potentially useful approach isothermal rate constants would be measured for dissociative chemisorption with appropriate “poisoning” of surface defects to measure reactivity on low index terraces86-87. Transition state theory (TST)88 instead of dynamics could then be used to validate electronic structure methods. With TST, an accurate treatment of polyatomic molecules and of phonons might be less problematic than with (quantum) dynamics. A major disadvantage of this approach is that TST cannot handle electronically non-adiabatic reactions88, ruling out its application to reactions affected by electron-hole pair excitation. Another disadvantage is that the type of experiment mentioned is hard to perform: it may be hard to ascertain that all the defects are poisoned (for instance, the steps fully decorated) without spillover to the terraces of which one wants to establish the reactivity86-87. Finally, TST has to be applied to molecule-surface reactions with care7: it may be necessary to find a dividing surface for which the reactive flux is minimized (variational transition state theory)88 rather than just consider the reaction barrier height with conventional TST, it will probably at least be necessary to accurately calculate vibrational entropy factors7, and it may be necessary to compute zero-point energy and/or tunneling corrections88, or even to use a version of quantum TST88. For all these reasons, we currently favor the dynamics approach with comparison to molecular beam experiments. Finally, another approach would make use of experiments in which defects have been deliberately introduced and would swamp contributions from other defects to the reactivity, again using TST for validation. This could involve experiments measuring reaction rates on stepped surfaces with high step densities, or on an inert surface with metal ad-atoms on it to drastically enhance its reactivity (for instance, H2 + Pd/Cu(111)89). A drawback of this approach


22

Page 23 of 45

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


is that the size of the system needed to model the experiment might become too large to allow the testing of potentially accurate, but computationally expensive electronic structure methods. The database. Ultimately the two electronic structure methods discussed above and other new methods will have to be benchmarked on accurate data describing the reactivity of molecules on metal surfaces. We anticipate that the semi-empirical version of SRP-DFT discussed in this paper will continue to be used in the near future to obtain the data that are required for this purpose. We also take the liberty to make a start with the introduction of the database of chemically accurate barriers for dissociation reactions of molecules on metal surfaces (Table 1). In compliance with the naming convention used by Truhlar and co-workers, we name the database BHMMS2, i.e., with an acronym representing the property considered (Barrier Heights for Molecule-Metal Surface reactions) followed by the number of systems for which we claim chemically accurate barriers are now available (sadly enough, only 2 at this time). We suggest that efforts be undertaken to extend the database with more accurate data, including more data for H2-metal systems such as H2 + Ru(0001) and Pt(111), with data for N2-metal systems like N2 + W(110) and Ru(0001), and for polyatomic molecules reacting on metal surfaces, such as CH4 + Pt(111) and Ni(111), but also H2O + Ni(111)27. Table 1. Chemically accurate barriers for dissociation reactions of molecules on metal surfaces. moleculesurface distance (Å)

length geometry dissociating bond (Å)

Refs. for details

H2 + Cu(111) 60.6

1.164

1.032

bridge-to-hollow

a

H2 + Cu(100) 71.4

1.005

1.228

bridge-to-hollow

b

system

barrier height (kJ/mol)

a. Ref.15 b. Ref. 36 AUTHOR INFORMATION


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 45

Corresponding Author *Email: [email protected] Notes The author declares no competing financial interests. Biography Dr. Geert-Jan Kroes obtained his Ph.D. in Chemistry in 1990, working with Prof. R.P.H. Rettschnick. He next worked as a post-doc with David Clary, with Marc van Hemert and Ewine van Dishoeck, and with Evert-Jan Baerends. At Leiden he became Assistant Professor in 1998, and Full Professor in 2003. ACKNOWLEDGMENT This work was supported by the European Research Council through an ERC-2013 advanced Grant No. 338580. Thanks are due to Prof. J.W. Niemantsverdriet for allowing the use of his photo of a catalytic plant (© J.W. Niemantsverdriet) in the TOC graphic with this paper. The author thanks his (former) graduate students F. Nattino, M. Wijzenbroek, M.F. Somers, and G.P. Krishnamohan, and his former post-docs C. Díaz, R.A. Olsen, M. Bonfanti, F. Costanzo, J.K. Vincent, and E. Pijper for their contributions to the work of the group, several examples of which are cited here.

REFERENCES


24

Page 25 of 45

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


(1)

Dong, W. R.; Xiao, C. L.; Wang, T.; Dai, D. X.; Yang, X. M.; Zhang, D. H. Transition-

State Spectroscopy of Partial Wave Resonances in the F + HD Reaction. Science 2010, 327, 1501-1502. (2)

Wang, X. G.; Dong, W. R.; Xiao, C. L.; Che, L.; Ren, Z. F.; Dai, D. X.; Wang, X. Y.;

Casavecchia, P.; Yang, X. M.; Jiang, B., et al. The Extent of Non-Born-Oppenheimer Coupling in the Reaction of Cl(2P) with para-H2. Science 2008, 322, 573-576. (3)

Xiao, C. L.; Xu, X.; Liu, S.; Wang, T.; Dong, W. R.; Yang, T. G.; Sun, Z. G.; Dai, D. X.;

Xu, X.; Zhang, D. H., et al. Experimental and Theoretical Differential Cross Sections for a FourAtom Reaction: HD+OH -> H2O+D. Science 2011, 333, 440-442. (4)

Peverati, R.; Truhlar, D. G. Quest for a Universal Density Functional: The Accuracy of

Density Functionals Accross a Broad Spectrum of Databases in Chemistry and Physics. Phil.Trans. R. Soc. A 2014, 372, 20120476. (5)

Chorkendorff, I.; Niemantsverdriet, J. W. Concepts of Modern Catalysis and Kinetics.

Student Edition ed.; Wiley-VCH Verlag GMBH & Co.: Weinheim, 2003; p 452. (6)

Medford, A. J.; Wellendorff, J.; Vojdovic, A.; Studt, F.; Abild-Pedersen, F.; Jacobsen, K.

W.; Bligaard, T.; Nørskov, J. Assessing the Reliability of Calculated Catalytic Ammonia Synthesis Rates. Science 2014, 345, 197-200. (7)

Sabbe, M. K.; Reyniers, M. F.; Reuter, K. First-Principles Kinetic Modeling in

Heterogeneous Catalysis: An Industrial Perspective on Best-Practice, Gaps, and Needs. Catal.Sci.Technol. 2012, 2, 2010-2024.


25


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

(8)

Page 26 of 45

Perdew, J. P.; Chevary, J. A.; Vosko, S. H.; Jackson, K. A.; Pederson, M. R.; Singh, D.

J.; Fiolhais, C. Atoms, Molecules, Solids, and Surfaces: Applications of the Generalized Gradient Approximation for Exchange and Correlation. Phys.Rev.B 1992, 46, 6671-6687. (9)

Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made

Simple. Phys.Rev.Lett. 1996, 77, 3865-3868. (10) Hammer, B.; Hansen, L. B.; Nørskov, J. K. Improved Adsorption Energetics within Density-Functional Theory Using Revised Perdew-Burke-Ernzerhof Functionals. Phys.Rev.B. 1999, 59, 7413-7421. (11) Perdew, J. P.; Ruzsinszky, A.; Csonka, G. I.; Constantin, L. A.; Sun, J. W. Workhorse Semilocal Density Functional for Condensed Matter Physics and Quantum Chemistry. Phys.Rev.Lett. 2009, 103, 026403. (12) Klippenstein, S. J.; Pande, V. S.; Truhlar, D. G. Chemical Kinetics and Mechanisms of Complex Systems: A Perspective on Recent Theoretical Advances. J. Am. Chem. Soc. 2014, 136, 528-546. (13) Dahl, S.; Logadottir, A.; Egeberg, R. C.; Larsen, J. H.; Chorkendorff, I.; Törnqvist, E.; Nørskov, J. K. Role of Steps in N2 Activation on Ru(0001). Phys. Rev. Lett. 1999, 83, 18141817. (14) Zambelli, T.; Wintterlin, J.; Trost, J.; Ertl, G. Identification of the ''Active Sites'' of a Surface-Catalyzed Reaction. Science 1996, 273, 1688-1690.


26

Page 27 of 45

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


(15) Díaz, C.; Pijper, E.; Olsen, R. A.; Busnengo, H. F.; Auerbach, D. J.; Kroes, G. J. Chemically Accurate Simulation of a Prototypical Surface Reaction: H2 Dissociation on Cu(111). Science 2009, 326, 832-834. (16) Salin, A. Theoretical Study of Hydrogen Dissociative Adsorption on the Cu(110) Surface. J.Chem.Phys. 2006, 124, 104704. (17) Karikorpi, M.; Holloway, S.; Henriksen, N.; Nørskov, J. K. Dynamics of MoleculeSurface Interactions. Surf.Sci. 1987, 179, L41-L48. (18) Nave, S.; Jackson, B. Methane Dissociation on Ni(111): The Role of Lattice Reconstruction. Phys.Rev.Lett. 2007, 98, 173003. (19) Luntz, A. C.; Persson, M. How Adiabatic Is Activated Adsorption/Associative Desorption. J.Chem.Phys. 2005, 123, 074704. (20) White, J. D.; Chen, J.; Matsiev, D.; Auerbach, D. J.; Wodtke, A. M. Conversion of LargeAmplitude Vibration to Electron Excitation at a Metal Surface. Nature 2005, 433, 503-505. (21) Libisch, F.; Huang, C.; Liao, P. L.; Pavone, M.; Carter, E. A. Origin of the Energy Barrier to Chemical Reactions of O2 on Al(111): Evidence for Charge Transfer, Not Spin Selection. Phys.Rev.Lett. 2012, 109, 198303. (22) Behler, J.; Delley, B.; Lorenz, S.; Reuter, K.; Scheffler, M. Dissociation of O2 at Al(111): The Role of Spin Selection Rules. Phys.Rev.Lett. 2005, 94, 036104. (23) Baule, B. Theoretische Behandlung Der Erscheinungen in Verdünnten Gasen.

Ann.

Phys. (Berlin) 1914, 349, 145-176.


27


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 28 of 45

(24) Gross, A. Theoretical Surface Science; a Microscopic Perspective. Springer: Berlin, 2003; p 275. (25) Golibrzuch, K.; Bartels, N.; Auerbach, D. J.; Wodtke, A. M. The Dynamics of Molecular Interactions and Chemical Reactions at Metal Surfaces: Testing the Foundations of Theory. Annu.Rev.Phys.Chem. 2015, 66, 399-425. (26) Nave, S.; Jackson, B. Vibrational Mode-Selective Chemistry: Methane Dissociation on Ni(100). Phys.Rev.B 2010, 81, 233408. (27) Hundt, P. M.; Jiang, B.; van Reijzen, M. E.; Guo, H.; Beck, R. D. Vibrationally Promoted Dissociation of Water on Ni(111). Science 2014, 344, 504-507. (28) Kroes, G. J. Frontiers in Surface Scattering Simulations. Science 2008, 321, 794-797. (29) Kroes, G. J. Towards Chemically Accurate Simulation of Molecule-Surface Reactions. Phys.Chem.Chem.Phys. 2012, 14, 14966-14981. (30) Kroes, G. J.; Somers, M. F. Six-Dimensional Quantum Dynamics of Dissociative Chemisorption of H2 on Metal Surfaces. J. Theor.Comp.Chem. 2005, 4, 493-581. (31) Díaz, C.; Olsen, R. A.; Auerbach, D. J.; Kroes, G. J. Six Dimensional Dynamics Study of Reactive and Non Reactive Scattering of H2 from Cu(111) Using a Chemically Accurate Potential Energy Surface. Phys.Chem.Chem.Phys. 2010, 12, 6499-6519. (32) Chuang, Y. Y.; Radhakrishnan, M. L.; Fast, P. L.; Cramer, C. J.; Truhlar, D. G. Direct Dynamics for Free Radical Kinetics in Solution: Solvent Effect on the Rate Constant for the Reaction of Methanol with Atomic Hydrogen. J.Phys.Chem.A 1999, 103, 4893-4909.


28

Page 29 of 45

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


(33) Nattino, F.; Genova, A.; Guijt, M.; Muzas, A. S.; Díaz, C.; Auerbach, D. J.; Kroes, G. J. Dissociation and Recombination of D2 on Cu(111): Ab Initio Molecular Dynamics Calculations and Improved Analysis of Desorption Experiments. J.Chem.Phys. 2014, 141, 124705. (34) Berger, H. F.; Leisch, M.; Winkler, A.; Rendulic, K. D. A Search for Vibrational Contributions to the Activated Adsorption of H2 on Copper. Chem.Phys.Lett. 1990, 175, 425428. (35) Rettner, C. T.; Michelsen, H. A.; Auerbach, D. J. Quantum State Specific Dynamics of the Dissociative Adsorption and Associative Desorption of H2 at a Cu(111) Surface. J.Chem.Phys. 1995, 102, 4625-4641. (36) Sementa, L.; Wijzenbroek, M.; van Kolck, B. J.; Somers, M. F.; Al-Halabi, A.; Busnengo, H. F.; Olsen, R. A.; Kroes, G. J.; Rutkowski, M.; Thewes, C., et al. Reactive Scattering of H2 from Cu(100): Comparison of Dynamics Calculations Based on the Specific Reaction Parameter Approach to Density Functional Theory with Experiment. J.Chem.Phys. 2013, 138, 044708. (37) Anger, G.; Winkler, A.; Rendulic, K. D. Adsorption and Desorption Kinetics in the Systems H2/Cu(111), H2/Cu(110) and H2/Cu(100). Surf.Sci. 1989, 220, 1-17. (38) Kresse, G. Dissociation and Sticking of H2 on the Ni(111), (100), and (110) Substrate. Phys.Rev.B 2000, 62, 8295-8305. (39) Nieto, P.; Farías, D.; Miranda, R.; Luppi, M.; Baerends, E. J.; Somers, M. F.; van der Niet, M. J. T. C.; Olsen, R. A.; Kroes, G. J. Diffractive and Reactive Scattering of H2 from Ru(0001): Experimental and Theoretical Study. Phys.Chem.Chem.Phys. 2011, 13, 8583-8597.


29


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 30 of 45

(40) Groot, I. M. N.; Ueta, H.; van der Niet, M. J. T. C.; Kleyn, A. W.; Juurlink, L. B. F. Supersonic Molecular Beam Studies of Dissociative Adsorption of H2 on Ru(0001). J. Chem. Phys. 2007, 127, 244701. (41) Wijzenbroek, M.; Somers, M. F. Static Surface Temperature Effects on the Dissociation of H2 and D2 on Cu(111). J.Chem.Phys. 2012, 137, 054703. (42) Dion, M.; Rydberg, H.; Schröder, E.; Langreth, D. C.; Lundqvist, B. I. Van Der Waals Density Functional for General Geometries. Phys.Rev.Lett. 2004, 92, 246401. (43) Lee, K.; Murray, E. D.; Kong, L. Z.; Lundqvist, B. I.; Langreth, D. C. Higher-Accuracy Van Der Waals Density Functional. Phys.Rev.B 2010, 82, 081101R. (44) Wijzenbroek, M.; Kroes, G. J. The Effect of the Exchange-Correlation Functional on H2 Dissociation on Ru(0001). J.Chem.Phys. 2014, 140, 084702. (45) Nattino, F.; Díaz, C.; Jackson, B.; Kroes, G. J. Effect of Surface Motion on the Rotational Quadrupole Alignment Parameter of D2 Reacting on Cu(111).

Phys.Rev.Lett. 2012, 108,

236104. (46) Kroes, G. J.; Díaz, C.; Pijper, E.; Olsen, R. A.; Auerbach, D. J. Apparent Failure of the Born-Oppenheimer Static Surface Model for Vibrational Excitation of Molecular Hydrogen on Copper. Proc. Natl. Acad. Sci. U.S.A 2010, 107, 20881-20886. (47) Mondal, A.; Wijzenbroek, M.; Bonfanti, M.; Díaz, C.; Kroes, G. J. Thermal Lattice Expansion Effect on Reactive Scattering of H2 from Cu(111) at Ts = 925 K. J. Phys. Chem. A 2013, 117, 8770-8781.


30

Page 31 of 45

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


(48) Marashdeh, A.; Casole, S.; Sementa, L.; Zacharias, H.; Kroes, G. J. Surface Temperature Effects on Dissociative Chemisorption of H2 on Cu(100). J.Phys.Chem.C 2013, 117, 8851-8863. (49) Schimka, L.; Harl, J.; Stroppa, A.; Grüneis, A.; Marsman, M.; Mittendorfer, F.; Kresse, G. Accurate Surface and Adsorption Energies from Many-Body Perturbation Theory. Nature Mater. 2010, 9, 741-744. (50) Peverati, R.; Truhlar, D. G. M11-L: A Local Density Functional That Provides Improved Accuracy for Electronic Structure Calculations in Chemistry and Physics. J.Phys.Chem.Lett. 2012, 3, 117-124. (51) Juaristi, J. I.; Alducin, M.; Díez Muiño, R.; Busnengo, H. F.; Salin, A. Role of ElectronHole Pair Excitations in the Dissociative Adsorption of Diatomic Molecules on Metal Surfaces. Phys.Rev.Lett. 2008, 100, 116102. (52) Füchsel, G.; Schimka, S.; Saalfrank, P. On the Role of Electronic Friction for Dissociative Adsorption and Scattering of Hydrogen Molecules at a Ru(0001) Surface. J. Phys. Chem. A 2013, 117, 8761-8769. (53) Nieto, P.; Pijper, E.; Barredo, D.; Laurent, G.; Olsen, R. A.; Baerends, E. J.; Kroes, G. J.; Farías, D. Reactive and Non-Reactive Scattering of H2 from a Metal Surface: The Electronically Adiabatic Picture. Science 2006, 312, 86-89. (54) Luntz, A. C.; Makkonen, I.; Persson, M.; Holloway, S.; Bird, D. M.; Mizielinski, M. S. Comment on "Role of Electron-Hole Pair Excitations in the Dissociative Adsorption of Diatomic Molecules on Metal Surfaces". Phys.Rev.Lett. 2009, 102, 109601.


31


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 32 of 45

(55) Juaristi, J. I.; Alducin, M.; Díez Muiño, R.; Busnengo, H. F.; Salin, A. Comment on "Role of Electron-Hole Pair Excitations in the Dissociative Adsorption of Diatomic Molecules on Metal Surfaces'' Juaristi et al. Reply. Phys.Rev.Lett. 2009, 102, 109602. (56) Grotemeyer, M.; Pehlke, E. Electronic Energy Dissipation During Scattering of Vibrationally Excited Molecules at Metal Surfaces: Ab Initio Simulations for Hcl/Al(111). Phys.Rev.Lett. 2014, 112, 043201. (57) Blanco-Rey, M.; Juaristi, J. I.; Díez Muiño, R.; Busnengo, H. F.; Kroes, G. J.; Alducin, M. Electronic Friction Dominates Hydrogen Hot-Atom Relaxation on Pd(100). Phys.Rev.Lett. 2014, 112, 103203. (58) Pavanello, M.; Auerbach, D. J.; Wodtke, A. M.; Blanco-Rey, M.; Alducin, M.; Kroes, G. J. Adiabatic Energy Loss in Hyperthermal H Atom Collisions with Cu and Au: A Basis for Testing the Importance of Nonadiabatic Energy Loss. J.Phys.Chem.Lett. 2013, 4, 3735-3740. (59) Groß, A.; Dianat, A. Hydrogen Dissociation Dynamics on Precovered Pd Surfaces: Langmuir Is Still Right. Phys.Rev.Lett. 2007, 98, 206107. (60) Nattino, F.; Costanzo, F.; Kroes, G. J. N2 Dissociation on W(110): An Ab Initio Molecular Dynamics Study on the Effect of Phonons. J.Chem.Phys. 2015, 142, 104702. (61) Martin-Gondre, L.; Alducin, M.; Bocan, G. A.; Díez Muiño, R.; Juaristi, J. I. Competition between Electron and Phonon Excitations in the Scattering of Nitrogen Atoms and Molecules Off Tungsten and Silver Metal Surfaces. Phys.Rev.Lett. 2012, 108, 096101.


32

Page 33 of 45

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


(62) Pfnür, H. E.; Rettner, C. T.; Lee, J.; Madix, R. J.; Auerbach, D. J. Dynamics of the Activated Dissociative Chemisorption of N2 on W(110) - a Molecular-Beam Study. J.Chem.Phys. 1986, 85, 7452-7466. (63) Rettner, C. T.; Schweizer, E. K.; Stein, H. Dynamics of the Chemisorption of N2 on W(100) - Precursor-Mediated and Activated Dissociation. J.Chem.Phys. 1990, 93, 1442-1454. (64) Bocan, G. A.; Diéz Muiño, R.; Alducin, M.; Busnengo, H. F.; Salin, A. The Role of Exchange-Correlation Functionals in the Potential Energy Surface and Dynamics of N2 Dissociation on W Surfaces. J.Chem.Phys. 2008, 128, 154704. (65) Martin-Gondre, L.; Juaristi, J. I.; Blanco-Rey, M.; Díez Muiño, R.; Alducin, M. Influence of the Van der Waals Interaction in the Dissociation Dynamics of N2 on W(110) from First Principles. J.Chem.Phys. 2015, 142, 074704. (66) Zheng, J. J.; Zhao, Y.; Truhlar, D. G. The DBH24/08 Database and Its Use to Assess Electronic Structure Model Chemistries for Chemical Reaction Barrier Heights. J.Chem.Theory Comp. 2009, 5, 808-821. (67) Díaz, C.; Vincent, J. K.; Krishnamohan, G. P.; Olsen, R. A.; Kroes, G. J.; Honkala, K.; Nørskov, J. K. Multidimensional Effects on Dissociation of N2 on Ru(0001). Phys.Rev.Lett. 2006, 96, 096102. (68) Díaz, C.; Perrier, A.; Kroes, G. J. Associative Desorption of N2 from Ru(0001): A Computational Study. Chem.Phys.Lett. 2007, 434, 231-236.


33


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 34 of 45

(69) Diekhöner, L.; Hornekaer, L.; Mortensen, H.; Jensen, E.; Baurichter, A.; Petrunin, V. V.; Luntz, A. C. Indirect Evidence for Strong Nonadiabatic Coupling in N2 Associative Desorption from and Dissociative Adsorption on Ru(0001). J.Chem.Phys. 2002, 117, 5018-5030. (70) Beck, R. D.; Maroni, P.; Papageorgopoulos, D. C.; Dang, T. T.; Schmid, M. P.; Rizzo, T. R. Vibrational Mode-Specific Reaction of Methane on a Nickel Surface. Science 2003, 302, 98100. (71) Smith, R. R.; Killelea, D. R.; DelSesto, D. F.; Utz, A. L. Preference for Vibrational over Translational Energy in a Gas-Surface Reaction. Science 2004, 304, 992-995. (72) Killelea, D. R.; Campbell, V. L.; Shuman, N. S.; Utz, A. L. Bond-Selective Control of a Heterogeneously Catalyzed Reaction. Science 2008, 319, 790-793. (73) Yoder, B. L.; Bisson, R.; Beck, R. D. Steric Effects in the Chemisorption of Vibrationally Excited Methane on Ni(100). Science 2010, 329, 553-556. (74) Nattino, F.; Ueta, H.; Chadwick, H.; van Reijzen, M. E.; Beck, R. D.; Jackson, B.; van Hemert, M. C.; Kroes, G. J. Ab Initio Molecular Dynamics Calculations Versus Quantum-StateResolved Experiments on CHD3 + Pt(111):

New Insights into a Prototypical Gas-Surface

Reaction. J.Phys.Chem.Lett. 2014, 5, 1294-1299. (75) Czakó, G.; Bowman, J. M. Quasiclassical Trajectory Calculations of Correlated Product Distributions for the F + CHD3( ν1=0,1) Reactions Using an Ab Initio Potential Energy Surface. J.Chem.Phys. 2009, 131, 244302. (76) Jackson, B.; Nave, S. The Dissociative Chemisorption of Methane on Ni(100): Reaction Path Description of Mode-Selective Chemistry. J.Chem.Phys. 2011, 135, 114701.


34

Page 35 of 45

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


(77) Jackson, B.; Nave, S. The Dissociative Chemisorption of Methane on Ni(111): The Effects of Molecular Vibration and Lattice Motion. J.Chem.Phys. 2013, 138, 174705. (78) Bisson, R.; Sacchi, M.; Dang, T. T.; Yoder, B.; Maroni, P.; Beck, R. D. State-Resolved Reactivity of CH4(2 ν3) on Pt(111) and Ni(111): Effects of Barrier Height and Transition State Location. J.Phys.Chem.A 2007, 111, 12679-12683. (79) Schiffel, G.; Manthe, U. A Transition State View on Reactive Scattering: Initial StateSelected Reaction Probabilities for the H + CH4 -> H2 + CH3 Reaction Studied in Full Dimensionality. J.Chem.Phys. 2010, 133, 174124. (80) Welsch, R.; Manthe, U. Loss of Memory in H + CH4 -> H2 + CH3 State-to-State Reactive Scattering. J.Phys.Chem.Lett. 2015, 6, 338-342. (81) Paier, J.; Marsman, M.; Hummer, K.; Kresse, G.; Gerber, I. C.; Ángyán, J. G. Screened Hybrid Density Functionals Applied to Solids. J.Chem.Phys. 2006, 124, 154709. (82) Stroppa, A.; Termentzidis, K.; Paier, J.; Kresse, G.; Hafner, J. CO Adsorption on Metal Surfaces: A Hybrid Functional Study with Plane-Wave Basis Set. Phys. Rev. B 2007, 76, 195440. (83) Libisch, F.; Cheng, J.; Carter, E. A. Electron-Transfer-Induced Dissociation of H2 on Gold Nanoparticles: Excited-State Potential Energy Surfaces via Embedded Correlated Wavefunction Theory. Z. Phys. Chem. 2013, 227, 1455-1466. (84) Pozzo, M.; Alfè, D. Hydrogen Dissociation on Mg(0001) Studied Via Quantum Monte Carlo Calculations. Phys.Rev.B 2008, 78, 245313.


35


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 36 of 45

(85) Hoggan, P. E. Quantum Monte Carlo Simulation of Carbon Monoxide Reactivity When Adsorbed at Metal and Oxide Catalyst Surfaces: Trial Wave-Functions with Exponential Type Basis and Quasi-Exact Three-Body Correlation. Int. J. Quantum Chem. 2013, 113, 277-285. (86) Dahl, S.; Törnqvist, E.; Chorkendorff, I. Dissociative Adsorption of N2 on Ru(0001): A Surface Reaction Totally Dominated by Steps. J. Catal. 2000, 192, 381-390. (87) Abild-Petersen, F.; Lytken, O.; Engbæk, J.; Nielsen, G.; Chorkendorff, I.; Nørskov, J. K. Methane Activation on Ni(111): Effects of Poisons and Step Defects. Surf.Sci. 2005, 590, 127137. (88) Truhlar, D. G.; Garrett, B. C.; Klippenstein, S. J. Current Status of Transition-State Theory. J.Phys.Chem. 1996, 100, 12771-12800. (89) Kyriakou, G.; Davidson, E. R. M.; Peng, G.; Roling, L. T.; Singh, S.; Boucher, M. B.; Marcinkowski, M. D.; Mavrikakis, M.; Michaelides, A.; Sykes, E. C. H. Significant Quantum Effects in Hydrogen Activation. ACS Nano 2014, 8, 4827-4835.

Quotes.

1. Databases with accurate barrier heights of reactions on metal surfaces do not exist. (page 3) 2. Efforts to construct the desired database would benefit from new, well-documented molecular beam experiments on dissociative chemisorption on metal surfaces. (page 7) 3. It would be desirable to base dynamics calculations on a first principles electronic structure method that exhibits chemical accuracy for molecule-metal surface reactions. (page 20)


36

Page 37 of 45

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


4. We introduce a database of chemically accurate barriers for dissociation reactions of molecules on metal surfaces. (page 23)


37


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 ACS Paragon Plus Environment

Page 38 of 45

0.6 rPW86-vdW-DF2 Page The 39 Journal of 45 of Physical Chemistry Letters RPBE-vdW-DF2

0.55 0.5

RPBE-vdW-DF revPBE-vdW-DF

PBELDA RPBELYP

Ehcp - Etop (eV)

1 PBE:RPBE(50:50)-vdW-DF 2 0.45 PBEαLDA BLYP 3 PBE-vdW-DF2 PBELYP 0.4 4 PBE-vdW-DF RPBE PBEα:RPBE(85:15)LYP 5 0.35 PBE/PW91 PBEαLYP 6 revTPSS BP Perdew86 0.3 PW91 7 HTBS LYP PBEP PBE 8 0.25 LDA 9 PBEα Meta-GGA 0.2 10 WC vdW-DF 11 0.15 ACS Paragon Plus Environment -0.05 0 0.05 0.1 0.15 12 Etop (eV) 13


H2 / Cu(110) 0.8

=0º

i

0.6 0.4 0.2 Sticking probability S0

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

0.8

=45º

i

0.6 0.4 0.2

0.075

=60º

i

0.05 0.025 0 0

1 2 0.5 1.5 Incidence kinetic energy Ei (eV) ACS Paragon Plus Environment

Page 40 of 45

(Pfnur et al. 1986) Page The Journal 41 Exp of 45 of Physical Chemistry Letters PBE 0.6 Exp (Rettner et al. 1990) CT - static surface AIMD AIMD-DF AIMD-IF

Dissociation Probability

1 2 0.4 3 4 5 0.2 6 A 7 8 0.0 9 RPBE 100.6 11 12 130.4 14 15 160.2 17 18 ACS Paragon Plus Environment B 190.0 1.0 2.0 0.5 1.5 2.5 20 0.0 Collision energy / eV 21


2 4 6 Theory Experiment

8 10


1

0.8

0.6

0.4

0 0

0.2

D(v,Ts=1000 K)

v

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 42 of 45

0

10 Page The43 Journal of 45 of Physical Chemistry Letters -1

ν1-excited

S0

1 10 T = 120 K S Laser-off 2 3 TS = 500 K 4 10-2 5 6 Laser-off 7 -3 TS = 120 K 8 10 AIMD 9 Exp 10 ACS Paragon Plus Environment 11 -4 10 12 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 / eV 13


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 44 of 45

Page 45 of 45

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



Toward a Database of Chemically Accurate Barrier Heights for

Recommend Documents