Comparative Parametric Method 6 (PM6) and Recife Model 1 (RM1) Study of Trans-Stilbene A

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Molecular Simulation Publication details, including instructions for authors and subscription information: http://www.tandfonline.com/loi/gmos20 Comparative parametric method 6 (PM6) and Recife model 1 (RM1) study of trans-stilbene A. Camilo Jr. a , R. P.B. dos Santos b c , V. R. Coluci d & D. S. Galvão c a Departamento de Física, Universidade Estadual de Ponta Grossa, 84010-330, Ponta Grossa, Paraná, Brazil b Universidade Estadual de Maringá, (UEM), 87020-900, Maringá, Paraná, Brazil c Instituto de Física “Gleb Wataghin”, Universidade Estadual de Campinas, Caixa Postal 6165, 13083-970, Campinas, São Paulo, Brazil d Faculdade de Tecnologia, Universidade Estadual de Campinas, 13484-332, Limeira, São Paulo, Brazil Available online: 15 Aug 2011

To cite this article: A. Camilo Jr., R. P.B. dos Santos, V. R. Coluci & D. S. Galvão (2011): Comparative parametric method 6 (PM6) and Recife model 1 (RM1) study of trans-stilbene, Molecular Simulation, DOI:10.1080/08927022.2011.597392 To link to this article: http://dx.doi.org/10.1080/08927022.2011.597392

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Comparative parametric method 6 (PM6) and Recife model 1 (RM1) study of trans-stilbene A. Camilo, Jr.a1, R.P.B. dos Santosb,c*, V.R. Colucid2 and D.S. Galvaõc3 aDepartamento de Fı´sica, Universidade Estadual de Ponta Grossa, 84010-330, Ponta Grossa, Parana´, Brazil; bUniversidade Estadual de Maringa´, (UEM), 87020-900, Maringa´, Parana´, Brazil; cInstituto de Fı´sica “Gleb Wataghin”, Universidade Estadual de Campinas, Caixa Postal 6165, 13083-970, Campinas, Saõ Paulo, Brazil; dFaculdade de Tecnologia, Universidade Estadual de Campinas, 13484-332, Limeira, Saõ Paulo, Brazil (Received 11 August 2010; final version received 5 June 2011)

In this paper, we report a comparative parametric method 6 (PM6) and Recife model 1 (RM1) study of trans-stilbene in its ground and (excited) singlet, triplet and ionic (positive and negative polarons and bipolarons) states. We evaluated the accuracy of the recently developed PM6 and RM1 comparing the obtained results with other semi-empirical, ab initio methods and available experimental data. PM6 and RM1 predict non-planar ground and singlet states for trans-stilbene, in agreement with the PM5 and the Austin model 1. On the other hand, the PM3 predicts planar conﬁgurations, which is in agreement with the available experimental data. PM6 and RM1 overestimate the cis–trans isomerisation energy as well as the ionisation potential of both cis- and trans-stilbene. In spite of the developments of these new methods, PM3 continues to be the only one of these methods to correctly predict the conformation of stilbene. Keywords: trans-stilbene; PM6; RM1; semi-empirical methods

1. Introduction lower than those obtained with AM1, PM3 and PM5. Semi-empirical methods have played an important role in Therefore, in principle, RM1 represents an improvement quantum chemistry since the ﬁrst attempts to develop over the cited methods. reliable methods at lower computational costs than those More recently, including changes in the neglect of related to more sophisticated ab initio approaches. The diatomic differential overlap core–core interaction term development of semi-empirical methods is a continuous and a new set parameterisation, Stewart [5] has introduced and important process that started several decades ago with the PM6. It consists of an optimisation of a large set of parameters that included 70 elements and has utilised 4492 the proposition of the Hu¨ckel method [1]. Despite the rapid compounds to optimise the heat of the formation (HF) and development of ab initio and density functional theory obtained an improvement in the average unsigned error (DFT) methods and the increase in computational power, compared to other methods, namely AM1, PM3, PM5, research in the improvement of semi-empirical methods RM1, B3LYP 6-31G* and HF 6-31G*. Another objective still attracts the attention of several research groups [2,3]. of the new method was to correct several weaknesses After the appearance of the very simple Hu¨ckel observed in AM1 and PM3. In addition, it resulted in some method, several methodologies have been proposed and improvements in the prediction of the geometries for tested using different approximations and parameterisa- several compounds. tions. Among them are the well-known Austin model 1 Since PM6 is still a very new method and its accuracy (AM1) and the parametric method 3 (PM3), which are Downloaded by [UNESP], [R. P.B. dos Santos] at 09:28 01 September 2011 has not been fully established for many materials, in this certainly two of the most used semi-empirical methods in study we tested its reliability in describing the geometrical the literature. Recently, a new re-parameterisation of the and electronic properties of an important molecule related AM1 for a small set of atoms (C, H, N, O, P, S, F, Cl, Br to the family of conducting polymers, poly( p-phenylene- and I) has been realised and called Recife model 1 (RM1) vinylene) (PPV). PPV presents excellent electrolumines- [4]. To obtain these new parameters, a set of 1736 cent and electronic properties [6]. In general, conjugated molecules was used. In contrast to AM1, and similar to polymers, such as PPV, are showing real promise in optic– PM3, all RM1 parameters have been optimised, and the electronic applications [6]. In particular, PPV and its authors [4] reported that the average errors for enthalpies derivatives can be used as photoactive layers in light- of formation, dipole moments, ionisation potentials (IPs) emitting diodes (LEDs) [7–10], lasers [11–13] and and inter-atomic distances for that set of molecules are photovoltaic cells [14]. Of all the polymers evaluated for

*Corresponding author. Email: paupitz@iﬁ.unicamp.br

ISSN 0892-7022 print/ISSN 1029-0435 online q 2011 Taylor & Francis DOI: 10.1080/08927022.2011.597392 http://www.informaworld.com 2 A. Camilo, Jr. et al.

simplest model compound for which we can mimic the (a) (b) 5 6 56 structural features of longer PPV oligomers [38]. 7 7 We carried out a comparative study of ground-state 4 4 1 1 geometry for trans-stilbene using AM1, PM3, PM5, RM1, 8 3 2 8 3 2 and PM6. These results were compared with the available experimental data and more recent theoretical (MM, DFT and MP2) studies. The ionic (positive and negative polarons and bipolarons), excited (singlet and triplet) Figure 1. Chemical structure of (a) trans-stilbene and (b) states, as well as the cis–trans inter-conversion barrier cis-stilbene. were also investigated.

LEDs, PPV has been one that has been investigated the most [15]. It is used in devices more than any other 2. Methodology polymer as either a light emitter [16,17] or the hole- In this study, we carried out RM1 and PM6 calculations transporting layer [18]. using the Mopac 2007 program [35]. The optimised We investigated the structural dimer (trans-stilbene) of geometries were calculated setting the gradient in the PPV (Figure 1(a)) to test the RM1 and PM6 predictions for hypersurface of the energy to be lower (in module) than this representative molecule of PPV. This structure has 0.01 kcal/mol, to assure good quality results. Ground-state, been very difficult to describe with semi-empirical positive and negative bipolaron calculations were carried methods and even with some ab initio methods, as out using restricted Hartree–Fock methodology. In the discussed below. Here, we use the same procedure case of singlet, triplet, positive and negative polarons, the previously used to contrast the PM3 and PM5 [19,20] calculations were carried out within unrestricted Hartree– results with the available experimental data. The X-ray Fock formalism, since it is the more appropriate way to data from crystal samples [21,22] indicate that trans- handle open shell systems. stilbene can be considered a co-planar structure with the We performed a comparative study of RM1 and PM6 phenyl rings slightly twisted (38–78) in relation to the results for lengths and angle values for trans-stilbene with plane of the vinyl group. For the isolated molecule, there those obtained with AM1, PM3 and PM5 (calculated in are some gas phase data [23] suggesting a large deviation our previous study [20]), X-ray data [36,37], Allinger’s from planarity (a dihedral angle ,308), although more MM [MM3(99)] [38–41] force field study and a DFT recent experimental data [24–29] clearly indicate a planar study employing B3LYP/6-31G basis set [42–48]. geometry for both ground and singlet excited states. From ** The MP2/6-31G geometries [34,38] were also used for the theoretical point of view, several results indicate ** comparative purposes, although calculations at this level clearly that trans-stilbene, in vacuum, is a planar molecule seem not to provide a very accurate description of the in its absolute energy minimum [30] and some geometry for trans-stilbene. Also, comparison with explanations for its conformal behaviour have been experimental data from X-ray diffraction methods using proposed [31,32]. crystal samples is presented [21,22]. The IP obtained from We have previously analysed the accuracy of the PM5 the RM1 and PM6, which was approximated by taking the in describing trans-stilbene properties [20]. In that study, negative value of the highest occupied molecular orbital we investigated the quality of PM5 description of that (HOMO) energy (1 ; Koopmans’ theorem), was compound and concluded that, at least for stilbene-like HOMO compared with the experimental IP values. Downloaded by [UNESP], [R. P.B. dos Santos] at 09:28 01 September 2011 structures, it did not represent an improvement over AM1 and PM3 [19]. In this study, we verify whether PM6 and RM1 can be considered an improvement over the AM1, PM3, and PM5 in the specific case of trans-stilbene 3. Results and discussions structures. Accordingly to the results obtained in a previous study Also, molecular mechanics (MM) simulations [33] [20], only the PM3 predicts a planar conformation based on classical force fields, second- and third-order (or practically planar) for trans-stilbene, for both ground Møller–Plesset and coupled cluster theories with single, and singlet excited states. Similarly to AM1 and PM5 [20], double and perturbative triple excitations in conjunction RM1 and PM6, both the methods incorrectly predict the with asymptotically complete basis sets [30] as well as non-planar ground and singlet excited states (Figure 2). DFT methods [34] using hybrid functionals have been Table 1 presents the values of the C8ZC7ZC1ZC2 0 0 successfully employed in the study of molecular dihedral angle (f1) and the C7ZC8ZC1 ZC6 dihedral geometries and the evaluation of conformational energies angle (f2) corresponding to the minimum energy and rotational barriers. These methodologies provide conformation. For the ground state, f1 and f2 are satisfactory geometry results for trans-stilbene, the about 438 and 428 from RM1 and PM6 calculations, Molecular Simulation 3

(a) 180 respectively. While the predicted angles with PM6 are

160 similar to those obtained with PM5, large differences, 60.93 larger than expected between the AM1 and RM1 values 140 60.77 60.63 are observed (Table 1) [35]. For the excited singlet state, 120 60.49 the AM1 and PM5 predict f1 to be about 0.38 and 8.08, 60.38 100 60.27 respectively, and f2 to be about 4.08 and 4.58, respectively, 2

φ 60.16 80 as previously reported in Ref. [20]. For the excited singlet 60.05 states calculated from the AM1, RM1 and PM5, a 60 distortion of about 908 from planarity is observed for the 40 C1ZC7ZC8ZC10 dihedral angle, while the PM6 predicts 20 this distortion to be of about 4.08. The RM1 and PM6 do

0 not provide a very accurate description of through-space 0 20 40 60 80 100 120 140 160 180 steric interactions, as well as of p-conjugation for both the φ 1 ground and singlet excited states for trans-stilbene. (b) 180 From Table 1, we can compare the bond lengths for 160 trans-stilbene obtained from RM1 and PM6 as well as 61.29 other semi-empirical and ab initio methods, classical force 140 60.81 ﬁeld calculations and experimental data. This comparison 60.56 120 60.32 is better visualised in Table 2 where we present the sum of 100 60.08 the absolute differences of the calculated values with

2 60.84 φ 80 60.59 respect to the experimental data. Considering all bond 60.35 lengths, PM6 presents the worst results with respect to the 60 experimental data 1 (EXP1), while RM1 and PM5 40 produced the best results. This tendency is changed 20 when the comparison is done with respect to experimental

0 data 2 (EXP2) where PM3 shows a better agreement. 0 20406080100120 140 160 180 PM5 and RM1 again present the worst values among the φ 1 semi-empirical methods, while PM6 and AM1 predicted values that are very similar. In the case where the hydrogen Figure 2. Conformational maps. (a) PM6 and (b) RM1. The darker (lighter) areas represent lower (higher) formation heats (in bonds are not considered, RM1 and PM6 represent an kcal/mol). f1 is the dihedral angle of C8ZC7ZC1ZC2 and f2 is improvement for the bond length description for both sets 0 0 the dihedral angle of C7ZC8ZC1 ZC6 (in degrees see Figure 1). of experimental data.

Table 1. Bond lengths (in A˚ ), labelled accordingly to Figure 1, for trans-stilbene ground state from AM1, PM3, PM5, PM6, RM1, MM3(99), MP2/6-31G**, B3LYP/6-31G** and from X-ray studies (EXP1 [37] and EXP2 [39]). AM1 PM3 PM5 PM6 RM1 MM3(99) MP2/6-31G(d,p) B3LYP/6-31G(d,p) Exp1 [38] Downloaded by [UNESP], [R. P.B. dos Santos] at 09:28 01 September 2011 (1) C1ZC2 1.402 1.399 1.393 1.406 1.395 1.408 1.406 1.409 1.391 (2) C2ZC3 1.393 1.388 1.386 1.397 1.388 1.397 1.393 1.391 1.382 (3) C3ZC4 1.394 1.391 1.387 1.398 1.389 1.409 1.397 1.407 1.376 (4) C4ZC5 1.396 1.391 1.387 1.399 1.390 1.396 1.396 1.395 1.369 (5) C5ZC6 1.392 1.389 1.386 1.396 1.388 1.394 1.394 1.393 1.375 (6) C6ZC1 1.405 1.399 1.397 1.409 1.397 1.409 1.405 1.407 1.379 (7) C7ZC1 1.453 1.457 1.463 1.469 1.456 1.475 1.464 1.466 1.478 (8) C7ZC8 1.343 1.342 1.327 1.344 1.340 1.355 1.351 1.348 1.300 (9) C2ZH2 1.100 1.102 1.096 1.089 1.096 – – – 0.940 (10) C3ZH3 1.100 1.095 1.095 1.089 1.094 – – – 0.980 (11) C4ZH4 1.100 1.095 1.094 1.088 1.094 – – – 0.980 (12) C5ZH5 1.100 1.095 1.095 1.089 1.094 – – – 0.960 (13) C6ZH6 1.100 1.096 1.095 1.089 1.094 – – – 0.950 (14) C7ZH7 1.101 1.103 1.098 1.096 1.099 – – – 1.020 f1 22.908 0.008 42.248 42.758 43.258 0.008 26.78 0.038 – f2 23.008 0.148 42.398 42.748 43.278 –– – – 4 A. Camilo, Jr. et al.

Table 2. Sum of the absolute error differences of the calculated values from AM1, PM3, PM5, PM6, RM1, MM3(99), MP2/6- 0.700 1.500 0.200 1.900 31G** and B3LYP/6-31G** bond lengths with respect to the 2.300 2 2 2 2 experimental data of X-ray diffraction studies (EXP1 [37] and 2 EXP2 [39] values).

Bond lengths 0.800 1.900 1.5000.100 0.400 2.300 Theoretical 0.600 0.300 2 2 2 2 2 method EXP1a [37] EXP2a [39] EXP1b [37] EXP2b [39] 2 AM1 0.178 0.041 0.953 0.166 PM3 0.148 0.039 0.904 0.145 PM5 0.106 0.057 0.849 0.150 PM6 0.186 0.041 0.896 0.101 RM1 0.137 0.048 0.878 0.139

MM3(99) 0.199 0.060 – Landscape 0.600 1.400 MP2/ 0.184 0.039 – – 2 2 6-31G** B3LYP/ 0.190 0.049 – – 6-31G** -stilbene from AM1, PM3, PM5, PM6, RM1, MM3(99), a Without considering bond lengths (9), (10), (11), (12), (13) and (14) listed in Table 1. b Considering bond lengths (9), (10), (11), (12), (13) and (14) listed in trans Table 1. 0.400 0.500 2 2

In Table 3, we show bond angle deviations from the standard 120.008 value from calculations and experimental data. From this table, we obtained the sum of the absolute

differences of the calculated values with respect to the 0.300 1.100 2 2 experimental data (Table 4). When all atoms are considered, PM6 presents better agreement with both EXP1 and EXP2, while RM1 results are worse than AM1. 0.236 0.696 0.134 – – – 0.769 – – – 0.6233.779 – – – – – – 1.010 1.100 0.010 When we consider only angles that do not involve 0.101 – – – 2 2 2 2 2 2 hydrogen atoms, PM6 still presents the best results among 2 the semi-empirical methods, while the RM1 description remains worse than that obtained with AM1. The PM6 0.281 1.118 0.085 0.026 – – – 0.215 1.112 0.372 5.242 improves the description of angle deviations when 0.139 2 2 2 2 2 2 2 compared with the semi-empirical methods and provides 2 results that are comparable to MM(99) and MP2/6-31 G** methods. 0.149 0.445 0.274 0.524 0.107 4.840 In Table 5, we show the HF (kcal/mol) for trans- 0.295 2 2 2 2 2 2 stilbene in its excited states, singlet (S) and triplet (T), and 2 Downloaded by [UNESP], [R. P.B. dos Santos] at 09:28 01 September 2011 charged states þ1, 21, þ2, 22 (positive and negative polarons and bipolarons, Pþ,P2,Bþ,B2, respectively) , and from X-ray studies (EXP1 [37], EXP2 [39] values). 0.085 0.310 1.483 0.199 0.098 0.767 0.029 2.732 0.150

relative to the ground-state value from AM1, PM3, PM5, ** 2 2 2 2 2 2 2 2 PM6 and RM1. We can conclude from these results that trans-stilbene is a good electron acceptor and that more stability for negative polarons and bipolarons than for the 0.256 0.946 0.060 0.218 1.109 0.087 5.168 0.135 positive ones is expected. AM1 PM3 PM5 PM6 RM1 MM3(99) MP2/6-31G(d,p) B3LYP/6-31G(d,p) Exp1 [38] Exp2 [35] 2 2 2 2 2 2 2 2 Table 6 shows the conformational energy difference and B3LYP/6-31G

(cis–trans isomerisation energy) between cis-and * C1 C2 C5 0.122 0.035 0.037 0.111 0.082 – – – 2.300 0.300 C5 C1 C6 C3 0.441 0.432 0.126 0.450 0.346 0.800 0.600 0.900 0.700 0.500 C6 0.188C1 0.277 4.530 0.279 3.032 0.243 3.043 0.213 4.802 0.100 3.242 5.300 0.100 4.900 0.100 7.100 0.500 0.300 6.600 6.000 C5 C6 C1 0.476 0.127 0.021 0.435 0.253 1.000 0.900 1.400 1.500 1.200 trans-stilbene (Figure 1(a),(b)), DE (kJ/mol), (DE ¼ C2 Z Z Z Z Z Z Z Z Z Z Z Z Z C2 C3 C4 C6 C7 E 2 E ). All the used methods indicate C5 C2 C5 C7 C4 C1 C6 cis-stilbene trans-stilbene C1 Z Z Z Z Z Z Z Z Z Z Z Z that the trans structure is more stable than the cis Z structure. The PM6 and RM1 overestimate the HF (1) C1 (3) C4 (7) C8 (2) C3 (6) C7 (4) C5 (8) H2 (9) H3 (5) C6 Table 3. Bond angle deviations (in degrees) from standard 120.00 value, labelled accordingly to Figure 1, for MP2/6-31G2mu* (10) H4 (12) H6 (13) H7 difference between cis and trans isomers. (11) H5 Molecular Simulation 5

Table 4. Sum of the absolute error differences of the calculated values on AM1, PM3, PM5, PM6, RM1, MM3(99), MP2/6-31G** and B3LYP/6-31G** bond angle deviations from standard 120.008 value with respect to the experimental data of X-ray diffraction studies (EXP1 [37] and EXP2 [39] values).

Bond angles Theoretical method EXP1a [37] EXP2a [39] EXP1b [37] EXP2b [39] AM1 6.354 4.154 17.920 8.210 PM3 9.270 7.070 16.875 10.241 PM5 9.713 7.513 21.211 11.303 PM6 5.859 3.659 17.763 8.111 RM1 8.545 6.345 19.334 9.526 MM(99) 3.600 2.200 MP2/6-31G** 4.600 3.000 – – B3LYP/6-31G** 1.900 2.100 – –

a Without considering bond angles (8), (9), (10), (11), (12) and (13) listed in Table 3. b Considering bond angles (8), (9), (10), (11), (12) and (13) listed in Table 3.

Table 5. HF (in kcal/mol) for excited states, singlet (S) and triplet (T), and charged states þ1, 21, þ2, 22 (positive and negative polarons and bipolarons, Pþ,P2,Bþ,B2, respectively) relative to the ground-state value.

STPþ P2 Bþ B2 AM1 88.259 46.557 183.292 222.574 452.358 40.779 PM3 93.331 47.119 187.526 224.729 461.490 37.527 PM5 83.875 45.119 181.628 217.850 442.642 45.959 PM6 91.377 44.159 185.938 226.973 453.649 30.199 RM1 92.977 45.416 179.615 217.620 443.699 49.805

In Table 7, we compared the IP results obtained from represent an improvement in the bond length description RM1, PM6 with the other semi-empirical methods and with only when hydrogen bonds are not considered. the experimental IP values [48] for trans- and cis-stilbene. Compared with EXP1 and EXP2, PM6 gives better The IP value obtained for the trans-stilbene with PM6 was bond angle results among all the semi-empirical methods the worst among all the semi-empirical methods, while the considered, and the RM1 is less accurate than AM1. AM1 value was the best. The RM1 result is similar to the B3LYP/6-31G** bond angles are still better described PM5 value. In relation to cis-stilbene, PM6 presents an than all the semi-empirical methods used in this study. improvement when compared with the PM3 result while Both PM6 and RM1 overestimate the cis–trans RM1 is equivalent to the PM5 result. RM1 and PM6 predict isomerisation energy, producing values that are larger IP (trans-stilbene) , IP (cis-stilbene), in agreement with than those obtained with all the other methods. For the IP the experimental data. calculations, if compared with experimental data, PM6 and RM1 overestimate their values for both cis- and 4. Summary and conclusions trans-stilbene. RM1 IP values are very close to PM5

Downloaded by [UNESP], [R. P.B. dos Santos] at 09:28 01 September 2011 We performed a comparative study of trans-stilbene in its values, while PM6 produces worse results for trans- ground, (excited) singlet, triplet and charged (positive and stilbene than PM3, but with improved values for cis- negative polarons and bipolarons) states using two stilbene. recently developed semi-empirical methods, PM6 and RM1. The results that were obtained contrasted with other Table 6. Conformational energy difference DE ¼ E 2 semi-empirical, ab initio methods and available exper- cis-stilbene Etrans-stilbene (in kJ/mol). imental data. The RM1 and PM6 methods continue to predict incorrectly non-planar ground and singlet excited Theoretical method DE (kJ/mol) states for trans-stilbene. PM3 predicts a planar (or AM1 þ13.9 practically planar) ground and singlet states for trans- PM3 þ17.1 stilbene in agreement with the experimental data [24–29]. PM5 þ03.3 PM6 þ40.6 The results obtained for ground-state geometry were RM1 þ63.0 compared with two different experimental data-sets MP2/6-31G(d,p) þ08.0 (EXP1 and EXP2), ab initio calculations and MM3(99). B3LYP/6-31G(d,p) þ21.0 Compared with EXP1 and EXP2, the PM6 and RM1 6 A. Camilo, Jr. et al.

Table 7. AM1, PM3, PM5, PM6, RM1 and experimental IP values (in eV).

IP AM1 PM3 PM5 PM6 RM1 EXP [46] Trans-stilbene 8.573 8.632 8.672 8.915 8.674 7.870 Cis-stilbene 8.724 9.165 8.963 8.963 8.683 8.170

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