Estimation of carbon-carbon bond lengths and medium-range internuclear distances by solid-state nuclear magnetic resonance.

We describe magic-angle-spinning NMR methods for the accurate determination of internuclear dipole-dipole couplings between homonuclear spins-(1/2) in the solid state. The new sequences use symmetry principles to treat the effect of magic-angle sample-rotation and resonant radio frequency fields. The pulse-sequence symmetries generate selection rules which reduce the interference of undesirable interactions and improve the robustness of the pulse sequences with respect to chemical shift anisotropies. We show that the pulse sequences may be used to estimate distances between 13C spins in organic solids, including bond lengths in systems with large chemical shift anisotropies, such as conjugated systems. For bond-length measurements, the precision of the method is +/-2 pm with a systematic overestimate of the internuclear distance by 3 +/- 1 pm. The method is expected to be a useful tool for investigating structural changes in macromolecules.     

Dependence of energies on the bond lengths in molecules and crystals

The dependence of the binding energies in molecules and crystals on the interatomic distances near the equilibrium position was established in the framework of the Mie equation using the force constants of molecules and the elasticity moduli of solids. To evaluate the repulsion forces, we used the Morse function for molecules and the Born-Landé approach for ionic crystals.     

Self-consistent group calculations on polyatomic molecules V. Molecules with a double or triple bond

SCGF calculations are reported for the ground state of ethylene, formaldehyde, acetylene and hydrogen cyanide. A minimum basis of contracted Gaussians was used and optimum hybridization was determined for each of the molecules by systematic variation of the hybridization parameters until the total electronic energy was a minimum. Properties of CH bonds as well as CC, CO and CN σ and π bonds are discussed in some detail. The results show that the assumption of transferable framework integrals β, basic to all semiempirical methods of calculating molecular wave functions, is strictly justified within the SCGF method.     

Valence bond studies of AH2 molecules

Minimal basis set (STO) molecular orbital and valence-bond calculations are reported for the³ B ₁ and¹ A ₁ states of CH₂. The open-shell molecular orbital calculations used the Roothaan formulation. The valence-bond calculations used the Prosser-Hagstrom biorthogonalisation technique to evaluate the cofactors required in using Löwdin's formulae. Optimisation of geometry and orbital exponents in the molecular orbital calculation on the³ B ₁ state gave a geometry of R_C-H=2.11 a.u. and H-C-H=123.2 °. The energy obtained was ?38.8355 a.u. The molecular orbital and valencebond calculations are compared. In the valence-bond calculations the variation with bond-length and bond-angle of the configuration energies was studied. Valence bond “build-up” studies are also reported. Valence-bond calculations using hybrid orbitals instead of natural atomic orbitals showed that the perfect-pairing approximation is not as good for CH₂ as BeH₂. The nature of the lone-pair and bonding orbitals is found to be significantly different between the³ B ₁ and¹ A ₁ states. In the³ B ₁ state the 2s and 2p orbitals are fairly equally mixed between both types of orbital. However in the¹ A ₁ state the bonding orbitals have mainly 2p character and the lone pair orbitals have mainly 2s character. As was found for H₂O, the bonding hybrid orbitals do not follow the hydrogen nuclei as the bond angle varies but continue to point approximately in their equilibrium directions.     

The relation between Sb-I bond lengths and charges on iodine atoms determined by 127I Mössbauer spectroscopy

We have compared the ¹²⁷I Mössbauer spectra of eleven organoantimony compounds with hypervalent bonding, E-Sb-I (E = O, I, N, C ). The charges on iodine atoms fall between -0.54 e for the compound with Sb-I bond length of 2.83 Å and -0.82 e for the compound with 3.34 Å. The negative charges on iodine atoms have been found to increase with the increase in the Sb-I bond lengths. Regarding to the dependence of the kind of E atoms, the negative charges on iodine atoms have been found to decrease with the increase in the electronegativities of E atoms. ¹²¹Sb Mössbauer spectra have shown the decrease of the group oxygen electronegativity of hexafluorocumyl alcohol by substituting CF₃ for CH₃, and this was reflected through O-Sb-I bonding as the increase in the negative charges of iodine atoms in the ¹²⁷I Mössbauer spectra.     

Valence bond and molecular orbital studies of the A-F bond lengths in some AFn type molecules and their fluorinated cations

The results of ab initio MP2(full)/cc-pVTZ and DFT MPW1PW91/cc-pVTZ molecular orbital calculations of the bond lengths are reported for non-hypercoordinate and hypercoordinate systems of the general type AF_n^q+, with q≥0 and A = N, P, O, S and Cl. They show that except for OF₄²⁺ the bond lengths decrease as the cationic character increases. Increased-valence structures are used to provide valence bond (VB) rationalizations for the bond length shortenings. In these valence bond structures, the degree of multiple bonding increases as the cationic character increases.     

Variation of calculated single bond lengths in saturated hydrocarbon and silicon hydride molecules

A series of saturated X_nH_m (X being either C or Si) molecules is studied using the MINDO /3 and MNDO quantum-chemistry procedures. We find that the proximity of H atoms tends to shorten X? X bonds, and that this effect is (especially for MINDO /3) much larger than a similar trend in experimental values. The connection between this and hybridization values calculated from localized orbitals is investigated. It is found that the hybridization model works well for X? H bonds, whereas for X? X bonds non-σ-bond effects also play a significant role. It is shown that the changes in electronic structure may be directly connected to differences in X and H atomic levels, so that similar bond length differences may be expected in other molecular orbital calculations.     

The role of water in lanthanide-catalyzed carbon-carbon bond formation

Luminescence-decay measurements in combination with high-performance liquid chromatography analyses were used to study the relationship between rates of catalysis and water-coordination numbers of europium-based precatalysts in the aqueous Mukaiyama aldol reaction. A correlation between reactivity and water-coordination number was observed and is reported here.     

Description of equilibrium bond lengths with the use of spectroscopic parametrization of the CNDO method including transition metals

Lensovet Leningrad Technological Institute. Plastpolimer Okhta Scientific-Production Association. Translated from Zhurnal Strukturnoi Khimii, Vol. 32, No. 4, pp. 22–28, July–August, 1991.     

To the theory of electron scattering by polyatomic molecules

Within the Born-Oppenheimer adiabatic perturbation theory, an equation was obtained for the intensity of fast electron scattering by polyatomic molecules. All of its parameters are explicitly defined by vibronic interaction in a molecule; due to this, quantum chemical calculations are fully applicable to electron diffraction studies of molecular geometries. Engels Anti-Aircraft Missile Higher Military School. Translated fromZhurmal Strukturnoi Khimii, Vol. 35, No. 2, pp. 40–45, March–April, 1994. Translated by L. Smolina     

The rotational structure of three-photon resonances of polyatomic molecules

A general formulation of the selection rules and line strengths of three-photon excitation spectra is presented for molecules of arbitrary symmetry. For symmetric-top molecules the paper extends the discussion by Nieman in the context of rovibronic transitions of NH₃. For asymmetric-top molecules it is shown that the rotational line strengths can be sensitive to quantum-mechanical interference between contributions from the various components of the three-photon vibronic transition tensor. This transition tensor is discussed within a perturbation-theory framework in terms of several models of intermediate-state participation.     

Differential and total (e,2e) cross sections of simple polyatomic molecules

In this paper, we present a theoretical approach to calculate differential and total ionization cross sections of polyatomic molecules by fast electron impact. More exactly, we have studied the ionization of ammonia (NH(3)) and methane (CH(4)) molecules, and previous results concerning the H(2)O molecule ionization are reported for comparison. The calculations are performed in the distorted wave Born approximation without exchange by employing the independent electron model. The molecular target wave functions are described by linear combinations of atomic orbitals. To describe the interaction between the inactive target electrons and the slow ejected electron, we have introduced a distortion via an effective potential calculated for each molecular orbital. The present theoretical calculations agree well with a large set of existing experimental data in terms of multiple differential and total cross sections.     

A simple method for quantitative estimation of C-H bond lengths in hydrocarbon radical cations

A quantitative correlation between deviations of the C-H bond lengths of hydrocarbon molecules during their adiabatic single ionization and isotropic hyperfine coupling constants with protons of their primary radical cations (RC) was established. A simple method for estimation of the C-H bond lengths of hydrocarbon RC was proposed on the basis of the correlation found. Specific features of the structure of the RC of methane and severaln-alkanes of the general formula [H^*(CH_{2 n} H^*]⁺,n = 0 to 12, were analyzed. A widely used empirical rule, according to which deprotonation of hydrocarbon RC during the ion-molecular process is determined by the proton possessing the highest spin density, was refined and geometrically substantiated.     

A spectroscopic investigation of carbon-carbon bond formation by methylene insertion on a Ag(111) surface: mechanism and kinetics

Using reflection-absorption infrared spectroscopy (RAIRS) and temperature-programmed reaction spectroscopy (TPRS), we have investigated the cross-coupling reaction between CH(2)(a) and CF(3)(a) on a Ag(111) surface. CH(2)(a) and CF(3)(a) are generated by thermal decomposition of adsorbed CH(2)I(2) and CF(3)I. RAIRS results unambiguously demonstrate that CH(2)(a) inserts into the Ag-CF(3) bond to produce adsorbed CF(3)CH(2)(a), which upon heating selectively undergoes beta-fluorine elimination to form CH(2)=CF(2). Increasing the CH(2)(a) and CF(3)(a) coverage leads to the sequential insertion of CH(2)(a) into Ag-CF(3), as evidenced by CH(2)CH(2)CF(3)(a) formation detected with RAIRS. Prior to the insertion reaction, the evidence favors islanding of fragments. The methylene insertion reaction is so facile that it occurs at cryogenic temperatures (120 K). Time-resolved RAIRS (TR-RAIRS) results at selected temperatures reveal an activation energy of 5.8 kJ/mol. Our results provide, for the first time, direct spectroscopic information about the mechanism and kinetics of the methylene insertion reaction.     

A theoretical study of carbon-carbon bond formation by a Michael-type addition

A theoretical study of the Michael-type addition of 1,3-dicarbonyl compounds to α,β-unsaturated carbonyl compounds has been performed in the gas phase by means of the AM1 semiempirical method and by density functional theory (DFT) calculations within the B3LYP and M06-2X hybrid functionals. A molecular model has been selected to mimic the role of a base, which is traditionally used as a catalyst in Michael reactions, an acetate moiety to modulate its basicity, and point charges to imitate the stabilization of the negative charge developed in the substrate during the reaction when taking place in enzymatic environments. Results of the study of six different reactions obtained at the three different levels of calculations show that the reaction takes place in three steps: in the first step the α proton of the acetylacetone is abstracted by the base, then the nucleophilic attack on the β-carbon of the α,β-unsaturated carbonyl compound takes place generating the negatively charged enolate intermediate, and finally the product is formed through a proton transfer back from the protonated base. According to the energy profiles, the rate limiting step corresponds to the abstraction of the proton or the carbon-carbon bond formation step, depending on substituents of the substrates and method of calculation. The effect of the substituents on the acidity of the α proton of the acetylacetone and the steric hindrance can be analyzed by comparing these two separated steps. Moreover, the result of adding a positive charge close to the center that develops a negative charge during the reaction confirms the catalytic role of the oxyanion hole proposed in enzyme catalysed Michael-type additions. Stabilization of the intermediate implies, in agreement with the Hammond postulate, a reduction of the barrier of the carbon-carbon bond formation step. Our results can be used to predict the features that a new designed biocatalyst must present to efficiently accelerate this fundamental reaction in organic synthesis.