Nonadditive Energy Research Articles

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.

NONADDITIVE EFFECTS IN H2 AND HF TETRAMERS

Nonadditive three- and four-body interaction energies have been calculated for HF tetramer at the MP2/aug-cc-pVTZ level and for H 2 tetramer at the MP4(SDTQ)/aug-cc-pVTZ level using the so-called fifteen-point method. Calculated results show that with intermolecular distances decreasing from 3.0 to 1.7 Å the nonadditive three- and four-body interactions may be: (a) more and more attractive; (b) more and more repulsive; or (c) extremely weak. Strangely the minimum point of nonadditive three- and four-body interaction potentials has not been found up to now. For both H 2 and HF tetramers the nonadditive four-body interaction energy makes a negligible contribution to total binding energy when intermolecular distances are compressed from 3.0 to 1.7 Å.

Altering the RNA-binding Mode of the U1A RBD1 Protein

The N-terminal RNA-binding domain (RBD1) of the human U1A protein is evolutionarily designed to bind its RNA targets with great affinity and specificity. The physical mechanisms that modulate the coupling (local cooperativity) among amino acid residues on the extensive binding surface of RBD1 are investigated here, using mutants that replace a highly conserved glycine residue. This glycine residue, at the strand/loop junction of β3/loop3, is found in U1A RBD1, and in most RBD domains, suggesting it has a specific role in modulation of RNA binding. Here, two RBD1 proteins are constructed in which that residue (Gly53) is replaced by either alanine or valine. These new proteins are shown by NMR methods and molecular dynamics simulations to be very similar to the wild-type RBD1, both in structure and in their backbone dynamics. However, RNA-binding assays show that affinity for the U1 snRNA stem-loop II RNA target is reduced by nearly 200-fold for the RBD1-G53A protein, and by 1.6×10 4-fold for RBD1-G53V. The mode of RNA binding by RBD1-G53A is similar to that of RBD1-WT, displaying its characteristic non-additive free energies of base recognition and its salt-dependence. The binding mode of RBD1-G53V is altered, having lost its salt-dependence and displaying site-independence of base recognition. The molecular basis for this alteration in RNA-binding properties is proposed to result from the inability of the RNA to induce a change in the structure of the free protein to produce a high-affinity complex.

Aspects of the kinetic energy non-additivity in molecular and model subsystems

Several manifestations of the kinetic energy non-additivity are examined and illustrated using model systems. The three different aspects discussed include the density partitioning non-additivity (pn), the subsystem density overlap non-additivity (on), and the so-called particle confinement non-additivity (cn). The possibilities of the marginal decomposition of the many-electron probability distribution are explored in the context of the subsystem resolved theory. The ‘stockholder’ analysis of Hirshfeld is shown to represent a particular, local case of such a decomposition. The two-orbital model of the overlap non-additivity, using the orthogonal orbitals reproducing the subsystem (overlapping) densities, gives explicit functionals for the additive (Weizsäcker-type) and non-additive parts of the kinetic energy. The confinement non-additivity is illustrated using simple non-interacting electron models, including the particle-in-the-box, hydrogen-like atom and the harmonic oscillator. It is shown that in the first case the cn-energy favours the division of electrons among asymmetric sub-boxes, while in the two remaining models the non-additive energy favours placing electrons in equal sub-spaces. The implications for the most efficient matching of the atomic orbitals and the reactant hardnesses are discussed.

Ab initio three-body interactions for water. I. Potential and structure of water trimer

A new ab initio three-body potential for water has been generated from the Hartree–Fock method and symmetry-adapted perturbation theory calculations performed at 7533 trimer geometries. The calculated nonadditive energies were then fitted to a physically motivated analytic formula containing representations of short-range exchange contributions and damped induction terms. To our knowledge, this is the first time the short-range nonadditive interactions have been explicitly included in a potential for water. The fitted nonadditive potential was then applied, together with an accurate ab initio pair potential, SAPT-5s, to evaluate the effects of nonadditivity on the structure and energetics of water trimer.

Extensive form of equilibrium nonextensive statistics

It is argued that, in nonextensive statistical mechanics with Tsallis entropy, the factorization of compound probability over subsystems is a consequence of the existence of thermodynamic equilibrium in the composite system and should be respected by all exact calculations concerning equilibrium subsystems. Using nonadditive energy satisfying this factorization, we propose an additive formalism of nonextensive statistical mechanics with additive q-deformed physical quantities and exponential distributions. This formalism leads to exact quantum gas distributions different from those given by factorization approximation with additive energy. The fermion distribution of the present work shows similar characteristics to the distribution of strongly correlated electrons given by numerical analysis with the Kondo t-J model.

Quantum dynamics of ultracold Na+ Na2 collisions.

Ultracold collisions between spin-polarized Na atoms and vibrationally excited Na2 molecules are investigated theoretically, using a reactive scattering formalism (including atom exchange). Calculations are carried out on both pairwise additive and nonadditive potential energy surfaces for the quartet electronic state. The Wigner threshold laws are followed for energies below 10(-5) K. Vibrational relaxation processes dominate elastic processes for temperatures below 10(-3)-10(-4) K. For temperatures below 10(-5) K, the rate coefficients for vibrational relaxation (v=1-->0) are 4.8x10(-11) and 5.2x10(-10) cm(3) s(-1) for the additive and nonadditive potentials, respectively. The large difference emphasizes the importance of using accurate potential energy surfaces for such calculations.

NMR Structures of Two Variants of Bovine Pancreatic Trypsin Inhibitor (BPTI) Reveal Unexpected Influence of Mutations on Protein Structure and Stability

Here we determined NMR solution structures of two mutants of bovine pancreatic trypsin inhibitor (BPTI) to reveal structural reasons of their decreased thermodynamic stability. A point mutation, A16V, in the solvent-exposed loop destabilizes the protein by 20 °C, in contrast to marginal destabilization observed for G, S, R, L or W mutants. In the second mutant introduction of eight alanine residues at proteinase-contacting sites (residues 11, 13, 17, 18, 19, 34, 37 and 39) provides a protein that denatures at a temperature about 30 °C higher than expected from additive behavior of individual mutations. In order to efficiently determine structures of these variants, we applied a procedure that allows us to share data between regions unaffected by mutation(s). NOAH/DYANA and CNS programs were used for a rapid assignment of NOESY cross-peaks, structure calculations and refinement. The solution structure of the A16V mutant reveals no conformational change within the molecule, but shows close contacts between V16, I18 and G36/G37. Thus, the observed 4.3 kcal/mol decrease of stability results from a strained local conformation of these residues caused by introduction of a β-branched Val side-chain. Contrary to the A16V mutation, introduction of eight alanine residues produces significant conformational changes, manifested in over a 9 Å shift of the Y35 side-chain. This structural rearrangement provides about 6 kcal/mol non-additive stabilization energy, compared to the mutant in which G37 and R39 are not mutated to alanine residues.

Intermolecular interaction energies from the total energy bifunctional: A case study of carbazole complexes

An approach in which the total energy of interacting subsystems is expressed as a bifunctional depending explicitly on two functions: electron densities of the two molecules forming a complex (ρ1 and ρ2) was used to determine the equilibrium geometry and the binding energy of several weak intermolecular complexes involving carbazole and such atoms or molecules as Ne, Ar, CH4, CO, and N2. For these complexes, the experimental dissociation energies fall within the range from 0.48 to 2.06 kcal/mol. Since the effect of the intermolecular vibrations on the dissociation energy is rather small, the experimental measurements provide an excellent reference set. The obtained interaction energies are in a good agreement with experiment and are superior to the ones derived from conventional Kohn–Sham calculations. A detailed analysis of relative contribution of the terms which are expressed using approximate functionals (i.e., exchange-correlation Exc[ρ1+ρ2] and nonadditive kinetic energy Tsnad[ρ1,ρ2]=Ts[ρ1+ρ2]−Ts[ρ1]−Ts[ρ2]) is made. The nonvariational version of the applied formalism is also discussed.

Coupled-cluster calculation of dispersion contributions to interaction energies and polarizabilities

The induced dipole dispersion-type contributions to the two-body and nonadditive three-body energies and electric dipole polarizabilities are studied for long-range interactions involving the He, Ne, Ar and Kr atoms and the H2 and N2 molecules. The coupled-cluster singles and doubles model and large basis sets are used. Comparison of the energy contributions with data derived from experiment shows in most cases the deviations to be less than 1%; therefore, it may be expected that the calculated polarizability increments are accurately determined and can be used to estimate the accuracy of approximate methods.

Potential lattice dynamical simulations of ice

Lattice dynamical calculations have been carried out for ice Ih, ice XI, ice II and ice VIII using seven rigid pair-wise potentials and a M-point polarizable potential that is a modification of the potential constructed by Dang and Chang [J. Chem. Phys. 106 (1997) 8149]. It was found that the M-point polarizable potential gives out a wide range of hydrogen bonds and a narrow librational band. MCY makes stretching and bending interactions too weak and it gives O–O bond lengths too long (∼5%) so its lattice densities are obviously lower than other potential lattices or experimental values. Other classic potentials (BF, SPC, Rowlinson, TIP3P, TIP4P and TIPS2) produce reasonable results and slightly short O–O bond lengths. The mean two-body interaction energy of M-point polarizable potential is −0.370 eV/molecule and the mean polarizable energy is −0.180 eV/molecule. Nonadditive energy takes about 32.7% of total ice Ih lattice energy, which is less than Molecular Dynamical result 39% for liquid.

Nature and importance of three-body interactions in the (H 2 O) 2 HCl 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.

Dark magnetism revisited

Bacry [Phys. Lett. B 317 (1993) 523] showed that, on the basis of the deformed Poincaré group, special relativity yields a non-additive 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 non-interacting spins in the presence of an external magnetic field, it was shown in Portesi et al. [Phys. Rev. E 52 (1995) R3317] that Tsallis’ non-extensive thermostatistics could account for a possible “dark” magnetism (the apparent number of particles being different from the actual one). The work of Pennini et al. [Physica A 258 (1998) 446]; Tsallis et al. [Physica A 261 (1998) 534] uses the so-called “generalized” expectation values, that were for some time considered indispensable in dealing with Tsallis’ formalism. Lately, a different sort of expectation values has been regarded as being superior to the old generalized ones [Pennini et al., Physica A 258 (1998) 446; Tsallis et al., Physica A 261 (1998) 534]. We revisit the dark magnetism question in the light of this new way of computing mean values.

Changes in sidechain and backbone dynamics identify determinants of specificity in RNA recognition by human U1A protein

The N-terminal RNA-binding domain (RBD1) of the human U1A protein is evolutionarily designed to bind its RNA targets with great affinity and specificity. The physical mechanisms that modulate the coupling (local cooperativity) among amino acid residues on the extensive binding surface of RBD1 are investigated here, using mutants that replace a highly conserved glycine residue. This glycine residue, at the strand/loop junction of β3/loop3, is found in U1A RBD1, and in most RBD domains, suggesting it has a specific role in modulation of RNA binding. Here, two RBD1 proteins are constructed in which that residue (Gly53) is replaced by either alanine or valine. These new proteins are shown by NMR methods and molecular dynamics simulations to be very similar to the wild-type RBD1, both in structure and in their backbone dynamics. However, RNA-binding assays show that affinity for the U1 snRNA stem-loop II RNA target is reduced by nearly 200-fold for the RBD1-G53A protein, and by 1.6×104-fold for RBD1-G53V. The mode of RNA binding by RBD1-G53A is similar to that of RBD1-WT, displaying its characteristic non-additive free energies of base recognition and its salt-dependence. The binding mode of RBD1-G53V is altered, having lost its salt-dependence and displaying site-independence of base recognition. The molecular basis for this alteration in RNA-binding properties is proposed to result from the inability of the RNA to induce a change in the structure of the free protein to produce a high-affinity complex.

Orthonormal orbitals from the overlapping densities of subsystems

The semi-orthogonal and fully orthogonal orbitals for overlapping subsystems A and B are constructed using the Harriman construction and its modification, assuring the inter-subsystem orthogonality. The orbital sets for subsystems include: the internally (intra-subsystem) and externally (inter-subsystem) semi-orthogonal equidensity orbitals, constructed via the equal partitioning of the subsystem densities ρA and ρB into orbital densities, and the fully (internally and externally) orthogonal orbitals conserving the subsystem densities. The two sets of the equidensity orbitals of AB as a whole, obtained via the equal division of the overall, ρ=ρA+ρB, and overlap, nAB=(ρAρB)1/2, densities are also discussed. The constrained search construction involving the orbitals conserving the subsystem densities is used to define the density functional for the nonadditive kinetic energy of the Kohn–Sham theory for subsystems.

Integral constraint on the density functional for nonadditive kinetic energy in Kohn-Sham theory for subsystems

Integral constraint on the density functional for nonadditive kinetic energy in Kohn-Sham theory for subsystems

On the non-additive second-order Coulomb energy for H3 in C2v geometries

For three identical spherical atoms in their ground electronic states, it is shown that a knowledge of the partial wave components of the additive non-expanded second-order induction energy allows the non-additive non-expanded second-order Coulomb energy to be calculated for certain interatomic geometries. The results of new partial wave calculations of the non-expanded second-order Coulomb energy are presented for H2 and H3, and are used to discuss the rate of convergence of the appropriate partial wave series. Comparison is made with relevant literature results.

On the non-additive second-order Coulomb energy for H3 in C2v geometries

For three identical spherical atoms in their ground electronic states, it is shown that a knowledge of the partial wave components of the additive non-expanded second-order induction energy allows the non-additive non-expanded second-order Coulomb energy to be calculated for certain interatomic geometries. The results of new partial wave calculations of the non-expanded second-order Coulomb energy are presented for H2 and H3, and are used to discuss the rate of convergence of the appropriate partial wave series. Comparison is made with relevant literature results.

Nonadditive Interactions in Trimers Containing H2, N2, and O2

A study comparing the magnitudes of the second-order nonadditive induction energy and the nonadditive triple-dipole dispersion energy for interactions in trimers containing the linear homonuclear molecules H2, N2, and O2 has been undertaken. The configurations are a linear, symmetric and an equilateral triangle arrangement of the trimers: H2−H2−H2, N2−N2−N2, O2−O2−O2, N2−N2−O2, and O2−N2−H2. The observed trends are discussed.

Anisotropy of non-additive energies for interactions in some trimers containing homonuclear molecules

The second-order non-additive induction energy for interactions in trimers containing the linear homonuclear molecules H2, N2 and O2 has been computed for two different configurations via expressions recently derived using the MAPLE symbolic computational language. The configurations are a linear, symmetric and an equilateral triangle arrangement of the trimers: H2–H2–H2, N2–N2–N2, O2–O2–O2, N2–N2–O2, N2–H2–O2 and O2–N2–H2. The induction energies are compared with the corresponding triple-dipole dispersion energies for the two different configurations. The significance of these results is also discussed.