Performance of the TPSS Functional on Predicting Core Level Binding

Article pubs.acs.org/JCTC

Performance of the TPSS Functional on Predicting Core Level Binding Energies of Main Group Elements Containing Molecules: A Good Choice for Molecules Adsorbed on Metal Surfaces Noèlia Pueyo Bellafont, Francesc Viñes, and Francesc Illas* Departament de Química Física & Institut de Química Teòrica i Computacional (IQTCUB), Universitat de Barcelona, C/Martí i Franquès 1, 08028 Barcelona, Spain S Supporting Information *

ABSTRACT: Here we explored the performance of Hartree−Fock (HF), Perdew− Burke−Ernzerhof (PBE), and Tao−Perdew−Staroverov−Scuseria (TPSS) functionals in predicting core level 1s binding energies (BEs) and BE shifts (ΔBEs) for a large set of 68 molecules containing a wide variety of functional groups for main group elements B → F and considering up to 185 core levels. A statistical analysis comparing with X-ray photoelectron spectroscopy (XPS) experiments shows that BEs estimations are very accurate, TPSS exhibiting the best performance. Considering ΔBEs, the three methods yield very similar and excellent results, with mean absolute deviations of ∼0.25 eV. When considering relativistic effects, BEs deviations drop approaching experimental values. So, the largest mean percentage deviation is of 0.25% only. Linear trends among experimental and estimated values have been found, gaining offsets with respect to ideality. By adding relativistic effects to offsets, HF and TPSS methods underestimate experimental values by solely 0.11 and 0.05 eV, respectively, well within XPS chemical precision. TPSS is posed as an excellent choice for the characterization, by XPS, of molecules on metal solid substrates, given its suitability in describing metal substrates bonds and atomic and/or molecular orbitals. Hartree−Fock (HF) theory8−10 to currently used density functional theory (DFT) based methods,11−13 especially with hybrid functionals as recently illustrated for N-containing molecules in the gas phase.14,15 Nevertheless, one must admit that prediction of BEs and especially of ΔBEs will be especially relevant and highly desirable for molecules adsorbed on metal surfaces. In fact, transition metal (TM) surfaces are ubiquitous in heterogeneous catalysis as supported active phases, but also employed in chemical resolution, nanotechnology, synthesis, and other related processes of technological interest. Unfortunately, hybrid functionals are not especially well suited for metals16,17 because of the failure to attain the exact homogeneous electron gas limit.18 In fact, recent studies19−21 show that, among various DFT methods including generalized gradient approximation (GGA) type, meta-GGA, and hybrid density functionals, the GGA-type Perdew−Burke−Ernzerhof (PBE)22 implementation of the exchange-correlation potential provides the best description of the structural, energetic, physical, and electronic properties for all 3d, 4d, and 5d TMs. On the other hand, hybrid functionals23 are required for a good description of the thermochemistry of main group elements.24 In heterogeneous catalysis one has simultaneously to describe main group element molecules and transition metal surfaces which leads to a dilemma regarding the appropriate choice of the DFT method, GGA type functionals being usually

1. INTRODUCTION X-ray photoelectron spectroscopy (XPS), also known as electron spectroscopy for chemical analysis (ESCA), is an experimental technique available in many materials and surface science laboratories and facilities, and is essentially used for the chemical or elemental analysis of bulk materials, but especially for surfaces because of its surface sensitivity.1,2 In addition, XPS is a technique currently used to observe in situ the evolution of an heterogeneously catalyzed reaction, allowing for the characterization of reactants, intermediates, and products, thus serving as a powerful tool to determine the reaction mechanism.3−5 The XPS performance on elemental analysis hangs on the measurements of core level electron binding energies (BEs). The BEs are characteristic of a given element and, more importantly, of a given element in a given chemical environment and electronic state. Thus, BEs provide quantitative information on the chemical composition and also on the physicochemical properties including insights of the electronic structure, thus providing more significant information apart from those obtained by the elemental analyses.1−5 BEs from XPS experiments in condensed phase systems provide chemical fingerprints but also reflect the chemical properties and bonding between the species in a given system.6 The small variations for a type of atom in different chemical environments are often referred to as BEs shifts (ΔBEs) and provide meaningful information. This is used to distinguish the structural as well as the oxidation state of the atom.7 Core level BEs and their respective shifts can be accurately predicted from ab initio calculations at the well-known © XXXX American Chemical Society

Received: October 17, 2015

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DOI: 10.1021/acs.jctc.5b00998 J. Chem. Theory Comput. XXXX, XXX, XXX−XXX

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Journal of Chemical Theory and Computation selected.25 Here it is worth mentioning that recently it has been shown that the meta-GGA type Tao−Perdew−Staroverov− Scuseria (TPSS)26 functional provides a description of the three transition metal series nearly as accurately as PBE.19 Note also that compared to PBE and other GGA functionals, being a meta-GGA, TPSS represents an improvement in describing the thermochemistry of main group molecules. In this sense, TPSS seems to be a good choice to describe the interaction of molecules with transition metal surfaces. In the present work we assess the performance TPSS in providing estimates of BEs and ΔBEs for a wide variety of molecules including the main group heteroatoms (B → F) and encompassing possible chemical interactions by selecting a vast data set, with the eye put on subsequent studies aimed at describing similar molecules in contact with metal surfaces. For comparison, HF and PBE are also used since HF is a standard method in molecular quantum chemistry and PBE is a prototypal functional used in theoretical heterogeneous catalysis and surface science.25

neighboring chemical environments and chemical functional groups are represented, allowing for obtaining meaningful general information about the proper physicochemical description of core electrons by the different computational methods explored. The calculations have been carried out using a large fully uncontracted basis set near the HF limit, ensuring an accurate and well-defined description of both neutral and ionized states. Specifically for B → F, an uncontracted Partridge (14s,9p) set augmented by a d function taken from the polarized valence triple ζ (pVTZ) set was used. For H atoms we used an uncontracted basis set (5s) taken from the VTZ basis set augmented with a p function.31 In the present work we use the HF method as reference since it has been widely used to interpret and predict BEs,9,10,32−34 even if it is not well suited for periodic calculation involving metals. From the different DFT methods available we have selected PBE as a prototype of the GGA family and the TPSS from the meta-GGA since both functionals are best suited to describe metal substrates,19,20 and, as commented, TPSS also constitutes an improvement of PBE for the thermochemistry of main group element containing molecules. Here, we explore the performance of TPSS in predicting BEs and ΔBEs of simple molecules representative of the systems one may encounter in surface science and heterogeneous catalysis. For each of the three methods explored, the equilibrium geometry of each molecule is optimized for the neutral molecule; the final optimized geometries are available upon request to the authors. In a recent work,15 it has been demonstrated that there are no significant differences in predicting BEs and ΔBEs as a function of the optimized geometry; i.e., a common geometry obtained at a given level can be safely used, frozen, at other levels, although here we decided to self-consistently optimize the structures. Using a common geometry, preferably experimental geometry, may be useful when aiming at analyzing the BEs and ΔBEs of a given molecule using different methods. However, using the optimized structures is preferred here since by appropriate frequency analyses one can ensure that they represent a minimum in the corresponding potential energy hypersurface, as this has been carried out for all cases. Note also that ΔSCF calculations aimed at obtaining BE and ΔBE values are carried out at the geometry of the neutral molecule, i.e., vertical transitions, which is a reasonable choice given the time scale of core level ionization in the XPS experiments. All calculations have been performed with the GAMESS program.35,36 For the core hole state the occupied orbitals are selected using an overlap criterion instead of the usual Aufbau approach. To this end, the appropriate option needs to be selected for the SCF calculation37 with the caveat that molecular orbitals from the ground state need to be used as guess orbitals and reordered so that the core level to be ionized is the last occupied orbital on the list; a complete example is provided in the Supporting Information file. All calculations have been carried out in a spin restricted fashion and are non-relativistic. However, relativistic effects are different for different core levels and increase with the atomic number of the ionized atom. Therefore, to discuss the accuracy of the different methods in predicting BEs, it is convenient to have a reliable estimate of the contribution of the relativistic effects. To this end, results from relativistic and non-relativistic calculations for the B → F isolated atoms at the HF level of theory provided by Bagus38 have been used. These relativistic calculations were carried out with the DIRAC program,39 and the non-relativistic calculations were carried out with the CLIPS code.40 The wave functions were

2. CORE LEVEL BINDING ENERGY THEORY BACKGROUND Core level BEs can be rather accurately predicted from ab initio calculations, such as HF or DFT based methods.8−15 Absolute BEs are obtained from the difference between the total energies of the neutral state and the same system with a core hole configuration generated by subtracting one electron in the desired core level as in BE = E(core hole state) − E(neutral state)

(1)

A possible way to obtain the energy values in eq 1 is to make use of separate self-consistent field (SCF) calculations. The resulting procedure usually referred to as the ΔSCF approach8,10 and eq 1 is usually written as BE i = E i N − 1(SCF) − E N (SCF)

(2)

where the subindex i in BEi indicates the ionized core whereas EN(SCF) and EiN−1(SCF) are the variationally optimized energy for the initial system with N electrons and the final systems with (N−1) electrons and the corresponding i core hole. It is customary to decompose BEi into initial and final states.9,10 This, however, will not be considered here since the main goal is to assess the accuracy on the BEs rather than to analyze the initial and final state contributions.

3. MOLECULAR DATA SET AND COMPUTATIONAL DETAILS Calculations have been performed on a series of main group molecules containing at least one of the following main group elements: B, C, N, O, and F. ΔBEs are, for each core level, computed with respect to a given reference molecule: diborane (B2H6), methane (CH4), ammonia (NH3), water (H2O), and fluoromethane (CH3F) for B → F, respectively. The chosen molecular data set is listed in Appendix A and it is fully described in Table S1 of the Supporting Information; overall it includes 68 molecules and 185 core level BEs whose experimental values, obtained from XPS experiments, are available.27−30 These molecules were carefully chosen featuring also different organic functional groups. Thus, the set ranges from very simple homonuclear diatomic molecules, such as O2 and F2, to very complex ones such as 1,2-C2B10H12. A criterion was set to select molecules so that the different possible B


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Journal of Chemical Theory and Computation based on the average of configurations and do not take into account the multiplet splittings for these open shell atoms.41 We compared fully relativistic four-component Dirac HF wave functions and energies with non-relativistic HF wave functions and energies for the B → F isolated atoms. The basis sets used for these calculations were the same as those for the other calculations. It is worth pointing out that previous works14,15 validated the GAMESS results for the core hole states by comparison with results obtained with CLIPS.

regardless of the studied element, are lower than those calculated with HF or TPSS, which in turn are closer to the experimental values. The statistical treatment of each B → F core level BEs is also given in Table 1 by calculating the mean error (ME), mean absolute error (MAE), and the mean absolute percentage error (MAPE). Note that ME and MAE for PBE are mostly the same value with the only difference being the sign; hence, PBE systematically underestimates BEs. Note that ME and MAE increase throughout the B → F series, a trend which is explained later. Nevertheless, keep in mind that MAPE, even though PBE leads to the worst absolute BE(ΔSCF) values, is of 0.38% only for the worst scenario. Thus, relying on MAPE for the absolute value of BEs may be misleading simply because BEs are very large. On the other hand, ME and MAE clearly indicate that, compared to HF and TPSS, PBE prediction of core level BE(ΔSCF) values is less accurate even if, in absolute terms, it presents a very small error with respect to experimental values. We focus now on the accuracy of HF and TPSS calculated BE(ΔSCF) values. In the N, O, and F cases the HF and TPSS results are, according to Table 1, similar, but HF values tend to be smaller than experiment whereas TPSS are often larger. The trend in HF is, as expected, since electron correlation effects, not included in HF, are larger for the neutral molecule thus leading to too small BEs. Nevertheless, the calculated core level BEs are most often consistently lower than the experimental BEs as seen in Figure 1, and thus behave similarly to PBE. Note that for O there are outliers, in particular, O2 and H2O2, whose disagreement is translated to the ΔBEs (see later text), although one has to keep in mind that we deal here with average behaviors, instead of particular agreements. When the BE(ΔSCF) values are analyzed for B- and C-containing molecules, the ME and MAE values start to show a higher disagreement with experiment; the error associated is not systematic, and this is reflected in Figure 1 by values above and below the experimental ones. Nevertheless, BEs for the 1s core of these molecules get really close to the experimental ones; note that the difference is only 0.3 eV for both HF and TPSS, close to the XPS experimental precision of ∼0.1 eV. TPSS is slightly better than HF by ∼0.04 eV. This better adequacy increases for N → F to improvements up to 0.31 eV. From another point of view one can analyze BEs of molecules in terms of their respective shifts relative to a reference molecule. Figure 2 represents the ΔBE(ΔSCF) values with respect to the experimental shifts, ΔBE(Exp.), for each element using the reference molecules indicated previously. The most evident difference, in comparison to BE(ΔSCF) values in Figure 1, is that there are no significant variations of the shifts with respect to the used method. As expected, the systematic errors cancel each other. To further analyze the core level ΔBEs the statistical analysis is reported in Table 2. The ME results at HF and TPSS levels of theory are, in general terms, negative, with the caveat for N1s, which appears to show an agreement within chemical accuracy. Curiously, this happens for all ME PBE values with the caveat of F1s results. Notwithstanding that, the MAE values do not follow the same trend previously

4. RESULTS AND DISCUSSION We first analyze the absolute BE(ΔSCF) results, the ΔBE(ΔSCF) values, and their respective dispersions with respect the experimental values for the entire molecular data set, but itemized according to different heteroatoms. The calculated BE(ΔSCF) values for the B → F atoms are represented in Figure 1. We start discussing the PBE results as shown in Figure 1. Generally speaking the PBE BE(ΔSCF) results,

Figure 1. Calculated, BE(ΔSCF), versus experimental, BE(Exp.), core level BEs for B → F elements in the molecular data set. All values are given in electronvolts.

Table 1. Summary of the BE(ΔSCF) Statistical Analysis (All Values Given in Electronvolts, Except MAPE, in Percent) B1s ME MAE MAPE

C1s

N1s

O1s

F1s

HF

PBE

TPSS

HF

PBE

TPSS

HF

PBE

TPSS

HF

PBE

TPSS

HF

PBE

TPSS

−0.16 0.22 0.11

−0.74 0.74 0.38

−0.07 0.18 0.09

0.00 0.30 0.10

−0.88 0.92 0.31

−0.17 0.27 0.09

−0.49 0.49 0.12

−0.98 0.98 0.24

−0.28 0.28 0.07

−0.82 0.79 0.16

−1.26 1.20 0.23

−0.44 0.48 0.09

−1.09 1.09 0.16

−1.78 1.78 0.26

−0.81 0.81 0.12

C


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Table 3. Relativistic Contributions (rel) and Non-relativistic (non-rel) Results for BE(ΔSCF) B → F Calculationsa (All Values Given in Electronvolts) BE(ΔSCF)

a

rel

non-rel

diff

B C N O F

200.87 297.08 412.04 545.85 698.36

200.81 296.95 411.79 545.40 697.62

0.06 0.13 0.25 0.45 0.75

The difference (diff) between rel and non-rel is also given.

initial state. Since we want to establish the relativistic contribution to the absolute core level BEs, the changes were studied for the BE(ΔSCF) values. The diff values in Table 3 show that the relativistic 1s core BEs are larger than the non-relativistic values, although the relativistic effects lead to a very small increase in the core level BEs for these light atoms as expected, from 0.06 eV for B to 0.75 eV for F, thus increasing along the B → F series, as expected. When we analyze the BE(ΔSCF) and the ΔBE(ΔSCF) for the whole data set, the previously obtained excellent agreement is maintained; i.e., mixing of B → F results does not disrupt the statistics. On the contrary, the overall performance is enhanced. The statistical analysis values for the overall calculations, with or without including the relativistic changes, are reported in Table 4. The absolute non-relativistic BEs and their ΔBEs are shown in Figures 3 and 4, respectively. Inspecting the data on Table 4, it is seen that for the absolute non-relativistic BEs for the entire set, the PBE results are worse than the HF or TPSS with ME and MAE values of ∼1 eV. The HF and TPSS BEs errors are similar and within 0.3−0.4 eV from experimental values. Note that when relativistic contributions are included, the BEs values approach the experimental ones, so discrepancies are owed, in part, due to such an approximation. However, even including relativistic effects, PBE results are still worse in comparison to the other two methods, with ME and MAE values of ∼0.8 eV. Still HF and TPSS statistics are similar, and ME and MAE values drop to 0.2−0.3 eV, very close to the XPS chemical accuracy. Relativistic effects explain in part the disagreements with respect the experimental values and the fact that, for a given core, this effect is constant implies that both HF and TPSS are excellent methods in predicting BEs with PBE performing slightly worse. We now analyze the ΔBE values for the different 1s cores. As is shown in Table 4 for both non-relativistic and relativistic results, the agreement between methods and with experimental values is really excellent and better than for the absolute BE(ΔSCF) values, leading to ME results from ∼0 to −0.2 eV and MAE values between 0.2 and 0.3 eV. Surprisingly, when using the full calculation set, the PBE method leads to ΔBE balanced results very close to HF and TPSS. Thus, the three methods perform excellently and are, a priori, adequate for assigning species based on ΔBEs, as was done previously for compounds on solid surfaces.42−44

Figure 2. Calculated, ΔBE(ΔSCF), versus experimental, ΔBE(Exp.), core level ΔBEs for B → F elements in the molecular data set. All values are given in electronvolt.

described. For the three studied methods the MAEs are similar to each other, as is shown in Table 2. For the ΔBE(ΔSCF) values, MAPE is not reported since here the values are much smaller and variations of a few tenths of an electronvolt translated into physically meaningless MAPE values. The full absolute core level BE(ΔSCF) and ΔBE(ΔSCF) data are reported in Table S1 in the Supporting Information. So far, the discussion concerned non-relativistic calculations. We indeed considered the influence of relativistic effect on the 1s BEs on the studied elements. Relativistic (rel) and non-relativistic (non-rel) calculations have been carried out for the B → F atoms, and the relativistic contributions and the comparison with the non-relativistic ones are shown in Table 3. The relativistic change in the final state, including the relaxation of the electrons with a core hole, diff, is defined as diff = BE(ΔSCF, rel) − BE(ΔSCF, non‐rel)

atom

(3)

15

It has been reported that the relativistic changes on the initial and final states are very close with each other, which means that the relativistic changes are dominant, already at the

Table 2. Summary of the ΔBE(ΔSCF) Statistics (All Values Given in Electronvolts) B1s ME MAE

C1s

N1s

O1s

F1s

HF

PBE

TPSS

HF

PBE

TPSS

HF

PBE

TPSS

HF

PBE

TPSS

HF

PBE

TPSS

−0.18 0.23

−0.01 0.17

−0.18 0.21

−0.16 0.28

0.01 0.23

−0.12 0.25

−0.07 0.13

0.03 0.11

−0.10 0.13

−0.22 0.32

−0.05 0.28

−0.13 0.28

−0.10 0.28

−0.44 0.45

−0.38 0.41

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Table 4. Summary of Non-relativistic (non-rel) and Relativistic (rel) BE(ΔSCF) and ΔBE(ΔSCF) Statistics for the Full Molecular Data Set (All Values Given in Electronvolts) non-rel

rel ΔBE

BE(ΔSCF) ME MAE

ΔBE

BE(ΔSCF)

HF

PBE

TPSS

HF

PBE

TPSS

HF

PBE

TPSS

HF

PBE

TPSS

−0.26 0.44

−1.01 1.03

−0.26 0.33

−0.16 0.27

−0.03 0.24

−0.15 0.25

−0.03 0.30

−0.78 0.81

−0.03 0.21

−0.16 0.27

−0.03 0.24

−0.15 0.25

note that regression coefficients of the full data set are above 0.98. We now consider the ΔBE for the different cores; the intercepts are near the ideal cut at 0 eV, with a slight dispersion, depending on the element analyzed and the method used, yet in average is ∼0.02 eV for PBE and HF and ∼0.27 eV for TPSS. Considering the mean variation between the experimental and the calculated values for the full set of data leads to offsets for the three different levels of calculation, small, with a positive difference ∼0.3 eV at HF and ∼−0.3 eV at TPSS and PBE; see Table 5. Table 5. Non-relativistic Offsets and the Ones Corrected by Relativistic Effects (rel-offset) for BEs and ΔBEs for Each Element and the Overall Molecular Data Seta (All Values Given in Electronvolts) B1s

BE(ΔSCF)

ΔBE

Figure 3. Calculated, BE(ΔSCF), versus experimental, BE(Exp.), core level BEs for the full data set. All values are given in electronvolts. C1s

BE(ΔSCF)

ΔBE

N1s

BE(ΔSCF)

ΔBE

O1s

BE(ΔSCF)

ΔBE

F1s

Figure 4. Calculated, ΔBE(ΔSCF), versus experimental, ΔBE(Exp.), core level ΔBEs for the full data set. All values are given in electronvolts.

BE(ΔSCF)

ΔBE

all

Figure 3 displays BE(ΔSCF) results versus experimental BEs; a perfect linear fitting is clearly seen. The linear trend is also observed when comparing calculated versus experimental ΔBE values. In Table 5 a summary of the offsets with respect to the ideal cases, with and without the relativistic contributions, is reported. The rest of the parameters of the regression treatment, regression coefficients, slopes, and interecepts are included in Table S2 in the Supporting Information. However,

BE(ΔSCF)

ΔBE

method

offset

rel-offset

HF PBE TPSS HF PBE TPSS HF PBE TPSS HF PBE TPSS HF PBE TPSS HF PBE TPSS HF PBE TPSS HF PBE TPSS HF PBE TPSS HF PBE TPSS HF PBE TPSS HF PBE TPSS

−0.13 −0.70 −0.02 −0.15 0.03 −0.13 0.23 −1.05 −0.30 0.38 −0.19 −0.26 −0.43 −0.93 −0.22 −0.01 0.08 −0.04 −0.75 −1.22 −0.39 −0.15 −0.08 −0.15 −1.09 −1.81 −0.82 −0.11 −0.47 −0.40 −0.44 −1.16 −0.38 0.31 −0.23 −0.27

−0.08 −0.64 0.04

0.36 −0.92 −0.17

−0.18 −0.68 0.04

−0.30 −0.77 0.06

−0.34 −1.06 −0.07

−0.11 −0.84 −0.05

a Offsets are the result of the difference between the ideal behavior and the adjusted one. Rel-offsets are obtained by adding diff in Table 4 to the non-relativistic offsets.

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When relativistic effects are included, BE(ΔSCF) deviations drop and estimations get much closer to the experimental values. Linear relationships have been found between experimental and estimated values, obtaining, for any method, and any set or subset of data, an offset with respect to ideal linearity. Correcting the values by including the relativistic effects leads to offsets of 0.11 and 0.05 eV for HF and TPPS, respectively. Both, HF and TPSS methods slight underestimate the experimental BEs but within the accuracy of the XPS measurement. Thus, TPSS is posed as an excellent choice for the characterization, by XPS, of molecules on metal solid substrates, given its suitability in describing metal substrate bonds and atomic and/or molecular orbitals.

This highlights once more that these three methods provide reliable estimates of the core level shifts, with very small differences with respect to the experimental values. Nevertheless, one should keep in mind that HF overestimates ΔBEs, whereas DFT underestimates them. Regarding the absolute BE(ΔSCF) values, the intercepts are much higher than for ΔBEs simply because a small deviation on the slope is magnified by the large range of energies considered; see Figure 3. One can better determine the ideal deviation by further analyzing the offsets. Here we gained the offsets for the nonrelativistic calculations and offsets taking into account the relativistic contributions. First, we analyze the non-relativistic offsets to give a brief idea of the cases studied and next, the study with the relativistic effects will be also discussed. For the full set, the overall obtained offsets, including or not the relativistic corrections, are always below the experiment. The non-relativistic offset results itemized for each B → F atom studied generally increase following the series, yet the tendency along methods is kept. Results from PBE, as previously shown, lead to results with the largest deviation with respect to the linearity, from −0.7 to −1.8 eV, with a global offset of ∼−1.2 eV. The results from HF and TPSS are akin to each other or, in many cases, better for TPSS. The offsets range from −0.02 to −0.8 eV, representing the closest or least deviated trend compared to ideality. When taking into account the full set, the offset is ∼−0.4 eV. Including the relativistic contribution to the BEs improves the already excellent agreement with experiment. For HF and TPSS, the offsets become now −0.11 and −0.05 eV, respectively, well within XPS chemical accuracy. In light of the previously presented discussion, the obtained results for the three explored methods, with and without relativistic corrections, are very good when computing ΔBEs of main group organic molecules and HF, and especially the TPSS exchange correlation functional are excellent in predicting absolute core level BEs, when relativistic effects are considered. Thus, TPSS poses itself as an convenient and accurate method for the study of core level BEs of adsorbates of main group elements on metallic surfaces which, given its suitability in describing bulk transition metals and the thermochemistry of organic molecules, appears to be an excellent choice for studying these types of systems.

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APPENDIX A A list of the studied molecules conforming the data set is given in Table 6. Table 6. Molecules of the Data Set

5. CONCLUSIONS Here we have explored the performance of HF, PBE, and TPSS methods in predicting 1s core level BEs of a set of 68 molecules (185 core levels explored in total) containing a wide variety of functional groups and chemical environments for main group elements B → F. The obtained results using ΔSCF methodology have been compared to reported experimental references. This has been carried out in a non-relativistic fashion, yet the relativistic effects have been explicitly considered on isolated atoms, and, since they are known to be independent of the particular chemical environment, added a posteriori on the obtained estimates. The analysis yields that computed absolute core level BEs are, overall, and regardless of the method, in very good agreement with the reported experimental values. Nevertheless, it is important to highlight that TPSS values are slightly better than those predicted from HF, and these two are clearly better than PBE. The BEs values have also been analyzed in terms of shifts, ΔBEs, from selected references. As far as ΔBEs are concerned, the three methods yield very similar and excellent results, with mean absolute deviations of ∼0.25 eV.

no.

molecule

no.

molecule

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

diborane trimethylborane triethylamine borane closo-C2B3H5 dipropyldiborane closo-1,5-C2B3(CH2CH3)5 nido-2,3-C2B4H8 closo-2,4-C2B5H7 o-carborane m-carborane methane propane dimethylpropane propene isobutene propyne toluene ammonia methylamine aniline N-methylaniline N,N-dimethylaniline cyanobenzene pyridine pyrrole hydrogen cyanide acetonitrile dimethylamine ethylamine trimethylamine diethylamine N,N-dimethylbenzene-1,4-diamine 4-cyanoaniline isopropylamine

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 61 62 63 64 65 66 67 68

tert-butylamine water acetaldehyde methanol isopropyl alcohol tert-butyl alcohol dimethyl ether diethyl ether acetic acid formic acid formaldehyde acetone propen-2-ol carbon monoxide carbon dioxide oxygen hydrogen peroxide ethenone phenol vinyl acetate fluorine hydrogen fluorine fluoromethane difluoromethane trifluoromethane tetrafluoromethane 1,1-difluoroethylene 1,1,1-trifluoroethane trifluoroethene fluorobenzene o-difluorobenzene m-difluorobenzene p-difluorobenzene 1,1,1-trifluoropropyne

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jctc.5b00998. Table S1 containing color-coded results for each nonequivalent atom in each studied molecule and, at F


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relationship to chemical bonding. J. Electron Spectrosc. Relat. Phenom. 1999, 100, 215. (11) Chong, D. P. Density-functional calculation of core-electron binding energies of C, N, O, and F. J. Chem. Phys. 1995, 103, 1842. (12) Chong, D. P.; Gritsenko, E. J.; Baerends, E. J. Interpretation of the Kohn−Sham orbital energies as approximate vertical ionization potentials. J. Chem. Phys. 2002, 116, 1760. (13) Segala, M.; Takahata, Y.; Chong, D. P. Density functional theory calculation of 2p core-electron binding energies of Si, P, S, Cl, and Ar in gas-phase molecules. J. Electron Spectrosc. Relat. Phenom. 2006, 151, 9. (14) Pueyo Bellafont, N.; Illas, F.; Bagus, P. S. Validation of Koopmans’ theorem for density functional theory binding energies. Phys. Chem. Chem. Phys. 2015, 17, 4015. (15) Pueyo Bellafont, N.; Bagus, P. S.; Illas, F. Prediction of core level binding energies in density functional theory: Rigorous definition of initial and final state contributions and implications on the physical meaning of Kohn-Sham energies. J. Chem. Phys. 2015, 142, 214102. (16) Zhao, Y.; Truhlar, D. G. Comparative assessment of density functional methods for 3d transition-metal chemistry. J. Chem. Phys. 2006, 124, 224105. (17) Schultz, N. E.; Zhao, Y.; Truhlar, D. G. Density Functionals for Inorganometallic and Organometallic Chemistry. J. Phys. Chem. A 2005, 109, 11127. (18) Paier, J.; Marsman, M.; Kresse, G. Why does the B3LYP hybrid functional fail for metals? J. Chem. Phys. 2007, 127, 024103. (19) Janthon, P.; Luo, S.; Kozlov, S. M.; Viñes, F.; Limtrakul, J.; Truhlar, D. G.; Illas, F. Bulk Properties of Transition Metals: A Challenge for the Design of Universal Density Functionals. J. Chem. Theory Comput. 2014, 10, 3832. (20) Janthon, P.; Kozlov, S. M.; Viñes, F.; Limtrakul, J.; Illas, F. Establishing the Accuracy of Broadly Used Density Functionals in Describing Bulk Properties of Transition Metals. J. Chem. Theory Comput. 2013, 9, 1631. (21) Notario-Estevez, A.; Kozlov, S. M.; Viñes, F.; Illas, F. Electronicstructure-based material descriptors: (in)dependence on self-interaction and Hartree−Fock Exchange. Chem. Commun. 2015, 51, 5602. (22) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865. (23) Becke, A. D. Density-functional thermochemistry. III. The role of exact Exchange. J. Chem. Phys. 1993, 98, 5648. (24) Sousa, S. F.; Fernandes, P. A.; Ramos, M. J. General performance of density functionals. J. Phys. Chem. A 2007, 111, 10439. (25) Nørskov, J. K.; Studt, F.; Abild-Pedersen, F.; Bligaard, T. Fundamental Concepts in Heterogeneous Catalysis; John Wiley and Sons: Hoboken, NJ, USA, 2014; ISBN 978-1118888957. (26) Tao, J.; Perdew, P.; Staroverov, V. N.; Scuseria, G. E. Climbing the Density Functional Ladder: Nonempirical Meta−Generalized Gradient Approximation Designed for Molecules and Solids. Phys. Rev. Lett. 2003, 91, 146401. (27) Bakke, A. A.; Chen, H. W.; Jolly, W. L. A table of absolute coreelectron binding-energies for gaseous atoms and molecules. J. Electron Spectrosc. Relat. Phenom. 1980, 20, 333. (28) Jolly, W. L.; Bomben, K. D.; Eyermann, C. J. Core-electron binding energies for gaseous atoms and molecules. At. Data Nucl. Data Tables 1984, 31, 433. (29) Takahata, Y.; Chong, D. P. DFT calculation of core-electron binding energies. J. Electron Spectrosc. Relat. Phenom. 2003, 133, 69. (30) Myrseth, V.; Saethre, L. J.; Borve, K. J.; Thomas, T. D. The Substituent Effect of the Methyl Group. Carbon 1s Ionization Energies, Proton Affinities, and Reactivities of the Methylbenzene. J. Org. Chem. 2007, 72, 5715. (31) See https://bse.pnl.gov/bse/portal for the basis sets. (32) Pueyo Bellafont, N.; Mañeru, D. R.; Illas, F. Identifying atomic sites in N-doped pristine and defective graphene from ab initio core level binding energies. Carbon 2014, 76, 155. (33) Bagus, P. S.; Pacchioni, G. Ionic and covalent electronic states for K adsorbed on Cu5 and Cu25 cluster models of the Cu(100) surface. J. Chem. Phys. 1995, 102, 879.

HF, PBE, and TPSS levels of theory, the obtained BEs and ΔBEs and the reported experimental values with sketches of the molecular structures provided, Table S2 containing the regression coefficients, slopes, and intercepts of the linear trends shown in Figures 1−4, and an example of an input file for carrying out the calculation of the H2O molecules with a O(1s) core hole (PDF)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Funding

This work has been supported by a Spanish MINECO CTQ2012-30751 grant and, in part, by Generalitat de Catalunya grants 2014SGR97 and XRQTC. F.V. thanks MINECO for a postdoctoral Ramón y Cajal (RyC) research contract (RYC2012-10129). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We are very much indebted to Paul S. Bagus not only for providing the relativistic values for the core level binding energies of atoms B−F and critically reading the manuscript but also for having inspired us to work on theoretical interpretation of XPS and for sharing his deep and sound knowledge. We acknowledge Consorci de Serveis Universitaris de Catalunya (CSUC; former CESCA) for providing access to computational resources.

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REFERENCES

(1) Siegbahn, K.; Nordling, C.; Falhman, A.; Nordberg, R.; Hamrin, K.; Hedman, J.; Johansson, G.; Bergmark, T.; Karlsson, S. E.; Lindgren, I.; Lindberg, B. ESCA (Atomic, Molecular and Solid State Structure Studied by Means of Electron Spectroscopy); Alwmvist and Wiksells Boktryckeri AB, Uppsala, Sweden, 1967. (2) Siegbahn, K.; Nordling, C.; Johansson, G.; Hedman, J.; Hedén, P. F.; Hamrin, K.; Gelius, U.; Bergmark, T.; Werme, L. O.; Manne, R.; Baer, Y. ESCA Applied to Free Molecules; North-Holland: Amsterdam, 1969. (3) Lykhach, Y.; Staudt, T.; Lorenz, M. P. A.; Streber, R.; Bayer, A.; Steinrück, H. P.; Libuda, J. Microscopic Insights into Methane Activation and Related Processes on Pt/Ceria Model Catalysts. ChemPhysChem 2010, 11, 1496. (4) Happel, M.; Luckas, N.; Viñes, F.; Sobota, M.; Laurin, M.; Görling, A.; Libuda, J. SO2 Adsorption on Pt(111) and Oxygen Precovered Pt(111): A Combined Infrared Reflection Absorption Spectroscopy and Density Functional Study. J. Phys. Chem. C 2011, 115, 479. (5) Niedermaier, I.; Kolbeck, C.; Taccardi, N.; Schulz, P. S.; Li, J.; Drewello, T.; Wasserscheid, P.; Steinrück, H. P.; Maier, F. Organic Reactions in Ionic Liquids Studied by in Situ XPS. ChemPhysChem 2012, 13, 1725. (6) Barr, T. L. Modern ESCA: The Principles and Practique of X-Ray Photoelectron Spectroscopy; Taylor and Francis: London, 1994. (7) Siegbahn, K. Electron Spectroscopy for Atoms, Molecules, and Condensed Matter. Science 1982, 217, 111. (8) Bagus, P. S. Self-Consistent-Field Wave Functions for Hole States of Some Ne-Like and Ar-Like Ions. Phys. Rev. 1965, 139, A619. (9) Bagus, P. S.; Ilton, E. S.; Nelin, C. J. The interpretation of XPS spectra: Insights into materials properties. Surf. Sci. Rep. 2013, 68, 273. (10) Bagus, P. S.; Illas, F.; Pacchioni, G.; Parmigiani, F. Mechanisms responsible for chemical shifts of core-level binding energies and their G


Article

Journal of Chemical Theory and Computation (34) Bagus, P. S.; Pacchioni. Ionicity of alkali-metal adsorbates. G. Phys. Rev. Lett. 1993, 71, 206. (35) Schmidt, M. W.; Baldridge, K. K.; Boatz, J. A.; Elbert, S. T.; Gordon, M. S.; Jensen, H. S. J.; Koseki, N.; Matsunaga, K.; Nguyen, A.; Su, S.; Windus, T. L.; Dupuis, M. J.; Montgomery, A. General Atomic and Molecular Electronic Structure System. J. Comput. Chem. 1993, 14, 1347. (36) Gordon, M. S.; Schmidt, M. W. Theory and Applications of Computational Chemistry: The First Forty Years; Dykstra, C. E., Frenking, G., Kim, K. S., Scuseria, G. E., Eds.; Elsevier: Amsterdam, 2005; p 1167. (37) In the case of the GAMESS code the appropriate option is the following: $scf rstrct = .t. $end. (38) Bagus, P. S. Private communication. (39) Sauer, T.; Visscher, L.; Jensen, H. J. A.; Bast, R. with contributions from Bakken, C.; Dyall, K. G.; Dubillard, S.; Ekström, U.; Eliav, E.; Enevoldsen, T.; Faßhauer, E.; Fleig, T.; Fossgaard, O.; Gomes, A. S. P.; Helgaker, T.; Henriksson, J.; Ilias, M.; Jacob, C. R.; Kencht, S.; Komorovsky, S.; Kullie, O.; Larsen, C. V.; Lærdhal, J. K.; Lee, Y. S.; Nataraj, H. S.; Norman, P.; Olejniczak, G.; Olsen, J.; Park, Y. C.; Pedersen, J. K.; Pernpointner, M.; di Remigio, R.; Ruud, K.; Salek, P.; Schimmelpfenning, B.; Sikkema, J.; Thorvaldsen, A. J.; Thyssen, J.; van Stralen, J.; Villaume, S.; Visser, O.; Winther, T.; Yamamoto, S. DIRAC, a relativistic ab initio electronic structure program, release DIRAC14, 2014; http://www.diracprogram.org. (40) CLIPS, is a program system to compute ab initio SCF and correlated wavefunctions for polyatomic systems. It has been developed based on the publicly available programs in the ALCHEMY package from the IBM San Jose Laboratory by: Bagus, P. S.; Liu, B.; McLean, A. D.; Yoshimine, M.. (41) Visscher, L.; Visser, O.; Aerts, P. J. C.; Merenga, H.; Nieuwpoort, W. C. Relativistic quantum chemistry: the MOLFDIR program package. Comput. Phys. Commun. 1994, 81, 120. (42) Luckas, N.; Viñes, F.; Happel, M.; Desikusumastuti, A.; Libuda, J.; Görling, A. Density Functional Calculations and IR Reflection Absorption Spectroscopy on the Interaction of SO2 with OxideSupported Pd Nanoparticles. J. Phys. Chem. C 2010, 114, 13813. (43) Desikusumastuti, A.; Happel, M.; Dumbuya, K.; Staudt, T.; Laurin, M.; Gottfried, J. M.; Steinruck, H. P.; Libuda, J. Modeling NOx Storage Materials: On the Formation of Surface Nitrites and Nitrates and Their Identification by Vibrational Spectroscopy. J. Phys. Chem. C 2008, 112, 6477. (44) Salvarezza, R. C.; Carro, P. Exploring the core level shift origin of sulfur and thiolates on Pd(111) surfaces. Phys. Chem. Chem. Phys. 2015, 17, 24349.

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Performance of the TPSS Functional on Predicting Core Level Binding

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