George L. Heard

Properties of atoms in molecules: Transition probabilities

The transition probability for electric dipole transitions is a measurable property of a system and is therefore, partitionable into atomic contributions using the physics of a proper open system. The derivation of the dressed property density, whose averaging over an atomic basin yields the atomic contribution to a given oscillator strength, is achieved through the development of perturbation theory for an open system. A dressed density describes the local contribution resulting from the interaction of a single electron at some position r, as determined by the relevant observable, averaged over the motions of all of the remaining particles in the system. In the present work, the transition probability density expressed in terms of the relevant transition density, yields a local measure of the associated oscillator strength resulting from the interaction of the entire molecule with a radiation field. The definition of the atomic contributions to the oscillator strength enables one to determine the extent ...

The importance of ligand–ligand interactions in determining molecular geometry: the ligand close packing model

Abstract In 1960 Bartell proposed that interligand repulsions in some simple organic molecules of the types CX 3 and CX 4 , are much more important in determining molecular geometry than had previously been generally supposed. In recent work we have shown that this concept can be extended to analogous molecules of beryllium and boron where X is F, OH, or O. Assuming as Bartell did that each ligand can be approximately represented as a hard sphere we have shown that each ligand can be assigned a radius that decreases in the series BeX n , BX n , CX n as the ligand charge decreases with increasing electronegativity of the central atom. In this article we present results that further extend this work to other ligands, such as Cl, CH 3 and NH 2 and to other central atoms, in particular nitrogen and oxygen which, unlike Be, B and C, have lone pairs in their valence shells. Bartells original suggestion has now been developed into a useful and widely applicable model that we call the ligand close packing (LCP) model.

QTAIM analysis of the HF, HCl, HBr, and HOH elimination reactions of halohydrocarbons and halohydroalcohols.

The 1,2-HX elimination reaction (where X = F, Cl, Br, OH) has been established as an important reaction in the degradation of compounds introduced into the upper atmosphere, including common CFC replacement compounds. By analyzing the electron densities of the transition state geometries of these reactions using QTAIM, we see that we can divide these reactions into two types. For HF and HOH elimination, the transition state is a complete ring of bonds, and neither the C-H nor the C-X bonds have been broken at the maximum of energy. There is very little accumulation of electron density on the X atom, with the majority of charge being lost by the hydrogen atom undergoing elimination, being transferred on to the two carbon atoms. In HCl and HBr elimination, a similar loss of electron density of the hydrogen atom is accompanied by significant accumulation of electron density on the X atom and a smaller change in electron density on the carbon atoms. The C-X bond is broken in the transition state geometry, with no ring critical point being present. This may explain the relative stabilities of halohydrocarbons and haloalcohols with respect to loss of H-X.

Theoretical calculations of product percentage yields for the thermal decomposition of 2-chloro-1,1-difluoroethane

Abstract Theoretical calculations of the product percentage yields for the thermal decomposition of CHF 2 CH 2 Cl are consistent with the experimental percentage product yields supporting the proposal that the unexpected formation of 1,2-difluoroethene can be explained by a 1,2-FCl interchange converting CHF 2 CH 2 Cl into CHFClCH 2 F, which then undergoes a 2,1-HCl elimination. Thermal activation rate constants and threshold energy barriers for dominant reactions in this system were calculated. Theoretical product percentage yields varied greatly because different basis sets produced a wide range of threshold energy barriers, but the computational results were generally consistent with a recent experimental report.

A computational study of the threshold energies of the 1,2-FCl interchange reaction of chlorofluoroethanes

The 1,2-FCl rearrangement reaction of a series of haloethanes is investigated by comparisons of the optimized ground- and transition-state geometries. Investigation of the effect of level of theory...

Characterization of the 1,1-HF Elimination Reaction from the Competition between the 1,1-HF and 1,2-DF Unimolecular Elimination Reactions of CD3CD2CHF2

The recombination of CHF2 and C2D5 radicals was used to produce CD3CD2CHF2* molecules with 96 kcal mol(-1) of vibrational energy in a room temperature bath gas. The formation of CD3CD═CHF and CD3CD═CDF was used to identify the 1,2-DF and 1,1-HF unimolecular elimination channels; CD3CD═CDF is formed by isomerization of the singlet-state CD3CD2CF carbene. The total unimolecular rate constant is 1.6 × 10(6) s(-1), and the branching ratio for 1,1-HF elimination is 0.25. Threshold energies of 64 ± 2 and 73 ± 2 kcal mol(-1) were assigned to the 1,2-DF and 1,1-HF reaction channels. The E and Z isomers of 1-fluoropropene were observed for each reaction; approximately 30% of the CD3CD═CDF molecules derived from 1,1-HF elimination retained enough energy to undergo cis-trans isomerization. Electronic structure calculations with density-functional theory were used to characterize the transition-state structures and the H atom migration barrier for CD3CD2CF. Adjustment of the rate constants to account for kinetic-isotope effects suggest that the branching ratio would be 0.20 for 1,1-HF elimination from C2H5CHF2. The results from an earlier study of CD3CHF2 and CH3CHF2 are also reinterpreted to assign a threshold energy of 74 kcal mol(-1) for the 1,1-HF elimination reaction. Because CHF2CHF2* is generated in the photolysis system, the 1,1-and 1,2-HF-elimination reactions of CHF2CHF2* are discussed. The 1,1-HF channel was identified by trapping the CF2HCF carbene with cis-butene-2.

Unimolecular reactions of 1,1,1-trichloroethane, 1,1,1-trichloropropane, and 3,3,3-trifluoro-1,1,1-trichloropropane: determination of threshold energies by chemical activation.

The recombination of CCl3 radicals with CH3, CH3CH2, and CF3CH2 radicals was used to generate CH3CCl3, CH3CH2CCl3, and CF3CH2CCl3 molecules with approximately 87 kcal mol(-1) of vibrational energy in a bath gas at room temperature. The competition between collisional deactivation and unimolecular reaction by HCl elimination was used to obtain the experimental rate constants for each molecule. These experimental rate constants were matched to calculated statistical unimolecular rate constants to assign threshold energies to the three HCl elimination reactions. The models needed for the calculations of the rate constants were obtained from molecular structure calculations using density functional theory (DFT) with the hybrid density-functional MO6-2X recommended by Truhlar for transition states. The assigned threshold energies are 52 ± 2, 50 ± 2, and 52 ± 2 kcal mol(-1) for CH3CCl3, CH3CH2CCl3, and CF3CH2CCl3, respectively, and the CH3 and CF3 groups have only a minor effect on the threshold energies for HCl elimination. The DFT calculated threshold energies are in agreement with the experimentally assigned values. The addition of Cl atoms to the same carbon atom lowers the threshold energy for HCl elimination in the CH3CH2Cl, CH3CHCl2, and CH3CCl3 series. This trend, which is the opposite of that for CH3CH2F, CH3CHF2, and CH3CF3, is discussed in terms of transition-state structure and correlated with the relative stabilities of CH3CH2(+), CH3CHCl(+), and CH3CCl2(+) ions; the relative stabilities are based on the hydride affinities obtained from calculations. Comparison of the reactions of CH3CCl3 and CH2ClCHCl2 shows that the threshold energy is much higher for the isomer with chlorine atoms on both carbon atoms.

Unimolecular isomerization of CH2FCD2Cl via the interchange of Cl and F atoms: assignment of the threshold energy to the 1,2-dyotropic rearrangement.

The room-temperature gas-phase recombination of CH2F and CD2Cl radicals was used to prepare CH2FCD2Cl molecules with 91 kcal mol(-1) of vibrational energy. Three unimolecular processes are in competition with collisional deactivation of CH2FCD2Cl; HCl and DF elimination to give CHF═CD2 and CH2═CDCl plus isomerization to give CH2ClCD2F by the interchange of F and Cl atoms. The Cl/F interchange reaction was observed, and the rate constant was assigned from measurement of CHCl═CD2 as a product, which is formed by HF elimination from CH2ClCD2F. These experiments plus previously published results from chemically activated CH2ClCH2F and electronic structure and RRKM calculations for the kinetic-isotope effects permit assignment of the three rate constants for CH2FCD2Cl (and for CH2ClCD2F). The product branching ratio for the interchange reaction versus elimination is 0.24 ± 0.04. Comparison of the experimental rate constant with the RRKM calculated rate constant permitted the assignment of a threshold energy of 62 ± 3 kcal mol(-1) for this type-1 dyotropic rearrangement. On the basis of electronic structure calculations, the nature of the transition state for the rearrangement reaction is discussed. The radical recombination reactions in the chemical system also generate vibrationally excited CD2ClCD2Cl and CH2FCH2F molecules, and the rate constants for DCl and HF elimination were measured in order to confirm that the photolysis of CD2ClI and (CH2F)2CO mixtures was giving reliable data for CH2FCD2Cl.

Characterization of the 1,1-HCl Elimination Reaction of Vibrationally Excited CD3CHFCl Molecules and Assignment of Threshold Energies for 1,1-HCl and 1,2-DCl plus 1,1-HF and 1,2-DF Elimination Reactions.

Vibrationally excited CD3CHFCl molecules with 96 kcal mol(-1) of energy were generated by the recombination of CD3 and CHFCl radicals in a room-temperature bath gas. The four competing unimolecular decomposition reactions, namely, 1,1-HCl and 1,2-DCl elimination and 1,1-HF and 1,2-DF elimination, were observed, and the individual rate constants were measured. The product branching fractions are 0.60, 0.27, 0.09, and 0.04 for 1,2-DCl, 1,1-HCl, 1,2-DF, and 1,1-HF elimination, respectively. Electronic structure calculations were used to define models of the four transition states. The statistical rate constants calculated from these models were compared to the experimental rate constants. The assigned threshold energies with ±2 kcal mol(-1) uncertainty are 60, 72, 65, and 74 kcal mol(-1) for the 1,2-DCl, 1,1-HCl, 1,2-DF, and 1,1-HF reactions, respectively. The loose structure of the 1,1-HX transition states, which is exemplified by the order of magnitude larger pre-exponential factor relative to the 1,2-HX elimination reactions, compensates for the high threshold energy; thus, the 1,1-HX elimination reaction rates can compete with the 1,2-HX elimination reactions for high levels of vibrational excitation in CD3CHFCl. The 1,1-HCl and 1,1-HF reactions are observed via the CD2═CDF and CD2═CDCl products formed from isomerization of the CD3CF and CD3CCl carbenes. These D-atom migration reactions are discussed, and the possibility of tunneling is evaluated. The transition states developed from the 1,1-HCl and 1,1-HF reactions of CD3CHFCl are compared to models for the HCl and HF elimination reactions of CHF2Cl, CHFCl2, and CH2FCl.

Characterization of the Unimolecular Water Elimination Reaction from 1-Propanol, 3,3,3-Propan-1-ol-d3, 3,3,3-Trifluoropropan-1-ol, and 3-Chloropropan-1-ol

The unimolecular reactions of 1-propanol, 3,3,3-propan-1-ol-d3, 3,3,3-trifluoropropan-1-ol, and 3-chloropropan-1-ol have been studied by the chemical activation technique. The recombination of CH3, CD3, CF3, and CH2Cl radicals with CH2CH2OH radicals at room temperature was used to generate vibrationally excited CH3CH2CH2OH, CD3CH2CH2OH, CF3CH2CH2OH, and CH2ClCH2CH2OH molecules. The principal unimolecular reaction for propanol and propanol-d3 with 90 kcal mol(-1) of vibrational energy is 1,2-H2O elimination with rate constants of 3.4 x 10(5) and 1.4 x 10(5) s(-1), respectively. For CH2ClCH2CH2OH also with 90 kcal mol(-1) of energy, 2,3-HCl elimination with a rate constant of 3.0 x 10(7) s(-1) is more important than 1,2-H2O elimination; the branching fractions are 0.95 and 0.05. For CF3CH2CH2OH with an energy of 102 kcal mol(-1), 1,2-H2O elimination has a rate constant of 7.9 x 10(5) and 2,3-HF elimination has a rate constant of 2.6 x 10(5) s(-1). Density functional theory was used to obtain models for the molecules and their transition states. The frequencies and moments of inertia from these models were used to calculate RRKM rate constants, which were used to assign threshold energies by comparing calculated and experimental rate constants. This comparison gives the threshold energy for H2O elimination from 1-propanol as 64 kcal mol(-1). The threshold energies for 1,2-H2O and 2,3-HCl elimination from CH2ClCH2CH2OH were 59 and 54 kcal mol(-1), respectively. The threshold energies for H2O and HF elimination from CF3CH2CH2OH are 62 and 70 kcal mol(-1), respectively. The structures of the transition states for elimination of HF, HCl, and H2O are compared.