Nonadditive Energy Research Articles

On the triple-dipole dispersion energy for non-spherical molecules with an application to the O 2O 2O 2 interaction

The symbolic computation language MAPLE is used to verify an exact expression for the tripple-dipole dispersion energy (DDD), derived previously, for interactions involving up to three linear (∑-state) molecules. The derivation of the original expression, which is complicated, was carried out manually and involved many tedious algebraic steps. Recent results for the anisotropic triple-dipole dispersion energy coefficients for the O 2O 2O 2 interaction, together with the exact expression for the DDD itself, are used to illustrate the importance of the anisotropic dispersion energy, relative to the isotropic triple-dipole energy, and to help investigate the validity of a frequently used average energy approximation for the anisotropic DDD. The discussion includes comments concerning the importance of the DDD energy in the context of the contribution of non-additive energies to the properties of matter.

Ab Initio Study of 4(5)-Methylimidazole in Aqueous Solution

The properties of the two tautomers of 4(5)-methylimidazole in aqueous solution have been studied through theoretical calculations using ab initio methods and various solvent models. We focus this study on the environmental effects due to cooperative solute−solvent interactions. The modifications of the tautomeric equilibrium and pKa value through hydrogen-bond formation and electrostatic solvation effects are discussed. The computations show that the polarizable continuum model of the solvent is able to give reasonable results for these properties. The prediction of absolute values of pKa is difficult, but relative values are reproduced quite well. We also consider a discrete-continuum model for the solution, but we show that this model leads to slightly stable (or unstable) complexes. Our results stress the importance of nonadditive energy contributions, which are presumably fundamental in order to explain the mechanism of several biological processes involving histidine residues.

Density functional theory with approximate kinetic energy functionals applied to hydrogen bonds

Applicability of the approximate kinetic energy functionals to study hydrogen-bonded systems by means of the formalism of Kohn–Sham equations with constrained electron density (KSCED) [Cortona, Phys. Rev. B 44, 8454 (1991); Wesołowski and Warshel, J. Phys. Chem. 97, 8050 (1993); Wesołowski and Weber, Chem. Phys. Lett. 248, 71 (1996)] is analyzed. In the KSCED formalism, the ground-state energy of a molecular complex is obtained using a “divide-and-conquer” strategy, which is applied to the Kohn–Sham-like equations to obtain the electron density of a fragment embedded in a larger system. The approximate kinetic energy functional enters into the KSCED formalism in two ways. First, the effective potential in which the electrons of each fragment move contains a component which is expressed by means of a functional derivative of an approximate kinetic energy functional (functional derivative of the non-additive kinetic energy). Second, the KSCED energy functional contains a component (non-additive kinetic energy) which is expressed using the approximate kinetic energy functional. In this work, the KSCED energies and densities of (H2O)2, (HF)2, (HCl)2, and HFṡṡṡNCH are compared to the ones obtained using the standard supermolecule Kohn–Sham approach. The following factors determining the agreement between the KSCED and supermolecule Kohn–Sham results are analyzed: the analytical form of the gradient-dependent terms in the approximate kinetic energy functional and the number of atom-centered orbitals used to expand electron density of fragments. The best agreement between the supermolecule Kohn–Sham and the KSCED results is obtained with the kinetic energy functional derived following the route of Lee, Lee, and Parr [Lee et al., Phys. Rev. A 44, 768 (1991)] from the exchange functional of Perdew and Wang [Perdew and Wang, in Electronic Structure of Solids ’91, edited by P. E. Ziesche and H. Eschrig (Academie Verlag, Berlin, 1991), p. 11]. The difference between the KSCED and the supermolecule Kohn–Sham energies of studied complexes amounts to less than 0.35 kcal/mol at the equilibrium geometry.

Non-additive intermolecular forces from the spectroscopy of Van der Waals trimers: A comparison of Ar2–HF and Ar2–HCl, including H/D isotope effects

Variational calculations of vibrational energies, rotational constants and angular expectation values are carried out for the trimers Ar2–HCl, Ar2–DCl, Ar2–HF and Ar2–DF. Calculations are performed on pairwise additive potential energy surfaces and on surfaces including a variety of non-additive contributions. Attention is focused on the bending levels corresponding to hindered internal rotation of the HX molecule in the complex, several of which have been observed by high-resolution spectroscopy. The results confirm that it is crucial to include dispersion, induction and short-range effects when modelling the non-additive forces in molecular systems. It is found that the model of non-additive forces previously proposed by Ernesti and Hutson [Phys. Rev. A 51, 239 (1995)] works well for the bending bands of Ar2–HCl, Ar2–DCl and Ar2–DF as well as Ar2–HF. In addition, a new distributed model of the non-additive dispersion energy is proposed, in which the triple-dipole energy is partitioned between two anisotropic sites in the HX molecule.

Ab initio calculation of three-body interaction in the (H2)3 trimer

The non-additivity in the (H2)3 trimer is calculated at different geometries using an extended geminal model. The isotropic part of the three-body non-additive potential energy is derived. It is shown that the three-body potential is converging relatively rapidly with respect to the size of the basis set. With a 6s,3p,2d basis, near the equilibrium geometry, the global error of the three-body potential is estimated to be of only 7%. At large distances the results are in accordance with the Axilrod-Teller-Muto triple-dipole approximation.

Nonadditive interactions in the H2 trimer

Explicit equations for the second order nonadditive induction energy for interactions involving three linear molecules have been derived using the MAPLE symbolic computational language. This nonadditive induction energy (involving the permanent quadrupole moments and dipole polarizabilities) is compared with the triple-dipole dispersion energy for a system consisting of three hydrogen molecules, in two different configurations. It is found that for most of the orientations studied the nonadditive induction energy is comparable in magnitude or larger than the triple-dipole dispersion energy.

Embedded density functional approach for calculations of adsorption on ionic crystals

We present an embedded density functional approach to study adsorption on crystalline surfaces. Following ideas suggested by Cortona, Wesolowski, and Warshel, we divide the total system into a quantum cluster and the surrounding lattice whose density is assumed to be the same as in the ideal crystal. In this case the Kohn–Sham Hamiltonian for electrons in the cluster contains additional terms corresponding to the Coulomb, exchange, correlation, and ‘‘nonadditive kinetic energy’’ potentials from the environment. Test calculations for the He and Ar dimers, X–H2O molecular complexes (X=Li+, Na+, K+, F− or Cl−) and water adsorption on the (001) surface of the NaCl crystal suggest that this model provides a promising alternative for cluster models employed earlier for calculations of defects and adsorption on ionic crystals.

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...

Kohn-Sham equations with constrained electron density: an iterative evaluation of the ground-state electron density of interacting molecules

A new method for calculating the ground state electron density of interacting molecules is presented. The supermolecule electron density is obtained using an iterative procedure. At each step the electron density of one molecule is calculated using previously introduced Kohn-Sham equations with constrained electron density. These equations contain terms representing the coupling between constrained and non-constrained electron densities. The coupling terms also involve a new functional, namely the non-additive kinetic energy functional that is not present in the original Kohn-Sham method. Its first-principles analytical form in not yet known. We examine the analytical form of this functional derived from Thomas-Fermi theory. The electron density obtained is compared with that calculated using the original Kohn-Sham method applied to the supermolecule. Good agreement has been found for a broad range of electron density overlaps.

Nonextensive thermostatistics can yield apparent magnetism.

Bacry [Phys. Lett. B 317, 523 (1993)] showed that, on the basis of a deformed Poincar\'e group, special relativity yields a nonadditive energy for large systems, i.e., a total energy (of the Universe) which would not be proportional to the number of particles. He consistently argued that this effect could explain (part of) the so-called dark matter. By considering noninteracting spins at thermal equilibrium in the presence of an external magnetic field, we show here that the recently introduced nonextensive (nonadditive) thermostatistics could account for a theoretically possible ``dark magnetism'' (the apparent number of spins being smaller or larger than the actual one).

Solvation Free Energies of Amides and Amines: Disagreement between Free Energy Calculations and Experiment

We present molecular dynamidfree energy calculations on the molecules acetamide, N-methylacetamide, N,N-dimethylacetamide, ammonia, methylamine, dimethylamine, and trimethylamine. Unlike the experimental data, which suggest a very non-additive solvation free energy (N-methylacetamide and methylamine having the most negative free energy of solvation), the calculations all find that the free energy of solvation monotonically increases as a function of methyl addition. The disagreement with experiment is surprising, given the very good agreement (within 0.5 kcaYmo1) with experiment for calculation of the solvation free energy of methane, ethane, propane, water, methanol, and dimethyl ether.

The non-additive exchange energies of H3and He3

Non-additive SCF energies are calculated for H3 (quartet spin state) and He3 using Hartree-Fock quality basis sets containing only s functions. The results are analysed using a modification of an effective Gaussian model, replacing the explicit dependence on Gaussians by related dimer and/or trimer properties. A good fit to the SCF results is obtained using a model based on dimer and trimer charge density overlap integrals, and two adjustable parameters.

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.

Sequence-dependent effects on DNA stability resulting from guanosine replacements by inosine.

The effect of replacing a G.C base-pair with an I.C base-pair on DNA stability was investigated for a related set of 14-mers. DNA melting analysis of the 14-mers was used to determine delta Hzero, delta Szero and delta G(zero)37 of the double to single stranded transition. All 14mers were shown to have B-DNA character by circular dichroism analysis. 14mers substituted with a single inosine in place of guanosine at different positions showed that consequences on DNA stability are sequence-dependent. Large changes in delta Hzero and delta Szero result when inosine is substituted within the trinucleotide sequence d(TCG).d(CGA) while substitution within d(TCC).d(GGA) causes minor changes in enthalpy and entropy. Moreover, some 14-mers with two inosine substitutions five base-pairs apart showed non-additive free energy changes for the double to single stranded transition. These results clearly indicate that the structural consequences of replacing a single guanosine with an inosine are transmitted over a significant distance.

Non-additivity in cation—peptide interactions. A molecular dynamics and ab initio study of Na + in the gramicidin channel

The importance of non-additive energy contributions in cation—peptide interactions is investigated, in the context of Na + binding to the gramicidin channel, using molecular dynamics simulations and ab initio calculations. SCF supermolecule calculations are performed for an ensemble of Na + and N-methylacetamide complexes constructed from configurations generated by a molecular dynamics trajectory of the full channel system to represent the gramicidin binding site. A main result is that the ab initio estimates of the excess many-body interactions due to the cation are very well correlated with second-order induction energy obtained from a simple approximation based on atomic polarizabilities.

The nonadditive intermolecular potential for water revised

The results of an improved version of a nonadditive intermolecular model for water that explicitly includes the nonadditive polarization energy are reported. The original polarizable water potential model (POL1), upon which the improved version is based, was developed by Caldwell, Dang, and Kollman [J. Am. Soc. Chem. 112, 9144 (1990)]. To improve the POL1 model, we developed a new set of atomic polarizabilities that reproduce the experimental molecular polarizability for water using the atom–dipole interaction model (Applequist, Carl, and Fung [J. Am. Soc. Chem. 94, 2952 (1972)]). Using the new atomic polarizabilities, we optimized the Lennard-Jones parameters for O–O interactions to improve the model. As expected, the new model has improved the radial distribution functions and the average potential energy for liquid water as well as the density and the average total dipole moment. The model is then used to compute the binding energies of Cs+–water clusters. Without the need for three-body forces (ion–water–water interaction), the agreement between the results of molecular-dynamics simulations and experimental energies of cluster formation is very good.

On the construction and use of reliable two- and many-body interatomic and intermolecular potentials

The Hartree-Fock dispersion (HFD), exchange-coulomb (XC) and Tang-Toennies (TT) potential models have been used with considerable success to represent two-body interactions. Various isotropic versions of these models are discussed and compared, with the help of an analytical expression for the damping functions associated with the individual multipolar dispersion energies in the first two models. A brief discussion is also given of the extensions of the potentials to interactions involving molecules, with an explicit example being provided for the N 2-N 2 interaction and the simplest of the XC potentials. The fundamental question of the representation of non-additive many-body interaction energies is a topic of considerable current interest. The effects occurring because of these three- and higher-body interactions become significant in the properties of dense gases, liquids, solids and surfaces. The non-additive contributions to these properties can be deduced by subtracting the additive part of the properties, calculated using reliable two-body potentials, from experimental results. At present such calculations can only be carried out meaningfully for rare gas systems, since it is only for these systems that the required input data are known with sufficient reliability. The second part of this paper discusses the problems associated with the representation and understanding of many-body interactions and also reviews the recent work along these lines.

Higher dispersion coefficients: Accurate values for hydrogen atoms and simple estimates for other systems

The dispersion coefficients Cn (n≤30) and Z(l,λ,L) (l+λ+L≤13) which appear in the multipole expansions of the pair and nonadditive three-body interaction energies, respectively, are calculated to an accuracy of no less than 15 decimal digits for interactions among ground state hydrogen atoms. The pseudostate technique used is as simple and accurate as the momentum-space method recently advocated for this problem. The oscillator and hydrogenic models are used to obtain simple formulas for the estimation of higher dispersion coefficients from two or three of the leading coefficients. These formulas should prove useful in models of intermolecular potentials.

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.