Table S1: DFT computed energies of high spin (HS) and broken symmetry (BS) state, <S 2 > values for different radical systems. HS BS1 BS2 BS3 < S 2 >
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1 Computational details: The magnetic exchange interaction between the Gd(III) centers in the non-radical bridged complex has been evaluated using the following Hamiltonian relation, = 2J J represents the Isotropic exchange coupling constant and S 1, S 2 are the spins of Gd (III) centers. J values are computed from the energy differences between the high spin (E HS ) state, which is calculated using single determinant wave functions and low spin (E BS ) state, determined using Broken Symmetry (BS) approach developed by Noodleman. 1, 2 The BS approach was proved to be handy in evaluating the J values to a good estimate in variety of complexes. All the calculations are performed using hybrid B3LYP 3 functional with a combination of CSDZ ECP on Gd 4 and TZV 5 triple- ζ basis set on other atoms as implemented in the Gaussian 09 suite of programs. 6 In the case of radical bridged dinuclear Gd(III) complex, the magnetic interaction between the metal-radical and Gd(III) Gd(III) interaction has to be taken into account. Four different configurations (all spins up, spin of down on N 2, spin down on Gd A, spin down on Gd B ) have been computed to obtain the values of J 1 and J 2. 2 Table S1: DFT computed energies of high spin (HS) and broken symmetry (BS) state, <S 2 > values for different radical systems. HS BS1 BS2 BS3 < S 2 > [Gd(Hbpz 3) 2(dtbsq)](3) [Gd(NITBzImH) 2(NO 3) 3](4) [Gd(hfac)(IM2py)](5) [Gd(NITBzImH) 4 ](ClO 4 ) 3 (6) Table S2: DFT computed spin densities of selected atoms of complexes 1 and 2. Complex (1) Complex (2) Atom specification Spin densities Spin densities HS BS1 BS2 BS3 HS BS Gd Gd O
2 N N N N O N N Table S3: DFT computed spin densities of selected atoms of complexes 3, 4, 5 and 6. Complex 3 Complex 4 Complex 5 Complex 6 Atom specificati on Spin densities Atom specificati on Spin densities Atom specificati on Spin densities Atom specificati on Spin densities HS BS HS BS HS BS HS BS Gd Gd Gd Gd O O O O O N O O N O O N N O O N N N O N N N O O N N N N O N O O N O O O N O O
3 Figure S1: Computed spin density plot for complexes 3, 4, 5 and 6.
4 Figure S2: Computed magnetic orbitals of the Gd(III) in Complex 1.
5 Mechanism- Overlap between 4f-orbitals of two Gd(III) ions and πp y * of N 2 3- (a) (b) (c) (d) Figure S3. Form overlap integral values ( Table S6 and S7), we infer that three 4f orbitals [(a) f x(x 2-3y 2 ), (b and c) f y(y 2-3x 2 ), (d) f z(x 2 -y 2 ) ] overlap with πp y * orbital of N 2 3- plays a prominent in deciding the interaction as antiferromagnetic and this can be evidenced from the superimposed figure shown above. The overlap of f y(y 2-3x 2 ) with πp y * orbital is found to be prominent in both Gd(III) ions whereas the f x(x 2-3y 2 ) overlap is found to be prominent in Gd 1 and f z(x 2 -y 2 ) in the case of Gd 2. δ [d xy - π y * ] d δ [d xy - π * y ] * π π y π x * π [d xz - π x * ] Figure S3: Qualitative Molecular diagram for complex 1.
6 Table S4: Exchange coupling values for certain {3d-4f} complexes. Complexes J (cm -1 ) Ref [Cu II Gd III {pyco(oet)pyc(oh)(oet)py} 3 ](ClO 4 ) 2 EtOH [Mn II Gd III {pyco(oet)pyc(oh)(oet)py} 3 ](ClO 4 ) 2 EtOH [Ni II Gd III {pyco(oet)pyc(oh)(oet)py} 3 ](ClO 4 ) 2 EtOH [LCo(MeOH)Gd(NO 3 ) 3 ] L 1 Fe(CH 3 OH)Gd(NO 3 ) 3 (CH 3 OH) L 1 Fe((CH 3 ) 2 CO)Gd(NO 3 ) L 2 Fe((CH 3 ) 2 CO)Gd(NO 3 ) [Gd 2 Ni 2 (pro) 4 (NO 3 ) 6 (CH 3 CN) 4 ] [LVOGd(hfa) 2 (CH3OH)] [L 2 V(O){(CH 3 ) 2 CO}Gd(NO 3 ) 3 ]
7 Magneto-structural correlations (Dihedral Correlation) J 1a and J 1b cm Gd 1 J1a dihedral J 2 cm -1 Gd J 1b Gd-N-Gd-N ( o ) Figure S4. Magneto-structural correlation developed by varying the Gd-N-Gd-N dihedral angle. The magnetic coupling between Gd 1 and N 2 3- has been taken as J 1a and J 1b in the case of Gd 2. The developed correlation by varying the dihedral angle (Gd-N-Gd-N) is shown in the above figure, in which J 1a is denoted in red lines and J 1b in black lines whereas J 2 (interaction between 2 Gd(III) atoms) is denoted by blue lines. Here the dihedral is varied by moving the Gd 2 atom out of the Gd 2 N 2 plane without affecting the position of Gd 1. Upon varying the dihedral, J 1a remains unaffected whereas J 1b and J 2 vary constantly. This variation routes from the large difference between the overlap between the 4f-orbitals and πp y * (Table S7 and S9) Table S5: Spin densities and NPA charges of different atoms in complex 1. Distance (N-N) N1 N
8 Distance (N-N) Gd1 Gd2 N1 N (1)
9 Table S6: Overlap integral (Sab) values for distance correlation in Complex 1 corresponding to coupling constant J1 (J1a and J1b). 1.4 fxz2 πpy* fxz2 πpy* fxz2 πpy* fxz2 πpy* Gd1 fyz fx(x2-3y2) fx(x2-3y2) fxyz fz f z f z f z fz(x2-y2) fyz fyz fyz fxyz fy(y 2-3x 2 ) fy(y 2-3x 2 ) f x(x 2-3y 2 ) fx(x2-3y2) fxyz fxyz f y(y2-3x2) x2) fz(x2-y2) fz(x2-y2) fz(x2-y2) Gd2 fxz2 πpy* fxz2 πpy* fxz2 πpy* fxz2 πpy* fyz fxyz fxyz fxyz fz f z f z f z fz(x2-y2) fyz fyz fyz fx(x2-3y2) f y(y2-3x2) x2) x2) fxyz fz(x2-y2) fz(x2-y2) f z(x2-y2) x2) fx(x2-3y2) fx(x2-3y2) fz(x2-y2)
10 Table S7: Overlap integral (Sab) values for dihedral correlation in Complex 1 corresponding to coupling constant J1 (J1a and J1b) 0 fxz2 πpy* fxz2 πpy* fxz2 πpy* fxz2 πpy* Gd1 fyz fyz fyz fyz fz f z f z f z fz(x2-y2) fxyz fxyz fxyz fxyz x2) x2) f y(y2-3x2) fx(x 2-3y 2 ) fx(x 2-3y 2 ) fx(x 2-3y 2 ) f x(x 2-3y 2 ) x2) fz(x2-y2) fz(x2-y2) fz(x2-y2) Gd2 fxz 2 πp y* fxz 2 πp y* fxz 2 πp y* fxz 2 πp y* fyz fyz fyz fyz fz fz fz fz fz(x2-y2) fx(x2-3y2) fx(x2-3y2) fx(x2-3y2) fx(x2-3y2) x2) x2) f y(y2-3x2) fxyz fz(x 2 -y 2 ) fz(x 2 -y 2 ) fz(x 2 -y 2 ) x2) fxyz fxyz fxyz
11 Table S8: Overlap integral (Sab) values for distance correlation in complex 1 corresponding to coupling constant J fxz2 fxz f xz2 fxz f xz2 fxz f xz2 fxz f yz f yz f yz f yz fz fz fz fz f z(x 2 -y 2 ) f z(x 2 -y 2 ) f z(x 2 -y 2 ) f z(x 2 -y 2 ) fxyz fxyz fxyz fxyz 6.818E-05 3x2) x2) x2) x2) f x(x 2-3y 2 ) f x(x 2-3y 2 ) f x(x 2-3y 2 ) f x(x 2-3y 2 ) fyz2 fxz fyz2 fxz fyz2 fxz fyz2 fxz f yz f yz f yz f yz fz fz fz fz f z(x 2 -y 2 ) f z(x 2 -y 2 ) f z(x 2 -y 2 ) f z(x 2 -y 2 ) fxyz fxyz fxyz 9.294E-05 fxyz 7.693E-05 3x2) x2) x2) x2) fx(x2-3y2) fx(x2-3y2) -5.95E-05 fx(x2-3y2) fx(x2-3y2) fz3 fxz fz3 fxz fz3 fxz fz3 fxz fyz fyz fyz fyz2-3.58e-05 f z f z f z f z fz(x2-y2) fz(x2-y2) fz(x2-y2) fz(x2-y2) f xyz f xyz f xyz f xyz 2.769E-05 3x2) x2) x2) x2) fx(x2-3y2) fx(x2-3y2) fx(x2-3y2) fx(x2-3y2)
12 y2) fxz y2) fxz y2) fxz2-5.86e-05 3x2) fxz E-05 f yz f yz f yz f yz fz fz fz fz fz(x2-y2) fz(x2-y2) fz(x2-y2) fz(x2-y2) f xyz f xyz f xyz f xyz x2) x2) x2) x2) f x(x 2-3y 2 ) f x(x 2-3y 2 ) f x(x 2-3y 2 ) f x(x 2-3y 2 ) fz(x2- fz(x2- fz(x2- fx(x2- fx(x2- fx(x2- fx(x2-3y2) fxz y2) fxz y2) fxz y2) fxz f yz f yz f yz f yz fz fz fz fz f z(x 2 -y 2 ) f z(x 2 -y 2 ) f z(x 2 -y 2 ) -6.04E-05 f z(x 2 -y 2 ) fxyz fxyz fxyz fxyz x2) x2) x2) x2) 5.044E-05 f x(x 2-3y 2 ) f x(x 2-3y 2 ) f x(x 2-3y 2 ) 9.336E-05 f x(x 2-3y 2 ) fxyz fxz fxyz fxz fxyz fxz fxyz fxz f yz f yz f yz f yz fz fz fz fz fz(x2-y2) fz(x2-y2) fz(x2-y2) fz(x2-y2) fxyz fxyz fxyz fxyz x2) x2) x2) x2) f x(x 2-3y 2 ) f x(x 2-3y 2 ) f x(x 2-3y 2 ) -5.61E-05 f x(x 2-3y 2 ) 5.012E-05 fz(x2-3x2) fxz x2) fxz x2) fxz y2) fxz
13 f yz f yz f yz f yz fz fz fz E-05 fz f z(x 2 -y 2 ) f z(x 2 -y 2 ) -9.62E-05 f z(x 2 -y 2 ) f z(x 2 -y 2 ) fxyz fxyz fxyz fxyz x2) x2) x2) x2) f x(x 2-3y 2 ) f x(x 2-3y 2 ) f x(x 2-3y 2 ) f x(x 2-3y 2 ) Table S9: Overlap integral (Sab) values for dihedral correlation in Complex 1 corresponding to coupling constant J2. 0 fxz2 fxz f xz2 fxz f xz2 fxz f xz2 fxz fyz fyz fyz fx(x2-3y2) f z f z f z f z fz(x2-y2) fz(x2-y2) fz(x2-y2) fyz f xyz f xyz f xyz f y(y 2-3x 2 ) x2) x2) x2) fz(x2-y2) fx(x2-3y2) fx(x2-3y2) fx(x2-3y2) fxyz fyz2 fxz fyz2 fxz fyz2 fxz fyz2 fxz fyz fyz fyz fx(x2-3y2) f z f z f z f z fz(x2-y2) fz(x2-y2) fz(x2-y2) fyz f xyz f xyz f xyz f y(y 2-3x 2 ) x2) x2) x2) fz(x2-y2) fx(x2-3y2) fx(x2-3y2) fx(x2-3y2) fxyz
14 fz3 fxz fz3 fxz fz3 fxz fz3 fxz fyz fyz fyz fyz fz fz fz fz f z(x 2 -y 2 ) f z(x 2 -y 2 ) f z(x 2 -y 2 ) f z(x 2 -y 2 ) f y(y 2-3x 2 ) fxyz fxyz fxyz fxyz x 2 ) f y(y 2-3x 2 ) f y(y 2-3x 2 ) fx(x2-3y2) fx(x2-3y2) fx(x2-3y2) fx(x2-3y2) f z(x 2 - y2) fxz y2) fxz y2) fxz y2) fxz f z(x 2 - f z(x 2 - f z(x 2 - fyz fyz fyz fyz fz fz fz fz f z(x 2 -y 2 ) f z(x 2 -y 2 ) -6.5E-05 f z(x 2 -y 2 ) 5.04E-05 f z(x 2 -y 2 ) fxyz fxyz fxyz fxyz f y(y 2-3x ) 3x 2 ) f y(y 2-3x 2 ) f y(y 2-3x ) fx(x2-3y2) fx(x2-3y2) fx(x2-3y2) fx(x2-3y2) f x(x 2 - f x(x 2 - f x(x 2 - f x(x 2-3y2) fxz y2) fxz y2) fxz y2) fxz fyz fyz fyz fyz fz fz fz fz f z(x 2 -y 2 ) f z(x 2 -y 2 ) f z(x 2 -y 2 ) f z(x 2 -y 2 ) fxyz fxyz fxyz fxyz f y(y 2-3x ) 3x 2 ) f y(y 2-3x 2 ) f y(y 2-3x ) fx(x2-3y2) fx(x2-3y2) fx(x2-3y2) fx(x2-3y2)
15 fxyz fxz fxyz fxz fxyz fxz fxyz fxz fyz fyz fyz fyz fz fz fz fz f z(x 2 -y 2 ) f z(x 2 -y 2 ) f z(x 2 -y 2 ) f z(x 2 -y 2 ) fxyz fxyz fxyz fxyz f y(y 2-3x ) 3x 2 ) f y(y 2-3x 2 ) f y(y 2-3x ) fx(x2-3y2) fx(x2-3y2) fx(x2-3y2) fx(x2-3y2) f y(y 2-3x 2 ) f xz x 2 ) f xz x 2 ) f xz x 2 ) f xz f y(y 2 - f y(y 2 - f y(y 2 - fyz fyz fyz fyz fz fz fz fz f z(x 2 -y 2 ) f z(x 2 -y 2 ) f z(x 2 -y 2 ) -5.3E-06 f z(x 2 -y 2 ) fxyz fxyz fxyz fxyz f y(y 2-3x ) 3x 2 ) f y(y 2-3x 2 ) f y(y 2-3x ) fx(x2-3y2) fx(x2-3y2) fx(x2-3y2) fx(x2-3y2)
16 References 1. L. Noodleman, J. Chem. Phys., 1981, 74, E. Ruiz, S. Alvarez, A. Rodriguez-Fortea, P. Alemany, Y. Pouillon and C. Massobrio, in Magnetism:Molecules to Materials, Vol. II ed J. S. Miller and M. Drillon, Wiley-VCH,Weinheim, 2001, pp A. D. Becke, J. Chem. Phys., 1993, 98, T. R. Cundari and W. J. Stevens, J. Chem. Phys., 1993, 98, (a) A. Schafer, H. Horn and R. Ahlrichs, J. Chem. Phys., 1992, 97, 2571; (b) A. Schafer, C. Huber and R. Ahlrichs, J. Chem. Phys., 1994, 100, Gaussian 09, Revision A.02, M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, G. Scalmani, V. Barone, B. Mennucci, G. A. Petersson, H. Nakatsuji, M. Caricato, X. Li, H. P. Hratchian, A. F. Izmaylov, J. Bloino, G. Zheng, J. L. Sonnenberg, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, T. Vreven, J. A. Montgomery, Jr., J. E. Peralta, F. Ogliaro, M. Bearpark, J. J. Heyd, E. Brothers, K. N. Kudin, V. N. Staroverov, R. Kobayashi, J. Normand, K. Raghavachari, A. Rendell, J. C. Burant, S. S. Iyengar, J. Tomasi, M. Cossi, N. Rega, J. M. Millam, M. Klene, J. E. Knox, J. B. Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R. E. Stratmann, O. Yazyev, A. J. Austin, R. Cammi, C. Pomelli, J. W. Ochterski, R. L. Martin, K. Morokuma, V. G. Zakrzewski, G. A. Voth, P. Salvador, J. J. Dannenberg, S. Dapprich, A. D. Daniels, Ö. Farkas, J. B. Foresman, J. V. Ortiz, J. Cioslowski, and D. J. Fox, Gaussian, Inc., Wallingford CT, A. N. Georgopoulou, R. Adam, C. P. Raptopoulou, V. Psycharis, R. Ballesteros, B. Abarca and A. K. Boudalis, Dalton. Trans., 2010, 39, J. -P. Costes, F. Dahan, J. Garcia-Tojal, Chem. Eur. J. 2002, 8, J. -P. Costes, J. M. C. Juan, F. Dahan, F. Dumestre and J. P. Tuchagues, Inorg. Chem. 2002, 41, S. Igarashi, S. I. Kawaguchi, Y. Yukawa, F. Tuna and R. E. P. Winpenny, Dalton. Trans., 2009, J. -P. Costes, S. Shova, J. M. C. Juan and N. Suet, Dalton. Trans., 2005, J. -P. Costes, F. Dahan, B. Donnadieu, J. Garcia-Tojal and J. -P Laurent, Eur. J. Inorg. Chem. 2001, 363.
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