Empirical Dispersion Research Articles

Control of Self‐Assembled 2D Nanostructures by Methylation of Guanine

Methylation of DNA nucleobases is an important control mechanism in biology applied, for example, in the regulation of gene expression. The effect of methylation on the intermolecular interactions between guanine molecules is studied through an interplay between scanning tunneling microscopy (STM) and density functional theory with empirical dispersion correction (DFT-D). The present STM and DFT-D results show that methylation of guanine can have subtle effects on the hydrogen-bond strength with a strong dependence on the position of methylation. It is demonstrated that the methylation of DNA nucleobases is a precise means to tune intermolecular interactions and consequently enables very specific recognition of DNA methylation by enzymes. This scheme is used to generate four different types of artificial 2D nanostructures from methylated guanine. For instance, a 2D guanine windmill motif that is stabilized by cooperative hydrogen bonding is revealed. It forms by self-assembly on a graphite surface under ambient conditions at the liquid-solid interface when the hydrogen-bonding donor at the N1 site of guanine is blocked by a methyl group.

Electron correlation decides the stability of cubic versus hexagonal boron nitride

Periodic local M\o{}ller-Plesset second-order perturbation theory (MP2) is applied to investigate the structural and energetic properties of the cubic and hexagonal polymorphs of boron nitride. While the Hartree-Fock (HF) solution significantly underbinds both systems and energetically favors $h$-BN, the post-HF correlation treatment recovers the lacking amount of the interaction energy and reverts the sign of the relative stability between the two compounds. It provides the physically correct picture and predicts cohesive energies, lattice constants, bulk moduli, and the relative stability in good agreement with experiment. Density-functional theory (DFT) results, on the other hand, are inconclusive and exhibit a strong dependence on the chosen functional. The results of MP2 as well as DFT with an empirical dispersion correction indicate that the dispersion contribution to binding is essential not only for the layered polymorph, but also (and even more so) for the cubic one.

A theoretical study on structural, spectroscopic and energetic properties of acetamide clusters [CH3CONH2] (n = 1–15)

Insights into the formation of hydrogen bonded clusters are of outstanding importance and quantum chemical calculations play a pivotal role in achieving this understanding. Structure and energetic comparison of linear, circular and standard forms of (acetamide)(n) clusters (n = 1-15) at the B3LYP/D95** level of theory including empirical dispersion correction reveals significant cooperativity of hydrogen bonding and size dependent structural preference. A substantial amount of impact of BSSE is observed in these calculations as the cluster size increases irrespective of the kind of arrangement. The interaction energy per monomer increases from dimer to 15mer by 90% in the case of the circular arrangement, by 76% in the case of the linear arrangement and by 34% in the case of the standard arrangement respectively. The cooperativity in hydrogen bonding is also manifested by a regular decrease in average OH and C-N bond distances, while average C=O and N-H bond lengths increase with increasing cluster size. Atoms-In-Molecules (AIM) analysis is used to characterize the nature of hydrogen bonding between the acetamide molecules in the cluster on the basis of electron density (ρ) values obtained at the bond critical point. An analysis of N-H bond stretching frequencies as a function of the cluster size shows a marked red shift as the cluster size increases from 1 to 15.

Application of London-type dispersion corrections to the solid-state density functional theory simulation of the terahertz spectra of crystalline pharmaceuticals

The effects of applying an empirical dispersion correction to solid-state density functional theory methods were evaluated in the simulation of the crystal structure and low-frequency (10 to 90 cm(-1)) terahertz spectrum of the non-steroidal anti-inflammatory drug, naproxen. The naproxen molecular crystal is bound largely by weak London force interactions, as well as by more prominent interactions such as hydrogen bonding, and thus serves as a good model for the assessment of the pair-wise dispersion correction term in systems influenced by intermolecular interactions of various strengths. Modifications to the dispersion parameters were tested in both fully optimized unit cell dimensions and those determined by X-ray crystallography, with subsequent simulations of the THz spectrum being performed. Use of the unmodified PBE density functional leads to an unrealistic expansion of the unit cell volume and the poor representation of the THz spectrum. Inclusion of a modified dispersion correction enabled a high-quality simulation of the THz spectrum and crystal structure of naproxen to be achieved without the need for artificially constraining the unit cell dimensions.

On the accuracy of DFT-SAPT, MP2, SCS-MP2, MP2C, and DFT+Disp methods for the interaction energies of endohedral complexes of the C60fullerene with a rare gas atom

Selected points on the potential energy surface for the complexes Rg@C(60) (Rg = He, Ne, Ar, Kr) are calculated with various theoretical methods, like symmetry-adapted perturbation theory with monomers described by density functional theory (DFT-SAPT), supermolecular Møller-Plesset theory truncated on the second order (MP2), spin-component-scaled MP2 (SCS-MP2), supermolecular density functional theory with empirical dispersion correction (DFT+Disp), and the recently developed MP2C method that improves the MP2 method for long-range electron correlation effects. A stabilization of the endohedral complex is predicted by all methods, but the depth of the potential energy well is overestimated by the DFT+Disp and MP2 approaches. On the other hand, the MP2C model agrees well with DFT-SAPT, which serves as the reference. The performance of SCS-MP2 is mixed: it produces too low interaction energies for the two heavier guests, while its accuracy for He@C(60) and Ne@C(60) is similar to that of MP2C. Fitting formulas for the main interaction energy components, i.e. the dispersion and first-order repulsion energies are proposed, which are applicable for both endo- and exohedral cases. For all examined methods density fitting is used to evaluate two-electron repulsion integrals, which is indispensable to allow studies of noncovalent complexes of this size. It has been found that density-fitting auxiliary basis sets cannot be used in a black-box fashion for the calculation of the first-order SAPT electrostatic energy, and that the quality of these basis sets should be always carefully examined in order to avoid an unphysical long-range behavior.

Differences in structure, energy, and spectrum between neutral, protonated, and deprotonated phenol dimers: comparison of various density functionals with ab initio theory

We have carried out extensive calculations for neutral, cationic protonated, anionic deprotonated phenol dimers. The structures and energetics of this system are determined by the delicate competition between H-bonding, H-π interaction and π-π interaction. Thus, the structures, binding energies and frequencies of the dimers are studied by using a variety of functionals of density functional theory (DFT) and Møller-Plesset second order perturbation theory (MP2) with medium and extended basis sets. The binding energies are compared with those of highly reliable coupled cluster theory with single, double, and perturbative triple excitations (CCSD(T)) at the complete basis set (CBS) limit. The neutral phenol dimer is unique in the sense that its experimental rotational constants have been measured. The geometry of the neutral phenol dimer is governed by the hydrogen bond formed by two hydroxyl groups and the H-π interaction between two aromatic rings, while the structure of the protonated/deprotonated phenol dimers is additionally governed by the electrostatic and induction effects due to the short strong hydrogen bond (SSHB) and the charges populated in the aromatic rings in the ionic systems. Our salient finding is the substantial differences in structure between neutral, protonated, and deprotonated phenol dimers. This is because the neutral dimer involves in both H(π)···O and H(π)···π interactions, the protonated dimer involves in H(π)···π interactions, and the deprotonated dimer involves in a strong H(π)···O interaction. It is important to compare the reliability of diverse computational approaches employed in quantum chemistry on the basis of the calculational results of this system. MP2 calculations using a small cc-pVDZ basis set give reasonable structures, but those using extended basis sets predict wrong π-stacked structures due to the overestimation of the dispersion energies of the π-π interactions. A few new DFT functionals with the empirical dispersion give reliable results consistent with the CCSD(T)/CBS results. The binding energies of the neutral, cationic protonated, and anionic deprotonated phenol dimers are estimated to be more than 28.5, 118.2, and 118.3 kJ mol(-1), respectively. The energy components of the intermolecular interactions for the neutral, protonated and deprotonated dimers are analyzed.

How to fragment a polypeptide? An ab initio computational study of pair interactions between amino acids and ligand-amino acids in proteins

To determine reasonably which amino acid side chain contributes significantly to the stability of a protein or to the stability of a protein–ligand complex is not a straightforward task. We suggest a partial but systematic solution of the problem by a specific fragmentation of a protein chain into blocks of single amino acid side chains with their corresponding backbone part. For such systems of building blocks, we have calculated the stabilisation/interaction energies by means of correlated ab initio calculations. We have shown that a reasonable way to treat an amino-acid residue composing the protein is to break the homonuclear C–C bond between the Cα atom and the C(O) carboxyl carbon. The reference data obtained by the RI-MP2 method with the cc-pVDZ basis set were compared with RIDFT, RIDFT augmented by the dispersion term, SCC-DFTB-D and Hartree–Fock calculations. The results clearly show the failure of those methods lacking an appropriate treatment of the correlation energy. The DFT methods augmented by the empirical dispersion term on the other hand describe the interaction in good agreement with the reference method.

Calculation of the Binding Energies of Different Types of Hydrogen Bonds Using GGA Density Functional and Its Long-Range, Empirical Dispersion Correction Methods

We investigated eleven exchange-correlation energy density functionals including generalized gradient approximation (GGA) (PBE, PW91), meta-GGA (M06-L), hyper-GGA (M06-2X, B3LYP, X3LYP), LC-DFT methods (CAM-B3LYP, LC-ωPBE, ωB97X), and density functional theory with dispersion corrections (DFT-D) methods (ωB97X-D, B97-D) for their performance in describing systems with conventional and non-conventional hydrogen bonds. After comparing the results using the benchmark CCSD(T)/aug-cc-pVQZ approach we found that the M06-2X and ωB97X-D functionals provided the most accurate and reliable results for the fifteen systems studied in this work with strong, moderate, and weak hydrogen bonds. It is important to employ an appropriate basis set to predict the binding energy of hydrogen bonds for all DFT methods and we found that the basis set of 6-311++G(2d, 2p) or aug-cc-pVDZ is adequate. The effect of the basis set superposition error (BSSE) is relatively small for the DFT methods tested. All the methods except for ωB97X and ωB97X-D were found to produce equally accurate or even more accurate results without BSSE correction.

Assessment of the Performance of DFT and DFT-D Methods for Describing Distance Dependence of Hydrogen-Bonded Interactions.

Noncovalent interactions such as hydrogen bonds, van der Waals forces, and π-π interactions play important roles influencing the structure, stability, and dynamic properties of biomolecules including DNA and RNA base pairs. In an effort to better understand the fundamental physics of hydrogen bonding (H-bonding), we investigate the distance dependence of interaction energies in the prototype bimolecular complexes of formic acid, formamide, and formamidine. Potential energy curves along the H-bonding dissociation coordinate are examined both by establishing reference CCSD(T) interaction energies extrapolated to the complete basis set limit and by assessing the performance of the density functional methods B3LYP, PBE, PBE0, B970, PB86, M05-2X, and M06-2X and empirical dispersion corrected methods B3LYP-D3, PBE-D3, PBE0-D3, B970-D2, BP86-D3, and ωB97X-D, with basis sets 6-311++G(3df,3pd), aug-cc-pVDZ, and aug-cc-pVTZ. Although H-bonding interactions are dominated by electrostatics, it is necessary to properly account for dispersion interactions to obtain accurate energetics. In order to quantitatively probe the nature of hydrogen bonding interactions as a function of distance, we decompose the interaction energy curves into physically meaningful components with symmetry-adapted perturbation theory (SAPT). The SAPT results confirm that the contribution of dispersion and induction are significant at and near equilibrium, although electrostatics dominate. Among the DFT/DFT-D techniques, the best overall results are obtained utilizing counterpoise-corrected ωB97X-D with the aug-cc-pVDZ basis set.

Local response dispersion method. II. Generalized multicenter interactions

Recently introduced local response dispersion method [T. Sato and H. Nakai, J. Chem. Phys. 131, 224104 (2009)], which is a first-principles alternative to empirical dispersion corrections in density functional theory, is implemented with generalized multicenter interactions involving both atomic and atomic pair polarizabilities. The generalization improves the asymptote of intermolecular interactions, reducing the mean absolute percentage error from about 30% to 6% in the molecular C(6) coefficients of more than 1000 dimers, compared to experimental values. The method is also applied to calculations of potential energy curves of molecules in the S22 database [P. Jurečka et al., Phys. Chem. Chem. Phys. 8, 1985 (2006)]. The calculated potential energy curves are in a good agreement with reliable benchmarks recently published by Molnar et al. [J. Chem. Phys. 131, 065102 (2009)]. These improvements are achieved at the price of increasing complexity in the implementation, but without losing the computational efficiency of the previous two-center (atom-atom) formulation. A set of different truncations of two-center and three- or four-center interactions is shown to be optimal in the cost-performance balance.

Inter‐ and intramolecular dispersion interactions

We have investigated the performance of a variety of density functional methods for weak intra- and intermolecular dispersion interactions. Grimme's empirical dispersion correction method is shown to give a good description for these interactions and helps to improve the description of water-hexamer isomers, noble-gas dimers, hydrocarbon C(12)H(12) isomers, branching energy of linear versus branched octane, dissociation of the covalently bound anthracene dimer, and stacking within the adenine dimer. However, the dispersion correction does not correct all shortcomings of the different density functionals, which leads to sizeable differences compared to ab initio CCSD(T) and experimental reference data. The only exception is shown to be our recently presented SSB-D functional that works well for all systems studied here.

Inclusion of Dispersion Effects Significantly Improves Accuracy of Calculated Reaction Barriers for Cytochrome P450 Catalyzed Reactions

Prediction of cytochrome P450 reactivity is of great importance to the development of new medicinal compounds. Density functional theory (DFT) has proven itself as a useful tool in the characterization of the elusive reactive species, compound I, and of the mechanisms of substrate oxidation. B3LYP is the most widely used density functional in the study of P450s; however, a major drawback of B3LYP is its inaccurate treatment of dispersion, leading to discrepancies between experiment and theory in some systems. Recent work has shown that an added empirical dispersion correction to B3LYP (B3LYP-D) yields more promising results for similar systems. In the present work, two previously studied systems, camphor hydroxylation and alkene oxidation, have been recalculated using B3LYP-D. Our work shows that inclusion of dispersion has a significant effect on the energies and geometries of transition states and encounter complexes; furthermore, an improved agreement with experimental data is observed.

Conformational Preferences of X-Pro Sequences: Ala-Pro and Aib-Pro Motifs

Conformational preferences and prolyl cis-trans isomerizations of the X-Pro motifs (Ac-X-Pro-NHMe, X = Ala and Aib) are explored using the meta-hybrid functional M06-2X and the double-hybrid functional B2PLYP-D with empirical dispersion corrections in the gas phase and in water, where solvation free energies were calculated using the implicit SMD model. Ac-Ala-Pro-NHMe favors the type VI β-turns in the gas phase and the open conformations in water. The populations of type VI β-turns decrease from 71% in the gas phase to 21% in water, which is reasonably consistent with IR and NMR experimental results on tBoc-Ala-Pro-NHMe. However, Ac-Aib-Pro-NHMe prefers the type I β-turns with α-helical structures for both residues in the gas phase and in water, whose populations are estimated to be 66% in both phases. These calculated results may rationalize why most of the peptaibiotics containing the Aib-Pro sequence have a regular α-helical conformation at the N- or C-terminus but a kinked α-helical structure in the middle of the helix. The cis-trans isomerizations of the Ala-Pro and Aib-Pro peptide bonds proceed via the clockwise rotation with the different backbone conformations. The rotational barriers to cis-to-trans isomerization are estimated to be 19.73 kcal/mol for the Ala-Pro tripeptide and 16.64 kcal/mol for the Aib-Pro tripeptide in water, which indicates that the rotational barrier becomes lower by ~3 kcal/mol for the Aib-Pro peptide bond. The calculated rotational barrier for Ac-Ala-Pro-NHMe is consistent with the observed value of 19.3 kcal/mol for Suc-Ala-Ala-Pro-Phe-pNA from NMR experiments in a buffered solution.

π Interactions Studied with Electronic Structure Methods: The Ethyne Methyl Isocyanide Complex and Thioanisole.

Two molecular systems for which previous studies had found qualitative differences in the results from calculations with the B3LYP and MP2 methods are investigated with a range of different electronic structure methods, including meta and double hybrid density functionals and DFT-D (DFT augmented with an empirical dispersion term). The performance of the different methods is assessed by comparison to estimated CCSD(T)/CBS (complete basis set) results. The first molecular system studied is the ethyne methyl isocyanide complex (CH3NC-C2H2), which exhibits π hydrogen bonds involving the C≡C and N≡C triple bonds. Earlier work on this system had shown that B3LYP predicts significantly longer hydrogen-bond distances than MP2. Here, we show that this is likely due to missing dispersion in the B3LYP calculations. On the basis of the CCSD(T) results, the ethyne methyl isocyanide interaction energy is estimated to be 12 ± 1 kJ/mol. B3LYP significantly underestimates the stability of the complex, whereas MP2 slightly overestimates. M05-2X, B3LYP-D, and (CP-corrected) mPW2-PLYP-D give results in close proximity to the CCSD(T) reference values. The second molecule investigated is thioanisole (C6H6SCH3), which can adopt two different conformations (thiomethyl group either planar or perpendicular with respect to the benzene ring). Potential energy curves for rotation around the C(sp(2))-S bond are computed and compared to the estimated CCSD(T)/CBS curve. CCSD(T) predicts the planar conformation to be the global minimum, with a plateau region near the perpendicular conformation (∼4 kJ/mol higher in energy than the planar conformation). The shape of the curve, and location of minima and barriers, is very dependent on the method and basis set employed. MP2, B3LYP, M05-2X, mPW2-PLYP, and mPW2-PLYP-D (employing basis sets of double- or triple-ζ quality) give results in reasonable agreement with the CCSD(T) results, whereas B3LYP-D and M06-L give vastly overestimated barriers at the perpendicular conformation.

Application of an empirical dispersion potential to van der Waals binding in nitromethane, pentaerythritol, and pentaerythritol tetranitrate

The use of an empirical dispersion potential to accurately represent the van der Waals interaction in molecular crystals is discussed. Results for nitromethane, pentaerythritol (PE), and pentaerythritol tetranitrate (PETN) are presented for equilibrium volumes using a variety of basis sets ranging in quality in the Crystal program. Agreement with experiment for equilibrium volumes is found to be within a few percent when the Grimme potential and a high-quality basis set is used.

On the Reliability of the AMBER Force Field and its Empirical Dispersion Contribution for the Description of Noncovalent Complexes

The reliability of the AMBER force field is tested by comparing the total interaction energy and dispersion energy with the reference data obtained at the density functional theory-symmetry-adapted perturbation treatment (DFT-SAPT)/aug-cc-pVDZ level. The comparison is made for 194 different geometries of noncovalent complexes (H-bonded, stacked, mixed, and dispersion-bound), at the equilibrium distances as well as at longer distances (up to a relative distance of two). The total interaction energies agree very well with the reference data and only the strength of H-bonded complexes is slightly underestimated. In the case of dispersion energy, the overall agreement is even better, with the exception of the stacked aromatic systems, where the empirical dispersion energy is overestimated. The use of AMBER interaction energy and AMBER dispersion energy for different types of noncovalent complexes at equilibrium as well as at longer distances is thus justified, except for a few cases, such as the water molecule, where the dispersion energy is highly inaccurate.

Assessment of density functionals with long‐range and/or empirical dispersion corrections for conformational energy calculations of peptides

Density functionals with long-range and/or empirical dispersion corrections, including LC-ωPBE, B97-D, ωB97X-D, M06-2X, B2PLYP-D, and mPW2PLYP-D functionals, are assessed for their ability to describe the conformational preferences of Ac-Ala-NHMe (the alanine dipeptide) and Ac-Pro-NHMe (the proline dipeptide) in the gas phase and in water, which have been used as prototypes for amino acid residues of peptides. For both dipeptides, the mean absolute deviation (MAD) is estimated to be 0.22-0.40 kcal/mol in conformational energy and 2.0-3.2° in torsion angles φ and ψ using these functionals with the 6-311++G(d,p) basis set against the reference values calculated at the MP2/aug-cc-pVTZ//MP2/aug-cc-pVDZ level of theory in the gas phase. The overall performance is obtained in the order B2PLYP-D ≈ mPW2PLYP-D > ωB97X-D ≈ M06-2X > MP2 > LC-ωPBE > B3LYP with the 6-311++G(d,p) basis set. The SMD model at the M06-2X/6-31+G(d) level of theory well reproduced experimental hydration free energies of the model compounds for backbone and side chains of peptides with MADs of 0.47 and 4.3 kcal/mol for 20 neutral and 5 charged molecules, respectively. The B2PLYP-D/6-311++G(d,p)//SMD M06-2X/6-31+G(d) level of theory provides the populations of backbone and/or prolyl peptide bond for the alanine and proline dipeptides in water that are consistent with the observed values.

Using Nonempirical Semilocal Density Functionals and Empirical Dispersion Corrections to Model Dative Bonding in Substituted Boranes.

Dative bonds to substituted boranes represent a challenge for the approximate exchange-correlation functionals typically used in density functional theory (DFT). Accurately modeling these bonds with DFT has usually required highly parametrized functionals, large admixtures of exact exchange, or computationally expensive double hybrids. This work shows that the nonempirical semilocal PBEsol functional, and the nonempirical semilocal PBE and TPSS functionals augmented with empirical interatomic dispersion corrections, accurately treat several representative problems in dative bonding. These methods typically surpass the MPW1K "kinetics" global hybrid previously recommended for dative bonds. This work also provides additional insights into the accuracy of the parametrized M06 functionals and indicates some deficiencies of the B97-D functional relative to PBE-D and TPSS-D. Applications to frustrated Lewis pairs illustrate the potential of these methods.

Distribution and gradient analysis of Ink disease in chestnut forests

SummaryDistribution and gradient analysis of Ink disease caused by Phytophthora cambivora were studied over a 2 years period in a chestnut forest in Italy. Ink disease incidence, severity and tree mortality increased during the period over the studied chestnut forest. Disease descriptors and landform datasets were analysed by Geographic Information System software and displayed as a multilayer thematic map. Indices of dispersion and empirical dispersion models were used to study spatial distribution of disease in the investigated area. Semivariograms were used to interpolate spatial data and to map Ink disease. A logical spatial dependence of the studied variables was found. Ink disease occurred preferentially along natural drainages routes where multicyclic inoculum build up was likely to occur. A negative relationship was found between Ink disease incidence, severity and tree mortality with respect to distance from the drainage.

An extended time-dependent numerical model of the mild-slope equation with weakly nonlinear amplitude dispersion

In the present paper, by introducing the effective wave elevation, we transform the extended elliptic mild-slope equation with bottom friction, wave breaking and steep or rapidly varying bottom topography to the simplest time-dependent hyperbolic equation. Based on this equation and the empirical nonlinear amplitude dispersion relation proposed by Li et al. (2003), the numerical scheme is established. Error analysis by Taylor expansion method shows that the numerical stability of the present model succeeds the merits in Song et al. (2007)’s model because of the introduced dissipation terms. For the purpose of verifying its performance on wave nonlinearity, rapidly varying topography and wave breaking, the present model is applied to study: (1) wave refraction and diffraction over a submerged elliptic shoal on a slope (Berkhoff et al., 1982); (2) Bragg reflection of monochromatic waves from the sinusoidal ripples (Davies and Heathershaw, 1985); (3) wave transformation near a shore attached breakwater (Watanabe and Maruyama, 1986). Comparisons of the numerical solutions with the experimental or theoretical ones or with those of other models (REF/DIF model and FUNWAVE model) show good results, which indicate that the present model is capable of giving favorably predictions of wave refraction, diffraction, reflection, shoaling, bottom friction, breaking energy dissipation and weak nonlinearity in the near shore zone.