ARTICLE pubs.acs.org/JPCA
Nuclear Shieldings with the SSB-D Functional Lluís Armangue,† Miquel Sola,† and Marcel Swart*,†,‡ † ‡
Institut de Química Computacional and Departament de Química, Universitat de Girona, Campus Montilivi, 17071 Girona, Spain Institucio Catalana de Recerca i Estudis Avanc- ats (ICREA), Pg. Lluís Companys 23, 08010, Barcelona, Spain
bS Supporting Information ABSTRACT: The recently reported SSB-D functional [J. Chem. Phys. 2009, 131, 094103] is used to check the performance for obtaining nuclear magnetic resonance (NMR) shielding constants. Four different databases were studied, which contain a diversity of molecules and nuclear shielding constants. The SSB-D functional is compared with its “parent” functionals (PBE, OPBE), the KT2 functional that was designed specially for NMR applications and the coupled cluster CCSD(T) method. The best performance for the experimentally most-used elements (1H, 13C) is obtained for the SSB-D and KT2 functionals.
’ INTRODUCTION Nuclear magnetic resonance (NMR)1 is a versatile technique used in many fields of science to investigate the (bio)molecular and electronic structure of matter in general, and of chemical compounds in particular. Because of its high sensitivity and ability to provide detailed information, NMR is crucial in experimental studies to confirm the presence of (transient) compounds and understand their function. Moreover, it can be used to probe the dynamics of protein folding,2 and in its multidimensional form can be used to investigate coupling patterns between different nuclei. Recently, advances have been made with theoretical chemistry methods for finding accurate reproductions of experimentally observed NMR shielding and spin-spin coupling constants.3 These can nowadays be obtained using both highlevel coupled cluster (CCSD(T))4 and density functional5-10 methods. The accuracy with which the shielding constants can be obtained, however, depends on several factors and is not uniformly accurate for all nuclei. For instance, Gregusova et al.11 observed an accuracy of 0.2-3.0 ppm for 15N nuclei in a wide range of simple molecules. However, several studies (among which those by Tozer et al.5,6 and Poater et al.7) showed that for 1 H these accuracies are much better (less than 1 ppm difference between theory and experiment), while for 13C they are somewhat less (3-10 ppm, depending on the method and basis set used). Surprisingly enough, the “golden” standard CCSD(T) method does not seem to improve upon the most accurate density functional methods in comparison with experimental data.5,10 However, this is probably due to the absence of zeropoint vibrational corrections in the computations, which, when taken into account, improves the agreement drastically for the CCSD(T).12 Recent studies by Xu et al.13,14 investigated a number of density functional methods and found that the OPBE functional15-17 performs remarkably well. On the other hand, Zhao and Truhlar10 showed that the M06-L (meta-GGA) functional r 2011 American Chemical Society
gives even smaller deviations than OPBE and is as good as the Keal-Tozer functionals6 (KT1 and KT2). These latter two functionals were specially designed to give a good description of the HOMO-LUMO gap and hence should be well suited for NMR shielding constants, as was shown to be indeed the case.6 Here, we use the same databases as used by Zhao and Truhlar to check the performance of the SSB-D functional,18 which was recently presented as a new all-round density functional. This new functional is a small correction to the nonempirical PBE functional,17 to mix in19 the good behavior of the OPBE functional for spin states20,21 and SN2 reaction barriers.22 At the same time, it retains an excellent description of weak interactions (hydrogen-bonding,23 π-π stacking24), which is for the stacking partly due to the inclusion of Grimme’s dispersion correction.25-27 The SSB-D functional also contains a portion of the KT1 functional, and therefore it might be expected that SSB-D should give a good description for NMR shielding constants as well. We anticipate here already that this indeed seems to be the case.
’ DATABASES We use the same databases as reported by Zhao and Truhlar,10 which were originally compiled by Tozer et al.,28 Gauss, Stanton et al.,4,29 and Helgaker et al.30,31 Each one of these databases (see Table 1) is interesting in its own right because of the chemical variety of the molecules. The first database called WT32 comes from Wilson and Tozer28 and contains a set of 21 molecules with 32 NMR shielding values which has been used previously to benchmark DFT functionals. The second one is HWAH8 from Helgaker et al.,30 a set of five molecules with eight NMR shielding constants. The third database (AGS11) was taken from Received: September 1, 2010 Revised: December 31, 2010 Published: February 3, 2011 1250
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The Journal of Physical Chemistry A Table 1. Molecules Contained in the Different Databases database WT32a
molecules HF, H2O, CH4, CO, N2, F2, O3, PN, H2S, NH3, HCN, C2H2, C2H4, H2CO, N2O, CO2, OF2, H2CNN, HCl, SO2, and PH3
HWAH8
CF4, NO2-, cis-N2F2, trans-N2F2, and C6H6
AGS11
C2H6, CH3OH, CH3NH2, CH3CN,
HLJ5
o-benzyne
CH3CHO, CH3COCH3 and CH2CCH2 a We included here the 1H NMR as well, where the reference values have been obtained from refs 52-55.
experiments by Gauss and co-workers4,29 and contains organic molecules (seven molecules with eleven 13C NMR values). Finally, the last database (HLJ5) is the o-benzyne molecule investigated by Helgaker et al.31 with five different NMR shielding constants. The molecules belonging to each of these databases are given in Table 1. Since it was shown that NMR shielding constants depend critically on the geometry used,32 we have used three different options: (i) the experimental or near-experimental geometry (see ref 28 for the difference between the two), where available, which is the case for the WT32 and HLJ5 databases; (ii) the geometry as obtained from high-level coupled cluster CCSD(T) method (using Dunning’s correlation-consistent basis sets), which were for many cases obtained from the Computational Chemistry Comparison and Benchmark Database (CCCBDB);33 (iii) the geometry as optimized by the density functionals under study with Slater-type orbital (STO) basis sets. All these different geometries are supplied in the Supporting Information.
’ COMPUTATIONAL DETAILS All calculations of the NMR shielding constants have been performed using gauge-including atomic orbitals (GIAO).34 The NMR calculations and geometry optimizations for the density functional methods were all carried out with the Amsterdam Density Functional (ADF) program (version 2009.01).35,36 The coupled cluster CCSD(T) geometries and NMR shielding constants not yet available (with Dunning basis sets) in the literature have been obtained with the CFOUR (Coupled-Cluster techniques for Computational Chemistry) program.37,38 In all cases, the mean absolute deviation (MAD) was calculated for all molecules with each geometry, method and database, by taking the experimental shielding constant as reference value. ’ DENSITY FUNCTIONALS AND BASIS SETS Apart from the SSB and SSB-D functionals, we include (i) the OPBE15 functional that combines Handy and Cohen’s OPTX exchange functional16 with the PBEc17 correlation functional; (ii) the nonempirical PBE functional17 from Perdew et al.; and (iii) the KT26 functional by Keal and Tozer, which was designed to give a good description of the HOMO-LUMO gap and hence NMR shielding constants. Uncontracted sets of Slater-type orbitals (STOs) of triple-ς and quadruple-ς quality were used for the density functional calculations: TZP, TZ2P, and the even-tempered ET-pVQZ.39 Finally, for the CCSD(T) NMR shielding constants that were computed here, the aug-cc-pVTZ basis set was used.40,41
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’ RESULTS AND DISCUSSION We have studied four different databases (see Table 1) containing a wide variety of bonding patterns and compare the results obtained with four different functionals (PBE, OPBE, SSB-D, and KT2) with coupled cluster CCSD(T) and/or experimental data, where available. The choice for these density functionals was based on the fact that the recent SSB-D functional combines the best of PBE with the best of OPBE,18,19 and it is a priori unknown if its performance for NMR shielding constants would be more like PBE or OPBE. Furthermore, the KT2 functional was designed to work well for nuclear regions and hence for NMR.6 Many previous studies have already focused on the performance of density functional methods,5-10 and wave function methods,9 for the WT32 database or others, and the reader is referred to these studies for the performance of other density functionals such as LDA,5 BLYP,9 B3LYP,5,9 M06-L,10 or SAOP.5,7,8 WT32 Database. We start with the WT32 database, as compiled by Tozer and co-workers over the years,28 which is by far the largest database studied here. First of all, we were interested to see the effect of the inclusion of Grimme’s dispersion correction in SSB-D vs SSB. Although this empirical atompair-based correction in itself does not have any influence on the NMR shielding constants, the SSB-D and SSB functionals do have different parameters for calculating the exchangecorrelation energy.18 In particular, the portion of the KT1 functional (as indicated by the u parameter within the SSB-D and SSB functionals) changes significantly with values of ca. -0.75 for SSB-D and ca. -1.21 for SSB.18 The mean unsigned error values for SSB-D compared to experimental values are quite similar to the SSB values (see Table 2). Depending on which geometry sets are taken (nearexperimental, CCSD(T), or the DFT-optimized), the overall best performance seems to be obtained with the TZ2P basis. This is mainly due to the 17O shieldings that seem to be less well described by the largest basis set (ET-pVQZ). However, for the most relevant elements in everyday experimental studies (1H, 13 C), the error decreases gradually with increasing basis set size, as one would expect. The difference between SSB and SSB-D is negligible, and SSB lacks the dispersion correction and therefore cannot give a good description of intra- and intermolecular dispersion interactions.42 Hence, from now on we will not focus anymore on SSB. Given that we have both the near-experimental and the CCSD(T) geometries for the WT32 set, we also examined how good the different density functionals work for reproducing these. Given in Table 3 are the MAD values for the four density functionals used in this study, together with three basis sets. In general, the best results are again obtained with the largest basis set (ET-pVQZ), and therefore we will report from here on only results obtained with this basis. The performance of the density functionals is similar to what was observed when presenting the SSB-D functional. In other words, the PBE functional gives a MAD value of just less than 1.0 pm, which is slightly improved upon by OPBE. Both SSB-D and KT2 further improve upon both of them and give deviations from the (near-)experimental values (0.004 Å) that approach the deviation of the CCSD(T) method compared to experiment (0.003 Å). However, it is not true that the density functionals give results similar to those of CCSD(T), as the deviations of the density functional results from the coupled cluster geometries are of the same order of magnitude as those from experiment. 1251
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Table 2. Mean Absolute Deviations (MAD, ppm) Compared to Reference Data for the WT32 Databasea Using the SSB-D and SSB Functionals with Three STO Basis Setsb and Three Different Geometriesc SSB-D nucleus
TZP
TZ2P
Table 4. Mean Absolute Deviations (MAD, ppm) in NMR Shielding Constants of WT32 Database for DFT/ET-pVQZ and CCSD(T)/aug-cc-pVTZ Compared to Experimenta nucleus
ET-pVQZ
TZP
TZ2P
ET-pVQZ
1.1
0.9
0.7
1
13
5.6
5.3
3.3
13
C
15
8.4
8.0
6.7
15
N
9.4
17
32.8
28.5
40.2
17
O
35.5
12.0
10.7
12.7
alle
11.6
13.0
11.7
H C N O
alle
H
H
H
13
C 15 N 17
O
alle
1.1
0.9
0.7
1
5.5 8.1
5.2 9.3
3.6 8.8
13
44.6
40.0
45.7
17
14.8
13.9
14.7
alle
H
C 15 N O
H
13
C
15
N
17
O alle
1.1
0.9
0.7
1
5.1
5.4
3.5
13
7.8
9.9
9.3
15
49.5 15.9
37.5 13.4
39.9 13.4
17
H
0.7
0.7
0.7
0.7
0.6
4.1
3.3
5.2
10.1
15
N
18.1
8.6
6.7
6.2
16.6
82.4 36.8
57.6 24.8
40.2 18.2
31.7 8.1
26.9 25.7
P
65.3
42.5
28.8
12.4
27.9
allc
35.6
23.1
16.3
10.7
18.0
6.3
6.0
3.9
O 19 F
8.7
7.3
31
31.0
36.9
17
d
CCSD(T) Optimized Geometry 0.7 (0.3)e
0.7 (0.3)e
e
3.6 (7.8)
4.6 (4.9)e
8.3
8.8 (12.7)e
7.6 (12.3)e
15.1
O
89.3 (96.8)e 64.3 (75.3)e 45.7 (61.5)e 36.3 (51.1)e
29.5
F 31 P
42.1 (62.8)e 30.1 (50.8)e 27.3 (48.0)e 12.9 (33.6)e 74.3 (95.3)e 50.4 (71.5)e 39.6 (60.7)e 21.0 (42.0)e
20.8 21.1
allc
39.5 (51.1)e 26.7 (37.9)e 21.0 (31.8)e 13.9 (24.0)e
15.9
1
H
0.8 (0.3)e
0.7 (0.4)e
1.1
0.9
0.7
13
C
10.5 (18.8)
6.1 8.4
5.9 9.7
3.6 9.4
15
N
20.2 (32.8)e 10.9 (18.9)e
17
42.0
37.5
43.4
19
14.4
13.5
14.3
e
e
4.0 (10.7)
1.0
0.8
0.7
C
6.0
5.7
3.4
1
N
8.6
9.9
9.6
13
C
O alle
37.4 13.2
36.5 13.2
39.2 13.2
15
N
20.9
9.8
9.3
5.2
17
O
102.8
46.6
39.9
39.6
19
F
50.3
9.2
4.0
10.6
P allc
70.8 42.9
46.4 19.5
23.9 13.6
6.0 11.1
Including 1H shielding constants, for which experimental data were taken from refs 52-55. b Slater-type orbital basis sets used: TZP, TZ2P, ET-pVQZ. c Using either (near-)experimental, CCSD(T)/(aug-)cc-p(C)VXZ geometries with X = T, Q (see Supporting Information) or the geometries optimized with DFT (e.g., at SSB-D/ET-pVQZ). d Geometries from ref 56 (see also Supporting Information). e Average of above four values. f Geometries from ref 33 (see also Supporting Information).
Table 3. Mean Absolute Deviations (MAD, Å) in Bond Lengths for DFT Compounds of the WT32 Database Compared to Experiment or CCSD(T)a TZ2P
CCSD(T)
10.3
0.7
ET-pVQZ
Compared to (Near-)Experimental PBE
0.0132
0.0099
0.0082
OPBE
0.0080
0.0070
0.0067
SSB-D
0.0058
0.0042
0.0044
KT2
0.0066
0.0043
0.0043
PBE
0.0123
0.0092
0.0078
OPBE SSB-D
0.0078 0.0052
0.0079 0.0048
0.0077 0.0051
KT2
0.0053
0.0037
0.0041
Compared to CCSD(T)
a
Mean absolute deviation between CCSD(T) and (near-)experimental is 0.0032 Å.
We now turn to the chemical shieldings constants for the WT32 set, where it is clear that CCSD(T) is not improving upon the results of density functionals (see Table 4) when compared to experimental results and without taking into account zero-point vibrational corrections. This is in particular true for carbon and nitrogen NMR parameters, where the MAD values of CCSD(T)
0.7
DFT Optimized Geometry H
a
TZP
KT2
C
1.0
DFT Optimized Geometry 1
SSB-D
13
1.0
CCSD(T) Optimized Geometryf 1
OPBE
Experimental Geometryb 1
Experimental Geometryd 1
PBE
SSB
31
1.1
0.6
0.7
0.8
11.5
4.1
3.5
4.6
a
Experimental 1H values were taken from refs 52-55; experimental 19F for OF2 (-59.3 ppm) from ref 57. b Geometries from ref 56 (see also Supporting Information). c Average of above six values. d Geometries from ref 33 (see also Supporting Information). e In parentheses the MAD values with respect to CCSD(T)/aug-cc-pVTZ.
are at least twice as large as the best density functionals. However, a recent study12 on related properties (rotational g-tensor and magnetizability) showed that zero-point vibrational corrections need to be taken into account when comparing to experiment. These corrections drastically improved the performance of the coupled cluster methods and deteriorated the density functional results. On the other hand, CCSD(T) seems to work better for oxygen and gives similarly good results as the best density functionals for 1H. The best performance for this WT32 set is observed for KT2 when looking at all six elements (1H, 13C, 15N, 17 O, 19F, 31P). Its average MAD value of 11-14 ppm (for the three sets of geometries, see Table 4) is mainly determined by the performance for 17O, with values between 32 and 40 ppm. For 15 N the MAD values are between 5.2 and 7.6 ppm, for 13C between 4.6 and 5.2 ppm, for 19F between 8.1 and 12.9 ppm, for 31 P between 6.0 and 21.0 ppm, and finally for 1H between 0.7 and 1.4 ppm. However, 17O has a nuclear spin of 5/2, which means that it is quadrupolar and yields broad signals. Therefore, large deviations from experimental data for 17O do not necessarily mean that the computations are wrong. Likewise, the experimental data for 15N might be influenced by 14N nuclei present in the samples. These 14N nuclei have nuclear spin 1 and therefore, similarly to 17O, lead to signal broadening. Furthermore, the number of 19F and 31P nuclei is very limited. Therefore, we will 1252
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The Journal of Physical Chemistry A focus only on the parameters for the most widely used 1H and 13 C nuclei from here on. For these experimentally most relevant elements (1H, 13C), SSB-D works best. It gives a MAD value of 0.7 ppm for 1H and 3.3-3.6 ppm for 13C, depending on which geometry is used (see Table 4). Similarly good results are obtained for OPBE (0.60.7 ppm for 1H, 4.0-4.1 ppm for 13C) and KT2 (0.7-1.4 ppm for 1H, 4.6-5.2 ppm for 13C), while PBE gives larger deviations for 13C (10.3-11.5 ppm). Therefore, similar to the case for spin states and SN2 barriers, the performance of SSB-D is more similar to OPBE than that of PBE. This seems to indicate that also the NMR chemical shielding is determined mainly by the region of the enhancement factor with s < 1 (where s is the usual reduced density gradient), similar to the situation for spin states and SN2 barriers.19 Note that this seems to be related more to the value of the enhancement factor F(s) at s = 0, than with the factor with which the gradient corrections are included. In other words, both PBE and PBEsol are of the form F(s) = 1 þ μ 3 s2/(1 þ c 3 s2), with different values of μ (μPBE ∼ 0.2195, μPBEsol ∼ 0.1234). Nevertheless, both give comparable performance for the WT32 set with MAD values of ca. 10 ppm for 13C (with the ET-pVQZ basis set). Likewise, both OPBE and SSB-D have values for F(s=0) that are larger than 1 (1.05151 for OPTX, 1.079966 for SSB-D), which seems to be related to their improved performance for NMR and spin states. This is similar to a study by Tozer and co-workers, who refitted the parameters of the HCTH formulation by minimizing the differences between the corresponding exchange-correlation HCTH-refit potential from ab initio xc-potentials. The best performance for nuclear shieldings needed in their study a value of ∼1.16 for the enhancement factor at s = 0.43 In a follow-up study,44 where they looked at whether or not a functional satisfies the uniform density scaling condition, an updated value of ca. 1.078 was found, which is very close to the value of SSB-D. The comparison with experimental data may need zero-point vibrational corrections,12 which are not needed for the comparison with the CCSD(T) data. Therefore, we also report the deviations from the CCSD(T) data in Table 4 for the WT32 set with CCSD(T) geometries. This showed MAD values from the CCSD(T) data of ca. 0.3-0.4 ppm for 1H for all four density functionals, and values of 4.9-18.8 ppm for 13C. With these values, we see that KT2 resembles CCSD(T) the most, followed by SSB-D, OPBE, and finally PBE. Future studies should clarify how important these vibrational corrections are for NMR chemical shieldings. HWAH8 Database. This set consists of five molecules with in total eight shielding constants of 13C, 15N, 17O, and 19F nuclei. The first molecule, tetrafluoromethane, is the simplest fluoroalkane, which has (partial) ionic character because of the large electronegativity of fluorine. There is also the nitrite ion, NO2-, the only ion present in all databases studied here. Furthermore, the HWAH8 database contains the cis and trans isomers of N2F2, for which Noggle et al.45 analyzed the double-resonance spectra in 1962. This study indicated that the FNN angle was probably different in these two isomers, with corresponding changes in the NMR parameters. Finally, the database contains benzene, which is together with the o-benzyne (HLJ5 database) the only aromatic species in these databases. According to Mitchell,46 NMR is the most frequently used experimental tool to decide whether a molecule is aromatic, although this is based more on 1 H than on 13C. Given in Table 5 are the computed NMR shielding constants for the five molecules, while Figure 1a shows the corresponding
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Table 5. NMR Shielding Constants (ppm) of HWAH8 Database for Experiment, DFT/ET-pVQZ,a and CCSD(T)/ aug-cc-pVTZa molecule nucleus CF4 NO2cis-N2F2 trans-N2F2 C6H6
expb
C
64.5
F
266 ( 6d
PBE
OPBE SSB-D
KT2
CCSD(T)c
42.6
54.3
52.1
54.8
70.2
229.3
240.2
239.8
236.1
269.0
N
-368.0
-446.1 -426.1 -329.5 -368.2 -376.6
O
-342.0
-393.4 -382.1 -380.4 -320.9 -289.3
N F
-119.8 52.8
-170.8 -148.5 -130.8 -145.0 -124.9 2.8 13.7 21.0 27.6 95.8 -238.7 -216.0 -202.5 -206.4 -183.4
N
-181.7
F
95.1
42.7
53.5
65.6
67.0
132.0
C
57.2
44.8
52.7
56.7
60.7
68.9
H
23.6e
23.8
23.8
23.9
24.0
24.2
a
Using CCSD(T)/aug-cc-pVTZ geometry58 for CF4, CCSD(T)/ccpVQZ geometry59 for C6H6 and CCSD(T)/cc-pVTZ geometry for other three molecules (see Supporting Information) b From ref 30. c CCSD(T)/aug-cc-pVTZ, this work. d From ref 60. e From ref 61.
MAD values compared to experiment. In the previous studies on this set neither the shielding constant for 19F in CF4 nor the 1H constant for benzene was taken into account, and therefore for consistency with these studies the MAD values are taken for the original eight shielding constants. However, the computed and experimental values for the two additional nuclei (19F in CF4, 1H in benzene) are reported in Table 5. The best performance is again obtained for KT2 and SSB-D, depending on which geometry one takes. When the CCSD(T) geometry is used (results reported in Table 5), the MAD values of KT2 (17.2 ppm) and SSB-D (18.3 ppm) are clearly much lower than those of OPBE (32.1 ppm) and PBE (46.8 ppm). AGS11 Database. This set is composed of six organic molecules with eleven 13C NMR values, which has been used often by Gauss and co-workers. For instance, they studied this set with second order many-body perturbation theory GIAOMBPT(2)29 and also with CCSD(T) calculations.4 The 1H nuclei were for this set also not taken into account before; however, here we report both the experimental and computed chemical shieldings for them as well (see Table 6). The MAD values for the 13C shielding constants obtained with the different density functionals are plotted in Figure 1b. Similar to what was observed for the WT32 database, the SSB-D functional gives the lowest MAD value compared to experiment (2.8-3.3 ppm, see Figure 1b), followed by KT2 (3.5-3.8 ppm), OPBE (4.6-5.5 ppm), and finally PBE (12.9-13.9 ppm). This ordering is the same irrespective if one uses the CCSD(T) or the DFT-optimized geometry for these molecules. HLJ5 Database. The last database is composed of o-benzyne, an interesting transient molecule.47 Acting as an intermediate, it is present/formed in many substitution reactions and more recently in cyclization reactions of enediynes.48,49 Although its experimental structural data is cumbersome to achieve, Kukolich et al.47 established and estimated geometric parameters and compared these with theoretical geometries and NMR measurements in a previous study. This paper followed a previous study by Schleyer, Houk, and co-workers,50 where they investigated the aromaticity and magnetic properties of the compound. Subsequently, Helgaker and co-workers31 studied this molecule, which has weakly biradical character because of a low-lying excited triplet state. They computed the NMR 1253
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Figure 1. Mean absolute deviations (MAD, ppm) in NMR shielding constants of HWAH8 (Figure 1a, left; for 13C, 15N, 17O and 19F) and AGS11 (Figure 1b, right; only 13C) databases for DFT/ET-pVQZ and CCSD(T)/aug-cc-pVTZ compared to experiment.
Table 6. NMR Shielding Constants (ppm) of AGS11 Database for DFT/ET-pVQZa and Experiment molecule
nucleus
expb
PBE OPBE SSB-D KT2 CCSD(T)c
C2H6
C
180.8
172.3 176.2 178.1 177.8
188.0
CH3OH
H C
30.0 136.5
30.5 30.6 30.5 30.5 124.6 131.7 133.8 131.7
30.7 145.0
CH3NH2
CH3CN
CH3CHO
H (CH3)d
27.4
H (OH)
30.6e
C
1.5
1.5
1.4
1.1c
8.0
7.0
11.8c
31.9
31.8
alld
11.4
7.1
4.8
4.2
6.5c
146.7 152.5 155.7 152.9
167.3
31.9
31.9
31.8
29.3
H (NH2)
30.3f
31.1
31.1
31.0
31.1
31.5
177.4 180.7 184.8 182.2
194.8
157.1
78.2 29.4
82.7 30.0
144.6 151.0 153.6 152.6
165.1
C (CHO) -6.8 -30.4 -16.1 -7.1 -8.9
5.8
62.2 29.5
71.1 29.5
76.8 29.5
H (CH3)d
28.6
29.2
29.2
29.2
29.3
29.7
H (CHO)
21.0
20.7
20.7
20.9
21.0
22.0
C (CO) Hd C (CH2) C (Csp) H
157.9
147.6 153.6 156.9 155.3
164.0
-13.2 -33.9 -19.0 -13.5 -13.0
-21.1
28.8 115.1
29.0 29.0 29.0 29.1 103.3 109.5 115.0 114.5
29.4 124.3
-29.4 -45.4 -28.9 -21.6 -24.9
-16.0
26.3
Experimental Geometryb 12.7
28.6
C (CH3)
CCSD(T)
1.5
28.7
73.7 28.9
KT2
21.2
27.7
28.7
187.6
SSB-D
C
27.8
28.6
C (CH3)
OPBE
13
27.8
28.5
C (CN) H
PBE
28.1
27.7
H (CH3)d
CH3COCH3 C (CH3)
CH2CCH2
162.3
Table 7. Mean Absolute Deviations (MAD, ppm) in NMR Shielding Constants of HLJ5 Database for DFT/ET-pVQZ Compared to Experimenta
26.4
26.4
26.4
26.5
1
H
a
CCSD(T) Optimized Geometry H C
1.4 22.1
1.4 13.5
1.2 5.9
1.3 5.1
0.9e 13.1e
alld
11.8
7.4
3.5
3.2
7.0e
1
13
DFT Optimized Geometry 1
H
1.5
1.5
1.3
1.1
C
18.2
8.5
3.4
3.5
alld
9.9
5.0
2.3
2.3
13
a
From ref 31. b From ref 47. c CCSD(T)/cc-pVTZ, this work. d Average of above two values. e CCSD(T)/aug-cc-pVTZ, this work.
27.0
a
At CCSD(T)/cc-pVTZ geometry, from ref 33 and this work (see Supporting Information). b Experimental 13C NMR from ref 4, experimental 1H data from ref 62 with σH(TMS) = 30.83 ppm.61 c CCSD(T)/ aug-cc-pVTZ, this work. d Average of the shielding values for the three hydrogens in the methyl group. e From ref 63. f From ref 64.
Figure 2. Atom numbering in o-benzyne.
shielding and nuclear spin-spin coupling with DFT functionals and CCSD. Their study concluded that CCSD followed by Keal and Tozer functionals (KT1 and KT2) perform quite well for shielding constants. The performance of the different density functionals is shown in Table 7 for both the 1H and 13C nuclear shieldings. The situation for the different functionals is the same as that reported above, with KT2 and SSB-D performing very well, followed by OPBE and finally PBE. The latter shows significantly less accurate results than the former two. This trend is seen throughout the study, and for all databases. An interesting and surprising pattern is shown in Table 7, where the 1H-MAD values for, e.g., SSB-D (1.2-1.5 ppm) are roughly twice as large as we have seen for the other sets where a typical value of 0.5-0.7 ppm was observed. This odd behavior
might be traced back to how the “experimental” proton shielding values had been obtained. In other words, according to all our computed data (i.e., for both the density functional methods and CCSD(T)) the proton shielding of (H3, H6) (see Figure 2 for atom numbers) is larger than that of (H4, H5). Experimentally, the opposite was proposed,51 but this was based on an estimate of the effect of incarceration of this delicate compound within a molecular container. Moreover, it was assumed that this incarceration effect should be the same for both protons. Given the good and consistent performance of the density functional methods and CCSD(T) for 1H shieldings (vide supra), we argue that the incarceration effect is not of equal magnitude for both hydrogens. This latter effect would be the only explanation to reconcile our computed values with the experimentally observed chemical shifts of incarcerated o-benzyne. 1254
dx.doi.org/10.1021/jp108327c |J. Phys. Chem. A 2011, 115, 1250–1256
The Journal of Physical Chemistry A
’ CONCLUSIONS We have studied nuclear magnetic resonance shielding constants for four databases (WT32, HWAH8, AGS11, HLJ5) that were previously compiled as reliable and diverse test sets. The databases were studied using both density functional and coupled cluster CCSD(T) methods. The overall performance of CCSD(T)/ aug-cc-pVTZ compared to experimental values seems to be slightly less accurate than the most accurate density functional methods studied here. This is in particular true for 13C shielding constants where CCSD(T)/aug-cc-pVTZ gives a mean absolute deviation (MAD) compared to experiment of ca. 8 ppm. For 1H shielding constants, the CCSD(T)/aug-cc-pVTZ method works well with MAD values of less than 1 ppm. It should be noted that we have not taken into account zero-point vibrational corrections. A recent study on rotational g-tensors and magnetizabilities showed that these corrections improved drastically the results for CCSD(T), and those of density functionals deteriorated. Future studies should clarify whether the same trend may be happening for the NMR chemical shieldings. The four density functionals studied here (PBE, OPBE, SSB-D, KT2) perform well in general, especially for the 1H shielding constants with MAD values of less than 1 ppm. Furthermore, the most accurate functionals (SSB-D, KT2) give small MAD values for 13C shielding constants as well (2-5 ppm). Some variation in the results is observed, depending on which geometry one takes for the molecules in the databases. Here we have studied (near-) experimental, CCSD(T) and DFT-optimized geometries for all four databases. For the Wilson-Tozer (WT32) database, the best performance is found for SSB-D with MAD values for 1H shieldings of 0.7 ppm and for 13C shieldings of 3.3-3.6 ppm (depending on which geometry is used for the molecules in the database). For the other three databases, both SSB-D and KT2 work best. The SSB-D functional was constructed as a small correction to PBE, to obtain the good results of OPBE for spin states and SN2 barriers. Here it is shown that this design also works excellently for NMR chemical shieldings and behaves more like OPBE than as PBE. This seems to indicate that the nuclear shieldings are determined by the region of the exchange enhancement factor with s < 1 (where s is the usual reduced density gradient), in a similar fashion as the situation for spin states. ’ ASSOCIATED CONTENT
bS
Supporting Information. Cartesian coordinates of all systems and DFT/CCSD(T) nuclear shieldings for the WT32 database. This material is available free of charge via the Internet at http://pubs.acs.org.
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected] ’ ACKNOWLEDGMENT The following organizations are thanked for financial support: the Ministerio de Ciencia e Innovaci on (MICINN, project numbers CTQ2008-03077/BQU and CTQ2008-06532/BQU), and the DIUE of the Generalitat de Catalunya (project numbers 2009SGR637 and 2009SGR528). Excellent service by the Centre de Supercomputacio de Catalunya (CESCA) is gratefully
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acknowledged. Support for the research of M. Sola was received through the ICREA Academia 2009 prize for excellence in research funded by the DIUE of the Generalitat de Catalunya.
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