Competition between HÂ·Â·Â·Ï and HÂ·Â·Â·O Interactions in Furan

Article pubs.acs.org/JPCA

Competition between H···π and H···O Interactions in Furan Heterodimers Elsa Sánchez-García*,† and Georg Jansen*,‡ †

Max-Planck-Institut für Kohlenforschung, Kaiser-Wilhelm-Platz 1, 45470 Mülheim an der Ruhr, Germany Theoretische Organische Chemie, Fakultät für Chemie, Universität Duisburg-Essen, 47057 Duisburg, Germany

‡

S Supporting Information *

ABSTRACT: Here the interactions of furan with HZ (Z = CCH, CCF, CN, Cl, and F) are studied using a variety of electron correlation methods (MP2, CCSD(T), DFT-SAPT) and correlationconsistent triple- and quadruple-ζ basis sets including complete basis set (CBS) extrapolation. For Fu−HF all methods agree that a n-type structure with a hydrogen bridge between the oxygen lonepair of furan and the hydrogen atom of HF is the global minimum structure. It is found to be significantly more stable than a π-type structure where the hydrogen atom of HF points toward the π system of furan. For the other four dimers MP2 and DFT-SAPT predict the π-type structure to be somewhat more stable, while CCSD(T) favors the n-type structure as the global minimum for Fu− HCl and predicts both structures as nearly isoenergetic for Fu−HCCH and Fu−HCCF. From a geometrical point of view, the Fu−HCN dimer structures are more related to those of the Fu−HCl complex than to Fu−HCCH. The different behavior of HCCF and HF upon complexation with furan evidence the effect of the presence of a π system in the aggregation of fluorine derivatives. It is shown that aggregates of furan cannot be understood by means of dipole−dipole and electrostatic analysis only. Yet, through a combined and detailed analysis of DFT-SAPT energy contributions and resonance effects on the molecular charge distributions a consistent explanation of the aggregation of furan with both π electron rich molecules and halogen hydrides is provided.

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halides4 found that for the n-type complexes the electrostatic component predominates while the π -type complexes are governed by electrostatic and orbital interactions. It was also concluded that the π-type geometry becomes preferred over the n-type geometry in Fu−HX complexes when going from F to I (X = F, Cl, Br, I). On the other hand, Asselin et al.12 found the coexistence of the two Fu−HCl structures in supersonic jet experiments. They also stated that MP2, although good for geometry optimization when a triple-ζ basis set is used, overestimates electron correlation and consequently the dispersion energy. A matrix isolation study of the furan−acetylene dimer16 showed that the n-type structure was the most likely to be found in the matrix, while helium nanodroplets spectroscopy experiments evidenced the existence of both structures at very low temperatures.10,17 The furan−acetylene n-type dimer structure, unlike the analogous furan−hydrogen halides structures deviates from the C2v symmetry because of the very weak CH-π interaction between one α hydrogen atom of furan and the π system of acetylene. This raises the question of how the presence of a π system in the acid affects the geometry of its heterodimer with furan, and how the CH-π and CH−O interactions compete in these systems. When writing this paper, a new study based on jet-cooled experiments and DFT

INTRODUCTION Interactions involving heteroaromatic rings, in particular furan, and hydrogen halides have been extensively studied both experimentally and theoretically,1−10 especially in view of the Legon and Millen11 rules which state that for B-HX complexes, the electrophilic end of a HX acid interacts preferentially with the region of higher electron density of the base B. According to these rules, for a base with a heteroatom and a π system such as furan, the structure in which the nonbonding n electron pair of furan interacts with the acid is expected to be preferred over the π-type structure. Nevertheless, several theoretical and experimental studies have shown something else: the π electrons direct the formation of the furan−HBr complex2,5 while both the n-type and π-type structures coexist for the furan−HCl heterodimer.12 Spectroscopic and density functional theory (DFT) studies of the aniline cation−furan complex show that the π-type structure is more stable than the n-type (σ-) structure which is attributed to the weakness of the NH-O interaction found in the latter.13 A second-order Møller−Plesset perturbation theory (MP2) and symmetry-adapted perturbation theory (SAPT) investigation of pyrrole−hydrides hydrogen bonded complexes indicates that, with the exception of complexes with water and ammonia, π-type pyrrole−HnX complexes are favored and dominated by electrostatic and dispersion interactions.14 It has been shown that, unlike furan, the thiophene−HX complexes are exclusively determined by the π system of thiophene.9,15 A theoretical study of the complexes of furan with hydrogen © 2012 American Chemical Society

Received: February 21, 2012 Revised: May 16, 2012 Published: June 1, 2012 5689

dx.doi.org/10.1021/jp301710y | J. Phys. Chem. A 2012, 116, 5689−5697

The Journal of Physical Chemistry A

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calculations of the indole−furan heterodimer appeared18 showing experimental evidence of an NH-π interacting dimer structure being preferred over the NH-O hydrogen bonded structure. This corroborates the necessity of studying the interactions of aromatic heterocyclic molecules, not only with hydrides as they have been traditionally investigated, but also with unsaturated systems. Therefore, here we study the π-type and n-type furan−HCN and furan−HCCF complexes as well as the furan−HF and furan−HCl heterodimers by means of high level ab initio calculations and symmetry-adapted perturbation theory19,20 employing molecular properties from density functional theory (DFT-SAPT).21−24 The results are compared to those for the furan−acetylene dimers from our previous work.16

aVTZ set was used. The CBS limit here was estimated by adding the difference between CCSD(T) and MP2 at the aVTZ level to the CBS extrapolated MP2 energies.44 In the DFT-SAPT calculations the PBE0AC exchangecorrelation (xc) potential23 in combination with the adiabatic local density approximation (ALDA) xc-kernel45 was employed.24 For the asymptotic correction contained in the PBE0AC xc potential the ionization potentials and highest occupied molecular orbital (HOMO) energies as calculated with PBE0/aVQZ at the MP2/aVTZ geometries were used. The ionization potentials obtained were 8.81 eV for furan, 11.16 eV for fluoroacetylene, 11.23 eV for acetylene, 12.71 eV for HCl, 13.50 eV for HCN, and 16.08 eV for HF, while the corresponding HOMO energies were −6.66, −8.32, −8.40, −9.51, −10.33, and −11.84 eV, respectively

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COMPUTATIONAL METHODS The quantum chemical calculations were performed using the Gaussian 03,25 Turbomole V 5.9,26−29 and Molpro 200630 program packages. Equilibrium geometries and vibrational frequencies were calculated with tight convergence criteria at the SCF level followed by second-order Møller−Plesset perturbation theory, MP2,31 correlating valence electrons only. Augmented and non-augmented Dunning’s correlation consistent triple-ζ basis sets (aug-cc-pVTZ and cc-pVTZ, hereafter denoted as aVTZ and VTZ, respectively) were used for geometry optimizations.32−34 The calculations with the aVTZ basis set were carried out with the resolution-of-theidentity (RI) approximation employing the appropriate auxiliary basis set.35 Vibrational frequencies were calculated for both triple-ζ basis set geometries to verify that the structures were minima at the given level of theory. Stabilization energies were calculated by subtracting the energies of isolated monomers from those of the complexes. On the other hand, the stabilization energies, Estab, can be also seen as the sum of two contributions:36 the relaxation energy, Erel, and the interaction energy, Eint. The former is the repulsive energy contribution accompanying changes of the monomer geometry parameters from their in vacuo values to the ones they assume in the dimer. The latter is the energy of interaction between the distorted monomers. The interaction (and in consequence also the stabilization) energies were corrected for the basis set superposition error (BSSE) using the counterpoise (CP) correction scheme of Boys and Bernardi.37 The energies of the various optimized structures were further analyzed with intermolecular perturbation theory employing the density functional theory combined with symmetry adapted perturbation theory (DFT-SAPT) approach.21−23,38,39 Valenceonly MP2 and coupled cluster calculations at the single and double plus perturbative triple excitation (CCSD(T))40 level calculations were also performed. The MP2 and DFT-SAPT calculations were made with the aVTZ and aug-cc-pVQZ (hereafter denoted as aVQZ) basis sets,32−34 using their efficient density-fitting (or resolution-of-the-identity) implementations along with the appropriate auxiliary basis sets.24 Extrapolation to the complete basis set (CBS) limit was performed with the standard two-point X−3 formula41−43 for the CP-corrected MP2 electron correlation contribution, using the CP-corrected Hartree−Fock interaction energy obtained with the quadruple-ζ basis set as reference. In case of DFTSAPT the extrapolation was carried out for the intermolecular electron correlation contributions, that is, the dispersion and exchange-dispersion, taking all other energy contributions from the aVQZ calculations. For the CCSD(T) calculations only the

RESULTS AND DISCUSSION

Geometries. The geometries of the ZH-π-type and ZH-ntype structure of the complexes between furan (Fu) and HZ (Z = CCH, CCF, CN, Cl, and F) were optimized at the MP2/ VTZ and MP2/aVTZ levels of theory. We include here also results for Fu−HCCH from our previous work for comparison. According to the naming system used for the acetylene complex, we call the π-type structures A and the n-type structures B. Structures A. The structures A are stabilized by the H-π interaction between one hydrogen atom of the HZ molecule and the π system of furan (Figure 1). The H···π distances and bond angles are defined with respect to a dummy atom located at the center of the molecule of furan (the center of the molecule was calculated from the average of the atomic coordinates of the ring atoms). With the exception of the Fu− HF system, the MP2/aVTZ geometries show H···π distances shorter than the MP2/VTZ structures (by less than 0.1 Å). On the latter level of theory in our previous work16 a red shift of the acetylene CH vibration frequency by −21.7 cm−1 was found for structure A of Fu−HCCH, which is accompanied by an elongation of the interacting CH bond by 0.003 Å. The corresponding shift and bond elongation for Fu−HCCF are calculated to be −41.5 cm−1 and 0.003 Å, respectively. In the following, we base most of our discussions on the MP2/aVTZ geometries. The order of H···π distances is HCN < HCl < HF < HCCH  HCCF. An overlay of all A geometries shows the different positions that the HZ molecules adopts in this type of complexes (Figure 2). Unlike in the Cs symmetrical structures of Fu−HCCH and Fu−HCCF, where the linear molecule points to the midpoint between the two β carbon atoms of the furan molecule, HCl, HF, and HCN point to one of the β carbon atoms of furan. The order of H··· Cβ distances is HF (2.175 Å) < HCl (2.314 Å) < HCN (2.490 Å) < HCCF (2.611 Å) < HCCH (2.623 Å). Structures B. The structures B are stabilized by the H···O interaction. Again, the MP2/VTZ and MP2/aVTZ geometries are very similar. The H···O distances decrease from 1.968 to 1.932 Å for Fu−HCl, from 2.131 to 2.104 Å for Fu−HCN, from 2.261 Å to 2.226 Å for Fu−HCCF, and from 2.313 to 2.297 Å for Fu−HCCH, when going from the VTZ to the aVTZ basis set. But perhaps the most noticeable variation is found for Fu−HF where the VTZ dimer displays Cs symmetry (∠FHO 174.2°) with a H···O distance of 1.786 Å, while the aVTZ structure is C2v symmetric with a H···O distance of 1.767 Å. 5690



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microwave spectroscopy. Our calculated H···O bond length is 1.93 (1.97) Å (MP2/aVTZ (MP2/VTZ) levels of theory) which compares very well to the experimental value of 1.97 Å. In the Fu−HCCH dimer (Figure 1) the acetylene molecule deviates from the C2v symmetry to allow for the interaction between the π system of acetylene and the closest α hydrogen atom of furan (Figure 2). This is also true for Fu−HCCF, though the deviation becomes smaller, with the O···H−C angle increasing from 143.0° to 153.6°. The distances from the closest α hydrogen atom of furan to the center of the π system of HCCH(F) (the center was calculated as the average of the atomic coordinates of the HCCH(F) atoms) are in agreement with the O···H−C angles. In the HCCH complex, the π system of acetylene is closer to furan (3.197 (3.305) Å at the MP2/ aVTZ(MP2/VTZ) levels of theory) with respect to the Fu− HCCF complex in which the HαFu···πHCCF distance is more than 0.24 Å larger (3.482 and 3.553, aVTZ and VTZ basis set, respectively). We note in passing that for Fu−HCCH and Fu− HCCF again red shifts of the vibration frequencies of the CH groups interacting with oxygen are found (−17.8 cm−1 for Fu− HCCH16 and −38.7 cm−1 for Fu−HCCF, at the MP2/VTZ level of theory), accompanied by corresponding bond elongations by 0.002−0.003 Å. Regardless of the presence of the π system in the HCN molecule, the minimum structure B of Fu−HCN does not show a CHFu···πHCN interaction. In contrast to acetylene, Fu, HCCF, HCl, HF, and HCN do have dipole moments, with values of 0.63, 0.69, 1.11, 1.81, and 3.02 D, respectively (MP2/ aVTZ). Dipole−dipole interactions favor linear C2v structures, and they should be strongest in Fu−HCN. In Fu−HCCF they are four times weaker, obviously not enough to result in the linear structure. Yet, this argument cannot be the only explanation, since it is mainly valid for larger distances where dipole−dipole interactions are the leading interaction energy contribution. By comparison of the slightly bent structure for Fu−HF at the MP2/VTZ level with the completely linear structure at the MP2/aVTZ level, one finds that the O···H distance decreases from 1.786 to 1.767 Å. This suggests that smaller O···H distances favor linear structures. MP2/VTZ geometry optimizations with frozen O···H distances (all other geometrical parameters optimized) show that the O···H−F angle increases from 174° to 180° when the O···H distance decreases by 0.1 Å from its equilibrium value of 1.786 Å. Correspondingly, the O···H−F angle decreases to 165° and 158° when the O···H distance increases by 0.1 and 0.2 Å, respectively. Thus, a double minimum structure is observed for larger distances, like the one found in our previous work for Fu−HCCH.16 Interaction Energies. The CP corrected interaction energies, Eint were calculated for the MP2/aVTZ geometries of all complexes using Hartree−Fock and a variety of electron correlation methods (MP2, CCSD(T), DFT-SAPT) with the aVTZ and aVQZ basis sets including CBS extrapolation (Table 1, Figure 3). The Hartree−Fock method systematically yields the ZH-n-type interacting structure B as the more stable of the two structures B and A. This is no surprise, since in structures B electrostatic interactions are expected to play a more important role than in the ZH-π-type interacting structures A, where dispersion interactions not described by HF should become more prominent. For the Fu−HCCH complex all electron correlation methods indicate that the ZH-π-type interacting structure A is slightly more stable, with the exception of CCSD(T), for

Figure 1. Geometries of the furan complexes with HCCH, HCCF, HCN, HCl, and HF. (a) MP2/aVTZ, (b) MP2/VTZ .

The Fu−HCl and Fu−HCN complexes show C2v symmetry with both basis sets. It is worth noticing the excellent agreement between our calculated structure of Fu−HCl and the Fu−HCl dimer identified by Shea and Kukolich46,47 using

Figure 2. Overlay of the MP2/aVTZ geometries of the furan complexes A and B with HCCH, HCCF, HCN, HCl, and HF. Orange, HCCH; yellow, HCCF; blue, HCN; magenta, HCl; and green, HF. 5691



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Table 1. Interaction Energies (in kJ/mol) at the MP2/aVTZ Optimized Geometries structure A HF/aVTZ HF/aVQZ MP2/aVTZ MP2/aVQZ MP2/CBS CCSD(T)/aVTZ CCSD(T)/CBS DFT-SAPT/aVTZ DFT-SAPT/aVQZ DFT-SAPT/CBS HF/aVTZ HF/aVQZ MP2/aVTZ MP2/aVQZ MP2/CBS CCSD(T)/aVTZ CCSD(T)/CBS DFT-SAPT/aVTZ DFT-SAPT/aVQZ DFT-SAPT/CBS HF/aVTZ HF/aVQZ MP2/aVTZ MP2/aVQZ MP2/CBS CCSD(T)/aVTZ CCSD(T)/CBS DFT-SAPT/aVTZ DFT-SAPT/aVQZ DFT-SAPT/CBS HF/aVTZ HF/aVQZ MP2/aVTZ MP2/aVQZ MP2/CBS CCSD(T)/aVTZ CCSD(T)/CBS DFT-SAPT/aVTZ DFT-SAPT/aVQZ DFT-SAPT/CBS HF/aVTZ HF/aVQZ MP2/aVTZ MP2/aVQZ MP2/CBS CCSD(T)/aVTZ CCSD(T)/CBS DFT-SAPT/aVTZ DFT-SAPT/aVQZ DFT-SAPT/CBS

Fu−HCCH 3.15 3.18 −11.29 −11.72 −12.06 −8.94 −9.70 −8.68 −8.95 −9.18 Fu−HCCF 2.76 2.80 −11.46 −11.93 −12.29 −9.28 −10.11 −8.88 −9.15 −9.38 Fu−HCN −2.47 −2.44 −17.19 −17.80 −18.27 −14.57 −15.66 −14.61 −14.97 −15.26 Fu−HCl 2.31 2.42 −17.69 −18.48 −19.15 −13.64 −15.10 −14.72 −15.12 −15.51 Fu−HF −8.61 −8.55 −18.87 −19.46 −19.93 −17.95 −19.01 −17.80 −18.10 −18.35

B −2.33 −2.37 −9.53 −9.94 −10.21 −9.15 −9.83 −8.03 −8.30 −8.47

Figure 3. CBS-extrapolated total interaction energies at the MP2/ aVTZ optimized geometries.

at the CBS level). CCSD(T)/CBS calculations of Fu−HCCF also yield both structures as nearly isoenergetic, but with a very slight preference for structure A. Thus A can be considered as the global minimum for the Fu−HCCF dimer at all levels of electron correlation theory. In the case of the Fu−HCN complex, the π-type structure is also clearly favored by all electron correlation methods. For Fu−HCl the π-type structure A is the most stable at all levels of theory except Hartree−Fock and CCSD(T), which yield the ntype structure as the global minimum. The n-type structure B of Fu−HF is the most stable at all levels of theory, as expected because of the strong electrostatic component of the interaction energy. The latter is in agreement with the results of a very recent QTAIM and NBO study of furan and thiophene complexes with hydrogen and lithium halides.15 MP2/CBS systematically overestimates the stability of structure A with respect to the CCSD(T)/CBS reference values, by −0.9 to −4.0 kJ/mol, while DFT-SAPT/CBS deviates by −0.4 to 0.7 kJ/mol only (Table 1). On the other hand, DFT-SAPT systematically underestimates the stability of structure B with respect to CCSD(T), by 1.4−3.9 kJ/mol, while MP2 deviates less, that is, by −1.4 to 1.1 kJ/mol. For all the structures the mean absolute deviation of DFT-SAPT/CBS from CCSD(T)/CBS is 1.4 kJ/mol, that of MP2/CBS 1.5 kJ/ mol. The interaction energies were also calculated for the MP2/ VTZ optimized structures (Supporting Information, Table S1). At the MP2/CBS level most of the interaction energies deviate by less than ±0.2 kJ/mol from the values given in Table 1. A larger deviation is found for HCCH and HF, where the Eint at the MP2/VTZ geometries are 0.5−0.6 kJ/mol lower in magnitude than at the MP2/aVTZ geometries. This is also true for the interaction energies calculated with CCSD(T)/ CBS and DFT-SAPT/CBS. For the other complexes, we note that the somewhat larger intermolecular distances of the MP2/ VTZ geometries tend to stabilize the A structures by up to −0.3 kJ/mol with CCSD(T) and DFT-SAPT, while structures B are affected by 0.1 kJ/mol at most. This changes the relative stability of structures A and B only in the case of Fu−HCCH: at the CCSD(T)/CBS level the ZH-π-type interacting structure A is found to be slightly more stable than structure B, though the energy difference is still less than 0.2 kJ/mol (Supporting Information, Figure S1). Relaxation and Stabilization Energies. The total stabilization energies, Estab, are calculated as the sum of the relaxation energies, Erel (as obtained with the method used for geometry optimization, see Table 2) and Eint. In general, Erel

−3.04 −3.08 −9.43 −9.85 −10.12 −9.30 −10.00 −7.92 −8.19 −8.35 −10.50 −10.60 −13.56 −14.07 −14.37 −13.94 −14.75 −12.35 −12.65 −12.79 −6.75 −6.80 −16.40 −17.24 −17.82 −15.04 −16.46 −13.27 −13.70 −13.98 −20.96 −21.13 −24.10 −25.01 −25.55 −25.20 −26.65 −21.87 −22.44 −22.71

which A and B are almost isoenergetic with a very slight preference of the ZH-n-type interacting structure B (0.1 kJ/mol 5692



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relaxation energies grow from Fu−HCCH to Fu−HF from small values below 0.1 to 0.8 kJ/mol. In no case is the energetic ordering between structures A and B affected by adding Erel to Eint. The relaxation energies at the MP2/VTZ level (Supporting Information, Table S2) in most cases agree within a few hundredth kJ/mol with the relaxation energies at the MP2/ aVTZ level. The only exception is observed for structure B of Fu−HF, with a deviation of about 0.1 kJ/mol. Clearly, this is by far not enough to change the energetic ordering of structures A and B. Furthermore, we note that the stabilization energies as directly obtained from the MP2/VTZ geometry optimizations without CP correction compare quite well with the values resulting for the same geometries via summation of Eint (MP2/ CBS) and Erel(MP2/VTZ): the magnitude of the former is by only 0.1−1.2 kJ/mol larger, with exception of Fu−HF, where the deviations amount to 3.7 (structure A) and 2.1 kJ/mol (B),

Table 2. Relaxation Energies (in kJ/mol) at the MP2/aVTZ Optimized Geometries system

struct.

Fu

HZ

total

Fu−HCCH

A B A B A B A B A B

0.01 0.05 0.01 0.05 0.04 0.14 0.06 0.21 0.11 0.42

0.02 0.02 0.04 0.03 0.05 0.05 0.19 0.19 0.24 0.38

0.04 0.07 0.05 0.08 0.09 0.19 0.25 0.40 0.35 0.79

Fu−HCCF Fu−HCN Fu−HCl Fu−HF

values for structures B are about twice as large as for structures A. In all cases mainly the distortion of the furan monomer geometry is responsible for the difference. As expected from the differences in the distances of the interacting partners, the

Table 3. DFT-SAPT Energy Contributions (in kJ/mol) at the MP2/aVTZ Optimized Geometries system

E(1) el

E(1) exch

E(2) ind

aVTZ aVQZ CBS

−10.12 −10.07 −10.07

19.68 19.66 19.66

−6.45 −6.46 −6.46

aVTZ aVQZ CBS

−11.97 −11.99 −11.99

16.13 16.12 16.12

−5.05 −5.06 −5.06

aVTZ aVQZ CBS

−10.37 −10.31 −10.31

20.00 19.99 19.99

−6.58 −6.60 −6.60

aVTZ aVQZ CBS

−12.24 −12.26 −12.26

16.52 16.51 16.51

−5.19 −5.21 −5.21

aVTZ aVQZ CBS

−16.21 −16.15 −16.15

26.55 26.53 26.53

−11.34 −11.35 −11.35

aVTZ aVQZ CBS

−18.64 −18.70 −18.70

20.79 20.78 20.78

−8.35 −8.38 −8.38

aVTZ aVQZ CBS

−18.71 −18.60 −18.60

34.00 33.99 33.99

−17.04 −17.05 −17.05

aVTZ aVQZ CBS

−26.30 −26.34 −26.34

37.25 37.24 37.24

−16.78 −16.78 −16.78

aVTZ aVQZ CBS

−21.04 −20.96 −20.96

29.39 29.39 29.39

−20.97 −21.02 −21.02

aVTZ aVQZ CBS

−36.67 −36.77 −36.77

44.20 44.16 44.16

−25.33 −25.27 −25.27

E(2) exch‑ind Fu−HCCH A 4.48 4.49 4.49 Fu−HCCH B 3.61 3.61 3.61 Fu−HCCF A 4.55 4.57 4.57 Fu−HCCF B 3.50 3.51 3.51 Fu−HCN A 6.72 6.73 6.73 Fu−HCN B 4.47 4.49 4.49 Fu−HCl A 11.68 11.71 11.71 Fu−HCl B 10.83 10.83 10.83 Fu−HF A 12.08 12.12 12.12 Fu−HF B 13.65 13.57 13.57 5693

E(2) disp

E(2) exch‑disp

δ(HF)

Eint

−15.70 −16.12 −16.42

2.06 2.17 2.25

−2.62 −2.63 −2.63

−8.68 −8.95 −9.18

−10.75 −11.07 −11.30

1.40 1.48 1.54

−1.39 −1.39 −1.39

−8.03 −8.30 −8.47

−15.87 −16.30 −16.61

2.09 2.20 2.28

−2.69 −2.70 −2.70

−8.88 −9.15 −9.38

−10.35 −10.65 −10.88

1.33 1.41 1.46

−1.49 −1.49 −1.49

−7.92 −8.19 −8.35

−17.88 −18.40 −18.79

2.38 2.52 2.61

−4.83 −4.84 −4.84

−14.61 −14.97 −15.26

−9.40 −9.68 −9.88

1.31 1.39 1.44

−2.53 −2.54 −2.54

−12.35 −12.65 −12.79

−21.07 −21.79 −22.31

3.34 3.52 3.66

−6.90 −6.90 −6.90

−14.72 −15.12 −15.51

−14.99 −15.53 −15.92

2.57 2.72 2.83

−5.84 −5.85 −5.85

−13.27 −13.70 −13.98

−14.21 −14.69 −15.03

2.30 2.43 2.52

−5.35 −5.36 −5.36

−17.80 −18.10 −18.35

−13.99 −14.52 −14.91

2.53 2.69 2.80

−6.27 −6.30 −6.30

−21.87 −22.44 −22.71



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and B, respectively (Figures 4 and 5). This shows again that molecular multipole moments have a limited value for the

respectively. This is the consequence of an approximate cancellation between the basis set superposition error and the basis set incompleteness error in the former cases. DFT-SAPT Energy Contributions. In symmetry adapted intermolecular perturbation theory (SAPT) the interaction energy is calculated as a sum of terms such as first-order (2) electrostatic E(1) el , second-order induction, Eind , and dispersion, (2) Edisp, contributions. For each term there is a corresponding exchange correction because of the simultaneous exchange of (2) (2) electrons between the monomers (E(1) exch, Eexch‑ind, and Eexch‑disp, respectively). In the efficient DFT-SAPT combination of density functional theory (DFT) with SAPT these quantities are calculated from Kohn−Sham density and linear response density matrices. Third and higher order contributions to the intermolecular interaction energy are estimated by the δ(HF) term.48 The δ(HF) term is the difference between the supermolecular CP-corrected Hartree−Fock energy and the (1) (2) (2) sum E(1) el + Eexch + Eind + Eexch‑ind as calculated from HF level properties. Table 3 lists the DFT-SAPT energy contributions obtained for the MP2/aVTZ optimized geometries. In structure A of Fu−HCCH the magnitude of the dispersion contribution is significantly larger than that of the electrostatic contribution, while in structure B they become very similar (Figure 4). In view of the charge distribution of

Figure 5. CBS-extrapolated SAPT interaction energies for Fu−HCCF at the MP2/aVTZ optimized geometries.

understanding of interacting molecules in close contact. In the Fu−HCN structure A the magnitude of E(2) disp is still somewhat larger than that of E(1) , but in structure B now E(1) el el is nearly (2) twice as large as Edisp (Figure 6). This can not only be explained

Figure 4. CBS-extrapolated SAPT interaction energies for Fu−HCCH at the MP2/aVTZ optimized geometries.

furan the relative importance of the electrostatic contribution is no surprise: according to a natural population analysis (NPA)49,50 at the MP2/aVTZ level the charge on the O atom is −0.41e, and that on a Cβ atom −0.31e (Cα: +0.09e), in agreement with the significantly but not dramatically larger magnitude of E(1) el in the O···H-interacting structure B. The relative increase in the magnitude of E(2) disp observed for structure A is partially compensated by an increase in the repulsive exchange contribution E(1) exch. Note that the second and higher order induction plus exchange-induction contributions E(2) ind , E(2) exch‑ind, and δ(HF) have larger values in the structure A, in agreement with the expectation of a relatively larger polarizability of the π system of furan compared to the O atom. Despite the nonvanishing dipole moment of HCCF, the interaction energy contributions are remarkably similar between Fu−HCCH and Fu−HCCF for both structure A

Figure 6. CBS-extrapolated SAPT interaction energies for Fu−HCN at the MP2/aVTZ optimized geometries.

by the partial charges of the closest atoms: the NPA partial charge on the oxygen atom of furan is −0.41e, while that on the hydrogen atom of HCN is essentially the same as in HCCH, that is, +0.22e. Consequently, the partial charge on the carbon atoms in HCCH is expected to be of opposite sign. However, the partial charge on the carbon atom in HCN is also slightly positive, that is, +0.08e. This is in agreement with the chemical resonance structure picture of HCN, where the first resonance structure with a CN triple bond has no formal charges while the second with a CN double bond displays a positive formal charge on carbon. In a simplified model the smaller electrostatic 5694



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sum amounts to roughly 40% of the total interaction energy, as is also the case for δ(HF). The interactions in Fu−HF, finally, are mainly governed by electrostatic and induction contributions (Figure 8), in

interaction found in Fu−HCCH can be explained on the grounds of a repulsive interaction between second neighbors, which becomes slightly attractive for Fu−HCN. The resonance model also helps to rationalize the NPA charges in HCCF: the fluorine atom has a surprisingly small charge of −0.26e, the hydrogen atom with +0.24e becomes only slightly more positive than in unsubstituted acetylene, while its neighboring carbon atom now displays a charge of −0.39e. The resonance in the π system of HCCF counteracts the polarity of its σ bonds because of the existence of a resonance structure with a CC and a CF double bond with a positive formal charge on fluorine and a negative formal charge on the carbon atom of the CH group. A resulting increase in repulsive second neighbor O···C charge−charge interactions also helps to understand the increase in the O···H−C angle when replacing HCCH with HCCF in structure B. On the other hand, that also means that the distance between this carbon atom and the positively charged Hα atom of furan (+0.19e) becomes somewhat larger, that is, by 0.18 Å, with a corresponding decrease in attractive charge−charge interactions. Clearly, induction, dispersion, and exchange interactions will also play an important role in the structural response of the system upon substitution of an H atom with F, and evidently in this case the structural response is such that none of the interaction energy contributions changes dramatically. In contrast, substitution of a CH group with a N atom leads to more significant changes in interaction energy contributions and geometrical parameters. The NPA charge of hydrogen in HCl (+0.26e) is not much larger than in the cases discussed above, and the relatively large size of the Cl atom leads one to expect dispersion interactions to play a relatively important role in Fu−HCl. Table 3 and Figure 7 nicely demonstrate the interplay between E(1) el and

Figure 8. CBS-extrapolated SAPT interaction energies for Fu−HF at the MP2/aVTZ optimized geometries.

agreement with the highly polar character of the HF molecule, for which the NPA charge on hydrogen is found to be +0.55e. Still, dispersion interactions highly contribute to the total interaction energy. They are of practically identical magnitude, however, in the two structures A and B, so that the much stronger electrostatic and induction interactions in structure B, which are only partially compensated by an increase in exchange interactions, lead to a clear preference of the FH-ntype interacting structure. This is in agreement with other theoretical and experimental studies of the complexes of furan with hydrogen halides.4,12 Here we found a good agreement between CCSD(T) and DFT-SAPT results, not only for the complexes of furan with HCl and HF, but also for the much less studied Fu−HCCH, Fu−HCCF, and Fu−HCN complexes. While the above analysis was based on the DFT-SAPT contributions obtained at the MP2/aVTZ geometries, it does not change when considering the corresponding data for the MP2/VTZ geometries as presented in Supporting Information, Table S3 and Figures S2−S6. All interaction energy contributions are somewhat smaller because of the increased intermolecular distances, yet their relative importance remains essentially unaltered. Dissociation Energies. To calculate the dissociation energy of a molecular aggregate not only its stabilization energy but also its vibrational zero point energy (ZPE) has to be known. While the ZPE can be easily calculated in the harmonic approximation, one has to be aware of its limitations. In particular in floppy systems such as the complexes considered here the potential energy surfaces (PES) tend to be very anharmonic, as exemplified by the distance-dependent double minimum feature observed for structure B of Fu− HCCH16 which is also expected for Fu−HCCF. One may safely assume that the PES of the other complexes considered here show similar features for the A structures. An accurate calculation of the ZPE for strongly anharmonic PES is not

Figure 7. CBS-extrapolated SAPT interaction energies for Fu−HCl at the MP2/aVTZ optimized geometries.

E(2) disp: their relative role is reversed in structures A and B, while most of the other interaction energy contributions do not change much. A significant change, however, is observed for E(1) exch, which increases from structure A to B reflecting the smaller intermolecular distance and accompanying stronger overlap of the molecular charge distributions. Note that the induction contributions become even more significant than for (2) Fu−HCN: while two-third of E(2) ind are canceled by Eexch‑ind, their 5695



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with CCSD(T)/CBS based on the MP2/aVTZ geometry, while D0 is 5.4 kJ/mol smaller for structure A. Here using the MP2/ VTZ geometries would lead to significantly smaller dissociation energies (by 0.5−0.6 kJ/mol) for both structures.

impossible; however, it is a formidable task, requiring the quantum chemical calculation of an extended region of the PES followed by a quantum mechanical treatment of a highdimensional nuclear dynamics problem. Despite our qualms we will therefore employ the harmonic approximation to get some feeling for the consequences of vibrations on stability and relative stability of the two structures A and B of each complex. Table 4 displays the harmonic ZPE as obtained with isotopeaveraged nuclear masses for all systems at the MP2/aVTZ level.

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CONCLUSION We studied the interaction of furan with linear molecules with π bonds and with halogen hydrides at various levels of electron correlation theory. For the Fu−HCCH and Fu−HCCF dimers according to the CCSD(T)/CBS the π- and n-structures are essentially isoenergetic. MP2 and DFT-SAPT both somewhat favor the π-type structure. In the case of Fu−HCN, the π-type structure is favored by all methods. However, there are interesting differences between the structures of Fu−HCN and Fu−HCCH(F): while the A structures of Fu−HCCH and Fu−HCCF display Cs symmetry, the HCN molecule is bent away from the mirror plane in this π-type structure. On the other hand, in the B structures the HCCH(F) molecules are bent away from the symmetry axis of furan to allow for a secondary weak interaction of furan with the π system of HCCH(F), but this interaction is absent in the C2v symmetric Fu−HCN n-type structure. Despite also having a π system, the interaction of the HCN molecule with furan is more related to that of HCl than to that of acetylene or HCCF. For Fu−HCl the π-type structure A is found to be the most stable structure with MP2 and DFT-SAPT, while CCSD(T) favors the n-type structure. For Fu−HF all methods agree that the n-type structure B is the most stable, as expected because of the strong electrostatic component of the interaction energy. Clearly, the presence of the π bond system (HCCF vs HF) results in a different interaction pattern with furan. The present study shows that the aggregation processes of furan cannot be understood only by means of dipole−dipole and electrostatic analysis. It requires a combined and detailed analysis of the SAPT energy contributions and of resonance effects on the molecular charge distributions to provide for an explanation of the aggregation of furan with both π electron rich molecules and halogen hydrides which is in agreement with previously reported experimental findings.

Table 4. Vibrational Zero Point Energies (in kJ/mol) from MP2/aVTZ system Fu HCCH HCCF HCN HCl HF Fu−HCCH Fu−HCCF Fu−HCN Fu−HCl Fu−HF

structure

ZPE

A B A B A B A B A B

183.81 69.66 52.39 41.42 18.21 24.67 255.86 255.76 238.01 238.22 228.38 228.28 206.12 206.88 214.25 216.07

In the cases Fu−HCl and Fu−HF one finds a clearly lower ZPE for structure A by 0.8 and 1.8 kJ/mol, respectively. In the other cases the ZPE for A and B agree within 0.2 kJ/mol. Adding the differences between the ZPE of the complex structures and of the isolated molecules to the stabilization energies gives D0. Using Estab from CCSD(T)/CBS we thus find the dissociation energy D0 for structure B of Fu−HCCH to be 7.5 kJ/mol, while structure A is 0.2 kJ/mol less stable. Note that the true dissociation energy is probably a few tenth of a kJ/mol larger: harmonic ZPE are likely to overestimate the energy of intermolecular vibrations and the CCSD(T)/CBS interaction energy of structure A obtained for the MP2/VTZ geometry is lower by −0.3 kJ/mol. As discussed above, the fact that the interaction energy of structure B is hardly affected by a corresponding change of the optimized geometry leads to a change in their relative stability. Despite this, it is likely that structure B was the one observed in a matrix isolation study.16 For Fu−HCCF the CCSD(T)/CBS based D0 of structure A is 8.3 kJ/mol, with structure B being less stable by 0.4 kJ/mol. This ordering is not affected by the underlying geometrical structure, while replacing the MP2/aVTZ geometries with MP2/VTZ geometries increases D0 by 0.2 kJ/mol. This is similar in the case of Fu−HCN, where D0 (CCSD(T)/CBS Eint at the MP2/aVTZ structures) for A is 12.4 kJ/mol, with B having a 0.9 kJ/mol smaller dissociation energy. In the case of Fu−HCl it is structure B which is found to have the larger D0: it is 11.2 kJ/mol, with that of A being 0.4 kJ/mol lower. The dissociation energy is hardly affected by geometrical uncertainties, while the energy difference may even drop to 0.2 kJ/mol. Finally in the case of Fu−HF structure B is clearly that with the larger dissociation energy, which is obtained as 18.3 kJ/mol

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ASSOCIATED CONTENT

S Supporting Information *

Tables and Figures corresponding to the energies at the MP2/ VTZ optimized geometries. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (E.S.-G.), georg. [email protected] (G.J.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank the Deutsche Forschungsgemeinschaft (DFG) for support of this work in the framework of the Forschergruppe 618 (FOR618). E.S.-G. thanks the Funds of the German Chemical Industry for financial support. G.J. thanks Professor John Dobson (Brisbane) for hospitality and support during a sabbatical stay where part of this work was carried out. 5696



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Competition between HÂ·Â·Â·Ï and HÂ·Â·Â·O Interactions in Furan

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