Density-functional theory-symmetry-adapted intermolecular perturbation theory with density fitting: A new efficient method to study intermolecular interaction energies

A B3LYP and MP2(full) theoretical investigation into cooperativity effects, aromaticity and thermodynamic properties in the Na(+)⋯benzonitrile⋯H2O ternary complex

The cooperativity effects between H-bonding and Na(+)⋯π or Na(+)⋯σ interactions in Na(+)⋯benzonitrile⋯H2O complexes were investigated using the B3LYP and MP2(full) methods with 6-311++G(2d,p) and aug-cc-pVTZ basis sets. The thermodynamic cooperativity and the influence of this cooperativity on aromaticity was evaluated by nucleus-independent chemical shifts (NICS). The results showed that the influence of the Na(+)⋯σ or Na(+)⋯π interaction on the hydrogen bond is more pronounced than that of the latter on the former. The cooperativity effect appeared in the Na(+)⋯σ interaction complex while the anti-cooperativity effect tended to be in the Na(+)⋯π system. The change in enthalpy is the major factor driving cooperativity. Thermodynamic cooperativity is not in accordance with the cooperativity effect evaluated by the change of interaction energy. The ring aromaticity of is weakened while the bond dissociation energy (BDE) of the C-CN bond increases upon ternary complex formation. The cooperativity effect (E coop) correlates with R c (NICS(1)ternary/NICS(1)binary) and ΔΔδ (Δδ ternary - Δδ binary) involving the ring and C ≡ N bond, as well as R BDE(C-CN) [BDE(C-CN)ternary/BDE(C-CN)binary], respectively. AIM (atoms in molecules) analysis confirms the existence of cooperativity.

Tractability gains in symmetry-adapted perturbation theory including coupled double excitations: CCD+ST(CCD) dispersion with natural orbital truncations

This work focuses on efficient and accurate treatment of the intermolecular dispersion interaction using the CCD+ST(CCD) dispersion approach formulated by Williams et al. [J. Chem. Phys. 103, 4586 (1995)]. We apply natural orbital truncation techniques to the solution of the monomer coupled-cluster double (CCD) equations, yielding substantial accelerations in this computationally demanding portion of the SAPT2+(CCD), SAPT2+(3)(CCD), and SAPT2+3(CCD) analyses. It is shown that the wholly rate-limiting dimer-basis particle-particle ladder term can be computed in a reduced natural virtual space which is essentially the same size as the monomer-basis virtual space, with an error on the order of a few thousandths of 1 kcal mol(-1). Coupled with our existing natural orbital techniques for the perturbative triple excitation contributions [E. G. Hohenstein and C. D. Sherrill, J. Chem. Phys. 133, 104107 (2010)], this technique provides speedups of greater than an order of magnitude for the evaluation of the complete SAPT2+3(CCD) decomposition, with a total error of a few hundredths of 1 kcal mol(-1). The combined approach yields tractability gains of almost 2× in the system size, allowing for SAPT2+3(CCD)/aug-cc-pVTZ analysis to be performed for systems such as adenine-thymine for the first time. Natural orbital based SAPT2+3(CCD)/aug-cc-pVTZ results are presented for stacked and hydrogen-bonded configurations of uracil dimer and the adenine-thymine dimer.

The nature of interactions in nicotinamide crystal

In this study, we analyze the nature of intermolecular interactions in nicotinamide complexes appearing in conformations found in the crystal structure, including many-body effects. In doing so, we employ symmetry-adapted perturbation theory based on density functional theory description of monomers, and we perform the many-body variational-perturbational interaction energy decomposition. The principal finding of this study is that the stability of nicotinamide complexes is a complicated interplay of four (large in magnitude) interaction-energy components, i.e. induction, dispersion, electrostatic and exchange repulsion. However, the last two contributions cancel each other out to a large extent. In the case of considered three-body complexes, the nonadditivity effects are found to be not important. Based on the results of topological analysis of charge densities we characterized also the properties of short H ⋯ H contact and identified it as a weak noncovalent closed shell interaction.

GEM*: A Molecular Electronic Density-Based Force Field for Molecular Dynamics Simulations

GEM*, a force field that combines Coulomb and Exchange terms calculated with Hermite Gaussians with the polarization, bonded, and modified van der Waals terms from AMOEBA is presented. GEM* is tested on an initial water model fitted at the same level as AMOEBA. The integrals required for the evaluation of the intermolecular Coulomb interactions are efficiently evaluated by means of reciprocal space methods. The GEM* water model is tested by comparing energies and forces for a series of water oligomers and MD simulations. Timings for GEM* compared to AMOEBA are presented and discussed.

Effect of stepwise microhydration on the guanidinium···π interaction

The characteristics of the interaction of microhydrated guanidinium cation with the aromatic moieties present in the aromatic amino acids side chains have been studied by means of computational methods. The most stable minima found for non-hydrated complexes correspond in all cases to structures with guanidinium oriented toward the ring and interacting by means of N-H···π hydrogen bonds. The interaction becomes stronger when going from benzene (-14 kcal mol⁻¹) to phenol (-17 kcal mol⁻¹) to indole (-21 kcal mol⁻¹). These complexes are held together mainly by electrostatics, but with important contributions from induction and dispersion. The presence of a small number of water molecules significantly affects the characteristics of the complexes. Hydrogen bonds formed by water with the cation, another water molecule, or the aromatic units become more and more similar in intensity as water molecules are included in the complex, leading to a great variety of minima with similar stability but showing very different structural patterns. The behavior is similar with the three aromatic units, the differences in stability mainly being a consequence of the different strength of the cation···π contact.

On the origin of the substantial stabilisation of the electron-donor 1,3-dithiole-2-thione-4-carboxyclic acid···I2 and DABCO···I2 complexes

The stabilisation energies of the crystal structures of 1,3-dithiole-2-thione-4-carboxyclic acid···I2 and DABCO···I2 complexes determined by the CCSD(T)/CBS method are very large and exceed 8 and 15 kcal mol(-1), respectively. The DFT-D method (B97-D3/def2-QZVP) strongly overestimates these stabilisation energies, which support the well-known fact that the DFT-D method is not very applicable to the study of charge-transfer complexes. On the other hand, the M06-2X/def2-QZVP method provides surprisingly reliable energies. A DFT-SAPT analysis has shown that a substantial stabilisation of these complexes arises from the charge-transfer energy included in the induction energy and that the respective induction energy is much larger than that of other non-covalently bound complexes. The total stabilisation energies of the complexes mentioned as well as of those where iodine has been replaced by lighter halogens (Br2 and Cl2) or by hetero systems (IF, ICH3, N2) correlate well with the magnitude of the σ-hole (Vs,max value) as well as with the LUMO energy. The nature of the stabilisation of all complexes between both electron donors and X2 (X = I, Br, Cl, N) systems is explained by the magnitude of the σ-hole but surprisingly also by the values of the electric quadrupole moment of these systems. Evidently, the nature of the stabilisation of halogen-bonded complexes between electron donors and systems where the first non-zero electric multipole moment is the quadrupole moment can be explained not only by the recently introduced concept of the σ-hole but also by the classical concept of electric quadrupole moments.

Penetration Barrier of Water through Graphynes' Pores: First-Principles Predictions and Force Field Optimization

Graphynes are novel two-dimensional carbon-based materials that have been proposed as molecular filters, especially for water purification technologies. We carry out first-principles electronic structure calculations at the MP2C level of theory to assess the interaction between water and graphyne, graphdiyne, and graphtriyne pores. The computed penetration barriers suggest that water transport is unfeasible through graphyne while being unimpeded for graphtriyne. For graphdiyne, with a pore size almost matching that of water, a low barrier is found that in turn disappears if an active hydrogen bond with an additional water molecule on the opposite side of the opening is considered. Thus, in contrast with previous determinations, our results do not exclude graphdiyne as a promising membrane for water filtration. In fact, present calculations lead to water permeation probabilities that are 2 orders of magnitude larger than estimations based on common force fields. A new pair potential for the water-carbon noncovalent component of the interaction is proposed for molecular dynamics simulations involving graphdiyne and water.

Structure and electronic spectra of purine-methyl viologen charge transfer complexes

The structure and properties of the electron donor-acceptor complexes formed between methyl viologen and purine nucleosides and nucleotides in water and the solid state have been investigated using a combination of experimental and theoretical methods. Solution studies were performed using UV-vis and (1)H NMR spectroscopy. Theoretical calculations were performed within the framework of density functional theory (DFT). Energy decomposition analysis indicates that dispersion and induction (charge-transfer) interactions dominate the total binding energy, whereas electrostatic interactions are largely repulsive. The appearance of charge transfer bands in the absorption spectra of the complexes are well-described by time-dependent DFT and are further explained in terms of the redox properties of purine monomers and solvation effects. Crystal structures are reported for complexes of methyl viologen with the purines 2'-deoxyguanosine 3'-monophosphate (DAD'DAD' type) and 7-deazaguanosine (DAD'ADAD' type). Comparison of the structures determined in the solid state and by theoretical methods in solution provides valuable insights into the nature of charge-transfer interactions involving purine bases as electron donors.

Diffraction of helium on MgO(100) surface calculated from first-principles

In this work we simulate the diffraction peak intensities of He beams scattered on the MgO(100) surface using hierarchical protocol, based on periodic and finite-cluster quantum-chemical calculations.

Squeezing water clusters between graphene sheets: energetics, structure, and intermolecular interactions

The behavior of water confined at the nanoscale between graphene sheets has attracted much theoretical and experimental attention recently.

Binding of O2 and NO to heme in heme-nitric oxide/oxygen-binding (H-NOX) proteins. A theoretical study

The binding of O2 and NO to heme in heme-nitric oxide/oxygen-binding (H-NOX) proteins has been investigated with DFT as well as dispersion-corrected DFT methods. The local protein environment was accounted for by including the six nearest surrounding residues in the studied systems. Attention was also paid to the effects of the protein environment, particularly the distal Tyr140, on the proximal iron-histidine (Fe-His) binding. The Heme-AB (AB = O2, NO) and Fe-His binding energies in iron porphyrin FeP(His)(AB), myoglobin Mb(AB), H-NOX(AB), and Tyr140 → Phe mutated H-NOX[Y140F(AB)] were determined for comparison. The calculated stabilization of bound O2 is even higher in H-NOX than that in a myoglobin (Mb), consistent with the observation that the H-NOX domain of T. tengcongensis has a very high affinity for its oxygen molecule. Among the two different X-ray crystal structures for the Tt H-NOX protein, the calculated results for both AB = O2 and NO appear to support the crystal structure with the PDB code 1XBN , where the Trp9 and Asn74 residues do not form a hydrogen-bonding network with Tyr140. A hydrogen bond interaction from the polar residue does not have obvious effects on the Fe-His binding strength, but a dispersion contribution to Ebind(Fe-His) may be significant, depending on the crystal structure used. We speculate that the Fe-His binding strength in the deoxy form of a native protein could be an important factor in determining whether the bond of His to Fe is broken or maintained upon binding of NO to Fe.

Open-shell pair interaction energy decomposition analysis (PIEDA): formulation and application to the hydrogen abstraction in tripeptides

An open-shell extension of the pair interaction energy decomposition analysis (PIEDA) within the framework of the fragment molecular orbital (FMO) method is developed. The open-shell PIEDA method allows the analysis of inter- and intramolecular interactions in terms of electrostatic, exchange-repulsion, charge-transfer, dispersion, and optional polarization energies for molecular systems with a radical or high-spin fragment. Taking into account the low computational cost and scalability of the FMO and PIEDA methods, the new scheme provides a means to characterize the stabilization of radical and open-shell sites in biologically relevant species. The open-shell PIEDA is applied to the characterization of intramolecular interactions in capped trialanine upon hydrogen abstraction (HA) at various sites on the peptide. Hydrogen abstraction reaction is the first step in the oxidative pathway initiated by reactive oxygen or nitrogen species, associated with oxidative stress. It is found that HA results in significant geometrical reorganization of the trialanine peptide. Depending on the HA site, terminal interactions in the radical fold conformers may become weaker or stronger compared to the parent molecule, and often change the character of the non-covalent bonding from amide stacking to hydrogen bonding.

Nature of noncovalent interactions in catenane supramolecular complexes: calibrating the MM3 force field with ab initio, DFT, and SAPT methods

The design and assembly of mechanically interlocked molecules, such as catenanes and rotaxanes, are dictated by various types of noncovalent interactions. In particular, [C-H···O] hydrogen-bonding and π-π stacking interactions in these supramolecular complexes have been identified as important noncovalent interactions. With this in mind, we examined the [3]catenane 2·4PF6 using molecular mechanics (MM3), ab initio methods (HF, MP2), several versions of density functional theory (DFT) (B3LYP, M0X), and the dispersion-corrected method DFT-D3. Symmetry adapted perturbation theory (DFT-SAPT) provides the highest level of theory considered, and we use the DFT-SAPT results both to calibrate the other electronic structure methods, and the empirical potential MM3 force field that is often used to describe larger catenane and rotaxane structures where [C-H···O] hydrogen-bonding and π-π stacking interactions play a role. Our results indicate that the MM3 calculated complexation energies agree qualitatively with the energetic ordering from DFT-SAPT calculations with an aug-cc-pVTZ basis, both for structures dominated by [C-H···O] hydrogen-bonding and π-π stacking interactions. When the DFT-SAPT energies are decomposed into components, we find that electrostatic interactions dominate the [C-H···O] hydrogen-bonding interactions, while dispersion makes a significant contribution to π-π stacking. Another important conclusion is that DFT-D3 based on M06 or M06-2X provides interaction energies that are in near-quantitative agreement with DFT-SAPT. DFT results without the D3 correction have important differences compared to DFT-SAPT, while HF and even MP2 results are in poor agreement with DFT-SAPT.

Effects of local protein environment on the binding of diatomic molecules to heme in myoglobins. DFT and dispersion-corrected DFT studies

The heme-AB binding energies (AB = CO, O2) in a wild-type myoglobin (Mb) and two mutants (H64L, V68N) of Mb have been investigated in detail with both DFT and dispersion-corrected DFT methods, where H64L and V68N represent two different, opposite situations. Several dispersion correction approaches were tested in the calculations. The effects of the local protein environment were accounted for by including the five nearest surrounding residues in the calculated systems. The specific role of histidine-64 in the distal pocket was examined in more detail in this study than in other studies in the literature. Although the present calculated results do not change the previous conclusion that the hydrogen bonding by the distal histidine-64 residue plays a major role in the O2/CO discrimination by Mb, more details about the interaction between the protein environment and the bound ligand have been revealed in this study by comparing the binding energies of AB to a porphyrin and the various myoglobins. The changes in the experimental binding energies from one system to another are well reproduced by the calculations. Without constraints on the residues in geometry optimization, the dispersion correction is necessary, since it improves the calculated structures and energetic results significantly.

Orbital-based insights into parallel-displaced and twisted conformations in π-π interactions

Dispersion and electrostatics are known to stabilize π-π interactions, but the preference for parallel-displaced (PD) and/or twisted (TW) over sandwiched (S) conformations is not well understood. Orbital interactions are generally believed to play little to no role in π-stacking. However, orbital analysis of the dimers of benzene, pyridine, cytosine and several polyaromatic hydrocarbons demonstrates that PD and/or TW structures convert one or more π-type dimer MOs with out-of-phase or antibonding inter-ring character at the S stack to in-phase or bonding in the PD/TW stack. This change in dimer MO character can be described in terms of a qualitative stack bond order (SBO) defined as the difference between the number of occupied in-phase/bonding and out-of-phase/antibonding inter-ring π-type MOs. The concept of an SBO is introduced here in analogy to the bond order in molecular orbital theory. Thus, whereas the SBO of the S structure is zero, parallel displacement or twisting the stack results in a non-zero SBO and overall bonding character. The shift in bonding/antibonding character found at optimal PD/TW structures maximizes the inter-ring density, as measured by intermolecular Wiberg bond indices (WBIs). Values of WBIs calculated as a function of the parallel-displacement are found to correlate with the dispersion and other contributions to the π-π interaction energy determined by the highly accurate density-fitting DFT symmetry adapted perturbation theory (DF-DFT-SAPT) method. These DF-DFT-SAPT calculations also suggest that the dispersion and other contributions are maximized at the PD conformation rather than the S when conducted on a potential energy curve where the inter-ring distance is optimized at fixed slip distances. From these results of this study, we conclude that descriptions of the qualitative manner in which orbitals interact within π-stacking interactions can supplement high-level calculations of the interaction energy and provide an intuitive tool for applications to crystal design, molecular recognition and other fields where non-covalent interactions are important.

On the importance and origin of aromatic interactions in chemistry and biodisciplines

Aromatic systems contain both σ- and π-electrons, which in turn constitute σ- and π-molecular orbitals (MOs). In discussing the properties of these systems, researchers typically refer to the highest occupied and lowest unoccupied MOs, which are π MOs. The characteristic properties of aromatic systems, such as their low ionization potentials and electron affinities, high polarizabilities and stabilities, and small band gaps (in spectroscopy called the N → V1 space), can easily be explained based on their electronic structure. These one-electron properties point to characteristic features of how aromatic systems interact with each other. Unlike hydrogen bonding systems, which primarily interact through electrostatic forces, complexes containing aromatic systems, especially aromatic stacked pairs, are predominantly stabilized by dispersion attraction. The stabilization energy in the benzene dimer is rather small (~2.5 kcal/mol) but strengthens with heteroatom substitution. The stacked interaction of aromatic nucleic acid bases is greater than 10 kcal/mol, and for the most stable stacked pair, guanine and cytosine, it reaches approximately 17 kcal/mol. Although these values do not equal the planar H-bonded interactions of these bases (~29 kcal/mol), stacking in DNA is more frequent than H-bonding and, unlike H-bonding, is not significantly weakened when passing from the gas phase to a water environment. Consequently, the stacking of aromatic systems represents the leading stabilization energy contribution in biomacromolecules and in related nanosystems. Therefore stacking (dispersion) interactions predominantly determine the double helical structure of DNA, which underlies its storage and transfer of genetic information. Similarly, dispersion is the dominant contributor to attractive interactions involving aromatic amino acids within the hydrophobic core of a protein, which is critical for folding. Therefore, understanding the nature of aromatic interactions, which depend greatly on quantum mechanical (QM) calculations, is of key importance in biomolecular science. This Account shows that accurate binding energies for aromatic complexes should be based on computations made at the (estimated) CCSD(T)/complete basis set limit (CBS) level of theory. This method is the least computationally intensive one that can give accurate stabilization energies for all common classes of noncovalent interactions (aromatic-aromatic, H-bonding, ionic, halogen bonding, charge-transfer, etc.). These results allow for direct comparison of binding energies between different interaction types. Conclusions based on lower-level QM calculations should be considered with care.