J. Phys. Chem. A 1997, 101, 1975-1981
1975
MSX Force Field and Vibrational Frequencies for BEDT-TTF (Neutral and Cation) Ersan Demiralp, Siddharth Dasgupta, and William A. Goddard III* Materials and Process Simulation Center, Beckman Institute (139-74), DiVision of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125 ReceiVed: September 30, 1996; In Final Form: December 30, 1996X
BEDT-TTF is the donor of the highest Tc organic superconductors. Isotopic shift experiments support an electron-phonon coupling mechanism for the superconductivity. However, the vibrational levels have been only partially observed and assigned, making testing of this mechanism difficult. In order to provide a complete consistent description of all vibrational levels, we carried out Hartree-Fock calculations (6-31G** basis set) to obtain the Hessians and fundamental vibrational frequencies of BEDT-TTF and BEDT-TTF+. With these Hessians and available experimental frequencies, we used Hessian-biased methods to develop the MSX force fields for the neutral and cation BEDT-TTF molecules. Comparison of the calculated frequencies with the available experimental frequencies for the neutral and cation BEDT-TTF molecule shows good agreement.
1. Introduction The organic superconductors all have in common organic donor molecules derived from tetrathiafulvalene (denoted as TTF), tetraselenafulvalene (denoted at TSeF), or some mixture of these two molecules, packed into quasi one- and twodimensional arrays and complexed to appropriate electron acceptors.1 Figure 1 shows BEDT-TTF (denoted also as ET) which is the donor of the best organic superconductors. About 30 organic superconductors based on ET have been synthesized with Tc up to 12.8 K. Changes in Tc for various isotope shifts indicate that electron-phonon coupling is important for the superconductivity of these materials. However, experimental data on the vibrational modes is incomplete and does not supply clear evidence about which vibrational modes are important for the superconductivity. Consequently, we carried out ab initio Hartree-Fock (HF) and force field (FF) calculations to obtain all modes of neutral ET and of ET+. With appropriate electron acceptors some modifications of ET show superconductivity and some do not. The relation between superconductivity and the molecular or crystal structures of these molecules has not yet been clearly identified by the experiments. In this paper, we present calculated vibrational levels for the equilibrium structures of ET (boat) and ET+ (planar). Using the calculated structures and Hessians with available experimental frequencies, we develop the MSX force fields for the neutral and cation ET molecules. These frequencies compare well with the available experimental frequencies9,10 and provide procedures for a number of unknown or uncertain levels. 2. Results 2.1. Structures. The structure of ET is often discussed in terms of D2 symmetry, which assumes a planar structure for the central TTF moiety. The crystal structures of neutral ET crystal are consistent with planarity but show a distinct boatlike distortion.11 Some deviations from planarity are also suggested in crystals containing electron acceptors, (ET)nXm.12 Here the ET molecules often form dimers (ET2)+ sharing a single positive charge. Recently we reported ab initio quantum chemical calculations [Hartree-Fock (HF) with 6-31G** basis set] for the structures * To whom correspondence should be addressed. X Abstract published in AdVance ACS Abstracts, February 15, 1997.
S1089-5639(96)03004-6 CCC: $14.00
Figure 1. Definition of atomic types for the atoms of ET.
of neutral and cation ET.7,8 These results show that the TTF framework for neutral ET is nonplanar deforming to a boat conformation with a well depth of 0.654 kcal/mol. However, the TTF framework for the cation, ET+, is planar. The terminal six-membered rings are nonplanar in order to avoid eclipsing of the CH2-CH2 groups at each end. This nonplanarity leads to two possible conformations:12 1. The staggered conformation indicated in Figure 1 in which the two C6-C6 bonds are pointing in opposite directions; assuming a planar TTF central region, this leads to D2 symmetry. 2. The eclipsed conformation in which the two C6-C6 bonds are parallel; with planar TTF, this leads to C2h symmetry. These conformations are essentially degenerate, differing by only 0.000 052 hartrees ) 0.000 14 eV ) 0.0032 kcal/mol (with eclipsed lower). We will consider hereafter the higher symmetry staggered case. To determine the structure and vibrational modes of ET, we carried out ab initio Hartree-Fock calculations using the 6-31G** basis set.13 Restricting the symmetry to D2 leads to an optimized structure with two imaginary frequency vibrational modes. The stable conformation is the boat structure with C2 symmetry (The optimized boat structure has vibration frequencies positive, indicating a stable structure). 2.2. Vibrational Analysis. Previous assignments of the vibrational spectra of ET have assumed planar molecule for both the neutral and cation cases. Planar ET would have D2 symmetry for the staggered conformation and C2h for the eclipsed conformation. For the staggered conformation this leads to fundamental modes with the following symmetries:
Γ(D2) ) 19A + 17B1 + 18B2 + 18B3
(1)
To simplify assignments, Kozlov et al.11,12 considered the ET to be totally flat leading to D2h symmetries (they were aware © 1997 American Chemical Society
1976 J. Phys. Chem. A, Vol. 101, No. 10, 1997
Demiralp et al.
TABLE 1: (A) Optimized Distances (in Å) for Boat and Planar ET Conformations and Experimental Distance (See Figure 1 for Notation) and (B) Optimized Angles (in deg) A. Optimized Distances ET CR-CR SR-C2 S32-C3 SR-CR C2-C2 S32-C2 C3-C3 C3-H
1 4 4 4 2 4 2 8
ET+
MSXa
HF
MSX
HF
1.325 1.773 1.812 1.769 1.325 1.769 1.523 1.083
1.326 1.774 1.814 1.771 1.323 1.767 1.523 1.082
1.389 1.751 1.816 1.721 1.336 1.765 1.523 1.082
1.389 1.751 1.816 1.721 1.336 1.765 1.523 1.082
B. Optimized Angles ET S32-C2-C2 SR-C2-S32 SR-CR-SR CR-SR-C2 S32-C3-C3 SR-C2-C2 SR-CR-CR C2-S32-C3 H-C3-H S32-C3-H C3-C3-H
4 4 2 4 4 4 4 4 4 8 8
ET+
MSX
HF
MSX
HF
128.68 113.80 112.74 94.41 112.87 117.22 123.63 100.74 108.58 107.18 110.36
128.45 114.29 112.55 94.55 113.17 117.22 123.71 100.81 108.48 107.15 110.31
128.83 114.75 114.49 96.33 113.10 116.42 122.76 100.50 108.51 106.84 110.60
128.83 114.75 114.49 96.33 113.10 116.42 122.76 100.50 108.51 106.84 110.60
a For the neutral molecule, the optimized HF structure is minimized to reduce the total force by using FF. The rms force is less than 0.1 (kcal/mol)/Å for ET and ET+.
that only the central C2S4 group is planar). This leads to the fundamental mode distribution
Γ(D2h) ) 12Ag + 7Au + 6B1g + 11B1u + 7B2g + 11B2u + 11B3g + 7B3u (2) Thus D2h leads to g and u branching of the D2 symmetry modes. However, the stable boat structure of ET has C2 symmetry, leading to the mode distribution
Γ(C2) ) 37A + 35B
(3)
Consequently, some modes become both infrared and Raman active. Table 4 shows that this is consistent with data of Kozlov et al.9 The twofold axis of B3 symmetry of the planar molecule and C2 axis of the boat molecule are perpendicular to the central plane of the molecule. The reduction of symmetry is as follows:
12Ag + 7Au + 11B3g + 7B3u f 19A + 18B3 f 37A (4a) and
11B1u + 6B1g + 11B2u + 7B2g f 17B1 + 18B2 f 35B (4b) Table 4 shows all calculated frequencies plus available experimental frequencies for neutral ET. Calculated Raman and IR intensities are also given for all the vibrational modes. We used the symmetry of the modes for assigning experimental frequencies to the HF modes. The calculated IR and Raman intensities are in good agreement with experimental intensities. ET+ molecules in planar (D2 symmetry), leading to the distribution of fundamental mode in eq 1. Table 5 shows all the vibrational modes of ET+ compared to the available experimental frequencies. 3. The Force Field The ET molecules appear to be distorted in the crystal structures, removing all symmetry. The assignment of frequen-
cies for ET and ET+ molecules by Kozlov et al.9,10 assumed D2h symmetry. We used the optimized HF geometries of the neutral and cation ET to develop the force fields. Neutral ET has C2 symmetry and cation ET has D2 symmetry. The optimized geometric parameters (distances, angles, dihedrals) for the neutral and cation ET molecules are given in Table 1. These structures are used in optimizing the force field (FF). (For the neutral molecule, the optimized HF structure is minimized to reduce the total force by using FF. The rms difference between HF and minimized structure (FF) are 0.002 Å for bonds, 0.680° for angles). We calculated the Hessian (second derivative of energy with respect to the 3N coordinates) at the HF optimized geometry. This Hessian was used to develop the force field by using Hessian-biased (HBFF) approach.14 The potential energy of the molecule is
E)
∑ Eb + angles ∑ Ea + torsions ∑ Et + inversions ∑ Ei + cross ∑ EX + ∑ EvdW + charges ∑ EQ (5) vdW
bonds
where the terms are defined below. This type of FF is denoted MSX to indicate that it is optimized for materials simulations and contains limited cross terms. Very often in fitting a FF to vibrational spectra, only valence force terms are used. We also include vdW and electrostatic parameters because we want to use the FF to predict the structures in crystal, where nonbonded interactions are critical. In the HBFF approach, the potential energy is expressed as a sum of valence, nonbonded interactions. We optimize the force field terms by fitting the experimental frequencies and the calculated geometries. 3.1. Valence Interactions. We used the following valence terms: (i) the harmonic bond stretch
Eb(R) ) 1/2kb(R - Rb)2
(6)
where Rb is the equilibrium bond distance and kb is the force constant. (ii) the harmonic angle bend
Ea(θ) ) 1/2kθ(θ - θ0)2
(7)
where θ0 is the equilibrium angle and kθ is the force constant. (iii) angle-stretch cross terms
Eab ) kRθ(θ - θ0)(R - Rb)
(8)
where kRθ is the force constant. (iv) stretch-stretch cross terms
Ebb ) kRR′(R - Rb)(R′ - R′b)
(9)
where kRR′ is the force constant for the bonds Rb and R′b that share a common atom. (v) the torsional potential
Et(φ) ) V0 + V1 cos φ + V2 cos 2φ + V3 cos 3φ (10) where Vi is in kcal/mol and the angle φ is defined as the angle between the JKL plane and the IJK plane of the way two bonds IJ and KL attached to a common bond JK.
Force Field and Vibrational Frequencies for BEDT-TTF
J. Phys. Chem. A, Vol. 101, No. 10, 1997 1977
(vi) the inversion potential
TABLE 2: Calculated Charges by Using Potential Derived Charge Method15 (See Figure 1 for Notation)
Ei(ω) ) Kω(1 - cos ω)
(11)
with a minimum for planar structure (φ0 ) 0°). ω is the angle between the IL axis and the IJK plane for an atom I with exactly three bonds IJ, IK, and IL. 3.2. Charges. Partial atomic charges for the various atoms were obtained using the potential derived charge method (PDQ).15 The electron density from Hartree-Fock wavefunction is used to calculate the electrostatic potential around the molecule. Then, a set of atomic point charges is obtained that reproduces the ab initio electrostatic potential and dipole and quadrupole moments. Table 2 shows the atomic charges for the neutral and cation molecules. We write total electrostatic energy as
no. of cases CR SR C2 S32 C3 Hi Ho net charge
[( )
(
∑ i)1
() ∂Ri
(δRi) +
1
3N
∑
( ) ∂2E
2 i,j)1 ∂Ri ∂Rj
(13)
(δRi)(δRj) + ... (14)
where
Fi ) -(∂E/∂Ri)
(16a)
(16b)
and diagonalizing (16b) leads to
H h U ) Uλ where diagonal λ contains the 3N vibrational frequencies
λi ) (108.5913νi)2
The biased Hessian has the property that
(19b)
That is, it leads to the theoretical modes (Ut) and the experimental frequencies (λx). If the λx is not available from experiment, it can be approximated from the theory by using appropriate scaling rules. We optimized the force field parameters to obtain the best fit to H h xt while leading to correct (theoretical) equilibrium geometry. The van der Waals parameters and charges were fixed during optimization of the valence parameters. The charges (Table 2) were based on potential derived charges (PDQ) by using quantum mechanical potentials and the vdW parameters (Table 3) were from previous fits to various crystals.16 The final force field parameters for the neutral and cation ET are shown in the first two columns of Table 3. Calculated frequencies for ET and ET+ are compared with the available experimental frequencies (Kozlov et al.9,10) in Tables 4 and 5. The average absolute error between theory and experiment is ∼13 cm-1 for ET and ∼16 cm-1 for ET+. Applying the MSX force field to planar neutral BEDT-TTF (D2 symmetry) led to two imaginary frequencies, which is consistent with the quantum mechanical results.8 5. Discussion
is the Hessian. Using the mass weighting
H h ij ) Hij(MiMj)-1/2
(19a)
(15)
is the force on the ith component and
Hij ) ∂2E/∂Ri ∂Rj
H h xt ) UtλxUTt
6
The potential energy is expanded around the equilibrium geometry.
∂E
(18)
where UTt is the transpose of Ut. We then replace λt with the experimental value λx. This leads to the experimental biased Hessian defined as
H h xtUt ) Utλx
)( ) ]
Rv 6 ζ eζ(1-(R/Rv)) ζ-6 ζ-6 R
4. Hessian-Biased Method14
3N
-0.0220 0.1390 0.0240 -0.0230 -0.2420 0.2440 0.1200 1.0
ij
Table 3 gives the bond strength (well depth) Dv (in kcal/mol) and the bond length Rv (in Å) and ζ are given for C, S, and H. The electrostatic and van der Waals interactions are excluded for 1-2, 1-3, and 1-4 interactions since they are considered to be already included in the bond stretch, angle bend, and torsion terms.
E ) E0 +
-0.0200 -0.0260 0.0265 -0.0955 -0.1770 0.1885 0.0935 0.0
H h t ) UtλtUTt
(12)
where is the dielectric constant, Rij is the distance in Å, and the conversion factor C0 ) 332.0637 puts the energy in kcal/ mol. We take ) 1 (i.e., vacuum). 3.3. van der Waals Parameters. We used the van der Waals parameters16 previously determined from empirical fits to lattice parameters. The exponential-6 potential is used for van der Waals interactions:
EvdW ) Dv
cation
six of which have λi ) 0 (here 108.5913 converts units so that energies are in kcal/mol, distances in Å, masses in amu, and νi in cm-1). In the Hessian-biased method, the theoretical Hessian (Ht) is biased with the experimental frequencies. From (17) the theoretical Hessian can be written
QiQj
∑ij R
ECoulomb ) C0
2 4 4 4 4 4 4
neutral
(17)
The best organic superconductors involve ET molecules. Isotopic shift experiments show that the mechanism for superconductivity in these materials must involve electron-phonon interactions.8 In order to understand the mechanism of the superconductivity in these materials, we need to know the character of the phonon modes for the molecular crystals containing ET molecules. This requires a full characterization of the structures and vibrations of ET and ET+. To provide this characterization, we performed quantum mechanical calculations determining the optimum structures for ET and ET+. These results clarified the stable conformations of ET molecules and their symmetries and give vibrational frequencies (Table 4) consistent with the experiment. On the basis of the quantum mechanical results, we obtained MSX force field which accurately describes the vibrational spectrum. This force field
1978 J. Phys. Chem. A, Vol. 101, No. 10, 1997
Demiralp et al.
TABLE 3: Force-Field Parameters Used in This Calculationa vdW params16 H
R0 D0 ζ R0 D0
C bond stretch C3-H C3-C3 C2-C2 CR-CR
Rb kb Rb kb Rb kb Rb kb
angle bend H-C3-H C3-C3-H S32-C3-H S32-C3-C3 S32-C2-C2 SR-C2-C2
θ0 kθ θ0 kθ θ0 kθ θ0 kθ θ0 kθ θ0
angle cross terms H-C3-H C3-C3-H S32-C3-H S32-C3-C3 S32-C2-C2 SR-C2-C2
kR1θ kR2θ kR1R2 kR1θ kR2θ kR1R2 kR1θ kR2θ kR1R2 kR1θ kR2θ kR1R2 kR1θ kR2θ kR1R2 kR1θ kR2θ
torsion terms H-C3-C3-H S32-C3-C3-H S32-C3-C3-S32 S32-C2-C2-S32 SR-C2-C2-S32 SR-C2-C2-SR SR-CR-CR-SR C2-S32-C3-H C2-S32-C3-C3 C3-S32-C2-C2
a
V3 V3 V3 V2 V2 V2 V2 V3 V3 V2
vdW params16
3.19500 0.01520 12.38200 3.89830 0.09510 neutral
cation
bond stretch
1.084 636.386 1.526 613.257 1.300 1280.633 1.319 1120.168
1.081 636.530 1.523 606.042 1.329 1073.148 1.399 995.272
S32-C3
neutral
cation
109.12 92.818 110.79 80.057 107.44 74.392 114.35 193.274 121.64 96.121 113.62
108.65 72.886 110.38 109.365 105.85 60.653 113.57 364.201 127.48 77.349 115.72
neutral
cation
-75.260 -75.260 -38.305 7.847 3.295 1.546 48.635 18.933 -13.325 -0.964 -4.778 20.436 96.007 -47.517 10.424 178.792 81.403
-27.305 -27.305 -22.977 6.245 86.784 -0.226 39.139 -10.670 -0.371 -6.689 68.070 34.745 119.264 -31.109 -2.801 162.888 82.593
ζ R0 D0 ζ
S
S32-C2 SR-C2 SR-CR
Rb kb Rb kb Rb kb Rb kb
angle bend SR-C2-S32 SR-CR-CR SR-CR-SR C2-S32-C3 CR-SR-C2
kθ θ0 kθ θ0 kθ θ0 kθ θ0 k0 θ0 kθ
angle cross terms SR-C2-S32 SR-CR-CR SR-CR-SR C2-C32-C3 CR-SR-C2
neutral
cation
torsion terms
5.958 19.558 -73.125 -25.759 10.814 -44.726 -19.943 1.531 -2.586 0.720
7.164 9.641 -57.046 -3.196 -13.975 0.876 -0.217 0.684 -2.605 1.825
C3-C32-C2-SR CR-SR-C2-C2 CR-SR-C2-S32 C2SR-CR-CR C2-SR-CR-SR
kR1R2 kR1θ kR2θ kR1R2 kR1θ kR2θ kR1R2 kR1θ kR2θ kR1R2 kR1θ kR2θ kR1R2 kR1θ kR2θ kR1R2
V2 V2 V2 V3 V1 V2 V3 V2 V3
14.03400 4.03000 0.34400 12.00000 neutral
cation
1.821 312.535 1.827 361.172 1.788 836.525 1.736 483.850
1.825 304.720 1.766 479.499 1.753 674.396 1.721 547.649
neutral
cation
130.018 108.09 89.224 130.18 98.621 128.78 154.837 100.03 198.691 98.32 250.173
233.544 114.96 90.533 121.61 129.464 116.13 148.992 100.67 191.985 96.85 322.658
neutral
cation
408.025 54.907 113.414 86.875 40.592 36.508 63.775 79.702 79.702 60.025 49.887 46.465 -11.975 52.029 59.718 10.704
264.133 35.455 135.257 91.696 69.328 104.725 29.613 126.993 126.993 19.556 148.984 33.800 -69.191 124.512 43.796 25.593
neutral
cation
-0.020 2.764 -0.774 1.845 6.756 0.844 -0.350 1.175 2.127
0.170 -3.149 -4.459 0.000 12.840 0.263 0.000 -1.393 0.000
inversion constant (Kω)
neutral
cation
inversion constant (Kω)
neutral
cation
C2-SR-S32-C2 C2-SR-C2-S32 C2-S32-C2-SR
5.738 85.778 6.745
4.917 155.854 1.651
CR-SR-SR-CR CR-SR-CR-SR
10.713 53.616
16.128 50.178
Units are kcal/mol for energies, Å for length, and degrees for angles. Angular force constants use radians.
can be used in molecular dynamic simulations for crystals containing ET and ET+. This should be useful in explaining the superconductivity of these systems.
are more symmetric (D2 symmetry). This may be important in the superconducting properties.
We find that some vibrational modes of staggered ET molecule (C2 symmetry) allow both IR and Raman activities. This allows the electrons coupling several vibrational modes which would be forbidden for planar donor molecules which
6. Summary We developed the MSX force fields for the neutral and cation ET molecules including both valence and nonbonded interactions. The Hessian-biased approach is used to obtain a force
Force Field and Vibrational Frequencies for BEDT-TTF
J. Phys. Chem. A, Vol. 101, No. 10, 1997 1979
TABLE 4: Calculated (HF) and Experimental Frequencies and Raman and Infrared (IR) Intensities for ETa HF intensity sym A B A B A B A B A B A A B A B A B A B A B A B A B A B A A B B A B A B B* B A A B A B B B A A B A B A B B A A A B A B A B A B A A A B B A B A B A av abs error a
modes
νi
IR
Raman
C-H str C-H str C-H str C-H str C-H str C-H str C-H str C-H str CdC str CdC str CdC str CH2 bend CH2 bend CH2 bend CH2 bend CH2 wag CH2 wag CH2 wag CH2 wag CH2 twist CH2 twist CH2 twist CH2 twist ring def (IP)c ring def (IP) ring def (IP) C-C str C-C str CH2 rock CH2 rock CH2 wag CH2 wag ring def (IP) ring def (IP) ring def (IP) ring def (IP) ring def (IP) ring def (IP) CH2 rock CH2 rock CH2 rock CH2 rock ring def (OP)d ring def (OP) ring def (OP) ring def (OP) ring def (IP) ring def (IP) ring def (IP) ring def (IP) ring def (IP) ring def (IP) ring def (IP) ring def (IP) ring def (OP) ring def (OP) ring def (OP) ring def (OP) ring def (OP) ring def (IP) ring def (OP) ring def (OP) ring def (OP) ring def (IP) ring def (OP) ring def (OP) ring def (IP) ring def (OP) ring def (OP) ring def (OP) ring def (OP) ring def (OP)
3302 3302 3290 3290 3237 3237 3229 3228 1815 1790 1772 1608 1608 1594 1594 1466 1466 1434 1434 1321 1321 1260 1260 1131 1128 1125 1093 1093 1033 1033 996 990 967 967 951 847 846 842 759 759 716 716 623 606 605 539 511 510 496 483 425 394 393 383 356 327 315 309 300 286 270 262 206 173 130 129 60 53 44 42 38 20
11.60 3.28 0.01 0.37 0.20 79.71 10.24 2.68 0.57 1.48 0.35 3.02 1.11 11.27 4.86 2.41 63.72 5.66 0.90 0.27 0.06 2.48 2.44 0.21 7.06 0.01 0.03 0.01 1.64 22.58 12.99 5.72 28.10 3.50 2.29 12.03 42.37 0.17 0.10 2.47 0.02 6.70 4.54 0.06 0.05 1.50 1.50 0.03 6.24 0.01 6.63 0.04 0.02 0.09 1.02 3.16 0.04 0.28 0.04 3.72 0.01 4.45 0.01 0.03 0.03 0.00 1.14 0.16 2.71 7.24 0.26 2.21
71.75 51.36 256.30 9.60 606.22 4.30 161.39 6.80 354.11 0.26 509.60 10.70 14.73 9.51 32.12 0.93 1.71 1.19 0.57 15.70 2.33 0.29 14.41 0.34 0.02 0.59 0.61 7.15 7.62 5.39 1.83 0.04 0.77 1.81 0.28 0.13 0.02 1.96 15.90 1.86 44.08 0.62 11.88 4.15 0.92 15.60 0.86 1.73 0.43 14.54 1.16 0.80 0.10 8.42 4.00 0.17 2.72 0.05 0.20 0.02 0.75 0.61 0.72 14.86 0.18 0.28 0.87 0.19 0.37 0.26 0.63 1.28
109
experiment IR
Raman
2958 wb
2958 w
1505 w
2916 w 1552 m 1511 m 1494 s
1420 w 1406 m 1409 vw 1285 vw 1282 m 1259 w 1253 vw
1256 Vw
1173 vw 1132 sh 1125 w
1175 Vw 1132 Vw 1126 vw 1016 vw
996 w 987 w
1002 w 990 w
938 vw 917 s 919 vw 905 m 890 m 875 vw 772 s 860 vw
911 vw 888 vw 875 w 765 w 860 Vw 687 w
687 w 653 m 653 w
486 m 499 m 625 w 624 w 450 w 390 m
440 m 334 m
335 m 278 m
348 w 308 w 272 vw
257 m
260 w 159 s 151 s 127 vw
96 m
30 w
31 vs
MSX 2957.9 2957.9 2915.0 2915.0 2958.3 2958.3 2909.8 2909.8 1546.9 1519.5 1490.0 1424.3 1424.3 1401.4 1401.4 1295.0 1295.0 1247.4 1247.4 1164.2 1164.2 1127.4 1127.4 1029.5 1013.0 1009.3 998.6 998.6 948.1 948.1 915.5 915.5 900.0 899.6 854.1 758.6 761.6 824.4 726.8 724.9 629.9 628.9 724.9 453.3 449.6 502.3 481.3 668.6 667.8 446.0 389.3 361.6 373.4 347.3 303.0 288.1 361.9 269.8 261.4 264.9 177.1 177.0 183.5 153.6 127.0 62.2 98.1 53.1 46.7 45.2 36.9 15.7
error 0
0 6 5 9 4 4 5 8 10 13 12 9 11 5 2 13 3 9 10 1 3 5 11 36 16 10 36 40 38 23 24
16 18 44 44 6 1 28 38 1 5 10
8 25 3 0 2
7 13
The frequencies are in cm-1, IR intensities are in km/mol (1 km/mol ) 0.0236 66 D2 Å-2 amu-1), Raman intensities are in Å4/amu. We used the italic ones (the assignments of Kozlov9) for the error calculations for the modes which appears both in IR and Raman spectra. b Relative intensities: vs, very strong; s, strong; m, medium; w, weak; vw, very wak; sh, shoulder; br, broad. c In-plane ring deformation mode. d Out-of-plane ring deformation mode.
1980 J. Phys. Chem. A, Vol. 101, No. 10, 1997
Demiralp et al.
TABLE 5: Calculated and Experimental Frequencies and Raman and Infrared (IR) Intensities for ET+a HF intensity sym B3 B2 A B1 A B1 B2 B3 A B1 A B1 B3 B2 A A B1 B3 B2 A B1 B3 B2 B3 B2 B3 A B1 A B1 B2 B3 B2 A B1 B1 B2 B3 B3 B2 A B1 B1 A2 B2 A B3 B2 B1 A B1 B2 B3 B3 B3 A B1 B2 B2 B3 A B1 B3 A A B1 B2 B2 B3 B2 A B3 av abs error a
modes C-H str C-H str C-H str C-H str C-H str C-H str C-H str C-H str CdC str CdC str CH2 bend CH2 bend CH2 bend CH2 bend CdC str CH2 wag CH2 wag CH2 wag CH2 wag CH2 twist CH2 twist CH2 twist CH2 twist ring def (IP)c ring def (IP) ring def (IP) C-C str. C-C str CH2 rock CH2 rock CH2 wag CH2 wag ring def (IP) ring def (IP) ring def (IP) ring def (IP) ring def (IP) ring def (IP) CH2 rock CH2 rock CH2 rock CH2 rock ring def (OP)d ring def (OP) ring def (OP) ring def (IP) ring def (IP) ring def (IP) ring def (IP) ring def (IP) ring def (IP) ring def (IP) ring def (IP) ring def (IP) ring def (OP) ring def (IP) ring def (IP) ring def (OP) ring def (IP) ring def (OP) CH2 wag CH2 wag ring def (IP) ring def (IP) ring def (OP) ring def (OP) ring def (OP) ring def (IP) ring def (OP) ring def (OP) ring def (OP) ring def (OP)
νi 3316 3316 3305 3305 3248 3248 3242 3242 1697 1620 1601 1601 1594 1594 1565 1469 1467 1435 1435 1325 1325 1264 1264 1171 1141 1138 1093 1093 1029 1029 997 991 969 963 927 881 857 853 749 749 707 706 610 607 596 570 514 512 504 492 438 392 387 371 357 348 328 309 295 294 294 283 187 175 120 120 86 61 49 43 36 28 121
IR 1.41 0.21 0.00 2.13 0.00 24.15 0.29 5.22 0.00 3060.40 0.00 5.04 23.93 4.55 0.00 0.00 209.74 7.32 0.00 0.00 1.47 1.38 2.21 0.25 16.86 0.10 0.00 0.30 0.00 5.24 0.04 8.04 4.06 0.00 5.84 5.86 6.11 0.29 0.00 4.23 0.00 36.60 0.01 0.00 0.02 0.00 0.35 2.91 605.79 0.00 3.85 0.49 0.06 0.00 1.70 0.00 21.53 0.52 4.79 0.07 0.00 0.00 0.01 0.00 0.00 0.48 0.07 0.16 8.93 0.02 0.00 2.04
experiment Raman
90.73 86.51 251.75 0.57 1086.34 1.76 13.57 179.42 60707.55 1.32 24.83 4.97 6.92 56.09 34573.66 279.93 1.47 3.71 0.72 16.62 2.08 1.56 18.511 623.99 0.06 5.88 31.22 0.61 247.37 5.10 2.42 0.00 74.29 7905.13 225.12 956.10 0.09 3.72 13.32 2.77 339.78 0.04 3.23 14.03 6.19 5148.20 0.04 1.11 0.00 2986.58 0.05 0.2 4.84 93.14 0.21 4.39 0.04 3.25 0.01 0.32 0.32 0.07 3.46 185.20 6.81 0.57 16.63 0.00 0.29 0.17 0.00 0.02
IR 2936
Raman
wb
2914 vw 2847 vw ? 2883 w 1455 m 1445 w 1422 sh 1411 s 1431 vs 1294 vw 1283 m 1274 vw 1277 sh 1180 w ? 1125 sh ? 1120 w 1056 w 1024 w 976 mw 1010 vw 931 vw ? 915 w 900 w 905 w 812 w 886 w,br 640 vw 672 vw
511 mw 503 w 489 m 406 w 357 vw 335 w
355 Vw 320 w
265 w
169 w
MSX
error
2935.9 2935.9 2916.5 2916.5 2871.1 2871.1 2857.5 2857.5 1496.0 1457.7 1422.2 1422.2 1416.4 1416.4 1385.1 1285.5 1485.3 1263.6 1263.6 1173.5 1173.5 1135.0 1135.0 1059.4 1026.3 1025.6 991.2 991.2 952.3 936.4 935.7 887.1 895.7 885.0 950.9 826.0 841.1 839.3 691.6 691.6 686.4 684.9 636.0 636.0 581.2 512.9 487.1 476.5 512.0 453.9 397.6 344.6 387.0 349.14 340.3 335.2 339.7 272.7 335.2 282.2 234.0 219.5 179.8 162.8 83.6 83.1 70.3 53.6 46.1 34.4 19.8 8.4
0 2 25 41 13 0 5 46 8 2 10 13
15 3 2 15 19 21 4 20 14 45 52 13
2 9 35 8 32 14 15 8
6
16
The frequencies are in cm-1, IR intensities are in km/mol (1 km/mol ) 0.0236 66 D2 Å-2 amu-1) 42.2547, Raman intensities are in Å4/amu. We used the italic ones (the assignments of Kozlov10) for the error calculations for the modes which appears both in IR and Raman spectra. ?: These experimentally uncertain modes are not included in error calculations.10 b Relative intensities: vs, very strong; s, strong; m, medium; w, weak; vw, very weak; sh, shoulder; br, broad. c In-plane ring deformation mode. d Out-of-plane ring deformation mode.
Force Field and Vibrational Frequencies for BEDT-TTF
Figure 2. Side view for optimum structures (a) ET+ and (b) ET. Here C is a solid circle, S is a cross-hatched circle, and H is an open circle.
field which reproduces experimental frequencies for the neutral and cation ET while retaining the correct structural and vibrational characteristics for the models. The calculated frequencies are in good agreement with the available experimental frequencies for the neutral and cation ET molecules. This should be useful in characterizing the superconductors. Acknowledgment. This research was supported by the NSF (CHE 95-22179 and ASC 92-17368). The facilities of the MSC are also supported by grants from DOE-AICD. Chevron Petroleum Technology, Asahi Chemical, Chevron Chemical Co., Hercules, Avery Dennison, Chevron Refinery Technology, and the Beckman Institute. Some of these calculations were carried out at Pittsburgh NSF Supercomputer Center and on the JPL Cray computers. References and Notes (1) Jerome, D.; Mazaud, A.; Ribault, M.; Bechgaard, K. J. Phys. Lett. 1980, 41, L95.
J. Phys. Chem. A, Vol. 101, No. 10, 1997 1981 (2) Yamaji, K. Solid State Commun. 1987, 61, 413. (3) Carlson, K. D.; Williams, J. M.; Geiser, U.; Kini, A. M.; Wang, H. H.; Klemm, R. A.; Kumar, S. K.; Schlueter, J. A.; Ferraro, J. R.; Lykke, K. R.; Wurz, P.; Parker, H.; Sutin, J. D. B. Mol. Crsyt. Liq. Cryst. 1993, 234, 127. (4) Carlson, K. D.; Kini, A. M.; Klemm, R. A.; Wang, H. H.; Williams, J. M.; Geiser, U.; Kumar, S. K.; Ferraro, J. R.; Lykke, K. R.; Wurz, P.; Fleshler, S.; Dudek, J. D.; Eastman, N. L.; Mobley, P. R.; Seaman, J. M.; Sutin, J. D. B.; Yaconi, G. A. Inorg. Chem. 1992, 31, 3346. (5) Carlson, K. D.; Kini, A. M.; Schlueter, J. A.; Wang, H. H.; Sutin, J. D. B.; Williams, J. M.; Schirber, J. E.; Venturini, E. L.; Bayless, W. R. Physica C 1994, 227, 10. (6) Carlson, K. D.; Williams, J. M.; Geiser, U.; Kini, A. M.; Wang, H. H.; Klemm, R. A.; Kumar, S. K.; Schlueter, J. A.; Ferraro, J. R.; Lyyke, K. R.; Wurz, P.; Parker, D. H.; Sutin, J. D. B. Mol. Cryst. Liq. Cryst. 1993, 234, 127. (7) Demiralp, E.; Goddard, III, W. A. Synth. Met. 1995, 72, 297. (8) Demiralp, E.; Dasgupta, S.; Goddard, W. A., III J. Am. Chem. Soc. 1995, 117, 8154. (9) Kozlov, M. E.; Pokhodnia, K. I.; Yurchencko, A. A. Spectrochim. Acta 1989, 45A, 323. (10) Kozlov, M. E.; Pokhodnia, K. I.; Yurchencko, A. A. Spectrochim. Acta 1989, 45A, 437. (11) Kobayashi, H.; Kobayashi, A.; Yukiyoshi, S.; Saito, G.; Inkuchi, H. Bull. Chem. Soc. Jpn. 1986, 59, 301. (12) Williams, J. M.; Ferraro, J. R.; Carlson, K. D.; Geiser, U.; Wang, H. H.; Kini, A. M.; Whangbo, M-H, Organic Superconductors (Including Fullerenes): synthesis, structure, properties, and theory; Prentice-Hall: New York, 1992. (13) The quantum chemical calculations were carried out using: Gaussian 92, Revision B; Frisch, M. J.; Trucks, G. W.; Head-Gordon, M.; Gill, P. M. W.; Wong, M. W.; Foresman, J. B.; Johnson, B. G.; Schlegel, H. B.; Robb, M. A.; Replogle, E. S.; Gomperts, R.; Andres, J. L.; Raghavachari, K.; Binkley, J. S.; Gonzalez, C.; Martin, R. L.; Fox, D. J.; Defrees, D. J.; Baker, J.; Stewart, J. J. P.; Pople, J. A. Gaussian, Inc.: Pittsburgh, PA, 1992. (14) Dasgupta, S.; Goddard, W. A., III J. Phys. Chem. 1989, 95, 7207. (15) (a) Ringnalda, M. N.; Langlois, J-M.; Greeley, B. H.; Russo, T. V.; Muller, R. P.; Marten, B.; Won, Y.; Donnelly, Jr., R. E.; Pollard, W. T.; Miller, G. H.; Goddard, W. A., III; Freisner, R. A. PS-GVB v1.0, Schro¨dinger, Inc., Pasadena, CA, 1994. (b) Greeley, B. H.; Russo, T. V.; Mainz, D. T.; Friesner, R. A.; Langlois, J-M.; Goddard, W. A., III; Donnelly, R. E.; Ringnalda, M. N. J. Chem. Phys. 1996, 101, 4028. (16) Mayo, S. L.; Olafson, B. D.; Goddard, W. A., III J. Phys. Chem. 1990, 94, 8897. (17) Eldridge, J. E.; Homes, C. C.; Wang, H. H.; Kini, A. M.; Williams, J. M. Synth. Met. 1995, 70, 983.
