The X40x10 Halogen Bonding Benchmark Revisited: Surprising

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The X40x10 Halogen Bonding Benchmark Revisited: Surprising Importance of (N-1)d Subvalence Correlation Manoj Kumar Kesharwani, Debashree Manna, Nitai Sylvetsky, and Jan M.L. Martin J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.7b10958 • Publication Date (Web): 01 Feb 2018 Downloaded from http://pubs.acs.org on February 3, 2018

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The Journal of Physical Chemistry

The X40x10 Halogen Bonding Benchmark Revisited: Surprising Importance of (n-1)d Subvalence Correlation (jp-2017-10958d) Manoj K. Kesharwani, Debashree Manna, Nitai Sylvetsky, and Jan M.L. Martin Department of Organic Chemistry, Weizmann Institute of Science, 76100 Reḥovot, Israel. Email: [email protected]. FAX: +972 8 934 3029

Abstract We have re-evaluated the X40x10 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 ccpVDZ-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 X40x10 data and the present revision.

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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 latter corresponds to a net attractive interaction between an electrophilic region (associated with a halogen atom) and a nucleophilic region,5 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 an σ-hole 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 coworkers 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 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 2 ACS Paragon Plus Environment

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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 coworkers.41–43 An accurate theoretical/computational description of noncovalent interactions requires some caution, as interaction 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 forcefield-based methods. However, for the purpose of conducting an appropriate benchmark study, statistics over a sufficiently large number of calculations are required. In the last decade, Hobza and coworkers 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 dataset,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 mixed-influence complexes. The S66 dataset46,47 was then extended to form the S66x8 dataset – in which each noncovalent pair is considered at eight different inter-



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monomer separations. Interaction energies of the latter dataset have been recently revised by our group.50 Nevertheless, none of the complexes included in the above datasets contain halogen atoms, and thus these benchmarks cannot represent halogen bonding or any other noncovalent interactions associated with halogen atoms. In order to describe such interactions, the Hobza group presented a new dataset 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

dataset was then

extended by considering dimer dissociation curves analogous to the S66x8 set, but with two additional points at more compressed distances: Thus, for each complex, the X40x10 dataset48 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 S66x8 and S66 dataset 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 X40x10 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. In order to render


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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 datasets particularly for halogen bonds: namely the XB18 and XB51 sets of 18 and 51 dimers, respectively. 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 X40x10 dataset, 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. Computational Details All conventional and explicitly correlated ab initio calculations were carried out using 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 cc-pVnZ-F1268 and cc-pVnZ-PP-F1265 basis set families were developed specifically for explicitly correlated calculations by Peterson and coworkers. 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 ccpVTZ-F12 and cc-pVQZ-F12 basis sets. The cc-pVnZ-PP-F12 basis sets for the heavy p-



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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 def2QZVPP/JKFIT for Br and I,73 and cc-pVnZ/JKFIT74 (augmented with a diffuse layer obtained by even-tempered expansion) for the remaining elements; while for the “MP2FIT” (DF-MP2) auxiliary basis sets, cc-pVnZ-F12-PP/MP2FIT from Ref.65 for Br and I is combined with aug-cc-pVnZ/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 CCSD-F12b/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. Most of the MP2-F12 results were obtained as by-products of the explicitly correlated coupled cluster calculations. However, for a subset of systems (vide infra), DF-MP2-F1280 calculations with the cc-pVQZ-F12 basis set were performed using MOLPRO 2015.1.


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Like in our previous studies on the S66x8 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 diffusefunction 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 by-product of the conventional coupled cluster calculations. However, for the haVQZ basis set, coupled cluster calculations were not feasible for all systems. Therefore, DF-MP2 (for F and Cl containing systems) and RI-MP2 (for Br and 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 E∞ = E(L) - [ E(L)- E(L-1)]/

− 1

(1)

where L is the highest angular momentum present in the basis set for elements B–Ne and Al–Ar and α an exponent specific 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 (so-called “half-CP”), as rationalized by Sherrill and coworkers88 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. Due to hardware limitations, explicitly correlated CCSD(T*)-F12b/cc-pVQZ-F12 calculations were limited to 22x10 systems only (this subset only contains two bromine and two iodine containing systems each). However, we managed to perform CCSD(T*)-F12b/ccpVTZ-F12 calculations for all dimers except one, as well as CCSD-F12b/cc-pVTZ-F12 and MP2-F12/cc-pVQZ-F12 calculations for all 40x10 complexes. Similarily, we were able to perform conventional CCSD(T)/ haVQZ calculations for 25x10 systems only, while CCSD(T)/ haVTZ was feasible for the complete list of systems. In all calculations, we were also considered (n-1)d electron correlation for bromine- and iodine-containing systems. The 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 half-counterpoise (half-CP) values, which differ by just 0.003 kcal/mol RMSD from the raw or full-CP values (Table S1, ESI). As expected, counterpoise-corrected VTZ-F12 and VDZ-


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F12 results are already found to be close to the basis set limit; this was also observed previously for the S66x8 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 half-CP 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 indicates 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 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, since the (T) term does



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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 25x10 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 [CCSD–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 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 22x10 complexes and CCSD-F12b/cc-pVnZ-F12 (n=D, T) calculations for the entire list of systems. For

the

[CCSD-F12b–MP2-F12]/cc-pV{T,Q}Z-F12

extrapolation

both

counterpoise

corrected and uncorrected results differ by only 0.005 kcal/mol from the half-CP 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}ZF12 extrapolation is also remarkable (RMSD 0.023 kcal/mol); even better than our current secondary reference.


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For explicitly correlated calculations, counterpoise corrections are less significant for fluorine- and chlorine- containing systems, but much more substantial for bromine- and iodine-containing 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 millihartree for Br2 and I2, respectively, compared to just 14 millihartree for CH4. When freezing the (n-1)d electrons, 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 halfcounterpoise corrected (T)/haV{T,Q}Z results, which are available for 25x10 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 kcal/mol 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 CPcorrections, 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-zeta basis sets, counterpoise corrections appear to be disadvantageous, while 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 section, 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



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deviation 0.014 kcal/mol), which are comparable to those obtained by conventional (T)/haV{D,T}Z (Table 5). While the computational cost associated with (Ts)-F12b/cc-pVTZF12 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*), on the other hand, is clearly inadequate for the systems under study. Considering the HLC as a combination of the two (CCSD–MP2) and (T) terms, of which the first term is obtained from explicitly correlated calculations and second term from orbitalbased ones (as was done before for water clusters76), then from the above discussion it is clear

that

[CCSD-F12b–MP2-F12]/cc-pV{T,Q}Z-F12

half-CP

+

[CCSD(T)–

CCSD]/haV{T,Q}Z half-CP will be the best combination and can rightfully be chosen as a Gold reference (feasible for 22x10 systems: 18x10 F- or Cl-containing systems and 4x10 Bror I-containing systems). In addition, [CCSD-F12b–MP2-F12]/cc-pV{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 fullCP corrected (T)/haV{T,Q}Z (results available for 20x10 systems) Silver: half-CP corrected MP2-F12/cc-pV{T,Q}Z-F12 combined with a HLC from full-CP corrected [CCSD-F12b–MP2-F12]/cc-pV{D,T}Z-F12 and conventional half-CP corrected (T)/haV{D,T}Z (results available for complete set)


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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 25x10 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 cc-pVnZ-F12 basis sets (Table 7). It should be noted that explicitly correlated HLCs are better for the F and Cl containing systems than for Br and I containing ones, while conventional HLCs perform comparably for both kinds of systems (Table 6 and Table 7). In our previous studies on water clusters76 and on the revision of the S66 dataset,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 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.94,95 in a different context). As it turns out for the X40x10 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



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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 iodine-containing 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 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 I containing X40x10 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. While the core-core correlation energies are obviously much larger in absolute value than their core-valence counterparts, conventional


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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, in order 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 8, 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, while 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



Page 16 of 38

systems where the maximum feasible level is cc-pVTZ-F12-PP, a conventional calculation is less problematic than an F12 calculation. [In order to rule out that the CCSD-F12b approximation caused the problem, we repeated calculations for these systems at the more rigorous CCSD(F12*) (a.k.a., CCSD-F12c) level,102 and found that the errors for the corecore 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 25 systems where both “Gold” and “Gold2” are available, the RMS difference between them is (Table 9) 0.028 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 0.018 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 (see ESI 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 final reference data in Table 1, although we acknowledge that the choice between Gold and Gold2 is somewhat arbitrary.


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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 X40x10 dataset 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 Br- and 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 X40x10 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 dataset 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.



Page 18 of 38

As to factor (c): the calculations of Hobza and coworkers do not consider (n-1)d subvalence correlation, which we have shown above is quite important for the Br and especially I containing species. This is also reflected in the RMS deviation for {Br,I} systems being about double that for {F,Cl} systems. For C6H5I…N(CH3)3 (system 24) and C6H5I…HSCH3 (system 26) we have indeed both (b) and (c) working against us, leading to the largest differences in the sample, 0.86 kcal/mol at 0.8 re in both cases.

Nature of the noncovalent interactions While revisiting the S66x8 set,50 we have proposed the correlation spin polarization index (CSPI) as an indicator for the type of noncovalent bonding character: CSPI = ()

()

()

()

(2)

()

()

where and 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 and become so small that CSPI can flip the sign. In order to avoid this problem, we have also proposed the DEBC index (dispersion-electrostatic balance in correlation): DEBC = #

$%&

$%&

(3)

Values for DEBC range from 0 (purely dispersive) to 1 (purely nondispersive). For the X40x10 set, CSPI and DEBC values calculated for MP2-F12/cc-pVQZ-F12 energies can be found in the supporting information, Table S4 (ESI). The maximum and minimum DEBC values observed are 0.999 to 0.196, respectively, indicating the presence of both highly- and 18 ACS Paragon Plus Environment

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less-electrostatic interactions in the dataset. 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 0.4100.543).

Conclusions The X40x10 benchmark for halogen bonding has been re-evaluated 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 three-quarters of a kcal/mol at compressed distances. For the bromine and iodine species, (n-1)d subvalence correlation enhances binding by nontrivial amounts, while the (n-1)sp orbitals below are about an order of magnitude less important. While 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 costeffectiveness. In previous studies on noncovalent interactions (S66x8,50 S66,92 water clusters76) and molecular atomization energies103

we found that the CCSD(T)–MP2 “high-level

corrections” (HLCs) is most efficiently obtained by combining the CCSD-MP2 part from an explicitly correlated CCSD-F12 calculation with the (T) triples obtained through orbitalbased CCSD(T) calculations (with basis set extrapolation). In this case, however, the cc-



Page 20 of 38

pVnZ-F12-PP basis sets for Br and I display erratic convergence of the (3d)Br and (4d)I inner-shell correlation (particularly the core-core component), and only for cc-pVQZ-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.

Acknowledgments MKK and DM 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 would like to acknowledge a reviewer for helpful suggestions.

Supporting Information Tables S1 through S4; Excel spreadsheet containing calculated total energies and interaction energies for the various X40x10 set. This material is available free of charge via the Internet at http://pubs.acs.org.

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Table 1. Systems in the X40x10 dataset and final recommended interaction energies (kcal/mol) obtained in the present work 1.50r Systems 01a CH4…F2 02a CH4…Cl2 03a CH4…Br2 04a CH4…I2 05a CH3F…CH4 06a CH3Cl…CH4 07a CHF3…CH4 08a CHCl3…CH4 09a CH3F…CH3F 10a CH3Cl…CH3Cl 11b C6H3F3…C6H6 12b C6F6…C6H6 13a CH3Cl…HCHO 14a CH3Br…HCHO 15b CH3I…HCHO 16a CF3Cl…HCHO 17a CF3Br…HCHO 18b CF3I…HCHO 19b C6H5Cl…CH3COCH3 20b C6H5Br…CH3COCH3 21b C6H5I…CH3COCH3 22b C6H5Cl…N(CH3)3 23b C6H5Br…N(CH3)3 24b C6H5I…N(CH3)3 25b C6H5Br…CH3SH 26b C6H5I…CH3SH 27a CH3Br…C6H6 28b CH3I…C6H6 29b CF3Br…C6H6 30b CF3I…C6H6 31a CF3OH…H2O 32a CCl3OH…H2O 33a HF…CH3OH 34a HCl…CH3OH 35a HBr…CH3OH 36a HI…CH3OH 37a HF…CH3NH2 38a HCl…CH3NH2 39a CH3OH…CH3F 40a CH3OH…CH3Cl a

0.80re -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

0.85re 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

0.90re 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

0.95re 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

1.00re 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

1.05re 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

1.10re 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

1.25re 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

e

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

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

b


2.00re 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


Page 30 of 38

Table 2. RMS deviations (kcal/mol) for the MP2 correlation components of X40x10 interaction energies calculated with various basis set using conventional and explicitly correlated methods All systems MP2-F12/cc-pVDZ-F12 MP2-F12/cc-pVTZ-F12 MP2-F12/cc-pVQZ-F12 MP2-F12/cc-pV{D,T}Z-F12 MP2-F12/cc-pV{T,Q}Z-F12 MP2/haVDZ MP2/haVTZ MP2/haVQZ MP2/haV{T,Q}Z

raw 0.126 0.069 0.027 0.130 0.015 0.754 0.319 0.117 0.081

CP 0.266 0.092 0.036 0.042 0.015 1.414 0.536 0.247 0.026

half-CP 0.192 0.031 0.009 0.060 REF 0.974 0.307 0.132 0.045

F and Cl containing systems MP2-F12/cc-pVDZ-F12 MP2-F12/cc-pVTZ-F12 MP2-F12/cc-pVQZ-F12 MP2-F12/cc-pV{D,T}Z-F12 MP2-F12/cc-pV{T,Q}Z-F12 MP2/haVDZ MP2/haVTZ MP2/haVQZ MP2/haV{T,Q}Z

0.082 0.018 0.008 0.039 0.008 0.684 0.386 0.140 0.102

0.164 0.059 0.022 0.025 0.008 1.144 0.472 0.216 0.025

0.118 0.031 0.009 0.023 REF 0.679 0.259 0.105 0.053

Br and I containing systems MP2-F12/cc-pVDZ-F12 MP2-F12/cc-pVTZ-F12 MP2-F12/cc-pVQZ-F12 MP2-F12/cc-pV{D,T}Z-F12 MP2-F12/cc-pV{T,Q}Z-F12 MP2/haVDZ MP2/haVTZ MP2/haVQZ MP2/haV{T,Q}Z

0.165 0.101 0.039 0.189 0.021 0.832 0.211 0.082 0.044

0.353 0.121 0.047 0.057 0.021 1.687 0.606 0.281 0.027

0.255 0.031 0.009 0.086 REF 1.243 0.357 0.159 0.032


Page 31 of 38 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


Table 3. RMS deviations (kcal/mol) for the CCSD–MP2 components of X40x10 interaction energies calculated with various basis seta For 25x10 systems raw CP half-CP CCSD-F12b–MP2-F12 cc-pVDZ-F12 0.057 cc-pVTZ-F12 0.032 cc-pVQZ-F12 0.017 cc-pV{D,T}Z-F12 0.033 cc-pV{T,Q}Z-F12 0.015 CCSD–MP2 (orbital based) haVDZ 0.143 haVTZ 0.046 haVQZ 0.021 haV{D,T}Z 0.068 haV{T,Q}Z 0.011

0.061 0.031 0.017 0.023 0.021

0.054 0.025 0.015 0.022 0.018

0.153 0.079 0.070 0.049 0.011

0.147 0.061 0.044 0.058 REF

18x10 F and Cl containing systems CCSD-F12b–MP2-F12 cc-pVDZ-F12 0.043 cc-pVTZ-F12 0.020 cc-pVQZ-F12 0.015 cc-pV{D,T}Z-F12 0.017 cc-pV{T,Q}Z-F12 0.015 CCSD–MP2 (orbital based) haVDZ 0.090 haVTZ 0.033 haVQZ 0.015 haV{D,T}Z 0.054 haV{T,Q}Z 0.011

half-CP

0.095 0.082

0.164 0.140

0.119 0.108

0.088

0.130

0.106

0.363 0.164

0.401 0.229

0.381 0.196

0.025

0.025

REF

F and Cl containing systems

0.058 0.027 0.015 0.020 0.021

0.049 0.022 0.015 0.017 0.018

0.068 0.061

0.070 0.050

0.067 0.055

0.063

0.045

0.054

0.092 0.061 0.062 0.036 0.011

0.089 0.044 0.037 0.044 REF

0.192 0.081

0.258 0.142

0.224 0.111

0.022

0.022

REF

7x10 Br and I containing systems CCSD-F12b–MP2-F12 cc-pVDZ-F12 0.083 cc-pVTZ-F12 0.050 cc-pVQZ-F12 0.024 cc-pV{D,T}Z-F12 0.056 cc-pV{T,Q}Z-F12 0.016 CCSD–MP2 (orbital based) haVDZ 0.229 haVTZ 0.069 haVQZ 0.032 haV{D,T}Z 0.095 haV{T,Q}Z 0.010

All systems raw CP

Br and I containing systems

0.068 0.039 0.024 0.029 0.023

0.063 0.031 0.017 0.030 0.019

0.120 0.102

0.232 0.201

0.161 0.148

0.112

0.188

0.146

0.249 0.113 0.085 0.073 0.010

0.239 0.091 0.059 0.084 REF

0.497 0.228

0.526 0.304

0.512 0.265

0.029

0.029

REF

a

Results with cc-pVQZ-F12 basis set are available for 18x10 F and Cl containing systems and 4x10 Br and I containing systems



Page 32 of 38

Table 4. RMS deviations (kcal/mol) for the (T) term of conventional CCSD(T) calculated for X40x10 interaction energies with various basis set For 25x10 systems

All systems

raw

CP

half-CP

raw

CP

half-CP

haVDZ

0.112

0.182

0.145

0.130

0.221

0.160

haVTZ

0.036

0.064

0.050

0.033

0.068

0.047

haVQZ

0.015

0.027

0.021

haV{D,T}Z

0.013

0.017

0.015

0.010

0.010

REF

haV{T,Q}Z

0.001

0.001

REF F and Cl containing systems

haVDZ

18x10 F and Cl containing systems 0.096 0.165 0.128

0.117

0.187

0.117

haVTZ

0.030

0.057

0.042

0.029

0.054

0.035

haVQZ

0.012

0.024

0.018

haV{D,T}Z

0.010

0.014

0.011

0.011

0.011

REF

haV{T,Q}Z

0.001

0.001

REF Br and I containing systems

haVDZ

7x10 Br and I containing systems 0.144 0.219 0.181

0.145

0.257

0.200

haVTZ

0.050

0.079

0.064

0.037

0.082

0.059

haVQZ

0.021

0.033

0.027

haV{D,T}Z

0.018

0.025

0.021

0.010

0.010

REF

haV{T,Q}Z

0.001

0.001

REF


Page 33 of 38 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


Table 5. RMS deviations (kcal/mol) for the (T) terms a of explicitly correlated CCSD(T)-F12b calculated for X40x10 interaction energies with various basis set.b Relative to [CCSD(T)–CCSD]/haV{T,Q}Z half-CP (reference available for 25x10 systems) raw raw raw raw CP CP CP CP All systems (T) (Ts) (T*sc) (Tbsc) (T) (Ts) (T*sc) (Tbsc) cc-pVDZ-F12 0.103 0.056 0.051 0.050 0.173 0.132 0.093 0.104 cc-pVTZ-F12 0.028 0.014 0.079 0.085 0.065 0.045 0.045 0.041 cc-pVQZ-F12 0.008 0.008 0.050 0.044 0.028 0.019 0.031 0.028 F and Cl containing systems cc-pVDZ-F12 0.091 0.050 0.034 0.038 0.159 0.122 0.093 0.104 cc-pVTZ-F12 0.024 0.013 0.025 0.018 0.058 0.039 0.022 0.029 cc-pVQZ-F12 0.009 0.007 0.016 0.012 0.026 0.017 0.007 0.011 Br and I containing systems cc-pVDZ-F12 0.130 0.069 0.080 0.073 0.206 0.155 0.093 0.103 cc-pVTZ-F12 0.037 0.016 0.144 0.158 0.082 0.057 0.078 0.062 cc-pVQZ-F12 0.006 0.012 0.112 0.100 0.035 0.024 0.071 0.061 Relative to [CCSD(T)–CCSD]/haV{D,T}Z half-CP (reference available for all systems) All systems cc-pVDZ-F12 0.121 0.063 0.093 0.075 0.221 0.149 0.087 cc-pVTZ-F12 0.026 0.025 0.109 0.121 0.077 0.047 0.050 F and Cl containing systems cc-pVDZ-F12 0.092 0.062 0.094 0.077 0.189 0.118 0.082 cc-pVTZ-F12 0.020 0.031 0.050 0.041 0.055 0.031 0.019 Br and I containing systems cc-pVDZ-F12 0.149 0.063 0.093 0.073 0.255 0.179 0.091 cc-pVTZ-F12 0.032 0.015 0.151 0.173 0.096 0.060 0.071

half-CP (T) 0.138 0.046 0.017

half-CP (Ts) 0.092 0.025 0.008

half-CP (T*sc) 0.058 0.059 0.039

half-CP (Tbsc) 0.067 0.059 0.035

0.124 0.040 0.017

0.084 0.022 0.008

0.053 0.011 0.008

0.065 0.013 0.005

0.168 0.059 0.018

0.112 0.033 0.007

0.068 0.111 0.091

0.072 0.109 0.081

0.102 0.039

0.170 0.050

0.097 0.023

0.058 0.078

0.060 0.077

0.096 0.022

0.139 0.035

0.073 0.020

0.059 0.029

0.060 0.022

0.110 0.052

0.201 0.063

0.119 0.026

0.056 0.110

0.061 0.110

a

(T*) values are not given in this table as those lead to unacceptable size-consistency errors, particularly for Br and I systems cc-pVQZ-F12 results are available for 22x10 systems, cc-pVTZ-F12 results are available for 39x10 systems and cc-pVDZ-F12 results available for the complete set b



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Table 6. RMS deviations (kcal/mol) for the High-Level Corrections (HLC = [CCSD(T)– MP2]) components of X40x10 interaction energies with various basis set w.r.t. Gold2a raw

CP

w.r.t. Silver2b half-CP

For 25x10 systems

a

raw

CP

half-CP

All systems

haVDZ

0.114

0.142

0.125

0.216

0.147

0.176

haVTZ

0.055

0.047

0.051

0.047

0.059

0.052

haVQZ

0.038

0.016

0.021 0.039

0.039

REF

haV{D,T}Z

0.043

0.022

0.027

haV{T,Q}Z

0.031

0.031

REF F and Cl containing systems

haVDZ

18x10 F and Cl containing systems 0.106 0.149 0.126

0.212

0.146

0.170

haVTZ

0.055

0.044

0.050

0.050

0.053

0.050

haVQZ

0.040

0.011

0.021

haV{D,T}Z

0.038

0.021

0.024

0.037

0.037

REF

haV{T,Q}Z

0.031

0.031

REF Br and I containing systems

haVDZ

7x10 Br and I containing systems 0.132 0.122 0.124

0.220

0.148

0.182

haVTZ

0.055

0.053

0.053

0.044

0.066

0.054

haVQZ

0.035

0.025

0.023

haV{D,T}Z

0.053

0.026

0.035

0.040

0.040

REF

haV{T,Q}Z

0.030

0.030

REF

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

b

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


Page 35 of 38 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


Table 7. RMS deviations (kcal/mol) for the High-Level Corrections (HLC = [CCSD(T)-F12b – MP2-F12]) componentsa of X40x10 interaction energies with various basis setb. w.r.t. Gold2c (reference available for 25x10 systems) raw raw raw raw For 20x10 HLC HLC HLC HLC systems (T) (Ts) (T*sc) (Tbsc) cc-pVDZ-F12 0.169 0.124 0.091 0.099 cc-pVTZ-F12 0.079 0.060 0.048 0.057 cc-pVQZ-F12 0.047 0.039 0.034 0.033 18x10 F and Cl containing systems cc-pVDZ-F12 0.139 0.099 0.074 0.083 cc-pVTZ-F12 0.061 0.044 0.033 0.037 cc-pVQZ-F12 0.038 0.031 0.024 0.027 7x10 Br and I containing systems cc-pVDZ-F12 0.228 0.171 0.124 0.132 cc-pVTZ-F12 0.114 0.090 0.074 0.090

CP HLC (T) 0.229 0.109 0.059

CP HLC (Ts) 0.192 0.090 0.050

CP HLC (T*sc) 0.161 0.074 0.039

CP HLC (Tbsc) 0.170 0.076 0.041

half-CP HLC (T) 0.197 0.093 0.052

half-CP HLC (Ts) 0.155 0.073 0.044

half-CP HLC (T*sc) 0.121 0.057 0.035

half-CP HLC (Tbsc) 0.130 0.061 0.036

0.230 0.108 0.054

0.196 0.090 0.046

0.169 0.074 0.036

0.179 0.081 0.040

0.184 0.084 0.046

0.145 0.066 0.038

0.117 0.050 0.029

0.128 0.057 0.033

0.228 0.112

0.182 0.090

0.137 0.073

0.144 0.060

0.228 0.112

0.176 0.088

0.129 0.073

0.137 0.072

cc-pVQZ-F12 0.073 0.063 0.060 0.053 0.075 0.065 0.050 0.043 0.074 0.064 0.055 0.048 d w.r.t. Silver2 (reference available for all systems) All Systems cc-pVDZ-F12 0.204 0.137 0.097 0.099 0.228 0.162 0.127 0.136 0.210 0.139 0.098 0.105 cc-pVTZ-F12 0.080 0.058 0.069 0.079 0.086 0.063 0.083 0.073 0.078 0.053 0.071 0.070 F and Cl containing systems cc-pVDZ-F12 0.131 0.083 0.091 0.082 0.240 0.176 0.144 0.156 0.184 0.121 0.098 0.104 cc-pVTZ-F12 0.044 0.042 0.050 0.044 0.093 0.072 0.057 0.063 0.066 0.050 0.043 0.045 Br and I containing systems cc-pVDZ-F12 0.268 0.182 0.104 0.117 0.212 0.143 0.104 0.108 0.237 0.158 0.097 0.107 cc-pVTZ-F12 0.108 0.072 0.086 0.107 0.078 0.051 0.105 0.083 0.090 0.056 0.093 0.092 a HLC(T*) values are not given in this table as those leads to unacceptable size-consistence errors, particularly for Br and I systems b cc-pVQZ-F12 results are available for 22x10 systems, cc-pVTZ-F12 results are available for 39x10 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”



Page 36 of 38

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 electrons. Core-core (CC) and core-valence (CV) contributions to CCSD component of interaction energies are also given.

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

valence + (n-1)d 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

valence + (n-1)spd 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

(n-1)d corecorecore valence -0.010 0.252 -0.003 0.154 0.001 0.094 0.002 0.057 0.002 0.035 0.002 0.022 0.002 0.014 0.001 0.004 0.000 0.001 0.000 0.000 -0.061 0.511 -0.029 0.325 -0.012 0.208 -0.004 0.136 0.000 0.090 0.001 0.060 0.001 0.041 0.001 0.015 0.000 0.005 0.000 0.001 -0.001 0.387 0.000 0.305 0.001 0.242 0.001 0.192 0.001 0.153 0.002 0.123 0.002 0.100 0.002 0.057 0.001 0.028 0.000 0.011 -0.073 0.596 -0.055 0.467 -0.041 0.366 -0.031 0.289 -0.023 0.230 -0.018 0.185 -0.013 0.150 -0.006 0.086 -0.002 0.041 -0.001 0.015

(n-1)sp corecorecore valence -0.029 0.052 -0.010 0.031 0.000 0.018 0.005 0.011 0.007 0.006 0.007 0.004 0.007 0.002 0.005 0.000 0.002 0.000 0.000 0.000 -0.018 0.081 0.000 0.048 0.009 0.028 0.012 0.017 0.012 0.010 0.011 0.006 0.009 0.003 0.005 0.001 0.003 0.000 0.001 0.000 -0.102 0.049 -0.080 0.037 -0.062 0.028 -0.048 0.021 -0.037 0.016 -0.029 0.012 -0.023 0.009 -0.012 0.004 -0.006 0.002 -0.003 0.000 -0.060 0.073 -0.045 0.055 -0.033 0.041 -0.025 0.031 -0.018 0.024 -0.014 0.018 -0.010 0.014 -0.005 0.007 -0.002 0.003 -0.001 0.001

The basis sets used are aug-cc-pwCVTZ for Br and I, haVTZ for all other elements (see text) 36 ACS Paragon Plus Environment

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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 REF REF REF 0.028 0.029 0.023 0.018 0.018 0.020

Gold2 0.028 0.029 0.023 REF REF REF 0.027 0.024 0.035

Silver2 0.018 0.018 0.020 0.027 0.024 0.035 REF REF REF

Silver 0.033 0.033 0.032 0.064 0.060 0.071 0.048 0.046 0.051

Hobza48 0.097 0.084 0.173 0.153 0.108 0.232 0.160 0.119 0.198



Page 38 of 38

TABLE OF CONTENTS GRAPHIC (scaled 50%)


The X40x10 Halogen Bonding Benchmark Revisited: Surprising

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