Correlated ab Initio Spin Densities for Larger Molecules: Orbital-Optimized Spin-Component-Scaled MP2 Method Simone Kossmann † and Frank Neese* ,†,‡ Institut fu ¨r Physikalische und Theoretische Chemie, UniVersita ¨t Bonn, Wegelerstrasse 12, D-53115 Bonn, Germany, and Max-Planck Institut fu ¨r Bioanorganische Chemie, Stiftstrasse 34-36, D-45470 Mu ¨lheim an der Ruhr, Germany ReceiVed: June 18, 2010; ReVised Manuscript ReceiVed: September 6, 2010 The performance of the orbital-optimized MP2 method (OO-MP2) and its spin-component-scaled variant is investigated for the prediction of atomic and molecular hyperfine coupling constants (hfccs). The calculated hfccs are compared to experimental as well as to CCSD(T) reference results. The OO-MP2 isotropic hfccs for a series of small radicals are almost of CCSD quality but are obtained with iterative O (N 5 ) effort. The dipolar hfccs are less well predicted by the OO-MP2 methods, whereas spin-component scaling improves the description of the hyperfine structure. The spin contamination in the OO-MP2 wave function is drastically reduced compared to the standard unrestricted Hartree-Fock wave function. The applicability of the OO- MP2 to fairly large systems is demonstrated for the solvated p-benzosemiquinone radical anion, where calculations with almost 2000 basis functions have been performed. Introduction The calculation of the hyperfine structure in electron para- magnetic resonance (EPR) spectra and its high resolution variants such as electron-nuclear double resonance (ENDOR) or hyperfine sublevel correlation spectroscopy (HYSCORE) has been recognized to be a difficult field for theoretical chemistry. Unlike the electron density, which is positive everywhere in space, the spin density is a strongly structured function that can be either positive or negative. This has been realized already by the pioneers of EPR spectroscopy that have referred to the phenomenon as “spin polarization”. Classical examples are the aromatic protons of benzylic radicals or the proton hyperfine couplings (hfcs) of CH 3 that are known to be negative. McConnell has given an intuitively appealing valence bond interpretation of the spin polarization phenomenon. 1 However, it is difficult to implement valence bond theory rigorously in terms of ab initio wave functions. In Hartree-Fock (HF) theory, the spin polarization arises in a rather natural way in the unrestricted HF variant (UHF). However, once calculations with large basis sets became feasible it quickly became clear that the UHF prediction of hyperfine couplings is very poor. Typically, spin polarization contributions are too large by about a factor of 3. This has been analyzed in some detail by Hameka 2 and Chipman. 3 Thus, the calculation of accurate first principles spin densities requires the incorporation of a substantial amount of dynamic correlation. The simplest correlation method, second- order Møller-Plesset perturbation theory (MP2), is known to be insufficient and often provides somewhat erratic results when applied to open-shell systems. Provided that basis sets with sufficient flexibility in the core region and adequate polarization functions to cover dynamic correlation are used (e.g., ref 4), the quadratic configuration interaction with single and double excitations (QCISD) or the more rigorous coupled cluster theory with single- and double excitations (CCSD) are known to provide essentially satisfactory results. 5-11 However, these methods involve iterative steps with O (N 6 ) scaling with respect to system size. Thus, their routine application to larger molecules is presently not possible. Density functional theory (DFT) often provides much better results than UHF theory, 12,4 and there are many successful applications of DFT to the calculation of hfccs. Among the multitude of functionals that could be used, the “gold standard” B3LYP functional provides good results for organic radicals. 8 For transition metal nuclei all functionals have difficulties since they underestimate the core level spin polarization. 13,14 This can to some extent be compensated by mixing more HF exchange into hybrid density functionals. This is, however, not a satisfac- tory solution to the problem since the optimum mixing depends strongly on the investigated system. In a previous study it was found that among the standard functionals, the meta-generalized gradient approximation based hybrid functional TPSSh 15 pro- vides the best results for transition metal complexes. 16 Other problem cases for DFT include strongly delocalized radicals where the self-interaction error strongly deteriorates the results. 17,18 In a recent study, we have investigated the behavior of a new class of double-hybrid density functionals (DHDFs) that have shown in many fields their high potential. In general, excellent results have been obtained for hyperfine couplings with the B2PLYP functional, 16 provided that the calculations are based on the relaxed density approach, 16 which arises naturally in analytic gradient theory of correlated wave function theories. 19-22 However, even B2PLYP was found to suffer to some extent from the unstable MP2 component despite the fact that it was found to be greatly superior to MP2 itself. Despite all recent progress, we feel that it would be desirable to have an affordable wave function based ab initio method available that reliably provides results of essentially QCISD or CCSD quality. Most recently, it was shown that the results of MP2 for open-shell molecules can be greatly improved in accuracy and stability if the orbitals are optimized alongside with the double excitation amplitudes. 23,24 This orbital optimiza- * To whom correspondence should be addressed. E-mail: theochem@ thch.uni-bonn.de. † Universita ¨t Bonn. ‡ Max-Planck Institut Mu ¨lheim a. d. Ruhr. J. Phys. Chem. A 2010, 114, 11768–11781 11768 10.1021/jp105647c  2010 American Chemical Society Published on Web 10/08/2010