Nonadditive Energy Research Articles

Three-Body Nonadditive Potential for Argon with Estimated Uncertainties and Third Virial Coefficient

The three-body nonadditive interaction energy between argon atoms was calculated at 300 geometries using coupled cluster methods up to single, double, triple, and noniterative quadruple excitations [CCSDT(Q)], and including the core correlation and relativistic effects. The uncertainty of the calculated energy was estimated at each geometry. The analytic function fitted to the energies is currently the most accurate three-body argon potential. Values of the third virial coefficient C(T) with full account of quantum effects were computed from 80 to 10000 K by a path-integral Monte Carlo method. The calculation made use of an existing high-quality pair potential [Patkowski, K.; Szalewicz, K. J. Chem. Phys. 2010, 133, 094304] and of the three-body potential derived in the present work. Uncertainties in the potential were propagated to estimate uncertainties in C(T). The results were compared with available experimental data, including some values of C(T) newly derived in this work from previously published high-accuracy density measurements. Our results are generally consistent with the available experimental data in the limited range of temperatures where data exist, but at many conditions, especially at higher temperatures, the uncertainties of our calculated values are smaller than the uncertainties of the experimental values.

A B3LYP and MP2 theoretical investigation into the synergetic effect between the O/N[sbnd]H⋯O and O/N[sbnd]H⋯F− anionic hydrogen-bonding interactions in N-(Hydroxymethyl)acetamide complex with F−

The synergetic effects between the O/NH⋯F− anionic hydrogen-bonding and conventional O/NH⋯O hydrogen-bonding interactions in the 1:2 (F−:N-(Hydroxymethyl)acetamide) ternary systems are investigated at the B3LYP/6-311++G** and MP2/6-311++G** levels. The non-additivity energies are also calculated. The result shows that the distance RF⋯H of the NH⋯F− H-bond in the ternary system is shortened greatly in comparison with that in the binary complex. The O/NH⋯O H-bonding interaction is increased due to the presence of the O/NH⋯F− H-bond upon ternary-system formation. Furthermore, the increase of the H⋯O interaction in the OH⋯OH, NH⋯OH or NH⋯OC link is more notable than that in the OH⋯OC contact. The synergetic effect is found in the conformation formed by the O/NH⋯F− and O/NH⋯O interactions, while the anti-synergetic effect is present in the complex where only the O/NH⋯F− H-bond is found and the O/NH⋯O H-bond is broken in going from the binary to ternary complex. Shift of electron density confirms the existence of cooperativity.

How well can polarization models of pairwise nonadditive forces describe liquid water?

Properties of liquid water have been computed using a near-exact rigid-monomer two-body (pairwise-additive) force field and the same field supplemented by a simple, non-empirical polarization model of pairwise nonadditive many-body forces. The inclusion of nonadditive polarization forces leads to a dramatic decrease, sometimes by an order of magnitude, of the deviations of water properties computed using classical molecular dynamics from experiment results. The remaining deviations are typically of the order of 10%. The model correctly predicts the temperature dependence of the properties except for the density of supercooled water. This good performance is achieved despite the known failure of the polarization model in reproducing trimer nonadditive interaction energies, confirmed here by showing that for a random set of trimers with all O-O separations smaller than 3.4 Å, selected from simulation snapshots, the average error of the model relative to accurate ab initio values is 71%. However, the errors gradually decrease for larger trimers, more abundant in liquid, and one can estimate that the polarization model should reproduce the exact liquid interaction energy to within about 6%. Although this accuracy is consistent with the observed performance of the polarization model, it does not explain the dramatic improvements over the two-body model. These improvements are due to the restructuring of liquid into tetrahedral arrangements instigated by the nonadditive polarization forces. The deviations of our predictions from experiments are generally also consistent with the estimated contributions from leading neglected effects other than the exchange nonadditive forces: the monomer flexibility and quantum nuclear motion effects.

Collective many-body van der Waals interactions in molecular systems.

Van der Waals (vdW) interactions are ubiquitous in molecules and condensed matter, and play a crucial role in determining the structure, stability, and function for a wide variety of systems. The accurate prediction of these interactions from first principles is a substantial challenge because they are inherently quantum mechanical phenomena that arise from correlations between many electrons within a given molecular system. We introduce an efficient method that accurately describes the nonadditive many-body vdW energy contributions arising from interactions that cannot be modeled by an effective pairwise approach, and demonstrate that such contributions can significantly exceed the energy of thermal fluctuations--a critical accuracy threshold highly coveted during molecular simulations--in the prediction of several relevant properties. Cases studied include the binding affinity of ellipticine, a DNA-intercalating anticancer agent, the relative energetics between the A- and B-conformations of DNA, and the thermodynamic stability among competing paracetamol molecular crystal polymorphs. Our findings suggest that inclusion of the many-body vdW energy is essential for achieving chemical accuracy and therefore must be accounted for in molecular simulations.

Cooperative effects of noncovalent bonds to the Br atom of halogen-bonded H3N…BrZ and HCN…BrZ (Z = F, Br) complexes

A series of complexes formed between halogen-bonded H(3)N/HCN...BrZ (Z = Br, F) dimers and H(3)N/HCN...BrZ...XY (XY = HF, ClF, BeH(2), LiF) trimers were investigated at the MP2 and B3LYP levels of theory using a 6-31++G(d,p) basis set. Optimized structures, interaction energies, and other properties of interest were obtained. The addition of XY to the H(3)N/HCN...BrZ dyad leads to enhanced intermolecular binding with respect to the isolated monomers. This enhanced binding receives contributions from the electrostatic and inductive forces between the constituent pairs, with, in some instances, substantial three-body non-additive contributions to the binding energy. It was found that the XY = LiF interaction causes the greatest distortion of the H(3)N/HCN...BrZ halogen bond from the preferred linear orientation and also provides the strongest binding energy via the nonadditive energy.

A Simple, Exact Density-Functional-Theory Embedding Scheme.

Density functional theory (DFT) provides a formally exact framework for quantum embedding. The appearance of nonadditive kinetic energy contributions in this context poses significant challenges, but using optimized effective potential (OEP) methods, various groups have devised DFT-in-DFT methods that are equivalent to Kohn–Sham (KS) theory on the whole system. This being the case, we note that a very considerable simplification arises from doing KS theory instead. We then describe embedding schemes that enforce Pauli exclusion via a projection technique, completely avoiding numerically demanding OEP calculations. Illustrative applications are presented using DFT-in-DFT, wave-function-in-DFT, and wave-function-in-Hartree–Fock embedding, and using an embedded many-body expansion.

On the accuracy of frozen density embedding calculations with hybrid and orbital-dependent functionals for non-bonded interaction energies

We analyze the accuracy of the frozen density embedding (FDE) method, with hybrid and orbital-dependent exchange-correlation functionals, for the calculation of the total interaction energies of weakly interacting systems. Our investigation is motivated by the fact that these approaches require, in addition to the non-additive kinetic energy approximation, also approximate non-additive exact-exchange energies. Despite this further approximation, we find that the hybrid/orbital-dependent FDE approaches can reproduce the total energies with the same accuracy (about 1 mHa) as the one of conventional semi-local functionals. In many cases, thanks to error cancellation effects, hybrid/orbital-dependent approaches yield even the smallest error. A detailed energy-decomposition investigation is presented. Finally, the Becke-exchange functional is found to reproduce accurately the non-additive exact-exchange energies also for non-equilibrium geometries. These performances are rationalized in terms of a reduced-gradient decomposition of the non-additive exchange energy.

Cooperativity effects in linear formaldehyde oligomers using density functional theory calculations

This work reports hydrogen bonding interaction in linear formaldehyde oligomers using density functional theory method. Many-body analysis technique has been used to study the various interactions in these oligomers and to obtain % contributions from individual many-body energy terms to the binding energies of these oligomers. Co-operativity effects are studied using different indicators viz. hydrogen bond strength, inter- and intramolecular distances, dissociation energy, dipole co-operativity, energy per hydrogen bond, excess energy and non-additive energy. All these indicators show strong positive hydrogen bond co-operativity in linear formaldehyde oligomers. The dipole moment changes from 2.51 D in monomer to 20.92 D in formaldehyde heptamer.

Cooperative effects of hydrogen, lithium and halogen bonding on F–H/Li⋯OH2 complexes

A comparative computational study of the cooperative effect of hydrogen-, lithium- and halogen-bonding on model F-H and F-Li complexes with H2O was undertaken at the MP2/6-311++G(d,p) level of theory. The general trend of increased attraction or a positive cooperative effect on introduction of a third molecule to the F-H/LiOH2 dimer shows that lithium bonding has the greatest effect, followed by hydrogen bonding and then halogen bonding. The computed three-body nonadditive energy has a more substantial contribution to the interaction energy of the cyclic trimers than to the open linear trimer clusters.

A theoretical study of 1:1 and 1:2 complexes of acetylene with nitrosyl hydride

Ab initio calculations at MP2 computational level using aug-cc-pVTZ basis set were used to analyze the interactions between 1:1 and 1:2 complexes of acetylene and nitrosyl hydride. The structures obtained have been analyzed with the atoms in molecules and the density functional theory–symmetry adapted perturbation theory methodologies. Four minima were located on the potential energy surface of the 1:1 complex. Twenty-four different structures have been obtained for the 1:2 complexes. Five types of interactions are observed, CH···O, CH···N, NH···π hydrogen bonds and orthogonal interactions between the π clouds of triple bond, or the lone pair of oxygen with the electron-deficient region of the nitrogen atom. Stabilization energies of the 1:1 and 1:2 clusters including basis set superposition error and ZPE are in the range 3–8 and 6–17 kJ mol−1 at MP2/aug-cc-pVTZ computational level, respectively. Blue shift of NH bond upon complex formation in the ranges between 18–30 and 20–96 cm−1 is predicted for 1:1 and 1:2 clusters, respectively. The total nonadditive energy in the 1:2 cluster, calculated as the sum of the supermolecular nonadditive MP2 energy and the three-body dispersion energy, presents values between −1.48 and 1.20 kJ mol−1.

Unsymmetrical Cyclotriazadisulfonamide (CADA) Compounds as Human CD4 Receptor Down-Modulating Agents

Cyclotriazadisulfonamide (CADA) inhibits HIV at submicromolar levels by specifically down-modulating cell-surface and intracellular CD4. The specific biomolecular target of CADA compounds is unknown, but previous studies led to an unsymmetrical binding model. To test this model, methods were developed for effective synthesis of diverse, unsymmetrical CADA compounds. A total of 13 new, unsymmetrical target compounds were synthesized, as well as one symmetrical analogue. The new compounds display a wide range of potency for CD4 down-modulation in CHO·CD4-YFP cells. VGD020 (IC(50) = 46 nM) is the most potent CADA compound discovered to date, and VGD029 (IC(50) = 730 nM) is the most potent fluorescent analogue. Structure-activity relationships are analyzed from the standpoint of additive or nonadditive energy effects of different substituents. They appear to be consistent with the zipper-type mechanism in which entropy costs are reduced for additional stabilizing interactions between the small molecule and its protein target.

Characterization of O–H⋯O interactions in linear and cyclic clusters of boric acid: An ab initio, DFT, QTAIM and NBO study

We investigated geometries, O–H stretching frequencies, binding energies, and n O → σ O – H ∗ charge transfer properties of linear and cyclic clusters of boric acid (BA) by means of density functional theory and MP2 method. Our calculations indicate that the structure and energetics of linear (BA) 2–8 clusters are qualitatively different from the conventional H-bonded systems, which usually exhibit distinct cooperative effects, as cluster size increases. M06/6-311++G ∗∗ calculations reveal that for the linear (BA) 2–8, the average H-bonding energy per monomer increases from −12.54 kcal/mol in dimer to −12.97 kcal/mol in octamer; i.e. 3.4% cooperativity enhancement. Because the n O → σ O – H ∗ interaction hardly exhibits cooperative effects, the capability of the linear BA clusters to localize electrons at the O⋯H bond critical point is almost independent of cluster size and thereby leads to the non-cooperative changes in the O⋯H lengths and strengths. In contrast, a ring-like cluster consisting of six monomers of the BA indicates significant cooperative effects in lengths of O⋯H HBs, ν O – H stretching frequency, charge transfers, and electron localization at O⋯H bond critical points. The calculated non-additive energies also show that the cooperative effects due to n O → σ O – H ∗ interactions in cyclic (BA) 6 indeed provide additional stabilities for the cluster.

Generalized Gradient Approximations of the Noninteracting Kinetic Energy from the Semiclassical Atom Theory: Rationalization of the Accuracy of the Frozen Density Embedding Theory for Nonbonded Interactions.

We present a new class of noninteracting kinetic energy (KE) functionals, derived from the semiclassical-atom theory. These functionals are constructed using the link between exchange and kinetic energies and employ a generalized gradient approximation (GGA) for the enhancement factor, namely, the Perdew-Burke-Ernzerhof (PBE) one. Two of them, named APBEK and revAPBEK, recover in the slowly varying density limit the modified second-order gradient (MGE2) expansion of the KE, which is valid for a neutral atom with a large number of electrons. APBEK contains no empirical parameters, while revAPBEK has one empirical parameter derived from exchange energies, which leads to a higher degree of nonlocality. The other two functionals, APBEKint and revAPBEKint, modify the APBEK and revAPBEK enhancement factors, respectively, to recover the second-order gradient expansion (GE2) of the homogeneous electron gas. We first benchmarked the total KE of atoms/ions and jellium spheres/surfaces: we found that functionals based on the MGE2 are as accurate as the current state-of-the-art KE functionals, containing several empirical parameters. Then, we verified the accuracy of these new functionals in the context of the frozen density embedding (FDE) theory. We benchmarked 20 systems with nonbonded interactions, and we considered embedding errors in the energy and density. We found that all of the PBE-like functionals give accurate and similar embedded densities, but the revAPBEK and revAPBEKint functionals have a significant superior accuracy for the embedded energy, outperforming the current state-of-the-art GGA approaches. While the revAPBEK functional is more accurate than revAPBEKint, APBEKint is better than APBEK. To rationalize this performance, we introduce the reduced-gradient decomposition of the nonadditive kinetic energy, and we discuss how systems with different interactions can be described with the same functional form.

Comment on “Accurate frozen-density embedding potentials as a first step towards a subsystem description of covalent bonds” [J. Chem. Phys. 132, 164101 (2010)

Several assertions which are incorrect or might be misleadingly interpreted as well as omissions of issues concerning the non-additive kinetic energy potential made by Fux et al. are analyzed. They concern issues of great importance for any computational method based on the orbital-free embedding theory: evaluation of the total energy, approximating the non-additive kinetic potential, exact properties of non-additive kinetic energy potential. In a nutshell, the authors do not distinguish between two different quantities: the functional, i.e., the correspondence assigning the non-additive kinetic potential to a pair of electron densities and the function (the potential itself).

Probing surface tension additivity on chemically heterogeneous surfaces by a molecular approach

Surface free energy of a chemically heterogeneous surface is often treated as an approximately additive quantity through the Cassie equation [Cassie ABD (1948) Discuss Faraday Soc 3:11-16]. However, deviations from additivity are common, and molecular interpretations are still lacking. We use molecular simulations to measure the microscopic analogue of contact angle, Θ(c), of aqueous nanodrops on heterogeneous synthetic and natural surfaces as a function of surface composition. The synthetic surfaces are layers of graphene functionalized with prototypical nonpolar and polar head group: methyl, amino, and nitrile. We demonstrate positive as well as negative deviations from the linear additivity. We show the deviations reflect the uneven exposure of mixture components to the solvent and the linear relation is recovered if fractions of solvent-accessible surface are used as the measure of composition. As the spatial variations in polarity become of larger amplitude, the linear relation can no longer be obtained. Protein surfaces represent such natural patterned surfaces, also characterized by larger patches and roughness. Our calculations reveal strong deviations from linear additivity on a prototypical surface comprising surface fragments of melittin dimer. The deviations reflect the disproportionately strong influence of isolated polar patches, preferential wetting, and changes in the position of the liquid interface above hydrophobic patches. Because solvent-induced contribution to the free energy of surface association grows as cos Θ(c), deviations of cos Θ(c) from the linear relation directly reflect nonadditive adhesive energies of biosurfaces.

Pion Production Via Resonance Decay in a Non-extensive Quark-Gluon Medium with Non-additive Energy Composition Rule

Resonance production and decay into pion pairs is simulated in a non-extensive quark matter with multi-particle interactions. Final state pion spectra are found to take the form of the Tsallis distribution, in accordance with measurements. It has also been shown that, if a large number of particles with these multi-particle interactions are constrained to a constant energy hyper-surface in phase space, the one-particle distribution is the Tsallis distribution.

Can lone pair-π and cation-π interactions coexist? A theoretical study

Abstract The interplay between two important noncovalent interactions involving different aromatic rings is studied by means of ab initio calculations (MP2/6-31++G**) computing the non-additivity energies. In this study we demonstrate the existence of cooperativity effects when cation-π and lone pair-π interactions coexist in the same system. These effects are studied theoretically using energetic and geometric features of the complexes. In addition we use Bader’s theory of atoms-in-molecules and Molecular Interaction Potential with polarization (MIPp) partition scheme to characterize the interactions. Experimental evidence for this combination of interactions has been obtained from the Cambridge Structural Database.

Phase diagram of the ABC model with nonconserving processes

The three species ABC model of driven particles on a ring is generalized to includevacancies and particle-nonconserving processes. The model exhibits phase separation athigh densities. For equal average densities of the three species, it is shown that althoughthe dynamics is local, it obeys detailed balance with respect to a Hamiltonian withlong-range interactions, yielding a nonadditive free energy. The phase diagrams of theconserving and nonconserving models, corresponding to the canonical and grand-canonicalensembles, respectively, are calculated in the thermodynamic limit. Both models exhibit atransition from a homogeneous to a phase-separated state, although the phase diagrams areshown to differ from each other. This conforms with the expected inequivalence ofensembles in equilibrium systems with long-range interactions. These results are based on astability analysis of the homogeneous phase and exact solution of the continuumequations of the models. They are supported by Monte Carlo simulations. This studymay serve as a useful starting point for analyzing the phase diagram for unequaldensities, where detailed balance is not satisfied and thus a Hamiltonian cannot bedefined.

Exact nonadditive kinetic potentials for embedded density functional theory

We describe an embedded density functional theory (DFT) protocol in which the nonadditive kinetic energy component of the embedding potential is treated exactly. At each iteration of the Kohn-Sham equations for constrained electron density, the Zhao-Morrison-Parr constrained search method for constructing Kohn-Sham orbitals is combined with the King-Handy expression for the exact kinetic potential. We use this formally exact embedding protocol to calculate ionization energies for a series of three- and four-electron atomic systems, and the results are compared to embedded DFT calculations that utilize the Thomas-Fermi (TF) and the Thomas-Fermi-von Weisacker approximations to the kinetic energy functional. These calculations illustrate the expected breakdown due to the TF approximation for the nonadditive kinetic potential, with errors of 30%-80% in the calculated ionization energies; by contrast, the exact protocol is found to be accurate and stable. To significantly improve the convergence of the new protocol, we introduce a density-based switching function to map between the exact nonadditive kinetic potential and the TF approximation in the region of the nuclear cusp, and we demonstrate that this approximation has little effect on the accuracy of the calculated ionization energies. Finally, we describe possible extensions of the exact protocol to perform accurate embedded DFT calculations in large systems with strongly overlapping subsystem densities.

Combinations of Affinity-Enhancing Mutations in a T Cell Receptor Reveal Highly Nonadditive Effects within and between Complementarity Determining Regions and Chains

Understanding the energetic and structural response to multiple mutations in a protein-protein interface is a key aspect of rational protein design. Here we investigate the cooperativity of combinations of point mutations of a T cell receptor (TCR) that binds in vivo to HLA-A2 MHC and a viral peptide. The mutations were obtained from two sources: a structure-based design study on the TCR alpha chain (nine mutations) and an in vitro selection study on the TCR beta chain (four mutations). In addition to combining the highest-affinity variants from each chain, we tested other combinations of mutations within and among the chains, for a total of 23 TCR mutants that we measured for binding kinetics to the peptide and major histocompatibility complex. A wide range of binding affinities was observed, from 2- to 1000-fold binding improvement versus that of the wild type, with significant nonadditive effects observed within and between TCR chains. This included an amino acid-dependent cooperative interaction between CDR1 and CDR3 residues that are separated by more than 9 A in the wild-type complex. When analyzing the kinetics of the mutations, we found that the association rates were primarily responsible for the cooperativity, while the dissociation rates were responsible for the anticooperativity (less-than-additive energetics). On the basis of structural modeling of anticooperative mutants, we determined that side chain clash between proximal mutants likely led to nonadditive binding energies. These results highlight the complex nature of TCR association and binding and will be informative in future design efforts that combine multiple mutant residues.