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Intermolecular phonons in BEDT-TTF crystals
ELSEVIER
Synthetic Metals 85 (1997) 1561-1562
Intermolecular A. Brillante’,
R. G. Della
a Dipartimento b Dip.
Ch imica
Generale
phonons in BEDT-TTF ValleO, A. Girlando’,
crystals
A. Painellib, E. Venuti’
di Chimica Fisica e Inorganica; Universith Kale Risorgimento 4, I-40136 Bologna, Italy
di Bologna,
ed Inorganica, Chimica Analitica, Chimica Fisica; Viale delle Scienze, I-43100, Parma, Italy
Universith
di Parma,
Abstract The crystallographic structure and the phonon frequencies temperature have been computed within a Quasi Harmonic Lattice Keywords:
Organic
superconductors,
Molecular
and lattice
1. Introduction Several theoretical models, supported by experimental evidences, suggest that intermolecular phonons may play a significant role in the mechanism of SuperconducJivity in BEDT-TTF (ET) salts [l]. However, a detailed description of the lattice phonon dynamics in ET salts is still lacking, and most of the theoretical models remain speculative. We have adopted the Quasi Harmonic Lattice Dynamics (QHLD) method [2] to determine an atom-atom potential able to reproduce the crystal structure and phonon In QHLD the Gibbs free frequencies of ET crystals. energy G(p, T) of the crystal is approximated with the free energy of the harmonic phonons calculated at the average lattice structure. The structure as a function of p and T is determined by minimizing G(p,T) with respect to the structural parameters, as fully described in Refs. [2,3]. Our strategy is to test and refine the atom-atom potential on neutral and semiconducting ET salts, in order to minimize ‘the perturbing effects coming from electronphonon coupling [4]. We shall then use the potential to describe the lattice dynamics of superconducting salts. In the present paper we report the results relevant to neutral ET and a-(ET)&.
2. Experimental
and Calculations
Room temperature crystals of ET are monoclinic, space group P21/c (C.&), with four molecules per unit cell [5]. The factor group analysis of the k = 0 intermolecular modes predicts 6A, + 6B, Raman modes, and 5Au + 4Bu infrared modes. Since very little is known about the intermolecular we have obtained polarized Raman phonons in ET, 0379-6779/97/$17.00 0 1997 Ekevier Science S.A. All rights reserved
PII SO379-5779(96)4487-6
of BEDT-TTF and Dynamics framework.
a-(BEDT-TTF)&
at
non
zero
dynamics
data, using 632.8 nm excitation in backscattering geometry, to discriminate between A, and B, modes. At room temperature CY-(ET)& behaves as a twodimensional metal [6], and at 135 I< it undergoes a first,order transition to an insulating state. The cr-(ET)& crystals are triclinic, space group Pi (Ci) [6,7], and have a large and complicated unit cell containing two 13 anions and four ET units with average charge +1/2. The factor group analysis predicts 16A, Raman active modes, and 15Au infrared active modes. We have chosen a &rwise additive potential of the form @o = 3 Cig[qiqj/rij + Aij exp(-Bijrij) - Cij/ri6j], where the sum is extended to all distances rij between pairs i,j of atoms. The model contains a Coulombic part qiqj/rij, meant to describe both ionized and neutral forms of the ET molecules, and a Buckingham atom-atom interaction. The Ewald’s method [S] has been used to accelerate the convergence of the Coulombic interactions. Since rigid molecules are adopted, intramolecular interactions are discarded. The atomic charges qi have been obtained from recent ab initio Hartree-Fock (HF) calculations (with the 6-31G** basis set) on ET and ET’1/2 [9]. For the Buckingham parameters Aij, Bij and Cij involving C and H atoms, we have used those of Hall and Williams (HW) [lo], which reproduce very well the thermal expansion of benzene [3,10]. These parameters have been obtained by including Coulombic interactions, unlike most other Buckingham models and are therefore preferable for our purposes. Since in the HW model [lo] C-H parameters are obtained from C-C and H-H parameters via “mixing rules”, we have adopted the same procedure for all heteroatom interactions. Three S-S and three I-I parameters remain as the only independent variables in the potential model. The S parameters have been determined first, by fitting
A. Brillante et al. /SyntheticMetals 85 (1997) 1561-1562
1562
the X-ray structure of ET at room T [5] with a QHLD calculation at 293 K. Then the I parameters have been fitted to the structure of o+(ET)& at 100 K [6]. Since “-(ET)& is insulating at 100 K, we can assume that electron-phonon perturbation is sufficiently small to be disregarded.
3. Results
and Conclusions
The computed thermodynamical equilibrium structure of ET at 293 K is compared with the experimental one [5] in Table 1, whereas the phonon frequencies are reported in Table 2. We note that only about a half of the expected k = 0 Raman active phonons have been experimentally identified. Although the potential has been fitted to the crystal structure only, the phonon frequencies The agreement with the are satisfactorily reproduced. experiments is comparable to that typically obtained for molecular crystals. data for the ET and cu-(ET)& Table 1. Structural crystals. The experimental structures [5,6] are compared to the thermodynamical equilibrium (minimum G) structures. (Y-(ET)& Expt.
at 100 K Min G
6.749 14.014 16.356
9.068. 10.721 17.403
9.367 11.070 17.145
109.55
109.57
96.56 97.75 91.14
95.05 98.82 91.15
1.760
1.752
2.294
2.183
ET at 293 K Min G Expt. 6.614 13.985 16.646
a (4 b (A) c 69
Q (degrees) /3 (degrees) y (degrees) P (dcm3)
Table 2. Frequencies (cm-l) for the intermolecular phonons of ET. The experimental frequencies are compared to those calculated at the minimum G structure at 293 K. Sym.
Expt.
117
Ag 76 57 35
Au
CaIc.
71 60 58 52 36 115 86 52 48 36
Sym.
Expt.
102 91
Bg 54 32 24
Bu
talc.
68 54 51 33
94 79 72 61
The experimental [6] and minimum G structures of cy(ET)213 at 100 K are compared in Table 1. Table 3 reports the calculated phonon frequencies. Studies are in progress to assign the experimental frequencies, in order to adjust the potential to fit both structure and phonon frequencies. In any case the potential we have singled out is rather stable and able to account for the crystal structures of ET and its iodine salts. Calculated frequencies (cm-‘) for the Table 3. intermolecular phonons of cr-(ET)& at the minimum G structure at 100 K. Sym.
Phonon frequencies (cm-l)
Ag
138
124
114
105
98
94
57 120 45
48 112 42
46 96 35
35
32
Au
71 130 57
91
85
29
20
85 28 73 13
76 24 70
Acknowledgments This work has been supported by the Ministry of University and of Scientific and Technological Research (M.U.R.S.T.) and by the National Reasearch Council (C.N.R.) References [l] T. Ishiguro and K. Yamaji, Organic Superconductors, Springer, FRG, (1990). [2] R. G. Della VaIIe, E. Venuti, and A. Brillante, Chem. Phys. 198(1995) 79. [3] R. G. Della VaIIe, E. Venuti, and A. Brillante, Chem. Phys. 2U.Z(1996) 231. [4] A. Girlando, A. PaineIIi, and Z. G. Soos, Acta Phys. Polonica 87 (1995) 735. [S] H. Kobayashi, A. Kobayashi, Y. Sasaki, G. Saito, and H. Inokuchi, Bull. Chem. Sot. Japan 59 (1986) 301. [6] H. Endres, H. J. Keller, R. Swietlik, D. Schweitzer, K. Angermund, and C. KrCger, Z. Naturforsch. 410 (1986) 1319. [7] T. J. Emge, P. C. W. Leung, M. A. Beno, H. H. Wang, J. M. Williams, M. H. Whangbo, and M. Evain, Mol. Cryst. Liq. Cryst. 138 (1986) 393. [8] M.Born and K.Huang, Dynamical theory of Crystal Lattices, Oxford University Press, UK, (1954); G.F.Signorini, RRighini and VSchettino, Chem.Phys. 154 (1991) 245. [9] E. Demiralp and W. A. Goddard III, J. Phys. Chem. 98 (1994) 9781. [lo] D. Hall and D. E. Williams, Acta Cryst. A 31 (1975) 56.
Synthetic Metals 85 (1997) 1561-1562
Intermolecular A. Brillante’,
R. G. Della
a Dipartimento b Dip.
Ch imica
Generale
phonons in BEDT-TTF ValleO, A. Girlando’,
crystals
A. Painellib, E. Venuti’
di Chimica Fisica e Inorganica; Universith Kale Risorgimento 4, I-40136 Bologna, Italy
di Bologna,
ed Inorganica, Chimica Analitica, Chimica Fisica; Viale delle Scienze, I-43100, Parma, Italy
Universith
di Parma,
Abstract The crystallographic structure and the phonon frequencies temperature have been computed within a Quasi Harmonic Lattice Keywords:
Organic
superconductors,
Molecular
and lattice
1. Introduction Several theoretical models, supported by experimental evidences, suggest that intermolecular phonons may play a significant role in the mechanism of SuperconducJivity in BEDT-TTF (ET) salts [l]. However, a detailed description of the lattice phonon dynamics in ET salts is still lacking, and most of the theoretical models remain speculative. We have adopted the Quasi Harmonic Lattice Dynamics (QHLD) method [2] to determine an atom-atom potential able to reproduce the crystal structure and phonon In QHLD the Gibbs free frequencies of ET crystals. energy G(p, T) of the crystal is approximated with the free energy of the harmonic phonons calculated at the average lattice structure. The structure as a function of p and T is determined by minimizing G(p,T) with respect to the structural parameters, as fully described in Refs. [2,3]. Our strategy is to test and refine the atom-atom potential on neutral and semiconducting ET salts, in order to minimize ‘the perturbing effects coming from electronphonon coupling [4]. We shall then use the potential to describe the lattice dynamics of superconducting salts. In the present paper we report the results relevant to neutral ET and a-(ET)&.
2. Experimental
and Calculations
Room temperature crystals of ET are monoclinic, space group P21/c (C.&), with four molecules per unit cell [5]. The factor group analysis of the k = 0 intermolecular modes predicts 6A, + 6B, Raman modes, and 5Au + 4Bu infrared modes. Since very little is known about the intermolecular we have obtained polarized Raman phonons in ET, 0379-6779/97/$17.00 0 1997 Ekevier Science S.A. All rights reserved
PII SO379-5779(96)4487-6
of BEDT-TTF and Dynamics framework.
a-(BEDT-TTF)&
at
non
zero
dynamics
data, using 632.8 nm excitation in backscattering geometry, to discriminate between A, and B, modes. At room temperature CY-(ET)& behaves as a twodimensional metal [6], and at 135 I< it undergoes a first,order transition to an insulating state. The cr-(ET)& crystals are triclinic, space group Pi (Ci) [6,7], and have a large and complicated unit cell containing two 13 anions and four ET units with average charge +1/2. The factor group analysis predicts 16A, Raman active modes, and 15Au infrared active modes. We have chosen a &rwise additive potential of the form @o = 3 Cig[qiqj/rij + Aij exp(-Bijrij) - Cij/ri6j], where the sum is extended to all distances rij between pairs i,j of atoms. The model contains a Coulombic part qiqj/rij, meant to describe both ionized and neutral forms of the ET molecules, and a Buckingham atom-atom interaction. The Ewald’s method [S] has been used to accelerate the convergence of the Coulombic interactions. Since rigid molecules are adopted, intramolecular interactions are discarded. The atomic charges qi have been obtained from recent ab initio Hartree-Fock (HF) calculations (with the 6-31G** basis set) on ET and ET’1/2 [9]. For the Buckingham parameters Aij, Bij and Cij involving C and H atoms, we have used those of Hall and Williams (HW) [lo], which reproduce very well the thermal expansion of benzene [3,10]. These parameters have been obtained by including Coulombic interactions, unlike most other Buckingham models and are therefore preferable for our purposes. Since in the HW model [lo] C-H parameters are obtained from C-C and H-H parameters via “mixing rules”, we have adopted the same procedure for all heteroatom interactions. Three S-S and three I-I parameters remain as the only independent variables in the potential model. The S parameters have been determined first, by fitting
A. Brillante et al. /SyntheticMetals 85 (1997) 1561-1562
1562
the X-ray structure of ET at room T [5] with a QHLD calculation at 293 K. Then the I parameters have been fitted to the structure of o+(ET)& at 100 K [6]. Since “-(ET)& is insulating at 100 K, we can assume that electron-phonon perturbation is sufficiently small to be disregarded.
3. Results
and Conclusions
The computed thermodynamical equilibrium structure of ET at 293 K is compared with the experimental one [5] in Table 1, whereas the phonon frequencies are reported in Table 2. We note that only about a half of the expected k = 0 Raman active phonons have been experimentally identified. Although the potential has been fitted to the crystal structure only, the phonon frequencies The agreement with the are satisfactorily reproduced. experiments is comparable to that typically obtained for molecular crystals. data for the ET and cu-(ET)& Table 1. Structural crystals. The experimental structures [5,6] are compared to the thermodynamical equilibrium (minimum G) structures. (Y-(ET)& Expt.
at 100 K Min G
6.749 14.014 16.356
9.068. 10.721 17.403
9.367 11.070 17.145
109.55
109.57
96.56 97.75 91.14
95.05 98.82 91.15
1.760
1.752
2.294
2.183
ET at 293 K Min G Expt. 6.614 13.985 16.646
a (4 b (A) c 69
Q (degrees) /3 (degrees) y (degrees) P (dcm3)
Table 2. Frequencies (cm-l) for the intermolecular phonons of ET. The experimental frequencies are compared to those calculated at the minimum G structure at 293 K. Sym.
Expt.
117
Ag 76 57 35
Au
CaIc.
71 60 58 52 36 115 86 52 48 36
Sym.
Expt.
102 91
Bg 54 32 24
Bu
talc.
68 54 51 33
94 79 72 61
The experimental [6] and minimum G structures of cy(ET)213 at 100 K are compared in Table 1. Table 3 reports the calculated phonon frequencies. Studies are in progress to assign the experimental frequencies, in order to adjust the potential to fit both structure and phonon frequencies. In any case the potential we have singled out is rather stable and able to account for the crystal structures of ET and its iodine salts. Calculated frequencies (cm-‘) for the Table 3. intermolecular phonons of cr-(ET)& at the minimum G structure at 100 K. Sym.
Phonon frequencies (cm-l)
Ag
138
124
114
105
98
94
57 120 45
48 112 42
46 96 35
35
32
Au
71 130 57
91
85
29
20
85 28 73 13
76 24 70
Acknowledgments This work has been supported by the Ministry of University and of Scientific and Technological Research (M.U.R.S.T.) and by the National Reasearch Council (C.N.R.) References [l] T. Ishiguro and K. Yamaji, Organic Superconductors, Springer, FRG, (1990). [2] R. G. Della VaIIe, E. Venuti, and A. Brillante, Chem. Phys. 198(1995) 79. [3] R. G. Della VaIIe, E. Venuti, and A. Brillante, Chem. Phys. 2U.Z(1996) 231. [4] A. Girlando, A. PaineIIi, and Z. G. Soos, Acta Phys. Polonica 87 (1995) 735. [S] H. Kobayashi, A. Kobayashi, Y. Sasaki, G. Saito, and H. Inokuchi, Bull. Chem. Sot. Japan 59 (1986) 301. [6] H. Endres, H. J. Keller, R. Swietlik, D. Schweitzer, K. Angermund, and C. KrCger, Z. Naturforsch. 410 (1986) 1319. [7] T. J. Emge, P. C. W. Leung, M. A. Beno, H. H. Wang, J. M. Williams, M. H. Whangbo, and M. Evain, Mol. Cryst. Liq. Cryst. 138 (1986) 393. [8] M.Born and K.Huang, Dynamical theory of Crystal Lattices, Oxford University Press, UK, (1954); G.F.Signorini, RRighini and VSchettino, Chem.Phys. 154 (1991) 245. [9] E. Demiralp and W. A. Goddard III, J. Phys. Chem. 98 (1994) 9781. [lo] D. Hall and D. E. Williams, Acta Cryst. A 31 (1975) 56.