Theoretical study of the molecular structure and the stability of neutral and reduced tetracyanoethylene

Chemical Physics Letters 375 (2003) 376–382 www.elsevier.com/locate/cplett

Theoretical study of the molecular structure and the stability of neutral and reduced tetracyanoethylene Bego~ na Mili an, Rosendo Pou-Amerigo *, Rafael Viruela, Enrique Ortı Departament de Quımica Fısica, Institut de Ci encia Molecular, Universitat de Val encia, Dr. Moliner 50, Burjassot, Val encia ES-46100, Spain Received 12 March 2003; in final form 13 May 2003 Published online:

Abstract The molecular structure and the stability of neutral, anionic, and dianionic tetracyanoethylene (TCNE) have been studied with MP2, coupled-cluster (CC), and density functional theory (DFT) procedures. The optimized geometries are in agreement with the available experimental data, although significant deviations for the CBN bond distance have been obtained at the MP2 level. The adiabatic electron affinity of TCNE calculated with the B3LYP method is overestimated by 0.32 eV. In the light of the CC results, the source of such an overestimation is suggested to lie on the theoretical approach, rather than on a too low experimental value. Ó 2003 Elsevier Science B.V. All rights reserved.

1. Introduction Electron-donor and electron-acceptor molecules have become key compounds in molecular materials chemistry, where they are used as electroactive building blocks. A thorough characterization of such species is a crucial step for the understanding of the interesting bulk properties exhibited by the systems in which they take part, as well as for the design of novel materials with enhanced characteristics. From a theoretical point of view, the determination of the ionization potential of electron donors is not usually a challenging problem. However, the accurate calculation of the electron

*

Corresponding author. Fax: +34-963-543-156. E-mail address: [email protected] (R. Pou-Amerigo).

affinity of electron acceptors requires considerable computational efforts, because the use of large oneelectron basis sets and a balanced incorporation of the electron correlation effects are mandatory [1,2]. For small molecules, ab initio methodologies such as coupled-cluster (CC) procedures have achieved a high degree of accuracy. However, their applicability to compounds of increasing size is severely hampered by computational limitations. In this sense, density functional theory (DFT) has emerged as a promising alternative. It has been demonstrated that DFT methods can be successfully applied to predict molecular electron affinities at a low computational cost, and, in most cases, the predicted results are within 0.2 eV or better of experiment [2]. Despite such an achievement, the performance of DFT has been shown to be quite poor for sev-

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eral systems [2]. Tetracyanoethylene (TCNE) is a well-known example. This compound is one of the most powerful organic electron acceptors, and it can be considered as the prototype of cyano-based acceptors such as 7,7,8,8-tetracyano-p-quinodimethane (TCNQ). These molecules form chargetransfer complexes and salts which have found a plethora of applications in the development of molecule-based conductors [3] and magnets [4]. The electron affinity of TCNE has been determined to be 3.17  0.2 eV from gas-phase electrontransfer equilibria [5]. Brown et al. [6] showed that DFT calculations overestimate this value by an average of 0.5 eV. Brinkmann et al. [7] analyzed whether this large deviation might be explained by a twisting of the structure of the anion and discarded such a possibility. Thus, they proposed that further CC calculations would be very useful in order to establish whether the discrepancy is due to the limitations of the DFT approach or if the experimental value is too low and needs to be redetermined. With the aim of giving an insight into this open question, we present here a theoretical study of the electron affinity of TCNE, including DFT and CC calculations. The equilibrium geometries and the stability of neutral and reduced (anion and dianion) TCNE have been analyzed.

2. Computational details Geometrical parameters and electron affinities have been computed by using DFT, second-order Møller–Plesset perturbation theory (MP2), and CC methods. For the DFT calculations, the B3LYP hybrid functional has been employed [8,9]. It has been shown to be an excellent choice for electron affinity predictions [2] and it properly reproduces structural parameters of cyanosubstituted ethylenes [7]. TCNE was computed using spin-unrestricted UB3LYP wave functions. Restricted and unrestricted MP2 calculations have been performed for the closed- and openshell systems, respectively. The projected MP2 method (PMP2), in which the major spin contaminating component is projected, has been also employed for the anion. As regards the CC

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methods, the coupled-cluster singles and doubles approach (CCSD) [10] has been utilized. Additional single-point calculations have been carried out with the CCSD(T) method, which includes a perturbational estimate of the effects of connected triple excitations [11]. The calculations have been performed with the correlation-consistent cc-pVDZ and aug-cc-pVDZ basis sets [12,13]. Neutral and monoanion TCNE possess D2h planar molecular structures, as it has been established both experimentally [14–17] and theoretically [7,18–21]. Hence, geometry optimizations for such species have been performed within D2h symmetry. For the dianion, the molecular structure determined by X-ray crystallographic analysis corresponds, however, to a twisted conformation, with two nearly perpendicular C(CN)2 groups [18,22]. The occurrence of a non-planar equilibrium structure has been confirmed by theoretical calculations, which predict a perpendicular D2d arrangement as the most stable conformation [18,19,21,23]. Thus, geometry optimizations have been carried out, in this case, by allowing the rotation around the central CAC bond. Standard orientations have been used for molecular axes. Adiabatic electron affinities were calculated as the energy difference between the neutral molecule and the anion at their respective optimized geometries. Calculations were performed with GA U S S I A N 98 [24].

3. Results and discussion 3.1. Molecular structure The optimized geometrical parameters computed at different levels of calculation for the neutral and anionic forms of TCNE are reported in Table 1, and correspond to the definitions pictured in Fig. 1. Available experimental data are also included for the sake of comparison. The analysis of the theoretical results reveals that the addition of diffuse functions to the cc-pVDZ basis set does not significantly affect the computed geometries.

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Table 1  and bond Geometrical parameters of TCNE, TCNE , and TCNE2 optimized at different levels of calculation (bond lengths in A angles in degrees) Parameter

Species

Level of calculation

Exp.

MP2/ cc-pVDZ

MP2/ aug-ccpVDZ

B3LYP/ B3LYP/ cc-pVDZ aug-ccpVDZ

CCSD/ aug-ccpVDZ

GEDa

XRDb

NDc

r1 (C@C)

Neutral Anion Dianion

1.381 1.440 1.495

1.382 1.440 1.494

1.373 1.443 1.505

1.373 1.442 1.502

1.367 1.440 1.500

1.357 – –

1.358d , 1.357e 1.392f , 1.423g 1.49i , 1.488j

1.355d , 1.353e 1.429h –

r2 (CAC)

Neutral Anion Dianion

1.437 1.426 1.419

1.437 1.426 1.415

1.432 1.416 1.411

1.432 1.415 1.406

1.451 1.431 1.422

1.435 – –

1.431d , 1.439e 1.417f , 1.418g 1.392i , 1.399j

1.431d , 1.435e 1.406h –

r3 (CBN)

Neutral Anion Dianion

1.191 1.164 1.183

1.192 1.166 1.206

1.164 1.172 1.183

1.162 1.171 1.183

1.171 1.179 1.190

1.162 – –

1.166d , 1.183e 1.140f , 1.155g 1.166i , 1.159j

1.160d , 1.173e 1.170h –

h1 (CAC@C)

Neutral Anion Dianion

120.9 121.0 121.6

120.7 121.0 121.3

121.5 121.6 121.4

121.5 121.7 121.3

121.3 121.5 121.7

121.1 – –

121.2e 121.2f , 121.0g 121.5i , 121.4j

121.9d , 121.1e 120.7h –

h2 (CACBN)

Neutral Anion Dianion

179.6 179.6 180.2

179.9 179.8 180.5

179.0 179.3 180.3

179.0 179.1 180.5

179.6 179.7 180.2

180.0k – –

179.1e 178.1f ;g 177.6i , 178.5j

177.9d , 179.1e 179.0h –

Available experimental data are also included. Values obtained from gas-phase electron diffraction analysis; Ref. [25]. b Values obtained from X-ray diffraction analysis. c Values obtained from neutron diffraction analysis. d Cubic phase; Ref. [15]. e Monoclinic phase; Ref. [26]. f Ref. [16]. g Ref. [31]. h Ref. [17]. i Ref. [18]. Dihedral angle between the C(CN)2 groups: 87.1°. j Ref. [22]. Dihedral angle between the C(CN)2 groups: 76.6°. k Assumed value. a

Fig. 1. Structural parameters of TCNE.

3.1.1. Neutral TCNE The optimized geometrical parameters for the neutral molecule compare well with the experimental data derived from gas-phase electron dif-

fraction measurements [25]. The bond lengths computed with the DFT method show the smallest  with the augmented basis average error, 0.006 A set. The corresponding errors for the CCSD and MP2 procedures are somewhat larger, 0.012 and , respectively. The most severe deviations 0.019 A between the different theoretical results are observed for the CBN bond distance; whereas the ) value calculated at the B3LYP level (1.162 A agrees with the experimental datum, that com) is overestimated puted at the MP2 level (1.192 A  by 0.030 A. Such a magnitude is particularly sensitive not only to the theoretical approach, but also to the experimental method employed for its

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determination. The CBN bond length determined ) is, for instance, by electron diffraction (1.162 A considerably shorter than that provided by X-ray diffraction analysis of the monoclinic phase of  [26]). The former value is, howTCNE (1.183 A ever, comparable to the distances reported for other molecules containing the nitrile moiety, such  [27]), HCN (1.156 A  as cyanoethylene (1.164 A  [29]). [28]), and benzonitrile (1.158 A In order to check whether the MP2 procedure is actually overestimating r3 , additional test calculations were performed for HCN, a system with a  [28]. The well-known CBN bond distance, 1.156 A values computed at the B3LYP and MP2 levels are , respectively (aug-cc-pVDZ 1.161 and 1.179 A basis set). Therefore, they corroborate the ability of the DFT method to yield accurate CBN bond lengths, as well as the incorrect treatment offered by the MP2 approach, which tends to overestimate such a parameter. As regards the bond angles, all theoretical results are in close agreement with each other and reproduce well the experimental findings. The values computed for h1 are within one degree of the angle reported in the electron diffraction study. The CACBN segment is predicted to deviate slightly from linearity. Such a behaviour is in accordance with the conclusions obtained through X-ray and neutron diffraction measurements [14,15,26]. 3.1.2. Reduced TCNE The computed structural parameters of TCNE significantly change upon addition of an electron (cf. Table 1). The r1 bond distance undergoes the , largest variation; it lengthens by about 0.06–0.07 A  whereas the r2 bond length shortens by 0.01–0.02 A. The CBN bond distance (r3 ) becomes 0.008–0.009  longer (DFT and CC calculations), although, at A  shorter. Since the the MP2 level, it becomes 0.026 A MP2, DFT, and CC r3 values for the anion are similar, the calculated shortening should be attributed to the incorrect CBN bond distance provided by the MP2 method for the neutral system. The geometrical modifications that occur upon reduction of TCNE can be easily explained on the basis of the topology of the lowest unoccupied molecular orbital (LUMO), depicted in Fig. 2. The LUMO belongs to the b2g symmetry and exhibits

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Fig. 2. Electronic density contours (0.03 e/bohr3 ) calculated for the LUMO of TCNE at the B3LYP/aug-cc-pVDZ level.

antibonding character over the C@C and CBN bonds and bonding character over the CAC bonds. Consequently, the electron attachment is expected to lengthen the multiple bonds and shorten the single ones. The computed parameters compare well with the experimental data derived from neutron diffraction analysis (see Table 1). Again, the B3LYP results exhibit the smallest average deviation for  (augmented basis set). the bond lengths: 0.008 A The calculated bond angles are within one degree of the experimental results, and they do not substantially change with respect to the angles found for the neutral molecule. The comparison with X-ray crystallographic data is more troublesome because the experimental values show, in some cases, large differences. For instance, the X-ray values reported for the CBN bond length are considerably shorter than the neutron-diffraction value and even shorter than the distance determined for the neutral molecule. However, it should be mentioned that the determination of the CBN bond distance in X-ray diffraction experiments is known to be particularly difficult and, therefore, the significance and accuracy of such a result is hard to establish [18]. When the system is further reduced by adding a second electron, the molecular structure is strongly modified. The optimization leads to a D2d twisted equilibrium geometry for the dianion, irrespective

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Table 2 Calculated energy difference between the D2h planar and the D2d twisted conformations of TCNE2 Level of calculation

E(D2h )–E(D2d ) (eV)

MP2/cc-pVDZ MP2/aug-cc-pVDZ B3LYP/cc-pVDZ B3LYP/aug-cc-pVDZ CCSD/aug-cc-pVDZ//B3LYP geom.a CCSD(T)/aug-cc-pVDZ//B3LYP geom.a

0.41 0.38 0.34 0.35 0.41 0.39

a

Single-point calculations carried out at the B3LYP/aug-ccpVDZ optimized geometries.

of the approach employed. This is in agreement with the results reported in previous theoretical studies [18,19,21,23] and is compatible with the available experimental information. X-ray crystallographic analyses of two charge-transfer salts containing TCNE2 showed that the C(CN)2 groups of the dianion were nearly perpendicular to each other, with dihedral angles of 87.1° [18] and 76.6° [22]. The energy differences between the planar and the 90°-twisted nuclear arrangements, computed with several methodologies, are collected in Table 2. The D2d conformation is predicted to be about 0.4 eV (9 kcal/mol) more stable than the D2h planar structure. The effect of increasing the negative charge on the bond lengths is illustrated in Table 1. The r1  with respect to bond distance elongates ca. 0.06 A the value calculated for the monoanion, whereas r2 . The CBN bond disis shortened by ca. 0.01 A  at the DFT and CC tance lengthens by ca. 0.01 A levels, showing larger elongations when the MP2 procedure is used. For the dianion, the only experimental data available are those derived from X-ray experiments [18,22]. The theoretical values compare well with the X-ray data, although the deviations for the CBN distance are, as expected, somewhat larger. 3.2. Electron affinity The results obtained for the adiabatic electron affinity (AEA) of TCNE at different levels of calculation are collected in Table 3.

Table 3 AEA obtained at different levels of calculation Level of calculation

AEA (eV)

MP2/cc-pVDZ MP2/aug-cc-pVDZ PMP2/cc-pVDZ PMP2/aug-cc-pVDZ B3LYP/cc-pVDZ B3LYP/aug-cc-pVDZ CCSD/aug-cc-pVDZ CCSD/aug-cc-pVDZ//B3LYP geom.a CCSD(T)/aug-cc-pVDZ//B3LYP geom.a Exp.b

1.70 2.17 2.18 2.65 3.10 3.49 2.99 3.00 2.94 3.17  0.2

a Single-point calculations carried out at the B3LYP/aug-ccpVDZ optimized geometries. b Ref. [5].

Unlike the geometrical parameters, the electron affinity is very sensitive to the inclusion of diffuse functions in the basis set. The values computed with the cc-pVDZ basis set are about 0.4–0.5 eV smaller than those calculated with the augmented one. The inclusion of diffuse functions is a wellknown requirement when a proper description of the electronic structure of an anion is pursued [1,2]. The MP2 procedure underestimates the electron affinity by 1 eV (aug-cc-pVDZ basis set), although an expectation value of S2 of 0.97 was found in the calculation of TCNE . Upon projection of the major spin contaminating component, such an expectation value reduces to 0.81 and the error in the computed electron affinity to ca. 0.5 eV, i.e., a smaller but still significant value. With the B3LYP procedure and the large basis set, the calculated AEA, 3.49 eV, is 0.32 eV larger than the experimental value. Such an overestimation is in accordance with the conclusions previously reported by Brown et al. [6]. In order to establish whether the overestimation is a consequence of the limitations of the DFT method or if the source of error might be the experimental value, CC calculations were carried out. The AEA computed at the CCSD level is found to be 2.99 eV, 0.50 eV smaller than the B3LYP result, and lies within the interval determined experimentally, 3.17  0.2 eV. To analyze if the large difference between the CC and DFT values comes from the

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use of different geometrical parameters, singlepoint CCSD calculations at the B3LYP optimized geometries were additionally performed. The change on the computed AEA was found to be negligible (cf. Table 3), revealing that this is not the reason for the discrepancy. Additional singlepoint calculations at the B3LYP geometries were also performed at the CCSD(T) level and the AEA was computed to be 2.94 eV. The results obtained with the CC methodologies confirm that the B3LYP method is overestimating the AEA of TCNE and, therefore, the source of the deviation with respect to the experimental datum should be attributed to defects on the DFT approach. Rienstra-Kiracofe et al. [2] showed that the performance of DFT for AEA predictions when the neutral species is closed shell, as it happens here, is quite poor. In such cases, it was found that the average absolute error obtained for B3LYP electron affinities was 0.30 eV. The error obtained in the present work, 0.32 eV, is perfectly comparable to this value. Furthermore, the CC results do not give support to the hypothesis suggesting that the experimental value for the electron affinity of TCNE might be too low [6,7]. In this sense, it should be mentioned that the electron affinity obtained from the magnetron method (2.88  0.06 eV) [30] is even lower than the value determined from the electron-transfer equilibria. Incidentally, the magnetron result agrees with the best theoretical estimate reported in the present work, 2.94 eV. As far as the doubly charged species is concerned, it is computed to lie higher in energy than the corresponding monoanion, irrespective of the theoretical method employed. Therefore, in the conditions in which the calculations have been performed, that is, in vacuo, the dianion is predicted to be unstable with respect to electron detachment.

4. Conclusions The molecular structures of and dianionic TCNE optimized and CCSD methods agree with perimental data. However, the

neutral, anionic, with the B3LYP the available exMP2 procedure

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does not properly describe the CBN bond length. The dianion is predicted to exhibit a D2d twisted conformation 9 kcal/mol more stable than the D2h planar structure. As regards the adiabatic electron affinity of TCNE, the PMP2 procedure yields an underestimation of ca. 0.5 eV with respect to the experimental datum, whereas the B3LYP method overestimates such a property by 0.32 eV. The result obtained at the CCSD level, 2.99 eV, lies within the experimental interval. Accurate values for the AEA have been also obtained by performing single-point CCSD and CCSD(T) calculations at the B3LYP optimized geometries. This strategy represents a valuable alternative for large electron-acceptor molecules, where geometry optimizations at highly correlated levels would be prohibitive. The AEA estimates obtained with CC methodologies suggest that the theoretical approach is responsible for the overestimation found at the DFT level.

Acknowledgements This work was supported by the Ministerio de Ciencia y Tecnologıa of Spain through the Projects PB98-1447 and BQU2002-10656-E. B.M. acknowledges the Ministerio de Educaci on, Cultura y Deporte of Spain for a doctoral grant.

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