Interfragment Distance Research Articles

Approximations for angular momentum-conserved polyatomic vibrational-rotational sum and density of states under a central potential

An approximation is suggested for the calculation of the angular momentum-conserved rotational sum of states for polyatomic molecules under a central potential, based on an interpolation between high- J and low- J forms ( J = total angular momentum). A similar procedure is suggested for an approximation to the angular momentum-conserved polyatomic vibrational-rotational sum of states, which obviates a computationally intensive convolution integral. The procedure is checked against rigorous results with satisfactory results. It can be applied to various fragment symmetries in both the phase space limit and at arbitrary interfragment distance, which is of some interest in variational routines.

A valence bond description of bond dissociation energy curves

Bond dissociation energy curves have been calculated ab initio using the valence bond self-consistent field (VBSCF) method for CH3-Y molecules, with Y = F, OH, NH2, CH3, BH2, CN and NO. Basis sets of at least double-zeta polarization quality for first row atoms have been used. The VB wavefunction is expanded in terms of one covalent (CH3:Y) and two ionic (CH3 +Y- and CH3 -Y+) structures. All results were referenced to the perfect pairing generalized valence bond method. The VB curves for CH3-F were calculated using both the same orbitals for the different structures (SODS) and tailored (different) orbitals for the three different structures (TODS). Each of these model levels was examined further using purely localized fragment (CH3 and Y) orbitals (L-SODS and L-TODS) and allowing delocalization between the CH3 and Y fragments among the passive orbitals (D-SODS and D-TODS), where only the electron pair bond undergoing homolytic dissociation uses purely localized fragment orbitals. Only the two SODS model levels were used for the other CH3-Y molecules. The lower energy covalent structure curve for CH3-F is found to be flat and essentially repulsive at all theory levels. The close but higher energy CH3 +F- ionic structure curve has a deep minimum (R ,m)at 0⋅3-0≐4 Å larger interfragment distance R than the corresponding ground state equilibrium bond length R e. The resultant normal Morse-type shape ground state dissociation curve results from the steeply rising covalent-ionic off-diagonal (resonance) interactions dominating the widening covalent-ionic energy gap as R decreases from R m. Within the SODS model, passive electron delocalization contributes a surprisingly large ~ 11 kcal mol-1 to the calculated bond dissociation energy, mainly by stabilizing the CH3:F curve. TODS adds ~ 16 kcal mol-1 to De mainly by stabilizing the CH3 +F- structure energy. In the series, Y = F → OH NH2 CH3, (a) the covalent curve develops an ever deeper energy minimum, approaching its ground state R e, (b) the contributing weight of the CH3:Y structure to the ground state wavefunction, and the ionic-covalent energy gap steadily increase, and (c) R m for the CH3 +Y- structure moves out to larger values. CH3-BH2 fits into these trends where the lower energy ionic structure is CH3-BH2 +. CH3-CN has a 70% covalent weight at its R e. CH3-NO is ~ 67% CH3:NO and 24% CH3 +NO-. CH3-CN has a Morse-type covalent structure energy curve while CH3:NO is unbound. The last three molecular species have empty low-lying valence orbitals and their explicit effect on the electronic structure description and energy dissociation curves within the VBSCF framework remains to be examined. The results obtained here have direct relevance to the VBSCF study of reaction paths.

A Valence bond description of bond dissociation energy curves

Bond dissociation energy curves have been calculated ab initio using the valence bond self-consistent field (VBSCF) method for CH3-Y molecules, with Y = F, OH, NH2, CH3, BH2, CN and NO. Basis sets of at least double-zeta polarization quality for first row atoms have been used. The VB wavefunction is expanded in terms of one covalent (CH3:Y) and two ionic (CH3 +Y- and CH3 -Y+) structures. All results were referenced to the perfect pairing generalized valence bond method. The VB curves for CH3-F were calculated using both the same orbitals for the different structures (SODS) and tailored (different) orbitals for the three different structures (TODS). Each of these model levels was examined further using purely localized fragment (CH3 and Y) orbitals (L-SODS and L-TODS) and allowing delocalization between the CH3 and Y fragments among the passive orbitals (D-SODS and D-TODS), where only the electron pair bond undergoing homolytic dissociation uses purely localized fragment orbitals. Only the two SODS model levels were used for the other CH3-Y molecules. The lower energy covalent structure curve for CH3-F is found to be flat and essentially repulsive at all theory levels. The close but higher energy CH3 +F- ionic structure curve has a deep minimum (R ,m)at 0⋅3-0≐4 Å larger interfragment distance R than the corresponding ground state equilibrium bond length R e. The resultant normal Morse-type shape ground state dissociation curve results from the steeply rising covalent-ionic off-diagonal (resonance) interactions dominating the widening covalent-ionic energy gap as R decreases from R m. Within the SODS model, passive electron delocalization contributes a surprisingly large ~ 11 kcal mol-1 to the calculated bond dissociation energy, mainly by stabilizing the CH3:F curve. TODS adds ~ 16 kcal mol-1 to De mainly by stabilizing the CH3 +F- structure energy. In the series, Y = F → OH NH2 CH3, (a) the covalent curve develops an ever deeper energy minimum, approaching its ground state R e, (b) the contributing weight of the CH3:Y structure to the ground state wavefunction, and the ionic-covalent energy gap steadily increase, and (c) R m for the CH3 +Y- structure moves out to larger values. CH3-BH2 fits into these trends where the lower energy ionic structure is CH3-BH2 +. CH3-CN has a 70% covalent weight at its R e. CH3-NO is ~ 67% CH3:NO and 24% CH3 +NO-. CH3-CN has a Morse-type covalent structure energy curve while CH3:NO is unbound. The last three molecular species have empty low-lying valence orbitals and their explicit effect on the electronic structure description and energy dissociation curves within the VBSCF framework remains to be examined. The results obtained here have direct relevance to the VBSCF study of reaction paths.

Microcanonical variational theory of radical recombination by inversion of interpolated partition function, with examples: methyl + hydrogen atom, methyl + methyl

A simple interpolation scheme involving the logarithms of partition functions for initial and final states in a bond-fission reaction is used to represent, as a function of distance along the reaction coordinate, the total partition function for the transition state. The inverse Laplace transform of this partition function yields a distance-dependent state count for the transition state that serves as input for a variational routine incorporated into a standard RRKM calculation. In this way, the number of states of so-called transitional modes, in particular, is made to connect smoothly with the proper number of states of fragment rotations. The interpolation makes use of simple Morse potential for the breaking bond and one of two similar S-type switching functions: a one-parameter Gaussian and a two-parameter hyperbolic tangent, either of which gave similar results for the title recombinations, in essential agreement with experiment. It is shown that the negative temperature coefficient of a radical recombination arises primarily from the above types of switching functions, which cause a late switch (i.e., at large interfragment distance) to product configuration.

Proposed experimental probes of chemical reaction molecular dynamics in solution: ICN photodissociation

Knowledge of how translational and rotational motions are influenced by the solvent during the course of a photodissociation ‘‘half-collision’’ reaction in solution is of interest in itself and can also help our understanding of how thermally activated reactions take place in solution by means of fluctuations in translational and rotational motion. With this goal, the molecular dynamics of the photodissociation of the triatomic molecule ICN are compared in the gas phase and in Xe solution. The time evolution of the trajectories (particularly with respect to interfragment distance and CN orientation) and of the energy partitioning (particularly into fragment translational recoil and into rotation of the CN) are displayed. Two types of solution experiments are proposed and simulated, both closely related to recent gas phase studies by Dantus, Rosker, and Zewail. These experiments are designed to probe the detailed dynamics of chemical reactions in solution during the time period the reaction is in progress, in particular to reveal the dramatic effects of the solvent on translational motions and energies. Both are pump–probe experiments in which the first photon dissociates the ICN and the second induces fluorescence in the CN fragment. In the first type of experiment, which is particularly sensitive to fragment translational motion, the fluorescence intensity is measured as a function of photon energy and of time delay. In the second type of experiment, which is particularly sensitive to fragment rotation, in addition the angle between the polarizations of the pump and probe photons is varied. In the calculations presented here, the effect of the absorption of the photodissociation photon is treated using the classical Frank–Condon principle. The coupling between the assumed two upper electronic surfaces is taken into account semiclassically using a generalization to the condensed phase of the classical electron model of Miller and Meyer, which was applied to ICN photodissociation in the gas phase by Goldfield, Houston, and Ezra.

Theory of polyatomic photodissociation: adiabatic description of the dissociative state and the translation-vibration interaction

An adiabatic method for the evaluation of the nuclear wave function describing the final dissociative state and a rigorous description of the D state following adiabatic formulation are presented in this paper. The vibrational frequencies of the fragments are found to depend on the interfragment distance. The role of the translation-vibration interaction in polyatomic photodissociation is also discussed.

Scattering of protons by fission fragments

The scattering of protons emitted from the neck area of the fissioning nucleus by fission fragments has been computed by solving the time-independent part of the Schrodinger equation for the symmetric fission of 235U+n. The current density (j=(h/2 pi )/2mi)( psi *GRAD psi - Psi GRAD psi *) is calculated as a function of the final energy of the protons and the interfragment distance. It was found that the ratio of 'polar emission' to 'equatorial emission' decreases with the interfragment distance. The possibility of explaining the 'polar emission' and 'equatorial emission' phenomena as a scattering of protons by fission fragments is discussed.