Are calculated enthalpies of formation sometimes more reliable than experimental? A test on alkyl substituted benzoic acids

Energies of 20 alkyl-substituted benzoic acids were calculated at the levels B3LYP/6-311+G(d,p)//B3LYP/6-311+G(d,p) and MP2/6-311+G(d,p)//MP2/6-311+G(d,p); the pertinent enthalpies at 298 K were calculated at the same levels. Comparison with experimental enthalpies of formation Delta(f)H degrees (g)(298) was carried out in terms of isodesmic reactions, that is, in the relative values. Of the four calculated quantities, the DFT enthalpies yielded best correlation with the standard deviation of 2.1 kJ mol(-1), near to the experimental uncertainty; the DFT energies are only slightly worse and the MP2 enthalpies or energies much worse. However, the DFT method overestimated systematically the substituent effects and had to be calibrated. Comparison with the experimental gas-phase acidities was less telling and the fit was worse because both methods overestimated the substituent effects. Extending the base in selected examples did not give better results. Although the systematic deviations are evidently due to the imperfections of the theoretical models, individual big deviations should be attributed to experimental errors or to the abnormal behavior of certain compounds at the experimental conditions. From this point of view, three examples of the so-called long-range effect claimed in the case of different benzoic acid derivatives, always for substituents in the meta position, must be refused as unproven because the experimental energies were not confirmed by calculations.     

A study of the conformation of some 3,3′-bithienyl and biselenienyl derivatives by measurements of twisting powers in nematic liquid crystals and of dipole moments

The conformation of chiral 2,2′-dinitro-3,3′-bithienyl-4,4′-dicarboxylic acid (Ia), its dimethylester (Ib), and analogous selenium derivatives Ic and Id was investigated by means of induced cholesteric mesophases. A parallel investigation on the diester (Ib) and on other model 3,3′-bithienyls was carried out with dipole moment measurements. The conclusions reached with the two independent methods for derivative Ib are in excellent agreement and indicate, if a single conformation is assumed, a preferred cisoid conformation with a dihedral angle somewhat smaller than 90°. Alternatively, if the existence of both cisoid and transoid conformations having supplementary dihedral angles is assumed, the data indicate a higher population for the cisoid form.     

Spectra of soft ring graphs

We discuss a ring-shaped soft quantum wire modelled by δ interaction supported by the ring with a generally nonconstant coupling strength. We derive the condition which determines the discrete spectrum of such systems, and analyse the dependence of the eigenvalues and eigenfunctions on the coupling and ring geometry. In particular, we illustrate that a random component in the coupling leads to a localization. The discrete spectrum is also investigated in the situation when the ring is placed into a homogeneous magnetic field or threaded by an Aharonov-Bohm flux and the system exhibits persistent currents.

(Some figures in this article are in colour only in the electronic version)     

Inequalities for Means of Chords, with Application to Isoperimetric Problems

We consider a pair of isoperimetric problems arising in physics. The first concerns a Schrödinger operator in $L^2(\mathbb{R}^2)We consider a pair of isoperimetric problems arising in physics. The first concerns a Schr?dinger operator in with an attractive interaction supported on a closed curve Γ, formally given by −Δ−αδ(x−Γ); we ask which curve of a given length maximizes the ground state energy. In the second problem we have a loop-shaped thread Γ in , homogeneously charged but not conducting, and we ask about the (renormalized) potential-energy minimizer. Both problems reduce to purely geometric questions about inequalities for mean values of chords of Γ. We prove an isoperimetric theorem for p-means of chords of curves when p ≤ 2, which implies in particular that the global extrema for the physical problems are always attained when Γ is a circle. The letter concludes with a discussion of the p-means of chords when p > 2.     

Protonated nitro group: structure, energy and conjugation

Structure of protonated nitro compounds was investigated by calculations at the levels MP2(FC)/6-311++G(2d,2p)//MP2(FC)/6-311++G(2d,2p)(nitromethane and reference compounds) or B3LYP/6-311+G(d,p)//B3LYP/6-311+G(d,p)(nitrobenzene and its 18 meta- and para-substituted derivatives). The group NO2H+ reveals many similarities with the isoelectronic group CO2H as the preferred conformation, conformational equilibrium, and stabilization by interaction (resonance) within the group quantified by means of isodesmic reactions. However, there is a difference in the interaction with donor groups (for instance in 4-nitroaniline) that is much stronger with NO2H+ than with CO2H. This interaction may be called resonance and may be described by standard resonance formulas, but these formulas predict only partially the geometry and cannot explain the great interaction energy.     

Evaluation of the field-adapted ADMA approach: absolute and relative energies of crambin and derivatives

A large number of conformations and chemically modified variants of the protein crambin were used to extensively test the field-adapted adjustable density matrix assembler (FA-ADMA) method developed for ab initio quality quantum chemistry computations of proteins and other macromolecules, introduced in an earlier publication. In this method, the fuzzy density matrix fragmentation scheme of the original adjustable density matrix assembler (ADMA) method has been made more efficient by combining it with an approach of using point charges to approximate the effects of additional, distant parts of a given macromolecule in the quantum chemical calculation of each fragment. In this way, smaller parent molecules can be used for fragment generation, while achieving accuracy that can be obtained only with large parent molecules in the original ADMA method. Whereas in both methods the error relative to the Hartree-Fock result can be reduced below any threshold by choosing large enough parent molecules, this can be done more efficiently with the new method. In order to obtain reliable test results for the accuracy obtainable by the new method when compared to conventional Hartree-Fock calculations, we performed a large number of energy calculations for the protein crambin using various conformations available in the Protein Data Bank, various protonation states, and side chain mutations. Additionally, in order to test the performance of the method for protein-solvent interaction studies, the energy changes due to the formation of complexes with ethanol and single and multiple water molecules were investigated.