Hyperfine Interactions 113 (1998) 351­355 351 Lamb­M¨ossbauer factor of electronically excited molecular states measured by time-differential M¨ossbauer emission spectroscopy S. Deisenroth a, H. Spiering a, D.L. Nagy b and P. G¨utlich a a Institut f¨ur Anorganische Chemie und Analytische Chemie, Universit¨at Mainz, Staudinger Weg 9, D-55099 Mainz, Germany b KFKI Research Institut for Nuclear and Particle Physics, H-1525 Budapest, Hungary The Lamb­M¨ossbauer Factor (LMF) of molecular crystals is expected to depend on the electronic molecular states by their different intramolecular vibrational frequencies. Revis- iting M¨ossbauer spectra obtained by time differential M¨ossbauer emission spectroscopy of the low spin compound [57Co/Mn(bipy)3](PF6)2 (bipy = 2, 2 -bipyridine) a ratio of 1.25 for the LMFs of the low spin ground state and of an excited high spin state decaying in the M¨ossbauer time window could be evaluated. The difference found is in line with the change of LMF observed for spin crossover compounds where the excited high spin state is populated by the so-called LIESST effect. The initial population of the high spin state is close to 100%. 1. Introduction The contribution of intra molecular vibrational frequencies in molecular crystals to the Lamb­M¨ossbauer Factor (LMF) was studied in great detail in a spin crossover system [1]. The so-called LIESST effect (Light Induced Excited Spin State Trapping) provides the unique opportunity to study the difference of the LMFs of molecules in two different electronic spin states. At low temperatures the molecules are in the low spin state and can be excited by green light to the metastable high spin state. This way the LMF of the iron nucleus as the center of a large molecule in two different molecular electronic states can be measured at the same temperature. Since the iron atoms are highly diluted in an isomorphous crystal of another metal M (= Co, Mn, Zn, . . . ) ion, and because the change of the electronic state at the iron center (high spin to low spin) has almost negligible influence on the bonding between the molecules, the observed decrease of the LMF is essentially due to the decrease of intra molecular vibrational frequencies accompanying the transition from low spin to the high spin state. The evaluation of the temperature dependence of the LMF in [FexZn1-x(ptz)6](BF4)2 (ptz = propyltetrazole, x = 0.005) between 4.2 K and 50 K (above 50 K the lifetime of the metastable high spin state is too short for M¨ossbauer measurements) yields a frequency ratio of LS/ HS = 1.24 and high spin frequencies of HST1u,b = 45 cm-1 and HST1u,s = 227 cm-1 of the two active T1u,b,s J.C. Baltzer AG, Science Publishers 352 S. Deisenroth et al. / Lamb­M¨ossbauer factor of electronically excited molecular states modes in cubic symmetry which were taken as an approximation for the octahedrally coordinating monodentate ptz-ligands. With these frequencies the ratio fLS/fHS of the LMF is calculated over the whole temperature range up to 400 K. It increases from 1.02 at 4.2 K almost linearly to 1.25 at 400 K [1]. In M¨ossbauer emission spectroscopy of low spin compounds which are related to Fe2+ spin crossover compounds three subspectra of the nucleogenic iron are ob- served besides the Fe2+ low spin ground state. These are two high spin states of Fe2+ and an aliovalent Fe3+ low spin state. In the system [57Co/Mn(bipy)3](PF6)2 (bipy = 2,2 -bipyridine) one of the high spin states could be identified as the LIESST state by comparing the lifetimes obtained from Time Differential M¨ossbauer Emission Spectroscopy (TDMES) measurements and the excited state of the Fe doped compound after laser excitation [2]. In analogy to LIESST the population of the exited HS state by nuclear decay has been called NIESST (Nuclear Induced Excited Spin State Trap- ping) [3]. TDMES has been used to separate the information of initial population of the different states of the nucleogenic iron from the decay time of the excited states, only a combination of both being accessible with Time Integral M¨ossbauer Emission Spectroscopy (TIMES) measurements. TDMES measurements were so far always evaluated with the constrain of equal LMFs of all subspectra. 2. Results and discussion The time integral and time differential M¨ossbauer emission spectra at 83 K of [57Co/Mn(bipy)3](PF6)2 (70 µCi, 6 weeks measureing time) are shown in figure 1. The spectrometer is described in [4]. The fitted curve is calculated by the time filtering theory for thick absorbers (teff = 4.5). The four subspectra are plotted in the time integral emission spectrum (top of figure 1). The parameters (isomer shift and quadrupole splitting) obtained from the time integral spectrum were fixed in fitting the time differential spectra. Also the distribution (of Lorentz type) of emission lines of natural widths fitted to the time integral spectra were used in fitting the TDME spectra. The time filtered spectra were calculated neglecting relaxation effects according to Lynch et al. [5]. The relative areas of the four species in each of the time windows are the free parameters for the time differential spectra. The time evolution of the areas ALS, AHS , A , and A 1 HS2 Fe3+ contain information about the initial populations N0 , the LMF f and the lifetime ( = LS(Fe2+), HS1(Fe2+), HS2(Fe2+), Fe3+) of the different states forming after the electron capture (EC) of the 57Co and the following Auger cascade and recombination processes at the nucleogenic iron. The areas at each time t are proportional to the LMF and the number of decays of the actual number N (t) of nuclei in state . The time spectra are evaluated using the assumption that the Fe3+ and HS2 do not decay in the measured time window at 83 K and 103 K. Then there is only the lifetime of the HS1 state ( = HS ) involved and the population of the HS 1 1 and LS states is S. Deisenroth et al. / Lamb­M¨ossbauer factor of electronically excited molecular states 353 Figure 1. TIMES (top) and TDMES of [57Co/Mn(bipy)3](PF6)2 at 83 K, the solid lines are calculated according to the time filtering theory with parameters taken from the four subspectra shown in the time integral spectra. given by NLS( , t) = N0LS + N0HS - N ( , t), (1) 1 HS1 NHS ( , t) = N exp(-t/ ), (2) 1 0HS1 where the decay of the HS1 state to the LS state is single-exponential. The number of decays NHS ( , t 1 a, te) in the time window {ta, te} after the detection of the preceding 122 keV quanta, which leads to the population of the 14.4 keV M¨ossbauer level at time T after the EC, is given by the double integral te NHS ( , t W (T ) dT N , t + T w t dt , 1 a, te) = HS1 0 ta 1 W (T ) = e-T/ 122keV, (3) 122 keV 1 w(t) = e-t/ 14.4keV, 14.4keV 354 S. Deisenroth et al. / Lamb­M¨ossbauer factor of electronically excited molecular states Figure 2. Area ratio of the HS1 and Fe3+ doublets versus time t (left) and of the LS and Fe3+ doublets versus (1 - / ) (right) at 83 K and 103 K. where W (T ) and w(t) are the probabilities at times T , t the nucleus being in the 122 keV and 14.4 keV states, respectively. The number of decays are expressed as NHS ( , t ( , t 1 a, te) = N0HS1 a, te), the function being the integral of eq. (3). For infinite lifetime the function reduces to ( , ta, te) = (ta, te) = exp(-ta/ 14.4) - exp(-te/ 14.4). The area AHS f N divided by the time independent area A 1 HS1 HS1 Fe3+ fFe3+NFe3+ of the Fe3+ fraction gives the ratio AHS /A 1 Fe3+ = 1 ( , ta, te) shown in figure 2 plotted versus the center of the time window t = (ta + te)/2. The expression for 1 is given in eq. (4). The fits determine the lifetimes (83 K) = 507 ± 43 ns, (103 K) = 111 ± 6 ns of the HS1 state and the factors 1(83 K) = 3.91 ± 0.31, 1(103 K) = 3.68 ± 0.16. With the known function ( , ta, te) the corresponding area ratios of ALS state and AFe3+ are then plotted versus (1 - ( , ta, te)/ (ta, te)). ALS/AFe3+ = 2 + 3(1 - / ) is a linear function of (1 - / ) defining two further constants: f N f f HS1 0HS1 LSN0LS LSN0HS1 1 = , , . (4) f 2 = 3 = Fe3+N0Fe3+ fFe3+N0Fe3+ fFe3+N0Fe3+ From ratios of the j the Fe3+ properties drop out and the ratio of the LMFs fLS/fHS = 1 1.30±0.13, 1.25±0.15 and the initial populations N0LS/N0HS = 0.16±0.08, 0.03± 1 0.12 at 83 K and 103 K are left, respectively. This result compares well with the LMF of the 5T2g LIESST state in the spin crossover compound [Fe/Zn(ptz6)](BF4)2 which is extrapolated to be 10% lower than the LMF of the LS state at 100 K. The much higher ligand field energy of the 5T2g state in a LS compound is expected to be responsible for the larger differences as a result of weaker bonding. The initial population of the HS1 state close to 100% has to be compared with the initial population observed in emission spectra of 57Co doped in spin crossover compounds. These experiments [6] S. Deisenroth et al. / Lamb­M¨ossbauer factor of electronically excited molecular states 355 show only the HS state with lifetimes much longer than the M¨ossbauer time window. The difference between a low spin compound and a spin crossover compound, the larger energy gap for the former one, does not obviously affect the initial population although it has dramatic effects on the lifetime of the HS state according to the inverse energy gap law of radiationless transitions [7]. Acknowledgement This work was supported by a NATO Collaborative Research Grant No. HTECH.CRG 930478, the Fonds der Chemischen Industrie and the Materialwis- senschaftliches Forschungszentrum der Universit¨at Mainz. References [1] J. Jung, H. Spiering and P. G¨utlich, Nuovo Cimento 50 (1996) 879. [2] A. Deisenroth, S. Hauser, H. Spiering and P. G¨utlich, Hyp. Interact. 93 (1994) 1573. [3] P. G¨utlich, J. Jung and H.A. Goodwin, Spin Transition in Iron(II) Complexes, NATO-ASI Series E: Applied Science, Vol. 321, ed. E. Coronado (1996). [4] M. Alflen, C. Hennen, F. Tuczek, H. Spiering, P. G¨utlich and Zs. Kajcsos, Hyp. Interact. 47 (1989) 15. [5] F.J. Lynch, R.E. Holland and M. Hammermesh, Phys. Rev. 120 (1960) 513. [6] P. G¨utlich, H. K¨oppen and H.G. Steinh¨auser, Chem. Phys. Lett. 74 (1980) 3. [7] E. Buhks, G. Navon, M. Bixon and J. Jortner, J. Am. Chem. Soc. 102 (1980) 2918.