Nonadditivity of the SCF interaction energy in the (LiH)3 complex

The role of nonadditivity of the interaction energy between three LiH molecules was investigated within the SCF ab initio framework. The nonadditive part of the interaction energy is more important in the case of a cyclic structure than in a linear trimer, and is stabilizing in both cases. The value of the ratio of three-body and two-body terms for different points on the energy hypersurface is discussed.     

Large changes of static electric properties induced by hydrogen bonding: an ab initio study of linear HCN oligomers

We report the partitioning of the interaction-induced static electronic dipole (hyper)polarizabilities for linear hydrogen cyanide complexes into contributions arising from various interaction energy terms. We analyzed the nonadditivities of the studied properties and used these data to predict the electric properties of an infinite chain. The interaction-induced static electric dipole properties and their nonadditivities were analyzed using an approach based on numerical differentiation of the interaction energy components estimated in an external electric field. These were obtained using the hybrid variational-perturbational interaction energy decomposition scheme, augmented with coupled-cluster calculations, with singles, doubles, and noniterative triples. Our results indicate that the interaction-induced dipole moments and polarizabilities are primarily electrostatic in nature; however, the composition of the interaction hyperpolarizabilities is much more complex. The overlap effects substantially quench the contributions due to electrostatic interactions, and therefore, the major components are due to the induction and exchange-induction terms, as well as the intramolecular electron-correlation corrections. A particularly intriguing observation is that the interaction first hyperpolarizability in the studied systems not only is much larger than the corresponding sum of monomer properties, but also has the opposite sign. We show that this effect can be viewed as a direct consequence of hydrogen-bonding interactions that lead to a decrease of the hyperpolarizability of the proton acceptor and an increase of the hyperpolarizability of the proton donor. In the case of the first hyperpolarizability, we also observed the largest nonadditivity of interaction properties (nearly 17%) which further enhances the effects of pairwise interactions.     

Many-orbital cluster expansion for the exchange-repulsion nonadditivity in the interaction of rare gas atoms. The neon trimer

Nonadditivity of the exchange repulsion for three neon atoms in the equilateral triangle configuration has been calculated in the first-order of the symmetry adapted perturbation theory. The relative nonadditive contribution to the first-order interaction energy has been found to be about twice as small as in the helium trimer. The many-orbital cluster partition of the exchange nonadditivity has been derived. It has been found that in the region of the van der Waals minimum about 95% of the exchange nonadditivity originates from the interaction of the L-shell electrons only. The five-orbital terms as well as terms of an order-higher than S³ have been found to be negligible. Approximate formulae for evaluation of the exchange repulsion nonadditivity has been proposed and discussed.This work was partly supported by the Polish Academy of Sciences within the project MR.I.9.     

Nonadditive nature of nucleobases interactions in model d(GpG) dinucleotide steps

High nonadditive character of intermolecular interaction energy (IIE) has been found for many d(GpG) dinucleotide steps in B‐DNA conformations. Although three‐ and four‐body terms posses opposite signs in all cases, positive nonadditivity is observed. On the other hand, the pairwise additive simplification may still be applied because there is linear correlation between magnitude of additive and nonadditive terms of IIE. The application of the linear regression leads to a higher accuracy with values of standard deviation about 0.5 kcal/mol. The heterogeneity of intermolecular interactions in two subsequent GC pairs was identified as the main source of nonadditivity. The higher the difference between hydrogen bonding and interstrand stacking, the higher the absolute values of three‐ and four‐body terms. This trend is of linear character and may be used for both parametric correction and measure of nonadditivity in d(GpG) steps without necessity of energy calculations for the whole tetramer. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Thermodynamic stability of fluid-fluid phase separation in binary athermal mixtures: the role of nonadditivity

We studied the thermodynamic stability of fluid-fluid phase separation in binary nonadditive mixtures of hard-spheres for moderate size ratios. We are interested in elucidating the role played by small amounts of nonadditivity in determining the stability of fluid-fluid phase separation with respect to the fluid-solid phase transition. The demixing curves are built in the framework of the modified-hypernetted chain and of the Rogers-Young integral equation theories through the calculation of the Gibbs free energy. We also evaluated fluid-fluid phase equilibria within a first-order thermodynamic perturbation theory applied to an effective one-component potential obtained by integrating out the degrees of freedom of the small spheres. A qualitative agreement emerges between the two different approaches. We also addressed the determination of the freezing line by applying the first-order thermodynamic perturbation theory to the effective interaction between large spheres. Our results suggest that for intermediate size ratios a modest amount of nonadditivity, smaller than earlier thought, can be sufficient to drive the fluid-fluid critical point into the thermodinamically stable region of the phase diagram. These findings could be significant for rare-gas mixtures in extreme pressure and temperature conditions, where nonadditivity is expected to be rather small.     

Do all pieces make a whole? Thiele cumulants and the free energy decomposition

The partitioning of the free energy into additive contributions originating from different groups of atoms or force field terms has the potential to provide relationship between structure and biological activity of molecules. In this article, the theoretical foundation for the free energy decomposition in the free energy perturbation (FEP) methodology is formulated using Thiele cumulants, a powerful tool from the arsenal of probability theory and mathematical statistics. We establish that rigorous decomposition of the free energy into its components is precluded by the presence of mixed potential energy terms in Thiele cumulants of second and higher orders. However, we also show that the resultant nonadditivity error can be reduced to an arbitrary value by increasing the number of FEP steps. Consequently, the whole system can be in the limit of small perturbation steps adequately represented by the sum of its constituent parts.     

Electrostatic Interaction between Two Dissimilar Spheres with Constant Surface Charge Density

Explicit exact analytic expressions are obtained in the form of infinite series for the potential energy of the electrostatic interaction for the system of two dissimilar hard spheres with constant surface charge density in an electrolyte solution on the basis of the linearized Poisson-Boltzmann equation. The effects of the particle polarization, that is, the internal fields induced within tim interacting spheres, which are found to be of the order of instead of 1/κa (where κ is the Debye-Hückel parameter and a is the sphere radius), are taken into account. As in the case of the interaction at constant surface potential, the zeroth-order approximation to the interaction energy corresponds to the interaction energy that would be obtained if both spheres were ion-penetrable spheres ("soft" spheres) and to that obtained by the linear superposition approximation. The first-order approximation corresponds to the interaction energy that would be obtained if either sphere were a soft sphere, with the other being a hard sphere with constant surface charge density. The first-order correction term can be interpreted as the image interaction between the soft sphere and its image with respect to the hard sphere.     

Symmetry-adapted perturbation theory analysis of the N...HX hydrogen bonds

The main aim of the study was the detailed investigation of the interaction energy decomposition in dimers and trimers containing N...HX bonds of different types. The study of angular dependence of interaction energy terms partitioned according to the symmetry-adapted perturbation theory (SAPT) was performed for the dimers containing N...HX bonds as mentioned above: ammonia-HX (X = F, Cl, Br) and pyridine-HF complexes. It was found that the electrostatic and induction terms exhibit strong angular dependence, while the exchange contributions are less affected. The dispersion terms are virtually nondirectional. In addition, the three-body SAPT interaction energy analysis for the mixed acid-base NH3...(HF)2 and (NH3)2...HF trimers revealed strong differences between interactions of similar strength but different types (i.e., hydrogen bond and general electrostatic interaction). The importance of the induction terms for the nonadditivity of the interaction energy in strongly polar systems was confirmed.     

Nonadditivity of secondary deuterium isotope effects on basicity of trimethylamine

Secondary deuterium isotope effects (IEs) on basicities of isotopologues of trimethylamine have been accurately measured by an NMR titration method applicable to a mixture. Deuteration definitely increases the basicity, by approximately 0.021 in the Delta pK per D. The IE is attributed to the lowering of the CH stretching frequency and zero-point energy by delocalization of the nitrogen lone pair into the C-H antibonding orbital. Because this depends on the dihedral angle between the lone pair and the C-H, a further consequence is a preference for conformations with H antiperiplanar to the lone pair and D gauche. This leads to a predicted nonadditivity of IEs, which is confirmed experimentally. It is found that the decrease in basicity, per deuterium, increases with the number of deuteriums. The nonadditivity of IEs is a violation of the widely assumed Rule of the Geometric Mean.     

Nonadditive interactions and the relative stability of neutral and anionic silver clusters

We discuss the physical nature of nonadditivity in many-particle systems and the methods of calculations of nonadditive contributions to the interaction energy. For neutral clusters, a closed recurrence formula which expresses the energy of m-body interactions through the energies of 2-, 3-, and (m – 1)-body ones is obtained. The general approach for calculation of the nonadditive contribution in the interaction energy of charged systems is developed. The comparative calculation of anionic and neutral silver clusters shows that the geometry of the most stable anionic clusters is established mainly by the additive forces. The stability of neutral silver clusters is determined by the competition of attractive additive forces and repulsive nonadditive ones. © 1995 John Wiley & Sons, Inc.     

First-order relativistic corrections to MP2 energy from standard gradient codes: Comparison with results from density functional theory

The evaluation of the first-order scalar relativistic corrections to MP2 energy based on either direct perturbation theory or the mass–velocity and Darwin terms is discussed. In a basis set of Lévy-Leblond spinors the one- and two-electron matrix elements of the relativistic Hamiltonian can be decomposed into a nonrelativistic part and a relativistic perturbation. Thus, a program capable of calculating nonrelativistic energy gradients can be used to calculate the cross-term between relativity and correlation. The method has been applied to selected closed-shell atoms (He, Be, Ne, and Ar) and molecules (CuH, AgH, and AuH). The calculated equilibrium distances and harmonic frequencies were compared with results from first-order relativistic density functional calculations. It was found that the cross-term is not the origin of the nonadditivity of relativistic and correlation effects. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1596–1603, 1998     

Spin–orbit and dispersion energy effects in XeF

Spin–orbit and dispersion energy contributions to the energy curves of XeF are examined. A rapid variation in the spin–orbit coupling with internuclear separation is found for both the ground and excited states. This result can explain the experimentally observed ordering of the ionic excited states when the spin–orbit perturbation couples ²σ and ²π energy curves obtained by both all-electron and effective core potential (ECP ) calculations at the first-order configuration interaction (FOCI ) level of accuracy. Damped dispersion energy contributions to the ground-state energy curve are shown to be comparable to the charge transfer contribution. The energy curve for XeF is in reasonable agreement with experimental results and a calculation of the analogous XeCl curve confirms the qualitative correctness of the calculation. The energy curves and transition moments were then applied to two problems related to the efficiency of the XeF laser. Photodissociation of the X state provides a means of removing a bottlenecked vibrational level but a calculation of the radiative transition probability between the X and A states finds the cross section is too small to yield rates competitive with collisional deactivation. The bottlenecked state may also be removed by electron dissociative attachment but the calculated energy curves for the X states of XeF and XeF^? do not cross at a low energy indicating a small cross section.     

Unexpected nonadditivity effects in anion-π complexes

Several complexes of fluorine-substituted ethyne, ethene, butadiene, benzene, and [n]radialenes (n = 3-5) with two anions have been optimized at the RI-MP2/aug-cc-pVTZ level of theory. The additivity of the anion-π interaction was studied depending on the number of double bonds and fluorine atoms. Interesting nonadditivity effects were observed in the aromatic and antiaromatic complexes, which were analyzed by partitioning the total interaction energy into individual components, using Bader's theory of "atoms in molecules" and changes in the aromatic character of the ring upon complexation.     

Phase behavior of polymer mixtures with nonadditive hard-sphere potential

The phase behavior of a binary mixture of homopolymers in which macromolecules are composed of tangent hard spheres was studied. The interaction of unlike units is characterized by the contact distance (1/2)(σ_A + σ_B)(1 + Δ), where σ _i is the diameter of the ith sphere (unit) and Δ is the nonadditivity parameter. The effect of nonadditivity was taken into account by means of the perturbation theory relative to the additive system (Δ = 0) considered earlier (Polymer Science, 47, 2146 (2005)) in terms of the Percus-Yevick approximation. The theoretical consideration presented is completely analytical. It was found that a polymer mixture experiences phase separation with an increase in pressure; the two-phase region extends with an increase in both the size ratio between the units α = σ_A/σ_B and the length of the chain per se. Closed phase diagrams were first predicted for athermal mixtures; such diagrams appear at Δ < 0 and certain values of α. It was shown that the thermodynamics of an incompressible mixture of hard-chain molecules at α = 1 follows the Flory-Huggins theory with the temperature-independent interaction parameter. Phase separation in polymer solutions with the nonadditive hard-sphere potential was also analyzed.     

Theoretical study of properties of H bonds and intermolecular interactions in linear cis-,trans-cyclotriazane clusters (n = 2-8)

Our calculations based upon Becke's three-parameter functional of density-functional theory (DFT) with the correlation of Lee, Yang, and Parr (B3LYP), natural bond orbital, and atoms in molecule indicate that in drastic contrast to most H-bonded systems, the anticooperative and cooperative effects coexist in the linear H-bonded cis-,trans (c,t)-cyclotriazane clusters (n = 2-8). As cluster size increases, the properties along the H-bonded chains at trans-positions take on the unexpectedly anticooperative changes which are reflected in elongation of the N...H hydrogen bonds, frequency blueshift in the N-H stretching vibrations, decay in the n(N)-->sigma*(N-H) charge transfers, and weakening of strengths of the N...H bonds. And the cooperative changes in the corresponding properties for the cis- H-bonded chains are observed to be concurrent with the anticooperativities. The rise and fall in the n(N)-->sigma*(N-H) interactions cause increment and decrement in capacities of the clusters to concentrate electrons at the bond critical points of the N...H bonds, and thereby leading to the cooperative and the anticooperative changes especially in the N...H lengths and the N-H stretching frequencies. In terms of three-body symmetry-adapted perturbation theory (three-body SAPT), the first exchange nonadditivity plays a more important role in stabilizing trimer than the nonadditive induction. However, the dominance of the first exchange nonadditivity in three-body interaction unexpectedly triggers the anticooperative effect that counteracts the concurrent cooperative effect. According to the SAPT(DFT), which is a combination of SAPT with asymptotically corrected DFT, DFT/B3LYP is able to succeed in describing the electrostatic, exchange, and induction components, but fails to yield satisfactory interaction energies due to the fact that about 40% of short-range dispersion energy is neglected by the DFT, which is different from many H-bonded described well by the DFT. A quantum cluster equilibrium model illustrates that the c,t-cyclotriazane liquid phase exhibits a weak cooperative effect.     

Joint effect of structure and temperature on the rates of the reactions of 3,5-dinitrophenyloxirane with arenesulfonic acids: Compensation effect and isoparametricity

The joint effect of structure and temperature on the rate and free energy of activation of the reactions of 3,5-dinitrophenyloxirane with arenesulfonic acids YC₆H₄SO₃H in a dioxane-diglyme (1: 1 vol/vol) mixture is reported. A correlation analysis of the results of a multifactor kinetic experiment has demonstrated the nonadditivity (interaction) of the effects of the substituent Y and temperature for a cross reaction series. The pronounced kinetic enthalpy-entropy compensation effect provided experimental evidence for the isoparametricity phenomenon: at the isoparametric temperature point (isokinetic temperature), the rate of the reaction is independent of the structure of Y. At the isoparametric point for the constant of the substituent Y, the free energy of activation is temperature-independent and the entropy of activation is ΔS ^≠ = 0. On passing through this point, ΔS ^≠ changes its sign. The isoparametric points for the parameters of the varied factors are used in the interpretation of the mechanism of oxirane ring opening.     

Calculation of the Gibbs Energy of the Reaction OH-·(H2O)n-1 + H2O = OH-·(H2O)n by the Monte-Carlo Method

The energy, the Gibbs energy of the reaction OH^-·(H₂O) _{n- 1} + H₂O = OH^-·(H₂O) _n are calculated by the Monte-Carlo method with a large canonical ensemble for n = 1, ..., 20. The ion-waternonpair interaction potential was obtained by numerical fitting of calculated Gibbs energy and entropy of (H₂O)_n clusters (n = 1, ..., 5) to experimental ones. A good fit to experiment both of the internal energy and the Gibbs energy can be obtained in terms of a model allowing for nonpair interaction. It is shown that constructing an ion-water interaction potential without allowance for the entropy factor can lead to considerable errors in the Gibbs energy of cluster formation and in the nucleation rate.     

Methodology of the spectrophotometric analysis of mixtures of organic substances: Nonadditivity of light absorption

The typology of the problems being solved in the analysis of multicomponent mixtures of organic substances (pharmaceutical preparations, petroleum products, and others) is proposed. The difficulties associated with the problems of each type are discussed, and the potential of spectrophotometry without the separation of components in overcoming the difficulties is considered. The nonadditivity of light absorption due to the interaction of components is the most complicated problem. The methods for revealing deviations from additivity, the correlation of these deviations with the composition of the mixture, the effect of nonadditivity on the results of determination, and the approaches to reducing the corresponding systematic errors based on chemometric algorithms are discussed.     

Quantum electrodynamic effects in atomic structure

Summary In high-Z atoms, quantum electrodynamic (QED) corrections are an important component in the theoretical prediction of atomic energy levels. The main QED effects in electronic atoms are the one-electron self-energy and vacuum-polarization corrections which are well known. At the next level of precision, estimates of the effect of electron interactions on the self energy and higher-order effects in two exchanged photon corrections are necessary. These corrections can be evaluated within the framework of QED in the bound interaction picture. For high-Z few-electron atoms, this approach provides a rapidly converging series in 1/Z for the corrections, which is the generalization of the well-known relativistic 1/Z expansion methods. This paper describes recent work on the effect of electron interactions on the self energy. The QED effects are particularly important for the theory for lithiumlike uranium where an accurate measurement of the Lamb shift has been made, as well as for numerous other cases where systematic differences appear between theory that does not include these QED effects and experiment.     

Modeling of adsorption of gases on graphite surfaces accounting for the solid-fluid nonadditivity correction

A series of graphitized carbon blacks have been studied using argon and nitrogen adsorption at their boiling points. Analysis of adsorption isotherms was performed with nonlocal density functional theory (NLDFT) accounting for the Axilrod-Teller equation to describe the effect of nonadditivity of the gas-solid interaction. In our previous study [Ustinov, E. A. J. Chem. Phys. 2010, 132, 194703] we have shown that the nonadditivity effect decreases the attractive component of Ar-Ar interaction in the first molecular layer adjacent to the graphite surface by about 23%. This is a source of a large error (up to 40%) when a standard NLDFT is applied to fitting the low-temperature Ar adsorption isotherm on a graphitized carbon black. A new approach that incorporates the Axilrod-Teller equation into the standard NLDFT diminishes the relative error from 40 to 4%, which suggests that the nonadditivity correction should not be ignored in most adsorption systems including crystalline and amorphous solids. The present study is an extension of our approach to N(2) adsorption isotherms at 77.3 K on graphitized carbon blacks. We show that the approach allows to reliably determine the gas-solid molecular parameters, the gas-solid nonadditivity coefficient, the Henry coefficient, and the specific surface area. The surface areas of different carbon blacks determined with the N(2) at 77.35 K and Ar at 87.29 K are very close to each other, though in the former case the values proved to be slightly smaller presumably due to nonspherical shape of the nitrogen molecule. A comparison with the Brunauer, Emmett, and Teller method is provided.