Density functional theory and hydrogen bonds: are we there yet?

DOI: 10.1002/cphc.201402786

Articles

Density Functional Theory and Hydrogen Bonds: Are We There Yet? A. Daniel Boese*[a, b] Density functional theory (DFT) has become more successful at introducing dispersion interactions, and can be thus applied to a wide range of systems. Amongst these are systems that contain hydrogen bonds, which are extremely important for the biological regime. Here, the description of hydrogen-bonded interactions by DFT with and without dispersion corrections is investigated. For small complexes, for which electrostatics are the determining factor in the intermolecular interactions, the

inclusion of dispersion with most functionals yields large errors. Only for larger systems, in which van der Waals interactions are more important, do dispersion corrections improve the performance of DFT for hydrogen-bonded systems. None of the studied functionals, including double hybrid functionals (with the exception of DSD-PBEP86 without dispersion corrections), are more accurate than MP2 for the investigated species.

1. Introduction Hydrogen bonds (HBs) are important in biology and many fields of chemistry. For example, the essential DNA double helix is held together by hydrogen-bonded base pairs. Also, many chemical reactions take place in water, thus HBs are of utmost importance and consequently a good description is necessary when simulating the liquid state.[1–4] Although this work is focused only on single or double HBs, in liquids and in macromolecules multiple HBs determine the interactions. Thus, even a small inaccuracy in the description of a single hydrogen bond may add up to huge errors for such systems. From a methodology perspective, post-Hartree–Fock methods, such as CCSD(T), can accurately describe HBs.[5] CCSD(T) can be considered as the gold standard in computational chemistry for single-reference systems. For a small set of 16 hydrogen-bonded complexes, a root mean square (RMS) error of 0.21 kJ mol 1 and a maximum deviation of 0.55 kJ mol 1 has been be achieved for valence-correlated CCSD(T), comparable with much more accurate calculations up to CCSDTQ and CCSDTQPH.[5] This set of 16 hydrogen-bonded complexes was extended to 49 complexes in the so-called HB49 set, for which CCSD(T) calculations at the basis-set limit were used as a benchmark.[6] There are several other benchmark sets for intermolecular interactions in general, and Hobza’s S22 set is one of the most prominent ones. This set contains seven neutral hydrogen-bonded species.[7, 8] Here, I will exclusively consider a large set of hydrogen-bonded systems. As density functional theory (DFT) is increasingly applied to weak interactions, especially when dispersion interactions are

included, the question arises as to how well HBs are described. Furthermore, DFT is the workhorse for Car–Parrinello molecular dynamics (CPMD) simulations in the liquid phase.[9, 10] Therefore, 52 density-functional-based methods with and without dispersion corrections were tested for the HB49 set of complexes. These methods range from the generalized gradient approximation (GGA) to double hybrid functionals including the MP2 correlation. By including different dispersion corrections, 85 different combinations of functionals and dispersion corrections were tested. For this purpose, both the performance and the basis-set dependence of DFT were investigated for a set of 16 small, hydrogen-bonded complexes.[11] Out of these complexes, special attention was paid to the ammonia dimer, which exhibits a delicate bonding situation.[12–24] Finally, to include larger systems, in which dispersion is more important, the DFT methods were investigated for the larger HB49 set.

Computational Details In this study, a range of functionals and dispersion corrections were assessed. First, functionals that include only the density and the gradient of the density (GGA functionals) were applied. 18 such functionals were investigated: B97-D,[25] BLYP,[26, 27] BOP,[26, 28] BP86,[26, 29] BPBE,[26, 30] HCTH/407,[31] LSDA,[32, 33] mPWLYP,[34, 27] OLYP,[35, 27] OPBE,[35, 30] PBE,[30] revPBE,[36, 30] TPSS,[37] vdW-DF04,[38, 39] vdW-DF2,[40] VSXC,[41] VV09,[42, 43] and VV10.[44] 11 hybrid functionals that include Hartree–Fock exchange were tested: APFD,[45] B3LYP,[26, 27, 46] B3PW91,[26, 46, 47] BHandHLYP,[26, 46, 48] BMK,[49] B97,[50] B97-1,[51] B97-2,[52] MCY2,[53–55] PBE0[56] and TPSSh.[37]

[a] Prof. Dr. A. D. Boese Department of Chemistry, Institute of Physical and Theoretical Chemistry University of Graz, Heinrichstraße 28/IV, 8010 Graz (Austria) E-mail: [email protected]

Calculations were also performed with 10 range-separated functionals: BNL,[57, 58] CAM-B3LYP,[59] HSE03,[60] HSE06,[61] HISSbPBE,[62] LRC-BOP,[26, 28, 63] LRC-wPBE,[64] LRC-wPBEh,[65] wB97,[66] and wB97X.[66, 67]

[b] Prof. Dr. A. D. Boese Department of Chemistry, University of Potsdam Karl-Liebknecht-Straße 24-25, 14476 Potsdam (Germany)

ChemPhysChem 0000, 00, 0 – 0

These are not the final page numbers! ÞÞ

1

0000 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

&

Articles Truhlar group has published a number of functionals that have been fitted to include weak interactions, and they behave differently to most other functionals. These 18 functionals were considered separately. Namely, I applied M05,[68] M052X,[69] M06 L,[70] M06,[70] M062X,[70] M06HF,[71] M08SO,[72] M08HX,[72] M11 L,[73] M11,[74] MN12 L,[75] N12,[76] MN12SX,[77] N12SX,[77] PW6B95,[78] SOGGA,[79] SOGGA11,[80] and SOGGA11X.[81]

etry optimizations and energy calculations. For the extension set of 33 complexes, smaller basis sets were used, because of the molecular size; the aug-pc-1 basis set was used for optimizing the geometries, and the aug-pc-2 basis set for calculating single point energies on these optimized geometries. As a result of the basis set assessment presented in Section 2, this combination is likely to be sufficient.

Finally, three double hybrid functionals, which include a fraction of MP2 correlation were considered: B2PLYP,[82, 83] MPW2PLYP,[83, 84] and DSDPBEP86.[85]

2. Basis Set Convergence of DFT

Thus, calculations were performed with almost all commonly used functionals .

Often, when using DFT, the choice of basis set is considered to be unimportant. The convergence of DFT to the basis-set limit with increasing size of basis set is rather quick, and as such, small basis sets are used. In many cases, diffuse functions on basis sets are not used for DFT calculations, as these lead to linear dependencies (which can, however, be eliminated) and a bad convergence of the self-consistent-field (SCF) Kohn– Sham equations for larger molecules. Of course, the basis-set error should be smaller than the error of the method itself to exclude possible basis-set effects. As the basis-set convergence of DFT and Hartree–Fock are rather similar, I used the PBE functional without any dispersion correction (which is basis-set independent by construction) as the test functional. As shown in the Supporting Information, similar results are obtained with the B3YLP functional. The basis-set limit obtained was comparable to that of the basis set with the lowest total energy, which is the aug-pc-4 basis set. All geometries were fully optimized with the respective basis sets. As there are also anionic complexes in the smaller set of 16 hydrogen-bonded complexes, these definitely require diffuse basis functions. Thus, only the 11 noncharged complexes were considered when the basis sets with and without diffuse functions were compared. In Figure 1, the errors of basis sets of double-z and triple-z quality for the 11 neutral complexes in the dissociation energy are compared. In addition, the square of the basis-set size (taking the average number of cartesian basis functions of all complexes) accounts for the approximate scaling of the method when n2 scaling is assumed for DFT (where n is the size of the basis set). The asymptotic n2 scaling was achieved in TURBOMOLE[108–114] with the exception of the diagonalization step, which scales as n3, but has, however, a low prefactor. This square of the basis-set size was then normalized to the largest basis set. As shown in Sections 3.1 and 3.2, the best functional achieved an error of about 1.6 kJ mol 1 for the small set of 16 complexes and 1.8 kJ mol 1 for the HB49 set. Hence, I would also like to achieve this accuracy with the basis set in comparison to the basis-set-limit value. Even for neutral complexes, it is difficult to achieve this error with the basis sets displayed. The lowest RMS error achieved for basis sets of double-z quality was obtained with the aug-cc-pVDZ and d-aug-cc-pVDZ basis sets with 2.6 kJ mol 1, followed by the aug-pc-1 basis set with 4.8 kJ mol 1. For basis sets of triple-z quality, only aug-pc2 (RMS error: 0.6 kJ mol 1), aug-cc-pVTZ, and d-aug-cc-pVTZ (0.7 kJ mol 1) surpassed an accuracy of 1 kJ mol 1. Both the TZVPPD and the 6-311++G(3df,2pd) basis sets gave somewhat larger, but still acceptable RMS errors of 1.3 and 1.6 kJ mol 1, respectively. Thus, the use of diffuse functions seems to be im-

For dispersion corrections, both D2[25] and D3[86, 87] corrections were included, whereas some functionals (B97-D, vdW-DF04, VV09, APFD, and wB97XD) have a built-in dispersion term. Here, vdWDF04, VV09, and APFD model the dispersion term somewhat differently than a site–site model (as done with D2, D3, B97-D and wB97XD), as they use the electron densities of the fragment atoms to derive the dispersion term. As basis sets, Pople’s 6-31G**,[88–90] 6-31++G**,[91] 6-311G,[92] 6311G**, 6-311++G**, 6-311G(2df,2pd),[93] 6-311++G(3df,2pd) basis sets were tested, as well as Jensen’s aug-pc-0, aug-pc-1, aug-pc-2, aug-pc-4,[94, 95] Dunning’s cc-pVDZ, aug-cc-pVDZ, d-aug-cc-pVDZ, cc-pVTZ, aug-cc-pVTZ, d-aug-cc-pVTZ, cc-pVQZ, aug-cc-pVQZ, daug-cc-pVQZ, cc-pV5Z, aug-cc-pV5Z, d-aug-cc-pV5Z, cc-pV6Z, augcc-pV6Z,[96–100] and Ahlrich’s SV(P), SVP, SVPD, TZVP, TZVPP, TZVPPD, QZVP, QZVPP, and QZVPPD basis sets.[101–103] For the calculations, the TURBOMOLE,[104] QChem,[105, 106] and Gaussian 09[107] program packages were used. In all cases, counterpoise corrections were not used. For cp-corrected values without any extrapolation, the errors are similar to those without cp-corrections for hydrogen-bonded systems and postHartree–Fock calculations.[6, 11] Two sets of complexes were investigated: the HB49[6] set as well as the smaller subset of 16 complexes.[5, 11] The subset of 16 hydrogen-bonded complexes consists of ClH···NH3, CN ···H2O, CO···HF, FH···NH3, H2O···H2O, H2O···NH3, HCC ···H2O, H3O + ···H2O, HCl···HCl, HF···HF, HF···H2O, HF···HCN, NH3···NH3, NH4 + ···H2O, OC···HF, and H2O···OH ; these complexes have 2–8 atoms. The values of the interaction energies of these complexes range from 7 to 141 kJ mol 1. The HB49 set also includes:[6] Ac ···H2O, Ac ···MeNH2, Ac ···MeOH, AcNH2···AcNH2, AcOH···AcOH, guand + ···CH2O, Guand + ···H2O, guand + ···MeNH2, guand + ···MeOH, H2O···MeNH2, H2O···MeOH, H2O···peptide, Imd + ···CH2O, Imd + ···H2O, Imd + ···MeNH2, Imd + ···MeOH, MeNH2···H2O, MeNH2··· MeNH2, MeNH2···MeOH, MeNH2···peptide, MeNH3 + ···CH2O, MeNH3 + ···H2O, MeNH3 + ···MeNH2, MeNH3 + ···MeOH, MeOH···H2O, MeOH···MeNH2, MeOH···MeOH, MeOH···peptide, peptide···H2O, peptide···MeNH2, peptide···MeOH, EtAc···EtAc, with the acetate anion (Ac ), acetic acid (AcOH), acetamide (AcNH2), methanol (MeOH), methylamine (MeNH2), methylammonium (MeNH3 + ), guanidinium (guand + ), imidazolium (Imd + ), N-methylacetamide (peptide), and ethylacetate (EtAc). Here, there are 8–28 atoms, and their interaction energies are in a similar range as the previous set, 13–101 kJ mol 1. This extension set mainly consists of organic molecules. For the small set of 16 hydrogen-bonded complexes, the aug-pc-3 basis set was employed for all DFT calculations, for both the geom-

&


www.chemphyschem.org

2


ÝÝ These are not the final page numbers!

Articles

Figure 2. RMS of the basis-set errors up to quadruple-z quality for basis sets including diffuse functions for 16 hydrogen-bonded systems (the SVPD basis set has an RMS error of 9 kJ mol 1). The basis-set size was determined by taking the square of the average of the number of cartesian basis functions of all complexes. Taking these values, the basis-set size was normalized to 5 for the d-aug-cc-pVQZ basis set.

lating HBs. For double hybrid functionals, even these large basis sets may not be big enough, as the fraction of MP2 correlation makes the basis-set convergence even worse and can be more comparable to MP2 rather than DFT. The convergence, however, is about two to three times better than for MP2.[6] The aug-pc-3 basis set was used to evaluate all functionals for the smaller set of 16 hydrogen-bonded complexes in Section 3.1. To encompass the HB49 set, the aug-pc-2 basis set was used at the geometries obtained with the aug-pc-1 basis set.

Figure 1. RMS of the basis-set errors and basis-set size for several basis sets of double-z (top) and triple-z (bottom) quality for the dissociation energies of 11 neutral complexes. The basis-set size was determined by taking the square of the average of the number of cartesian basis functions of all complexes. Taking these values, the basis-set size was normalized to 30 for the largest basis set of double-z-quality (d-aug-cc-pVDZ) and to 5 for the largest basis set of triple-z-quality (d-aug-cc-pVTZ; see text). All basis sets mentioned in the Computational Details, but not displayed here, have larger errors and can be found in the Supporting Information.

3. Performance of Density Functional Theory portant when calculating hydrogen-bonded complexes, and cannot be neglected: Even when going as large as QZVPP, ccpVQZ, and cc-pV5Z basis sets, the RMS errors remained as large as 2.1, 4.0, and 1.7 kJ mol 1. This means that even when testing/developing functionals or dispersion coefficients, basis sets used without diffuse functions are likely to be too small. Such a choice will introduce a large, unacceptable bias when no diffuse functions are used in the basis set, even when considering dissociation energies of neutral complexes. This largely overlooked problem has a significant impact not only when investigating HBs, but also when calculating strong adsorption energies on surfaces. In Figure 2 shows a comparison of the different errors for the set of 16 complexes when diffuse functions were included in the basis set. From basis sets of triple-z quality, only the aug-pc-2 and d-aug-cc-pVTZ basis sets exhibited an RMS error less than 1 kJ mol 1, and even the aug-cc-pVQZ basis set gave an RMS error of 1.2 kJ mol 1 when compared to the basis-set limit. The smallest basis set with an RMS error of less than 2.0 kJ mol 1 is TZVPPD (RMS error: 1.3 kJ mol 1). This is probably also the minimum basis-set size that can be used with DFT, so that larger basis-set errors are not introduced when calcuChemPhysChem 0000, 00, 0 – 0



3.1. The Set of 16 Hydrogen-Bonded Complexes Having established which basis sets to use, I turned towards the performance of density functionals for the small set of hydrogen-bonded complexes. For the GGA functionals, widespread performance with an RMS error of 2–9 kJ mol 1 was obtained. For many popular functionals, namely BP86, PBE, TPSS, and BLYP, the inclusion of dispersion interactions increased the RMS error of the functional. In the more popular functionals, only the error of revPBE decreased by a significant amount. The performance of the different GGA functionals is displayed in Figure 3. The lowest error achieved by using a GGA functional was 2.70 kJ mol 1 by using BLYP without any dispersion; this explains its success in the CPMD program. A similar error was achieved with B97-D, vdW-DF04 and vdW-DF2, whereas all other combinations of functionals with dispersion exhibited errors larger than 3 kJ mol 1. The GGA functionals with the largest errors were the uncorrected BOP, OLYP, OPBE and the dispersion-corrected PBE functional. The RMS errors of the hybrid functionals (Figure 4) were somewhat improved in comparison to the GGA functionals; 3


&

Articles

Figure 5. RMS errors of several functionals with and without dispersion terms developed by the Truhlar group for the smaller set of 16-hydrogen bonded complexes.

Figure 3. RMS errors of several GGA functionals with and without dispersion terms for the smaller set of 16 hydrogen-bonded complexes. As vdW-DF04, vdW-DF2, VV09, and VV10 include dispersion terms they are marked as D3.

(2.3 kJ mol 1), and B2PLYP+D3 (1.9 kJ mol 1) were larger. DSDPBEP86 even gave an RMS error of 1.0 kJ mol 1, this however, increased to 1.8 kJ mol 1 when D3 dispersion was included in DSDPBEP86+D3. MPW2PLYP+D yielded the largest error with 3.3 kJ mol 1. Of course, one may argue that this accuracy is not necessary for hydrogen-bonded systems. However, these errors add up, especially when computing liquid and solid phases in which HBs are dominant. Imagine a small water cluster of 20 water molecules; this already includes 30– Figure 4. RMS errors of several hybrid functionals with and without dispersion terms for the smaller set of 16 hydrogen-bonded complexes. 36 HBs, adding up to an error of only 6–7 kJ mol 1 if an accuracy 1 1 of 0.2 kJ mol per hydrogen bond is assumed for CCSD(T). For most of them yielded errors of 2–5 kJ mol . The range-separated BNL and LRC-BOP functionals gave the largest errors of 16 MP2, this error would already amount to 39–47 kJ mol 1, and for all density functionals, a much larger error of more than and 5.8 kJ mol 1, respectively. Of all hybrid functionals tested, 100 kJ mol 1 would be obtained from such calculations. In only BMK yielded a lower error (1.8 kJ mol 1) when a dispersion term was included. All functionals, however, gave a much many cases, error cancellation will be in place, but neverthelarger error than MP2, which yielded an RMS error of about less, this is a rather large maximum error deviation. This thor1.3 kJ mol 1 for these systems.[5] Only the errors of some of the ough experiment shows the difficulty of calculating such species and the errors we are dealing with, which are much larger older functionals from the Truhlar group came close to this than just the errors displayed in Tables 2–4. (displayed in Figure 5), such as M08SO (1.6 kJ mol 1), M05, and M08HX (1.7 kJ mol 1). Of the functionals published in recent years (from 2011 to the present), only the SOGGA11X function3.2 The Ammonia Dimer al yielded a lower error than 2 kJ mol 1. The PW6B95-D3 funcThe ammonia dimer (Figure 6) is a good example case for the tional, which is viewed as one of the preferable functionals, for potential energy surface of a close-range hydrogen bond. Most example, for the calculation of water clusters, still has an error of the complexes investigated have a directional hydrogen of 2.5 kJ mol 1 for these small hydrogen-bonded species, bond with an X···H Y angle of 180 degrees, whereas most of which is almost twice the RMS error of MP2. the HBs in biological systems have a smaller angle. Concerning the double hybrid functionals, their performance The ammonia dimer exhibits a X···H Y angle smaller than was also somewhat disappointing compared with that of MP2: 180 degrees; it has a nonlinear hydrogen bond with an angle Whereas pure B2PLYP without any dispersion correction gave that is between a that of a totally symmetric ammonia dimer a comparable error of 1.2 kJ mol 1, the errors of B2PLYP+D2

&



4



Articles Table 1. Energy difference of the points on the potential energy surface of the ammonia dimer and dissociation energy for several methods in respect to the reference values. In some cases, the structure of the ammonia dimer assumed either a linear (indicated by an energy deviation of the linear eclipsed conformer of 67.5 cm 1) or a symmetric geometry (indicated by an energy deviation of the C2h conformer of 2.8 cm 1). Points on the potential energy surface[a] [cm 1] ecl. sta. lin. ecl C2h Figure 6. The different configurations of the ammonia dimer.

Reference[24] CCSD[24] MP2[24] HF APFD B2PLYP+D3 B3LYP B3LYP+D3 B3PW91+D3 B97D B97D3 BHandHLYP+D3 BLYP+D3 BMK+D3 BP86+D3 CAM-B3LYP+D3 DSDPBEP86+D3 HCTH/407 LSDA LC-wPBE+D3 M06 L+D3 M06+D3 M062X+D3 M06HF+D3 MN12SX MPW2PLYPD N12 N12SX PBE0+D3 PBE+D3 PW6B95+D3 revPBE+D3 SOGGA11 SOGGA11X TPSS+D3 TPSSh+D3 wB97XD vdW-DF2 VV10

with two HBs and that of linear N···H N (180 degrees). It was extremely difficult to describe these interactions correctly with density functionals without dispersion corrections, resulting in a density functional with new parameters, HCTH/407+.[24] Perhaps, with dispersion correction, it is possible to describe the effects of this special hydrogen bond better. Here, different points on the potential energy surface of the ammonia dimer were calculated: the totally symmetrical C2h structure, the staggered and eclipsed Cs conformations of the ammonia dimer, which have a nonlinear structure and are comprised of the local and global minimum, and the two linear staggered and eclipsed structures. As can be seen from Table 1 and the numerous selected functionals tested, most of them including dispersion corrections (the full list is available in the Supporting Information), all exhibited large errors for the energy differences of the potential energy surface points of the ammonia dimer. The small energy difference (or none at all) for the symmetric C2h structure and the minimum eclipsed structure was mainly reproduced by functionals with more than 40 % exact exchange, namely BHandHLYP+D3, BMK+D3, CAM-B3LYP+D3, LCwPBE+D3, M062X+D3, and M06HF+D3 together with MN12X, SOGGA11, and PW6B95. The correct energy difference between the eclipsed and staggered conformation was reproduced well by most density functionals that include dispersion, in contrast to linear HBs. Here, energy differences of 70 cm 1 are only obtained by the simplest LSDA functional. In contrast to the density functional methods, CCSD and MP2 were good for calculating the energy differences in question, with MP2 yielding errors of less than 5 cm 1 for the energy differences calculated, and CCSD giving values of less than 8 cm 1. Of the double hybrid functionals, which include exact exchange, only DSDPBEP86+D3 performed better than most functionals, whereas MPW2PLYPD and B2PLYP+D3 yielded much larger errors. This finding implies that for the ammonia dimer, for post-Hartree–Fock methods an error cancellation is in place that does not seem to be present for current density functional theory,[24] either with or without dispersion corrections. Here, large errors (albeit for rather subtle energy differences) were obtained, and even the most modern functionals were not capable of capturing the effects exhibited by the ammonia dimer.




2.8 0.0 0.1 21.8 61.8 26.4 72.4 26.3 63.7 359.5 51.1 5.2 46.9 -2.8 96.8 12.0 12.6 24.3 28.3 9.0 31.1 30.5 -2.5 0.6 -2.8 -2.8 97.5 52.2 47.4 73.0 -21.8 -2.8 2.0 56.3 92.5 103.8 37.4 37.4 52.5

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

23.5 5.1 3.2 10.9 13.9 9.3 14.3 13.1 14.6 59.4 13.4 6.9 15.7 25.8 16.8 7.4 6.4 11.8 7.7 10.6 10.4 11.7 51.8 35.6 41.2 30.5 16.1 12.0 13.2 15.2 10.6 11.3 54.6 14.6 16.6 15.9 23.5 0.9 16.6

67.5 6.8 4.3 35.2 67.5 67.5 28.1 15.7 25.6 302.2 22.3 67.5 18.2 25.9 27.2 67.5 7.6 27.2 0.3 67.5 27.0 67.5 67.5 25.9 25.4 67.5 29.2 26.9 22.4 24.5 39.3 35.3 67.5 33.7 67.5 47.0 52.0 3315 45.5

lin. sta. 69.9 6.1 2.8 39.6 27.1 51.9 29.9 17.5 27.4 300.7 24.2 9.6 20.7 25.0 63.2 53.9 9.5 28.4 3.2 53.9 27.3 37.5 56.1 10.7 29.7 34.7 31.3 58.4 24.1 61.6 31.9 29.6 141.0 61.0 62.9 49.0 47.6 45.5 46.4

Dissociation energy [kJ mol 1] 13.26 1.95 0.99 5.68 0.11 0.31 3.06 0.17 0.84 0.98 0.86 0.34 0.19 1.19 0.26 1.03 0.31 2.05 11.09 2.31 2.05 1.09 0.81 1.80 3.31 1.19 4.27 1.16 1.18 2.42 0.93 1.06 0.39 2.85 0.50 0.01 0.37 0.35 1.55

[a] ecl. = eclipsed, lin. = linear, sta. = staged.

3.3 The HB49 Set Finally, the full HB49 set was investigated. As the molecules in this set are mainly organic molecules with 20 or more atoms, their dispersion contribution can be expected to be larger. For larger molecules, the effects of dispersion become more important (Table 2). For the HB49 set, the error of all functionals with the exception of PBE and mPWLYP was decreased when dispersion contributions were included. The best functional for the HB49 set was vdW-DF2 with an RMS error of 2.44 kJ mol 1, whereas the worst functional including dispersion was OPBE+D3, followed by VV09 and PBE+D3. 5


&

Articles Table 2. RMS errors of the smaller and the larger set of hydrogenbonded molecules for the GGA functionals tested. 16 HBonds pure D2 B97-D BLYP BOP BP86 BPBE HCTH/407 mPWLYP OLYP OPBE PBE revPBE TPSS vdW-DF04 vdW-DF2 VSXC VV09 VV10

2.70 9.05 3.78 4.25 3.66 3.26 9.59 10.29 5.60 5.81 3.14

2.70 3.86 6.22

8.03

D3 2.81 3.21 4.26 5.81 4.15 6.61 3.56 4.71 7.14 3.24 4.93 2.86 2.81

6.38

HB49 Set pure D2 6.97 13.31 6.05 8.89 7.31 4.32 14.62 17.83 4.29 9.77 5.09

3.63 3.44 5.62

6.97 4.00

Table 4. RMS errors of the smaller and the larger set of hydrogen bonded complexes for the functionals tested from the Truhlar group. 16 HBonds pure

D3 3.17 2.74 4.63 5.29 3.97

M05 M052X M06 L M06 M062X M06HF M08SO M08HX M11 L M11 MN12 L MN12SX N12 N12X PW6B95 SOGGA SOGGA11 SOGGA11X

5.43 4.03 7.09 5.82 3.35 3.97 3.53 2.44

24.61 7.03 3.84

6.09 4.15

Concerning the RMS errors of several hybrid functionals in Table 3, only the errors of CAM-B3LYP and PBE0 increased from 2.98 to 4.73 kJ mol 1 and from 4.17 to 4.29 kJ mol 1, respectively, when dispersion contributions were included. The lowest RMS errors were achieved with omegaB97XD and LRCwPBE+D3 (2.18 and 2.16 kJ mol 1), followed by B3LYP+D3 (2.67 kJ mol 1). Most of the functionals developed by the Truhlar group (Table 4) already performed well without including dispersion contributions, as they have been fitted to include as much short-range dispersion as possible. Some of the more recent functionals, however, do not seem to be as good as the previ-

APF B3LYP B3PW91 BHandHLYP BMK B97 B97-1 B97-2 BNL CAM-B3LYP HISSbPBE HSE03 HSE06 LRC-BOP LRC-wPBE LRC-wPBEh MCY2 omegaB97 omegaB97X PBE0 TPSSh

&

2.87 1.90 3.34 1.75 2.88 3.21 2.62 4.56 15.42 3.75 4.06 4.55 4.06 5.81 2.53 3.38 4.01 3.18 3.07 3.79 2.61


4.01

D3 4.77 3.20 3.41 2.75 1.79

5.36

2.97

3.11 5.28 4.16

HB49 Set pure D2 4.87 5.24 6.94 4.15 5.48 5.72 3.11 7.47 13.74 2.98 4.00 3.35 4.13 4.82 5.16 4.16 8.35 2.97 2.41 4.17 4.93

3.70


2.29 4.32 2.06 1.61 3.48 6.76

2.46

HB49 Set pure 3.47 2.77 3.29 3.09 2.26 8.96 2.44 1.93 7.54 1.97 6.80 5.44 5.92 4.56 2.23 8.66 8.68 4.75

D3 1.83 2.92 2.91 1.94 2.29 5.34

1.98

ously developed M05, M06, and M08 family of functionals. From the latter, only the errors of M06HF and M06HF+D3 are rather large. Inclusion of dispersion correction for double hybrid functionals increased RMS errors even for the HB49 set: B2PLYP gave an RMS error of 1.85 kJ mol 1, B2PLYP+D2 2.8 kJ mol 1, and B2PLYP+D3 1.96 kJ mol 1. DSDPBEP86 gave an RMS error of 1.10 kJ mol 1, even surpassing the RMS error of MP2. With dispersion, however, the RMS error was increased to 2.75 kJ mol 1 for DSD-PBEP86+D3. The largest RMS error was exhibited by mPW2PLYPD with 3.78 kJ mol 1. Finally, it can be concluded that all these errors (with the exception of DSDPBEP86 without dispersion) are still larger than that of MP2, which has an error of around 1.3 kJ mol 1, depending on the basis set.[6] Thus, for HBs, the accuracy of MP2 (with one exception) is not surpassed, neither by any form of DFT+D nor by the potentially more accurate double hybrid density functionals. Only for even larger systems, where the van-der-Waals interaction becomes even more dominant and the interaction becomes more mixed, will MP2 probably be surpassed in error by those methods.

Table 3. RMS errors of the smaller and the larger set of hydrogenbonded complexes for the hybrid functionals tested. 16 HBonds pure D2

1.65 4.23 2.10 1.65 2.88 14.64 1.56 1.74 7.02 2.19 5.36 4.98 4.98 5.19 3.08 5.80 5.80 1.81

D3

D3 4.42 2.67 2.93 3.01 3.01

4. Conclusions A range of functionals, including dispersion corrections, were investigated for a medium-sized set of hydrogen-bonded complexes (HB49) of CCSD(T)/cbs reference values. With regards to the basis-set dependence of DFT, diffuse functions are, even for DFT, of utmost importance, as neglecting them introduces unnecessarily large errors for the calculation of intermolecular interactions. Thus, a basis set of triple-z quality that includes diffuse functions should be used when calculating such interactions even with DFT. For functionals for smaller systems of 4–8 atoms, the inclusion of dispersion corrections increased the RMS error. When

4.73

2.16

2.18 4.29 3.30

6



Articles somewhat larger, organic species, in which dispersion plays a larger part, were investigated, the errors were decreased, and only a few functionals still exhibited large errors when a semiempirical dispersion term was included. In particular, the somewhat older functionals of the Truhlar group, which were developed to include some short-range dispersion, performed well when long-range dispersion was included, the M06+D3 functional gave the smallest errors. When restricted to pure GGA functionals, BLYP+D3, vdW-DF2, and M06 L+D3 are probably the methods of choice for such larger systems. None of the density functionals (including most double hybrid functionals) surpassed the accuracy of MP2.

[23] J. Stlring, M. Schtz, R. Lindh, G. Karlstrçm, P.-O. Widmark, Mol. Phys. 2002, 100, 3389. [24] A. D. Boese, A. Chandra, J. M. L. Martin, D. Marx, J. Chem. Phys. 2003, 119, 5965. [25] S. Grimme, J. Comput. Chem. 2006, 27, 1787. [26] A. D. Becke, Phys. Rev. A 1988, 38, 3098. [27] C. Lee, W. Yang, R. G. Parr, Phys. Rev. B 1988, 37, 785. [28] T. Tsuneda, T. Suzumura, K. Hirao, J. Chem. Phys. 1999, 110, 10664. [29] J. P. Perdew, Phys. Rev. B 1986, 33, 8822. [30] J. P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 1996, 77, 3865; J. P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. E 1997, 78, 1396. [31] A. D. Boese, N. C. Handy, J. Chem. Phys. 2001, 114, 5497. [32] W. Kohn, L. Sham, Phys. Rev. 1965, 140, A1133. [33] S. H. Vosko, L. Wilk, M. Nusair, Can. J. Phys. 1980, 58, 1200. [34] C. Adamo, V. Barone, J. Chem. Phys. 1998, 108, 664. [35] N. C. Handy, A. J. Cohen, Mol. Phys. 2001, 99, 403. [36] Y. Zhang, W. Yang, Phys. Rev. Lett. 1998, 80, 890. [37] J. M. Tao, J. P. Perdew, V. N. Staroverov, G. E. Scuseria, Phys. Rev. Lett. 2003, 91, 146401. [38] M. Dion, H. Rydberg, E. Schrçder, D. C. Langreth, B. I. Lundqvist, Phys. Rev. Lett. 2005, 92, 246401. [39] M. Dion, H. Rydberg, E. Schrçder, D. C. Langreth, B. I. Lundqvist, Phys. Rev. Lett. 2005, 95, 109902. [40] K. Lee, E. D. Murray, B. I. Lundqvist, D. C. Langreth, Phys. Rev. B 2010, 82, 081101. [41] T. van Voorhis, G. E. Scuseria, J. Chem. Phys. 1998, 109, 400. [42] O. A. Vydrov, T. van Voorhis, Phys. Rev. Lett. 2009, 103, 063004. [43] O. A. Vydrov, T. van Voorhis, J. Chem. Phys. 2010, 132, 164113. [44] O. A. Vydrov, T. van Voorhis, J. Chem. Phys. 2010, 133, 244103. [45] A. Austin, G. Petersson, M. J. Frisch, F. J. Dobek, G. Scalmani, K, Throssell, J. Chem. Theory Comput. 2012, 8, 4989. [46] A. D. Becke, J. Chem. Phys. 1993, 98, 5648. [47] J. P. Perdew, J. A. Chevary, S. H. Vosko, K. A. Jackson, M. R. Pederson, D. J. Singh, C. Fiolhais, Phys. Rev. B 1992, 46, 6671; J. P. Perdew, J. A. Chevary, S. H. Vosko, K. A. Jackson, M. R. Pederson, D. J. Singh, C. Fiolhais, Phys. Rev. E 1993, 48, 4978. [48] A. D. Becke, J. Chem. Phys. 1993, 98, 1372. [49] A. D. Boese, J. M. L. Martin, J. Chem. Phys. 2004, 121, 3405. [50] A. D. Becke, J. Chem. Phys. 1997, 107, 8554. [51] F. A. Hamprecht, A. J. Cohen, D. J. Tozer, N. C. Handy, J. Chem. Phys. 1998, 109, 6264. [52] P. J. Wilson, T. J. Bradley, D. J. Tozer, J. Chem. Phys. 2001, 115, 9233. [53] F. Liu, E. Proynov, J.-G. Liu, T. R. Furlani, J. Kong, J. Chem. Phys. 2012, 137, 114104. [54] P. Mori-Snchez, A. J. Cohen, W. Yang, J. Chem. Phys. 2006, 124, 091102. [55] A. J. Cohen, P. Mori-Sanchez, W. Yang, J. Chem. Phys. 2007, 127, 034101. [56] C. Adamo, V. Barone, J. Chem. Phys. 1999, 110, 6158. [57] R. Baer, D. Neuhauser, Phys. Rev. Lett. 2005, 94, 043002. [58] E. Livshits, R. Baer, Phys. Chem. Chem. Phys. 2007, 9, 2932. [59] T. Yanai, D. Tew, N. C. Handy, Chem. Phys. Lett. 2004, 393, 51. [60] J. Heyd, G. E. Scuseria, M. Ernzerhof, J. Chem. Phys. 2003, 118, 8207; J. Heyd, G. E. Scuseria, M. Ernzerhof, J. Chem. Phys. E 2006, 124, 219906. [61] A. V. Krukau, O. A. Vydrov, A. F. Izmaylov, G. E. Scuseria, J. Chem. Phys. 2006, 125, 224106. [62] T. Henderson, A. F. Izmaylov, G. E. Scuseria, A. Savin, J. Chem. Theory Comput. 2008, 4, 1254. [63] J. W. Song, T. Hirosawa, T. Tsuneda, K. Hirao, J. Chem. Phys. 2007, 126, 154105. [64] M. A. Rohrdanz, J. M. Herbert, J. Chem. Phys. 2008, 129, 034107. [65] M. A. Rohrdanz, K. M. Martins, J. M. Herbert, J. Chem. Phys. 2009, 130, 054112. [66] J.-D. Chai, M. Head-Gordon, J. Chem. Phys. 2008, 128, 084106. [67] J.-D. Chai, M. Head-Gordon, Phys. Chem. Chem. Phys. 2008, 10, 6615. [68] Y. Zhao, N. E. Schultz, D. G. Truhlar, J. Chem. Phys. 2005, 123, 161103. [69] Y. Zhao, N. E. Schultz, D. G. Truhlar, J. Chem. Theory Comput. 2006, 2, 364. [70] Y. Zhao, D. G. Truhlar, Theor. Chem. Acc. 2008, 120, 215. [71] Y. Zhao, D. G. Truhlar, J. Phys. Chem. A 2006, 110, 13126. [72] Y. Zhao, D. G. Truhlar, J. Chem. Theory Comput. 2008, 4, 1849.

Acknowledgements I would like to thank Prof. P. Saalfrank and Jun.-Prof. T. Kçrzdçrfer (University of Potsdam) for providing me with computational resources at the University of Potsdam. Furthermore, I would like to thank Prof. P. Saalfrank for useful discussions. Keywords: ab initio calculations · basis sets · density functional calculations · hydrogen bonds · intermolecular interactions [1] K. Laasonen, M. Sprik, M. Parrinello, R. Car, J. Chem. Phys. 1993, 99, 9080. [2] K. Laasonen, M. Parrinello, R. Car, C. Lee, D. Vanderbilt, Chem. Phys. Lett. 1993, 207, 208. [3] M. E. Tuckerman, K. Laasonen, M. Sprik, M. Parrinello, J. Phys. Chem. 1995, 99, 5749. [4] M. E. Tuckerman, K. Laasonen, M. Sprik, M. Parrinello, J. Chem. Phys. 1995, 103, 150. [5] A. D. Boese, J. Chem. Theory Comput. 2013, 9, 4403. [6] A. D. Boese, Mol. Phys. in press, DOI:10.1080/00268976.2014.100180 [7] P. Jurecka, J. Sponer, J. Cerny, P. Hobza, Phys. Chem. Chem. Phys. 2006, 8, 1985. [8] T. Takatani, E. G. Hohenstein, M. Malagoli, M. S. Marshall, C. D. Sherrill, J. Chem. Phys. 2010, 132, 144104. [9] R. Car, M. Parrinello, Phys. Rev. Lett. 1985, 55, 2471. [10] D. Marx, J. Hutter, in Modern Methods and Algorithms of Quantum Chemistry, edited by J. Grotendorst ~ NIC, FZ Jlich, 2000; for downloads see www.theochem.ruhr-uni-bochum.de/go/cprev.html. [11] A. D. Boese, J. M. L. Martin, W. Klopper, J. Phys. Chem. A 2007, 111, 11122. [12] M. Havenith, R. C. Cohen, K. L. Busarow, D. H. Gwo, Y. T. Lee, R. J. Saykally, J. Chem. Phys. 1991, 94, 4776. [13] M. Havenith, H. Linnartz, E. Zwart, A. Kips, J. J. ter Meulen, W. L. Meerts, Chem. Phys. Lett. 1992, 193, 261. [14] J. G. Loeser, C. A. Schmuttenmaer, R. C. Cohen, M. J. Elrod, D. W. Steyert, R. J. Saykally, R. E. Bumgarner, G. A. Blake, J. Chem. Phys. 1992, 97, 4727. [15] R. J. Saykally, G. A. Blake, Science 1993, 259, 1570. [16] H. Linnartz, A. Kips, W. L. Meerts, M. Havenith, J. Chem. Phys. 1993, 99, 2449. [17] N. Heineking, W. Stahl, E. H. T. Olthof, P. E. S. Wormer, M. Havenith, J. Chem. Phys. 1995, 102, 8693. [18] H. Linnartz, W. L. Meerts, M. Havenith, Chem. Phys. 1995, 193, 327. [19] G. Cotti, H. Linnartz, W. L. Meerts, A. van der Avoird, E. H. T. Olthof, J. Chem. Phys. 1996, 104, 3898. [20] E. H. T. Olthof, A. van der Avoird, P. E. S. Wormer, J. Chem. Phys. 1994, 101, 8430. [21] E. H. T. Olthof, A. van der Avoird, P. E. S. Wormer, J. G. Loeser, R. J. Saykally, J. Chem. Phys. 1994, 101, 8443. [22] J. S. Lee, S. Y. Park, J. Chem. Phys. 2000, 112, 230.




7


&

Articles [73] [74] [75] [76] [77] [78] [79] [80] [81] [82] [83] [84] [85] [86] [87] [88] [89] [90] [91] [92] [93] [94] [95] [96] [97] [98] [99] [100] [101] [102] [103] [104]

[105]

&

R. Perverati, D. G. Truhlar, J. Phys. Chem. Lett. 2012, 3, 117. R. Perverati, D. G. Truhlar, J. Phys. Chem. Lett. 2011, 2, 2810. R. Perverati, D. G. Truhlar, Phys. Chem. Chem. Phys. 2012, 10, 13171. R. Perverati, D. G. Truhlar, J. Chem. Theory Comput. 2012, 8, 2310. R. Perverati, D. G. Truhlar, Phys. Chem. Chem. Phys. 2012, 14, 16187. Y. Zhao, D. G. Truhlar, J. Phys. Chem. A 2005, 109, 5656. Y. Zhao, D. G. Truhlar, J. Chem. Phys. 2006, 128, 184109. R. Perverati, D. G. Truhlar, J. Phys. Chem. Lett. 2011, 2, 1991. R. Perverati, D. G. Truhlar, J. Chem. Phys. 2011, 135, 191102. S. Grimme, J. Chem. Phys. 2006, 124, 034108. T. Schwabe, S. Grimme, Phys. Chem. Chem. Phys. 2007, 9, 3397. T. Schwabe, S. Grimme, Phys. Chem. Chem. Phys. 2006, 8, 4398. S. Kozuch, J. M. L. Martin, Phys. Chem. Chem. Phys. 2011, 13, 20104. S. Grimme, J. Antony, S. Ehrlich, H. Krieg, J. Chem. Phys. 2010, 132, 154104. S. Grimme, S. Ehrlich, L. Goerigk, J. Comput. Chem. 2011, 32, 1456. W. J. Hehre, P. Ditchfield, J. A. Pople, J. Chem. Phys. 1972, 56, 2257. P. C. Hariharan, J. A. Pople, Theor. Chim. Acta 1973, 28, 213. M. M. Francl, W. J. Petro, W. J. Hehre, J. S. Binkley, M. S. Gordon, D. J. DeFrees, J. A. Pople, J. Chem. Phys. 1982, 77, 3654. T. Clark, J. Chandrasekhar, G. W. Spitznagel, P. v. R. Schleyer, J. Comput. Chem. 1983, 4, 294. R. Krishnan, J. S. Binkley, R. Seeger, J. A. Pople, J. Chem. Phys. 1980, 72, 650. M. J. Frisch, J. A. Pople, J. S. Binkley, J. Chem. Phys. 1984, 80, 3265. F. Jensen, J. Chem. Phys. 2002, 116, 7372. F. Jensen, J. Phys. Chem. A 2007, 111, 11198. T. H. Dunning Jr, J. Phys. Chem. A 1989, 104, 9062. R. A. Kendall, T. H. Dunning Jr., R. J. Harrison, J. Chem. Phys. 1992, 96, 6796. T. H. Dunning Jr, D. E. Woon, J. Chem. Phys. 1994, 100, 2975. D. E. Woon, T. H. Dunning Jr, J. Chem. Phys. 1993, 98, 1358. A. K. Wilson, T. van Mourik, T. H. Dunning Jr, J. Mol. Struct. 1996, 388, 339. F. Weigend, R. Ahlrichs, Phys. Chem. Chem. Phys. 2005, 7, 3297. F. Weigend, Phys. Chem. Chem. Phys. 2006, 8, 1057. D. Rappoport, F. Furche, J. Chem. Phys. 2010, 133, 134105. TURBOMOLE 6.5 2013, a development of the University of Karlsruhe and Forschungszentrum Karlsruhe GmbH, 1989 – 2007, TURBOMOLE GmbH, since 2007; available from http://www.turbomole.com. Y. Shao, Z. Gan, E. Epifanovsky, A. T. B. Gilbert, M. Wormit, J. Kussmann, A. W. Lange, A. Behn, J. Deng, X. Feng, D. Ghosh, M. Goldey, P. R. Horn, L. D. Jacobson, I. Kaliman, R. Z. Khaliullin, T. Kus´, A. Landau, J. Liu, E. I. Proynov, Y. M. Rhee, R. M. Richard, M. A. Rohrdanz, R. P. Steele, E. J. Sundstrom, H. L. Woodcock, P. M. Zimmerman, D. Zuev, B. Albrecht, E. Alguire, B. Austin, G. J. O. Beran, Y. A. Bernard, E. Berquist, K. Brandhorst, K. B. Bravaya, S. T. Brown, D. Casanova, C.-M. Chang, Y. Chen, S. H. Chien, K. D. Closser, D. L. Crittenden, M. Diedenhofen, R. A. DiStasio, H. Do, A. D. Dutoi, R. G. Edgar, S. Fatehi, L. Fusti-Molnar, A. Ghysels, A. Golubeva-Zadorozhnaya, J. Gomes, M. W. D. Hanson-Heine, P. H. P.



[106] [107]

[108] [109] [110] [111] [112] [113] [114]

Harbach, A. W. Hauser, E. G. Hohenstein, Z. C. Holden, T.-C. Jagau, H. Ji, B.n Kaduk, K. Khistyaev, J. Kim, J. Kim, R. A. King, P. Klunzinger, D. Kosenkov, T. Kowalczyk, C. M. Krauter, K. U. Lao, A. D. Laurent, K. V. Lawler, S. V. Levchenko, C. Y. Lin, F. Liu, E. Livshits, R. C. Lochan, A. Luenser, P. Manohar, S. F. Manzer, S.-P. Mao, N. Mardirossian, A. V. Marenich, S. A. Maurer, N. J. Mayhall, E. Neuscamman, C. M. Oana, R. Olivares-Amaya, D. P. O’Neill, J. A. Parkhill, T. M. Perrine, R. Peverati, A. Prociuk, D. R. Rehn, E. Rosta, N. J. Russ, S. M. Sharada, S. Sharma, D. W. Small, A. Sodt, T. Stein, D. Stck, Y.-C. Su, A. J. W. Thom, T. Tsuchimochi, V. Vanovschi, L. Vogt, O. Vydrov, T. Wang, M. A. Watson, J. Wenzel, A. White, C. F. Williams, J. Yang, S. Yeganeh, S. R. Yost, Z.-Q. You, I. Y. Zhang, X. Zhang, Y. Zhao, B. R. Brooks, G. K. L. Chan, D. M. Chipman, C. J. Cramer, W. A. Goddard, M. S. Gordon, W. J. Hehre, A. Klamt, H. F. Schaefer, M. W. Schmidt, C. D. Sherrill, D. G. Truhlar, A. Warshel, X. Xu, A. Aspuru-Guzik, R. Baer, A. T. Bell, N. A. Besley, J.-D. Chai, A. Dreuw, B. D. Dunietz, T. R. Furlani, S. R. Gwaltney, C.-P. Hsu, Y. Jung, J. Kong, D S. Lambrecht, W. Liang, C. Ochsenfeld, V. A. Rassolov, L. V. Slipchenko, J. E. Subotnik, T. V. Voorhis, J. M. Herbert, A. I. Krylov, P. M. W. Gill, M. Head-Gordon, Mol. Phys. 2015, 113, 184. A. I. Krylov, P. M. W. Gill, WIREs Comput. Mol. Sci. 2013, 3, 317. Gaussian 09 (Revision D.01), M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, G. Scalmani, V. Barone, B. Mennucci, G. A. Petersson, H. Nakatsuji, M. Caricato, X. Li, H. P. Hratchian, A. F. Izmaylov, J. Bloino, G. Zheng, J. L. Sonnenberg, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, T. Vreven, J. A. Montgomery Jr., J. E. Peralta, F. Ogliaro, M. Bearpark, J. J. Heyd, E. Brothers, K. N. Kudin, V. N. Staroverov, R. Kobayashi, J. Normand, K. Raghavachari, A. Rendell, J. C. Burant, S. S. Iyengar, J. Tomasi, M. Cossi, N. Rega, J. M. Millam, M. Klene, J. E. Knox, J. B. Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R. E. Stratmann, O. Yazyev, A. J. Austin, R. Cammi, C. Pomelli, J. W. Ochterski, R. L. Martin, K. Morokuma, V. G. Zakrzewski, G. A. Voth, P. Salvador, J. J. Dannenberg, S. Dapprich, A. D. Daniels, . Farkas, J. B. Foresman, J. V. Ortiz, J. Cioslowski, D. J. Fox, Gaussian, Inc, Wallingford, CT, 2009. http://www.cosmologic.de/files/downloads/white-papers/WP Turbomole-HF-exchange.pdf. M. Hser, R. Ahlrichs, J. Comput. Chem. 1989, 10, 104. C. Ochsenfeld, C. A. White, M. Head-Gordon, J. Chem. Phys. 1998, 109, 1663. F. Weigend, Phys. Chem. Chem. Phys. 2002, 4, 4285. R. A. Friesner, Chem. Phys. Lett. 1985, 116, 39. F. Neese, F. Wennmohs, A. Hansen, U. Becker, Chem. Phys. 2009, 356, 98 . P. Plessow, F. Weigend, J. Comput. Chem. 2012, 33, 810.

Received: November 3, 2014 Revised: December 12, 2014 Published online on && &&, 2014

8



ARTICLES A. D. Boese* && – && Density Functional Theory and Hydrogen Bonds: Are We There Yet?

A good description? The description of hydrogen-bonded interactions by DFT with and without dispersion corrections is investigated for a range of 49 different complexes with special attention


being paid to the ammonia dimer. For small complexes, DFT(+ D) gives large errors. Including dispersion corrections improves the performance of DFT only for larger systems.



9


&

Are we there yet?

Are we nearly there yet?

Keratoprostheses: are we there yet?

Participation: are we there yet

CMV and glioma--are we there yet?

Artificial lungs: are we there yet?

CPAP holiday: are we there yet?

Fetal cardiac therapy: are we there yet?

Predicting seizures: are we there yet?

Chagas disease: are we there yet?

Personalized medicine: are we there yet?

HLA-DP1 matching: are we there yet?

The artificial pancreas: are we there yet?

Are we there yet? Hmmnot quite.

Quality-by-design: are we there yet?

CPAP holiday: are we there yet?

Improving CPR measurement: are we there yet?

Myocardial Inflammation-Are We There Yet?

Clinical transplantation and tolerance: are we there yet?

Focal and segmental glomerulosclerosis--are we there yet?

Convergence of nanotechnology and cancer prevention: are we there yet?

Personalised medicine and genetic prediction--are we there yet?

Stem Cells in Skin Wound Healing: Are We There Yet?

Therapeutic modulation of Notch signalling--are we there yet?