Stacking interactions

The structure of biomacromolecules and complex molecular systems is influenced by a variety of contributions. Among them the non-covalent interactions of aromatic, pseudoaromatic or conjugated subunits are of key importance. Non-covalent interactions occurring either intermolecularly (between distinct molecules) or intramolecularly (between segments of a given molecule that are not directly linked by a covalent bond) are involved mainly in two qualitatively different interaction motifs, planar hydrogen bonding and vertical stacking. Hydrogen bonding is one of the most successful concepts in science and nowadays its nature is well known. The electrostatic and hyperconjugation mechanisms describe all different features of hydrogen bonding and, further, what is particularly important, its theoretical description is rather straightforward. Basically any quantum mechanical (QM) procedure, including the Hartree–Fock (HF) and density functional theory (DFT) methods, provides qualitatively acceptable structural and energetic predictions. The very opposite is true about stacking, where the dominant interaction energy contribution is the London dispersion energy. The theoretical description of stacking is computationally demanding and only the most accurate QM procedures yield fully satisfactory results. Reliable studies on stacked systems and especially on extended stacked systems have appeared only recently which is mainly due to the fact that popular DFT methods (with most standard functionals) fail completely. An adequate description is obtained only when at least the coupled cluster procedure covering single, double and triple electron excitations (CCSD(T)) is used. Accurate calculations require the use of extended basis sets or even the complete basis set (CBS) limit. Such a procedure cannot, however, be used for larger complexes and much faster QM procedures should be applied. The use of MP2 is limited since the method overestimates the stacking energies. The newly introduced SCS-MP2 procedure removes the problem and for stacked clusters the method provides reliable results. Very promising data were obtained with new generation DFT methods which cover the dispersion energy and two different approaches were adopted. In the first one the dispersion energy is explicitly added to the DFT energy and the abbreviation DFT-D is used while in the second one a functional is modified and parameterized with the aim to cover the dispersion energy (e.g. the M06-2X functional).

Theoretical studies of noncovalent interactions and especially of stacking are very tedious and clearly belong to the most difficult parts of today’s computational chemistry. An essential advantage of a theoretical description is the fact that it provides a complete description of a complex, i.e. structure, geometry, energy, enthalpy and properties. Experimental description of these interactions is also complicated and despite enormous progress made in experimental techniques in the last decades, we are still very far from obtaining unambiguous information about non-covalent (stacked) complexes. Experiments do not yield complete information about a complex, though progress is being made by combining various techniques. The problem is that not many properties of a complex can be unambiguously observed. The structure is not directly observable and can only be determined by measuring the rotational constants. Rotational constants, however, do not provide an unambiguous answer concerning the structure and geometry. A very similar situation exists for the determination of the second piece of key information on the complex—its stabilization energy. The only directly observable characteristics of a complex are thus vibrational frequencies which provide, though indirectly, structural information.

Comparison of theoretical and experimental results is of vital importance for theory as well as for experiments because it allows for the testing of the ability and accuracy of newly developed procedures and techniques. The combination of experiment and theory also gives a deeper insight into the problem studied and so leads to deeper understanding.

The goal of this Themed Issue of PCCP is to demonstrate the recent developments in experimental and theoretical procedures, aiming at extended systems to play a role in biodisciplines, chemistry and physics. Future developments as well as limitations of both procedures will also be touched upon.

We collected in this Themed Issue 32 contributions covering the area from both theoretical and experimental views, and most of these papers study the stacking interactions in the gas phase. We start from joint experimental and theoretical studies bringing a more complete description of a system. Competition between stacked and H-bonded structures of the phenol⋯Ar cation and neutral complex was studied¹ by a combination of highly accurate QM procedures (CCSD(T)/CBS procedure) and MATI and ZEKE experimental techniques, which allows the presentation of a “complete” description in terms of geometry, relative energy, interaction energy and enthalpy and vibration frequencies. Let us add that this combined treatment is still impractical for extended complexes (having more than 24 atoms, which is the size of the benzene dimer). Experimental and theoretical (CCSD(T)) studies of methane with naphthalene and pyrene revealed² that complexes are rather stable (1.9 and 2.5 kcal mol⁻¹, respectively) and are not of the expected C–H⋯π type. UV and IR laser spectroscopy combined with SCS-MP2-R12 and CCSD(T) calculations were used³ for the study of H-bonded and stacked structures of complexes of 2-pyridone with various fluorobenzenes. Two-color ionization spectroscopy was used⁴ to determine the surprisingly large stabilization energies of benzene⋯CH₂Cl₂ and benzene⋯CHCl₃ complexes (3.8 and 5.2 kcal mol⁻¹, respectively) and these energies were reproduced by high-level QM calculations. Two-photon ionization and IR-UV double resonance spectroscopy together with MP2 calculations were applied⁵ to study the H-bonded and stacked structures of methyl xanthine clusters. A concerted action of experiment and theory identifies H-bonded structure for 7-methylxanthine, but a stacked structure for the theobromine dimer and the trimethylxanthine dimer. The nature and origin of CH⋯π interactions were investigated⁶ by gas-phase spectroscopic measurements and high-level QM calculations; it was shown that this bond is considerably different from the conventional H-bond. Pulsed supersonic jet expansion experiments were used⁷ to study the N–H⋯π interactions in the pyrrole dimers, trimers and tetramers. A combination of both procedures was also successfully used for the study of noncovalent interactions in isolated (complex) molecules. IR/UV double resonance spectroscopy and DFT calculations covering the dispersion energy calculations were applied⁸ for investigating different structures of Trp-Ser dipeptide; the important role of dispersion energy was underlined. Highly-resolved resonance-enhanced two-photon ionization two-color spectroscopy and QM calculations were used⁹ to study different structures of 2-(p-fluorophenyl)ethanol. The solubility of adenine in the presence of various sacharides was studied¹⁰ as an approach to investigate the interaction between adenine and sugars. Molecular mechanics simulations demonstrated the role of C–H⋯π interactions, and experiments and theory indicated the unique position of galactose. Using the Protein Data Bank and the potential of mean force the π–π pair interactions between planar residues in proteins were investigated¹¹ and the most probable structures for aromatic–aromatic and aromatic–ion pairs were found.

Base stacking in nucleic acids was reviewed¹² with attention to the highest accuracy QM calculations including the CCSD(T)/CBS results. The very complex relationship between the gas phase stacking energies and the highly variable roles of these interactions in nucleic acids was explained. Future prospects of computational studies of base stacking were also discussed. The stacking interactions of two guanine molecules appearing in B-DNA were analyzed¹³ using the MP2 method.

The development of new computational procedures requires the knowledge of the benchmark data and the JCSH-2005 and S22 datasets from the Prague laboratory were recently frequently used. The same laboratory presented¹⁴ the new dataset with the benchmark data (CCSD(T)/CBS) on 5 di- and tripeptides.

The development and testing of various theoretical procedures suitable for the study of stacking interactions is still underway. A new version of dispersion-corrected DFT method was suggested¹⁵ and tested toward the JCSH-2005 database. The resulting interaction energies and geometries agreed quite well with the benchmark data. The DFT-D and PM3-D methods were used¹⁶ for the study of amino acid⋯aromatic and carbohydrate⋯aromatic interactions and resulted in a re-parameterization of the latter procedure; in this case the S22 set was also utilized.

Stacking interactions play a key role in aromatic clusters and three families of these clusters were thoroughly investigated in this issue. They are benzene containing clusters, clusters of nucleic acid bases and clusters of aromatic amino acids. The DFT-D and CCSD(T) calculations were used¹⁷ for searching potential energy curves for the benzene dimer. High-quality QM methods including MP2, SCS-MP2 and CCSD(T) procedures were applied¹⁸ to study the substituent effects in parallel-displaced π–π interactions in the benzene dimer. It was shown that these effects have a significant effect on the π–π interactions investigated. The π–π stacked structures of dimers of benzene, 1,3,5-triazine, cyanogens and diacetylene were studied¹⁹ by MP2/CBS, SCS-MP2, SCSN-MP2 and CCSD(T)/CBS methods and also by the perturbation DFT-SAPT method. The perturbation SAPT(DFT) procedure was utilized²⁰ for the study of stacked dimers of benzene, naphthalene, anthracene and pyrene. The theoretical results were compared with experimental findings; in the case of the naphthalene dimer different global structures resulted while for the antracene dimer theory agreed with experiment. The π–π interactions in the parallel-offset arenes were studied²¹ by various DFT methods including the M06-2X functional properly covering the dispersion energy. This energy was shown to be an important factor in stabilizing the titled complexes. The MP2 and CCSD(T) calculations have been used²² to investigate the interactions of dimethyl ether with aromatic rings and dispersion energy was found to be a large component of the dimer stabilization. On the basis of DFT calculations and statistical analysis it was shown²³ that the crystal packing of TCNQ anion π-radicals is governed by intermolecular π–π bonding. The role of polarization in the stabilization of various X⁺⋯benzene complexes was investigated²⁴ by MP2 and SAPT calculations.

Stacked structures of uracil and cytosine with aromatic and non-aromatic amino acids were investigated²⁵ by the MP2 method. A similar study on stacking interactions between the aromatic amino acids and natural or methylated nucleobases was performed²⁶ using the MP2 calculations. A QM/MM study of fluoroaromatic interactions at the binding site of carbonic anhydrase II was made²⁷ with the DFT-D method. LMP2, SCS-MP2 and SCSN-LMP2 methods were utilized²⁸ for calculating the stacking interactions in 10 B-DNA base-pair steps and the very good performance of the SCSN-LMP2/aug-cc-pVTZ procedure was highlighted. The structure and interaction energies of stacked graphene⋯nucleobase and graphene⋯H-bonded base pairs were investigated²⁹ at the DFT-D and SCS-MP2 levels. Buckyball tweezers and its supramolecular complexes were studied³⁰ by the DFT/M06-L and DFT/M06-2X methods, properly covering the dispersion energy. A parameter-free DFT/CCSD(T) correction scheme was proposed³¹ for accurate, close to the CCSD(T), calculations of molecular solids.

All previous studies concerned the electronic ground state. The excited states of stacked 9-methylguanine oligomers adapting the B-DNA conformation were investigated³² by using TD-DFT calculations.

Finally, I would like to thank all the authors who contributed to the Themed Issue. Thanks are also due to the staff of PCCP who came with the idea for this issue and have also done an excellent job in finishing the issue in a very short time.

Guest Edited by Pavel Hobza (Prague)

Papers in this issue
1	K. Muller-Dethlefs et al., DOI: 10.1039/b801460b
2	S. Tsuzuki et al., DOI: 10.1039/b718550b
3	S. Leutwyler et al., DOI: 10.1039/b718494h
4	A. Fujii et al., DOI: 10.1039/b717053j
5	M. S. de Vries et al., DOI: 10.1039/b719874d
6	S. Tsuzuki et al., DOI: 10.1039/b718656h
7	M. A. Suhm et al., DOI: 10.1039/b717823a
8	K. Kleinermanns et al., DOI: 10.1039/b718710f
9	H. J. Neusser et al., DOI: 10.1039/b718974e
10	D. J. Fantini et al., DOI: 10.1039/b802594k
11	P. Procacci et al., DOI: 10.1039/b718519g
12	P. Hobza et al., DOI: 10.1039/b719370j
13	P. Cysewski et al., DOI: 10.1039/b718635e
14	H. Valdes et al., DOI: 10.1039/b719294k
15	U. Rothlisberger et al., DOI: 10.1039/b718594d
16	I. H. Hillier et al., DOI: 10.1039/b719764k
17	S. Chakrabarti et al., DOI: 10.1039/b717983a
18	C. D. Sherrill et al., DOI: 10.1039/b718742d
19	G. S. Tschumper et al., DOI: 10.1039/b718720c
20	R. Podeszwa et al., DOI: 10.1039/b719725j
21	J. S. Siegel et al., DOI: 10.1039/b800031j
22	B. W. Gung et al., DOI: 10.1039/b718722j
23	J. Huang et al., DOI: 10.1039/b717752f
24	F. J. Luque et al., DOI: 10.1039/b719461g
25	P. Cysewski, DOI: 10.1039/b718394a
26	S. D. Wetmore et al., DOI: 10.1039/b718621e
27	I. H. Hillier et al., DOI: 10.1039/b715514j
28	J. A. Platts et al., DOI: 10.1039/b718691f
29	S. Grimme et al., DOI: 10.1039/b718788b
30	D. G. Truhlar et al., DOI: 10.1039/b717744e
31	O. Bludsky et al., DOI: 10.1039/b718701g
32	R. Improta, DOI: 10.1039/b718562f

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