Many-orbital cluster expansion for the exchange-repulsion energy in the interaction of closed-shell systems

The energy of exchange repulsion between two closed-shell systems described by determinantal wave functions has been represented as a sum of contributions arising from the interaction of two, three and four orbitals at a time. These contributions have been calculated for the interaction of two neon atoms. It has been found that in the van der Waals minimum region the two-orbital components are of secondary importance and that about 90% of the total exchange energy originates from the three-orbital interactions ofL-shell electrons. The four-orbital as well as the double-exchange terms have been found negligible. The approximate algorithms for evaluation of the exchange repulsion energy have been tested 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     

Theoretical study of intermolecular potential energy surface for HCl dimer: Example of nonspherical atom–atom exchange repulsion interaction

The intermolecular part of the potential energy surface for the HCl dimer has been studied with ab initio quantum chemical methods. An intermolecular potential, based on quantum chemical calculations has been constructed. The interaction energy consists of electrostatic, induction, and dispersion terms calculated from the monomer properties of the interacting molecules and an exchange repulsion term. The latter term was parameterized from the results of the quantum chemical calculations and estimates of the electrostatic and induction energies. It was found necessary to use nonspherical atom–atom exchange repulsion interaction parameters, and the parameters describing the deviation from spherical behavior could be obtained from the expectation values of r² for the electrons assigned to an atom. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1816–1825, 1998     

SCF perturbation theory and intermolecular interactions

A self-consistent perturbation theory is derived in the framework of Roothaan's MOLCAO procedure for closed shell systems. Contrary to previous investigations which have considered only one particle perturbations, two particle perturbation operators are considered. Expressions for the first-order density matrix and first- and second-order energy corrections are obtained. A diagram formulation of the complete perturbation expansion is presented. The results are applied to the treatment of the intermolecular interaction problem. The interaction energy is represented as a sum of several contributions: Coulomb, exchange, resonance, polarization and exchange repulsion. A semi-empirical version of the theory is suggested which explicitly involves all the physically significant energy terms and may be useful for the investigation of complex systems.     

Analysis of nonadditivity effects and estimation of many-body effects in linear water chains

Calculations have been carried out on small linear water chains in order to investigate nonadditivity and cooperativity effects and to study the rate of convergence of the many-body interaction potential. Ab initio wave functions were computed for the pentamer and all related subgroups by using the self-consistent, nonorthogonal group function approximation. The interaction energy and its electrostatic, exchange, polarization, and charge-transfer components were decomposed into a sum of n-body terms. Simple formulas were developed for estimating the interaction energy of higher-order complexes, which also allow an extrapolation to be made to infinite chain length. Comparison of the extrapolated interaction energies, with and without including the nonadditivity effects, showed that the latter increases the H-bond's stability by more than 25%. The results further suggest that the interaction potential can be truncated at either the three- or four-body level, depending on the accuracy required, but that, at best, only rough qualitative results can be expected when pair additivity is assumed. Finally, the dipole moment appears to be sufficiently converged with the inclusion of trimeric terms.     

The nature of interactions in the ionic crystal of 3-pentenenitrile, 2-nitro-5-oxo, ion(-1), sodium

The hybrid variation -- perturbation many-body interaction energy decomposition scheme has been applied to analyze the physical nature of interactions in the ionic 3-pentenenitrile, 2-nitro-5-oxo, ion(-1), sodium crystal, which can be regarded as a model for a large group of aromatic quaternary nitrogen salts. In the crystal structure the sodium ions and water molecules of adjacent unit cells form a positively charged "inorganic layer" with the sodium ions clustered together along the ab faces with the organic (negative) part in between. This puzzling crystal packing is due to a strong favorable interaction between the water molecule and the sodium ions and a substantial charge transfer from the carbanions that balances out the destabilizing sodium-sodium ion repulsion. Although the majority of cohesion energy of the crystal structure comes from the electrostatic interactions of ions, the resulting net stabilization also depends heavily on the nonadditive delocalization components, due to a counterbalance between the two-body delocalization and exchange effects. The estimated nonadditivity of interactions varies between 12% and 22%.     

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.     

Many-body exchange-repulsion in polarizable molecular mechanics. I. Orbital-based approximations and applications to hydrated metal cation complexes

We have quantified the extent of the nonadditivity of the short-range exchange-repulsion energy, E(exch-rep), in several polycoordinated complexes of alkali, alkaline-earth, transition, and metal cations. This was done by performing ab initio energy decomposition analyses of interaction energies in these complexes. The magnitude of E(exch-rep(n-body, n > 2)) was found to be strongly cation-dependent, ranging from close to zero for some alkali metal complexes to about 6 kcal/mol for the hexahydrated Zn(2+) complex. In all cases, the cation-water molecules, E(exch-rep(three-body)), has been found to be the dominant contribution to many-body exchange-repulsion effects, higher order terms being negligible. As the physical basis of this effect is discussed, a three-center exponential term was introduced in the SIBFA (Sum of Interactions Between Fragments Ab initio computed) polarizable molecular mechanics procedure to model such effects. The three-body correction is added to the two-center (two-body) overlap-like formulation of the short-range repulsion contribution, E(rep), which is grounded on simplified integrals obtained from localized molecular orbital theory. The present term is computed on using mostly precomputed two-body terms and, therefore, does not increase significantly the computational cost of the method. It was shown to match closely E(three-body) in a series of test cases bearing on the complexes of Ca(2+), Zn(2+), and Hg(2+). For example, its introduction enabled to restore the correct tetrahedral versus square planar preference found from quantum chemistry calculations on the tetrahydrate of Hg(2+) and [Hg(H(2)O)(4)](2+).     

Intermolecular interaction energy of CH4 trimer by symmetry-adapted perturbation theory

The interaction energy for the cyclic CH₄ trimer is studied in terms of symmetry-adapted perturbation theory. The interaction energy around the van der Waals minimum is dominated by attractive dispersion energy, and the repulsive contribution at the smaller angle region is due to the first-order exchange energy. The total interaction energy is approximated by additive two-body components, because of a mutual cancellation between nonadditive three-body ones.     

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.     

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     

Molecular mechanics on bonding and non-bonding interactions in (atom@C60)

The interactions between the embedded atom X (X = Li, Na, K, Rb, Cs; F, Cl, Br, I) andC60 cage in the endohedral-form complexes (X@C₆₀) are calculated and discussed according to molecular mechanics from the point of view of the bonding and non-bonding. It is found from the computational results that for atoms with radii larger than Li’s, their locations with the minimum interaction in (X@C₆₀) are at the cage center, while atom Li has an off-center location with the minimum interaction deviation of ~0.05 nm, and the cage-environment in C₆₀ can be regarded as syhero-symmetry in the region with radiusr of ~0.2 nm. It is shown that the interaction between X and C₆₀ cage is of non-bonding characteristic, and this non-bonding interaction is not purely electrostatic. The repulsion and dispersion in non-bonding interactions should not be neglected, which make important contribution to the location with minimum interaction of X, at center or off center. Some rules about the variations of interactions with atomic radii have been obtained. Project supportt:d by the National Natural Science Foundation of China.     

Calculation of 13C shielding of the isotopomers CH3Cl,CH2DCl,CHD2Cl,and CD3Cl

The ¹³C shielding of the isotopomers CH₃Cl, CH₂ DCl, CHD₂Cl, and CD₃Cl has been calculated for a range of temperatures from an self-consistent field (SCF) shielding surface computed by Buckingham and Olegario. It is found that each successive deuterium substitution increases the shielding by about 0.19 ppm and that a very slight nonadditivity occurs. The principal factor which governs the nuclear motion correction for each isotopomer is the stretching of the bonds with both first- and second-order terms being significant. Angle bending contributions are very small at first order but quite substantial at second order. Not only should the ¹³C-isotope shifts in this experimentally uninvestigated series be easily measured but the temperature dependence of the shielding in any one isotopomer should be observable provided that careful measurements are made. The ¹³C-shielding difference between CH₃ ³⁵Cl and CH₃ ³⁷Cl has also been calculated and is found to agree well with experiment. © 1996 John Wiley & Sons, Inc.     

On exchange-repulsion non-additivity in the interaction of three argon atoms

The non-additive contribution to the exchange repulsion for the argon trimer in the equilateral-triangle configuration has been calculated in the first order of symmetry-adapted perturbation theory. Approximation of the non-additivity by the interaction of outer-shell electron is as efficient as for Ne₃. The role of higher-order contributions to the non-additivity is discussed.     

Nature and importance of three-body interactions in the (H2O)2HCl trimer

 The nature and importance of nonadditive three-body interactions in the (H₂O)₂HCl cluster have been studied by the supermolecule coupled-cluster method and by symmetry-adapted perturbation theory (SAPT). The convergence of the SAPT expansion was tested by comparison with the results obtained from the supermolecule coupled-cluster calculations including single, double, and noniterative triple excitations [CCSD(T)]. It is shown that the SAPT results reproduce the converged CCSD(T) results within 3% at worst. The SAPT method has been used to analyze the three-body interactions for various geometries of the (H₂O)₂HCl cluster. It is shown that the induction nonadditivity is dominant, but it is partly quenched by the first-order Heitler–London-type exchange and higher-order exchange–induction/deformation terms. This implies that the classical induction term alone is not a reliable approximation to the nonadditive energy and that it will be difficult to approximate the three-body potential for (H₂O)₂HCl by a simple analytical expression. The three-body energy represents as much as 21–27% of the pair CCSD(T) intermolecular energy. Received: 15 September 1999 / Accepted: 3 February 2000 / Published online: 2 May 2000     

Nonadditivity and the stability of Ag3. A multireference configuration interaction study

Variational (?30 000 determinants) and perturbational (?3.5 million determinants) Localized Multireference Configuration Interaction (LMRCI) calculations includingf polarization functions are made to study the role played by the three-body terms in the stabilization energy of three selected geometries of the silver trimer: linear, equilateral and a Jahn-Teller obtuse triangle conformation. A comparative analysis of the relative stability of these geometries is done through a many-body decomposition of the interaction energy. Like in Cu₃, the most symmetrical arrangement (i.e. an equilateral triangle) is found to be less stable than the obtuse triangle because it has the highest three-body repulsion energy. The absolute minimum is the obtuse triangle having a Jahn-Teller stabilization energy of 328 cm^?1. Unlike Cu₃, the linear geometry is found to be less stable than the equilateral by 1282cm^?1. Results show again the importance of three-body terms in the total interaction energy of these trimers.     

Recognition Polymers

From the universe of polymeric materials which appear in biology and medicine we select for discussion that set whose principal function is to recognize and respond appropriately to specific substances in their environment. They may be 1.2, 2.2, or 3 dimensional shapes such as messenger RNA, cellulose acetate membranes, or artificial esophagi. They may function by recognizing the difference between right and wrong chemical species and responding by binding the correct ones and rejecting the wrong ones, e.g., enzymes and their substrates, codons and their anticodons. What happens after recognition and response is not of interest at the moment, e.g., the catalytic effect of the enzyme on the bound substrate or the codonanticodon binding effect on protein synthesis.

Another example is in the chemical senses where there is sketchy evidence that proteins are involved in recognizing tastants. This could be done by having a protein on the tongue bind all tastants (rather close contact is required to make fine distinctions) and then recognize them by very intimate contacts and sending signals to the brain for conscious recognition. Alternatively, each taste modality may have a protein that excludes all but one type and generates only one signal for the CNS.

Another important class are antibodies that recognize their own antigens out of about 10⁴ different ones and complex with them and exclude the others. A model for antigen-antibody interaction must account for the non-binding of nonantigens as well as the much simpler case of the binding of the antigen.

Another class are the permselective membranes that recognize some species and let them pass while recognizing others and not let them pass. A final class to be discussed will be implant polymers which have an un-desired ability to recognize and bind platelets.

The question we are asking is whether it is possible to establish general principles in chemical physics that govern these different types of molecular recognition so that the principles could be incorporated into polymer design. Recent advances in “intermolecular” force theory suggests that this goal is achievable in the foreseeable future. Intermolecular has been put in quotes because when two molecules are in sufficiently close contact to recognize one another they probably have an appreciable exchange term and are therefore not two molecules but one.

The recent advances referred to involve computer simulation of complex formation using the new 1-4-6-12 potential forms corresponding to a long range (R^?1) coulombic electrostatic interaction, a medium range (R^?4) electrostatic-induced dipole attraction, a short range (R^?6) dispersive attraction, and a very short range (R^?12) orbital overlap repulsion. In the cases of interest, e.g., in an aqueous environment, all four terms are important and statements such as “the binding is purely electrostatic,” i.e., all R^?1, are misleading as well as wrong (since even ions need the R^?12 repulsion to keep them at their equilibrium distance). Discussions of permeability in terms of “pore sizes” is equally limiting for it implies that only the R^?12repulsion is appreciable. The fallacy of using competitive equilibria to determine the relative contributions of terms will be discussed. The im: portant use in biology of “other contacts” within the system to give a variable base line so that the typical binding-no binding discrimination can be made with attraction-less attraction rather than the more awkward attraction-repulsion potentials will also be discussed.     

Halogen bonded complexes between volatile anaesthetics (chloroform, halothane, enflurane, isoflurane) and formaldehyde: a theoretical study

The structures and intermolecular interactions in the halogen bonded complexes of anaesthetics (chloroform, halothane, enflurane and isoflurane) with formaldehyde were studied by ab initio MP2 and CCSD(T) methods. The CCSD(T)/CBS calculated binding energies of these complexes are between -2.83 and -4.21 kcal mol(-1). The largest stabilization energy has been found for the C-Br···O bonded halothane···OCH(2) complex. In all complexes the C-X bond length (where X = Cl, Br) is slightly shortened, in comparison to a free compound, and an increase of the C-X stretching frequency is observed. The electrostatic interaction was excluded as being responsible for the C-X bond contraction. It is suggested that contraction of the C-X bond length can be explained in terms of the Pauli repulsion (the exchange overlap) between the electron pairs of oxygen and halogen atoms in the investigated complexes. This is supported by the DFT-SAPT results, which indicate that the repulsive exchange energy overcompensates the electrostatic one. Moreover, the dispersion and electrostatic contributions cover about 95% of the total attraction forces, in these complexes.     

Calculation of high pressure vapour—liquid equilibria for systems containing polar substances with the use of an augmented van der Waals equation of state

An augmented van der Waals equation of state based on a perturbation theory has been applied to the calculation of high pressure vapour—liquid equilibria for systems containing polar substances. The equation of state comprises four terms, which imply the contributions from repulsion, symmetric, non-polar asymmetric, and polar asymmetric interactions. The characteristic parameters of each pure substance have been determined by three methods with the use of vapour pressures and saturated liquid densities. Mixing models for the terms of the repulsion, symmetric, and non-polar asymmetric interactions are the same as used previously. Two types of mixing models based on a three-fluid model and/or a one-fluid model are developed for the polar asymmetric term. The polar asymmetric term has a large effect on the prediction of the vapour—liquid equilibrium. With the introduction of a binary interaction parameter, the equation is found to be useful in correlating the vapour—liquid equilibria for a system containing a polar substance except near a critical region.     

Rate Coefficient for Self-Association Reaction of CF2 Radicals Determined in the Afterglowof Low-Pressure C4F8 Plasmas

We have analyzed decay kinetics of CF₂ radicals in the afterglow of low-pressure, high-density C₄F₈ plasmas. The decay curve of CF₂ density has been approximated by the combination of first- and second-order kinetics. The surface loss probability evaluated from the frequency of the first-order decay process has been on the order of 10^–4. This small surface loss probability has enabled us to observe the second-order decay process. The mechanism of the second-order decay is self-association reaction between CF₂ radicals (CF₂+CF₂C₂F₄). The rate coefficient for this reaction has been evaluated as (2.6–5.3)×10^–14 cm³/s under gas pressures of 2 to 100 mTorr. The rate coefficient was found to be almost independent of the gas pressure and has been in close agreement with known values, which are determined in high gas pressures above 1 Torr.