Theoretical studies of molecular conformation. Derivation of an additive procedure for the computation of intramolecular interaction energies. Comparison withab initio SCF computations

An additive procedure (SIBFA) is developed for the rapid computation of conformational energy variations in very large molecules. The macromolecule is built out of constitutive molecular fragments and the intramolecular energy is computed as a sum of interaction energies between the fragments. The electrostatic and the polarization components are calculated using multicenter multipole expansions of theab initio SCF electron density of the fragments. The repulsion component is obtained as a sum of bond and lone pair interactions.Tests of the procedure on a series of model compounds containing ether oxygens and pyridine-like nitrogens are reported and compared with the results of correspondingab initio SCF calculations. The resulting methodology is compatible with the simultaneous computation of intermolecular interactions.     

Theoretical study of the interaction of tetramethylammonium with double-stranded oligonucleotides

Computations are performed on the interaction specificities of tetramethylammonium (TMA) for double-stranded oligonucleotides held in the B conformation. The effects of base sequence and chain length are investigated. In the short oligomers (helices formed from dinucleoside monophosphates and trinucleoside diphosphates), the interaction energies of TMA are larger in the major groove of (dG)_n · (dC)_n than in the minor groove of either (dA)_n · (dT)_n or (dA—dT)_n. Upon lengthening the oligomers, and owing to the gradual shaping of the grooves of the helix and cumulative effect of the phosphates, TMA is shown to increasingly favor the minor groove of (dA)_n · (dT)_n with respect to the major groove of (dG)_n · (dC)_n, with a sizeable energy difference computed at the pentanucleoside hexaphosphate level. The binding of TMA in the minor groove of (dA)_n · (dT)_n involves stabilizing contacts with several sites, on the bases and on the deoxyriboses. Configurations locating the cation closer to the thymine strand are slightly preferred over configurations locating it closer to the adenine strand.     

Theoretical studies of molecular conformation. II: Application of the SIBFA procedure to molecules containing carbonyl and carboxylate oxygens and amide nitrogens

The SIBFA procedure (Sum of Interactions Between Fragments computedAb initio, Ref [1]) is extended to the study of the conformational behavior of representative molecules containing amide nitrogens and carbonyl and carboxylate oxygens. The molecules studied are C- and N-ethylammonium formamide, C- and N-ethanol-formamide, ethylammonium formate and ethanolformate. The cases investigated include interactions of the types which occur between functional groups in proteins or ionophores. The accuracy of the procedure, assessed by comparing the results to those of correspondingab initio SCF computations, is very satisfactory. An application of the procedure to study the conformation of the glycyl and alanyl dipeptides as a function of the backbone torsional angles and is presented.     

A theoretical study of the relative affinities of an aliphatic and an aromatic bisguanylhydrazone for the minor groove of double-stranded (dA-dT) n oligomers

The nonintercalative binding of an aliphatic and an aromatic bisguanylhydrazone (BGH) to the minor groove of double-stranded (dA-dT) _n oligomers is investigated by means of theoretical computations. The preferred binding arrangements of both BGHs are stabilized by a number of H-bonding interactions with sites O₂(T), N₃(A) and o₁ on the two strands, and require limited conformational rearrangements of the BGHs around their C-C single bonds. The intermolecular interaction energy is larger with the aliphatic BGH than with the aromatic one. The energy difference is, however, considerably reduced when the oligomer is lengthened: it passes from 16.1 kcal/mole at the heptamer level, to 7.9 kcal/mole at the undecamer level and to 4.6 kcal/mole when each strand of the undecamer is flanked with a complementary complete helical turn of phosphates, on both the 3 and 5 termini.The interaction energies of the BGHs with water molecules in the first hydration shell are, however, also larger with the aliphatic BGH, than with the aromatic BGH. This energy difference is further enhanced when one considers also the water molecules in the second shell. It becomes greater than the difference in the interaction energy of the two BGHs with (dA-dT) _n for large values of n. When the dehydration energy of BGHs is taken into account the overall energy balance is then more favorable for the interaction of the aromatic than of the aliphatic BGH with the polynucleotide. This last conclusion is in agreement with experimental results.     

Cation–ligand interactions: Reproduction of extended basis set Ab initio SCF computations by the SIBFA 2 additive procedure

In the framework of the additive SIBFA 2 procedure, the intermolecular interaction energy is computed as a sum of five terms: ΔE = E_MTP + E_rep + E_pol + E_CT + E_disp. In order to assess the accuracy of the procedure to compute cation–ligand interactions, the interaction of alkali (Na⁺, K⁺) and alkaline-earth (Mg²⁺, Ca²⁺) cations with two representative ligands H₂O and HCOO^? has been studied and the results compared with those of ab initio SCF extended basis set computations. The additive procedure reproduces very satisfactorily the results of ab initio computations as concerns the numerical values of the interaction energies and the equilibrium cation–ligand distances, as well as the evolution of the energy components. A detailed study of these components at different distances helps, in particular, to delineate the relative weights of the charge-transfer and polarization contributions within the second-order energy.     

Theoretical study of the interaction of nonactin with Na+, K+, and NH

In an attempt to account for the preferential binding to nonactin of K⁺ relative to Na⁺, theoretical computations are performed using the intermolecular interaction energies of the ionophore with the two cations. Both K⁺ and Na⁺ liganding conformations are considered, and an evaluation is made of the intramolecular energy expenditure caused by the reduction of the size of the cavity. The energy balance for the complexation of the two cations computed by taking into account the cation–ionophore interactions, the interactions between the liganding groups, as well as the desolvation enthalpies of the cations in methanol, favors K⁺ over Na⁺ by 4 to 5 kcal/mol, in fair agreement with the difference in the measured enthalpies of binding. The binding of NH to nonactin is also investigated.     

Towards a force field based on density fitting

Total intermolecular interaction energies are determined with a first version of the Gaussian electrostatic model (GEM-0), a force field based on a density fitting approach using s-type Gaussian functions. The total interaction energy is computed in the spirit of the sum of interacting fragment ab initio (SIBFA) force field by separately evaluating each one of its components: electrostatic (Coulomb), exchange repulsion, polarization, and charge transfer intermolecular interaction energies, in order to reproduce reference constrained space orbital variation (CSOV) energy decomposition calculations at the B3LYP/aug-cc-pVTZ level. The use of an auxiliary basis set restricted to spherical Gaussian functions facilitates the rotation of the fitted densities of rigid fragments and enables a fast and accurate density fitting evaluation of Coulomb and exchange-repulsion energy, the latter using the overlap model introduced by Wheatley and Price [Mol. Phys. 69, 50718 (1990)]. The SIBFA energy scheme for polarization and charge transfer has been implemented using the electric fields and electrostatic potentials generated by the fitted densities. GEM-0 has been tested on ten stationary points of the water dimer potential energy surface and on three water clusters (n = 16,20,64). The results show very good agreement with density functional theory calculations, reproducing the individual CSOV energy contributions for a given interaction as well as the B3LYP total interaction energies with errors below kBT at room temperature. Preliminary results for Coulomb and exchange-repulsion energies of metal cation complexes and coupled cluster singles doubles electron densities are discussed.     

Toward accurate solvation dynamics of lanthanides and actinides in water using polarizable force fields: from gas-phase energetics to hydration free energies

In this contribution, we focused on the use of polarizable force fields to model the structural, energetic, and thermodynamical properties of lanthanides and actinides in water. In a first part, we chose the particular case of the Th(IV) cation to demonstrate the capabilities of the AMOEBA polarizable force field to reproduce both reference ab initio gas-phase energetics and experimental data including coordination numbers and radial distribution functions. Using such model, we predicted the first polarizable force field estimate of Th(IV) solvation free energy, which accounts for −1,638 kcal/mol. In addition, we proposed in a second part of this work a full extension of the SIBFA (Sum of Interaction Between Fragments Ab initio computed) polarizable potential to lanthanides (La(III) and Lu(III)) and to actinides (Th(IV)) in water. We demonstrate its capabilities to reproduce all ab initio contributions as extracted from energy decomposition analysis computations, including many-body charge transfer and discussed its applicability to extended molecular dynamics and its parametrization on high-level post-Hartree–Fock data.     

Carcinogenicity of naphthylamines: A theoretical study of the stacking interaction of 1- and 2-naphthylnitrenium ions with guanine,adenine, and the dinucleoside monophosphate cytidyl-(3′-5′)-guanosine

Theoretical computations are performed with the stacking interactions of the 2-naphthylnitrenium ion, the ultimate metabolite of 2-naphthylamine and N-hydroxy-2-naphthylamine, with guanine and adenine. The most stable stacked complex of guanine with this compound is found to be distinctly more stable than that of adenine. The optimized stacking interaction of guanine with 1-naphthylnitrenium ion yields an energy close to that with 2-naphthylnitrenium. By contrast, the dinucleoside monophosphate cytidyl-(3′-5′)-guanosine held in two preselected intercalated conformations is seen to favor 2-naphthylnitrenium over 1-naphthylnitrenium by a significant amount of energy. The possible relevance of this finding to explain the difference in adduct formation with guanine in DNA by the isomeric naphthylnitrenium ions is discussed.     

Partitions of a set satisfying certain set of conditions

In this paper we present a new combinatorial class enumerated by Catalan numbers. More precisely, we establish a bijection between the set of partitions π₁π₂?π_n of [n] such that π_i+1−π_i≤1 for all i=,1,2…,n−1, and the set of Dyck paths of semilength n. Moreover, we find an explicit formula for the generating function for the number of partitions π₁π₂?π_n of [n] such that either π_i+?−π_i≤1 for all i=1,2,…,n−?, or π_i+1−π_i≤m for all i=1,2,…,n−1.