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Is there a satisfactory description of the molecular structure of Roesky’s ketone?
Chemical Physics Letters 413 (2005) 440–444 www.elsevier.com/locate/cplett
Is there a satisfactory description of the molecular structure of RoeskyÕs ketone? Karla Tersago a, Julianna Ola´h a,b, Jan M.L. Martin c, Tama´s Veszpre´mi b, Christian Van Alsenoy a, Frank Blockhuys a,* b
a University of Antwerp, Department of Chemistry, Universiteitsplein 1, B-2610 Wilrijk, Belgium Budapest University of Technology and Economics, Department of Inorganic Chemistry, Gelle´rt te´r 4, H-1521 Budapest, Hungary c Weizmann Institute of Science, Department of Organic Chemistry, IL-76100 Rechovot, Israe¨l
Received 8 June 2005; in final form 1 August 2005 Available online 30 August 2005
Abstract By means of a number of computationally more advanced methods the search for an acceptable overall calculated gas-phase geometry of RoeskyÕs ketone (5-oxo-1,3,2,4-dithiadiazole) is continued. The results of CCSD, QCISD and MP4(SDQ) calculations are compared with the results of different CASSCF and DFT calculations. The results obtained with the wave-function-based methods are better than those generated by a large number of different DFT functionals, especially for the description of the carbon–sulfur bond. However, even at the CCSD and QCISD levels of theory no convergence is achieved: upon increasing the level of theory from CCSD to CCSD(T) the quality of the description actually becomes worse. Ó 2005 Elsevier B.V. All rights reserved.
1. Introduction Five- and six-membered ring systems containing an –N@S@N–S– fragment continue to fascinate structural chemists as the bonding in this fragment seems to be quite sensitive to the nature of the ring-closing moiety. When the latter is the benzene ring in 1,3k4d2,2,4benzodithiazines [1–3] the heterocycle shows very clear signs of localisation of p-bonds and antiaromaticity. When it is the carbonyl group in 5-oxo-1,3,2,4-dithiadiazole (RoeskyÕs ketone) [4–6] p-density is delocalised over the entire –N@S@N–S– fragment and the heterocycle becomes aromatic. When the ring-closing moiety is the cobalt atom in 5-(g5-cyclopentadienyl)5-cobalta-1,3,2,4-dithiadiazole [7] delocalisation over the entire heterocycle is observed and this further increases the aromaticity. Since bonding studies greatly depend upon accurate experimental and theo*
Corresponding author. Fax: +32 3 820 23 10. E-mail address: [email protected] (F. Blockhuys).
0009-2614/$ - see front matter Ó 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2005.08.017
retical geometries considerable attention has been paid to obtaining these, especially in the case of RoeskyÕs ketone since it is one of the smallest possible compounds in this family of molecules, which makes it ideal for studies at higher levels of theory [6]. The calculation of the molecular geometry of RoeskyÕs ketone at the HF, DFT and MP2 levels of theory showed that obtaining an adequate description of the molecular geometry of this deceptively simple molecule is a complicated problem [6]. While the DFT/B3LYP/ 6-311+G* combination was found to reproduce the chemically important NSNS fragment quite successfully, the method completely failed to reproduce the CS bond length. A systematic study of the effect of correlation, DFT functional and basis set on the structure of the compound showed that while some functionals gave a clearly better result for the CS bond length than others, they simultaneously generated worse results for the NSNS fragment. In the end a systematic way to improve the overall calculated geometry of the title compound could not be found [6].
K. Tersago et al. / Chemical Physics Letters 413 (2005) 440–444
In the latter study, the performance of these less sophisticated levels of theory was evaluated using the QCISD/6-311+G* geometry. Even though this method is supposed to produce a reliable molecular geometry ˚ ) still remains the calculated CS bond length (1.874 A uncomfortably long when compared to the one observed ˚ ). Using the solid-state strucin the solid (about 1.830 A ture – in this case determined by low-temperature [125(2) K] X-ray diffraction (XRD) [4] – as a reference for calculations on an isolated molecule is questionable at least (the two structures are based on different physical properties), but in the absence of an experimental gas-phase structure which for RoeskyÕs ketone could not yet be obtained, it is the only option. Naturally, great care has to be taken that one does not pursue the absolute values but rather the trends in the bond lengths, the bonding and the electron distribution which are obvious from the crystal data. Even though we are of the opinion that this approach is valid for the evaluation of the sophisticated levels of theory in the present letter, we admit that an experimental gas-phase structure is still necessary to come to a final decision. Based on these considerations we continued our search for an acceptable description of the molecular structure of RoeskyÕs ketone – a method/basis set combination which produces a shorter CS bond than QCISD/6-311+G*, while retaining the satisfactory description of the NSNS fragment, with the X-ray structure as a guide – by increasing the level of theory to CCSD(T), QCISD, MP4(SDQ), a number of different multi-configurational methods and additional DFT functionals. The results reported in this letter show that a limited number of sophisticated methods do generate an acceptable geometry, but that several fundamental issues remain to be addressed.
2. Computational details All geometry optimisations were performed in Cs symmetry [4]. The calculations were performed on isolated molecules using MOLPRO 2002.6 [8], GAUSSIAN 03 (modified at the Weizmann Institute) [9] and MOLCAS 5 [10], at the Density Functional (DFT) [11,12], the Quadratic Configuration Interaction (QCISD using the frozen-core approximation) [13], the MP4(SDQ) [14], the Coupled Cluster (CCSD [15] and CCSD(T) [16]), the CASSCF [17] and multi-configurational second order perturbation (CASPT2) [18] levels of theory. Within the DFT approximation calculations were performed with BeckeÕs three-parameter-type [19] functionals B3LYP [20] and B3PW91 [19], and the B97-1 [21], BMK [22], HCTH/407 [23], s-HCTH and its hybrid [24], VSXC [25], TPSSh [26] and B1B95 [27] functionals. CASSCF and CASPT2 calculations were performed with a varying active space containing eight electrons.
441
Fig. 1. Molecular structure and atomic numbering of RoeskyÕs ketone.
To identify the active space the generic designation [8,n(m,p)] in which n is the total number of orbitals in the active space, m is the number of orbitals with a 0 symmetry and p is the number of orbitals with a00 symmetry (n = m + p), has been used. The 6-311(+)G* [28,29] and the Dunning correlation-consistent basis sets cc-pVDZ, cc-pVTZ and cc-pVQZ [30–33] were used, the latter three in a number of cases with additional hard d-functions on sulfur [34], in addition to JensenÕs polarization-consistent basis set aug-pc3 [35]. For a number of the CAS calculations the ANO basis sets were used as implemented in Molcas. The molecular framework and atomic numbering are shown in Fig. 1. The results of the calculations have been compiled in Table 1.
3. Results and discussion In the crystal 5-oxo-1,3,2,4-dithiadiazole is a fivemembered ring structure characterised by one longer ˚ ) and two shorter SN bonds, of which (about 1.642 A the central N(2)–S(3) bond is only slightly longer ˚ ) than the peripheral (1.576 A ˚ ), a regular CN (1.581 A ˚ ), a longer CS bond (about 1.830 A ˚ ) and bond (1.385 A ˚ ). The experimental data a localized C@O bond (1.211 A in Table 1 shows that the geometries of the two independent molecules in the unit cell are identical within the experimental errors. The NSNS fragment being the most prominent feature of this compound, the ability of the methods to reproduce the relative bond lengths in it is of the utmost importance. The different method/basis set combinations can then be evaluated based on two criteria: (1) the difference between the bond lengths of the two shorter bonds [N(2)–S(3) and S(3)–N(4)] must ˚ ) as is the case in the crystal, and be small (< 0.01 A ˚. (2) these two distances should be larger than 1.57 A The latter criterion is based on the fact that calculated re distances are expected to be longer than experimentally determined ra distances. Criterion (1) eliminates all CAS calculations with the (8,8) active space, both CASPT2[8,7(3,4)] calculations
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K. Tersago et al. / Chemical Physics Letters 413 (2005) 440–444
Table 1 ˚ ) calculated for 5-oxo-1,3,2,4-dithiadiazole at various levels of theory and different basis sets and the experimental solidMolecular geometries (re in A ˚ ) for the two independent molecules in the asymmetric unit state geometrical data (distances in A S1–N2
N2–S3
S3–N4
N4–C5
C5–S1
C5–O5
XRD
Molecule 1 Molecule 2
1.640(1) 1.643(2)
1.581(2) 1.581(2)
1.576(2) 1.575(2)
1.386(2) 1.384(2)
1.831(2) 1.829(2)
1.211(2) 1.211(2)
QCISD
6-311G* 6-311+G* cc-pV(T+d)Z aug-cc-pV(Q+d)Z 6-311G* 6-311+G* cc-pV(T+d)Z 6-311G* 6-311+G* cc-pV(T+d)Z 6-311+G* cc-pVTZ aug-cc-pVTZ
1.653 1.657 1.651 1.645 1.653 1.653 1.649 1.656 1.656 1.651 1.657 1.657 1.657
1.588 1.595 1.569 1.563 1.585 1.587 1.567 1.610 1.612 1.592 1.594 1.583 1.584
1.582 1.591 1.561 1.556 1.577 1.581 1.558 1.590 1.594 1.572 1.583 1.572 1.573
1.389 1.389 1.393 1.389 1.390 1.388 1.392 1.395 1.394 1.397 1.393 1.391 1.390
1.865 1.874 1.840 1.830 1.858 1.856 1.836 1.881 1.877 1.858 1.859 1.849 1.845
1.197 1.201 1.197 1.195 1.195 1.198 1.195 1.200 1.203 1.201 1.200 1.197 1.199
cc-pV(T+d)Z aug-pc3 cc-pV(T+d)Z cc-pV(T+d)Z cc-pV(T+d)Z cc-pV(T+d)Z cc-pV(T+d)Z cc-pV(T+d)Z cc-pV(T+d)Z cc-pV(T+d)Z cc-pV(T+d)Z aug-pc3
1.634 1.632 1.628 1.634 1.619 1.634 1.625 1.630 1.636 1.634 1.624 1.621
1.585 1.582 1.579 1.584 1.559 1.584 1.595 1.585 1.588 1.595 1.569 1.567
1.570 1.568 1.563 1.568 1.550 1.568 1.570 1.567 1.570 1.572 1.554 1.552
1.375 1.375 1.376 1.380 1.374 1.380 1.374 1.378 1.381 1.381 1.374 1.373
1.899 1.889 1.872 1.892 1.884 1.892 1.904 1.895 1.893 1.898 1.850 1.845
1.194 1.194 1.194 1.195 1.187 1.195 1.195 1.195 1.198 1.198 1.192 1.191
cc-pV(D+d)Z cc-pVDZ cc-pVTZ ANO4s3p1dc cc-pV(T+d)Z ANO3s2pb ANO4s3p1dc cc-pVDZ cc-pVDZ cc-pVTZ cc-pV(T+d)Z cc-pVQZ cc-pV(Q+d)Z cc-pVDZ cc-pVTZ cc-pVDZ cc-pVTZ ANO4s3p1dc
1.661 1.680 1.657 1.650 1.653 1.729 1.702 1.723 1.676 1.661 1.657 1.656 1.654 1.673 1.658 1.656 1.635 1.645
1.559 1.585 1.556 1.591 1.546 1.599 1.572 1.603 1.579 1.555 1.545 1.551 1.546 1.584 1.560 1.649 1.611 1.633
1.554 1.564 1.555 1.550 1.544 1.551 1.544 1.558 1.602 1.579 1.567 1.568 1.562 1.587 1.566 1.604 1.576 1.590
1.414 1.390 1.410 1.367 1.413 1.403 1.375 1.373 1.387 1.388 1.391 1.390 1.392 1.387 1.387 1.393 1.382 1.403
1.815 1.822 1.812 1.823 1.806 1.826 1.819 1.875 1.866 1.847 1.841 1.808 1.805 1.833 1.817 1.895 1.848 1.857
1.176 1.204 1.173 1.178 1.173 1.208 1.177 1.175 1.175 1.172 1.172 1.172 1.172 1.177 1.174 1.206 1.201 1.208
CCSD
CCSD(T)
MP4(SDQ)
B3LYP B3PW91 B97-1 BMK HCTH/407 s-HCTH s-HCTHa TPSSh VSXC B1B95 CASSCF[8,7(3,4)]
CASSCF[8,8(6,2)]
CASSCF[8,8(4,4)]
CASSCF[8,13(8,5)] CASPT2[8,7(3,4)] CASPT2[8,8(6,2)] a b c
Hybrid functional. 4s3p1d on sulfur. 4s3p2d on sulfur.
and the two at the CASSCF[8,7(3,4)] level with the cc-pVDZ and ANO4s3p1d basis sets. Furthermore, none of the CCSD(T) or DFT calculations, except the one with the BMK functional, satisfy this requirement. Technically, the three MP4(SDQ) calculations should be eliminated as well – the three relevant differences ˚ – but since these are so close to our cut-off are 0.011 A value we decided not to remove them. After applying criterion (2), which eliminates the three remaining
CASSCF[8,7(3,4)] calculations, the CCSD/ccpV(T+d)Z, the DFT/BMK/cc-pV(T+d)Z, the CASSCF[8,13(8,5)]/cc-pVTZ and the QCISD calculations with the cc-pV(T+d)Z and aug-cc-pV(Q+d)Z basis sets, eight results are retained: QCISD/6-311(+)G*, CASSCF[8,13(8,5)]/cc-pVDZ, CCSD/6-311(+)G* and the three MP4(SDQ) calculations. The remaining CASSCF calculation can be easily dismissed since it produces an unrealistically small C@O bond length
K. Tersago et al. / Chemical Physics Letters 413 (2005) 440–444
˚ ). It is interesting to note that only two impor(1.177 A tant configurations can be found in the CAS wave functions: the ground state (with a weight of about 90%) and a doubly excited closed-shell state (with a weight of about 10%); all the other determinants are negligible. In addition, we draw attention to the fact that the B1B95 functional is the only one in the current series which produces a geometry which is close to our acceptability criteria. In particular, its description of the CS bond is remarkable in comparison with the other functionals. Even though it is difficult to mutually compare these seven combinations and select one which produces the most satisfying description, MP4(SDQ)/aug-cc-pVTZ seems to generate a combination of a well-described NSNS fragment with a CS bond short enough to be comfortably compared to the corresponding solid-state parameter. Inspection of the geometries obtained from the seven method/basis set combinations indicates that the addition of diffuse functions to the basis set changes very little in the overall geometry: for QCISD the largest ˚ and for difference between the two geometries is 0.009 A ˚ . It is CCSD and MP4(SDQ) this value is a mere 0.004 A interesting to observe that increasing the basis set to cc-pV(T+d)Z (for QCISD and CCSD) and even augcc-pV(Q+d)Z (for CCSD) does not really improve the description: even though the CS distance converges to the experimental value the S(3)–N(4) distance is too short. Of even greater importance is the fact that upon increasing the level of theory from CCSD to CCSD(T) the quality of the description of the geometry of RoeskyÕs ketone actually becomes worse: the difference between the two shorter SN bond lengths becomes too ˚ . It large and the CS distance increases by about 0.02 A seems that at these considerable levels of theory convergence of the different geometrical parameters has not been obtained. In this context we would like to note that further increasing the level for this six-atom molecule is virtually beyond the possibilities of computational chemistry at this moment: a CCSDTQ calculation could only be performed using a very small basis set and the molecule is clearly too large for a CAS calculation with a full valence space.
4. Conclusion The MP4(SDQ)/aug-cc-pVTZ combination produces a calculated geometry for RoeskyÕs ketone which correlates most satisfactorily with the experimental solid-state data, even though the differences with six other method/basis set combinations [QCISD/6-311(+)G*, CCSD/6-311(+)G*, MP4(SDQ)/ 6-311+G* and MP4(SDQ)/cc-pVTZ] are small. In contrast, increasing the size of the basis set for QCISD and CCSD consistently leads to inferior
443
results, as does increasing the level of theory from CCSD to CCSD(T). Even for these considerable levels of theory no convergence of the geometrical parameters seems to have been reached. It appears that several fundamental issues pertaining to a correct description of the gas-phase geometry of RoeskyÕs ketone deserve further attention.
Acknowledgments This work was supported by the Flemish-Hungarian Scientific and Technological Joint Fund (TeT B-2/01, BIL 01/72 and BIL 01/17). J.O. and T.V. acknowledge financial support from OTKA Grant T048796.
References [1] F. Blockhuys, S.L. Hinchley, A.Y. Marakov, Y.V. Gatilov, A.V. Zibarev, J.D. Woollins, D.W.H. Rankin, Chem. Eur. J. 7 (2001) 3592. [2] A.Y. Makarov, I.Y. Bagryanskaya, F. Blockhuys, C. Van Alsenoy, Y.V. Gatilov, V.V. Knyazev, A.M. Maksimov, T.V. Mikhalina, V.E. Platonov, M.M. Shakirov, A.V. Zibarev, Eur. J. Inorg. Chem. (2003) 77. [3] A.R. Turner, F. Blockhuys, C. Van Alsenoy, H.E. Robertson, S.L. Hinchley, A.V. Zibarev, A.Y. Marakov, D.W.H. Rankin, Eur. J. Inorg. Chem. (2005) 572. [4] J. Van Droogenbroeck, K. Tersago, C. Van Alsenoy, S.M. Aucott, H.L. Milton, J.D. Woollins, F. Blockhuys, Eur. J. Inorg. Chem. (2004) 3798. [5] K. Tersago, J. Van Droogenbroeck, C. Van Alsenoy, W.A. Herrebout, B.J. van der Veken, S.M. Aucott, J.D. Woollins, F. Blockhuys, Phys. Chem. Chem. Phys. 6 (2004) 5140. [6] J. Van Droogenbroeck, K. Tersago, C. Van Alsenoy, F. Blockhuys, Chem. Phys. Lett. 399 (2004) 516. [7] J. Van Droogenbroeck, C. Van Alsenoy, S.M. Aucott, J.D. Woollins, A.D. Hunter, F. Blockhuys, Organometallics 24 (2005) 1004. [8] MOLPRO is a package of ab initio programs written by H.-J. Werner et al. [9] M.J. Frisch et al., Gaussian 03, Revision C.01, Gaussian, Inc., Wallingford CT, 2004. [10] K. Andersson et al., MOLCAS Version 5.4, Lund University, Sweden (2002). [11] W. Kohn, L.J. Sham, Phys. Rev. A 140 (1965) 1133. [12] P. Hohenberg, W. Kohn, Phys. Rev. B 136 (1964) 864. [13] J.A. Pople, M. Headgordon, K. Raghavachari, J. Chem. Phys. 87 (1987) 5968. [14] R. Krishnan, J.A. Pople, Int. J. Quant. Chem. 14 (1978) 91. [15] G.D. Purvis III, R.J. Bartlett, J. Chem. Phys. 76 (1982) 1910. [16] R.J. Bartlett, J.D. Watts, S.A. Kucharski, J. Noga, Chem. Phys. Lett. 165 (1990) 513. [17] B.O. Roos, in: K.P. Lawley (Ed.), Ab Initio Methods in Quantum Chemistry II, John Wiley & Sons Ltd., Chichester, 1987. ˚ . Malmqvist, B.O. Roos, J. Chem. Phys. 96 [18] K. Andersson, P.A (1992) 1218. [19] A.D. Becke, J. Chem. Phys. 98 (1993) 5648. [20] P.J. Stephens, F.J. Devlin, C.F. Chabalowski, M.J. Frisch, J. Phys. Chem. 98 (1994) 11623. [21] F.A. Hamprecht, A.J. Cohen, D.J. Tozer, N.C. Handy, J. Chem. Phys. 109 (1998) 6264.
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A.D. Boese, J.M.L. Martin, J. Chem. Phys. 121 (2004) 3405. A.D. Boese, N.C. Handy, J. Chem. Phys. 114 (2001) 5497. A.D. Boese, N.C. Handy, J. Chem. Phys. 116 (2002) 9559. T. Van Voorhis, G.E. Scuceria, J. Chem. Phys. 109 (1998) 400. [26] J.M. Tao, J.P. Perdew, V.N. Staroverov, G.E. Scuceria, Phys. Rev. Lett. 91 (2003) 146401. [27] A.D. Becke, J. Chem. Phys. 104 (1996) 1040. [28] R. Krishnan, J.S. Binkley, R. Seeger, J.A. Pople, J. Chem. Phys. 72 (1980) 650.
[29] A.D. McLean, G.S. Chandler, J. Chem. Phys. 72 (1980) 5639. [30] R.A. Kendall, T.H. Dunning, R.J. Harrison, J. Chem. Phys. 96 (1992) 6796. [31] D.E. Woon, T.H. Dunning, J. Chem. Phys. 98 (1993) 1358. [32] K.A. Peterson, D.E. Woon, T.H. Dunning, J. Chem. Phys. 100 (1994) 7410. [33] T.H. Dunning, J. Chem. Phys. 90 (1989) 1007. [34] T.H. Dunning Jr., K.A. Peterson, A.K. Wilson, J. Chem. Phys. 114 (2001) 9244. [35] F. Jensen, J. Chem. Phys. 115 (2001) 9113.
Is there a satisfactory description of the molecular structure of RoeskyÕs ketone? Karla Tersago a, Julianna Ola´h a,b, Jan M.L. Martin c, Tama´s Veszpre´mi b, Christian Van Alsenoy a, Frank Blockhuys a,* b
a University of Antwerp, Department of Chemistry, Universiteitsplein 1, B-2610 Wilrijk, Belgium Budapest University of Technology and Economics, Department of Inorganic Chemistry, Gelle´rt te´r 4, H-1521 Budapest, Hungary c Weizmann Institute of Science, Department of Organic Chemistry, IL-76100 Rechovot, Israe¨l
Received 8 June 2005; in final form 1 August 2005 Available online 30 August 2005
Abstract By means of a number of computationally more advanced methods the search for an acceptable overall calculated gas-phase geometry of RoeskyÕs ketone (5-oxo-1,3,2,4-dithiadiazole) is continued. The results of CCSD, QCISD and MP4(SDQ) calculations are compared with the results of different CASSCF and DFT calculations. The results obtained with the wave-function-based methods are better than those generated by a large number of different DFT functionals, especially for the description of the carbon–sulfur bond. However, even at the CCSD and QCISD levels of theory no convergence is achieved: upon increasing the level of theory from CCSD to CCSD(T) the quality of the description actually becomes worse. Ó 2005 Elsevier B.V. All rights reserved.
1. Introduction Five- and six-membered ring systems containing an –N@S@N–S– fragment continue to fascinate structural chemists as the bonding in this fragment seems to be quite sensitive to the nature of the ring-closing moiety. When the latter is the benzene ring in 1,3k4d2,2,4benzodithiazines [1–3] the heterocycle shows very clear signs of localisation of p-bonds and antiaromaticity. When it is the carbonyl group in 5-oxo-1,3,2,4-dithiadiazole (RoeskyÕs ketone) [4–6] p-density is delocalised over the entire –N@S@N–S– fragment and the heterocycle becomes aromatic. When the ring-closing moiety is the cobalt atom in 5-(g5-cyclopentadienyl)5-cobalta-1,3,2,4-dithiadiazole [7] delocalisation over the entire heterocycle is observed and this further increases the aromaticity. Since bonding studies greatly depend upon accurate experimental and theo*
Corresponding author. Fax: +32 3 820 23 10. E-mail address: [email protected] (F. Blockhuys).
0009-2614/$ - see front matter Ó 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2005.08.017
retical geometries considerable attention has been paid to obtaining these, especially in the case of RoeskyÕs ketone since it is one of the smallest possible compounds in this family of molecules, which makes it ideal for studies at higher levels of theory [6]. The calculation of the molecular geometry of RoeskyÕs ketone at the HF, DFT and MP2 levels of theory showed that obtaining an adequate description of the molecular geometry of this deceptively simple molecule is a complicated problem [6]. While the DFT/B3LYP/ 6-311+G* combination was found to reproduce the chemically important NSNS fragment quite successfully, the method completely failed to reproduce the CS bond length. A systematic study of the effect of correlation, DFT functional and basis set on the structure of the compound showed that while some functionals gave a clearly better result for the CS bond length than others, they simultaneously generated worse results for the NSNS fragment. In the end a systematic way to improve the overall calculated geometry of the title compound could not be found [6].
K. Tersago et al. / Chemical Physics Letters 413 (2005) 440–444
In the latter study, the performance of these less sophisticated levels of theory was evaluated using the QCISD/6-311+G* geometry. Even though this method is supposed to produce a reliable molecular geometry ˚ ) still remains the calculated CS bond length (1.874 A uncomfortably long when compared to the one observed ˚ ). Using the solid-state strucin the solid (about 1.830 A ture – in this case determined by low-temperature [125(2) K] X-ray diffraction (XRD) [4] – as a reference for calculations on an isolated molecule is questionable at least (the two structures are based on different physical properties), but in the absence of an experimental gas-phase structure which for RoeskyÕs ketone could not yet be obtained, it is the only option. Naturally, great care has to be taken that one does not pursue the absolute values but rather the trends in the bond lengths, the bonding and the electron distribution which are obvious from the crystal data. Even though we are of the opinion that this approach is valid for the evaluation of the sophisticated levels of theory in the present letter, we admit that an experimental gas-phase structure is still necessary to come to a final decision. Based on these considerations we continued our search for an acceptable description of the molecular structure of RoeskyÕs ketone – a method/basis set combination which produces a shorter CS bond than QCISD/6-311+G*, while retaining the satisfactory description of the NSNS fragment, with the X-ray structure as a guide – by increasing the level of theory to CCSD(T), QCISD, MP4(SDQ), a number of different multi-configurational methods and additional DFT functionals. The results reported in this letter show that a limited number of sophisticated methods do generate an acceptable geometry, but that several fundamental issues remain to be addressed.
2. Computational details All geometry optimisations were performed in Cs symmetry [4]. The calculations were performed on isolated molecules using MOLPRO 2002.6 [8], GAUSSIAN 03 (modified at the Weizmann Institute) [9] and MOLCAS 5 [10], at the Density Functional (DFT) [11,12], the Quadratic Configuration Interaction (QCISD using the frozen-core approximation) [13], the MP4(SDQ) [14], the Coupled Cluster (CCSD [15] and CCSD(T) [16]), the CASSCF [17] and multi-configurational second order perturbation (CASPT2) [18] levels of theory. Within the DFT approximation calculations were performed with BeckeÕs three-parameter-type [19] functionals B3LYP [20] and B3PW91 [19], and the B97-1 [21], BMK [22], HCTH/407 [23], s-HCTH and its hybrid [24], VSXC [25], TPSSh [26] and B1B95 [27] functionals. CASSCF and CASPT2 calculations were performed with a varying active space containing eight electrons.
441
Fig. 1. Molecular structure and atomic numbering of RoeskyÕs ketone.
To identify the active space the generic designation [8,n(m,p)] in which n is the total number of orbitals in the active space, m is the number of orbitals with a 0 symmetry and p is the number of orbitals with a00 symmetry (n = m + p), has been used. The 6-311(+)G* [28,29] and the Dunning correlation-consistent basis sets cc-pVDZ, cc-pVTZ and cc-pVQZ [30–33] were used, the latter three in a number of cases with additional hard d-functions on sulfur [34], in addition to JensenÕs polarization-consistent basis set aug-pc3 [35]. For a number of the CAS calculations the ANO basis sets were used as implemented in Molcas. The molecular framework and atomic numbering are shown in Fig. 1. The results of the calculations have been compiled in Table 1.
3. Results and discussion In the crystal 5-oxo-1,3,2,4-dithiadiazole is a fivemembered ring structure characterised by one longer ˚ ) and two shorter SN bonds, of which (about 1.642 A the central N(2)–S(3) bond is only slightly longer ˚ ) than the peripheral (1.576 A ˚ ), a regular CN (1.581 A ˚ ), a longer CS bond (about 1.830 A ˚ ) and bond (1.385 A ˚ ). The experimental data a localized C@O bond (1.211 A in Table 1 shows that the geometries of the two independent molecules in the unit cell are identical within the experimental errors. The NSNS fragment being the most prominent feature of this compound, the ability of the methods to reproduce the relative bond lengths in it is of the utmost importance. The different method/basis set combinations can then be evaluated based on two criteria: (1) the difference between the bond lengths of the two shorter bonds [N(2)–S(3) and S(3)–N(4)] must ˚ ) as is the case in the crystal, and be small (< 0.01 A ˚. (2) these two distances should be larger than 1.57 A The latter criterion is based on the fact that calculated re distances are expected to be longer than experimentally determined ra distances. Criterion (1) eliminates all CAS calculations with the (8,8) active space, both CASPT2[8,7(3,4)] calculations
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Table 1 ˚ ) calculated for 5-oxo-1,3,2,4-dithiadiazole at various levels of theory and different basis sets and the experimental solidMolecular geometries (re in A ˚ ) for the two independent molecules in the asymmetric unit state geometrical data (distances in A S1–N2
N2–S3
S3–N4
N4–C5
C5–S1
C5–O5
XRD
Molecule 1 Molecule 2
1.640(1) 1.643(2)
1.581(2) 1.581(2)
1.576(2) 1.575(2)
1.386(2) 1.384(2)
1.831(2) 1.829(2)
1.211(2) 1.211(2)
QCISD
6-311G* 6-311+G* cc-pV(T+d)Z aug-cc-pV(Q+d)Z 6-311G* 6-311+G* cc-pV(T+d)Z 6-311G* 6-311+G* cc-pV(T+d)Z 6-311+G* cc-pVTZ aug-cc-pVTZ
1.653 1.657 1.651 1.645 1.653 1.653 1.649 1.656 1.656 1.651 1.657 1.657 1.657
1.588 1.595 1.569 1.563 1.585 1.587 1.567 1.610 1.612 1.592 1.594 1.583 1.584
1.582 1.591 1.561 1.556 1.577 1.581 1.558 1.590 1.594 1.572 1.583 1.572 1.573
1.389 1.389 1.393 1.389 1.390 1.388 1.392 1.395 1.394 1.397 1.393 1.391 1.390
1.865 1.874 1.840 1.830 1.858 1.856 1.836 1.881 1.877 1.858 1.859 1.849 1.845
1.197 1.201 1.197 1.195 1.195 1.198 1.195 1.200 1.203 1.201 1.200 1.197 1.199
cc-pV(T+d)Z aug-pc3 cc-pV(T+d)Z cc-pV(T+d)Z cc-pV(T+d)Z cc-pV(T+d)Z cc-pV(T+d)Z cc-pV(T+d)Z cc-pV(T+d)Z cc-pV(T+d)Z cc-pV(T+d)Z aug-pc3
1.634 1.632 1.628 1.634 1.619 1.634 1.625 1.630 1.636 1.634 1.624 1.621
1.585 1.582 1.579 1.584 1.559 1.584 1.595 1.585 1.588 1.595 1.569 1.567
1.570 1.568 1.563 1.568 1.550 1.568 1.570 1.567 1.570 1.572 1.554 1.552
1.375 1.375 1.376 1.380 1.374 1.380 1.374 1.378 1.381 1.381 1.374 1.373
1.899 1.889 1.872 1.892 1.884 1.892 1.904 1.895 1.893 1.898 1.850 1.845
1.194 1.194 1.194 1.195 1.187 1.195 1.195 1.195 1.198 1.198 1.192 1.191
cc-pV(D+d)Z cc-pVDZ cc-pVTZ ANO4s3p1dc cc-pV(T+d)Z ANO3s2pb ANO4s3p1dc cc-pVDZ cc-pVDZ cc-pVTZ cc-pV(T+d)Z cc-pVQZ cc-pV(Q+d)Z cc-pVDZ cc-pVTZ cc-pVDZ cc-pVTZ ANO4s3p1dc
1.661 1.680 1.657 1.650 1.653 1.729 1.702 1.723 1.676 1.661 1.657 1.656 1.654 1.673 1.658 1.656 1.635 1.645
1.559 1.585 1.556 1.591 1.546 1.599 1.572 1.603 1.579 1.555 1.545 1.551 1.546 1.584 1.560 1.649 1.611 1.633
1.554 1.564 1.555 1.550 1.544 1.551 1.544 1.558 1.602 1.579 1.567 1.568 1.562 1.587 1.566 1.604 1.576 1.590
1.414 1.390 1.410 1.367 1.413 1.403 1.375 1.373 1.387 1.388 1.391 1.390 1.392 1.387 1.387 1.393 1.382 1.403
1.815 1.822 1.812 1.823 1.806 1.826 1.819 1.875 1.866 1.847 1.841 1.808 1.805 1.833 1.817 1.895 1.848 1.857
1.176 1.204 1.173 1.178 1.173 1.208 1.177 1.175 1.175 1.172 1.172 1.172 1.172 1.177 1.174 1.206 1.201 1.208
CCSD
CCSD(T)
MP4(SDQ)
B3LYP B3PW91 B97-1 BMK HCTH/407 s-HCTH s-HCTHa TPSSh VSXC B1B95 CASSCF[8,7(3,4)]
CASSCF[8,8(6,2)]
CASSCF[8,8(4,4)]
CASSCF[8,13(8,5)] CASPT2[8,7(3,4)] CASPT2[8,8(6,2)] a b c
Hybrid functional. 4s3p1d on sulfur. 4s3p2d on sulfur.
and the two at the CASSCF[8,7(3,4)] level with the cc-pVDZ and ANO4s3p1d basis sets. Furthermore, none of the CCSD(T) or DFT calculations, except the one with the BMK functional, satisfy this requirement. Technically, the three MP4(SDQ) calculations should be eliminated as well – the three relevant differences ˚ – but since these are so close to our cut-off are 0.011 A value we decided not to remove them. After applying criterion (2), which eliminates the three remaining
CASSCF[8,7(3,4)] calculations, the CCSD/ccpV(T+d)Z, the DFT/BMK/cc-pV(T+d)Z, the CASSCF[8,13(8,5)]/cc-pVTZ and the QCISD calculations with the cc-pV(T+d)Z and aug-cc-pV(Q+d)Z basis sets, eight results are retained: QCISD/6-311(+)G*, CASSCF[8,13(8,5)]/cc-pVDZ, CCSD/6-311(+)G* and the three MP4(SDQ) calculations. The remaining CASSCF calculation can be easily dismissed since it produces an unrealistically small C@O bond length
K. Tersago et al. / Chemical Physics Letters 413 (2005) 440–444
˚ ). It is interesting to note that only two impor(1.177 A tant configurations can be found in the CAS wave functions: the ground state (with a weight of about 90%) and a doubly excited closed-shell state (with a weight of about 10%); all the other determinants are negligible. In addition, we draw attention to the fact that the B1B95 functional is the only one in the current series which produces a geometry which is close to our acceptability criteria. In particular, its description of the CS bond is remarkable in comparison with the other functionals. Even though it is difficult to mutually compare these seven combinations and select one which produces the most satisfying description, MP4(SDQ)/aug-cc-pVTZ seems to generate a combination of a well-described NSNS fragment with a CS bond short enough to be comfortably compared to the corresponding solid-state parameter. Inspection of the geometries obtained from the seven method/basis set combinations indicates that the addition of diffuse functions to the basis set changes very little in the overall geometry: for QCISD the largest ˚ and for difference between the two geometries is 0.009 A ˚ . It is CCSD and MP4(SDQ) this value is a mere 0.004 A interesting to observe that increasing the basis set to cc-pV(T+d)Z (for QCISD and CCSD) and even augcc-pV(Q+d)Z (for CCSD) does not really improve the description: even though the CS distance converges to the experimental value the S(3)–N(4) distance is too short. Of even greater importance is the fact that upon increasing the level of theory from CCSD to CCSD(T) the quality of the description of the geometry of RoeskyÕs ketone actually becomes worse: the difference between the two shorter SN bond lengths becomes too ˚ . It large and the CS distance increases by about 0.02 A seems that at these considerable levels of theory convergence of the different geometrical parameters has not been obtained. In this context we would like to note that further increasing the level for this six-atom molecule is virtually beyond the possibilities of computational chemistry at this moment: a CCSDTQ calculation could only be performed using a very small basis set and the molecule is clearly too large for a CAS calculation with a full valence space.
4. Conclusion The MP4(SDQ)/aug-cc-pVTZ combination produces a calculated geometry for RoeskyÕs ketone which correlates most satisfactorily with the experimental solid-state data, even though the differences with six other method/basis set combinations [QCISD/6-311(+)G*, CCSD/6-311(+)G*, MP4(SDQ)/ 6-311+G* and MP4(SDQ)/cc-pVTZ] are small. In contrast, increasing the size of the basis set for QCISD and CCSD consistently leads to inferior
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results, as does increasing the level of theory from CCSD to CCSD(T). Even for these considerable levels of theory no convergence of the geometrical parameters seems to have been reached. It appears that several fundamental issues pertaining to a correct description of the gas-phase geometry of RoeskyÕs ketone deserve further attention.
Acknowledgments This work was supported by the Flemish-Hungarian Scientific and Technological Joint Fund (TeT B-2/01, BIL 01/72 and BIL 01/17). J.O. and T.V. acknowledge financial support from OTKA Grant T048796.
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