The X40Ã10 Halogen Bonding Benchmark Revisited: Surprising

Article Cite This: J. Phys. Chem. A XXXX, XXX, XXX−XXX

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The X40×10 Halogen Bonding Benchmark Revisited: Surprising Importance of (n−1)d Subvalence Correlation Published as part of The Journal of Physical Chemistry virtual special issue “Manuel Yáñez and Otilia Mó Festschrift”. Manoj K. Kesharwani, Debashree Manna, Nitai Sylvetsky, and Jan M. L. Martin* Department of Organic Chemistry, Weizmann Institute of Science, 76100 Reḥovot, Israel S Supporting Information *

ABSTRACT: We have re-evaluated the X40×10 benchmark for halogen bonding using conventional and explicitly correlated coupled cluster methods. For the aromatic dimers at small separation, improved CCSD(T)-MP2 “high-level corrections” (HLCs) cause substantial reductions in the dissociation energy. For the bromine and iodine species, (n−1)d subvalence correlation increases dissociation energies and turns out to be more important for noncovalent interactions than is generally realized; (n−1)sp subvalence correlation is much less important. The (n−1)d subvalence term is dominated by core−valence correlation; with the smaller cc-pVDZ-F12-PP and cc-pVTZ-F12-PP basis sets, basis set convergence for the core−core contribution becomes sufficiently erratic that it may compromise results overall. The two factors conspire to generate discrepancies of up to 0.9 kcal/mol (0.16 kcal/mol RMS) between the original X40×10 data and the present revision.

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The phenomenon of halogen bonding was first observed by Colin9 in 1814, as part of an adduct formation between iodine and ammonia. Subsequently, many significant studies on this subject have been performed over the past two centuries.10−12 In recent years, interest in halogen bonds has greatly increased in many fields (for recent reviews see refs 13−26). For instance, noncovalent interactions associated with halogens are expected to have profound implications for drug discovery:18,24,27,28 many widely used drugs are halogenated, and now there is good reason to believe that halogen bonds contribute directly to their efficiency.27 In the context of supramolecular assembly through hydrogen bonds, we mention two recent imaging studies, by atomic force microscopy29 and by electron microscopy.30 Our current knowledge regarding noncovalent interactions in halogenated molecules, and particularly of halogen bonds, is primarily based on computational and crystallographic studies of organic molecules and biomolecules.31−39 Studies on the influence of halogen bonds in medicinal chemistry have also typically been performed by computational techniques. Cooperativity in noncovalent interactions (see ref 40 for a recent review) opens further perspectives, as shown by Mó, Yañez, and co-workers.41−43 An accurate theoretical/computational description of noncovalent interactions requires some caution, as interaction

INTRODUCTION

Physical and chemical properties of many (supra)molecular systems are strongly influenced by noncovalent interactions (NCIs).1,2 In biochemistry, for example, noncovalent interactions are known to play important roles in protein folding, protein−ligand interaction, and nucleobase packing and stacking.3,4 In addition, noncovalent interactions are of great importance in various chemical contexts such as organocatalysis, supramolecular chemistry, and conformational stability. A molecule that includes halogen atoms (such as I, Br, Cl, etc.) can participate in many kinds of noncovalent interactions, e.g., electrostatic interactions, dispersion interactions, hydrogen bonding, halogen−π interactions and most importantlyhalogen bonding. The last corresponds to a net attractive interaction between an electrophilic region (associated with a halogen atom) and a nucleophilic region5 and can be schematically represented as R−X···Y, where X is a halogen atom (I, Br, Cl, or rarely F) that unconventionally acts as a σhole electron acceptor,6−8 and Y is an electron-rich atom or functional group (such as O, N, S, or a X-donor group). X can be part of a dihalogen, e.g., Br2, or a substituent on some other molecule. Politzer and co-workers also referred to halogen bonds as “σ-hole bonds”, as the three lone electron pairs on the X atom form a belt of negative electrostatic potential around its central region, while a positive σ-hole (which can interact with nucleophiles) is formed on the outermost portion of its surface.6−8 © XXXX American Chemical Society

Received: November 6, 2017 Revised: January 31, 2018 Published: February 1, 2018 A

DOI: 10.1021/acs.jpca.7b10958 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry A

These halogen bonding benchmarks are in use for the development and validation of DFT functionals as part of the large training set of the Berkeley ωB97X-V and ωB97M-V functionals,58,59 as well as of the very large GMTKN55 validation set of Goerigk et al.60 In the present work, we shall report a revision of the reference interaction energies for Hobza’s X40×10 data set, which was carried out by means of explicitly correlated MP2 and coupled cluster methods. We will also examine the significance of (n−1)d electron correlation, particularly for Br and I, in the calculated interaction energies.

energies of noncovalent complexes cannot be easily measured experimentally. Fortunately, state-of-the-art correlated ab initio calculations can provide accurate results for noncovalent interactions, which can further serve as a benchmark for the calibration of more approximate computational methods, such as DFT functionals and force-field-based methods. However, for the purpose of conducting an appropriate benchmark study, statistics over a sufficiently large number of calculations are required. In the past decade, Hobza and co-workers have developed a number of databases for noncovalent interactions.44−48 The earliest of them, the S22 set,44 includes 22 noncovalent complexes, ranging from water and methane dimers to the adenine−thymine base pair. Its ab initio reference data were recently comprehensively revised by Sherrill and coworkers.49 Subsequently, the Hobza group published the larger S66 data set,47 which includes 66 noncovalent pairs, representative of noncovalent interactions most commonly found in biomolecules. The S66 set consists of hydrogen bonding, π-stacking, London dispersion complexes, and mixedinfluence complexes. The S66 data set46,47 was then extended to form the S66×8 data set, in which each noncovalent pair is considered at eight different intermonomer separations. Interaction energies of the latter data set have been recently revised by our group.50 Nevertheless, none of the complexes included in the above data sets contains halogen atoms, and thus these benchmarks cannot represent halogen bonding or any other noncovalent interactions associated with halogen atoms. To describe such interactions, the Hobza group presented a new data set of 40 halogen-containing dimers.48 This set includes all relevant halogen atoms (F to I) and covers London dispersion (1−4), electrostatic interactions (5−10), stacking of halogenated aromatic rings (11,12), halogen bonding (13−26), halogen−π interactions (27−30), and hydrogen bonded complexes (31− 40). This data set was then extended by considering dimer dissociation curves analogous to the S66×8 set, but with two additional points at more compressed distances. Thus, for each complex, the X40×10 data set48 includes ten data points: aside from the dimer at equilibrium distance re, four compressed dimers (at 0.80re, 0.85re, 0.90re, and 0.95re) and five stretched dimers (1.05re, 1.10re, 1.25re, 1.50re, and 2.00re).48 The smaller X40 set48 was obtained by quartic interpolation of the association energies at {0.9,0.95,1.0,1.05,1.10}re, similar to the relationship between the earlier S66×8 and S66 data set of {HCNO} biomolecule dimers. X40 has been used as a benchmark for the development and calibration of various lower-level ab initio and DFT methods,51−54 with the originally reported CCSD(T)/CBS calculated interaction energies48 as the reference values. These values are based on HF/aVQZ energies with MP2 correlation energy extrapolated from aVTZ and aVQZ basis sets, combined with the additive “high-level corrections” (or HLCs; i.e., [CCSD(T)-MP2]). HLCs were calculated using aVDZ and haVTZ basis sets for the X40×10 and X40 sets, respectively, where haVnZ (n = D, T or Q) stands for the combination of cc-pVnZ basis set on hydrogen and aug-cc-pVnZ (or aVnZ) basis set on all other atoms except Br and I. To render calculations on bromine and iodine less computationally demanding, pseudopotentials have been used together with the aug-cc-pVnZ-PP basis set.55,56 In addition, Kozuch and Martin57 have developed two benchmark data sets particularly for halogen bonds: namely the XB18 and XB51 sets of 18 and 51 dimers, respectively.

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COMPUTATIONAL DETAILS All conventional and explicitly correlated ab initio calculations were carried out using the MOLPRO 2015.1 program package61 and TURBOMOLE62 running on the Chemfarm cluster of the Faculty of Chemistry at the Weizmann Institute of Science. Explicitly correlated CCSD(T)-F12b63,64 single-point energy calculations were performed using the cc-pVnZ-PP-F12 basis sets65 for Br and I, and cc-pVnZ-F12 (where n = D, T, Q) basis sets for the other atoms, together with the associated auxiliary and complementary auxiliary (CABS) basis sets.65−67 Both ccpVnZ-F1268 and cc-pVnZ-PP-F1265 basis set families were developed specifically for explicitly correlated calculations by Peterson and co-workers. The cc-pVnZ-PP-F12 basis set family is based on small-core pseudopotentials69 covering [Ne] and [Ar](3d10) cores for Br and I, respectively, and were designed to some extent with core−valence correlation in mind.65 For valence electrons, as recommended in ref 70, the geminal exponent (β) value was set to 0.9 for cc-pVDZ-F12, and 1.0 for both cc-pVTZ-F12 and cc-pVQZ-F12 basis sets. The cc-pVnZPP-F12 basis sets for the heavy p-block elements were developed to some degree with (n−1)d subvalence correlation in mind (as the small core−valence gaps in group 13 and 14 make this unavoidable): we used a different geminal exponent value (β = 1.5) for core−valence pair correlation.71 In addition, a “CABS correction”63,72 was employed throughout to improve the SCF component. As for the remaining auxiliary basis sets in the F12 calculations, the MOLPRO defaults were used: for the “JKFIT” (Coulomb and exchange) fitting basis sets, this is def2-QZVPP/JKFIT for Br and I,73 and cc-pVnZ/JKFIT74 (augmented with a diffuse layer obtained by even-tempered expansion) for the remaining elements, whereas for the “MP2FIT” (DF-MP2) auxiliary basis sets, cc-pVnZ-F12-PP/ MP2FIT from ref 65 for Br and I is combined with aug-ccpVnZ/MP2FIT75 for the lighter elements. As discussed in a previous study,76 F12 approaches do not benefit the calculation of the (T) term. Hence, three different corrections were considered: (a) (T*), in which the (T) contribution is scaled by the MP2-F12/MP2 correlation energy ratio (also known as Marchetti−Werner approximation77,78); (b) (Tb), in which the (T) contribution is scaled by the CCSDF12b/CCSD correlation energy ratios; and (c) (Ts),79 in which the (T) contributions are multiplied by constant scaling factors of 1.1413, 1.0527, and 1.0232 for cc-pVDZ-F12, cc-pVTZ-F12, and cc-pVQZ-F12, respectively. (T*) and (Tb) are not exactly size-consistent; this problem, however, can be circumvented by applying the correlation energy ratios Ecorr[MP2-F12]/Ecorr[MP2] obtained for the dimers also to the monomers. Corrected (T*) and (Tb) contributions are thus denoted (T*sc) and (Tbsc), respectively. B


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Table 1. Systems in the X40×10 Dataset and Final Recommended Interaction Energies (kcal/mol) Obtained in the Present Work systems a

01 02a 03a 04a 05a 06a 07a 08a 09a 10a 11b 12b 13a 14a 15b 16a 17a 18b 19b 20b 21b 22b 23b 24b 25b 26b 27a 28b 29b 30b 31a 32a 33a 34a 35a 36a 37a 38a 39a 40a

CH4···F2 CH4···Cl2 CH4···Br2 CH4···I2 CH3F···CH4 CH3Cl···CH4 CHF3···CH4 CHCl3···CH4 CH3F···CH3F CH3Cl···CH3Cl C6H3F3···C6H6 C6F6···C6H6 CH3Cl···HCHO CH3Br···HCHO CH3I···HCHO CF3Cl···HCHO CF3Br···HCHO CF3I···HCHO C6H5Cl···CH3COCH3 C6H5Br···CH3COCH3 C6H5I···CH3COCH3 C6H5Cl···N(CH3)3 C6H5Br···N(CH3)3 C6H5I···N(CH3)3 C6H5Br···CH3SH C6H5I···CH3SH CH3Br···C6H6 CH3I···C6H6 CF3Br···C6H6 CF3I···C6H6 CF3OH···H2O CCl3OH···H2O HF···CH3OH HCl···CH3OH HBr···CH3OH HI···CH3OH HF···CH3NH2 HCl···CH3NH2 CH3OH···CH3F CH3OH···CH3Cl

0.80re

0.85re

0.90re

0.95re

1.00re

1.05re

1.10re

1.25re

1.50re

2.00re

−0.282 −1.724 −2.074 −2.231 −0.736 −1.698 −0.264 −1.588 −0.595 −1.172 −9.096 −12.508 −2.940 −3.169 −2.114 −0.988 −1.118 −0.948 −0.788 −1.476 −1.117 −1.430 −2.479 −2.771 −8.955 −10.857 −4.225 −6.403 −3.866 −6.013 5.203 5.739 5.514 3.023 2.922 1.954 9.426 7.095 1.727 0.238

0.253 0.104 0.134 0.128 0.303 0.128 0.458 0.227 0.907 0.462 −1.890 −2.152 −0.113 −0.281 0.703 1.101 1.559 2.238 0.694 0.918 1.742 0.752 1.146 2.230 −1.202 −3.132 −0.724 −1.420 0.203 −0.398 7.679 8.338 7.871 4.790 4.344 3.124 12.256 9.441 3.037 2.315

0.456 0.855 1.059 1.121 0.682 0.805 0.687 0.957 1.504 1.134 1.904 3.061 0.907 1.102 1.981 2.011 2.755 3.676 1.330 2.028 3.058 1.771 2.945 4.714 1.507 1.538 0.960 1.101 2.179 2.443 9.033 9.768 9.108 5.783 5.142 3.796 13.747 10.768 3.681 3.356

0.497 1.075 1.340 1.424 0.763 0.984 0.697 1.156 1.660 1.329 3.679 5.354 1.172 1.697 2.408 2.281 3.130 4.127 1.509 2.409 3.490 2.126 3.662 5.700 2.275 2.959 1.642 2.202 2.962 3.660 9.629 10.405 9.605 6.249 5.509 4.117 14.333 11.394 3.907 3.761

0.465 1.051 1.320 1.402 0.718 0.955 0.622 1.114 1.614 1.305 4.294 6.050 1.132 1.715 2.393 2.224 3.075 4.051 1.457 2.405 3.442 2.123 3.764 5.833 2.288 3.101 1.794 2.524 3.105 3.976 9.725 10.514 9.622 6.359 5.583 4.198 14.315 11.537 3.880 3.793

0.406 0.931 1.177 1.246 0.628 0.848 0.522 0.978 1.487 1.191 4.283 5.922 0.985 1.500 2.172 2.019 2.817 3.722 1.301 2.214 3.158 1.943 3.540 5.508 2.029 2.780 1.687 2.449 2.929 3.826 9.500 10.279 9.339 6.239 5.464 4.118 13.905 11.353 3.709 3.617

0.343 0.785 0.999 1.053 0.529 0.722 0.424 0.819 1.335 1.052 3.960 5.411 0.814 1.232 1.874 1.765 2.485 3.294 1.111 1.945 2.778 1.693 3.168 4.967 1.710 2.334 1.473 2.196 2.618 3.465 9.078 8.519 8.878 5.975 5.224 3.939 13.253 10.952 3.461 3.338

0.189 0.422 0.542 0.566 0.293 0.407 0.214 0.431 0.934 0.690 2.574 3.486 0.410 0.592 1.052 1.074 1.552 2.076 0.568 1.149 1.682 0.963 1.956 3.172 0.914 1.215 0.803 1.288 1.634 2.205 7.360 7.977 7.123 4.837 4.213 3.154 10.729 9.145 2.620 2.392

0.070 0.148 0.193 0.200 0.111 0.158 0.071 0.145 0.551 0.376 1.060 1.501 0.119 0.154 0.315 0.440 0.689 0.942 0.107 0.382 0.649 0.304 0.739 1.288 0.319 0.405 0.228 0.443 0.700 0.953 4.745 5.096 4.564 3.074 2.653 1.943 6.873 6.050 1.553 1.094

0.014 0.028 0.036 0.037 0.024 0.035 0.012 0.025 0.257 0.169 0.219 0.370 0.003 −0.005 0.024 0.114 0.194 0.274 −0.033 0.001 0.090 0.002 0.097 0.226 0.054 0.067 −0.005 0.052 0.180 0.247 2.044 2.081 1.983 1.284 1.082 0.760 2.816 2.490 0.627 0.353

a

Level of theory: Gold2, MP2-F12/cc-pV{T,Q}Z-F12 half-CP + [CCSD(T)-MP2]/haV{T,Q}Z half-CP. bLevel of theory: Silver2, MP2-F12/ccpV{T,Q}Z-F12 half-CP + [CCSD(T)-MP2]/haV{D,T}Z half-CP.

Most of the MP2-F12 results were obtained as byproducts of the explicitly correlated coupled cluster calculations. However, for a subset of systems (vide inf ra), DF-MP2-F1280 calculations with the cc-pVQZ-F12 basis set were performed using MOLPRO 2015.1. Like in our previous studies on the S66×8 biomolecule dimers benchmark and on water clusters,50,76 for conventional ab initio calculations we used the combination of Dunning correlation consistent cc-pVnZ (n = D, T, Q, 5) basis sets on hydrogens and their diffuse-function augmented counterparts, aug-cc-pVnZ, on nonhydrogens other than Br and I.81−84 For the latter atoms, we employed the awCVnZ-PP basis set,85 which was developed to capture core−valence correlation contributions, specifically (n−1)d and (n−1)sp. In the remainder of the paper, this combination of up to three different basis sets will be denoted haVnZ for short.

For the haVDZ and haVTZ basis sets all MP2 results were obtained as a byproduct of the conventional coupled cluster calculations. However, for the haVQZ basis set, coupled cluster calculations were not feasible for all systems. Therefore, DFMP2 (for F- and Cl-containing systems) and RI-MP2 (for Brand I-containing ones) calculations were performed using MOLPRO 2015.161 and TURBOMOLE,62 respectively. Basis set extrapolations were carried out using the two-point formula ⎡⎛ L ⎞ α ⎤ ⎟ − 1⎥ E∞ = E(L) − [E(L) − E(L − 1)]/⎢⎜ ⎝ ⎠ ⎣ L−1 ⎦ (1)

where L is the highest angular momentum present in the basis set for elements B−Ne and Al−Ar and α is an exponent specific C


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Table 2. RMS Deviations (kcal/mol) for the MP2 Correlation Components of X40×10 Interaction Energies Calculated with Various Basis Set Using Conventional and Explicitly Correlated Methods

Due to hardware limitations, explicitly correlated CCSD(T*)-F12b/cc-pVQZ-F12 calculations were limited to 22×10 systems only (this subset only contains two bromine- and two iodine-containing systems each). However, we managed to perform CCSD(T*)-F12b/cc-pVTZ-F12 calculations for all dimers except one, as well as CCSD-F12b/cc-pVTZ-F12 and MP2-F12/cc-pVQZ-F12 calculations for all 40×10 complexes. Similarily, we were able to perform conventional CCSD(T)/ haVQZ calculations for 25×10 systems only, whereas CCSD(T)/ haVTZ was feasible for the complete list of systems. In all calculations, we also considered (n−1)d electron correlation for bromine- and iodine-containing systems. SCF and MP2 Components. Let us first discuss the SCF component, which also includes the CABS corrections. As is well-known, the addition of a CABS correction greatly accelerates basis set convergence of the SCF component, as can be seen by comparison with the conventional results. At the HF+CABS/cc-pVQZ-F12 level, the RMS counterpoise corrections are so small that the choice between raw, CP, and half-CP becomes somewhat arbitrary: we have selected the halfcounterpoise (half-CP) values, which differ by just 0.003 kcal/mol RMSD from the raw or full-CP values (Table S1,

to the level of theory and basis set pair. The basis set extrapolation exponents (α) were taken from Table 2 of ref 50. Aside from Boys−Bernardi counterpoise corrections86,87 and the uncorrected values, we also apply the average of both (socalled “half-CP”), as rationalized by Sherrill and co-workers88 for orbital-based ab initio methods and by our group89 for F12 calculations. Briefly, this technique exploits the balance between basis set superposition error (which causes overestimated interaction energies) and intrinsic basis set incompleteness (which causes underestimates).89

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RESULTS AND DISCUSSION All reference geometries were downloaded from the BEGDB website90 and used “as is”, without further optimization; the 1.0re structures had originally been optimized at the MP2 level using the cc-pVTZ-PP basis set for the Br and I, and cc-pVTZ for other atoms, and the remaining structures obtained by scaling the intermonomer distances by {0.80, 0.85, 0.90, 0.95, 1.05, 1.10, 1.25, 1.50, 2.00}.48 The complete list of systems, together with our best values for the interaction energies obtained in the present work, are presented in Table 1. D


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Table 3. RMS Deviations (kcal/mol) for the CCSD-MP2 Components of X40×10 Interaction Energies Calculated with Various Basis Setsa

a

Results with cc-pVQZ-F12 basis set are available for 18×10 F- and Cl-containing systems and 4×10 Br- and I-containing systems.

Supporting Information). As expected, counterpoise-corrected VTZ-F12 and VDZ-F12 results are already found to be close to the basis set limit; this was also observed previously for the S66×8 set50 and BEGDB set of water clusters.76 RMSD values for the MP2 correlation component are reported in Table 2. As the references, we have chosen the halfCP corrected cc-pV{T,Q}Z-F12 extrapolation, which differs by an RMS deviation of just 0.015 kcal/mol from both

counterpoise-corrected and uncorrected results. (The small counterpoise corrections indicate that we are quite close to the basis set limit.) Counterpoise-corrected cc-pV{D,T}Z-F12 extrapolated results are quite close to the reference values, with RMS deviation of 0.042 kcal/mol. cc-pVQZ-F12 results seem to benefit less from counterpoise corrections, whereas half-CP corrected cc-pVTZ-F12 produces results rather close to the basis set limit (RMSD 0.031 kcal/mol). For the relatively E


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Table 4. RMS Deviations (kcal/mol) for the (T) Term of Conventional CCSD(T) Calculated for X40×10 Interaction Energies with Various Basis Sets

MP2]/haV{T,Q}Z extrapolation, as both counterpoise corrected and uncorrected results differ by only 0.011 kcal/mol from the half-CP results (Table 3). Thus, we have chosen the half-CP corrected haV{T,Q}Z extrapolation as our primary reference level. The second best result with the conventional method is obtained by the haV{D,T}Z extrapolation (RMSD 0.058 and 0.049 kcal/mol for half-CP and full-CP corrected values, respectively), and to keep the balance in raw and counterpoise correction, we have considered half-CP corrected haV{D,T}Z results as a secondary reference (feasible for the entire list of complexes, unlike half-CP corrected haV{T,Q}Z). Let us now quickly examine the results obtained by explicitly correlated methods, for which we were able to complete CCSD-F12b/cc-pVQZ-F12 calculations for 22×10 complexes and CCSD-F12b/cc-pVnZ-F12 (n = D, T) calculations for the entire list of systems. For the [CCSD-F12b-MP2-F12]/ccpV{T,Q}Z-F12 extrapolation both counterpoise corrected and uncorrected results differ by only 0.005 kcal/mol from the halfCP results, which indicates that with explicitly correlated method we are quite close to the basis set limit and this level of theory can also serve as a primary reference; however, RMS deviation with actual considered primary reference is just 0.018 kcal/mol. Performance of cc-pV{D,T}Z-F12 extrapolation is also remarkable (RMSD 0.023 kcal/mol); even better than our current secondary reference. For explicitly correlated calculations, counterpoise corrections are less significant for fluorine- and chlorine-containing systems, but much more substantial for bromine- and iodinecontaining systems. Upon inspection, the latter display very substantial F12 contributions to the correlation energy: for instance, with the cc-pVTZ-F12-PP basis set, 387 and 447

small cc-pVDZ-F12 basis set, uncorrected results are more accurate than counterpoise corrected ones; none of them, however, is close to the basis set limit. Conventional MP2 calculations display much slower basis set convergence, as even haVQZ results are not adequate. Counterpoise-corrected MP2/ haV{T,Q}Z values, i.e., the level parallel to the MP2 component in Hobza’s work,48 deviate from our reference values by 0.026 kcal/mol RMS. (Said work does not consider subvalence correlation for Br and I, and hence a direct comparison is not possible.) Post-MP2 Corrections. As mentioned above, we were unable to perform coupled cluster calculations with large (n > T) basis sets for the complete set of systems. As an alternative, we have considered the usual additivity approximation, in which MP2 (or MP2-F12) energies, calculated with a relatively large basis set, are combined with high-level corrections (HLCs, defined as the CCSD(T)-MP2 difference) obtained using smaller basis sets. It is well-known that approximations of this sort produce excellent results when used to examine noncovalent interactions.50,89,91 Furthermore, in explicitly correlated calculations, because the (T) term does not benefit from F12 approaches, we have divided the HLCs into two separate contributions; HLC = (CCSD-MP2) + (T); and considered the two terms separately using both explicitly correlated and conventional coupled cluster approaches (as was done in our previous work76). First, let us focus on the CCSD-MP2 term. As said, we were able to complete CCSD/haVQZ calculations for 25×10 systems, and CCSD/haVTZ ones for the complete set; we recall that this actually entails aug-cc-pwCVnZ on Br and I. Counterpoise corrections seem insignificant for the [CCSDF


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Table 5. RMS Deviations (kcal/mol) for the (T) Termsa of Explicitly Correlated CCSD(T)-F12b Calculated for X40×10 Interaction Energies with Various Basis Setsb

a

(T*) values are not given in this table as those lead to unacceptable size-consistency errors, particularly for Br and I systems. bcc-pVQZ-F12 results are available for 22×10 systems, cc-pVTZ-F12 results are available for 39×10 systems, and cc-pVDZ-F12 results available for the complete set.

mhartree for Br2 and I2, respectively, compared to just 14 mhartree for CH4. When the (n−1)d electrons are frozen, the F12 contributions for Br2 and I2 drop to 49 and 51 millihartree, respectively: as pointed out in ref 65, the cc-pVnZ-F12-PP basis sets do offer a partial account for (n−1)d correlation but are inferior in this regard to a proper core−valence correlation basis set. What about the (T) component? RMS deviations for conventional (T) contributions are given in Table 4. Uncorrected and counterpoise corrected (T)/haV{T,Q}Z results are effectively indistinguishable (RMS difference = 0.002 kcal/mol); thus, we chose half-counterpoise corrected (T)/haV{T,Q}Z results, which are available for 25×10 systems, to serve as the primary reference. Among the results obtained by lower levels of theory, those of (T)/haV{D,T}Z (RMS deviations 0.013 and 0.015 kcal/mol for raw and half-CP, respectively) are the most accurate; this level of theory is fairly inexpensive and is expected to be feasible for larger systems as well. To preserve balance between raw and CP corrections, we have chosen half-CP haV{D,T}Z extrapolation as a secondary reference (results obtained at this level of theory are available for all systems). For the double- and triple-ζ basis sets, counterpoise corrections appear to be disadvantageous, whereas for larger sets they become immaterial. (See also ref 89 for a more detailed discussion on counterpoise in F12 calculations.) As mentioned in the Computational Details, we have also considered a number of approximations for (T) contributions calculated with explicitly correlated methods. Scaled (Ts)F12b/cc-pVTZ-F12 without counterpoise corrections yields excellent results (RMS deviation 0.014 kcal/mol), which are comparable to those obtained by conventional (T)/haV{D,T}Z

(Table 5). Though the computational cost associated with (Ts)-F12b/cc-pVTZ-F12 and (T)/haVTZ is roughly the same, (Ts)-F12b can be obtained as the byproduct of a single CCSD(T)-F12b calculation. Thus, it is more cost-effective than (T)/haV{D,T}Z, which requires an additional (T)/haVDZ calculation for basis set extrapolation. The cheapest available alternative appears to be raw (T*sc)/cc-pVDZ-F12, with a RMS deviation of 0.051 kcal/mol. The unmodified Marchetti− Werner approximation77,78 (T*), however, is clearly inadequate for the systems under study. Considering the HLC as a combination of the two (CCSDMP2) and (T) terms, of which the first term is obtained from explicitly correlated calculations and the second term from orbital-based ones (as was done before for water clusters76), then from the above discussion it is clear that [CCSD-F12bMP2-F12]/cc-pV{T,Q}Z-F12 half-CP + [CCSD(T)-CCSD]/ haV{T,Q}Z full-CP will be the best combination and can rightfully be chosen as a Gold reference (feasible for 22 ×10 systems: 18×10 F- or Cl-containing systems and 4×10 Br- or Icontaining systems). In addition, [CCSD-F12b-MP2-F12]/ccpV{D,T}Z-F12 CP + [CCSD(T)-CCSD]/haV{D,T}Z half-CP (available for the complete set) can serve as a Silver reference. It should be noted that the RMS difference between these two reference levels is only 0.029 kcal/mol. The above discussion leads us to suggest two different levels of theory for complete interaction energies (ordered by decreasing computational costs): Gold: half-CP corrected CCSD-F12b/cc-pV{T,Q}Z-F12 combined with conventional full-CP corrected (T)/haV{T,Q}Z (results available for 22×10 systems) G


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Table 6. RMS Deviations (kcal/mol) for the High-Level Correction (HLC = [CCSD(T)-MP2]) Components of X40×10 Interaction Energies with Various Basis Sets

a

[CCSD(T)-MP2]/ haV{T,Q}Z half-CP “Gold2”. b[CCSD(T)-MP2]/ haV{D,T}Z half-CP “Silver2”.

offers a significant advantage, as (T) tends to converge more quickly and smoothly with the basis set than CCSD-MP2 (Boese93 made similar observations in a benchmark study on hydrogen bonds; see also refs 94 and 95 in a different context). As it turns out, for the X40×10 set (see below), the F12 methods hold their own for the {F, Cl} cases and the valence part of the {Br, I} cases, but the (n−1)d core−valence pairs are “the fly in the ointment” for the latter, at least with the ccpVnZ-F12 basis sets. Effect of (n−1)d Electron Correlation. Most quantum chemical calculations of noncovalent interactions employ the frozen core approximation, in which the core electrons (found in energetically lower lying orbitals) are excluded from the correlation treatment. For B−Ne and P−Ar, the core−valence orbital energy gaps are quite large, and this is definitely the case for F and Cl (24.8 and 7.0 hartree, respectively96). However, for the heavy p-block halogens Br and I, the valence orbitals are fairly close in energy to the (n−1)d orbitals (2.2 and 1.6 hartree, respectively96), which might be expected to lead to nontrivial core−valence correlation effects. Thus, it would seem that the correlation contribution of (n−1)d, and perhaps (n− 1)spd, electrons needs to be appropriately treated for an accurate benchmark. For calculations on bromine- and iodinecontaining systems, core−valence corrections have been applied by several authors.97−100 That being said, it has recently been reported that contributions to bond energies from (n−1)sp correlation are typically an order of magnitude smaller than those from (n−1)d correlation.85

Silver: half-CP corrected MP2-F12/cc-pV{T,Q}Z-F12 combined with a HLC from full-CP corrected [CCSD-F12b-MP2F12]/cc-pV{D,T}Z-F12 and conventional half-CP corrected (T)/haV{D,T}Z (results available for the complete set) It has been argued (e.g., section 2.6 in ref 2) that for the HLC, joint extrapolation of conventional CCSD(T)-MP2 may offer error compensation advantages. At the request of a referee, we thus define two additional levels: Gold2: half-CP corrected MP2-F12/cc-pV{T,Q}Z-F12 combined with conventional HLC from half-CP corrected [CCSD(T)-MP2]/haV{T,Q}Z (results available for 25×10 systems) Silver2: half-CP corrected MP2-F12/cc-pV{T,Q}Z-F12 combined with a conventional HLC half-CP corrected [CCSD(T)-MP2]/haV{D,T}Z (results available for complete set) The error statistics with respect to the latter two reference levels are displayed in Table 6. In this context, it should be mentioned that for the explicitly correlated calculations, uncorrected HLC(T*sc) seems more appropriate for ccpVnZ-F12 basis sets (Table 7). It should be noted that explicitly correlated HLCs are better for the F- and Clcontaining systems than for Br- and I-containing ones, whereas conventional HLCs perform comparably for both kinds of systems (Tables 6 and 7). In our previous studies on water clusters76 and on the revision of the S66 data set,92 we found that the ability to converge the CCSD-F12b-MP2-F12 difference to the basis set limit and effectively suppress basis set superposition error in it H


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Table 7. RMS Deviations (kcal/mol) for the High-Level Correction (HLC = [CCSD(T)-F12b-MP2-F12]) Componentsa of X40×10 Interaction Energies with Various Basis Setsb

a HLC(T*) values are not given in this table as those leads to unacceptable size-consistence errors, particularly for Br and I systems. bcc-pVQZ-F12 results are available for 22×10 systems, cc-pVTZ-F12 results are available for 39×10 systems, and cc-pVDZ-F12 results available for the complete set. c [CCSD(T)-MP2]/ haV{T,Q}Z half-CP “Gold2”. d[CCSD(T)-MP2]/ haV{D,T}Z half-CP “Silver2”.

For the purpose of examining core−valence correlation contributions, we have chosen four complexes, namely, (03) CH4···Br2, (04) CH4···I2, (35) HBr···CH3OH, and (36) HI··· CH3OH as test systems; we then performed CCSD(T)/ haVTZ,awCVTZ(Br,I) half-CP calculations for (i) valence electrons only, (ii) valence + (n−1)d electrons, and (iii) valence + (n−1)d + (n−1)sp electrons. The calculated contributions to the interaction energies are given in Table 8. The (n−1)d inner-shell correlation component amounts to 0.168 kcal/mol RMS. Additionally including (n−1)sp correlation contributions slightly increases this difference to RMSD 0.177 kcal/mol. Hence, these test calculations clearly indicate that (n−1)d correlation contributions can indeed be nontrivial for the calculated interaction energies in the Br- and Icontaining X40×10 species, and that the (n−1)sp contributions are of a lower order of magnitude and can thus be neglected. The CCSD component can be partitioned into core−core (CC), core−valence (CV), and valence contributions as the sums of pair correlation energies εij in which, respectively, both, either, or neither of {i,j} are inner-shell orbitals. Although the core−core correlation energies are obviously much larger in absolute value than their core−valence counterparts, conventional wisdom would have it101 that the core−core contributions would largely cancel across a reaction surface: indeed, inner-shell contributions to thermochemical properties are commonly referred to as “core−valence contributions”. For our test systems (Table 8), we do find that when it comes to the (n−1)d subvalence orbitals, the CC contributions are an order of magnitude smaller than the CV terms. For the (n−1)sp contributions, however, the CC and CV are both small and comparable in magnitude: interestingly, CV tends to be

attractive and CC repulsive, causing the two (n−1)sp correlation terms to largely cancel each other. Basis Set Convergence for the (n−1)d Correlation Contribution. It is not obvious that the awCVTZ basis set considered above, or the F12 sets for that matter, would achieve convergence in the subvalence component. Thus, to have a reliable HLC benchmark for some {Br,I} cases, we have calculated CCSD(T)/haV{Q,5}Z,awCV{Q,5}Z potential curves for the same four systems as in the preceding section: 03, 04, 35, and 36, i.e., CH4···X2 and CH3OH···HX (X = Br, I), both with and without (n−1)d correlation. The (n−1)d subvalence correlation contributions can be found in Table S2, Supporting Information, together with those obtained at the CCSD-F12b/cc-pVnZ-F12 (n = T,Q) level. First of all, the (T) component of the (n−1)d correlation is found to be surprisingly small, which might prove useful in future work, as keeping the calculations including (n−1)d correlation down to the CCSD level leads to very substantial savings in CPU time and memory/mass storage overhead. Second, though the cc-pVQZ-F12-PP basis set appears to handle especially the core−valence component quite well (remaining errors likely smaller than those caused by neglect of (n−1)sp subvalence correlation), the cc-pVTZ-F12-PP basis set appears to have some trouble with the core−core component at compressed distances. For the iodine species, the error approaches 0.1 kcal/mol, which is clearly unacceptable. Both cc-pVTZ-F12-PP and cc-pVQZ-F12-PP have an easier time with the core−valence component: overall, however, it appears that for systems where the maximum feasible level is cc-pVTZF12-PP, a conventional calculation is less problematic than an F12 calculation. [To rule out that the CCSD-F12b approximation caused the problem, we repeated calculations for these I


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Table 8. CCSD(T)/hawCVTZ half-CP Calculated Interaction Energies for Selected Systems with Valence Electrons Only, Valence + (n−1)d Electrons and Valence + (n−1)spd Electronsa (n−1)d systems 03 CH4···Br2 0.80re 03 CH4···Br2 0.85re 03 CH4···Br2 0.90re 03 CH4···Br2 0.95re 03 CH4···Br2 1.00re 03 CH4···Br2 1.05re 03 CH4···Br2 1.10re 03 CH4···Br2 1.25re 03 CH4···Br2 1.50re 03 CH4···Br2 2.00re 04 CH4···I2 0.80re 04 CH4···I2 0.85re 04 CH4···I2 0.90re 04 CH4···I2 0.95re 04 CH4···I2 1.00re 04 CH4···I2 1.05re 04 CH4···I2 1.10re 04 CH4···I2 1.25re 04 CH4···I2 1.50re 04 CH4···I2 2.00re 35 HBr···CH3OH 0.80re 35 HBr···CH3OH 0.85re 35 HBr···CH3OH 0.90re 35 HBr···CH3OH 0.95re 35 HBr···CH3OH 1.00re 35 HBr···CH3OH 1.05re 35 HBr···CH3OH 1.10re 35 HBr···CH3OH 1.25re 35 HBr···CH3OH 1.50re 35 HBr···CH3OH 2.00re 36 HI···CH3OH 0.80re 36 HI···CH3OH 0.85re 36 HI···CH3OH 0.90re 36 HI···CH3OH 0.95re 36 HI···CH3OH 1.00re 36 HI···CH3OH 1.05re 36 HI···CH3OH 1.10re 36 HI···CH3OH 1.25re 36 HI···CH3OH 1.50re 36 HI···CH3OH 2.00re RMSD (kcal/mol)

valence only 2.932 0.422 −0.700 −1.110 −1.175 −1.087 −0.945 −0.542 −0.204 −0.040 3.387 0.631 −0.628 −1.107 −1.201 −1.121 −0.977 −0.555 −0.207 −0.040 −1.627 −3.288 −4.281 −4.805 −5.005 −4.990 −4.834 −3.990 −2.553 −1.053 −0.540 −1.984 −2.875 −3.370 −3.589 −3.621 −3.529 −2.915 −1.833 −0.725 REF

(n−1)sp

valence + (n−1)d

valence + (n−1)spd

core−core

core−valence

core−core

core−valence

2.718 0.291 −0.780 −1.159 −1.204 −1.105 −0.956 −0.545 −0.205 −0.041 2.977 0.364 −0.804 −1.224 −1.280 −1.174 −1.013 −0.568 −0.212 −0.041 −1.943 −3.538 −4.478 −4.961 −5.130 −5.090 −4.916 −4.037 −2.576 −1.062 −0.975 −2.327 −3.146 −3.586 −3.762 −3.761 −3.644 −2.981 −1.865 −0.737 0.168

2.693 0.268 −0.800 −1.176 −1.218 −1.116 −0.965 −0.550 −0.207 −0.041 2.909 0.313 −0.843 −1.255 −1.303 −1.192 −1.026 −0.574 −0.215 −0.041 −1.901 −3.504 −4.452 −4.941 −5.115 −5.078 −4.907 −4.032 −2.573 −1.060 −0.995 −2.343 −3.160 −3.598 −3.773 −3.770 −3.652 −2.986 −1.867 −0.737 0.177

−0.010 −0.003 0.001 0.002 0.002 0.002 0.002 0.001 0.000 0.000 −0.061 −0.029 −0.012 −0.004 0.000 0.001 0.001 0.001 0.000 0.000 −0.001 0.000 0.001 0.001 0.001 0.002 0.002 0.002 0.001 0.000 −0.073 −0.055 −0.041 −0.031 −0.023 −0.018 −0.013 −0.006 −0.002 −0.001

0.252 0.154 0.094 0.057 0.035 0.022 0.014 0.004 0.001 0.000 0.511 0.325 0.208 0.136 0.090 0.060 0.041 0.015 0.005 0.001 0.387 0.305 0.242 0.192 0.153 0.123 0.100 0.057 0.028 0.011 0.596 0.467 0.366 0.289 0.230 0.185 0.150 0.086 0.041 0.015

−0.029 −0.010 0.000 0.005 0.007 0.007 0.007 0.005 0.002 0.000 −0.018 0.000 0.009 0.012 0.012 0.011 0.009 0.005 0.003 0.001 −0.102 −0.080 −0.062 −0.048 −0.037 −0.029 −0.023 −0.012 −0.006 −0.003 −0.060 −0.045 −0.033 −0.025 −0.018 −0.014 −0.010 −0.005 −0.002 −0.001

0.052 0.031 0.018 0.011 0.006 0.004 0.002 0.000 0.000 0.000 0.081 0.048 0.028 0.017 0.010 0.006 0.003 0.001 0.000 0.000 0.049 0.037 0.028 0.021 0.016 0.012 0.009 0.004 0.002 0.000 0.073 0.055 0.041 0.031 0.024 0.018 0.014 0.007 0.003 0.001

a

Core−core (CC) and core−valence (CV) contributions to CCSD component of interaction energies are also given. The basis sets used are aug-ccpwCVTZ for Br and I and haVTZ for all other elements (see text).

systems at the more rigorous CCSD(F12*) (aka, CCSD-F12c) level102 and found that the errors for the core−core correlation were even more erratic with cc-pVnZ-F12 (n = D, T) basis sets. Detailed inspection reveals that the geminal corrections are overwhelmingly large for these pairs, with Ecorr[CCSD-F12x]/ Ecorr[CCSD] (x = b, c) ratios that approach 2. It thus appears that the smaller cc-pVnZ-F12-PP basis sets simply are not adequate for this role.] Selection of the Final Reference Data Level. For the subset of 22 systems where both “Gold” and “Gold2” are available, the RMS difference between them is (Table 9) 0.039 kcal/mol; this can be taken as a proxy for the residual uncertainty in the reference values. For comparison, the RMSD of Silver2 from the Gold values is 0.023 kcal/mol, compared to

0.033 kcal/mol for Silver. Relative to Gold2, the difference is clearer, at just 0.027 kcal/mol for Silver2 and 0.064 kcal/mol for Silver. We have hence elected to select Silver2 over Silver; for Gold vs Gold2, no decision is possible based on Table 9; the results for the inner-shell contributions in Table S2 of the ESI indicate a marginal advantage for Gold2 over Gold. For the whole set, the difference between “Silver” and “Silver2” amounts to 0.048 kcal/mol RMS. The differences are, as expected, most prominent at the highly compressed 0.80re geometries (Supporting Information for detailed results). In light of the somewhat erratic core−core component with cc-pV{D,T}Z-F12 basis sets, and out of a desire to have a consistent level of theory for {F, Cl, Br, I} species, we have decided to use Silver2 and Gold2 for the HLCs used for the J


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us, leading to the largest differences in the sample, 0.86 kcal/ mol at 0.8re in both cases. Nature of the Noncovalent Interactions. While revisiting the S66×8 set,50 we have proposed the correlation spin polarization index (CSPI) as an indicator for the type of noncovalent bonding character:

Table 9. RMS Differences (kcal/mol) between Our Different Levels of Theory, as Well as with the Older Reference Values all systems F- and Cl-containing systems Br- and I-containing systems all systems F- and Cl-containing systems Br- and I-containing systems all systems F- and Cl-containing systems Br- and I-containing systems

Gold

Gold2

Silver2

Silver

Hobza48

REF REF

0.039 0.029

0.023 0.018

0.033 0.033

0.123 0.084

REF

0.069

0.037

0.032

0.228

0.039 0.029

REF REF

0.027 0.024

0.064 0.060

0.153 0.108

0.069

REF

0.035

0.071

0.232

0.023 0.018

0.027 0.024

REF REF

0.048 0.046

0.160 0.119

0.037

0.035

REF

0.051

0.198

CSPI =

(2) IE(2) ss − IEab (2) IE(2) ss + IEab

(2)

(2) where IE(2) ss and IEab are the same-spin and opposite-spin MP2 correlation components of the interaction energy, respectively. The CSPI value is expected to be close to zero for dispersion dominated systems, and significantly different from zero for systems of significant electrostatic and induction character. However, for highly elongated systems, absolute values of IE(2) ss and IE(2) ab become so small that CSPI can flip the sign. To avoid this problem, we have also proposed the DEBC index (dispersion-electrostatic balance in correlation):

final reference data in Table 1, although we acknowledge that the choice between Gold and Gold2 is somewhat arbitrary. Readers curious about which reference values would have been obtained using Gold and Silver may consult Table S3 in the Supporting Information. Comparison with the Original X40×10 Data Set. In this context, it would be appropriate to compare our calculated results with the originally reported values of Hobza and coworkers.48 For the 25 systems where Gold2 is available, their interaction energies differ from ours by 0.153 kcal/mol RMSD, which drops to 0.108 if only F- and Cl-containing systems are considered but increases to 0.232 kcal/mol for the seven Brand I-containing curves in that subset. For the entire sample compared to Silver2, the corresponding statistics are overall 0.160, {F, Cl} 0.119, and {Br, I} 0.198 kcal/mol. The difference between our present results and the earlier X40×10 reference data can be broken down into three factors: (a) the MP2-F12 CBS limit in the present work version CPcorrected MP2/haV{T,Q}Z calculations; (b) the HLC; (c) for the Br- and I-containing species, our inclusion of (n−1)d subvalence correlation. Concerning (a), we can compare MP2/haV{T,Q}Z for our entire data set with our MP2-F12 limits: the RMSD is just 0.026 kcal/mol, with the largest difference of about 0.1 kcal/ mol found for C6F6···C6H6 at the 0.8re geometry. Hence, this is not the major source of the discrepancy. Factor (b) is more significant: it stands to reason that CCSD(T)/aVDZ would not be the most felicitous level of theory for the HLCs in general, but particularly not those of aromatic ring complexes, where the HLCs are on the order of the interaction energy.50 And indeed, for C6H3F3···C6H6 and C6F6···C6H6 [where (c) cannot possibly be a factor], we find discrepancies as large as 0.5 and 0.7 kcal/mol, respectively, which clearly dwarf the 0.1 kcal/mol found for (a). As MP2 tends to overbind such complexes, a HLC with a too-small basis set will lead to net overbinding overall, which is indeed what we observe. As to factor (c): the calculations of Hobza and co-workers do not consider (n−1)d subvalence correlation, which we have shown above is quite important for the Br- and especially Icontaining species. This is also reflected in the RMS deviation for {Br, I} systems being about double that for {F, Cl} systems. For C 6 H 5 I···N(CH 3 ) 3 (system 24) and C6 H 5 I···HSCH 3 (system 26) we have indeed both (b) and (c) working against

DEBC =

CSPI2 1 + CSPI2

(3)

Values for DEBC range from 0 (purely dispersive) to 1 (purely nondispersive). For the X40×10 set, CSPI and DEBC values calculated for MP2-F12/cc-pVQZ-F12 energies can be found in the Supporting Information, Table S4. The maximum and minimum DEBC values observed are 0.999 and 0.196, respectively, indicating the presence of both highly and less electrostatic interactions in the data set. At equilibrium geometries, hydrogen bonded systems (31−40) are, as expected, more electrostatic in nature (DEBC values 0.493− 0.802). The halogen bonded systems (13−26), however, are less electrostatic (DEBC values 0.410−0.543).

■

CONCLUSIONS The X40×10 benchmark for halogen bonding has been reevaluated using conventional and explicitly correlated coupled cluster methods. In the process, we were able to make the following observations. Particularly for the aromatic dimers at small separation, [CCSD(T)-MP2]/aVDZ high-level corrections are manifestly inadequate and lead to overbinding by as much as threequarters of a kcal/mol at compressed distances. For the bromine and iodine species, (n−1)d subvalence correlation enhances binding by nontrivial amounts, whereas the (n−1)sp orbitals below are about an order of magnitude less important. Whereas core−valence correlation dominates the (n−1)d contribution, core−core and core−valence correlation effects are about equally important in the differential contributions of (n−1)sp correlation but tend to cancel each other. In all, subvalence correlation is more important in halogen bonding energetics than previously realized. Triple excitations (T) contributions to the subvalence correlation are small and can be omitted for reasons of cost-effectiveness. In previous studies on noncovalent interactions (S66×8,50 S66,92 water clusters76) and molecular atomization energies,103 we found that the CCSD(T)-MP2 “high-level corrections” (HLCs) are most efficiently obtained by combining the CCSDMP2 part from an explicitly correlated CCSD-F12 calculation with the (T) triples obtained through orbital-based CCSD(T) calculations (with basis set extrapolation). In this case, however, the cc-pVnZ-F12-PP basis sets for Br and I display erratic K


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convergence of the (3d)Br and (4d)I inner-shell correlation (particularly the core−core component), and only for ccpVQZ-F12-PP is basis set convergence truly achieved. Switching to the more rigorous CCSD(F12*) method does not help: apparently the smaller basis sets do not adequately cover subvalence correlation. Hence, we have elected to combine MP2-F12 basis sets limits with fully conventional HLCs for the problem at hand.

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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.jpca.7b10958. RMS deviations, inner-shell contributions, systems in the X40×10 dataset and interaction energies, and CSPI and DEBC values (PDF) Excel spreadsheets containing calculated total energies and interaction energies for the various X40×10 sets (ZIP)

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AUTHOR INFORMATION

Corresponding Author

*J. M. L. Martin. E-mail: [email protected]. Fax: +972 8 934 3029. ORCID

Jan M. L. Martin: 0000-0002-0005-5074 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS M.K.K. and D.M. acknowledge postdoctoral fellowships and N.S. acknowledges a graduate fellowship from the Feinberg Graduate School. This research was supported by the Israel Science Foundation (grant 1358/15), the Minerva Foundation, the Lise Meitner-Minerva Center for Computational Quantum Chemistry, and the Helen and Martin Kimmel Center for Molecular Design (Weizmann Institute of Science). The authors acknowledge a reviewer for helpful suggestions.

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REFERENCES

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