ARTICLE pubs.acs.org/JPCC
Charge Sensitive Vibrations and Electron-Molecular Vibration Coupling in Bis(ethylenedithio)-tetrathiafulvalene (BEDT-TTF) Alberto Girlando* Dipartimento Chimica GIAF and INSTM-UdR Parma, Universita di Parma, Parco Area delle Scienze, 43100-I Parma, Italy
bS Supporting Information ABSTRACT: A complete analysis of the vibrational dynamics of the most important molecule in the field of organic superconductors, bis(ethylenedithio)-tetrathiafulvalene (BEDT-TTF), has been performed through first-principles calculations. Different ionization states have been investigated, both as isolated BEDTTTF unit, and as symmetric self-dimer. The ionization process affects the frequencies of some vibrations, the “charge sensitive modes”, but also their intensities. In particular, a 100-fold increase in the infrared intensity of the antisymmetric CdC stretching mode is predicted to occur upon removal of one electron. The discovery of this dramatic difference will help to interpret the spectral phenomena observed in correspondence to the charge-order processes undergone by some BEDT-TTF salts. The electronmolecular vibration (e-mv) coupling and its effects on the infrared spectra is also fully reanalysed by adopting the proper molecular symmetry of the BEDT-TTF+ monomer, and by investigating (BEDT-TTF)22+ and (BEDT-TTF)2+ dimers. A new approach to estimate the relative values of the e-mv coupling constants is proposed.
’ INTRODUCTION Since the discovery of superconductivity in its iodide salts, about 25 years ago,1,2 the bis(ethylene-dithio)-tetrathiafulvalene (BEDT-TTF) molecule (Scheme 1) and its variants have remained the most important structure in the field of organic superconductors. It is practically impossible to refer to the huge number of papers that has been devoted to the characterization of this molecule and its salts, to the point one may doubt there is still something to discover.3 I will show here that this is not the case. The BEDT-TTF molecule still has some surprises that can be evidenced through modern computational techniques. Superconducting and conducting BEDT-TTF charge-transfer (CT) salts have the stoichiometry (BEDT-TTF)2X, where X is a monovalent anion. In the crystal, BEDT-TTF molecules are typically arranged in two-dimensional arrays separated by the counterions. When Coulomb interaction prevails, BEDT-TTF salts may undergo a charge order (CO) instability, with unequal charge distribution between the BEDT-TTF molecular units. The charge localization induces an insulating state. In recent years, there as been accumulating evidence of the interplay between CO fluctuations close to the CO instability and the superconductivity. 3,4 CO can be conveniently characterized through vibrational spectroscopy, provided a proper identification and calibration of the charge sensitive normal modes is carried out.59 In the course of optical investigations of the CO instability in BEDT-TTF conducting and superconducting salts,1012 it became clear that a better characterization of charge sensitive vibrational modes was needed to properly understand the spectroscopic signatures of the CO instability and associated fluctuation regime. This has been the initial motivation of the present paper. In the course of the work, I decided to amplify the r 2011 American Chemical Society
Scheme 1
original aim and to fully revise the characterization of the BEDTTTF molecular vibrations and of their coupling with the electronic system.13 The latter coupling may indeed also be involved in the CO and superconductivity mechanism.14,15
’ COMPUTATIONAL METHODS Quantum chemical calculation were performed with the GAMESS package,16 using DFT-B3LYP, and the 6-31G(d) basis set. This combination is know to satisfactorily reproduce the molecular vibrations of relatively large organic molecules, provided tight geometry optimization and fine grids are used in the DFT analysis.17 Whenever comparison with experiment is involved, I report the scaled frequencies, adopting the recently proposed scaling factors, 0.9679 and 1.0100, for frequencies above and below 1300 cm1.18 The GAMESS code has been slightly modified to allow a proper computation of the e-mv coupling constants, requiring the numerical derivatives of the HOMO energies. The results have been analyzed and visualized with the help of Jmol19 package. Received: June 30, 2011 Revised: August 23, 2011 Published: August 30, 2011 19371
dx.doi.org/10.1021/jp206171r | J. Phys. Chem. C 2011, 115, 19371–19378
The Journal of Physical Chemistry C
ARTICLE
Table 1. Calculated Frequencies (cm1) of Selected Charge Sensitive Modes of BEDT-TTFa mode
a
BEDT-TTF0
(BEDT-TTF)20
(BEDT-TTF)2+
(BEDT-TTF)22+
BEDT-TTF+
a ν3
1580
1565
1501
1457
a ν4
1533
1533
1476
1415
1407
b1 ν22
1549 (0.10)
1533 (0.60)
1469 (22.69)
1413 (65.20)
1404 (67.31)
b1 ν29
778 (1.49)
780 (2.08)
795 (1.08)
813 (0.30)
817 (0.34)
b2 ν44
864 (0.10)
874 (0.41)
876 (0.10)
909 (0.04)
903 (0.23)
1458
The corresponding IR intensities (D2 Å2 amu1) are reported in parentheses.
’ MOLECULAR CONFORMATIONS AND VIBRATIONAL SELECTION RULES BEDT-TTF molecules has 26 atoms, hence 72 vibrational degrees of freedom. The assignment of the vibrational spectra is then a rather complex task. To simplify the analysis, the early vibrational assignments were based on the D2h molecular symmetry of the tetrathiafulvalene planar central skeleton.2022 This simplification ended up introducing some confusion, as the mode classification and associated selection rules are more stringent than in the actual lower symmetry induced by the position of the CH2CH2 end groups. In the solid state, the CH2CH2 groups of a ionized BEDT-TTF molecule can be either staggered, giving rise to an approximate D2 molecular symmetry, or eclipsed (C2h symmetry).23 At room temperature, disorder in the CH2CH2 groups is often present. Slow cooling below ∼80 K may yield a (partially) ordered structure.2427 To add further complication, the equilibrium geometry of fully neutral BEDT-TTF has a boat conformation (C2 symmetry), as indicated by X-ray measurements28 and ab initio calculations.29 Since the paper is essentially devoted to ionized molecules, I adopt the most common symmetry in the solid state, namely the D2 one,30,31 which has also the advantage of an easy correlation with both the early adopted D2h symmetry and with the C2 symmetry of the neutral molecule. With this choice, and with reference to the Cartesian axes defined in Scheme 1, the mode numbering, and Raman (R) and infrared (IR) activity, is as follows: ½ν1 ν19 aðαxx , αyy , αzz Þ þ ½ν20 ν36 b1 ðμx , αxy Þ þ ½ν37 ν54 b2 ðμy , αzx Þ þ ½ν55 ν72 b3 ðμx , αyz Þ The ag and au modes in D2h correlate with a in D2, b1g and b1u with b1, b2g and b2u with b2, and b3g and b3u with b3. In turn, a and b1 modes in D2 correlate with a in C2, and b2, b3 in D2 with b in C2. I have also performed calculations of dimers of BEDT-TTF, mimicking the structure occurring in many BEDT-TTF salts.3 In this case, the only imposed symmetry is the inversion center between the dimers, so the two BEDT-TTF molecules are equivalent. Therefore, all the modes of each molecule couple in-phase (ag, R active) and out-of-phase (au, IR active).
’ CHARGE SENSITIVE VIBRATIONAL MODES The degree of ionicity, or average charge per molecule (F) is one of the fundamental parameters characterizing the physical properties of CT salts. As stated in the Introduction, vibrational spectroscopy is one of the most convenient methods to determine F, also because there are sound theoretical reasons to expect a practically linear dependence of the vibrational frequency on F.6,13 This expectation is now supported by many experiments on
different electron donor or acceptor molecules.57 Actually, the apparent nonlinearities sometimes found experimentally were the results of incorrect interpretations of the spectra.8,9 The Supporting Information reports the calculated frequencies for neutral and fully ionized BEDT-TTF, both in the D2 symmetry to ease the comparison. As pointed out by Yamamoto,8 this is also the most reasonable approach to investigate the linear dependence of the vibrational frequencies from F. Indeed, BEDT-TTF is bent (C2 symmetry) only in gas phase and in the neutral crystal, whereas the central part remains planar also when the molecule is only partially charged, as in the CO states. To fully evaluate the effective linearity at the computational level, I have also calculated the vibrational frequencies of the (BEDTTTF)2 dimer, in the neutral, +1, and +2 states. To ensure equal distribution of the charges between the two molecules, the Ci symmetry has been imposed to the dimer but no other constrain. The initial geometry of the molecular units was D2, with the barycenter of the two molecules shifted along the long molecular axis to simulate one common arrangement in the solid state. However, in the geometry optimization process the molecules have relaxed the original D2 symmetry. Therefore, on one hand we can estimate the effect of the changed molecular conformation on the vibrational frequencies and intensities, but on the other hand the relaxed symmetry yields to mixing of the normal modes. As a consequence, in some cases the correlation between the normal modes in the monomer and those of the dimers becomes ambiguous. In the following, the correlation and comparison between monomer and dimer results is limited to a few selected and important cases. Table 1 reports the calculated frequencies of the modes which have a ionization frequency shift (from 0 to +1) of at least 40 cm1. Modes below 300 cm1 have been excluded since they are sensitive to the molecular conformation and to the crystalline packing.14 Figure 1 plots the frequencies of the above modes against the ionicity, to better evaluate the (linear) functional dependence. The three CdC stretching modes a ν3, a ν4, and b1 ν22 (known respectively as ag ν2, ag ν3, and b1u ν27 in the D2h molecular symmetry)2022 exhibit the largest ionization frequency shift (120130 cm1), and have been already widely used and discussed.7,8 We shall then start the analysis from the b1 ν29 and b2 ν44 modes, which can be roughly described as breathing of the penta-atomic tetrathiafulvalene rings and which exhibit a ionization frequency shift of about 40 cm1. From the bottom panel of Figure 1, one sees immediately that the b2 ν44 mode does not display a very linear dependence on F. In addition, the corresponding bands may be difficult to identify. The R intensity is in fact expected to be very weak, as for all nontotally symmetric modes in resonance or preresonance regime, and the calculated IR intensity (Table 1) is rather weak. Therefore, despite the appreciable ionization frequency shift, the 19372
dx.doi.org/10.1021/jp206171r |J. Phys. Chem. C 2011, 115, 19371–19378
The Journal of Physical Chemistry C
Figure 1. Plot of the frequencies of the five most relevant charge sensitive vibrational modes of BEDT-TTF against the ionicity. Top panel: high frequency CdC stretching modes. The continuous lines are the regressions based on the experimental data (see text). Bottom panel: ring breathing modes. The continuous lines are the regressions based on the presently calculated frequencies.
b2 ν44 mode can hardly be proposed to probe the ionicity of BEDT-TTF salts. On the opposite, the calculated frequencies of the b1 ν29 mode stay perfectly on the regression line. It is not difficult to identify the experimental assignment at 771 cm1 for the neutral molecule,22 and at 789 cm1 for the F = 0.5 molecule,32 in correspondence with the calculated frequencies at 778 and at 795 cm1 (Table 1). A possible assignment of the b1 ν29 mode in fully ionic BEDT-TTF+ is to the weak band observed at 812 cm1 in powder spectra.21 The assignement is tentative, as experimental data on 1:1 BEDT-TTF salts are scarce.8,14,21 Furthermore, the b1 modes are in general difficult to identify because their oscillating transition dipole moment is directed along the BEDT-TTF z axis (scheme), and in the crystals of the salts this axis is almost invariably directed perpendicularly to the most developed crystal face. Therefore the b1 bands can be detected either in the powders IR spectra, but in this case the confirmation of the assignment may be difficult, or one has to grow large crystals where other faces can by investigated in polarized light, as done for instance in ref 32. The just mentioned difficulty in identifying the bands of b1 symmetry has of course affected the proper assignment of the antisymmetric CdC stretching (b1 ν22): Before the careful study of Yamamoto et al.,8 this mode was indeed thought to exhibit a nonlinear dependence of F. The top panel of Figure 1 compares the presently calculated frequencies (red triangles) with the experimentally derived regression line ω(F) = 1398 + 140(1 F).8 As expected, the F = 0.5 frequency lies perfectly on the regression curve, confirming the results of ref 8. However, there is an aspect that so far has been overlooked in all of the calculations,8,29 i.e., the 2 orders of magnitude increase of the IR intensity in passing
ARTICLE
Figure 2. Top panel: Calculated IR spectra of b1 modes of BEDT-TTF0 and BEDT-TTF+1. Bandwidth: 5 cm1. Notice the 10 scale increase of BEDT-TTF0 spectrum. Bottom panel: Comparison between the polarized conductivity spectrum of k (BEDT-TTF)2Cu[N(CN)2]Br (adapted from ref 32) and the calculated IR spectrum of b1 modes in the (BEDT-TTF)2+1 dimer (assumed bandwidth: 10 cm1). The latter spectrum has been empirically scaled to reproduce the intensity of the b1 ν22 mode. In both panels the bands corresponding to the b1 ν22 and b1 ν29 modes, discussed in text, are marked.
from the neutral to the fully ionized molecule (Table 1). This fact is dramatically evidenced in the top panel of Figure 2, where the calculated IR spectra of the two species are shown. The bandwidth of the assumed Lorentzian band-shape is 5 cm1 and the intensity of neutral BEDT-TTF spectrum has been multiplied by a factor of 10. The figure reports the only b1 modes, simulating spectra polarized along the BEDT-TTF long molecular axis. The strong IR intensity variation of some modes upon ionization is not unexpected. In the case of chloranil (tetrachlorop-benzoquinone) for instance, we have shown that the IR intensity of the CdC antisymmetric stretch decreases by 2 orders of magnitude upon addition of one electron.9 In that case, the intensity decrease could be intuitively understood, since the frontier MO of the ionized molecule has a quite different spatial distribution with respect to the HOMO of the neutral molecule. In the present case, the removal of one electron from the HOMO does not alter significantly the description of the orbital. Some hint about the factors yielding the intensity increase can by gained by looking directly at the alteration of the atomic Mulliken charges upon ionization. Figure 3 reports a cartoon of the eigenvectors of BEDT-TTF+ b1 ν22 mode, together with a plot of the frontier MO, and an indication of the percentage increase of the atomic Mulliken charges. From the figure, it is seen that the vibration almost exclusively involves the lateral CdC bonds, and it is quite analogous to the corresponding vibration of tetrathiafulvalene (TTF) molecule. In TTF+, however, the IR intensity is about 20 times lower than in BEDT-TTF+.33 This can be understood 19373
dx.doi.org/10.1021/jp206171r |J. Phys. Chem. C 2011, 115, 19371–19378
The Journal of Physical Chemistry C
ARTICLE
Figure 3. Representation of the eigenvectors BEDT-TTF+ b1 ν22 mode. The frontier MO is also shown, together with the percentage increase of the Mulliken atomic charges upon ionization.
by considering that in BEDT-TTF the frontier MO extends over the external S atoms, and the increase of atomic charges upon ionization is localized also on these atoms (Figure 3). Thus the length and the value of the resulting oscillating dipole moment is higher in BEDT-TTF+ than in TTF+. The IR intensity (∼65 D2 Å2 amu1) of b1 ν22 mode in BEDT-TTF+ is really huge, if one considers that ordinary IR intensities range from some tenths to a few D2 Å2 amu1, as exemplified in the top panel of Figure 2. It is rather strange that this fact went experimentally almost unnoticed, but I have already mentioned how the measurement of the IR intensities of b1 modes is in general rather difficult, in particular for what concerns absolute intensities. These require careful IR reflectance measurements, from which the corresponding conductivity can be derived. One of the first examples of such a kind of measurement is reported as a dashed line in the bottom panel of Figure 2, and concerns k (BEDT-TTF)2Cu[N(CN)2]Br.32 The peak conductivity of the b1 ν22 mode is about 100 Ω1 cm1, a quite remarkable value, and corresponds to a calculated squared oscillating dipole moment ∼23 D2 Å2 amu1 for the (BEDTTTF)2+ dimer, less than a half of that of the fully ionic molecule (Table 1). The calculated relative intensities of the main b1 modes (magenta in the bottom panel of Figure 2) also compare well with experiment. The other two modes displaying large ionization frequency shifts, the central and lateral CdC symmetric stretches a ν3 and ν4, are R active only. They have been the first ones to be proposed for the determination of F in BEDT-TTF,7 and the linear dependence has been experimentally verified (lines drawn in the top panel of Figure 1). However, totally symmetric modes are coupled to the electronic system, and in some cases the frequencies may be perturbed by the coupling, as pointed out by Yamamoto et al.,8 and as I will discuss in some detail below.
’ ELECTRON-MOLECULAR VIBRATION (E-MV) COUPLING Totally symmetric (ts) vibrations of electron donor or acceptor molecules involved in CT complexes or salts may couple to the CT electron through the energy modulation of the frontier MOs. This coupling, customarily referred as e-mv coupling, has been thought to be involved in the superconductivity mechanism14 and gives rise to a series of peculiar spectroscopic effects.6,13 To the aim of the present paper, the latter can be summarized in terms of the Rice’s dimer model.34 The basic parameters of the theory are the e-mv coupling constants: gj ¼ ð∂ε=∂Q jÞ
ð1Þ
where ε is the energy of the frontier MO and Qj is one of the ts dimensionless normal coordinates of the molecule. Let us consider a symmetric CT self-dimer, like for instance (BEDTTTF)22+. The CT electronic transition between the two moieties of the dimer occurs at low-energy, in the NIR or IR spectral region, and is polarized perpendicularly to the molecular planes. The molecular ts normal coordinates couple in-phase and out-ofphase. The former are R active, and are decoupled from the electronic system. The latter, modulating in antiphase the frontier MO energies, favor the electron transfer from one molecule to the other, and are therefore coupled to the CT transition. Due to the coupling, the IR active out-of-phase coupled modes borrow intensity from the nearby CT electronic transition, and occur at a frequency lower than that of the corresponding in-phase R active modes. Therefore the IR spectra of the CT self-dimer are characterized by the occurrence of very strong bands, polarized perpendicularly to the molecular planes, like the CT transition. These characteristic bands have been named e-mv induced, or vibronic, bands.6,13 According to Rice,34 the frequency dependent conductivity in the direction of the CT transition is given by (p = 1) " # e2 a2 χðωÞχð0Þ Nd σðωÞ ¼ Re iω ð2Þ χð0Þ χðωÞDðωÞ 4 where e is the electronic charge, a is the intradimer distance, Nd is the number of dimers per unit volume, and χ(ω) is the CT electronic susceptibility χðωÞ ¼
2jμCT j2 ωCT ωCT 2 ω2 iωγCT
ð3Þ
The spectrum of e-mv coupled phonons is given by the phonon propagator DðωÞ ¼ χð0Þ
g 2ω
∑j ωj2 ωj 2 j iωγj
ð4Þ
where ωj and γj are the frequencies and damping factors of the uncoupled (in-phase combination, R active) ts molecular modes. The poles of the phonon propagator of eq 4 give the frequencies Ωj of the IR e-mv induced modes. Conversely, from the experimental ωj and Ωj one can estimate the square of the coupling constants by solving a set of linear equations, that in simplified form are written as6,13,35 Y ωCT 2 χð0Þ gk 2 ωk ðωl 2 Ωj 2 Þ
∑k
l6¼ k
¼ ðωCT 2 Ωj 2 Þ
Y ðωl 2 Ωj 2 Þ
ð5Þ
l
Thus for a symmetric dimer only the IR active modes can be coupled to the CT electron, and the R ones are decoupled. Now suppose the dimer is not symmetric, as it happens if the components are two different molecules, or if the two molecules are or become inequivalent, for instance as a consequence of CO instability. Then the modes of the two molecules are no more degenerate and coupled in-phase and out-of-phase. Due to the lack of inversion center, the mutual exclusion rule does not hold, all of the modes of the two components become both R and IR active, and all of the ts molecular modes can be coupled to the CT electron.36 Due to this coupling, the frequencies of ts molecular modes may exhibit a nonlinear dependence on F.6 The same may 19374
dx.doi.org/10.1021/jp206171r |J. Phys. Chem. C 2011, 115, 19371–19378
The Journal of Physical Chemistry C
ARTICLE
Table 2. Main e-mv Coupling Constants of BEDT-TTF+a calculationb
experimentc
ωj
gmon j
gdim j
ωj
gj
a ν3
1458
102
54
1460
43
ν5
1444
6
4
ν4
1407
43
51
1414
71
ν6
1305
23
8
1288
12
ν10
896
6
9
899
12
ν13
516
36
35
513
40
ν14
459
20
11
453
12
ν16
274
6
10
mode
a Frequencies (ω) in cm1, and absolute values of the coupling constants (g) in meV. b The gmon and gdim refer respectively to the coupling constants evaluated for a BEDT-TTF+ unit through eq 1 or for a dimer (BEDT-TTF)22+ through eq 5 (see text). c From ref 35.
Figure 4. Eigenvectors of the eight most strongly coupled ts mode of BEDT-TTF+.
happen if the structure of the CT salt is not characterized by the presence of dimers, but exhibit a more complex molecular arrangement.37 There have been several reports on computation of BEDTTTF+ e-mv coupling constants,15,21,3840 but they were limited to a few strongly coupled modes, and/or they used the D2h symmetry of the central skeleton. I then believe it is useful to report the coupling constants of all 19 ts modes in D2 molecular symmetry, computed by the numerical derivative of the frontier MO energy on the normal coordinates (cf. Equation 1). Although the Supporting Information reports the full set of coupling constants, both for the pristine and deuterated BEDT-TTF+ isolated molecule, Table 2 shows only the 8 modes exhibiting e-mv coupling constants greater than 5 meV (values in the third column of the Table). The corresponding eigenvectors are shown in Figure 4. The a ν3, ν4, and ν10 (ag ν2, ν3, and ν9 in D2h symmetry)35 all involving the TTF central skeleton are the well-known and more strongly coupled modes. The former two are also strongly mixed, both involving symmetric CdC stretching. In this case, the association of each coupling constant to the respective mode is ambiguous but irrelevant. The a ν5, ν6, and ν16 vibrations mostly
involve the external rings, including the CH2 groups, so that the coupling constants are rather small. Of these three modes, only the ν6 (ag ν5 in D2h) has been experimentally identified.35 The ν16 mode implies the torsion of the CH2 groups and has not been explicitly considered so far.31 Its e-mv coupling is weak, and its value might change when the molecule is embedded in the crystal.41 On the other hand, its vibronic signature is likely associated with the recently detected IR band at 260 cm1,12 and a careful investigation of the R counterpart is needed. Apart from the e-mv coupling, one has to consider that the ν16 might be involved in the ethylene glass-like transition detected in some superconducting salts.2427 Finally, the vibronic signatures of the ν5 are very difficult to identify, since this mode is in between the two more strongly coupled vibrations ν3 and ν4, and there is strong redistribution of the intensities between nearby coupled modes. Indeed, simulation of the vibronic spectrum through eq 2 shows that the intensity of this vibration is almost undetectable. The a ν10 CS stretching mode requires some additional comment, since its vibronic signatures are particularly sensitive to the environment and/or external perturbations.23 In addition, an erroneous assignment based on empirical calculations in D2h symmetry associated the observed R and vibronic bands to the b3g ν60 vibration.22 This assignment puzzled many,23 since non-ts modes cannot be linearly coupled to the CT electron.13,34 The issue is definitely solved by the present DFT calculations, which, adopting a more realistic molecular symmetry, show that the a ν10 has a sizable e-mv coupling constant. Furthermore, the origin of the misassignment can be traced back to the fact that four modes, of different symmetry species, but similar description, are found in the narrow spectral region 880920 cm1 (see the Supporting Information). It is known that DFT-B3LYP calculations do not model very well intermolecular and CT interaction. So it came as some surprise the fact that the calculation performed for the BEDTTTF dimers could reproduce the e-mv induced signatures. The black line in the top panel of Figure 5 shows the DFT-calculated vibronic spectrum of (BEDT-TTF)22+. The relative intensities of the bands compare quite well with those of the experimental conductivity spectrum of (BEDT-TTF)2MoO19,35 shown in the bottom panel of Figure 5. Actually, one should not expect precise match, since both the IR intensity of the vibronic bands and their shift with respect to the R counterpart depend from g2 and from the static CT susceptibility χ(0) (eq 4). Our calculation refer to a dimer in gas phase, and in any case is not aimed to reproduce the χ(0), i.e., |μCT|2/ωCT. To illustrate the effect of χ(0), the top panel of Figure 5 also shows the conductivity spectrum computed inserting the experimental e-mv coupling constants and susceptibility in eq 2. It is seen that the conductivity vibronic spectrum (green line) shows lower frequencies with respect with the DFT-computed spectrum, namely, the DFT susceptibility is slightly underestimated. The above findings suggest an alternative route to extract the values of the e-mv coupling constants from DFT calculations. Rather than the numerical derivative of the monomer frontier MO on the normal coordinates, one can look at the frequencies of the in-phase and out-of-phase combinations of ts modes computed for the dimer. From the frequency difference one derives the relative values of the coupling constants by solving the linear equation in eq 5. The g values extracted in this way are shown in the fourth column of Table 2. To obtain the absolute values reported in the table, I have taken χ(0) = 2.9 eV1, as experimentally derived for (BEDT-TTF)2MoO19.35 It is seen 19375
dx.doi.org/10.1021/jp206171r |J. Phys. Chem. C 2011, 115, 19371–19378
The Journal of Physical Chemistry C
ARTICLE
Table 3. Main e-mv Coupling Constants of BEDT-TTF+0.5a calculationb ωj
Ωj
a ν3
1501
ν5
1437
ν4 ν6
experimentc
Ij
gdim j
ω0j
gj
1498
0.11
77
1460
75
1437
1.02
3
1476
1395
142.79
30
1307
1304
6.21
10
1287
10
ν10
897
895
0.97
12
878
15
ν13
516
480
9.35
60
445
30
ν14
464
451
1.23
18
ν16
286
286
0.13
3
mode
Frequencies (ω, Ω) in cm1, IR intensities (I) in D2 Å2 amu1, and absolute values of the coupling constants (g) in meV. b The reported calculated frequencies are the scaled ones. The ordering of the modes and the association between ωj and Ωj is not made on the basis of their decreasing frequency, but on the basis of the mode description (Figure 4), so there is correspondence between the present and Table 2 mode labels. c From ref 43. The ω0j are adjustable parameters, like the gj, in a nonlinear curve fitting of conductivity. a
2+
Figure 5. Vibronic IR bands of (BEDT-TTF)2 dimer. Top panel: Black line: DFT-computed vibronic IR bands (assumed bandwidth: 5 cm1); IR intensity scale on the left. Green dashed line: conductivity spectrum calculated through eq 2, with the experimentally determined g’s (sixth column in Table 2); conductivity scale on the right. Bottom panel: Experimental spectrum of a BEDT-TTF salts containing isolated (BEDT-TTF)22+ dimers, (BEDT-TTF)2MoO19 (adapted from ref 35). The IR bands of nonvibronic origin are marked.
that there is good agreement between e-mv coupling constants computed by the two routes and the experimental ones. The coupling constants of the ν3 and ν5 have always to be considered together in these comparison, due to the already mentioned mixing of the corresponding normal coordinates. The DFT calculation on the (BEDT-TTF)2+ dimer correctly predict a higher effect of e-mv coupling with respect to (BEDTTTF)22+. However, the discrepancy with respect to experiment is much higher. For instance, the e-mv induced band of the a ν5 mode is calculated around 1400 cm1, vs an experimental value around 1300 cm1.42 Its intensity is almost doubled in going from (BEDT-TTF)22+ to (BEDT-TTF)2+ (85.21 to 142.79 D2 Å2 amu1), but experimentally one finds a 3 to 5 factor for the peak conductivity increase.35,42 In other words, the electronic parameters are not correctly computed in the case of BEDT-TTF+0.5 salts, where the CT transition occurs in the mid-IR region and overlaps the vibronic bands. Therefore the direct comparison between the calculated vibronic spectrum of the (BEDT-TTF)2+ dimer, and the experimental conductivity spectrum of some 2:1 BEDT-TTF salts42,43 is not very instructive. However, one can again extract the relative values of the e-mv coupling constants from the frequency difference between the in-phase and out-out-phase (ωj and Ωj) combination of the ts molecular modes. The results are summarized and compared with experimentally derived e-mv coupling constants in Table 3. Many experimental estimates of the e-mv coupling constants are reported in the literature,42 but these have been derived through models different from the dimer model, in an attempt to reproduce also the complex electronic spectra of BEDT-TTF 2:1 salts.
These models contain several adjustable parameters, and as a consequence there is a wide scattering in the g’s estimates. For the experimental comparison, I report in Table 3 results of a recent paper,43 where the dimer model has been used to disentangle the vibronic and electronic contribution of this unit to the complex experimental spectra. To get the computed g values reported in column five of the table, I have chosen χ(0) = 2.5 eV1 and ωCT = 3100 cm1 to mimic the experiment of ref 43. The comparison with the experiment is in any case partial, because extracting the values of the coupling constants from the spectra of 2:1 salts is a difficult task. Actually, the computed relative g values presented here could be profitably used to assist the interpretation of the experimental optical spectra.
’ DISCUSSION AND CONCLUSIONS In this paper I have presented an exhaustive DFT characterization of the vibrations of BEDT-TTF in different ionization states, both as isolated molecule, and as a pair to form a symmetric dimer. The aim has not been to revise and/or complete the previous vibrational assignment,8,2022 although this is entirely possible with the assistance of the data in the Supporting Information. Rather, I have tried to provide information which will help to shed some light on the still open questions concerning the complex phase diagrams of BEDT-TTF salts.3 According to some theoretical models, e-mv coupling may be involved in the superconductivity mechanism.3,14 It certainly plays a role in the CO instabilities, as the modulation of the frontier MO, pushing charges back and forth, will ultimately provoke their localization on the molecular sites. The DFT calculations essentially confirm the previous experimental characterization,35 definitely clarifying the role of the so-called “mystery mode” around 890 cm1.23 The calculations also suggest to consider the e-mv coupling of two other modes, the a ν5 and ν16 (Figure 4). The predicted coupling of these modes is not strong, but they still deserve attention. The first mode is in between two strongly coupled modes, ν3 and ν4. Since all of the vibronic modes are also coupled among themselves through the common interaction with the CT transition, nearby modes interact with strong intensity redistribution. Therefore the presence of the ν5 has 19376
dx.doi.org/10.1021/jp206171r |J. Phys. Chem. C 2011, 115, 19371–19378
The Journal of Physical Chemistry C to be taken into account for a correct interpretation of the vibronic spectra. The ν16 mode occurs at low frequency and may change its coupling according to the type of crystal packing. The mode implies the torsion of the CH2 groups, and this kind of vibration has been so far considered unimportant for e-mv coupling.31 In addition, the role of this mode in the observed glass-like (disorder to partial order) transition2427 is worth a careful investigation, by changing the conter-ion and/or by using deuterated BEDT-TTF. Indeed, the transition affects the lowtemperature physical properties (superconductivity included) of BEDT-TTF salts, and subtly depends on the crystalline environment.26 By using the deuterated analogue, one can also exploit the fact that the ν16 vibrational frequency changes considerably upon deuteration (see the Supporting Information). The correct qualitative reproduction of the e-mv induced IR spectra through DFT calculations of BEDT-TTF dimers (Figure 5) is another important result of the present paper. A more quantitative agreement with experiment could probably be obtained by imposing the geometry of the dimer in the crystal (but it will likely produce bad or imaginary values for the low-frequency modes). However, the estimate of the relative value of the e-mv coupling constants, obtained here for (BEDT-TTF)22+ and (BEDT-TTF)2+ dimers, are sufficiently accurate to assist a proper interpretation of the spectra, disentangling the various contributions.43 In this way one could also get estimations of other microscopic parameters, like for instance χ(0), by a simple analysis of the R and IR frequencies of e-mv coupled modes. The full characterization of the charge sensitive modes has led to the identification of another mode (b1 ν29) which might be used to estimate F but has also allowed to discover the 100-fold increase of the IR intensity of the b1 ν22 mode (formerly b1u ν27) upon ionization. However the really important finding it is the absolute value of the ν22 IR intensity in the ionic molecule. Indeed, in BEDT-TTF+ the intensity is of the same order of magnitude of the most intense e-mv induced band, a ν4, as can be easily seen by comparing the ordinate scale in the top panels of Figure 2 and of Figure 5. Years ago, the observation that the temperature dependence of the IR b1 ν22 band intensity is similar to that of vibronic bands led S0 wietlik et al. to suggest a sort of interaction between b1 modes and intramolecular CT.44 On the basis of the present results, one could explain the observed parallel temperature dependence of the vibronic and ν22 mode by assuming a parallel T-induced dimerization and CO instability: The first phenomenon would lead to the intensity increase of the vibronic bands,6,13 the second to the intensity increase of the b1 ν22 mode corresponding to the charge-enriched molecule. However, the above simple idea does not apply to recently studied BEDT-TTF salts, which already are in the CO state at room temperature, and for which the above concept of the interaction between the vibration and intramolecular CT has been resumed.45 The concept of a coupling between a molecular vibration and an intramolecular CT, analogous to the well-known coupling between the molecular vibration and the intermolecular CT, is certainly strongly suggestive. However, whereas the CT state between two separated molecular units is a well established concept, that of a CT between two halves of the molecule, where the HOMO is distributed between the two lateral and the central CdC bonds (Figure 3), remains difficult to formulate, in particular in the lack of a detailed characterization of the intramolecular electronic excited states. I rather suggest to think in terms an asymmetric charge distribution induced by the b1 ν22
ARTICLE
mode, with associated possible symmetry breaking. The high intensity of the ν22 might be an indication of the proximity of the molecule to such symmetry-broken state. Whether of not such (possible) intramolecular disproportionation is connected or interacts with the intermolecular CO instability is a matter which certainly deserves deeper investigation.
’ ASSOCIATED CONTENT
bS
Supporting Information. Computed vibrational frequencies of BEDT-TTF and BEDT-TTF+, in D2 molecular symmetry, and e-mv coupling constants of pristine and deuterated BEDT-TTF+. This material is available free of charge via the Internet at http://pubs.acs.org.
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
’ ACKNOWLEDGMENT I gratefully acknowledge the many enlightening discussions with Natalia Drichko and Martin Dressel, which also prompted me to undertake this work. Many thanks also to Roman S0 wietlik, for the correspondence and for sharing unpublished data. Ongoing discussions with my colleagues Matteo Masino and Anna Painelli are also acknowledged. ’ DEDICATION This paper is dedicated to the memory of my mentor, Cesare Pecile, who 40 years ago directed my research interests to the fascinating field of CT crystals. ’ REFERENCES (1) Yagubskii, E. B.; Schegolev, I. F.; Laukhin, V. N.; Kononovich, P. A.; Kartsovnik, M. V.; Zvarykina, A. V.; Buravov, L. I. Sov. Phys. JEPT Lett. 1984, 39, 12. (2) Williams, J. M.; Emge, T. J.; Wang, H. H.; Beno, M. A.; Copps, P. T.; Hall, L. N.; Carlson, K. D.; Crabtree, G. W. Inorg. Chem. 1984, 23, 2558. (3) Singleton, J.; Mielke, C. Contemp. Physics 2002, 43, 63. (b) Ouahab, L., Yagubskii, E., Eds.; Organics Conductors, Superconductors and Magnets: From Synthesis to Molecular Electronics; NATO Science Series Vol. 139; Kluwer: Dordrecht The Netherlands, 2004. (c) Molecular Conductors, Batail, P. Guest Editor, Chem. Rev. 2004, 104 (11). (d) Lebed, A. G., Ed.; The Physics of Organic Superconductors and Conductors; Springer: Berlin, 2008. (d) Lang, M.; M€uller, J. Organic Supercondutors, in Superconductivity Vol. 2: Novel Superconductors; Bennemann, K. H., Ketterson, J. B., Eds.; Springer: Berlin, 2008; p 1155. (4) Merino, J.; McKenzie, R. H. Phys. Rev. Lett. 2001, 87, 237002. (5) Bozio, R.; Pecile, C. In The Physics and Chemistry of Low Dimensional Solids; Alcacer, L., Ed.; Reidel: Dordrecht, The Netherlands, 1980; p 165. (6) Pecile, C.; Painelli, A.; Girlando, A. Mol. Cryst. Liq. Cryst. 1989, 171, 69 and references therein. (7) Wang, H. H.; Ferraro, J. R.; Williams, J. M.; Geiser, U.; Schlueter, J. A. J. Chem. Soc., Chem. Commun. 1994, 1893. (8) Yamamoto, T.; Uruichi, M.; Yamamoto, K.; Yakushi, K; Kawamoto, A.; Taniguchi, H. J. Phys. Chem. B 2005, 109, 15226. (9) Ranzieri, P.; Masino, M.; Girlando, A. J. Phys. Chem. B 2007, 111, 12844. 19377
dx.doi.org/10.1021/jp206171r |J. Phys. Chem. C 2011, 115, 19371–19378
The Journal of Physical Chemistry C (10) Drichko, N.; Kaiser, S.; Sun, Y.; Clauss, C.; Dressel, M.; Mori, H.; Schlueter, J.; Zhyliaeva, E. I.; Torunova, S. A.; Lyubovskaya, R. N. Physica B 2009, 404, 490. (11) Kaiser, S.; Dressel, M.; Sun, Y.; Greco, A.; Schlueter, J. A.; Gard, G. L.; Drichko, N. Phys. Rev. Lett. 2010, 105, 206402. (12) Ivek, T.; Korin-Hamzic, B.; Milat, O.; Tomic0 , S.; Clauss, C.; Drichko, N.; Schweitzer, D.; Dressel, M. Phys. Rev. B 2011, 83, 165128. (13) Painelli, A.; Girlando, A. J. Chem. Phys. 1986, 84, 5655. (14) Girlando, A.; Masino, M.; Brillante, A.; Della Valle, R. G.; Venuti, E. Phys. Rev. B 2002, 66, 100507(R). (15) Girlando, A.; Masino, M.; Brillante, A.; Della Valle, R. G.; Venuti, E. In New Developments in Superconductivity Research; Stevens, R. W., Ed.; Nova Science Publisher: New York, 2003; p 15. (16) Schmidt, M. W.; Baldridge, K. K.; Boatz, J. A.; Elbert, S. T.; Gordon, M. S.; Jensen, J. H.; Koseki, S.; Matsunaga, N.; Nguyen, K. A.; Su, S.; Windus, T. L.; Dupuis, M.; Montgomery, J. A. J. Comput. Chem. 1993, 14, 1347.Gordon, M. S.; Schmidt, M. W. In Theory and Applications of Computational Chemistry: the first forty years; Dykstra, C. E., Frenking, G., Kim, K. S., Scuseria, G. E., Eds.; Elsevier: Amsterdam, 2005; p 1167. (17) Barone, V.; Festa, G.; Grandi, A.; Rega, N.; Sanna, N. Chem. Phys. Lett. 2004, 388, 279. (18) Andersson, M. P.; Uvdal, P. J. Phys. Chem. A 2005, 109, 2937. The scale factors reported in this paper were actually optimized for the 6-311G(d,p) basis set rather than for 6-31G(d) used here. However, universal scaling factors give the best compromise in the overall frequency spectrum, from the highest frequency CH stretching region, which require the highest downwards correction, to the lowest frequency bendings and torsions, which hardly require any correction. Since we are not interested in the CH stretching vibrations, we have found that the scaling factors suggested above give results better than the usually adopted scaling of 0.9613 of Scott, A. P.; Radon, L. J. Phys. Chem. 1996, 100, 16502.The 1300 cm1 frequency separating high and low frequency scaling factors has been suggested by: Bauschicher, C. W.; Ricca, A.; Partridge, H.; Langhoff, S. R. In Recent Advances in DFT Methods, Part II; Chong, D. P., Ed.; World Scientific: Singapore, 1997; p 165. (19) Jmol: an open-source Java viewer for chemical structures in 3D. http://www.jmol.org/. (20) Kozlov, M. E.; Pokhodnia, K. I.; Yurchenko, A. A. Spectrochim. Acta A 1987, 43, 323. 1989, 45, 437. (21) Kozlov, M. E.; Pokhodnia, K. I.; Yurchenko, A. A. Spectrochim. Acta A 1989, 45, 437. (22) Eldridge, J. E.; Homes, C. C.; Williams, J. M.; Kini, A. M.; Wang, H. H. Spectrochim. Acta A 1995, 51, 947. (23) Munsfeldt, J. L.; S0 wietlik, R.; Olejniczak, I.; Eldridge, J. E.; Geiser, U. Phys. Rev. B 2005, 72, 014516. (24) Whangboo, M.-H.; Williams, J. M.; Schultz, A. J.; Emge, T. J.; Beno, M. A. J. Am. Chem. Soc. 1987, 109, 90. (25) Geiser, U.; Schultz, A. J.; Wang, H. H.; Watkins, D. M.; Stupka, D. L.; Williams, J. M.; Schirber, J. E.; Overmeyer, D. L.; Jung, D.; Novoa, J. J.; Whangbo, M.-H. Physica C 1991, 174, 475. (26) M€uller, J.; Lang, M.; Steglich, F.; Schlueter, J. A.; Kini, A. M.; Sasaki, T. Phys. Rev. B 2002, 65, 144521. (27) M€uller, J.; Lang, M.; Steglich, F.; Schlueter, J. A. J. Phys. IV France 2004, 114, 341. (28) Kobayashi, H.; Kobayashi, A.; Sasaki, Y.; Saito, G.; Inokuchi, H. Bull. Chem. Soc. Jpn. 1986, 59, 301. (29) Demiralp, E.; Dasgupta, S.; Goddard, W. A., III. J. Am. Chem. Soc. 1995, 117, 8154. (30) Demiralp, E.; Dasgupta, S.; Goddard, W. A., III. J. Phys. Chem. A 1997, 101, 1975. (31) Meneghetti, M.; Bozio, R.; Pecile, C. J. Phys. (Paris) 1986, 47, 1377. (32) McGuire, J. J.; R~o~om, T.; Pronin, A.; Timusk, T.; Schlueter, J. A.; Kelly, M. E.; Kini, A. M. Phys. Rev. B 2001, 64, 094503. (33) Girlando, A. unpublished. The calculated IR intensity of the antisymmetric CdC stretching of TTF+ is 3.16 D2 Å2 amu1.
ARTICLE
(34) Rice, M. J. Solid State Commun. 1979, 31, 93. (35) Visentini, G.; Masino, M.; Bellitto, C.; Girlando, A. Phys. Rev. B 1998, 58, 9460. There is a misprint in Table II for the experimental ag v5 e-mv coupling constant, which should read 12 rather than 6 meV. (36) Girlando, A.; Bozio, R.; Pecile, C.; Torrance, J. B. Phys. Rev. B 1982, 26, 2306. (37) Yamamoto, K.; Yakushi, K.; Miyagawa, K.; Kanoda, K.; Kawamoto, A. Phys. Rev. B 2002, 65, 085110. (38) Faulhaber, J. C. R.; Ko, D. Y. K.; Briddon, P. Synth. Met. 1993, 60, 227. (39) Shumway, J.; Chattopadhyay, S.; Satpathy, S. Phys. Rev. B 1996, 53, 6677. (40) Shizu, K.; Sato, T.; Tanaka, K. Chem. Phys. Lett. 2010, 491, 65. (41) Girlando, A; Grisanti, L.; Masino, M.; Bilotti, I.; Brillante, A.; Della Valle, R. G.; Venuti, E. Phys. Rev. B 2010, 82, 035208. (42) Yartsev, V. M.; Graja, A. Int. J. Mod. Phys. B 1998, 12, 1643. (43) Faltermeier, D.; Barz, J.; Dumm, M.; Dressel, M.; Drichko, N.; Petrov, B.; Semkin, V.; Vlasova, R.; Mez0 iere, C.; Batail, P. Phys. Rev. B 2007, 76, 165113. (44) S0 wietlik, R.; Garrigou-Lagrange, C. Synth. Met. 1993, 5557, 2217. (45) Olejniczak, I.; Barszcz, B.; Szutarska, A.; Graja, A.; Wojciechowski, R.; Schlueter, J. A.; Hata, A. N.; Ward, B. H. Phys. Chem. Chem. Phys. 2009, 11, 3910.
19378
dx.doi.org/10.1021/jp206171r |J. Phys. Chem. C 2011, 115, 19371–19378
