Journal of Molecular Structure (Theochem), 287 (1993) 89-92 0166-1280/93/%06.00 0 1993 - Elsevier Science Publishers B.V. All rights reserved
Ab initio calculations of isotropic hyperfine coupling constants in ,8-ketoenolyl radicals Alessandro Fortunelli*, Istituto
di Chimica Quantistica ed Energetica Molecolare de1 CNR, Via Risorgimento 35, 56126 Pisa, Italy
(Received 12 October 1992; accepted 9 March 1993) Abstract Ab initio unrestricted Hartree-Fock (UHF), unrestricted second-order Msller-Plesset (UMPZ) perturbation and unrestricted coupled cluster (UCCD) calculations have been performed on the organic radicals CHs, CHsCH2, CH2CHCH2, CHsCHCOOand CH$OCHCOCHs, using double zeta and double zeta plus polarization basis sets. The geometry of the radicals has been optimized at the UHF level. From such calculations, values for the isotropic hype&e coupling constants are predicted and compared with the experimental results. The usefulness of semiempirical extrapolations based on limited basis sets and treatment of electron correlation effects is checked in the examples considered and found to be valid if (at least) UMP2 calculations are performed.
Introduction In a recent paper [ 11,the possibility of producing in situ organic radicals directly attached to a transition metal atom has been advanced. In particular, tris(&ketoenolato)cobalt(III) chelates have been considered as generating complexes, where the “P-ketoenolato” fragment represents, for example, the formylacetonate ion H-CO-CHCO-CH;, the acetylacetonate ion CHs-COCH-CO-CH;, etc. A large variety of such organic ligands has been considered in Ref. 1, to which we refer for all details. The radicals so obtained have been characterized through Electron Spin Resonance (ESR) measurements, so that experimental values of the isotropic hyperfine coupling constants (HFCCs) are available. Parallel to the experimental work, an ab initio study of such systems has been initiated in our laboratory: in the present paper preliminary
results concerning the acetylacetonyl radical CHs-CO-CH-CO-CH3 are presented and compared with calculations on well-characterized analogous organic compounds. The aim of this paper is to explore the capability of ab initio techniques to predict isotropic HFCCs in such systems, to assess the relative importance of the various contributions to the final HFCC values, and to check the viability of semiempirical extrapolations (i.e. with respect to the approximate treatment of electron correlation effects, the use of limited basis sets, etc.) which can then be utilized for the study of the P-ketoenolato complexes. The method In this section, the main ideas on which the present calculations are based are briefly discussed, and we refer to Ref. 2 for an interesting review of the general problem. The experimental spectra give the isotropic HFFCs for the various hydrogen atoms in the organic ligands. The quantities to be evaluated ‘at the theoretical level are therefore the
A. Fortune& and 0. Salvetti/J. Mol. Struct. (Theochem) 287 (1993) 89-92
electron spin densities at the hydrogen atoms, which - through the Fermi contact interaction - determine the isotropic HFFCs (through a proportionality factor). Let us first consider an a-hydrogen atom, i.e. a hydrogen atom directly bound to the radical center. Only r radicals are considered here, so the spin densities at such atoms are rigorously null at the restricted Hartree-Fock (RHF) level. In contrast, however, this is no longer true within the unrestricted Hartree-Fock (UHF) approximation, which however tends to overestimate such quantities, because the wavefunction gains in stabilization energy by allowing the Q- and pspin orbitals to differ (spin polarization of the “doubly occupied” orbitals; partially spurious due to spin contamination effects ). However, if one allows the UHF determinant to interact with all the doubly excited configurations in which the (Y-and P-spin orbitals are promoted into their antibonding counterparts, one obtains a contribution to the HFFCs of opposite sign, which corrects (in the right direction) the UHF contribution and hopefully gives semi-quantitative results. The procedure here adopted thus consists of performing an UHF calculation, followed by an unrestricted second-order Moller-Plesset perturbative expansion (UMP2) or an unrestricted coupled cluster with doubles (UCCD) calculation, and therefore corresponds essentially to that proposed in Ref. 3. Note that only double excitations are considered in the UCCD calculation, because the contribution of the singles to the spin density is a minor one  (for further justification - with respect to spin contamination problems of the procedure here adopted, see, for example, Ref. 4). The reasoning remains essentially the same for the P-hydrogen atoms, even though in this case: (a) the induced UHF spin polarization is of opposite sign; (b) there also appears a direct effect due to the unpaired electron density at the hydrogen sites. In HFCC calculations, the choice of an appropriate basis set is fundamental . In the present paper, the standard LANLlDZ  and 6-31G** 
basis sets have been utilized, which are of double zeta (DZ) and double zeta plus polarization (DZ + P) quality, respectively. We are aware of the fact that the reasonable results produced by such basis sets (see below) probably contain compensation effects [I, but this is part of what we are pursuing in the present work. Note also that only spin densities at the hydrogen atoms must be evaluated, which greatly simplifies the theoretical problem: the results would have been very different if spin densities at heavier atoms had to be considered. Finally, most of the calculations here reported have been performed with the GAUSSIAN 92 set of programs. The results In Table 1 the results of the UHF, UMP2 and UCCD calculations employing the two previously mentioned basis sets are reported for the radicals CHs, CH$H2, CH2CHCH2, CHsCHCOO- and CHsCOCHCOCHs. The first four molecules have been chosen as test cases, because they are well characterized from the experimental point of view (the experimental values are taken from Refs. 2 and 8). The stability of the UHF wavefunction with respect to complex variations, symmetry breaking, etc. has been checked in each case. For all molecules, the geometry has been optimized at the UHF level (using the DZP basis set for CHsCHCOOand the DZ set for the others). This corresponds to choosing the isolated molecule as a model. When comparing the theoretical and experimental results, however, one should take into account the influence of solvent or solidstate perturbing factors, both as an additional field and for their indirect influence on the geometry. Vibrational effects have also been neglected. These effects were assumed to be accounted for by the semiempirical extrapolation (see below). Let us thus analyze the results of Table 1. Small basis sets and an incomplete treatment of electron correlation effects (limited essentially to double excitations) are considered in the present paper,
A. Fortunelli and 0. SalvettilJ. Mol. Struct. (Theochem) 287 (1993) 89-92
Table 1 HFCC values (in gauss) for the CH3, CHsCH2. CH2CHCH2, CHsCHCOGand CH,COCHCOCHs radicals, obtained through UHF, UMP2 and UCCD calculations using the LANLlDZ (DZ) or6-31G** (DZP) basis sets, and compared with experimental resultsa Systemb
CH3CH1 H, Ho CH2CHCH2 HA Hi HP CH,CHCOOH, H0 CH3COCHCOCH3 H, H,
50.5 (23.4) 25.7
47.5 (23.4) 23.5
37.9 (22.6) 23.8
30.8 (22.5) 20.9
33.8 (22.7) 22.4
28.6 (22.8) 20.0
39.3 (18.2) 40.4 (18.7) 27.6 (28.9)
36.2 (17.8) 37.4 (18.4) 24.6 (28.2)
22.6 (13.5) 23.6 (14.2) 5.6 (6.3)
16.9 (12.3) 17.7 (13.0) 1.5 (1.9)
20.0 (13.5) 20.9 (14.1) 4.1 (4.9)
16.5 (13.2) 17.3 (13.8) 2.6 (3.5)
13.9 14.8 4.2
47.5 (22.0) 24.3 (25.4)
43.5 (21.4) 22.0 (25.2)
33.7 (20.1) 22.0 (24.9)
26.8 (19.6) 19.0 (24.5)
30.5 (20.5) 20.8 (25.0)
25.5 (20.4) 18.6 (25.0)
39.8 (18.5) 13.0
35.9 (17.7) 10.8
23.5 (14.0) 2.1
18.9 (13.8) 0.5
a Values obtained through the semiempirical extrapolation are given in parentheses. b H,, Hp and H, represent (Y-,/3- and y-hydrogen atoms, respectively.
so one should not expect to obtain fully quantitative results. However, one can check the validity of a semiempirical extrapolation, i.e. one can see if the ab initio HFCCs can be related to the experimental values through scaling factors obtained from the simplest possible molecule which contains the kind of atom of interest (i.e. CHs for a-hydrogen atoms and CH3CH2 for P-hydrogen atoms). In Table 1 the ab initio HFCC values thus scaled are given in parentheses.
Conclusion From the analysis of the results reported in Table 1, the following conclusions can be drawn. (a) The theoretical predictions - before the semiempirical correction - usually improve as the basis set is enlarged and correlation effects are included at a more refined level, but do not furnish quantitative answers.
(b) The ab initio HFCCs - before the semiempirical correction - converge to values which are larger than the experimental values for (Yhydrogen atoms and smaller than the experimental values for P-hydrogen atoms. Most of the remaining error is presumably due to basis set problems. In general, it seems that the error is amplified by these problems, such as, for example, in Ref. 7: (i) lack of tight (and diffuse) s-functions; (ii) lack of polarization functions (a more thorough analysis of this point is in progress). Note, however, that the correct prediction of P-hydrogen HFCCs also represents a problem within the SC1 approach of Ref. 2, probably because of correlation effects which are absent in the cited procedure (see the results on the ethyl and ally1 radicals). (c) For a-hydrogen atoms, electron correlation effects are slightly more important when the unpaired orbital is part of a conjugate system: for P-hydrogen atoms, correlation effects are less important than for o-hydrogen atoms when considering non-conjugate systems, but are of
A. Fortunelli and 0. Salvetti/J. Mol. Struct. (Theochem) 287 (1993) 89-92
dramatic importance when the spin polarization is transmitted through the conjugate system (see the ally1 radical). The same seems to be true for the y-hydrogen atoms of the acetylacetonyl radical (for which we could not find ESR experimental data, nor a “safe” molecule to compare with): in general, x conjugation amplifies correlation effects. (d) The semiempirical extrapolation does not give very good results at the UHF level. This is especially true for those /?-hydrogen atoms for which the correlation is particularly important (e.g. in the ally1 radical). (e) The extrapolation is very much improved at the UMP2 or UCCD level (which both give similar results, nearly independently of the basis set utilized) and thus represents a simple and efficient way to make theoretical predictions of reasonable accuracy. The worst case is still represented by the P-hydrogen atom of the ally1 radical: for it, the correlation effects reduce the UHF value by a factor of approximately 7.
Acknowledgments We wish to thank Professor G. Ingrosso of the University of Pisa and Dr. C. Pinzino of ICQEM for many useful discussions. This research has been performed in the framework of the “Progretto Finalizzato Materiali Speciali per Tecnologie Avanzate” of the Consiglio Nazionale delle Ricerche (Italy).
References P. Diversi, C. Forte, M. Franceschi, G. Iagrosso, A. Lucherini, M. Petri and C. Pinzino, J. Chem. Sot., Chem. Commun., (1992) 1345. D.M. Chipman, Theor. Chim. Acta, 82 (1992) 93. H. Sekino and R.J. Bartlett, J. Chem. Phys., 82 (1985) 4225. G.D. Purvis, H. Se&no and R.J. Bartlett, Collect. Czech. Chem. Commun., 53 (1988) 2203. P.J. Hay and W.R. Wadt, J. Chem. Phys., 82 (1985) 270. W.J. Hehre, R. Ditchfield and J.A. Pople, J. Chem. Phys., 56 (1972) 2257. D.M. Chipman, J. Chem. Phys., 91 (1989) 5455. S. Kuroda and I. Miyagawa, J. Chem. Phys., 76 (1982) 3933.