On the use of pseudopotentials in molecular calculations

A series of tests was performed of the Kahn-Goddard-Melius-Topiol pseudopotentials in view of their utilization with small contracted basis sets in molecular computations. The effects of inner-shell separability and of basis set contraction are underlined. The utilizability of Topiol's valence least-squares fitted Gaussian basis sets is studied.     

Basis set dependence of localized orbitals

The effects of Gaussian basis set contraction and addition of polarization functions on H₂O localized orbitals have been studied at the experimental geometry. It is shown that the electric moments and moment features of localized orbitals are not influenced very much by basis set quality variations, as going from medium size to enlarged basis sets. The difference between bond pair and lone pair charge densities was found to be larger on approaching the Hartree-Fock limit. A minimal basis set, however, does not suitably characterize the localized charge distributions.     

A test of the Hirshfeld definition of atomic charges and moments

Summary The Hirshfeld population analysis scheme which carves the molecular density into atomic density contributions is tested. This method does not require a reference to basis sets or their respective locations, but is based on a different physical and mathematical footing. The advantage of this method is that, when the molecular deformation density converges to the true solution, the computed net charges will necessarily converge. This method also allows a straightforward definition for local moments. About 36 molecules have been used to compute the conventional Mulliken and Löwdin population analyses with STO3G, 6311G** and Dunning-Hay split valence basis sets. These results have been compared to the estimates provided by the Hirshfeld model. The charges found in the Hirshfeld method are smaller than those from the other methods.     

Quantum chemical studies on electrophilic addition

The geometries of the 2-aminoethyl cation and the isomeric protonated aziridine have been optimized using ab initio molecular orbital calculations employing the split-valence shell 4-31G basis set. The protonated aziridine is computed to be the more stable ion by 46.5 kcal/mole (4-31G level) and 44.9 kcal/mole (double-zeta basis set). The profile to interconversion is found to have a barrier of less than 15 kcal/mole (relative to the 2-aminoethyl cation) and this profile is compared with those computed for the similar ions XCH₂CH ₂ ⁺ where X=OH, F, SH and Cl.     

Testing the arbitrariness and limits of a pseudopotential technique through calculations on the series of diatoms HF,AlH, HCl,AlF, AlCl,F2, Cl2

The pseudopotential techniques present some degrees of freedom, the influence of which on molecular calculations must be tested to assess the stability and accuracy of the results. The present work uses a semi-local pseudopotential extracted from near Hartree-Fock atomic calculations; the shape of the inner part of the pseudoorbital, the analytic form of the pseudopotential are shown to have less influence than the choice of the valence basis set which must be optimized. The calculated molecular constants perfectly agree with the large basis set all-electron calculations, even for polar molecules.Equipe de Recherche Associée au CNRS No. 821.     

Non-empirical calculations and basis set effects on the inversion geometry of the aniline molecule

The geometry of the amine group and the barrier to internal conversion in aniline have been studied by single-determinantab initio SCF calculations using several basis sets from minimal to double-zeta quality. The results obtained from different types and sizes of basis sets are discussed. Calculations performed with the two most flexible basis sets yield inversion barriers of 0.9–1.1 kcal/mole and angles of pyramidalization at the nitrogen atom of 38–39 ° which are in good agreement with the experimental results (1.3 kcal/ mole and 38 °). Orbital and overlap population analyses are performed and compared with the expected mesomeric and inductive effect. The calculated dipole moment 1.48–1.49 D also agrees with the experimental values (1.48–1.50 D).Dedicated to Professor O. E. Polansky, Mülheim/Ruhr, on the occasion of his 60th birthday.     

Multipole expansion of diatomic overlap

The systematic extension of Ruedenberg's expansion formula proposed in Part I [1] is applied to a series of diatomic and polyatomic molecules (BH, NH, HF, Be₂, C₂, F₂, CO, BH₃, CH₄, NH₃, H₂O, HCN and H₂CO). In general, good agreement with the results of full SCF calculations with the same minimum STO basis set is achieved. Thus, the errors due to this integral approximation scheme called MEDO (Multipole Expansion of Diatomic Overlap) are almost negligible compared to those introduced by basis set truncation.     

Molecular orbital calculations based on linear combinations of fragment orbitals

A semiempirical MO method based on localized fragment orbitals has been developed, which is particularly suited for the construction of orbital correlation diagrams for the discussion of the electronic structure of complex molecules in terms of fragments and their interactions. The method allows for the inclusion of experimental ionization potentials and electron affinities of the fragments within the calculation of the Fock matrix elements and may thus form the basis of an interpretation of photoelectron spectra, comparable to the interpretation of UV spectra by means of the MIM method of Longuet-Higgins and Murrell. Several levels of approximation are discussed using the acrolein molecule as an example.     

Improving numerical integration through basis set expansion

Calculations are presented to assess a theorem presented by S.F. Boys [(1969) Proc. R. Soc. A. 309:195], regarding the accuracy of numerical integration in quantum chemical calculations. The theorem states that the error due to numerical integration can be made proportional to the error due to basis set truncation, and thus goes to zero in the limit of a complete basis. We test this theorem on the hydrogen atom, showing that with a solution-spanning basis, the numerically exact orbital energy can indeed be calculated with a small number of integration points. Moreover, tests for H and H₂⁺ demonstrate that even when only a near-complete basis is employed, Boys Theorem can significantly reduce integration error. However, for other systems, like the oxygen atom and the CO₂ molecule, the theorem yields no advantage for some occupied orbitals. It is concluded that the theorem would be most useful for calculations that demand large basis sets.     

Conformational behaviour of 2,2′-bipyrrole

The rotational potential around the interannular bond in 2,2-bipyrrole has been calculated making use of standard minimal STO-3G and split valence 4-31G basis sets. Geometrical optimization concerning the most significant interannular internal parameters has been performed with both basis sets. The trans conformer is predicted to be more stable than the cis. The minimal basis set predicts the existence of a cisoid-gauche minimum which after limited optimization becomes very shallow and it seems to be an artifact of the rigid rotor approximation. At 4-31G level, both the trans and cis conformers represent maxima in the potential curve and two gauche minima appear at =46.0° and =147.6°, the latter being the absolute minimum. The absolute maximum of the potential curve corresponds to the cis conformer.     

In Situ Crystallization of Bacterial Cellulose III. Influences of Different Polymeric Additives on the Formation of Microfibrils as Revealed by Transmission Electron Microscopy

Effects of polymer additives on the formation of microfibrils of bacterial cellulose have been examined by transmission electron microscopy. Among additives with different degrees of polymerization (DP) or substitution (DS), carboxymethyl cellulose sodium salt (CMC) with DP = 80 and DS = 0.57 is the most effective in producing separate, smaller-size microfibrils. By increasing the concentration of this CMC from 0.1 to 1.5%, the percentage of microfibrils measuring 3–7 nm wide is increased and levels off at around 1.0%. Other polymer additives such as xyloglucan are less effective than CMC in producing microfibrils with smaller sizes and the resulting microfibrils still tend to aggregate. The number of charged substituents and the molecular weight seem to be important factors in the production of highly separate smaller-size microfibrils. The reduction in average microfibril size is well correlated to the decrease in mass fraction of cellulose I in bacterial cellulose crystals. On the basis of these results, the mechanism of the crystallization of celluloses I and I is discussed. The effect of colony types, smooth and rough, on the formation of microfibrils in the presence of CMC is also described.     

Spectroscopic and quantum chemical investigation of enol-enol tautomerism of 2-acetyltetronic acid

Vibratonal spectra of 2-acetyltetronic acid (ATA) (3-acetyloxolane-2,4-dione) were investigated in different aggregate states.Ab initio quantum chemical calculations (3-21G basis set) of 2-formyltetronic acid as analogue of ATA and semi empirical calculation of ATA were carried out. The tautomeric forms of ATA can be arranged in the following series with respect to thermodynamic stability (in decresing order):1a,1b,2a,2b.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 6, pp. 1043–1048, June, 1995.     

An investigation of the reliability of the Galerkin-Petrov method

The Galerkin-Petrov method is applied to the determination of the ground state energy of the beryllium atom. The basis set of the coordinate subspace consists of correlated wavefunctions of the combined configuration-interaction-Hylleraas type. The basis set of the projective subspace is of the configuration-interaction type. The usefulness of a previously proposed way of characterization of pairs of subspaces has been further confirmed. Experience in constructing close pairs of subspaces gathered in the case of two-electron systems is used for the larger system. Two methods for constructing pairs of subspaces are used in the calculations.     

Quantum chemical studies on electrophilic addition

The geometries of the 2-hydroxyethyl and isomeric oxiranium cations have been fully optimized using ab initio molecular orbital calculations employing the split valence shell 4-31G basis set. These species are possible intermediates in both the electrophilic addition of OH to ethylene and in the acid catalysed ring opening of oxirane. The optimized structures were then used to compute more accurate wave functions using Dunning's double-zeta basis set, and with this large basis set the bridged oxiranium ion was found to be the more stable by 7.2 kcal/mole. The barrier to interconversion of these two C₂H₄OH ions was computed to be 25.0 kcal/mole above the oxiranium ion.     

An optimum minimal basis of exponential atomic orbitals

An analysis of some of the energetic properties of the conventional minimal STO basis is used to suggest a new optimum set of exponential functions for use in molecular calculations.     

Multipole expansion of diatomic overlap

A systematic extension of Ruedenberg's expansion formula is applied to evaluate two-electron integrals occurring in calculations on molecular structure. Minimum STO basis sets are used for all SCF-calculations within the framework of the MEDO-method (Multipole Expansion of Diatomic Overlap). The errors due to this approximation scheme are almost negligible compared to those introduced by the truncated basis set: LiH, Li₂ and N₂ are chosen as examples.     

Geometry optimization inab initio SCF calculations

The floating orbital geometry optimization (FOGO) described previously [1, 2] for atoms without polarized inner-shell electrons, is extended to the general case. Instead of the Hellmann-Feynman force a special gradient is calculated analytically and utilized in a variable metric procedure simultaneously with the ordinary energy gradient. Test calculations on a sample of 12 molecules were performed to check the efficiency of the method. The geometries obtained are better than those obtained with the corresponding double-zeta basis set. The most striking results, however, are excellent dipole moments.     

Phase and structural transitions in vicinal water on protein surfaces by means of the DSC

This paper presents investigations of phase and structural transitions occurring in water adsorbed on the surface of bovine serum albumin (BSA) and on the so-called intelligentrs or smart silica gel surface covered with a chemically bonded BSA phase. Cyclic changes of heat flow (HF) were observed in the samples studied during cooling and heating of the measuring cell of the differential scanning calorimetry (DSC) apparatus. These cyclic changes reflect structural transitions occurring in the water adsorbed on the surface at subambient and elevated temperatures. This is connected with cyclic changes (decay and reproduction) of ice-like structures existing in the adsorbed water layers. On the basis of quantitative investigations it appears that, depending on the direction of the cooling or heating process of the samples studied, the number of ice-like water structures in the surface film increases or decreases. It has been stated that the observed fluctuations occur spontaneously and suddenly in the whole volume of adsorbed water in different and not regular temperature ranges, especially at the paradoxical effect temperatures.Support from the Research Council (Dr. R. K. Gilpin and Dr. M. Jaroniec) of Kent State University (Ohio, USA) is acknowledged. The author thanks Dr. V. Tittlebach for providing the samples of pure BSA and silica gel with chemically, bonded BSA phase.     

Quantum mechanical studies of environmental effects on biomolecules

LCAO SCF calculations with a (7s, 3p/3s) atomic basis are performed on urea and hydrated urea in order to determine the preferred sites of water fixation using the supermolecule approach. It appears that up to five water molecules can be directly bound to urea in the first hydration shell.