An ab initio study of the potential surface for the reaction H2COH → HCO + H2

The potential surface for the reaction H₂CO⁺H → HCO⁺ + H₂ has been studied by ab initio SCF calculations, using gaussian-type basis functions. A saddle point on the surface has been found, and a reaction path is proposed to explain the observed release of kinetic energy. The energy of activation and ΔE for the reaction have been estimated.     

Models for the theory of the hydrogen bond: Linear H3/−

An analogy is drawn between the hydrogen bond and the interaction of H₂ with H^– as a prototype. The energy surface for linear H^3/– is calculated using a minimal basis set of 1s orbitals and complete configuration interaction. The appearance of single and double minimum potentials on this surface is discussed.Contribution No. 359 from the Department of Chemistry, Tufts University.     

Isotope Effect on Fractional Dilatability of Solute Water as an Indicator of the H-Bonding Ability of an Aprotic Dipolar Solvent

Based on experimental data about the density of very dilute solutions of H₂O and D₂O in 1,4-dioxane, hexamethylphosphotriamide, and acetonitrile at 278.15 K-318.15 K we determined the limiting partial molar volume (error ±0.03 cm³·mol⁻¹) and dilatability of the water component. A correlation equation has been derived which relates the isotope effect (IE) in the limiting excess partial molar dilatability of water to the energy of the H₂O-solvent hydrogen bond. The stated IE may be used as a “structural indicator” for evaluating the ability of an aprotic dipolar solvent to undergo specific interactions through hydrogen bonding.Original Russian Text Copyright © 2004 by E. V. Ivanov, V. K. Abrosimov, and E. Yu. Lebedeva__________Translated from Zhurnal Strukturnoi Khimii, Vol. 45, No. 6, pp. 1020–1026, November–December, 2004.     

Unimolecular rearrangement of α-silylcarbenium ions. An ab initio study

The unimolecular rearrangements of hydrogen, methyl and phenyl groups at the Si atom in α-silylcarbenium ions have been investigated using an ab initio molecular orbital method. MP2/6–31 + G^*//HF/6–31G^* calculations predict that all three groups migrate from the Si to an adjacent C_α with no energy barrier. Thus, the silicenium ion is the only stable species in each potential energy surface. The conformation of the benzylsilicenium ion, (C₆H₅)CH₂−SiH₂⁺, indicates that the phenyl ring is significantly bent toward the silyl cationic center in order to interact with the vacant 3p(Si⁺) orbital. In contrast to MP2 results, Hartree-Fuck calculations (both HF/3–21G^* and HF/6–31G^* levels) predict small energy barriers for 1,2-migrations of H and Me (1.4 kcal mol⁻¹ for H migration, and 1.5 kcal mol⁻¹ for Me migration, respectively, at the HF/6–31G^* level). This difference provides convincing evidence that the incorporation of electron correlation is of particular importance in describing the potential energy surface for the rearrangement of α-silylcarbenium ions to silicenium ions. The results of the calculations have also been applied to the possible rearrangement mechanism of α-chlorosilanes to chlorosilanes, assuming that the experimental conditions are favorable toward the generation of ionic species. Various factors which may govern the migratory aptitudes of various R groups, i.e. (1) activation energies, (2) overall reaction energies and (3) the conformational preference of reactants have been investigated. The calculated activation energy obtained, namely the energy for the generation of the silicenium ion and the C⁻¹ ion from an α-chlorosilane, is consistent with the experimental migratory aptitude in the gas phase observed in mass spectrometers.     

Basis Set Orbital Relaxation in Atomic and Molecular Hydrogen Systems

Orbital relaxation (OR) amounts to variation of the orbital exponents in hydrogen molecules and ions relative to the exponents of the isolated atom; it is represented as the sum of the one- and two-center contributions depending on the effective atomic charge and on the presence of other atoms in the molecule. The procedure for isolating the contributions of the exponent includes treatment of the OR of hydrogen in a special set of neutral and charged atoms and molecules with certain multiplicities of their electronic states. Within the framework of the spin-unrestricted Hartree-Fock method, we found and discussed the optimal values of the exponents of the basis orbitals of hydrogen atoms and molecules using the minimal split valence-shell basis set, the basis set that includes the polarization function, and the expanded set of grouped natural orbitals. A simple energy model is suggested for OR. Expressions are derived for evaluating the exponents of the relaxed orbitals in hydrogen-containing systems.Original Russian Text Copyright © 2004 by A. I. Ermakov, A. E. Merkulov, A. A. Svechnikova, and V. V. Belousov__________Translated from Zhurnal Strukturnoi Khimii, Vol. 45, No. 6, pp. 973–978, November–December, 2004.     

A B3LYP study on counterpoise-corrected geometry optimizations for hydrated complexes of [K(H2O)n] and [Na(H2O)n]

We report the basis set dependencies and the basis set superposition errors for the hydrated complexes of K⁺ and Na⁺ ions in relation to the recent studies of the KcsA potassium channel. The basis set superposition errors are estimated by the geometry optimizations at the counterpoise-corrected B3LYP level. The counterpoise optimizations alter the hydration distances by about 0.02–0.03 Å. The enthalpies and free energies for K⁺ + n(H₂O) → [K(H₂O)_n]⁺ and Na⁺ + n(H₂O) → [Na(H₂O)_n]⁺ (n = 1–6) are compared between the theoretical and experimental values. The results show that the addition of diffuse functions to K, Na, and O species are effective. However, it is also found that the counterpoise corrections using diffuse functions work so as to underestimate the free energies for the complexes with increasing the hydration number. The stabilization energies in aqueous solution are larger for a Na⁺ ion than for a K⁺ ion, suggesting the contributions of their dehydration processes to the ion selectivity of the KcsA potassium channel. The changes in coordination distance between the isolated [K(H₂O)₈]⁺ and the [K(H₂O)₈]⁺ in the KcsA potassium channel indicate the importance of hydrogen bondings between the first hydration shell and the outer hydration shells.     

Structure and stability of ion pairs A−·K+·H2O with a strong anion

Characteristics of the ion pairs HCOO^–·Na⁺·H₂O, HCOO^–·K⁺·H₂O, and also Na⁺·H₂O and K⁺·H₂O were calculated by the nonempirical Hartree—Fock—Roothan linear-combination-of-atomic-orbitals self-consistent-field (SCF) molecular-orbital method in a two-exponent Dunning basis using an extended set of Huzinaga—Dunning Gaussian functions. The basis was supplemented by polarization functions ofd type for the oxygen atom andp type for the H atom and also by diffusion functions ofp type for the oxygen atom. Characteristics of the ion pairs HCOO^–·Li⁺ and HCOO^–·Na⁺ were calculated taking into account the electronic correlation according to the Möller — Plesset second-order perturbation theory. Significant quantitative difference was observed in the hydration of ionogens and free cations. The stability of the ionogens HCOOMe in aqueous solutions, increasing from Li⁺ to Cs⁺, is not explained by the difference between the energies of complexation and the energies of hydration of the cations. The better solubility of the salt molecule with a cation of smaller radius is due to the higher degree of hydration of that ionogen.N. N. Semenov Institute of Chemical Physics, Russian Academy of Sciences, 117977 Moscow. Translated fromIzvestiya Akademii Nauk, Seriya Khimicheskaya, No. 12, pp. 2700–2707, December, 1992.     

Proton chemical shift tensors in neutral and ionic OH⋯O hydrogen bonds

Proton nuclear magnetic shielding tensors are calculated for some OH?O hydrogen bonds: (H₃O₂)^?, (H₂O)₂, and (H₅O₂)⁺. The effects of charge, geometry, and basis set are studied. Agreement with single crystal pulsed NMR experiments is obtained. A linear dependence between the proton chemical shift and the O?O separation is observed, correcting a previous misinterpretation of the data.     

DFT study on the intermolecular interactions between Aun (n = 2–4) and thymine

Density functional B3LYP method with 6-31++G** basis set is applied to optimize the geometries of the luteolin, water and luteolin–(H₂O)_n complexes. The vibrational frequencies are also studied at the same level to analyze these complexes. We obtained four steady luteolin–H₂O, nine steady luteolin–(H₂O)₂ and ten steady luteolin–(H₂O)₃, respectively. Theories of atoms in molecules (AIM) and natural bond orbital (NBO) are used to investigate the hydrogen bonds involved in all the systems. The interaction energies of all the complexes corrected by basis set superposition error, are within −13.7 to −82.5 kJ/mol. The strong hydrogen bonding mainly contribute to the interaction energies, Natural bond orbital analysis is performed to reveal the origin of the interaction. All calculations also indicate that there are strong hydrogen bonding interactions in luteolin–(H₂O)_n complexes. The OH stretching modes of complexes are red-shifted relative to those of the monomer.     

Floating spherical gaussian orbital open-shell calculations on the four-electron H4 system

Floating spherical Gaussian orbital (FSGO ) open-shell calculations have been made to determine the potential energy surface of planar square and rectangular arrangements of the four-electron system H₄. This surface is discussed in relation to the bimolecular isotope exchange reaction H2+D2-→ 2HD. The changes in energy and geometry accompanying the coplanar approach of two hydrogen molecules interacting chemically have also been investigated. Calculations on the electronic energies of planar T-shaped and kite arrangements of H4 of various sizes show that it is unlikely that these configurations can serve as transition states for the exchange reaction. However, the energy curve for linear configurations of H4 (H? H? H … H), calculated as a function of the H₃ … H distance with the symmetric linear H₃ (H-H-H) unit fixed at the internuclear distance of 1.9080 a.u., is found to have a deep minimum (?1.9176 a.u.) at an r(H₃ … H) distance of 1.5846 a.u. The overall results suggest that the following mechanism for the exchange reaction, H₂+H₂→H₂+H+H→H₃+H→H+H₂+ H→H₂+H₂ could be advantageous as it requires a barrier height of 0.1604 a.u. which is significantly lower than that calculated from the saddle point energy (0.1950 a.u.). However, the problem of reconciling this with the experimental activation energy of 0.0685 a.u. still remains.     

Electrochemical, spectroelectrochemical and theoretical studies on the reduction and deprotonation of the photovoltaic sensitizer [(H3-tctpy)Ru(NCS)3] (H3-tctpy=2,2′:6′,2′′-terpyridine-4,4′,4′′-tricarboxylic acid)

The electrochemical reduction of the black dye photosensitizer [(H₃-tctpy)Ru^II(NCS)₃]⁻ (H₃-tctpy=2,2′:6′,2′′-terpyridine-4,4′,4′′-tricarboxylic acid) used in photovoltaic cells has been found to be a complex process when studied in dimethylformamide. At low temperatures, fast scan rates and at a glassy carbon electrode, the chemically reversible ligand based one-electron reduction process [(H₃-tctpy)Ru(NCS)₃]⁻+e⁻[(H₃-tctpy√⁻)Ru(NCS)₃]²⁻ is detected. This process has a reversible half-wave potential (E^r_1/2) of −1585±20 mV versus Fc/Fc⁺ at 25°C. Under other conditions, a deprotonation reaction occurs upon reduction, which produces [(H_3−x-tctpy^x−)Ru(NCS)₃]^(1+x)− and hydrogen gas. Mechanistic pathways giving rise to the final products are discussed. The E^r_1/2-value for the ligand based reductions of the deprotonated complex is 0.70 V more negative than for [(H₃-tctpy)Ru(NCS)₃]⁻. Consequently, data obtained from molecular orbital calculations are consistent with the reaction [(H₃-tctpy)Ru(NCS)₃]⁻+e⁻→[(H₂-tctpy⁻)Ru(NCS)₃]²⁻+1/2H₂ yielding the monodeprotonated complex as the major product obtained after electrochemical reduction of [(H₃-tctpy)Ru(NCS)₃]⁻. The E^r_1/2-values for the metal based Ru^II/III process differ by 0.30 V when data obtained for the protonated and deprotonated forms of the black dye are compared. Electronic spectra obtained during the course of experiments in an optically transparent thin layer electrolysis configuration are consistent with the overall reaction scheme proposed on the basis of voltammetric measurements and molecular orbital calculations. Reduction studies on the free ligand, H₃-tcpy, are consistent with results obtained with [(H₃-tctpy)Ru(NCS)₃]⁻.     

Study of the hydrogen bond and of the proton transfer between two H2S molecules

The potential energy surface for the H₂S dimer is calculated as the sum of the SCF-MO-LCGO energy with a new, modified, basis set and the estimated dispersion energy. Proton affinities for SH^– and H₂S, and, as their difference, the energy of the proton transfer between two H₂S molecules, are also calculated. Despite the limited basis set used, the results are consistent with experimental data.This work was partly supported by the Polish Academy of Sciences within the project PAN-3.     

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.     

Molecular orbital studies on small molecules using H2+-type elliptical basis orbitals. Application to H2+, H2, He2++ and H3+

H₂⁺-type elliptical orbitals are defined in Section 1. These orbitals, which in elliptical coordinates involve a factor (1 + ξ)^σ, are employed in variational calculations on the ground states of H₂⁺ and H₂ (Sections 2 and 3). Various choices of σ are explored for H₂⁺, while two choices are used for H₂ : the “boundary condition” (Equation 6) and the “cusp condition” (Equation 9) values. Variational energies are calculated and compared to the results of similar calculations. Section 3 concludes by employing the H₂⁺-type orbitals in LCETO-MO-SCF calculations on the ground states of H₂ and He₂⁺⁺. For both molecules a four-function basis set with two (nonlinear) variational parameters yields more than 99% of the Hartree-Fock limit. Section 4 deals with LCETO-MO-SCF calculations on triangular H₃⁺. Three four-function basis sets are used, and the best energy is -1.2306 a.u., which is in reasonable agreement with the Hartree-Fock limit, -1.2999 a.u. Our best basis set is a four-term two-center expansion of the wave function with only one nonlinear variational parameter. Section 5 concludes the paper with a summary of the methods used to evaluate the integrals which arise in SCF calculations in the H₂⁺-type elliptical orbital basis.     

Intermolecular complexes of nido-C<Subscript>2</Subscript>B<Subscript>3</Subscript>H<Subscript>7</Subscript> with HF and LiH molecules: the theoretical studies,bonding properties and natural bond orbital (NBO) analysis

The changes in stabilization energy upon the formation of intermolecular hydrogen, dihydrogen and lithium bond complexes between C₂B₃H₇, LiH and HF have been investigated using MP2 method with aug-cc-pVDZ basis set. The interaction of HF with nido-C₂B₃H₇ could occur through the formation of B–H^?δ···^+δH–F, C–H^+δ···F^?δ–H and B–C···H–F classical and non-classical hydrogen bonds. The B–C bonds in backbone of the C₂B₃H₇ as electron donor interact with σ* orbital of HF as electron acceptor. Also interaction of LiH with nido-C₂B₃H₇ resulted in B–C···Li–H and B–H···LiH lithium bonds as well as C–H···H–Li dihydrogen bond complexes. In some of these complexes, LiH interacts with B–C bonds. Results are indicating that more stable complexes belong to interaction of HF and LiH with backbone of the nido-C₂B₃H₇. The AIM and NBO methods were used to analyze the intermolecular interactions; also the electron density at the bond critical point and the charge transfer of obtained complexes were studied.     

The reactions between negative hydrogen ions and silane

Contracted CI-calculations have been performed in order to find out the mechanisms of the reactions involved when negative hydrogen ions react with silane. There were initially severe problems to find a balanced basis set to describe the reactions including correlation, particularly for the choice of diffuse functions. Finally, in agreement with earlier calculations, SiH ₅ ^– was found to be more stable than SiH₄+H^– by 21 kcal/mol but less stable than SiH ₃ ^– and H₂ by 6 kcal/mol. A barrier in the S _N2 reaction SiH₄+H^– SiH₅ has previously been predicted by calculations, which was not confirmed by the present CI calculations. The lack of a barrier is in agreement with experimental evidence. Contrary to what is expected from the orbital symmetry rules, which predict two allowed pathways, SiH ₅ ^– does not dissociate easily to the lower lying SiH ₃ ^– + H₂. A barrier of 57 kcal/mol, which was very difficult to locate, was finally found. In order to explain the experimental observation of SiH ₃ ^– and the lack of observation of SiH ₅ ^– a different mechanism for the reaction SiH₄+H^– SiH ₃ ^– + H₂ is suggested. For a direct proton transfer a barrier of less than 10 kcal/mol is predicted.     

On the energy transfer at the radiolysis of CO-H2S gas mixture

The kinetics of hydrogen formation at various amounts of H₂S /1–60%/ in the radiolysis of CO–H₂S mixture has been studied. The ratio of the reaction rate constants for reactions CO^x+COproduct and CO^x+H₂SH+SH=CO, which amounts to 5×10^–2, has been estimated. The effective activation energy of hydrogen formation /E_eff/ has been determined at various amounts of H₂S in the temperature interval 323–573 K.     

金(I)配合物催化乙烯加氢的反应机理

采用密度泛函理论B3LYP方法, 对两类金(I)配合物AuX (X=F, Cl, Br, I)和AuPR₃⁺(R=F, Cl, Br, I, H, Me,Ph)催化C₂H₄加氢反应的机理进行了理论研究. 计算显示Au(I)配合物对C₂H₄氢化具有较好的催化效果, 其作用下的加氢反应存在“活化H―H键后再与C₂H₄反应”和“活化C＝C键后再与H₂反应”两种途径, 前者的活化能较后者低90-120 kJ·mol^-1, 因而具有明显的能量优势. 研究表明AuPR₃⁺ 的催化能力明显强于AuX. 此外, X/PR3基团供、吸电子能力的变化对配合物的催化能力也具有较为显著的影响. 电子结构分析显示Au(I)配合物在C₂H₄ 加氢反应中不仅能够削弱H―H、C＝C 键的强度, 还使H₂ σ_H―H^*、C₂H₄ π_C＝C^* 轨道能级下降, 从而缩小了π_C＝C-σ_H―H^*或σ_H―H-π_C＝C^*轨道间的能级差, 促进了C₂H₄-H₂反应中的电子离域, 从而降低禁阻反应发生的难度.σ_H―H^*、π_C＝C^*轨道能级改变量与加氢反应活化能E_a的降低值之间存在较好的一致性关系, 因此使上述轨道能级下降幅度越大的Au(I)配合物可以获得较好的催化效果.     

Study on Pair Correlation Energies of Isoelectronic Systems F^－, HF and H2F^＋

The intrapair and interpair correlation energies of F-, HF and H2F^ systems are calculated and analyzed using MP2-OPT2 method of MELD program with cc-PVSZ^* basis set. From the analysis of pair correlation energies of these isoelectronlc sysoterns, it is found that the 1sF^2 pair correlation energy is trans-ferable in these three isociectronic systems. According to the definition of pair correlation contribution of one electron pair to a system, the pair correlation contribution values of these three systems are calculated. The correlation contribution values of inner electron pairs and H—F bonding electron pair in HF molecule with those in H2F^ system are compared. The results indicate that the bonding effect of a molecule is one of the im-portant factors to influence electron correlation energy of the system. The comparison of correlation energy contributions in-cluding triple and quadruple excitations with those only includ-ing singles and doubles calculated with 6-311 G(d) basis set shows that the higher.excitation correlation energy contribution gives more than 2 % of the total correlation energy for these sys-tems.     

Minimization of the energy of a molecule with respect to nonlinear parameters of the basis set

We study characteristic features of minimization of the Hartree-Fock-Roothaan energy with respect to nonlinear parameters of the Gaussian basis set. We describe and apply regularization of the discrete Newton-Raphson method based on the analysis of eigenvalues of the Hessian matrix. We discuss results of groundstate energy calculations for the molecules LiH, CH⁺, CH^–, He₃ ²⁺, BH₂ ⁺, and H₂O in optimal ls-Gaussian basis sets. We find that, for molecules with four to six electrons, good accuracy is obtained with small basis sets consisting of ls-functions only.Translated from Teoreticheskaya i Éxperimental'naya Khimiya, Vol. 24, No. 2, pp. 215–218, March–April, 1988.