ARTICLE pubs.acs.org/JPCA
Why Benchmark-Quality Computations Are Needed To Reproduce 1-Adamantyl Cation NMR Chemical Shifts Accurately Michael E. Harding,*,†,§ J€urgen Gauss,† and Paul von Rague Schleyer‡ † ‡
Institut f€ur Physikalische Chemie, Universit€at Mainz, Jakob-Welder-Weg 11, D-55099 Mainz, Germany Department of Chemistry and Center for Computational Chemistry, University of Georgia, Athens, Georgia 30602, United States
bS Supporting Information ABSTRACT: While the experimental 1H NMR chemical shifts of the 1-adamantyl cation can be computed within reasonably small error bounds, the usual Hartree-Fock and density functional quantum-chemical computations, as well as those based on rather elaborate second-order Møller-Plesset perturbation theory, fail to reproduce its experimental 13C NMR chemical shifts satisfactorily. This also is true even if the NMR shielding calculations treat electron correlation adequately by the coupledcluster singles and doubles model augmented by a perturbative correction for triple excitations (i.e., at the CCSD(T) level) with quadruple-ζ basis sets. We demonstrate that good agreement can be achieved if highly accurate 1-adamantyl cation equilibrium geometries based on parallel computations of CCSD(T) gradients are employed for the NMR shielding computations.
1. INTRODUCTION Carbocation structure elucidations were the first extensive practical applications1,2 of the generally important capability of computing NMR chemical shifts accurately by quantum-chemical methods.3-30 Schindler’s comprehensive study in 19871 employed Kutzelnigg’s IGLO method5,6 to compare computed 1H and 13C chemical shifts with experimental values, determined in superacid media. But success was mixed. While good agreement was achieved for “non-classical (delocalized)” cations, ions expected to have “classical” structures gave computed chemical shifts far more deshielded than the experimental values. These unacceptably large discrepancies were later shown mostly to be due “to the use of assumed or inadequate [e.g., non-optimized] geometries and could be eliminated by the employment of refined structures.”2,19,37b,37c The quantum-chemical capability of computing magnetic properties was developed into the “ab initio/ IGLO or GIAO/NMR” method of structural determination:2,19 computed chemical shifts for various candidate geometries were compared with the measured values. Good agreement was decisive in establishing or verifying many structures of carbocations and electron-deficient boron compounds (see e.g. refs 2 and 18-26). Olah’s group has refined such computational investigations at increasing levels of sophistication recently.27-36 This paper is concerned with the vexing difficulty in computing the chemical shifts of the 1-adamantyl cation (Figure 1) accurately, despite its enforced, rigid C3v symmetry. As adamantane, the cage hydrocarbon prototype, has been employed extensively both in synthetic and physical organic chemistry,37 it is not surprising that its bridgehead 1-cation (Figure 1), was r 2011 American Chemical Society
one of the first carbocations to be prepared and characterized under long-lived stable ion conditions in superacid solution.38 The 1H and 13C NMR spectra were unusual, since the more remote bridgehead carbon and hydrogens (H2 in Figure 1) exhibited the largest deshielding. This behavior was attributed originally to a “cage effect,” but later was ascribed to CC hyperconjugation of the C2C3 bonds parallel to the “vacant” orbital at C1.38 Exceptionally, the first 13C chemical shift computations (at the IGLO level) deviated by 37 ppm from experiment for C1, the carbocation center.38 Subsequent computations using other quantum-chemical procedures, even those39 including rather elaborate second-order Møller-Plesset perturbation theory (MP2),10,11 also failed to reproduce the experimental NMR data38 for the 1-adamantyl cation satisfactorily.39,40 We have now employed further methodological developments to revisit this problem and have identified the difficulties. A careful analysis of possible error sources has been carried out. As recent progress in the parallel calculation of coupled-cluster gradients and second derivatives41 identified the importance of using precise geometries, we suspected that this might be the accuracy-determining requirement for the 1-adamantyl cation. Indeed, we now demonstrate that good agreement with experimental 13C NMR chemical shifts can be achieved by employing highly refined equilibrium geometries obtained with a triple-ζ quality basis set at the CCSD(T) level of theory (i.e., coupledReceived: October 28, 2010 Revised: January 14, 2011 Published: March 01, 2011 2340
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cluster singles and doubles model augmented by a perturbative correction for triple excitations)42 for the computation of NMR shieldings using quadruple-ζ basis sets with adequate electron correlation treatment by MP210,11 or CCSD(T).17
2. COMPUTATIONAL DETAILS Shielding constants were computed at the HF-SCF,9,12 MP2,10,11 and CCSD(T)17 ab initio as well as at the BP8643,44 and B3LYP45 density-functional theory (DFT)15,16 levels, as implemented in the TURBOMOLE program.46 The shielding tensors were evaluated at all computational levels via the second derivatives of the energy with respect to the external magnetic field and the nuclear magnetic moments. Gauge-including atomic orbitals (GIAO)3,4,9,47 provided rapid basis-set convergence and ensured gauge-origin independence. NMR chemical shifts are reported relative to those of tetramethylsilane (TMS) computed at the same level. The electroncorrelated computations did not employ the frozen-core approximation. Previous experience (see, e.g., ref 48) indicates that Sch€afer et al.’s.49 basis sets augmented with polarization functions11 are well suited for chemical shift computations. Basis-set convergence was monitored by computing the shielding tensors with dzp and then larger tzp, tz2p, and qz2p contracted sets. The contraction schemes are given in Table 1 of the Supporting Information. The importance of zero-point
Figure 1. C3v-symmetric 1-adamantyl cation with the numbering scheme employed.
vibrational corrections was investigated by computing the corresponding contributions via second-order vibrational perturbation theory (VPT2).48,50,51 Temperature effects are taken into account by a semiclassical treatment within the framework of VPT2. Ref 51 gives details of the calculation of the zero-point and temperature corrections. Except for the DFT computations (with the QZVPP basis set52) with TURBOMOLE,46 the CFOUR (coupled cluster techniques for computational chemistry) quantum-chemical program package was employed.53 The most demanding computations used the recently developed parallel version.41 To illustrate the resources needed details for the most challenging computations in this study are given in the following. The CCSD(T)/cc-pVTZ geometry optimizations of the adamantyl cation were carried out on 9 single core 3.4 GHz Intel Xeon (EM64T) servers equipped with each 16 GB RAM. Using 9 GB main memory per node the completion of one geometry optimization step required 3.8 days. The CCSD(T)/qz2p computation of the absolute shielding tensors of the adamantyl cation took 12 days using 28 cores and 14 GB main memory for each core from a 22 node cluster featuring nodes with two dual core Intel Xeon 5160 processors running at 2.93 GHz, 32 GB RAM, and eight striped SATA disks.
3. RESULTS AND DISCUSSION All five theoretical levels shown in Table 1 reproduce the experimental 13C shielding order qualitatively, but fairly large numerical discrepancies (up to 32 ppm) persist, especially for C1 and C3. The variation of the latter is nearly 50 ppm over the whole set. The discrepancies for C2 and especially for C4 are smaller, since these positions are less directly involved in the charge delocalization due to CC hyperconjugation. The MP2 computation performs best overall; but the average 13C NMR error is still 6 ppm. Reference 40 reports similar results for the C1 carbocationic center employing HF-SCF and B3LYP calculations with much smaller Pople split-valence basis sets. The HFSCF results are the worst (note the C1 and C3 deviations), especially when the poor 1H performance also is considered. The other computed 1H NMR chemical shifts in Table 1 agree reasonably well with experiment. Our more detailed study now resolves this unsatisfactory situation. Since computed chemical shieldings often are very sensitive to the geometrical details, comparative geometry optimizations (Table 2) were carried out using the cc-pVTZ basis set54 uniformly at the HF-SCF, MP2, and CCSD(T) levels. On the basis of deviations from HF-SCF, the correlation effects at MP2 are generally greater than at the CCSD(T) level. The ca.
Table 1. NMR Chemical Shifts (in ppm) of the 1-Adamantyl Cation Computed with Various Methodsa
a
geometry
HF/3-21G
BP86/def2-QZVPP
B3LYP/def2-QZVPP
HF-SCF/tz2p
MP2/cc-pVTZ
experiment
chemical shifts
IGLO-DZ [ref 38c]
BP86/def2-QZVPP
B3LYP/def2-QZVPP
HF-SCF/tz2p
MP2/qz2p
ref 38
C1
337.7
299.9
314.8
332.4
299.7
C2
57.7
75.1
73.2
60.9
72.4
C3
67.8
112.9
104.5
63.9
96.7
86.8
C4
37.2
44.3
42.4
32.2
40.5
34.5
300 65.7
H1
3.89
3.83
3.75
3.96
4.19
H2 H3
5.60 2.32
5.17 2.15
3.74 1.81
5.23 2.14
5.19 2.42
H4
2.14
2.01
1.74
2.17
2.30
The atom numbering is given in Figure 1. 2341
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Table 2. Geometrical Parameters (Bond Lengths in Å, Angles in Degrees) of the 1-Adamantyl Cationa parameter
a
HF-SCF/cc-pVTZ
MP2/cc-pVTZ
CCSD(T)/cc-pVTZ
Table 4. NMR Chemical Shifts (in ppm) of the 1-Adamantyl Cation Computed at the CCSD(T) and MP2 Level Using the CCSD(T)/cc-pVTZ Geometrya method
CCSD(T)
CCSD(T)
CCSD(T)
experiment
MP2
1.610 1.524
basis set
dzp
tzp
qz2p
ref 28
qz2p
C1
290.6
301.0
306.8
300
308.5
1.082
1.085
1.080
1.087
1.088
65.1 85.6
67.9 88.9
69.9 91.8
65.7 86.8
73.3 96.3
R(C4-H3)
C2 C3
1.083
1.088
1.089
C4
35.6
37.5
36.1
34.5
40.7
R(C4-H4)
1.083
1.087
1.090
H1
3.73
3.84
3.90
4.19
3.97
R(C1-C2)
1.457
1.438
1.449
R(C2-C3) R(C3-C4)
1.599 1.531
1.611 1.516
R(C2-H1)
1.078
R(C3-H2)
— (C1C2C3)
98.4
97.9
98.2
4.72
4.84
4.95
5.19
5.11
— (H1C2H1)
H2
111.1
112.4
112.2
1.95
2.12
2.13
2.42
2.13
— (C2C3C4) — (C3C4C3)
H3
108.7 109.7
108.2 109.7
108.3 109.7
H4
1.93
2.08
2.10
2.30
2.12
— (H3C4H4)
106.9
107.1
107.3
— (C2C3H2)
106.0
104.9
105.3
a
Atom numbering according to Figure 1.
Table 5. Final Analysis of the Theoretically Evaluated Chemical Shifts (in ppm) of the 1-Adamantyl Cation Including Vibrational Correctionsa
Atom numbering according to Figure 1.
Table 3. NMR Chemical Shifts (in ppm) of the 1-Adamantyl Cation Computed at the MP2/tzp Level Using Different Geometriesa geometry
a
HF-SCF/cc-pVTZ
MP2/cc-pVTZ
CCSD(T) /cc-pVTZ
δe
δ0
δT=193K
experiment
equilibrium
ZP corrected
temp. corrected
(T = 193 K)38
C1
306.8
300.8
300.4
C2
69.9
69.7
69.7
300 65.7
C1
317.0
293.8
302.5
C3
91.8
93.1
93.0
86.8
C2
71.9
70.3
71.3
C4
36.1
36.8
36.7
34.5
C3
90.6
93.7
93.4
H1
3.90
3.92
3.87
4.19
C4
39.3
38.9
39.1
H2
4.95
5.07
5.06
5.19
H1
3.90
3.84
3.91
H3
2.13
2.21
2.21
2.42
H2
4.84
4.84
5.00
H4
2.06
2.16
2.16
2.30
H3
2.10
2.12
2.12
H4
2.02
2.08
2.13
Atom numbering according to Figure 1.
0.01 Å C1-C2 and C3-C4 distance variations are largest and influence the shielding of the carbocationic center significantly (see Table 3). The C-H bond lengths changes are small and the bond angle differences are negligible. The CCSD(T)/cc-pVTZ geometry was employed for NMR chemical shift computations at the MP2/qz2p and at the CCSD(T) levels with several basis sets (data in Table 4). The 13C NMR shifts computed at the intermediate CCSD(T)/tzp level actually agree best with experiment (average deviation 2 ppm). Using the largest qz2p basis set, the average 13C deviation from experiment is 3.9 ppm for CCSD(T) and are twice as large, 8.0 ppm, for MP2. The 1H shielding agreement is best at MP2. Since all the computed chemical shifts are relative to TMS, we wondered if the cc-pVTZ basis set was adequate for the secondrow atom silicon. However, tests with cc-pCVTZ55 on silicon showed negligible differences from the CCSD(T)/qz2p chemical shieldings, only þ0.04 ppm and -0.68 ppm for 13C, and 0.00 and -0.13 ppm for 1H for cc-pCVTZ and the partially dropped core levels, respectively. The qz2p basis set seems to be close to the basis-set limit (compare the dzp and tzp results in Table 4), but further variations of the 13C shifts might be 1-2 ppm with even larger basis sets. Although the CCSD(T)/qz2p results are reasonable, we considered possible additional influences. Zero-point vibrational effects (determined by applying VPT2) usually are important.48,51 Unfortunately, high-level vibrational
a
Atom numbering according to Figure 1.
correction treatments for molecules as large as the 1-adamantyl cation are too demanding at present. However, the compromise use of HF-SCF/tz2p for the required harmonic and anharmonic force fields and the NMR chemical shifts should describe the zero-point vibrational effects appropriately. Additional temperature corrections at the same level were applied.51 The equilibrium CCSD(T)/qz2p shieldings δe at the CCSD(T)/cc-pVTZ geometry are shown in the first data column of Table 5; the δ0 zeropoint vibrational corrections are added in the next column, and the final theoretical values including the δT=193K temperature corrections follow. Inclusion of the zero-point vibrational effects improves the C1 value by 6 ppm, but the C3 shielding deteriorates slightly. The much smaller temperature corrections bring no significant improvement. The final C1 value agrees perfectly with experiment, and the computed C2, C3, and C4 shieldings deviate by only 4, 6, and 2 ppm, respectively. The remaining uncertainty may be 1-2 ppm due to basis-set incompleteness in the NMR chemical shift computations, the low-level treatment of vibrational effects, the neglect of superacid solvent effects, and the use of the TMS reference in an external capillary, rather than dissolved in the same solution. However, an even more refined geometry is not expected to change the computed shieldings.48
4. CONCLUSIONS Accurate computations of NMR chemical shifts remain a challenging task. Nevertheless, we demonstrate again (see, e.g., 2342
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The Journal of Physical Chemistry A refs 48, 51, 56, and 57) that good agreement with experiment can be achieved in difficult cases like the 1-adamantyl cation if accurate geometries are employed, electron correlation is treated adequately, large basis sets are used with GIAO, and VPT2 vibrational averaging is included. In particular, a highly refined geometry of the 1-adamantyl cation is crucial in order to match its experimental NMR data well theoretically.
’ ASSOCIATED CONTENT
bS
Supporting Information. In addition to some details on basis-set contraction, all optimized geometries and the absolute shieldings for TMS and the 1-adamantyl cation. This material is available free of charge via the Internet at http://pubs.acs.org.
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected] Present Addresses
§ Present address: Department of Chemistry and Biochemistry, The University of Texas at Austin, Austin, Texas 78712, United States
’ ACKNOWLEDGMENT Most fittingly, we dedicate this paper to Professor George A. Olah. The work was supported in Mainz by the Deutsche Forschungsgemeinschaft (DFG, GA 370/5-1) and the Fonds der Chemischen Industrie, and in Georgia by U.S. NSF Grant CHE-0716718. ’ REFERENCES (1) Schindler, M. J. Am. Chem. Soc. 1987, 109, 1020. (2) Buzek, P.; Schleyer, P.v.R.; Sieber, S. Chem. Unserer Zeit 1992, 26, 116. Also see refs. 19 and 37c. (3) Hameka, H. Mol. Phys. 1958, 1, 203. (4) Ditchfield, R. J. Chem. Phys. 1972, 56, 5688. (5) Kutzelnigg, W. Isr. J. Chem. 1980, 19, 193. (6) Schindler, M.; Kutzelnigg, W. J. Chem. Phys. 1982, 76, 1919. (7) Hansen, A. E.; Bouman, T. D. J. Chem. Phys. 1985, 82, 5035. (8) Bouman, T. D.; Hansen, A. E. Chem. Phys. Lett. 1990, 175, 292. (9) Wolinski, K.; Hinton, J. F.; Pulay, P. J. Am. Chem. Soc. 1990, 112, 8251. (10) Gauss, J. Chem. Phys. Lett. 1992, 191, 614. (11) Gauss, J. J. Chem. Phys. 1993, 99, 3629. (12) H€aser, M.; Ahlrichs, R.; Baron, H. P.; Weis, P.; Horn, H. Theor. Chim. Acta 1993, 83, 455. (13) Gauss, J. Chem. Phys. Lett. 1994, 229, 198. (14) Gauss, J.; Stanton, J. F. J. Chem. Phys. 1995, 102, 251. (15) Schreckenbach, G.; Ziegler, T. J. Phys. Chem. 1995, 99, 606. (16) Rauhut, G.; Puyear, S.; Wolinski, K.; Pulay, P. J. Phys. Chem. 1996, 100, 6310. (17) Gauss, J.; Stanton, J. F. J. Chem. Phys. 1996, 104, 2574. (18) Gauss, J. J. Chem. Phys. 2002, 116, 4773. (19) Schleyer, P.v.R.; Maerker, C. Pure Appl. Chem. 1995, 67, 755. See footnote 4 for references to the application of the ab initio/IGLOGIAO/NMR approach to the structure elucidation of carbocations. For leading references to applications to boron compounds, see: B€uhl, M.; Schleyer, P.v.R. In Electron Deficient Boron and Carbon Clusters; Olah, G. A., Wade, K., Williams, R. E., Eds., Wiley: New York, 1991, Chapter 4, p. 113ff. B€uhl, M.; Schleyer, P.v.R. J. Am. Chem. Soc. 1992, 114, 477. Hnyk, D.; Hofmann, M.; Schleyer, P.v.R.; B€uhl, M.; Rankin, D. W. H. J. Phys. Chem. 1996, 100, 3435 and refs. 20,21.
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(53) CFOUR (Coupled Cluster techniques for Computational Chemistry), a quantum-chemical program package by Stanton, J. F. ; Gauss, J. ; Harding, M. E.; Szalay, P. G. with contributions from Auer, A. A.; Bartlett, R. J.; Benedikt, U.; Berger, C.; Bernholdt, D. E.; Bomble, Y. J. ; Cheng, L.; Christiansen, O.; Heckert, M.; Heun, O.; Huber, C.; Jagau, T.-C.; Jonsson, D.; Juselius, J.; Klein, K.; Lauderdale, W. J.; Matthews, D.; Metzroth, T.; O’Neill, D. P. ; Price, D. R.; Prochnow, E.; Ruud, K.; Schiffmann, F.; Schwalbach, W.; Stopkowicz, S.; Tajti, A.; Vazquez, J.; Watts, J. D.; Wang, F. and the integral packages MOLECULE (Alml€of, J.; Taylor, P. R.), PROPS (Taylor, P. R.), ABACUS (Helgaker, T. ; Jensen, H. J. Aa.; Jørgensen, P.; Olsen, J.), and ECP routines by Mitin, A. V.; van W€ullen, C. For the current version, see http://www.cfour.de. (54) Dunning, T. H., Jr. J. Chem. Phys. 1989, 90, 1007. (55) Woon, D. E.; Dunning, T. H., Jr. J. Chem. Phys. 1995, 103, 4572. (56) Auer, A. A. J. Chem. Phys. 2009, 131, 024116. (57) Prochnow, E.; Auer, A. A. J. Chem. Phys. 2010, 132, 064109.
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