Nonadditive Interaction Energies Research Articles

The nature of three-body interactions in DFT: Exchange and polarization effects.

We propose a physically motivated decomposition of density functional theory (DFT) 3-body nonadditive interaction energies into the exchange and density-deformation (polarization) components. The exchange component represents the effect of the Pauli exclusion in the wave function of the trimer and is found to be challenging for density functional approximations (DFAs). The remaining density-deformation nonadditivity is less dependent upon the DFAs. Numerical demonstration is carried out for rare gas atom trimers, Ar2-HX (X = F, Cl) complexes, and small hydrogen-bonded and van der Waals molecular systems. None of the tested semilocal, hybrid, and range-separated DFAs properly accounts for the nonadditive exchange in dispersion-bonded trimers. By contrast, for hydrogen-bonded systems, range-separated DFAs achieve a qualitative agreement to within 20% of the reference exchange energy. A reliable performance for all systems is obtained only when the monomers interact through the Hartree-Fock potential in the dispersion-free Pauli blockade scheme. Additionally, we identify the nonadditive second-order exchange-dispersion energy as an important but overlooked contribution in force-field-like dispersion corrections. Our results suggest that range-separated functionals do not include this component, although semilocal and global hybrid DFAs appear to imitate it in the short range.

Interaction of Boron-Nitrogen Doped Benzene Isomers with Water.

The interaction of 1,2-dihydro-1,2-, 1,3-dihydro-1,3- and 1,4-dihydro-1,4-azaborine isomers with one and two water molecules has been studied using a variety of supermolecular (Møller-Plesset = MP, and coupled cluster = CC) as well as perturbational (symmetry-adapted perturbation theory = SAPT) electron-correlation methods in the complete basis-set limit. It has been found that the water molecule binds to azaborine isomers through O-H···π, π-H···O, and dihydrogen bonding linkages. The SAPT interaction energy decomposition shows that these complexes are mostly stabilized by dispersion followed closely by induction contributions. Pauli repulsion hinders water molecule to be polarized by azaborine in the O-H···π type of complexes. According to the interacting-quantum-atoms analysis, the structures with a primary binding of the O-H···π type benefit from an additional stabilization factor resulting from the interaction of the oxygen and the second hydrogen atom of water, i.e., the one which does not point toward the ring, while the interaction of hydrogens from water with azaborines plays a destabilizing role for the π-H···O type. The same method states that the intermolecular bindings between azaborines and the water molecule have a multicenter character with a small bond polarization, and they are classified as closed-shell (noncovalent) by quantum theory of atoms-in-molecules analysis at bond critical points. The complexes of azaborines with two water molecules tend to arrange in a circular fashion with a recognizable water dimer attached to the azaborine molecule. A comparison with the CCSD(T) benchmarks shows that the nonadditive contribution to the interaction energy of the trimers is negative and with a good accuracy can be accounted for by the MP2 method. A good agreement between Hartree-Fock (HF) and MP2 nonadditive energy, as well as the decomposition of HF nonadditive interaction energies divulge the importance of nonadditive induction energy in the trimers. The interaction energies for the azaborine with one water calculated with the SAPT(DFT), MP2, SCS-MP2, and MP2C methods are in satisfactory agreement with each other. Finally, it has been found that the population analysis from the electron localization function offers the most comprehensive explanation of the orientational preferences of the water molecule in the complex.

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.

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.

Full-configuration-interaction calculation of three-body nonadditive contribution to helium interaction potential

The three-body nonadditive interaction energy between helium atoms was calculated at 253 trimer configurations using the full-configuration-interaction (FCI) method. The analytic potential fitted to these energies is the best current representation of the three-body nonadditive interactions between helium atoms. At the equilateral triangle configuration with R=5.6 bohr, near the minimum of the total potential, the nonadditive three-body energy calculated at the FCI level amounts to -88.5 mK, compared to -98.5 mK at the coupled cluster with single, double, and noniterative triple excitations [CCSD(T)] level. The uncertainty of the former result resulting from basis set incompleteness is estimated to be 1.5 mK. The relative uncertainty of our present complete three-body fit, including the uncertainties resulting from the fitting procedure, is estimated at 2%, a fivefold improvement over the previous best potential. Overall, the FCI contribution beyond CCSD(T) is rather important, being of the same order of magnitude as the uncertainty of the sum of two-body interactions. The inclusion of this contribution makes uncertainties of the total trimer interaction energies dominated by the uncertainties of the two-body component.

Dipole oscillator strength distributions, properties, and dispersion energies for ethylene, propene, and 1-butene

A recommended isotropic dipole oscillator strength distribution (DOSD) has been constructed for the ethylene molecule through the use of quantum mechanical constraint techniques and experimental dipole oscillator strength (DOS) data; the DOS data employed are recent experimental results not available at the time of the original constrained DOSD analysis of this molecule. The constraints are furnished by molar refractivity data and the Thomas–Reiche–Kuhn sum rule. The DOSD is used to evaluate a variety of isotropic dipole oscillator strength sums, logarithmic dipole oscillator strength sums, and mean excitation energies for ethylene. Pseudo-DOSDs for this molecule, and for propene and 1–butene, which are based on an earlier constrained DOSD analysis for these molecules, are developed. They are used to obtain reliable results for the isotropic dipole–dipole dispersion-energy coefficients C6, for the interactions of the alkenes with each other and with 47 other species, and the triple-dipole dispersion-energy coefficients C9 for interactions involving any triple of molecules taken from ethylene, propene, and 1–butene.Key words: alkenes, dipole properties, pseudo-states, dipole–dipole and triple-dipole dispersion energies, long-range additive, non-additive interaction energies.

Intermolecular interactions and nature of cooperative effects in linear cis, cis-cyclotriazane clusters ( n=2–8)

Intermolecular interactions in the linear cis, cis( c, c)-cyclotriazane clusters ( n=2–8) have been investigated via several theoretical methods including the SAPT (DFT) method is a combination of symmetry-adapted perturbation theory (SAPT) with the asymptotically corrected DFT. The SAPT(DFT) calculation indicates that the hydrogen-bonded c, c-cyclotriazane clusters, which are bound mainly by electrostatic interactions exhibit remarkable dispersion interactions. However, the dispersion interactions are only partially reproduced by DFT/B3LYP. Accuracy of the B3LYP interaction energies is markedly inferior to that of the MP2 interaction energies, which is very different from the H-bonded systems described well by B3LYP. Thereby, the B3LYP interaction energies are corrected to arrive at the same accuracy as the MP2 energies. The computation based upon the three-body SAPT shows the inductive effect contributes most importantly to the nonadditive three-body interaction. The induction nonadditivity plays a key role in stabilizing the clusters in the process of contraction in their N⋯H hydrogen bonds. Because of the weak nonadditive exchange–dispersion effect, B3LYP is able to represent well the nonadditive interaction energy even in higher cluster. The quantum cluster equilibrium (QCE) calculations illustrate that the nonadditive energies and the dispersion energies neglected by the DFT in the clusters can seriously affect properties of the c, c-cyclotriazane liquid.

Density Functional Theory Study of the Properties of N−H···N, Noncooperativities, and Intermolecular Interactions in Linear trans-Diazene Clusters up to Ten Molecules

We investigate aspects of N-H...N hydrogen bonding in the linear trans-diazene clusters (n=2-10) such as the N...H and N-H lengths, n(N) --> sigma(N-H) interactions, N...H strengths, and frequencies of the N-H stretching vibrations utilizing the DFT/B3LYP theory, the natural bond orbital (NBO) method, and the theory of atoms in molecules (AIM). Our calculations indicate that the structure and energetics are qualitatively different from the conventional H-bonded systems, which usually exhibit distinct cooperative effects, as cluster size increases. First, a shortening rather than lengthening of the N-H bond is found and thus a blue rather than red shift is predicted. Second, for the title clusters, any sizable cooperative changes in the N-H and N...H lengths, n(N) --> sigma(N-H) charge transfers, N...H strengths, and frequencies of the N-H stretching vibrations for the linear H-bonded trans-diazene clusters do not exist. Because the n(N) --> sigma(N-H) interaction hardly exhibits cooperative effects, the capability of the linear trans-diazene cluster to localize electrons at the N...H bond critical point is almost independent of cluster size and thereby leads to the noncooperative changes in the N...H lengths and strengths and the N-H stretching frequencies. Third, the dispersion energy is sizable and important; more than 30% of short-range dispersion energy not being reproduced by the DFT leads to the underestimation of the interaction energies by DFT/B3LYP. The calculated nonadditive interaction energies show that, unlike the conventional H-boned systems, the trans-diazene clusters indeed exhibit very weak nonadditive interactions.

Cooperativity and Proton Transfer in Hydrogen‐Bonded Triads

Ab initio MP2/6-311+G(3df,2pd) and MP2/aug-cc-pVTZ calculations have been carried out to investigate the structures and properties of AHXHYH(3) (A=F, Cl; X=F, Cl; Y=N, P) hydrogen-bonded complexes. Significant cooperative effects are observed in the XHYH3 dyads in the triads due to the presence of the polar near-neighbor AH. These effects are greater when the polar partner is HF, which is a better proton donor than HCl. Structural changes, red shifts of proton-donor stretching frequencies, nonadditive interaction energies, and electron density redistributions unambiguously demonstrate that the X--HY hydrogen bond (HB) is stronger in the triads than in the corresponding dyads, while the X--H bond of the proton donor becomes weaker. Even more pronounced cooperative effects are observed in the AHXH dyads due to the presence of the YH3 partner. These effects are weaker in complexes having PH3 rather than NH3 as the proton acceptor, since NH3 is a stronger base. Cooperativity also enhances the proton-donating ability of the YH3 moiety, with the result that all complexes except FHFHPH3 are cyclic. Cooperativity, together with the ease of breaking the Cl--H bond in ClHClHNH3 and FHClHNH3, leads to proton transfer (PT), so that these two complexes are better described as approaching hydrogen-bonded ClHCl- x +HNH3 and FHCl- x +HNH3 ion pairs.

Spectral Theory of Physical and Chemical Binding,

A spectral method which provides unified quantum mechanical descriptions of both physical and chemical binding phenomena is reported for constructing the adiabatic electronic potential energy surfaces of aggregates of atoms or other interacting fragments. The formal development, based on use of a direct product of complete sets of atomic spectral eigenstates and the pairwise-additive nature of the total Hamiltonian matrix in this basis, is seen to be exact when properly implemented and to provide a separation theorem for N-body interaction energies in terms of response matrices which can be calculated once and for all for atoms and other fragments of interest. Its perturbation theory expansion provides a generalization of familiar (Casimir−Polder) second-order pairwise-additive and (Axilrod−Teller) third-order nonadditive interaction energies, expressions which are recovered explicitly in the long-range-dipole expansion limit. A program of ab initio computational implementation of the formal development i...

An accurate determination of three-body intermolecular forces in the helium trimer

Three-body nonadditive interaction energies in the helium trimer are calculated by the complete fourth-order Møller—Plesset perturbation theory with large basis sets including bond functions. It is shown that the three-body energy can be easily converged to the complete basis set limit only if the counterpoise procedure is properly employed. The exchange—repulsion effect dominates the contribution to the three-body energy while the correlation contribution is in accord with the Axilrod—Teller—Muto triple-dipole perturbation expression.

Non-additive three-body interaction energies for H3(quartet spin state)

The results of an Unsold average energy calculation of the non-additive interaction energy for H3 (quartet spin state) are presented for equilateral triangular configurations. They are discussed in the context of the problems associated with the representation of non-additive energies for the interaction of closed-shell species.

Structure, energetics and vibrational spectra of H-bonded systems. Dimers and trimers of HF and HCl

The title complexes are studied by ab initio methods using double-ζ basis sets augmented by diffuse sp and two sets of polarization functions. The binding energies decrease in the order (HF) 2 > HF…HCl > (HCl) 2, all of which form pseudolinear H bonds. While not important for (HF) 2, correlation plays an increasingly larger role as each HF is replaced by HCl, contributing 2 3 of the total binding energy of (HCl) 2. (HF) 3 and (HCl) 3 are both C 3h cyclic and exhibit cooperativity, particularly (HF) 3; correlation appears to be negligible in the three-body nonadditive interaction energies. The red shift of the HF stretch in (HF) 3 is nearly twice as great as in the dimer while little enhancement is observed in the HCl analogues. The other two observable bands in the trimers are of fairly high intensity and correspond to an out-of-plane and in-plane bend. The intermolecular stretching modes in the dimers and trimers are of very low intensity. A clear relationship is noted between the intermolecular frequencies and the strength of the interaction.

Quasichemical approximation for lattice models with nonadditive interatomic interactions.

A statistical mechanical theory based on the quasichemical approximation is developed for lattice models where atoms are bonded to each other with nonadditive interaction energies. The theory is applied to lattice gases where the bond energy varies linearly with the number of nearest-neighbor atoms. Calculated critical points show good agreement with the existing Monte Carlo simulation results.

Spherical tensor theory of long-range interactions in a system ofNarbitrary molecules including quantum-mechanical many-body effects

In the previous two papers of this series we have applied the spherical tensor formalism to the perturbation treatment of long-range anisotropic forces in a collection of N molecules. In this paper we derive the compact formulas for all categories of the isotropic pairwise additive as well as pair wise non-additive interaction energies which occur in the first three orders of the perturbation theory of long-range forces between N arbitrary molecules. In this way the most important types of the isotropic induction and dispersion pairwise non-additive interactions are taken into account and clearly described.

On the validity of the triple-dipole interaction as a representation of non-additive intermolecular forces

A complete partial wave analysis of the non-expanded non-additive coulomb interaction energy for three non-degenerate S-state atoms is given through third-order in the interatomic potential energy function. Pseudo state techniques are used to evaluate various partial wave components of the non-expanded second and third-order non-additive interaction energies for various isosceles triangular configurations of three interacting ground-state hydrogen atoms. These second and third-order non-expanded coulomb results are used, in conjunction with Heitler-London results for the first-order non-additive energies for the quartet spin state of the H(1s)-H(1s)-H(1s) interaction, to discuss the relative importance of various parts of the non-additive energy as a function of the geometrical configuration of the atoms, and the validity of both the non-expanded triple-dipole energy and the expanded Axilrod-Teller-Muto triple-dipole result as a representation of non-additive coulomb energies. For example, in the non-bond...

Long-range molecular interaction coefficients computed from frost-model wave functions

The average long-range interaction energy between two molecules can be written as an inverse asymptotic series in the intermolecular separation distanceR. Using Frost-model wave functions, the dispersion coefficients of the first three (R −6,R −8,R −10 terms in the series are obtained. Coefficients of three- and four-body non-additive interaction energies are also calculated and the form of the dispersion interaction when retardation effects are included is examined.