Analysis of non-covalent interactions in (bio)organic molecules using orbital-partitioned localized MP2

Localized molecular orbitals (LMO) are used as basis for an MP2 treatment (LMP2) of electron correlation energies. The major aim is an improved understanding of the non-covalent interactions in large molecules with an emphasis on intra-molecular dispersion effects. A partitioning of the inter-fragment electron correlation energy into electron pairs of different orbital type (i.e., sigma, pi, lone-pairs) is presented. The benzene dimer, 1,4-diphenylbutane conformations, and the tyrosine-glycine dipeptide are used as model systems. For the benzene dimer, comparisons with CCSD(T) data are made in order to analyse the MP2 problems for pi-pi stacking. A comparison of phenyl-phenyl interactions in the benzene dimer and for 1,4-diphenylbutane conformations reveals a very good transferability of dispersion-type contributions to binding from an inter-molecular to an intra-molecular situation. In both systems, the relative (percentage) contributions of sigma-sigma, sigma-pi, and pi-pi pairs to the total inter-fragment correlation energy is a clear signature for the binding mode (pi-stacked vs. T-shaped). For various benzene dimer conformations, we find a linear relation between the MP2 interaction energy error and the correlation contribution from pi-pi pairs. In the dipeptide, also dispersion-type electron correlations between the glycyl amino acid residue and the phenol group are most relevant for folding. This convincingly explains problems of DFT with such systems reported previously. Although in this case only one aromatic ring (and a glycyl moiety) is involved, the same sigma-sigma, sigma-pi, and pi-pi correlations seem to dominate the shape of the potential energy surface.     

High-accuracy quantum mechanical studies of pi-pi interactions in benzene dimers

Although supramolecular chemistry and noncovalent interactions are playing an increasingly important role in modern chemical research, a detailed understanding of prototype noncovalent interactions remains lacking. In particular, pi-pi interactions, which are ubiquitous in biological systems, are not fully understood in terms of their strength, geometrical dependence, substituent effects, or fundamental physical nature. However, state-of-the-art quantum chemical methods are beginning to provide answers to these questions. Coupled-cluster theory through perturbative triple excitations in conjunction with large basis sets and extrapolations to the complete basis set limit have provided definitive results for the binding energy of several configurations of the benzene dimer, and benchmark-quality ab initio potential curves are being used to calibrate new density functional and force-field models for pi-pi interactions. Studies of substituted benzene dimers indicate flaws in the conventional wisdom about substituent effects in pi-pi interactions. Three-body and four-body interactions in benzene clusters have also been examined.     

Understanding of assembly phenomena by aromatic-aromatic interactions: benzene dimer and the substituted systems

Interactions involving aromatic rings are important in molecular/biomolecular assembly and engineering. As a consequence, there have been a number of investigations on dimers involving benzene or other substituted pi systems. In this Feature Article, we examine the relevance of the magnitudes of their attractive and repulsive interaction energy components in governing the geometries of several pi-pi systems. The geometries and the associated binding energies were evaluated at the complete basis set (CBS) limit of coupled cluster theory with singles, doubles, and perturbative triples excitations [CCSD(T)] using a least biased scheme for the given data set. The results for the benzene dimer indicate that the floppy T-shaped structure (center-to-center distance: 4.96 A, with an axial benzene off-centered above the facial benzene) is isoenergetic in zero-point-energy (ZPE) corrected binding energy (D0) to the displaced-stacked structure (vertical interplanar distance: 3.54 A). However, the T-shaped structure is likely to be slightly more stable (D0 approximately equal to 2.4-2.5 kcal/mol) if quadruple excitations are included in the coupled cluster calculations. The presence of substituents on the aromatic ring, irrespective of their electron withdrawing or donating nature, leads to an increase in the binding energy, and the displaced-stacked conformations are more stabilized than the T-shaped conformers. This explains the wide prevalence of displaced stacked structures in organic crystals. Despite that the dispersion energy is dominating, the substituent as well as the conformational effects are correlated to the electrostatic interaction. This electrostatic origin implies that the substituent effect would be reduced in polar solution, but important in apolar media, in particular, for assembling processes.     

Estimates of the ab initio limit for pi-pi interactions: the benzene dimer

State-of-the-art electronic structure methods have been applied to the simplest prototype of aromatic pi-pi interactions, the benzene dimer. By comparison to results with a large aug-cc-pVTZ basis set, we demonstrate that more modest basis sets such as aug-cc-pVDZ are sufficient for geometry optimizations of intermolecular parameters at the second-order M?ller-Plesset perturbation theory (MP2) level. However, basis sets even larger than aug-cc-pVTZ are important for accurate binding energies. The complete basis set MP2 binding energies, estimated by explicitly correlated MP2-R12/A techniques, are significantly larger in magnitude than previous estimates. When corrected for higher-order correlation effects via coupled cluster with singles, doubles, and perturbative triples [CCSD(T)], the binding energies D(e) (D(0)) for the sandwich, T-shaped, and parallel-displaced configurations are found to be 1.8 (2.0), 2.7 (2.4), and 2.8 (2.7) kcal mol(-1), respectively.     

Substituent effects in pi-pi interactions: sandwich and T-shaped configurations

Sandwich and T-shaped configurations of benzene dimer, benzene-phenol, benzene-toluene, benzene-fluorobenzene, and benzene-benzonitrile are studied by coupled-cluster theory to elucidate how substituents tune pi-pi interactions. All substituted sandwich dimers bind more strongly than benzene dimer, whereas the T-shaped configurations bind more or less favorably depending on the substituent. Symmetry-adapted perturbation theory (SAPT) indicates that electrostatic, dispersion, induction, and exchange-repulsion contributions are all significant to the overall binding energies, and all but induction are important in determining relative energies. Models of pi-pi interactions based solely on electrostatics, such as the Hunter-Sanders rules, do not seem capable of explaining the energetic ordering of the dimers considered.     

Aromatic-aromatic interactions in proteins: beyond the dimer

Aromatic residues are key widespread elements of protein structures and have been shown to be important for structure stability, folding, protein-protein recognition, and ligand binding. The interactions of pairs of aromatic residues (aromatic dimers) have been extensively studied in protein structures. Isolated aromatic molecules tend to form higher order clusters, like trimers, tetramers, and pentamers, that adopt particular well-defined structures. Taking this into account, we have surveyed protein structures deposited in the Protein Data Bank in order to find clusters of aromatic residues in proteins larger than dimers and characterized them. Our results show that larger clusters are found in one of every two unique proteins crystallized so far, that the clusters are built adopting the same trimer motifs found for benzene clusters in vacuum, and that they are clearly nonlocal brining primary structure distant sites together. We extensively analyze the trimers and tetramers conformations and found two main cluster types: a symmetric cluster and an extended ladder. Finally, using calmodulin as a test case, we show aromatic clsuters possible role in folding and protein-protein interactions. All together, our study highlights the relevance of aromatic clusters beyond the dimer in protein function, stability, and ligand recognition.     

Hydrogen-bonded structures for self-aggregates of 2,5-dimethylpyrrole and its binary clusters with pyrrole studied by IR cavity ringdown spectroscopy

N-H···π hydrogen-bonded (H-bonded) structures were studied by applying vibrational spectroscopy to self-aggregate clusters of 2,5-dimethylpyrrole (DMPy) and its binary clusters with pyrrole (Py). The NH stretching vibrations of jet-cooled clusters were observed by IR cavity ringdown spectroscopy. A combination of experiments and density functional theory calculations revealed the stable structures, intermolecular binding energies, and harmonic vibrational frequencies. The IR spectrum of the DMPy self-aggregate clusters was very similar in spectral features to that of the Py clusters in a previous work. The observed NH stretching vibrations at 3505, 3420, 3371, and 3353 cm(-1) are simultaneously red-shifted by ～25 cm(-1) from the Py monomer, dimer, trimer, and tetramer, respectively. Based on a spectral analogy of DMPy with Py, and a consistency of the calculated harmonic frequencies with experiments, the H-bonded structures of the DMPy clusters were determined to be of a T-shape for a dimer and a cyclic for a trimer and a tetramer. For the DMPy-Py binary clusters, we discussed the stability and geometry of the N-H···π interactions in the T-shaped dimer and the cyclic trimer. The binary dimer showed the only single NH stretch at 3419 cm(-1) in the IR spectrum. A vibrational analysis of the H-bonded NH stretches as well as the calculated stabilization energies deduced that only the binary dimer by DMPy as an acceptor and Py as a donor can exist in a supersonic jet. For binary trimers, NH stretches were observed due to both (DMPy)(2)-(Py)(1) and (DMPy)(1)-(Py)(2). They were found to have different vibrational patterns from each other; the former showed three dispersed NH stretches, and the other had two quasi-degenerate NH stretches. Throughout this study, we also considered the intermolecular geometries, such as the H-bond distance and the angle in terms of the methyl group substitution effect.     

A theoretical investigation on the effect of π–π stacking interaction on 1H isotropic chemical shielding in certain homo- and hetero-nuclear aromatic systems

Significant changes in the proton chemical shielding (and hence the chemical shift) are predicted in going from the monomer to the dimer of benzene, naphthalene, pyridine and quinoline systems and also the trimer of benzene and pyridine. The computed NMR spectra show additional splitting in going from the monomer to the dimer and the trimer of different species. The aromatic protons show a significant upfield shift due to the enhancement of anisotropic shielding by the π electron cloud of the neighboring molecule(s). The nature of the NMR spectra also changes with the orientation of the stacked conformers. The results obtained using M?ller-Plesset second-order perturbation theory along with the GIAO method show the changes in isotropic shielding, in a reasonable basis set independent fashion.     

Accurate description of van der Waals complexes by density functional theory including empirical corrections

An empirical method to account for van der Waals interactions in practical calculations with the density functional theory (termed DFT-D) is tested for a wide variety of molecular complexes. As in previous schemes, the dispersive energy is described by damped interatomic potentials of the form C6R(-6). The use of pure, gradient-corrected density functionals (BLYP and PBE), together with the resolution-of-the-identity (RI) approximation for the Coulomb operator, allows very efficient computations for large systems. Opposed to previous work, extended AO basis sets of polarized TZV or QZV quality are employed, which reduces the basis set superposition error to a negligible extend. By using a global scaling factor for the atomic C6 coefficients, the functional dependence of the results could be strongly reduced. The "double counting" of correlation effects for strongly bound complexes is found to be insignificant if steep damping functions are employed. The method is applied to a total of 29 complexes of atoms and small molecules (Ne, CH4, NH3, H2O, CH3F, N2, F2, formic acid, ethene, and ethine) with each other and with benzene, to benzene, naphthalene, pyrene, and coronene dimers, the naphthalene trimer, coronene. H2O and four H-bonded and stacked DNA base pairs (AT and GC). In almost all cases, very good agreement with reliable theoretical or experimental results for binding energies and intermolecular distances is obtained. For stacked aromatic systems and the important base pairs, the DFT-D-BLYP model seems to be even superior to standard MP2 treatments that systematically overbind. The good results obtained suggest the approach as a practical tool to describe the properties of many important van der Waals systems in chemistry. Furthermore, the DFT-D data may either be used to calibrate much simpler (e.g., force-field) potentials or the optimized structures can be used as input for more accurate ab initio calculations of the interaction energies.     

CH/pi interactions involving aromatic amino acids: refinement of the CHARMM tryptophan force field

High-level ab initio calculations have been carried out to study weak CH/pi interactions and as a check of the CHARMM force field for aromatic amino acids. Comparisons with published data indicate that the MP2/cc-pVTZ level of theory is suitable for calculations of CH/pi interaction, including the T-shape benzene dimer. This level of theory was, therefore, applied to investigate CH/pi interactions between ethene or cis-2-butene and benzene in a variety of orientations. In addition, complexes between ethene and a series of model compounds (toluene, methylindole and p-cresol) representing the aromatic amino acids were studied motivated by the presence of CH/pi interactions in biological systems. Ab initio binding energies were compared to the binding energies obtained with the CHARMM22 force field. In the majority of orientations, CHARMM22 reproduces the preferred binding modes, with excellent agreement for the benzene dimer. Small discrepancies found in the calculations involving methylindole along with a survey of published thermodynamic data for the aromatic amino acids prompted additional optimization of the tryptophan force field. Partial atomic charges, Lennard-Jones parameters, and force constants were improved to obtain better intra- and intermolecular properties, with significant improvements obtained in the reproduction of experimental heats of sublimation for indole and free energies of aqueous solvation for methylindole.     

H‐bonding and stacking interactions between chloroquine and temozolomide

The interactions between temozolomide and chloroquine were examined via Dispersion‐Corrected Density Functional Theory and MP2 methods. Chloroquine was considered in both its lowest energy structure and in a local minimum where its aromatic system and secondary amine group are free to interact directly with temozolomide. The accessibility of these two components to intermolecular interaction makes the lowest energy dimer of this local monomer minimum competitive in total energy with that involving chloroquine's most stable monomer geometry. In either case, the most stable heterodimer places the aromatic ring systems of the two molecules parallel and directly above one another in a stacked geometry. Most of the local minima are also characterized by a stacked geometry as well. Comparison between B3LYP and B3LYP‐D binding energies confirms dispersion is a primary factor in stabilizing these structures. © 2016 Wiley Periodicals, Inc.     

DFT study on cooperativity in the interactions of hydrazoic acid clusters

Density functional theory at the B3LYP level with the 6‐311G** basis set is performed to calculate the systems consisting of up to four hydrazoic acid molecules. The dimers are found to exhibit cyclic and chain structures with N … H contacts at ca. 2.1–2.7 Å. However, there are only cyclic structures with N … H contacts at ca. 2.0–2.3 Å and 2.0–2.1 Å in the trimer and tetramer, respectively. Hydrogen bond distances in the trimer and tetramer are shorter than those in the cyclic dimer as a result of the stronger interaction between molecules. The contribution of cooperative effect to the interaction energy is significant. After the correction of the basis set superposition error and zero‐point energy, the binding energies are ?10.69, ?29.34, and ?54.26 kJ·mol^?1 for the most stable dimer, trimer, and tetramer, respectively. The calculated IR shifts for N? H stretching mode increase with the size of the cluster growths, reaching more than 200 cm^?1 in the tetramer. For the most stable clusters, the transition from the monomer to dimer, dimer to trimer, and trimer to tetramer involve changes of ?14.40, ?25.68, and ?31.88 kJ·mol^?1 for the enthalpies at 298.15 K and 1atm, respectively. We also perform Mulliken populations analysis and find the Mulliken populations on intermolecular N … H increasing in the sequence of the dimer, trimer, and tetramer. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem 94: 279–286, 2003     

Stacking of triphenylene: characterization of the potential energy surface

The interaction potential energy of triphenylene dimer has been calculated with Møller–Plesset second-order perturbation theory for various geometrical configurations. Different types of geometrical perturbations such as rotation, displacements and their combinations are studied in terms of their effects on the stability of the dimer. Minimum energy conformers for face to face, rotated, parallel displaced and T-shape structures are obtained. For the unsubstituted triphenylene, the 35° rotation of one of the monomers results in the global minimum. However, the dimer is still very flexible in terms of displacements. A helical structure seems to be the most stable form for the trimer. For large stacked clusters, the two body forces dominate the interactions while at small monomer–monomer separation, three body terms behave like z ^?9 where z is the vertical distance between two adjacent monomers.     

Highly Accurate CCSD(T) and DFT–SAPT Stabilization Energies of H‐Bonded and Stacked Structures of the Uracil Dimer

The CCSD(T) interaction energies for the H‐bonded and stacked structures of the uracil dimer are determined at the aug‐cc‐pVDZ and aug‐cc‐pVTZ levels. On the basis of these calculations we can construct the CCSD(T) interaction energies at the complete basis set (CBS) limit. The most accurate energies, based either on direct extrapolation of the CCSD(T) correlation energies obtained with the aug‐cc‐pVDZ and aug‐cc‐pVTZ basis sets or on the sum of extrapolated MP2 interaction energies (from aug‐cc‐pVTZ and aug‐cc‐pVQZ basis sets) and extrapolated ΔCCSD(T) correction terms [difference between CCSD(T) and MP2 interaction energies] differ only slightly, which demonstrates the reliability and robustness of both techniques. The latter values, which represent new standards for the H‐bonding and stacking structures of the uracil dimer, differ from the previously published data for the S22 set by a small amount. This suggests that interaction energies of the S22 set are generated with chemical accuracy. The most accurate CCSD(T)/CBS interaction energies are compared with interaction energies obtained from various computational procedures, namely the SCS–MP2 (SCS: spin‐component‐scaled), SCS(MI)–MP2 (MI: molecular interaction), MP3, dispersion‐augmented DFT (DFT–D), M06–2X, and DFT–SAPT (SAPT: symmetry‐adapted perturbation theory) methods. Among these techniques, the best results are obtained with the SCS(MI)–MP2 method. Remarkably good binding energies are also obtained with the DFT–SAPT method. Both DFT techniques tested yield similarly good interaction energies. The large magnitude of the stacking energy for the uracil dimer, compared to that of the benzene dimer, is explained by attractive electrostatic interactions present in the stacked uracil dimer. These interactions force both subsystems to approach each other and the dispersion energy benefits from a shorter intersystem separation.     

Substituent effects in the benzene dimer are due to direct interactions of the substituents with the unsubstituted benzene

The prevailing views of substituent effects in the sandwich configuration of the benzene dimer are flawed. For example, in the polar/pi model of Cozzi and co-workers (J. Am. Chem. Soc. 1992, 114, 5729), electron-withdrawing substituents enhance binding in the benzene dimer by withdrawing electron density from the pi-cloud of the substituted ring, reducing the repulsive electrostatic interaction with the nonsubstituted benzene. Conversely, electron-donating substituents donate excess electrons into the pi-system and diminish the pi-stacking interaction. We present computed interaction energies for the sandwich configuration of the benzene dimer and 24 substituted dimers, as well as sandwich complexes of substituted benzenes with perfluorobenzene. While the computed interaction energies correlate well with sigmam values for the substituents, interaction energies for related model systems demonstrate that this trend is independent of the substituted ring. Instead, the observed trends are consistent with direct electrostatic and dispersive interactions of the substituents with the unsubstituted ring.     

Pi-pi interaction in pyridine

pi-pi Interaction in pyridine dimer and trimer has been investigated in different geometries and orientations at the ab initio (HF, MP2) and DFT (B3LYP) levels of theory using various basis sets (6-31G, 6-31G, 6-311++G) and corrected for basis set superposition error (BSSE). While the HF and DFT calculations show the pyridine dimer and the trimer to be unstable with respect to the monomer, the MP2 calculations show them to be clearly stable, thus emphasizing the need to include electron correlation while determining stacking interaction in such systems. The calculated MP2/6-311++G binding energy (100% BSSE corrected) of the parallel-sandwich, antiparallel-sandwich, parallel-displaced, antiparallel-displaced, T-up and T-down geometries for pyridine dimer are 1.53, 3.05, 2.39, 3.97, 1.91, 1.47 kcal/mol, respectively. The results show the antiparallel-displaced geometry to be the most stable. The binding energies for the trimer in parallel-sandwich, antiparallel-sandwich, and antiparallel-displaced geometry are found to be 3.18, 6.14, and 8.04 kcal/mol, respectively.     

Studies in hydrogen bonding: Association in methanol using an empirical potential

The empirical potential, EPEN , has been used to establish the structures of isolated hydrogen-bonded clusters in methanol. The most stable configuration of the dimer is found to have a trans near-linear form, whereas the most stable forms of the trimer and tetramer are cyclic. Charge interactions in the tetramer make it the most stable, in terms of energy per hydrogen bond, of these three species. These results are in conformity with various types of experiment. Other species of dimer, trimer, and tetramer, corresponding to local energy minima, have also been identified.     

Synthesis of cyclic chlorophyll oligomers

As a new model of photosynthetic light-harvesting antennas, cyclic dimer, trimer, and tetramer of chlorophyllous moieties were prepared by intermolecular transesterification of a hydroxy-methoxycarbonyl-chlorin using 1,3-dichlorotetrabutyl distannoxane as a catalyst. ¹H NMR and UV-vis spectra showed that the cyclic oligomers tended to form stacked conformers through intramolecular π-π interactions of the chlorin macrocycles. It was demonstrated that the cyclic trimer could form a complex with fullerenes in CDCl₃.     

Gas-phase ion mobilities and structures of benzene cluster cations (C6H6)n+, n = 2-6

Benzene clusters are generated by pulsed supersonic beam expansion, ionized by electron impact, mass-selected and then injected into a drift cell for ion mobility measurements in a helium buffer gas. The measured collision cross sections and theoretical calculations are used to determine the structures of the cluster cations (C(6)H(6))(n)(+) with n = 2-6. Density functional theory calculation, at an all-electron level and without any symmetry constraint, predicts that the dimer cation has two nearly degenerate ground state structures with the sandwich configuration more stable than the T-configuration by only 0.07 eV. The ion mobility experiment indicates that only one structure is observed for the mass-selected dimer cation at room temperature. The calculated cross section for the sandwich structure agrees very well (within 2.4%) with the experimental value. For the n = 3-6 clusters, the experiments suggest the presence of at least two structural isomers for each cluster. A Monte Carlo minimum-energy search technique using the 12-site OPLS potential for benzene is used to determine the structures of the lowest-energy isomers. The calculated cross sections for the two lowest-energy isomers of the n = 3-6 clusters agree well with the experimental results. The clusters' structures reveal two different growth patterns involving a sandwich dimer core or a pancake trimer stack core. The lowest-energy isomers of the n = 3-6 clusters incorporate the pancake trimer stack as the cluster's core. The trimer stack allows the charge to hop between two dimers, thus maximizing charge resonance interaction in the clusters. For larger clusters, the appearance of magic numbers at n = 14, 20, 24, 27, and 30 is consistent with the incorporation of a sandwich dimer cation within icosahedral, double icosahedral, and interpenetrating icosahedral structures. On the basis of the ion mobility results and the structural calculations, the parallel-stacked motif among charged aromatic-aromatic interactions is expected to play a major role in determining the structures of multi aromatic components. This conclusion may provide new insights for experimental and theoretical studies of molecular design and recognition involving aromatic systems.