SUPPORTING INFORMATION. Modeling the Peroxide/Superoxide Continuum in 1:1 Side-on Adducts of O 2 with Cu

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1 SI-1 SUPPORTING INFORMATION Modeling the Peroxide/Superoxide Continuum in 1:1 Side-on Adducts of O 2 with Cu Benjamin F. Gherman and Christopher J. Cramer* Department of Chemistry and Supercomputer Institute, University of Minnesota, 207 Pleasant St. SE, Minneapolis, MN, 55455, USA. Contents Section 1: General discussion of CASPT2 vs. DFT for modeling CuO 2 SI-2 fragments Section 2: Computational Methods Section 3: Geometries and energies for all species at various levels of theory Section 3.1: CAS(12,9) geometries Section 3.2: BLYP (Jaguar) geometries Section 3.3: UBLYP (Gaussian 98) geometries Section 3.4: mpwpw91 (Gaussian 98) geometries SI-4 SI-7 SI-7 SI-15 SI-23 SI-31 Section 1: General discussion of CASPT2 vs. DFT for modeling CuO 2 fragments There is occasionally debate in the literature over the relative utility of CASPT2 compared to DFT for transition-metal systems, in part because one or two worst-case scenarios have been identified. For example, Pierloot 1 has demonstrated that CASPT2 is poorly suited to describing the electronic structure of CrF 6 compared to DFT because the high degree of covalency between the central metal atom and its six ligands is such that a minimally sufficient CAS active space must include too many orbitals to be practical. In another example, Choe et al. 2 found DFT to do better than CASPT2 in describing the ground state of Fe(II)-porphine. 1 Pierloot, K. Mol. Phys. 2003, 101, Choe, Y.-K.; Nakajima, T.; Kirao, K.; Lindh, R. J. Chem. Phys. 1999, 111, 3837.

2 SI-2 However, while these two examples are interesting in the extent to which they delineate limitations in the applicability of CASPT2 vs. DFT, for the purposes of the systems studied in this paper there are far more relevant comparisons that offer precedent for CASPT2 being considerably more likely to be appropriate than DFT. One study of some relevance is that of Ryde et al. 3 which examined the role of strain in blue copper proteins, where the active site is a monocopper center. Although that study relied on the efficiency of DFT for a number of calculations, it specifically noted that key bond-length errors in DFT geometries were resolved by reoptimization at the CASPT2 level. Another comparison that is particularly germane has been provided by Hasegawa et al. 4 who carried out a study of the ground electronic state of bare CuO 2, the exact fragment of interest for this paper, at a number of different levels of theory. Comparisons of MRCI, MCPF, CCSD(T), CASPT2, and DFT revealed large qualitative and quantitative errors in the ability of DFT to predict minimum energy structures and activation energies for conversions between structures. CASPT2, on the other hand, was in very good agreement with the other levels so long as the O O σ and σ* orbitals were included in the CAS active space. We note that these orbitals were indeed included in the present work (see reference 9 of published paper; the orbitals have a 1 and b 1 symmetry, respectively). A final comparison of some interest concerns a dicopper-dioxo system. Flock and Pierloot 5 compared DFT and CASPT2 with respect to their predictions for the relative energetics of bis(µ-oxo) and µ-η 2 :η 2 -peroxo isomers of [(NH 3 ) 3 Cu] 2 (µ-o) 2 ], a system first studied by Cramer et al. 6 Flock and Pierloot found DFT (in particular B3LYP) to predict the peroxo isomer to be 14.4 kcal mol 1 lower in energy than the bis(µ-oxo) isomer (19.9 kcal mol 1 with a broken-symmetry B3LYP approach for the peroxo isomer). CASPT2, on the other hand, predicted the bis(µ-oxo) isomer to be 12.7 kcal mol 1 lower in energy than the peroxo isomer. Although the system has not been experimentally described, Flock and Pierloot concluded that the CASPT2 level was more likely to be accurate, and ascribed to DFT an inability to adequately model large changes in dynamical and non-dynamical correlation effects occurring along the relevant isomerization coordinate (Cramer et al. had previously noted the large change in nondynamical correlation as well.) Siegbahn 7 later revisited the analysis of this same dicopper-dioxo system. Without providing any particularly new insights into which, if either, might be the more accurate, Siegbahn pointed out that the large difference between the CAS and CASPT2 predictions for an 8-electrons-in-10-orbitals active space (34.4 kcal mol 1!) was a significant cause 3 Ryde, U.; Olsson, M. H. M.; Roos, B. O.; De Kerpel, J. O. A.; Pierloot, K. J. Biol. Inorg. Chem. 2000, 5, Hasegawa, J.-y.; Pierloot, K. Roos, B. O. Chem. Phys. Lett. 2001, 335, Flock, M.; Pierloot, K. J. Phys. Chem. 1999, 103, 95 6 Cramer, C. J.; Smith, B. A.; Tolman, W. B. J. Am. Chem. Soc. 1996, 118, Siegbahn, P. E. M. Faraday Discuss. 2003, 124, 289.

3 SI-3 for concern, and may indicate an instability in second-order perturbation theory for this system. With respect to this penetrating observation, we note that in the present work the difference between singlet-triplet splittings computed at the CAS and CASPT2 levels is usually substantially smaller than 10 kcal mol 1. This is a fairly typical magnitude of effect that may be taken to be chemically meaningful with a much higher degree of confidence. A separate point that merits some discussion is the correct approach to take when modeling a system with biradical character using DFT. The energy of the singlet, for example, may be taken from a restricted calculation, from a broken-symmetry (BS; unrestricted) calculation, and, in the latter instance, the BS density may be interpreted to derive from a sum of singlet and triplet state densities, from which the pure singlet energy may be derived following the approach of Ziegler et al. 8 This is sometimes referred to as spin projection, although the use of the term is somewhat objectionable since there is no formal wave function or spin operator involved. We have examined the utility of spin projection in the present system, and its performance is improved compared to either restricted DFT or direct use of BS singlet energies. However, it suffers from two significant problems. One is that, as demonstrated in Figure 2 of the text, the mixed-state geometries are not particularly good, and one really should optimize geometries for the purified state (something that is achievable but tedious). A more difficult problem is that the triplet that is needed to carry out the manipulations of the sum method is the one having the same spatial symmetry as the singlet, i.e., 3 A 1. Because of the high symmetry of the model system used here, an SCF density and energy for this state can be determined. However, in a system without symmetry, variational collapse would preclude use of the sum method. This too, then, is a reason to prefer multireference models in the present system. Lastly, we do consider unprojected BS singlet energies in our discussion, and we do so using the BLYP functional. Cremer and co-workers 9 have pointed out in several papers that the use of BLYP in BS-UDFT calculations is problematic when trying to mimic multi-reference effects. BLYP includes via the self-interaction error of the exchange functional non-specific non-dynamical correlation effects. If, simultaneously, one tries to include non-dynamical correlation effects via the (implicitly two-configurational) BS form of the KS wave function, this leads to a double counting of non-dynamical electron correlation. In such cases, it has been shown to be better to use B3LYP, in which functional non-dynamical electron correlation is reduced due to the admixture of exact exchange. Our motivation in using BLYP in the present paper is simply to make direct comparison with the work of Pantazis and McGrady, 10 which did indeed employ this functional, and the conclusions with respect to the appropriateness of formally single- 8 Ziegler, T.; Rauk, A.; Baerends, E. J. Theor. Chim. Acta 1977, 43, (a) Gräfenstein, J.; Kraka, E.; Filatov, M.; Cremer, D. Int. J. Mol. Sci. 2002, 3, 360. (b) Cremer, D.; Filatov, M.; Polo, V.; Kraka, E.; Shaik, S. Int. J. Mol. Sci. 2002, 3, 604. (c) Polo, V.; Gräfenstein, J.; Kraka, E.; Cremer, D. Theor. Chem. Acc. 2003, 109, Pantazis, D. A.; McGrady, J. E. Inorg. Chem. 2003, 42, 7734.

4 SI-4 reference DFT vs. multireference methods are not much affected by choice of functional in any case. Section 2: Computational Methods Optimized geometries for all species were obtained at 4 different levels of theory. We describe each level in turn and note key points with respect to comparisons of our results both internally and also with those of Pantazis and McGrady. 10 First, in calculations most closely related to those of Pantazis and McGrady, we employed a locally modified version of Gaussian to carry out unrestricted density functional calculations at the BLYP and mpwpw91 levels of theory. 12 For almost all singlets, instability of the single-determinantal formalism led to symmetry breaking of the singlet Kohn-Sham non-interacting wave functions, and <S 2 > values in excess of the correct singlet value of zero were obtained. The values are reported with the structures and energies in Sections 5 and 6 of this Supporting Information. The nature of the local modification to Gaussian 98 involved the Gaussian keyword MASSAGE; this keyword ordinarily permits nuclear charges to be zeroed out, but not to take on any other values. We expanded the keyword to permit such choices (a fairly trivial affair as nuclear charge is simply a constant in the nuclear attraction integrals). As noted in the text, this is equivalent to changing the electronegativity of the atom, which is useful when one wants to monitor the behavior of a property as a function of this quantity. We verified that our modification did not change results obtained using correct nuclear charges. We further verified that Gaussian 98 results agreed with Gaussian Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Zakrzewski, V. G.; Montgomery, J. A.; Burant, J. C.; Dapprich, S.; Millam, J. M.; Daniels, A. D.; Kudin, K. N.; Strain, M. C.; Farkas, O.; Tomasi, J.; Barone, V.; Cossi, M.; Cammi, R.; Mennucci, B.; Pomelli, C.; Adamo, C.; Clifford, S.; Ochterski, J.; Petersson, G. A.; Ayala, P. Y.; Cui, Q.; Morokuma, K.; Rega, N.; Salvador, P.; Dannenberg, J. J.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Cioslowski, J.; Ortiz, J. V.; Baboul, A. G.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Gomperts, R.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Andres, J. L.; Gonzalez, C.; Head-Gordon, M.; Replogle, E. S.; Pople, J. A., Gaussian 98 (Revision A.11.3); Gaussian, Inc.: Pittsburgh, PA, BLYP (a) Becke, A. D. Phys. Rev. A 1988, 38, (b) Lee, C.; Yang, W.; Parr, R. G. Phys. Rev. B 1988, 37, 785. mpwpw91: (c) Adamo, C.; Barone, V. J. Chem. Phys. 1998, 108, Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.;

5 SI-5 results for all cases where we did not invoke MASSAGE (i.e., the two codes are equivalent for routine use of the BLYP and mpwpw91 functionals). In the Gaussian suite of programs, we employed the 6-311G(d,p) basis set 14 for all atoms other than copper. For copper, we employed the 10-electron effective core potential of Stevens et al. 15 (called CEP-31G in the Gaussian suite). We note that Pantazis and McGrady 10 employed an all-electron basis set for copper, although their paper fails to properly describe it. Rather, they state that the 6-311G(d,p) basis set was used for all atoms. However, that basis set is not defined for copper. Instead, the Gaussian suite substitutes the basis set of Wachters 16 when no other specification is made. That basis set, however, is incorrectly coded in the Gaussian suite of programs. In particular, the Gaussian code took the exponents and contraction coefficients for the s and p function primitives from Wachters tabulation for the 2 S state of the atom, while it took the exponents and contraction coefficients for the d function primitives from his tabulation for the 2 D state. This basis is thus fundamentally unbalanced, and must account at least in part for the difference between our UBLYP results for the singlet-triplet splitting of 3a (0.3 kcal mol 1 ) and theirs ( 5.0 kcal mol 1 ). It is fortuitous that this error acts to counterbalance some of the intrinsic error in the DFT approach, so that for 3a the allelectron result is closer to the rigorous CASPT2 result than is that computed with the effective core potential. However, it does not change the fact that unrestricted DFT calculations show large instability to increasing biradical character and become increasingly in error compared to CASPT2 as that character increases. We also carried out BLYP calculations at the restricted level of theory for the singlets and unrestricted level of theory for the triplets using the Jaguar code of Schrödinger. 17 In this case, 6-311G(d,p) was again used for all atoms other than copper, while the 10-electron effective core potential of Hay and Wadt 18 was used for copper. Triplet geometries obtained in this manner (reported in Section 4 of this supporting information) showed negligible differences with those from the Gaussian program, as did singlet geometries for those few cases where symmetry-breaking did not take place in the Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A., Gaussian 03 (Revision B.05); Gaussian, Inc.: Pittsburgh, PA, Krishnan, R.; Binkley, J. S.; Seeger, R.; Pople, J. A. J. Chem. Phys. 1980, 72, Stevens, W. J.; Krauss, M.; Basch, H.; Jasien, P. G. Can. J. Chem. 1992, 70, Wachters, A. J. H. J. Chem. Phys. 1970, 52, Jaguar 5.0. Schrödinger, Inc.: Portland, OR, Hay, P. J.; Wadt, W. R. J. Chem. Phys. 1985, 82, 299.

6 SI-6 Gaussian calculations. In addition, predicted singlet-triplet splittings from the two BLYP protocols agree with one another to within 0.1 kcal mol 1 for those same cases where 3a shows zero or very small spin contamination (i.e., for larger negative values of ΔZ N ). Results therefore appear insensitive to choice of core potential and suggest, again, that the difference with the reported results of Pantazis and McGrady derives in part from the incorrect Wachters basis set coded in Gaussian. As noted in the text, a comparison of CASPT2 energies for the singlet geometries from all three DFT protocols (restricted BLYP, unrestricted BLYP, and unrestricted mpwpw91) as well as from CAS(12,9) optimizations described below, revealed the restricted BLYP singlet geometries to be the lowest in energy over the full range of biradical character in 3a. Geometry optimization at the CAS(12,9) level was carried out in the MOLCAS suite of programs. 19 For all atoms other than copper, these calculations employed the polarized split-valence atomic natural orbital basis set of Pierloot et al. 20 For copper, the Cowan-Griffin ab initio model potential basis set of Barandiaran and Seijo 21 was used. The active space for the CAS calculations was chosen by first examining singlet and triplet wave functions from CAS(18,12) calculations including all copper valence orbitals and electrons (s and d) and all of the σ, σ*, π, and π* type orbitals/electrons deriving from the O 2 fragment. This set includes 5 orbitals belonging to the a 1 irrep, four occupied and one virtual, 2 orbitals belonging to the a 2 irrep, both occupied, 2 orbitals corresponding to the b 1 irrep, one occupied and one virtual, and 3 orbitals belonging to the b 2 irrep, two occupied and one virtual. In a variety of charge/state combinations, it was observed that 3 occupied orbitals, two belonging t the a 1 irrep and one belonging to the b 2 irrep, had occupation numbers greater than These orbitals were removed from the active space to generate that final (12,9) space used in our calculations. That space contained the key orbitals identified by Hasegawa et al., 4 as discussed in Section 1 of this supporting information above. CASPT2 single-point calculations using the same active space were carried out with the CAS reference wave functions for geometries optimized at all four of the levels of theory described thus far. Absolute energies for the singlets indicated restricted BLYP geometries to be the most accurate (as judged by having the lowest energies for cases with high biradical character); for the triplets, all levels of theory delivered very similar geometries as judged by CASPT2 energies that varied by less than 0.5 kcal mol 1 over all four possibilities. 19 Karlstrom, G.; Lindh, R.; Malmqvist, P. A.; Roos, B. O.; Ryde, U.; Veryazov, V.; Widmark, P. O.; Cossi, M.; Schimmelpfennig, B.; Neogrady, P.; Seijo, L. Comput. Matl. Sci. 2003, 28, Pierloot, K.; Dumez, B.; Widmark, P.-O.; Roos, B. O. Theor. Chim. Acta 1995, 90, Barandiaran, Z.; Seijo, L. Can. J. Chem. 1992, 70, 409.

7 SI-7 Section 3: Geometries and energies for all species at various levels of theory Note: For energies (a.u.), the first value is for the level of theory at which the geometry was optimized. The second value is the single-point CASPT2 energy at that geometry. S 2 values are from optimized unrestricted DFT wave functions. Section 3.1: CAS(12,9) geometries All-carbon backbone: singlets Z N = 6.6 a.u. Energy: ( ) Cu O O C C C N N H H H H H Z N = 6.7 a.u. Energy: ( ) Cu O O C C C N N H H H H H

8 SI-8 Z N = 6.8 a.u. Energy: ( ) Cu O O C C C N N H H H H H Z N = 6.9 a.u. Energy: ( ) Cu O O C C C N N H H H H H Z N = 7.0 a.u. Energy: ( ) Cu O O C C C N N H H H H H

9 SI-9 Z N = 7.1 a.u. Energy: ( ) Cu O O C C C N N H H H H H Z N = 7.2 a.u. Energy: ( ) Cu O O C C C N N H H H H H Z N = 7.3 a.u. Energy: ( ) Cu O O C C C N N H H H H H

10 SI-10 Z N = 7.4 a.u. Energy: ( ) Cu O O C C C N N H H H H H triplets Z N = 6.6 a.u. Energy: ( ) Cu O O C C C N N H H H H H Z N = 6.7 a.u. Energy: ( ) Cu O O C C C N N H H H H H

11 SI-11 Z N = 6.8 a.u. Energy: ( ) Cu O O C C C N N H H H H H Z N = 6.9 a.u. Energy: ( ) Cu O O C C C N N H H H H H Z N = 7.0 a.u. Energy: ( ) Cu O O C C C N N H H H H H

12 SI-12 Z N = 7.1 a.u. Energy: ( ) Cu O O C C C N N H H H H H Z N = 7.2 a.u. Energy: ( ) Cu O O C C C N N H H H H H Z N = 7.3 a.u. Energy: ( ) Cu O O C C C N N H H H H H

13 SI-13 Z N = 7.4 a.u. Energy: ( ) Cu O O C C C N N H H H H H Boron-backbone singlet Energy: ( ) Cu O O C B C N N H H H H H triplet Energy: ( ) Cu O O C B C N N H H H H H

14 SI-14 Nitrogen-backbone singlet Energy: ( ) Cu O O C N C N N H H H H H triplet Energy: ( ) Cu O O C N C N N H H H H H

15 SI-15 Section 3.2: BLYP (Jaguar) geometries All-carbon backbone: singlets (restricted formalism) Z N = 6.6 a.u. Energy: ( ) Cu O O C C C N N H H H H H Z N = 6.7 a.u. Energy: ( ) Cu O O C C C N N H H H H H Z N = 6.8 a.u. Energy: ( ) Cu O O C C C N N H H H H H

16 SI-16 Z N = 6.9 a.u. Energy: ( ) Cu O O C C C N N H H H H H Z N = 7.0 a.u. Energy: ( ) Cu O O C C C N N H H H H H Z N = 7.1 a.u. Energy: ( ) Cu O O C C C N N H H H H H

17 SI-17 Z N = 7.2 a.u. Energy: ( ) Cu O O C C C N N H H H H H Z N = 7.3 a.u. Energy: ( ) Cu O O C C C N N H H H H H Z N = 7.4 a.u. Energy: ( ) Cu O O C C C N N H H H H H

18 SI-18 triplets Z N = 6.6 a.u. Energy: ( ) S 2 = Cu O O C C C N N H H H H H Z N = 6.7 a.u. Energy: ( ) S 2 = Cu O O C C C N N H H H H H Z N = 6.8 a.u. Energy: ( ) S 2 = Cu O O C C C N N H H H H H

19 SI-19 Z N = 6.9 a.u. Energy: ( ) S 2 = Cu O O C C C N N H H H H H Z N = 7.0 a.u. Energy: ( ) S 2 = Cu O O C C C N N H H H H H Z N = 7.1 a.u. Energy: ( ) S 2 = Cu O O C C C N N H H H H H

20 SI-20 Z N = 7.2 a.u. Energy: ( ) S 2 = Cu O O C C C N N H H H H H Z N = 7.3 a.u. Energy: ( ) S 2 = Cu O O C C C N N H H H H H Z N = 7.4 a.u. Energy: ( ) S 2 = Cu O O C C C N N H H H H H

21 SI-21 Boron-backbone singlet (restricted formalism) Energy: ( ) Cu O O C B C N N H H H H H triplet Energy: ( ) S 2 = Cu O O C B C N N H H H H H Nitrogen-backbone singlet (restricted formalism) Energy: ( ) Cu O O C N C N N H H H H H

22 triplet Energy: ( ) S 2 = Cu O O C N C N N H H H H H SI-22

23 SI-23 Section 3.3: UBLYP (Gaussian 98) geometries All-carbon backbone: singlets (broken-symmetry) Z N = 6.6 a.u. Energy: ( ) S 2 =.0000 Cu O O C C C N N H H H H H Z N = 6.7 a.u. Energy: ( ) S 2 =.0448 Cu O O C C C N N H H H H H

24 SI-24 Z N = 6.8 a.u. Energy: ( ) S 2 =.2047 Cu O O C C C N N H H H H H Z N = 6.9 a.u. Energy: ( ) S 2 =.3481 Cu O O C C C N N H H H H H Z N = 7.0 a.u. Energy: ( ) S 2 =.4689 Cu O O C C C N N H H H H H

25 SI-25 Z N = 7.1 a.u. Energy: ( ) S 2 =.5797 Cu O O C C C N N H H H H H Z N = 7.2 a.u. Energy: ( ) S 2 =.6719 Cu O O C C C N N H H H H H Z N = 7.3 a.u. Energy: ( ) S 2 =.7501 Cu O O C C C N N H H H H H

26 SI-26 Z N = 7.4 a.u. Energy: ( ) S 2 =.8152 Cu O O C C C N N H H H H H triplets Z N = 6.6 a.u. Energy: ( ) S 2 = Cu O O C C C N N H H H H H Z N = 6.7 a.u. Energy: ( ) S 2 = Cu O O C C C N N H H H H H

27 SI-27 Z N = 6.8 a.u. Energy: ( ) S 2 = Cu O O C C C N N H H H H H Z N = 6.9 a.u. Energy: ( ) S 2 = Cu O O C C C N N H H H H H Z N = 7.0 a.u. Energy: ( ) S 2 = Cu O O C C C N N H H H H H

28 SI-28 Z N = 7.1 a.u. Energy: ( ) S 2 = Cu O O C C C N N H H H H H Z N = 7.2 a.u. Energy: ( ) S 2 = Cu O O C C C N N H H H H H Z N = 7.3 a.u. Energy: ( ) S 2 = Cu O O C C C N N H H H H H

29 SI-29 Z N = 7.4 a.u. Energy: ( ) S 2 = Cu O O C C C N N H H H H H Boron-backbone singlet (broken-symmetry) Energy: ( ) S 2 =.3715 Cu O O C B C N N H H H H H triplet: No geometry for this case, due to difficulties in the geometry optimization.

30 SI-30 Nitrogen-backbone singlet (broken-symmetry) Energy: ( ) S 2 =.8096 Cu O O C N C N N H H H H H triplet Energy: ( ) S 2 = Cu O O C N C N N H H H H H

31 SI-31 Section 3.4: mpwpw91 (Gaussian 98) geometries All-carbon backbone: singlets (broken-symmetry) Z N = 6.6 a.u. Energy: ( ) S 2 =.0000 Cu O O C C C N N H H H H H Z N = 6.7 a.u. Energy: ( ) S 2 =.0558 Cu O O C C C N N H H H H H

32 SI-32 Z N = 6.8 a.u. Energy: ( ) S 2 =.2148 Cu O O C C C N N H H H H H Z N = 6.9 a.u. Energy: ( ) S 2 =.3599 Cu O O C C C N N H H H H H Z N = 7.0 a.u. Energy: ( ) S 2 before annihilation.4750, after.0025 Cu O O C C C N N H H H H H