J Mol Model (2014) 20:2225 DOI 10.1007/s00894-014-2225-5

ORIGINAL PAPER

Natural bond orbital/natural J-coupling study of vicinal couplings José M. García de la Vega & Jesús San Fabián

Received: 16 December 2013 / Accepted: 26 March 2014 # Springer-Verlag Berlin Heidelberg 2014

Abstract NBO-NJC decomposition of vicinal 3JHH spin-spin coupling constants into Lewis, delocalization, and repolarization contributions are presented. A deep study allows to assign the main contributions to specific orbitals or electron delocalizations between two orbitals. 3JHH torsional dependence and the substituent effect are analyzed according to the main orbital contributions for ethane and fluoroethane molecules using different basis sets. The torsional dependence for the energies corresponding to electron delocalization is also studied. Keywords Natural bond orbital/natural J coupling . NMR . Spin-spin coupling constants PACS 82.56.-b . 31.15.E-

Introduction Spin-spin couping constants (SSCCs) is one of the most important NMR parameters for studying fine details of electronic molecules structures [1–4]. On the other hand, vicinal proton-proton coupling constants 3JHH have been used extensively in conformational studies since Karplus pioneering works [5, 6]. Several studies about the main dependences of these SSCCs, the torsional orientation, and the effects of substituents attached to coupling pathway have been reported [7–10]. Calculated SSCCs can be formulated within the Ramsey nonrelativistic theory as originating in four different terms,

Fermi contact (FC), spin-dipole (SD), paramagnetic spin-orbit (PSO), and diamagnetic spin-orbit (DSO), 3

3 SD 3 PSO 3 DSO J HH ¼3 J FC HH þ J HH þ J HH þ J HH :

The present study will be restricted to the FC term because 3JHH couplings are known to be dominated by this term [11]. The combination of natural bond orbital (NBO) [12, 13] and natural J-coupling (NJC) [14, 15] methods allows the decomposition of FC term into contributions from Lewis and non-Lewis: 3

3 Lewis 3 non−Lewis J FC : HH ¼ Δ J HH þ Δ J HH

ð2Þ

Lewis or localized contributions correspond to steric interactions, while non-Lewis are those derived from electron density delocalizations. Within the NBO-NJC, the nonLewis term is split in two contributions: those corresponding to electron density delocalization from a donor to an acceptor orbital centered in some different region of the molecule, hereinafter called delocalized part, and those delocalizations between orbitals centered at the same bonding region, called repolarization part: 3 repol Δ3 J non−Lewis ¼ Δ3 J deloc HH HH þ Δ J HH

ð3Þ

3 non−Lewis Additionally, Δ3JLewis contributions can HH and Δ JHH be decomposed into individual contribution from different localized occupied and unoccupied NBOs [14, 15].

This paper belongs to Topical Collection QUITEL 2013 J. M. García de la Vega (*) : J. San Fabián Departamento de Química Física Aplicada, Facultad de Ciencias, Universidad Autónoma de Madrid, Madrid, Spain e-mail: [email protected]

ð1Þ

Δ3 J Lewis HH ¼

occ X

ΔLewis ; i

i

Δ

3

J non−Lewis HH

¼

occ unocc X X i

j

Δijnon−Lewis :

ð4Þ

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The importance of the density electron delocalizations can be assessed using the stabilization interactions that can be approximated by second-order perturbation theory [15]:

ð2Þ

ΔE ωω ¼ −2

b  2 < ω F ω >

ð5Þ

εω −εω

where ω and ω* are the donor and acceptor NBOs, εω and εω b is the off-diagonal correspond to their orbital energies and F NBO Fock matrix element. Deep studies about the performance of different functionals or basis sets on vicinal 3JHH SSCCs can be found in the literature [10, 16]. In this work the breakdown of those SSCCs on the orbital contributions is analyzed following, in part, the works of Wilkens et al. [15] and Esteban et al. [17]. The NBO analysis has been extensively used to study the effect of hyperconjugative interaction on SSCCs. Recently, the unusual relation 3JHH (ϕ=180°)< 3JHH(ϕ =0°) was rationalized in propanal, thiopropanal, and 1-butene models [18] and in valine [19] considering hyperconjugative interactions. A revision of the NJC methology has also been published [20], where the angular dependence of 1JCF SSCC in fluoroethane was analyzed. It shows that for this type of SSCC and using the EPR-III basis set [21] the NBO-NJC predict that the electron delocalizations into Rydberg orbitals are significant. In the present work, the NBO-NJC approach is applied to the vicinal SSCC 3JHH in ethane and fluoroethane (Fig. 1). The former is the pattern molecule to study the torsional dependence of 3JHH SSCCs, and the second allow us to analyze the contribution effects of an electronegative substituent on these SSCCs.

Computational methods Standard geometries [22], tetrahedral bond angles, and constant bond lengths (rCC =1.54 Å, rHH =1.09 Å, and rCF =1.36 Å), were used in this study. Thus, additional contributions from changes in local geometry (bond angles and bond length) are not considered, avoiding their correlation with the remaining effects. SSCCs were calculated as a function of the H–C– H8

H3

H8

H3

H7

φ C1 H5 H4

H7

C–H torsional angle ϕ which was driven in 30° steps over the minimum range necessary to cover a complete rotation, allowing for symmetry where appropriate. Torsional dependence for calculated SSCCs and for different contributions studied in this work were treated by Fourier inversion [7]. The hybrid B3LYP functional that has been applied successfully for calculating vicinal SSCCs were used in combination with the following basis sets: 6-311G(p,d) [23], aug-cc-pVTZ [24], aug-cc-pVTZ-J [25], BS2 [26], 6-311G(p,d)t1, and 6311G(p,d)t2. Those later basis sets have been built from 6311G(p,d) basis set plus one and two tight s functions, respectively. We choose two types of basis sets, the standard as 6311G and aug-cc-pVTZ and the other specially designed for calculating SSCCs as the BS2 and the aug-cc-pVTZ-J. More comprehensive studies about the basis sets effect on ethane 3 JHH SSCCs can be found in the literature [9, 10, 16, 27]. All the results shown here have been obtained with the Gaussian 03 [28] and the NBO 5.0G [29] packages.

Results and discussion The calculation of FC contributions within the NBO-NJC method is based on the finite perturbation theory (FPT) [30, 31]. FPT introduces the Fermi contact operator into the Hamiltonian as a finite field perturbation λ on one of the coupled nuclei obtaining the spin density at the position of the second coupled nucleus. NBO-NJC method uses, by default, a λ perturbation of 200×10−4 a.u. In order to detect if the field perturbation is adequate for these SSCCs, the FC NBO-NJC calculated values are compared in Table 1 with the results obtained using the coupled-perturbed DFT (CP-DFT) approach [32, 33] implemented also in the Gaussian package. The largest deviations between both methods are found for the anti conformer (see Table 1). Basis sets with tight s functions, BS2, 6-31G**t1, 6-31G**t2, and to a lesser extent the aug-ccpVTZ-J, yield important deviations with λ=200×10−4 a.u. and sometimes also with λ=100×10−4. It is also observed that when the perturbation field is too small the repolarization contributions, that usually are small, increase in magnitude. Similar results are obtained for fluoroethane. Therefore, we use λ=200×10−4 a.u. with aug-cc-pVTZ and 6-31G**; λ= 100×10−4 a.u. with aug-cc-pVTZ-J and 6-31G**t1; and λ= 50×10−4 a.u. with BS2 and 6-31G**t2. Basis set dependence

φ C2

C1

H6

H5 F4

Figure 2 shows the Karplus dependence for the total FC term

C2

3 FC JHH together with the decomposition into Lewis Δ3JLewis HH and delocalization Δ 3 J deloc contributions for ethane and HH

H6

Fig. 1 Structures of ethane and fluoroethane. Coupled protons indicated in bold type

fluoroethane using different basis sets. The repolarization contribution represents, in general, less than 1 % of the FC term values for the anti conformer of ethane (see Table 1) and

J Mol Model (2014) 20:2225 Table 1 Values of FC contributions (Hz) calculated for the anti conformer of ethane using different field perturbations

Page 3 of 7, 2225

Basis set

Lewis

aug-cc-pVTZ-J aug-cc-pVTZ BS2 6-31G**

NBO (field=200×10−4 a.u.) 12.81 −0.11 10.13 −0.05 9.24 −0.13 9.78 −0.12

6-31G**t1 6-31G**t2 aug-cc-pVTZ-J aug-cc-pVTZ BS2 6-31G** 6-31G**t1 6-31G**t2 aug-cc-pVTZ-J aug-cc-pVTZ BS2 6-31G** 6-31G**t1 6-31G**t2

Repol

12.53 −0.12 12.90 −0.18 NBO (field=100×10−4 a.u.) 12.74 −0.12 10.12 −0.04 8.78 −0.24 9.80 −0.14 12.54 −0.44 11.74 −0.08 NBO (field=50×10−4 a.u.) 12.76 −0.20 10.04 0.04 8.80 −0.44 9.76 −0.08 12.12 0.20 11.52 −0.24

for comparison purpose has been shown in Fig. 3. The repolarization values increase up to 3 % only for the anti conformer of ethane when the 6-31G**t1 with λ=100×10−4 a.u. and the BS2 with λ=200×10−4 a.u. are used. The torsional dependence of 3JFC HH in both molecules, ethane and fluoroethane, is qualitatively similar for all basis sets and a simple scale factor would make all of them equivalent. Thus, for ethane, aug-cc-pVTZ-J calculated values, considered as a reference, can be obtained from those calculated with BS2, 6-311G**t2, 6-311G**t1, 6-311G**, and aug-cc-pVTZ multiplying them by 0.9959, 1.0105, 1.0741, 1.2320, and 1.2341, respectively. It is noteworthy to indicate that the corresponding coefficients for fluoroethane are similar (0.9959, 1.0051, 1.0682, 1.2259 and 1.2440, respectively). Considering the FC contribution, we see that the three basis sets with two or more tight s-functions yield the highest values and that these are similar to the three basis (see the factor indicated before) despite their different origin. Clearly, the lowest values, that are also similar to each other, are those obtained with aug-cc-pVTZ and 6-311G**. The above indicated proportionality between the results obtained with different basis sets is broken when Lewis and delocalization contributions are considered (see Fig. 2). The allocation of these contributions depends strongly on basis sets and on torsional angles. BS2 basis set, a basis set specially built for SSCCs and which has proved to give good results [26, 34–37], seems to yield within the NBO-NJC approach

Deloc

FC-NBO

CP-DFT

3.78 3.33 8.73 3.63

16.48 13.40 17.84 13.30

16.30 13.40 16.33 13.29

3.05 5.46

15.46 18.19

15.18 16.10

3.74 3.32 8.14 3.62 3.14 4.90

16.34 13.40 16.68 13.30 15.24 16.58

3.73 3.32 8.04 3.64 2.88 4.92

16.32 13.40 16.40 13.28 15.20 16.20

anomalous values. In ethane the delocalization contributions for ϕ=0° is too small (0.7 Hz) while that for ϕ=180° is too large (8.0 Hz). In fluoroethane the curves for BS2 also present strange behavior and therefore these results should be considered carefully. The remaining results are mixed, for instance, in both molecules since aug-cc-pVTZ-J and aug-cc-pVTZ predict delocalization contributions that are larger for ϕ=0° than for ϕ=180° while all the other basis sets yield opposite results. The delocalization contributions are always smaller than those of Lewis although significant. Their relative size dependents on the basis set.

Individual Lewis and delocalization contributions 3 FC JHH

values can be split within the NBO-NJC in the individual contributions from Lewis and electron delocalization. To analyze the individual contributions, we will take the results from two different basis sets, aug-cc-pVTZ-J, and 6-311G**. In Fig. 3, the torsional dependence of the main individual contributions are represented together with the total Lewis and repolarization contributions. As regards the Lewis contribution, only the effect of the C–H bonds (σC1=2 −H 3=6 ) involved in the coupling pathway is important. In the ethane, the curves for total Lewis and that corresponding to (σC1=2 −H 3=6 ) almost overlap. These results are in agreement with those obtained previously [15]. For fluoroethane, the curve for the

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J Mol Model (2014) 20:2225

Ethane

18

16

14

14

12

12

3 FC JHH(Hz)

16

10

8

8

6

6

4

4

2

2

0

0

12

12

10

10

Δ 3JLewis HH (Hz)

10

8

8

6

6

4

4

2

2 0

-2 10

-2 10

8

8

6

6

4

4

2

2

0

0

Δ 3Jdeloc HH (Hz)

0

-2

0

60

120

φ (deg)

Fluoroethane

18

180

-2

contributions from (σC1=2 −H 3=6 ) reproduces qualitatively that of total Lewis. However, the differences are larger than in ethane and a strange behavior is detected for ϕ=180° when aug-ccpVTZ-J is used. Excluding this anomalous behavior, the pattern for ethane and fluoroethane holds equally for both used basis sets. In order to complete and compare the results, the negligible repolarization contribution is also represented in Fig. 3. The angular dependence for delocalization effects are represented in Fig. 4. The total delocalization contribution is qualitatively reproduced with the effect of the electron density delocalization into (σC 2=1 −H 6=3 ) orbitals (i.e., into σC1 −H 3 and σC2 −H 6 ) which

aug-cc-pVTZ-J BS2 6-311G**t2 6-311G**t1 aug-cc-pVTZ 6-311G**

are shown in Fig. 4. Among these, the most important are those delocalizations from the (σC1=2 −H 3=6 ) bonds (i.e., σC1 −H 3 and σC2 −H 6 ) to their respective vicinal (σC2=1 −H 6=3 ) antibonds (i.e.,

0

60

120

180

φ (deg)

240

300

360

Fig. 2 Torsional dependence for the FC, Lewis, and delocalization contributions to 3JHH in ethane and fluoroethane calculated with the NBO-NJC

σC1 −H 3 →σC2 −H 6 and σC2 −H 6 →σC 1 −H 1 ). Figure 5 shows a representation of those bonding and antibonding NBOs. Moreover, when aug-cc-pVTZ-J basis set is used, a non-negligible effect corresponding to the electron density delocalization into the Rydberg orbitals appear. Among these, the most important are those delocalizations from σC−H involved in the coupling to Rydberg orbitals of the geminal carbon (σC 1=2 −H 3=6 →RY 2=1 ). These contributions are important for dihedral angles around ϕ=0 and ϕ=180° and for both ethane and fluoroethane when calculated with aug-cc-pVTZ-J. However, they become smaller, although not insignificant, when 6-311G** is used (see Fig. 4). The effects from the remaining delocalizations are negligible.

Ethane Ethane

Fluoroethane 12 (b)

8

8

4

4

0

0

-4

-4

(c)

6-311G**

Δ 3JHH (Hz)

8

8

4

4

0

0 0

60

120

φ (deg)

180 0

8

aug-cc-pVTZ-J

Δ 3JHH (Hz)

aug-cc-pVTZ-J

(d)

60

120

180

φ (deg)

240

300

360

Fig. 3 Torsional dependence for total Lewis (red solid line), sum of Lewis contributions from σC 1 −H 3 and σC 2 −H 6 (dash line), remaining Lewis contributions (dot line) and repolarization (green solid line). Results for ethane (a and c) and fluoroethane (b and d) calculated with the indicated basis sets

aug-cc-pVTZ-J

Fluoroethane 8

4

4

0

0

-4 8

-4 8

(c)

6-311G**

Δ 3JHH (Hz)

Δ 3JHH (Hz)

12 (a)

(a)

6-311G**

4

4

0

0

-4

0

60

120

φ (deg)

-4 180 0

(b)

aug-cc-pVTZ-J

(d)

6-311G**

60

120

180

φ (deg)

240

300

360

Fig. 4 Torsional dependence for the delocalization effects of: total delocalization (solid line), delocalizations into σC 2 −H 6 and σC1 −H 3 (dash line), delocalizations into the Rydberg orbitals (dash-dot line), and remaining delocalizations (dot line). Results for ethane (a and c) and fluoroethane (b and d) calculated with the indicated basis sets

J Mol Model (2014) 20:2225

Page 5 of 7, 2225

Δ3Jfluoroethane − Δ3Jethane (Hz) HH HH

4

4

(a)

2

2

0

0

-2

-2

-4

-4

aug-cc-pVTZ-J

2

(b)

(d)

-2

aug-cc-pVTZ-J

0

6-311G**

0

0 -2

(c)

60 120 180 240 300 360 φ (deg)

6-311G**

0

60 120 180 240 300 360 φ (deg)

Fig. 6 Differences between the following fluoroethane and ethane contribution. (a) and (c): total FC (red line), total Lewis (blue dash line), two main individual Lewis effects (σC 1 −H 3 plus σC2 −H 6 , brown dot line) and remaining Lewis effects (green dash-dot line); (b) and (d): total delocalization (blue dash line), effects of delocalizations σC 1 −H 3 →σC 2 −H 6 and σC 2 −H 6 →σC 1 −H 3 (brown dash line), effects of delocalizations to Rydberg orbitals (brown dot line), and remaining delocalization effects (green dash-dot line). Values obtained with the indicated basis sets

Delocalization energies Second orden delocalization energies, ΔE(2) (Eq. 5), corre* sponding to both main delocalizations, vicinal σC−H →σC−H * and geminal σC − H → RYC, where C–H bonds are those (a)

In Fig. 6, the differences between the calculated SSCC contributions from fluoroethane and ethane molecules, that is the fluorine effect, are represented. In general, the effect of an electronegative substituent, such as fluorine, is a negative contribution to the SSCC [38]. In these results, the substituent effect is positive only in a narrow interval around 60 and 240°, see Fig. 6. The main effect is due to Lewis contributions that, as indicated above, corresponds to the direct Lewis transmission through the σCH bond involved in the coupling pathway. The contributions corresponding to the delocalizations from both σC−H bonds to their respective vicinal σ*C − H antibond and to their respective geminal RY*C Rydberg are presented (see Fig. 6b and d). Relatively large and negative contributions are found for ϕ≈ 330° when using aug-cc-pVTZ-J (see Fig. 6b). A good agreement between total delocalization differences and those obtained with the main individual contributions is obtained using the 6-311G**.

(c)

aug-cc-pVTZ-J

6

aug-cc-pVTZ-J

4

4 2

2

0

0

-2 -4

-2

6

6

(b) Δ 3Jdeloc HH (Hz)

Fluorine substituent effect

Δ 3Jdeloc HH (Hz)

6

Fluoroethane

(d)

6-311G**

6-311G**

4

4

2

2

0

0

-2

Δ E(2) (kcal/mol)

Ethane

8

0

60 120 φ (deg)

180 0

60

Δ E(2) (kcal/mol)

Fig. 5 σC−H and σ*C−H NBOs for syn and anti conformers

-2 120 180 240 300 360 φ (deg)

Fig. 7 Comparison of main delocalization effects (Δ3Jdeloc HH , blue lines) and their corresponding second order energies (ΔE(2), green lines) for ethane (a and b) and fluoroethane (c and d). Delocalizations (σC 1 −H 3 →σC 2 −H 6 plus σC2 −H 6 →σC 1 −H 3 (in dash lines); and σC 1 −H 3 →RY C2 plus σC 2 −H 6 →RY C 1 (in dotted lines). Values obtained with the indicated basis sets

2225, Page 6 of 7

involved directly in the coupling pathway, are represented in Fig. 7. For comparison, Δ3Jdeloc HH effects corresponding to the same delocalizations are also included in Fig. 7. For vicinal electron density delocalization, both curves, those of Δ3Jdeloc HH and ΔE(2), are qualitatively similar, showing a clear relationship between the second order energies and the effects on the SSCCs. This behavior is presented by the results of both analyzed basis sets and for both molecules. A similar agreement is found for the geminal delocalizations when 6-311G** results are analyzed. Although, for this basis set, the effect of these delocalizations is small. On the other hand, a strange behavior is observed for aug-cc-pVTZ-J results where the angular dependence for this geminal effects is rather different of that corresponding to ΔE(2).

Conclusions Torsional dependence of 3JHH calculated for ethane and fluoroethane is qualitatively similar for all basis set employed in this work. However, this similarity is broken when the Lewis and delocalization effects are analyzed. Aug-cc-pVTZ and aug-cc-pVTZ-J basis sets predict delocalization contributions on vicinal 3JFC HH term, that are larger for anti conformer than for syn conformer, while the remaining basis sets show a reverse effect. The main electron density delocalizations are those from * σC−H bond to its vicinal σC−H anti-bond and to its geminal * RYC Rydberg, where H is the coupled proton. However, the effects corresponding to delocalizations into Rydberg orbitals are not well established. For these molecules and SSCCs, those delocalizations into Rydberg orbitals could be artifacts derived from the use of basis sets with s tight functions. Second order stabilization energies, corresponding to density delocalizations, follow a torsional dependence that is proportional to the effects of those delocalizations on 3JHH SSCCs. This concordance is mainly supported for the delocalizations * σC−H →σC−H and to a lesser extent, for σC−H →RY*C Acknowledgments The following financial supports are gratefully acknowledged: Dirección General de Enseñanza Superior e Investigación Científica of Spain (DGESIC), projects: CTQ2010-19232 and CTQ201017338, Spanish Agency of International Co-operation, project: A1/ 035856/11. Computer time provided by the Centro de Computación Científica of Universidad Autónoma de Madrid is gratefully acknowledged.

References 1. Helgaker T, Jaszunski M, Ruud K (1999) Chem Rev 99:293 2. Cremer D, Grafenstein J (2007) Phys Chem Chem Phys 9:2791

J Mol Model (2014) 20:2225 3. Krivdin LB, Contreras RH (2007) Annu Rep NMR Spectrosc 61:133 4. Helgaker T, Jaszunski M, Pecul M (2008) Prog Nucl Magn Reson Spectrosc 53:249 5. Karplus M (1959) J Chem Phys 30:11 6. Karplus M (1963) J Am Chem Soc 85:2870 7. Díez E, San Fabián J, Guilleme J, Altona C, Donders LA (1989) Mol Phys 68:49 8. Altona C (1996) In: Grant DM, Harris RK (eds) Encyclopedia of nuclear magnetic resonance. Wiley, Chichester, pp 4909–4922 9. Pecul M, Jaszunski M, Sadlej J (1999) Chem Phys Lett 305:139 10. Pecul M, Helgaker T (2003) Int J Mol Sci 4:143 11. Díez E, Casanueva J, San Fabián J, Esteban AL, Galache MP, Barone V, Peralta JE, Contreras RH (2005) Mol Phys 103:1307 12. Reed AE, Curtiss LA, Weinhold F (1988) Chem Rev 88(6):899–926 13. Weinhold F (1998) Natural bond orbital methods, in encyclopedia of computational chemistry, vol 3. Wiley, Chichester, p 1792 14. Peralta JE, Contreras RH, Snyder JP (2000) Chem Commun 20: 2025–2026 15. Wilkens SJ, Westler WM, Markley JL, Weinhold F (2001) J Am Chem Soc 123:12026 16. Kupka T, Nieradka M, Stachów M, Pluta T, Nowak P, Kjær H, Kongsted J, Kaminsky J (2012) J Phys Chem 116:3728 17. Esteban AL, Galache MP, Mora F, Diez E, Casanueva J, San Fabián J, Barone V, Peralta JE, Contreras RH (2001) J Phys Chem A 105: 5298 18. Contreras RH, Suardíaz R, Pérez C, Crespo-Otero R, San Fabián J, García de la Vega JM (2008) J Chem Theory Comput 4:1494 19. Suardíaz R, Pérez C, García de la Vega JM, San Fabián J, Contreras RH (2007) Chem Phys Lett 442:119 20. García de la Vega JM, San Fabián J (2013) Analysis of contributions to spin-spin coupling constants by the natural J-coupling method. In High resolution NMR spectroscopy: understanding molecules and their electronic structures vol. 3, chap. 6. Elsevier, pp 161–207 21. Barone V (1994) J Chem Phys 101:6834 22. Pople JA, Gordon M (1967) J Chem Phys 89:4253 23. Krishnan R, Binkley JS, Seeger R, Pople JA (1980) J Chem Phys 72: 650 24. Dunning TH Jr (1989) J Chem Phys 90:1007 25. Provasi PF, Aucar GA, Sauer SPA (2001) J Chem Phys 115:1324 26. San Fabián J, Casanueva J, San Fabián E, Guilleme J (2000) J Chem Phys 112:4143 27. Guilleme J, San Fabián J, Casanueva J, Díez E (1999) Chem Phys Lett 314:168 28. Frisch MJ, Trucks GW, Schlegel HB, Scuseria GE, Robb MA, Cheeseman JR, Montgomery JA Jr, Vreven T, Kudin KN, Burant JC, Millam JM, Iyengar SS, Tomasi J, Barone V, Mennucci B, Cossi M, Scalmani G, Rega N, Petersson GA, Nakatsuji H, Hada M, Ehara M, Toyota K, Fukuda R, Hasegawa J, Ishida M, Nakajima T, Honda Y, Kitao O, Nakai H, Klene M, Li X, Knox JE, Hratchian HP, Cross JB, Bakken V, Adamo C, Jaramillo J, Gomperts R, Stratmann RE, Yazyev O, Austin AJ, Cammi R, Pomelli C, Ochterski JW, Ayala PY, Morokuma K, Voth GA, Salvador P, Dannenberg JJ, Zakrzewski VG, Dapprich S, Daniels AD, Strain MC, Farkas O, Malick DK, Rabuck AD, Raghavachari K, Foresman JB, Ortiz JV, Cui Q, Baboul AG, Clifford S, Cioslowski J, Stefanov BB, Liu G, Liashenko A, Piskorz P, Komaromi I, Martin RL, Fox DJ, Keith T, Al-Laham MA, Peng CY, Nanayakkara A, Challacombe M, Gill PMW, Johnson B, Chen W, Wong MW, Gonzalez C, Pople JA (2004) Gaussian 03, revision E.01. Gaussian, Inc, Wallingford 29. Glendening ED, Badenhoop JK, Reed AE, Carpenter JE, Bohmann JA, Morales M, Weinhold F (2001) Theoretical Chemistry Institute, University of Wisconsin, Madison 30. Pople JA, McIver JW, Ostlund NJ (1968) J Chem Phys 49:2960 31. Pople JA, McIver JW, Ostlund NJ (1968) J Chem Phys 49:2965 32. Sychrovský V, Gräfenstein J, Cremer D (2000) J Chem Phys 113: 3530

J Mol Model (2014) 20:2225 33. Barone V, Peralta JE, Contreras RH, Snyder JP (2002) J Phys Chem A 106:5607 34. Casanueva J, San Fabián J, Díez E, Esteban AL (2001) J Mol Struct 565–566:449 35. San Fabián J, Casanueva J, Díez E, Esteban A (2002) Chem Phys Lett 361:159

Page 7 of 7, 2225 36. San Fabián J, Westra Hoekzema AJA (2004) J Chem Phys 121:6268 37. San Fabián J, Díez E, García de la Vega JM, Suardíaz R (2008) J Chem Phys 128:084108 38. Guilleme J, San Fabián J, Diez E, Bermejo F, Esteban AL (1989) Mol Phys 68:65