Can Stacking Interactions Exist Beyond the Commonly Accepted

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Can Stacking Interactions Exist Beyond the Commonly Accepted Limits? Rafal Kruszynski, and Tomasz Siera#ski Cryst. Growth Des., Just Accepted Manuscript • Publication Date (Web): 29 Sep 2015 Downloaded from http://pubs.acs.org on September 29, 2015

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Crystal Growth & Design

Can Stacking Interactions Exist Beyond the Commonly Accepted Limits? Rafal Kruszynski*, Tomasz Sierański Institute of General and Ecological Chemistry Lodz University of Technology, Zeromskiego 116, 90-924, Lodz, Poland

Abstract Systematic study of π-π interactions of structurally characterised compounds containing parallel benzene and/or pyridine rings was carried out. The gathered geometrical parameters were analysed in statistical terms. The quantum mechanical calculations were made for the above mentioned ring systems in different arrangements and the calculated interaction energy values were referred to the statistical data. The maximum bonding energy of the studied systems is about 3 kcal/mol. The ring rotation about the vertical axis has almost no influence on the system binding energy. In the specific ring arrangements, the stacking interactions can be bonding even for ring centroids distances larger than 6 Å. The results prove that the appliance of the generally accepted geometrical criteria of stacking interactions leads to the omission of the multiple bonding intermolecular interactions during the interpreting of the reactivity, self assembly as well as the properties of the supramolecular compounds.

Corresponding author: Rafal Kruszynski Institute of General and Ecological Chemistry Lodz University of Technology Zeromskiego 116 90-924 Lodz, Poland Phone number: + 48 42 631 31 37 Fax number: +48 42 631-31-03 Email address: [email protected]

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Can Stacking Interactions Exist Beyond the Commonly Accepted Limits? Rafal Kruszynski*, Tomasz Sierański Institute of General and Ecological Chemistry Lodz University of Technology, Zeromskiego 116, 90-924, Lodz, Poland

Abstract Systematic study of π-π interactions of structurally characterised compounds containing parallel benzene and/or pyridine rings was carried out. The gathered geometrical parameters were analysed in statistical terms. The quantum mechanical calculations were made for the above mentioned ring systems in different arrangements and the calculated interaction energy values were referred to the statistical data. The maximum bonding energy of the studied systems is about 3 kcal/mol. The ring rotation about the vertical axis has almost no influence on the system binding energy. In the specific ring arrangements, the stacking interactions can be bonding even for ring centroids distances larger than 6 Å. The results prove that the appliance of the generally accepted geometrical criteria of stacking interactions leads to the omission of the multiple bonding intermolecular interactions during the interpreting of the reactivity, self assembly as well as the properties of the supramolecular compounds.


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1. Introduction Stacking or π•••π interactions are one of the most common (together with hydrogen and halogen bonds) noncovalent interactions found in both natural and synthetic systems.1 These interactions play a very important role in controlling of the crystal packing2, stabilizing force),

6, 7, 8

3, 4, 5

and recognition of aromatic compounds (as the auxiliary

in regulation of stereoselectivity in synthetic organic reactions,9 they are significant in

biological systems (for example in nucleic acids – DNA and RNA),10 and also govern the processes important in many areas of science, such as analytical chemistry,11 medical chemistry 12, 13 and nanotechnology. 14, 15 Thus, the studies on their role in both model and real systems evolved drastically during past decades. The one of accepted models of π•••π interactions postulates that the interactions appear when the attractive interactions between π-electrons and the σ-framework outweigh unfavourable contributions such as πelectron repulsion.16, 17 This model was criticised in considerations of purely electrostatic interactions18, 19, 20 and it was suggested that the quadrupole model should be used instead, but Hunter & Sanders Model (HSM hereafter) describes the interaction of the orbitals themselves (without limiting of orbital-orbital interactions only to purely electrostatic ones), and thus, the suggested importance of interaction between quadrupoles does not disqualify the HSM, and finally both models should be considered as alternative approach to the same phenomenon. The HSM idea was confirmed e.g. by appliance of NBO method to the π•••π stacked systems,17, 21 what shows that, in orbital terms, the stacking interactions are formed primarily by the bonding π orbitals of one ring donating electron density primarily to the antibonding π orbitals of the second ring, and secondarily to the one-centre Rydberg antibonding orbitals of the π-bonded atoms of the second ring, and vice versa.22 It must be noted, that generalised knowledge of the π•••π interactions origins, quantitative predictions of geometries and energies are not available yet, however, recently a lot of theoretical calculations have been made in this field, associated with both real and model systems.21, 23,

24, 25, 26, 27

The model systems, that are extensively analysed,

are those ones containing small aromatic molecules like pyridine and benzene, arranged in selected arbitrary geometries.23,

28, 29, 30, 31, 32

They are good examples of systems in which π•••π interactions are present and they

are easy to explore with the quantum chemistry methods. Although a lot of theoretical and experimental studies have been made in this field, there is no general description of geometrical factors which enable to resolve the stacking interactions. The theoretical approaches typically are based on restrained geometrical boundaries of the ring centroids distance (dCg•••Cg), which, during the calculation process, is increased with the a priori selected increment.29,

33

To find the optimized geometry for “parallel displaced” arrangement, after establishing the

appropriate Cg•••Cg distance, one ring system is shifted sideways, with the vertical separation constrained at a fixed distance (being usually in the range of 3 - 4 Å29, 33). Such approach can be effective in finding the system geometry corresponding to global energy minimum (for the studied system arrangement), but it states nothing about other geometrical arrangements, associated with local energy minima (since the geometrical boundaries are too restrictive, the local energy minima might exists at larger Cg•••Cg distance). Some other methods introduce a number of degrees of freedom e.g. the rotation of one ring around its normal line accompanied by changes of the ring mutual arrangement about one trajectory (one set of pairs: rings interplanar distance – distance between one ring centroid and point on the normal line to the second ring),34 changes of the distance between rings centroids,35 or determination of the π•••π interactions after full optimisation of all geometrical parameters.36 Apart from determining of the interaction local maxima, the appliance of multidimensional analysis (in the current case the analysis of system energy as a function of ring centroids distance and mutual



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arrangement in polar coordinate system) also allows the establishing of the universal geometrical boundaries of stacking interactions. The complete understanding of the stacking interaction phenomenon and, in a consequence, molecules behaviour in real systems (e.g. in predicting the packing patterns in crystal engineering processes), cannot be achieved without the unambiguous criterion discriminating the bonding and non-bonding interactions. There is lack of systematic analysis of π•••π interactions based on known real chemical systems, in which these interactions play a significant role, and there is no statistical analyses of geometrical parameters of aromatic rings arrangements. The some limited studies were presented (e.g. for pyridine molecules37 and square-planar metal coordination compounds containing bipyridine ligands38), but they did not give any generalized rules about the geometrical parameters (including the possibility of existence of π•••π interactions for long dCg•••Cg distances). The systematic analysis can help to learn the limits of π•••π interactions solely on the basis of geometrical parameters, what can be useful in many fields of science (e.g. in pharmacy for drugs designing, in material sciences for crafting of functional materials). Moreover, the realistic approximation of the interaction energy between molecules containing an aromatic ring, especially N-heterocyclic one, is essential in designing of multiple biological systems (e.g. containing DNA bases and amino acids). To fill the gap in the discussed topic the geometrical parameters of the closed packed delocalised benzene-benzene, pyridine-pyridine and benzenepyridine ring systems were gathered and statistically analysed. The preferred molecules arrangements were determined and the energy of interactions was calculated for the model systems arranged in the preferred geometries. It must be noted that the possibility of existence of the long-range hydrogen bonds have been confirmed, even in case of the weak hydrogen bonds donors. The analogous possibility of existence of the longrange interactions between π systems has never been previously confirmed, as well as has never been previously rejected.

2. Experimental The compounds, included in the Cambridge Structural Database39 (v. 5.36, November 2014) containing benzene•••benzene (1), pyridine•••pyridine (2) and benzene•••pyridine (3) rings close to parallelism (the maximum dihedral angle between these rings was 5°) and with the distances between the ring centroids smaller than 7 Å were selected for analysis. The 7 Å was set arbitrary as the maximum distance between the ring centroids, because this value is definitely larger than the largest one reported for the π•••π bonded systems,40 and allows reasonable analysis of the border conditions as well as permits the establishing of the limit of formation of the bonding interactions. For the compound with six membered ring fulfilling the above criteria the following pairs of parameters were determined: the aromatic ring centre distance (d), the angle between the line connecting the aromatic rings centres and the normal line to the aromatic ring in which the connecting centres line starts (α) (Figure 1). The frequency of occurrence of data pairs (d, α) was statistically analysed for each type of ring system (1, 2 and 3, Figure 2a), and the regression curves going through the most frequent d, α pairs were calculated (Figure 2d, Table 1). To determine the equations of the regression curves the points of local maxima of occurrence (d, α pairs) were selected and the different combination of functions (among others logarithmic, exponential, power functions) of nonlinear model were tested. The expressions were checked for agreement between the observed and modelled data via the χ2 test (the d were used as explanatory variables, and α as


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response variables). In case of systems 1 and 2 the part of maxima possesses the same d or α values, i.e. the one input has multiple outputs. To fulfil the definition of the function (the one input can have only one permissible output), the maxima were separated into the sets (four in case of system 1 and two in case of 2) containing the pair located at the border of the statistics (i.e. for each d, the pairs with the smallest and largest α were placed in different sets) and along the “islands” of occurrence (Figure 2a and 2d). The equations of the regression curves were determined separately for each set. The pairs of parallel benzene-benzene, pyridine-pyridine or benzenepyridine molecules (with initial geometry optimized at the B3LYP/6-311++g(3df,2p) level of theory) were arranged in geometries with α varying in arithmetic progression from 0° to 90° with common difference of 5° and d calculated from the regression equations (Table 1). For each arrangement the two geometric models were used. In the first one the vertexes of both rings were placed in the same directions (geometric model A, Figure 1a) and in the second one the opposite vertexes of the one ring were directed along the in-plane lines perpendicular to bonds of the second ring (geometric model B, Figure 1b) i.e. the model B was created by twisting one of model A ring by 30°. The model A was studied for all the above described arrangements, while the model B was used for calculation of molecules arrangements based on the d, α pairs related by equation 1.1 (Table 1) to check the influence of ring twist (about its local six-fold axis) on the energy of the rings system. For all the above described ring pairs the quantum mechanical calculations of the intermolecular interaction energy were carried out. The 6-31++G(d,p) and 6-311++G(3df,2p) basis sets were applied to Hartree-Fock calculations followed by Moller-Plesset correlation energy correction41 truncated at second-order42 and by spin component-scaled second-order Moller-Plesset (SCS-MP2) correlation energy correction53 (as described below), as well as to B3LYP density functional based calculations43. Additionally, the cc-pVDZ → cc-pVTZ extrapolation scheme44 was applied to allow the calculation of the SCS(MI)-MP2 intermolecular interaction energies (with optimized spin-component scaling factors)44 All calculations were made by means of Gaussian09 software.45 The three dimensional data (E(d,α)) were calculated for α varying from 0° to 90° with common difference of 10° increments and for d varying from 3 Å to 7 Å with common difference of 1 Å. The SCS-MP2 calculations were accompanied by B3LYP ones to estimate the contribution of dispersion energy in the interaction energy. In all cases the intermolecular interactions energy values were corrected for basis set superposition error by usage of the counterpoise method.46 Currently, the most accurate wave-function based method enabling calculation of dispersion interactions (for model stacking interaction systems the dispersion energy contributes in noticeable amount into total interaction energy), is the one based on coupled-cluster (CC) theory.47 However, for many applications, the simple CC methods, such as CC with single and double replacements (CCSD), do not provide sufficient accuracy, and often an approximate treatment of triple excitations (triples) is necessary.48 The most known CC method, providing an estimate of connected triples, is CC with single and double and perturbative triple excitations (CCSD(T)).47,48 This method cannot be used routinely, because of the N7 scaling of the computational effort,47 (where N is the size of the electronic system), and it is applicable only to the single point calculations of small molecular systems.49 Moreover, computational costs are increased further, when the counterpoise (CP) corrections is employed to estimate the basis set superposition error (BSSE), which is significant, unless extremely large basis sets are used. The multiple approaches to the improvement of the efficiency of CC methods50,

51

were presented, but none of them makes these methods of general use. The simpler, and much



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cheaper approach of incorporating electronic correlation effect in ab initio calculations is second-order MollerPlesset perturbation theory (MP2)52 (the formal scaling in this case is N5)49. MP2 method reproduces well the electronic structure of saturated or hydrogen-bonded systems, but it often overestimates the contribution of dispersion energy in π-stacked systems.47 The Grimme53 modifies the standard MP2 method via separate scaling of the correlation-energy contributions from antiparallel- and parallel-spin pairs of electrons by two scaling factors. This method, the spin-component-scaled MP2 (SCS-MP2), radically improves the original MP2 method and it allows to obtain interaction energies very close to the ones obtained from CCSD(T) method.54 In the SCSMP2 method, the second-order correlation correction is respectively scaled, i.e. Ecorr(SCS-MP2) = pSE↑↓ + pTE↑↑+↓↓, where E↑↓ and E↑↑+↓↓ are the second-order perturbation contributions from double excitations of electron pairs with antiparallel and parallel-spin, pS and pT are the scaling factors and are equal to 6/5 and 1/3, respectively.53 It must be noted that the SCS-MP2 approach does not require additional computational effort since SCS-MP2 energies can be obtained from standard MP2 calculations.53 The benzene•••benzene, pyridine•••pyridine and benzene•••pyridine ring systems were successfully studied with usage of SCS-MP2 method, and these results were comparable with the CCSD(T) results, 33, 48 but it must be outlined that SCS-MP2 method has not been developed specifically for weakly bonded systems.47 Hence, all the calculations were also carried out using SCS(MI)-MP2 method (where MI is an abbreviated of "Molecular Interactions"). In this modification, the spin-component scaling factors were optimized, for a given basis set, against the intermolecular binding energies of the S22 test set,38 which includes hydrogen-bonded systems, dispersion-dominated systems and mixed systems. All the calculations were performed with usage of Dunning's correlation consistent basis sets55 and utilizing cc-pVDZ → cc-pVTZ extrapolation scheme (ccpV(DT)Z). Usage of this extrapolation scheme and the SCS(MI)-MP2 method is a cost-effective approach, allowing obtainment of accurate intermolecular binding energies.44 The SCS(MI)-MP2/cc-pV(DT)Z energies were calculated by following equation44:

E XY = E SCF,Y +

X 3 E CORR,X + Y 3 E CORR,Y X3 − Y3

where X = 2 and Y = 3, for the cc-pVDZ → cc-pVTZ extrapolation used in this work. The electron correlation energies (ECORR,X and ECORR,Y) were calculated using the spin-component scaling factors developed by Distasio and Head-Gordon44 and they are equal to 0.29 and 1.46, respectively for , pS and pT.

3. Results and discussion The energies derived from the SCS(MI)-MP2/cc-pV(DT)Z calculations are between those ones derived from MP2/6-31++G(d,p) and MP2/6-311++G(3df,2p). The interaction energies based on the SCS(MI)-MP2 calculations are larger of about 0.4 - 0.6 kcal/mol than those derived from SCS-MP2 calculations, and these differences mostly exist in the region with dominant π•••π interactions (as described below). The bonding energy regions are almost the same for these both methods, and the differences are negligible (Figure 2b,c). It was proven that the SCS-MP2 method reflects correctly the π•••π interactions between the stacked parallel rings and in case of the studied systems (1, 2 and 3) it excellently estimates the CCSD(T) method.33, 48 The SCS(MI)-MP2 method was developed for studying of intermolecular interactions but it is probably not the best replacement of CCSD(T) for the studied systems, because pyridine•••pyridine and benzene•••pyridine systems are not included


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in the S22 test set (which was used for this method parameterization). Taking into account the above considerations, if not explicitly stated otherwise, the further discussion is based on the SCS-MP2/6311++G(3df,2p) results of calculations. The detailed discussion of the differences between the result obtained from the usage of different basis sets and methods is placed in the Supplemental Discussion section of the Supporting Information.

Benzene-benzene systems In case of the ring system 1 the selected geometric parameters (d, α) show one strong dependence (represented by an “island” of population maxima for a given d) and three weaker dependences (along local maxima for a given d). Thus, four regression curves were calculated along favoured pairs of the selected parameters (Table 1, Figure 2d). The analysis of the population of the d, α pairs (Figure 2a) shows that three pairs of these parameters are privileged (mean d, α values for these maxima are: 3.85 Å and 24.90°, 4.97 Å and 46.31°, 5.89 Å and 65.14°, respectively). The most populated region is for d within the range of 5.5 Å - 6.0 Å and for α within the range of 60° - 70°. Because in this global maximum the d distance is larger than generally accepted for π•••π bonding interactions,56, 57 it can be assumed that such large population of the d, α pairs is caused by the phenomena other than the π•••π interactions (e.g. by the closest packing phenomenon or other than π•••π intermolecular interactions). Analysis of energies, calculated for systems with geometry based on parameters (d, α) related by regression curves, shows that the least energetic system (with the largest binding energy) is that based on the function 1.1.A. The global binding energy maximum exists for α = 25° and d = 3.92 Å and the energy is equal to 2.57 kcal/mol. This maximum binding energy occurs for parameters related by equation 1.1, but local binding energy maxima of the d, α pairs related by functions 1.2, 1.3 and 1.4 are close to the global one. It must be noted that among the studied systems the binding energy range of the model systems 1.1.A and 1.2 is the largest one (the α = {x∈R: 5°

Can Stacking Interactions Exist Beyond the Commonly Accepted

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