Importance of the basis set for the spin-state energetics of iron complexes

We have performed a systematic investigation of the influence of the basis set on relative spin-state energies for a number of iron compounds. In principle, with an infinitely large basis set, both Slater-type orbital (STO) and Gaussian-type orbital (GTO) series should converge to the same final answer, which is indeed what we observe for both vertical and relaxed spin-state splittings. However, we see throughout the paper that the STO basis sets give consistent and rapidly converging results, while the convergence with respect to the basis set size is much slower for the GTO basis sets. For example, the large GTO basis sets that give good results for the vertical spin-state splittings of compounds 1-3 (6-311+G**, Ahlrichs VTZ2D2P) fail for the relaxed spin-state splittings of compound 4 (where 1 is Fe-(PyPepS)2 (PyPepSH 2 = N-(2-mercaptophenyl)-2-pyridinecarboxamide), 2 is Fe(tsalen)Cl (tsalen = N, N'-ethylenebis-(thiosalicylideneiminato)), 3 is Fe(N(CH2-o-C6H4S) 3)(1-Me-imidazole), and 4 is FeFHOH). Very demanding GTO basis sets like Dunning's correlation-consistent (cc-pVTZ, cc-pVQZ) basis sets are needed to achieve good results for these relaxed spin states. The use of popular (Pople-type) GTO, effective core potentials basis set (ECPB), or mixed ECPB(Fe):GTO(rest) basis sets is shown to lead to substantial deviations (2-10 kcal/mol, 14-24 kcal/mol for 3-21G), in particular for the high spin states that are typically placed at too low energy. Moreover, the use of an effective core potential in the ECPB basis sets results in spin-state splittings that are systematically different from the STO-GTO results.     

On the use of Gaussian shell type basis orbitals for single-center expansions. I. Evaluation of integrals

Formulas are derived for all Hamiltonian integrals required for molecular computations using a novel basis for single-center expansions. The basis orbitals depend exponentially upon α(r ? ρ)² where r and ρ are the distance from center to electron and to a variationally scaled spherical shell, respectively. Comparisons are made between these so-called Gaussian shell orbitals (GSO ) and the conventional GTO and STO bases for single-center calculations. A preliminary comparison on H using a single GSO , a non-integer STO , and a GTO gives the optimized energies: ?0.51089 a.u., ?0.50504 a.u., and ?0.50422 a.u., respectively.     

Gaussian expansions of minimal STO basis for calculations in molecular quantum mechanics

By means of minimal basis SCF calculations for HF, H₂O, NH₃ and CH₄ different expansions of Slater orbitals (STO) in terms of Gaussian orbitals (GTO) are tested in order to find an appropriate compromise between sufficient accuracy of the results and reasonable computing times. The least squares fit of the GTO expansion to STO does not appear to have any advantages over the expansion based on a variational procedure. It turns out that for hydrogens an expansion of the 1s orbital in terms of three GTO is quite sufficient, whereas for first row atoms an expansion of the 1s orbital in terms of three to five GTO, of the 2s orbital in terms of two GTO and of the 2p orbitals in terms of three GTO seems to be adequate.

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Zusammenfassung An Hand von SCF-Rechnungen mit minimaler Basis für die Moleküle HF, H₂O, NH₃ und CH₄ wurden verschiedene Entwicklungen von Slater-Orbitalen (STO) nach Gauß-Orbitalen (GTO) getestet, um einen geeigneten Kompromiß zwischen ausreichender Genauigkeit der Ergebnisse und vertretbaren Rechenzeiten zu finden. Es zeigt sich, daß die Entwicklung der STO nach GTO mit Hilfe der Methode der kleinsten Fehlerquadrate keine Vorteile gegenüber der auf einem Variationsverfahren basierenden Entwicklung aufweist. Für H-Atome erweist sich eine Entwicklung des 1s-Orbitals nach drei GTO als ausreichend, für Atome der 1. Periode erscheint eine Entwicklung des 1s-Orbitals nach drei bis fünf GTO, des 2s-Orbitals nach zwei GTO und der 2p-Orbitale nach drei GTO als geeignet.

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Résumé En vue de trouver un compromis approprié entre la précision et la durée des calculs, différents développements des orbitales de Slater (STO) en termes d'orbitales gaussiennes (GTO) sont testés au moyen de calculs SCF en bases minimales pour HF, H₂O, NH₃ et CH₄. L'ajustement par les moindres carrés du développement des STO en GTO ne présente apparemment d'avantages sur le développement fondé sur un procédé variationnel. Il apparaît que pour l'hydrogène un développement de l'orbitale 1s en fonction de trois gaussiennes est largement suffisant, alors que pour les atomes de la première rangée il semble nécessaire de développer l'orbitale 1s en 3 à 5 GTO, l'orbitale 2s en 2 GTO et les orbitales 2p en 3 GTO.

     

Biocompatible water-in-oil emulsion as a model to study ascorbic acid effect on lipid oxidation

A biocompatible water-in-oil (W/O) emulsion has been used as a model to study the effect of ascorbic acid (AA) on the oxidation of the oil (glycerol trioleate, GTO) continuous phase. The model system consisted of 3 wt % water dispersed in GTO containing 0.5 wt % sodium oleate (NaO)/oleic acid (OA) mixture (NaO/OA = 20/80 mol/mol %) as a stabilizer. To study the ascorbic acid effect on GTO light-promoted oxidation, we added aqueous solutions of ascorbic acid to GTO in place of distilled water. Results obtained as peroxide values show that ascorbic acid activity depends on its concentration and it is affected by the characteristics of the W/O interface. In the presence of ascorbyl palmitate (AP) or sorbitan trioleate (Span 85) in the continuous phase, ascorbic acid activity increases in the first few hours of oxidation. The effect of ascorbic acid has been related to emulsion structure by calculating characteristic parameters of the droplet size distributions by means of optical microscopy.     

A comparison between plane wave and Gaussian-type orbital basis sets for hydrogen bonded systems: formic acid as a test case

The formic acid molecule, its dimers, and its molecular crystal are adopted as test systems to compare results obtained with plane wave (PW) basis sets and norm-conserving pseudopotentials to all-electron Gaussian-type orbital (GTO) calculations. The CPMD and CRYSTAL06 codes, respectively, are applied with the PBE, PW91, and BLYP density functionals. Hydrogen bonding is the leading interaction in the dimers and the crystal. In the latter, dispersive and weak C-H...O interactions are also relevant. Irrespective of the adopted functional, for all considered structures PW and GTO results converge smoothly as a function of the quality of the adopted basis sets to the same values for structures, energies of interaction, and harmonic vibrational features. To achieve a high level of mutual agreement the use of GTO basis sets of at least of triple-zeta quality including one set of polarization functions and PW basis sets with a kinetic energy cutoff higher than 110 Ry is recommended. Pros and cons of both approaches for studying molecular crystals are also discussed.     

改进压缩性近似并导出新的硬球微扰理论表达式

提出在Barker与Henderson的压缩性近似推导中,相邻壳层之间的分子数应该相关,导出了相关系数和改进的二级微扰项,提高了高级微扰项在较高密度区的准确性。对二级以上的高级微扰项采用Barker与Henderson的近似方法,得到一个简单的微扰理论表达式,以硬球势为参考势,方阱势为微扰势,用一新的级数形式的径向分布函数导出了自由能、内能、比热、压缩因子的级数表达式。其四项截断式的计算结果与MC、MD计算机模拟值符合较好。     

The rotational spectrum and theoretical study of a dinuclear complex, MnRe(CO)(10)

The first rotational spectrum of a dinuclear complex, MnRe(CO)(10), has been obtained using a high-resolution pulsed beam microwave spectrometer. Sixty-four hyperfine components of the J=11-->J(')=12 and J=12-->J(')=13 rotational transitions were measured for two rhenium isotopomers. The B values obtained from the experiment are B=200.36871(18) MHz for the (187)Re isotopomer and B=200.5561(10) MHz for the (185)Re isotopomer. The measured rotational constants are in reasonably good agreement with the B values calculated from the x-ray diffraction structural data, and from theoretical calculations. The gas-phase Mn-Re bond distance is approximately 2.99 A, and the calculated value is only slightly longer. The experimental quadrupole coupling constant for the manganese atom is eQq(aa) ((55)Mn)=-16.52(5) MHz, and the corresponding quadrupole coupling constants for the two rhenium isotopomers are eQq(aa) ((187)Re)=370.4(4) MHz and eQq(aa) ((185)Re)=390.9(6) MHz. The quadrupole coupling constants were also determined from a variety of theoretical calculations, with very large Gaussian orbital bases. The best estimates, at a nonrelativistic level, are eQq(aa) ((55)Mn)=0.68 MHz and eQq(aa) ((187)Re)=327.6 MHz with a 874 GTO basis set, but the results are very basis set dependent, especially the sign of the Mn quadrupole coupling. Very slight bending of angles MnC(eq)O(eq) and ReC(eq)O(eq) angles is found in the calculations.     

The general Gaussian product theorem

The Gaussian Product Theorem between two 1s Gaussian Type Orbitals (GTOs) is extended to an arbitrary number of s-type functions, giving a compact formula which permits to express the condensed GTO result. Then, this new formulation is combined with the product of arbitrary GTO Cartesian angular parts, obtaining a finite expansion expressing this product as a multilinear combination of such functions sharing a common center. The combination of both results constitutes the General Gaussian Product Theorem (GGPT), a final compact expression for the product of an arbitrary number of Cartesian GTOs. The notation provides an easy way to express algebraically any general multicenter GTO product expression. It is also shown how by means of Nested Summation Symbols the computational implementation can be easily and elegantly achieved. Computational parallelizable schemes of the GGPT are provided.     

Density-functional generalized-gradient and hybrid calculations of electromagnetic properties using Slater basis sets

In this paper we extend our density-functional theory calculations, with generalized gradient approximation and hybrid functionals, using Slater-type orbitals (STOs), to the determination of second-order molecular properties. The key to the entire methodology involves the fitting of all STO basis function products to an auxiliary STO basis, through the minimization of electron-repulsion integrals. The selected properties are (i) dipole polarizabilities, (ii) nuclear magnetic shielding constants, and (iii) nuclear spin-spin coupling constants. In all cases the one-electron integrals involving STOs were evaluated by quadrature. The implementation for (ii) involved some complexity because we used gauge-including atomic orbitals. The presence of two-electron integrals on the right-hand side of the coupled equations meant that the fitting procedure had to be implemented. For (iii) in the hybrid case, fitting procedures were again required for the exchange contributions. For each property we studied a number of small molecules. We first obtained an estimate of the basis set limit using Gaussian-type orbitals (GTOs). We then showed how it is possible to reproduce these values using a STO basis set. For (ii) a regular TZ2P quality STO basis was adequate; for (i) the addition of one set of diffuse functions (determined by Slater's rules) gave the required accuracy; for (iii) it was necessary to add a set of 1s functions, including one very tight function, to give the desired result. In summary, we show that it is possible to predict second-order molecular properties using STO basis sets with an accuracy comparable with large GTO basis sets. We did not encounter any major difficulties with either the selection of the bases or the implementation of the procedures. Although the energy code (especially in the hybrid case) may not be competitive with a regular GTO code, for properties we find that STOs are more attractive.     

Medium-size polarized basis sets for high-level-correlated calculations of molecular electric properties

Summary The basis set polarization approach is employed for the generation of medium-size polarized GTO/CGTO basis sets for calculations of molecular dipole moments and polarizabilities. The excellent performance of the [13.10.4/7.5.2] GTO/CGTO polarized basis sets derived for Si through Cl is illustrated by the atomic polarizability results and SCF and MBPT data for dipole moments and polarizabilities of the second-row atom hydrides. The possible applications of the electric-property oriented polarized basis sets are discussed. The basis set data for Si through Cl are those for H and C through F append the paper.     

A first-principle study of the adsorption of 1-amino-3-cyclopentene on the (100) silicon surface

The adsorption of 1-amino-3-cyclopentene on the (100) silicon surface has been studied by methods rooted in the density-functional theory using both delocalized (plane waves, PWs) and localized (Gaussian-type orbitals, GTOs) basis functions. The results obtained by modeling the surface by silicon clusters of different sizes are quite similar, thus confirming that the reaction is quite localized. Furthermore, PW and GTO computations give comparable results, provided that the same density functional and carefully chosen computational parameters (contraction of GTO, pseudopotentials, etc.) are used. Slab computations performed in the PW framework show that the cluster results are retrieved when low-coverage adsorption on the surface is considered. On these grounds, we are quite confident that reaction parameters obtained by the more reliable hybrid density functional (PBE0) are essentially converged, our best estimates of reaction and activation free energies are thus -40 and 6 kcal/mol, respectively.     

ESCA Peak intensities in the dipole and generalized sudden approximations using fourier transforms of GTO's

Analytical expressions for the square of the spherical average of Fourier transforms of Gaussian type orbitals (GTO 's) are given. A direct application of these expressions to the calculation of molecular photoionization cross sections is considered under the generalized sudden (GSA ) and dipole (DA ) Approximations. Numerical calculations were done on the CO molecule using bound orbitals obtained by ab initio LCAO –MO calculations with Gaussian basis sets. The results are in good agreement with experiments. Those obtained by the GSA method however, suggest a limitation in its use: the GSA method is only applicable when comparing photoionization intensities of neighboring ionization energy orbitals. Applications to other molecules are immediate.     

A systematic preparation of new contracted Gaussian-type orbitals. IX [54/5], [64/5], [64/6], [74/6], [74/7] and MAXI-1–MAXI-5 from Li to Ne

The new contracted Gaussian-type orbitals (CGTO s) for molecular calculations have been developed from Li to Ne. The CGTO s are minimal type, i.e. composed of two s-type CGTO s, s₁, s₂, and one p-type CGTO , p₁. They are new family of CGTO s given by Tatewaki and Huzinaga, and others. In the previous works three primitive GTO s are used for s₂, which is the main part of the 2s orbital, whereas four primitive GTO s are employed in the present work. The sets generated are [54/5], [64/5], [64/6], [74/6], and [74/7]. In almost all the cases the errors in the 2s and 2p orbital energies are smaller than those of DZ . The resulting 2s orbitals are close to the orbitals of the uncontracted GTO sets, (13/n) and (14/n) of Duijneveldt. It is found that the 2s and 2p orbitals given by [64/6], [74/6], and [74/7] are satisfactorily near to those of Hartree–Fock. The basis sets [54/5], [64/6], and [74/7] are applied to the N₂ molecule in the split valence forms of [5211/311], [6211/3111], and [7211/4111]. Adding the d-type polarization functions from one through three, the quality of the basis sets has been examined. All of the three sets show good behavior and the sets augmented with three d-type polarization functions give almost entirely the same results as the very extended basis set.     

The parameterization and validation of generalized born models using the pairwise descreening approximation

Generalized Born Surface Area (GBSA) models for water using the Pairwise Descreening Approximation (PDA) have been parameterized by two different methods. The first method, similar to that used in previously reported parameterizations, optimizes all parameters against the experimental free energies of hydration of organic molecules. The second method optimizes the PDA parameters to compensate only for systematic errors of the PDA. The best models are compared to Poisson-Boltzmann calculations and applied to the computation of potentials of mean force (PMFs) for the association of various molecules. PMFs present a more rigorous test of the ability of a solvation model to correctly reproduce the screening of intermolecular interactions by the solvent, than its accuracy at predicting free energies of hydration of small molecules. Models derived with the first method are sometimes shown to fail to compute accurate potentials of mean force because of large errors in the computation of Born radii, while no such difficulties are observed with the second method. Furthermore, accurate computation of the Born radii appears to be more important than good agreement with experimental free energies of solvation. We discuss the source of errors in the potentials of mean force and suggest means to reduce them. Our findings suggest that Generalized Born models that use the Pairwise Descreening Approximation and that are derived solely by unconstrained optimization of parameters against free energies of hydration should be applied to the modeling of intermolecular interactions with caution.     

On the electron affinity of Cu atom

The electron affinity (EA) of the Cu atom is computed using large STO and GTO basis sets at several levels of correlation. The best computed value is 1     

CDW and CDW-EIS investigations in an independent electron approximation for the resonant double electron capture by swift He2+ in helium

The CDW and CDW-EIS approximations are used to study the resonant double electron capture by He²⁺ in helium at intermediate and high impact velocities. Calculations of the total cross sections as a function of the impact energy are performed in an Independent Electron Approximation. A very good agreement with recent experimental data for capture into all states of the projectile is found although neither angular nor dynamical electron correlations are included in the calculations.     

Darzens reaction of acyl phosphonates with alpha-bromo ketones: selective synthesis of cis- and trans-epoxyphosphonates

Acyl phosphonates with alpha-halo ketones in the presence of bases at room temperature afford cis- and trans-epoxyphosphonates in good chemical yields and high selectivities using different bases. The diastereoselectivity of this reaction is easily controlled by changing the base. Changing the base from Cs2CO3 to DBU changed the diastereomeric ratio (trans/cis) from 3/2 to 9/1. Moreover, the treatment of the trans isomer with DBU showed a complete conversion to the corresponding cis isomer.     

Electronic structure of spheroidal metal containing carbon shells: study of the LaC60 and C60 clusters and their ions within the local density approximation

Ionization thresholds and electron affinities have been calculated within the Local Density Approximation (LDA) for the neutral, positively and negatively charged clusters of LaC₆₀ and C₆₀. The evaluated energies are found to be in good agreement with available experimental data. More accurate measurements are however necessary to verify the suggested spheroidal cage structure for these molecules.     

Analysis of basic compounds by reversed-phase high-performance liquid chromatography using hybrid inorganic/organic phases at high pH

The retention and mass overload of five bases and a quaternary ammonium compound were studied on a bridged ethyl hybrid inorganic/organic phase (XBridge C18) over a pH range 2.7-12.0 using acetonitrile-phosphate and carbonate buffers. Some comparisons were drawn with results on a methyl hybrid (XTerra) phase. At low pH, rapid mass overload was observed with severe decreases in efficiency as sample mass was increased over the range 0.04-5 microg of solute. At intermediate pH (swpH 7.0), generally good peak shapes for small sample mass were still obtained on the ethyl hybrid, but with somewhat increased tailing of bases compared with swpH 2.7. At higher pH (swpH 10), good peak shape and improved loadability were obtained for moderately strong bases, due to their occurrence mostly as neutral species. However, stronger bases gave poor efficiency, attributed to interaction of the charged basic solute with increasingly ionised column silanol groups. Results were broadly similar on the methyl hybrid at swpH 10. At swpH 11, unusual profiles of increasing followed by decreasing efficiency were obtained on the ethyl hybrid for some bases as sample mass was increased; improved results were obtained at swpH 12. While the column loadability increased substantially at the highest pH studied, tailing for small sample mass was still more severe than at low pH, even though all compounds were <1% ionised in the mobile phase.