EOMCC, MRPT, and TDDFT Studies of Charge Transfer Processes in Mixed-Valence Compounds: Application to the Spiro Molecule † Kurt R. Glaesemann, ‡ Niranjan Govind, ‡ Sriram Krishnamoorthy, § and Karol Kowalski* ,‡ William R. Wiley EnVironmental Molecular Sciences Laboratory, Pacific Northwest National Laboratory, 902 Battelle BouleVard, Richland, Washington 99352 USA, and Fundamental and Computational Sciences Directorate, Pacific Northwest National Laboratory, 902 Battelle BouleVard, Richland, Washington 99352 USA ReceiVed: February 26, 2010; ReVised Manuscript ReceiVed: May 24, 2010 The proper description of electron transfer (ET) processes in mixed-valence compounds poses a significant challenge for commonly used theoretical approaches. In this paper we analyze the 1 2 A 2 and 2 2 A 2 potential energy surfaces of the Spiro cation (5,5′(4H,4H′)-spirobi[cyclopenta[c]pyrrole]2,2′,6,6′-tetrahydro cation) which is a frequently used model to study ET processes. We compare and contrast the results obtained with three different methods: multireference perturbation theory, equation-of-motion coupled cluster theory, time- dependent density functional theory. We demonstrate that the proper inclusion of dynamical correlation effects plays a crucial role in the description of an avoided crossing between potential energy surfaces. We also find that proper balancing of the ground- and excited-state correlation effects is especially challenging in the vicinity of the 1 2 A 2 and 2 2 A 2 avoided crossing region. 1. Introduction An accurate theoretical description of electron transfer (ET) processes is crucial to the fundamental understanding of a plethora of processes in chemistry and biology. 1,2 In particular, ET processes in mixed-valence (MV) compounds are an important challenge for theory. The prototype system used in studies of ET in MV compounds is the model π-σ-π Spiro system (5,5′(4H,4H′)-spirobi[cyclopenta[c]pyrrole]2,2′,6,6′-tet- rahydro cation). Recently, the Spiro cation (Figure 1) was the subject of intensive studies 3 (see also ref 4) using high-level theory including multireference perturbative (MRPT) approaches such as CASPT2, 5 and various orders of the NEVPT method. 6 Using the approximate pathway, which corresponds to the ET from one π to other π moiety, it was demonstrated that the second-order CASPT2 and NEVPT2 formalisms stumble onto a serious problem (an unphysical minimum) in the description of dynamic correlation effects in the vicinity of the avoided crossing between the 1 2 A 2 and 2 2 A 2 states. This unphysical minimum on the ground-state potential energy surface (PES) in the vicinity of the avoided crossing region can be removed either by invoking higher orders of theory (NEVPT3) or by averaging the orbital energies of two charge-localized one particle states. In this paper we extend this study to other methodologies. Natural candidates include the equation-of-motion coupled cluster methods (EOMCC), alternative multireference ap- proaches (multiconfiguration quasi-degenerate perturbation theory (MCQDPT2)), and time-dependent density functional theory (TDDFT). To the best of our knowledge, this is the first combined study of this very interesting and challenging problem using these approaches. EOMCC theory 7-9 (or closely related linear response CC 10-12 and symmetry adapted cluster CI (SAC-CI) 13-15 approaches) has evolved into an array of formalisms that include various rank correlation effects and consequently provide more accurate estimates of excitation energies. Among them, the singles- and doubles-based iterative methods such as the EOMCCSD (EOM- CC with singles and doubles), 7-9 STEOM, 16-20 CC2, 21,22 spin- flip EOMCC model, 23-25 and SAC-CI methods have been used in numerous calculations for excited states dominated by single excitations. Iterative methods such as the CC3 model, 26-28 active-space EOMCCSDT (EOMCC with singles, doubles, and triples), 29,30 or the genuine EOMCCSDT method 29-31 account for the correlation effects due to triples and provide further refinement of the EOMCCSD energies. However, this improve- ment happens at the expense of high computational overhead. In order to approximate the expensive yet accurate EOMCCSDT method several noniterative methods accounting for triples have been proposed. This includes the EOMCCSD(T) and EOM- CCSD(T ˜ ) methods; 32,33 linear-response (LR) based methods CCSDR(3), CCSDR(T), CCSDR(1a), CCSDR(1b), 34,35 EOM- CCSD(2) T , EOM-CCSD(3) T , EOM-CCSD(2) TQ approaches; 36 spin-flip triples corrections EOM-SF-CCSD(fT) and EOM-SF- CCSD(dT); 37 and CR-EOMCCSD(T)/N-EOMCCSD(T) meth- ods 38-43 derived from the excited state extension of the method of moments of the coupled cluster equations (MMCC). 44,45 Given the progress in computer implementations of the EOMCC formalism, calculations using the latter class of methods on open-shell systems of the size of the Spiro molecule are † Part of the “Klaus Ruedenberg Festschrift”. * To whom correspondence should be addressed. E-mail: karol.kowalski@ pnl.gov. ‡ Environmental Molecular Sciences Laboratory § Fundamental and Computational Sciences Directorate Figure 1. Spiro molecule. J. Phys. Chem. A 2010, 114, 8764–8771 8764 10.1021/jp101761d  2010 American Chemical Society Published on Web 06/11/2010