Temperature dependence of OH(8;6) equilibration in an air-like gas ensemble

We present a quantum state-resolved computational investigation of the equilibration of rovibrationally excited OH, present as the minor component in an air-like mixture of N(2) and O(2), over the temperature range 100-1200 K. Generic features of the equilibration that are present over the entire range are identified, and the increase in speed of the principal energy exchange mechanism as the temperature increases is quantified. The data demonstrate that partitioning of excess energy and angular momentum among the modes of the three different molecules is independent of the magnitude of excess energy and of its form. The rotational temperature of OH is found to vary widely over the equilibration process, varying with number of collision cycles and with initial temperature. However, at equilibration, the rotational temperature of OH is invariably the lowest of all modes of all three species present in the ensemble. This suggests that rotational temperatures of OH obtained from rotational state populations are unlikely to provide a reliable guide to other modal temperatures in ensembles of the kind we consider.     

Non-statistical energy partitioning in the gas phase reactions of polyatomic molecules

The internal energy distributions in the HF products from the reactions of F atoms with H₂CO and HFCO have been determined via arrested-relaxation infrared chemiluminescence experiments. The results show that the HF vib-rotational levels are strongly excited and suggest that the HCO and FCO radical products are created with excitation in the ν₁ (asymmetric stretch) and ν₂ (bend) modes respectively.     

Fragment state distribution,energy partitioning and rotational alignment in the state-to-state photodissociation of methylnitrite

The photodissociation of methylnitrite, CH₃ONO, generates vibrationally, rotationally, and translationally excited NO and CH₃O fragments. Following selective excitation via the localizedS ₁(nπ*) ←S ₀ transition into different overtones (v′=1, 2, 3) of theN=0 stretching modeν ₃, the complete state distribution and the energy partitioning of the NO fragment was determined. For the CH₃O fragment the complete energy, the translational energy and the sum of the rotational and vibrational energy was obtained. Owing to strong exit channel interactions between the initialν ₃ mode and the translational and rotational motions, the fragment energy redistribution is highly selective with respect to the vibrational excitation and alignment of NO. Energywise the CH₃O moiety behaves almost like a spectator. Furthermore the rotational alignment \(\overline {A_0^{(2)} } \) of NO(v″) in the populated vibrational states (v″ = 0, 1, 2, 3) was measured as a function of the initial overtone excitation. In accord with theoretical predictions based on an ab initioS ₁-potential surface, the highest geometrical selectivity of the dissociation process is obtained when the vibrational quantum numbersv′ ofν ₃ andv″ of NO are the same. With increasing mismatch the deviation from a planar dissociation process is increasing.     

Global energy minimization by rotational energy embedding

Given a sufficiently good empirical potential function for the internal energy of molecules, prediction of the preferred conformations is nearly impossible for large molecules because of the enormous number of local energy minima. Energy embedding has been a promising method for locating extremely good local minima, if not always the global minimum. The algorithm starts by locating a very good local minimum when the molecule is in a high-dimensional Euclidean space, and then it gradually projects down to three dimensions while allowing the molecule to relax its energy throughout the process. Now we present a variation on the method, called rotational energy embedding, where the descent into three dimensions is carried out by a sequence of internal rotations that are the multidimensional generalization of varying torsion angles in three dimensions. The new method avoids certain kinds of difficulties experienced by ordinary energy embedding and enables us to locate conformations very near the native for avian pancreatic polypeptide and apamin, given only their amino acid sequences and a suitable potential function.     

Assessing an impulsive model for rotational energy partitioning to acetyl radicals from the photodissociation of acetyl chloride at 235 nm

This work uses the photodissociation of acetyl chloride to assess the utility of a recently proposed impulsive model when the dissociation occurs on an excited electronic state that is not repulsive in the Franck-Condon region. The impulsive model explicitly includes an average over the vibrational quantum states of acetyl chloride when it calculates an impact parameter for fission of the C-Cl bond, as well as the distribution of thermal energy in the photolytic precursor. The experimentally determined stability of the resulting acetyl radical to subsequent dissociation is the key observable that allows us to test the model's ability to predict the partitioning of energy between rotation and vibration of the radical. We compare the model's predictions for three different assumed geometries at which the impulsive force might act, generating the relative kinetic energy and the concomitant rotational energy in the acetyl radical. Assuming that the impulsive force acts at the transition state for C-Cl fission on the S(1) excited state gives a poor prediction; the model predicts far more energy in rotation of the acetyl radical than is consistent with the measured velocity map imaging spectrum of the stable radicals. The best prediction results from using a geometry derived from the classical trajectory calculations on the excited state potential energy surface. We discuss the insight gained into the excited state dissociation dynamics of acetyl chloride and, more generally, the utility of using the impulsive model in conjunction with excited state trajectory calculations to predict the partitioning of internal energy between rotation and vibration for radicals produced from the photolysis of halogenated precursors.     

Translational to rotational energy transfer in molecule-surface collisions

A theoretical approach that combines classical mechanics for treating translational and rotational degrees of freedom and quantum mechanics for describing the excitation of internal molecular modes is applied to the scattering of diatomic molecules from metal surfaces. Calculations are carried out for determining the extent of energy transfer to the rotational degrees of freedom of the projectile molecule. For the case of observed spectra of intensity versus final rotational energy, quantitative agreement with available experimental data for the scattering of NO and N(2) from close packed metal surfaces is obtained. It is shown that such measurements can be used to determine the average rotational energy of the incident molecular beam. Measurements of the exchange of energy between translational and rotational degrees of freedom upon collision are also described by calculations for these same systems.     

M-dependence of collisional transfer of rotational energy in methanol

An M-resolved microwave double resonance experiment on methanol is described. Relative signal intensities and M-selection rules in pure CH₃OH are consistent with a dipole—dipole collisional interaction, while those for CH₃OHHe and CH₃OHH₂ mixtures indicate more complex interactions.     

Hartree-Fock energy partitioning in terms of Hirshfeld atoms.

A Hirshfeld decomposition scheme of the Hartree-Fock total molecular energy into atomic energies is presented. The calculations are performed by direct numerical integration and the results are compared for a set of 28 molecules containing different kinds of atoms. The calculated atomic energies show a strong dependency on changes of atomic electron population and hybridization. Linear correlations are found between the energy and the population for H, these being related to the electronegativity of this atom and to the external potential created by the remaining atoms. The proposed energy partitioning scheme appears to be useful for studies such as proton acidity, the anomeric effect and group transferability, and allows atomic virial ratios to be obtained. Finally, the atomic potential energies are found to mimic trends based on exact expressions as well as trends displayed by molecular quantities, thus lending credibility to the partitioning scheme used.     

A comment on SCF energy partitioning schemes

Starting from the symmetry groupG × SU(2) for the special case of negligible spin-orbit coupling, a general character formula is derived for them-tuplet representation, which is realized in the space of state functions ofn-electron systems in fields with symmetryG. Apart from the characters of the initial representation for the single electron space function, the formula only contains the number of particlesn and the multiplicitym.

Herrn Professor Dr. Hermann Hartmann zu seinem 60. Geburtstag gewidmet.     

Vibrational and rotational energy transfer in Ar + HF

State-to-state energy transfer cross sections for Ar + HF (v = 2, 4, and 6; J = 4, 6, 8, and 10) were computed using quasiclassical trajectories. Rotational energy transfer is invariant with increasing v, but vibrational energy transfer is significantly enhanced by increasing J.     

Catchment region partitioning of energy hypersurfaces,I

The space of internal coordinates of a molecular system is partitioned into catchment regions of various critical points of the energy hypersurface. The partitioning is based on an ordering of steepest descent paths into equivalence classes. The properties of these catchment regions and their boundaries are analyzed and the concepts of chemical structure, reaction path and reaction mechanism are discussed within the framework of the Born-Oppenheimer and energy hypersurface approximations. Relations between catchment regions and the chemically important reactive domains of energy hypersurfaces, as well as models for branching of reaction mechanisms, caused by instability domainsD , 1, are investigated.     

Ab initio study of the rotational energy barrier in carbonylylide

The rotational energy barrier in carbonylylide CH₂OCH₂ is studied using RHF CI calculations. Depending on the size of the CI and the basis set (STO-3G and 4–31G), values in the range 13–17 $\text{kcal}\text{mol}$ are found. At this level of calculation, the mid-point of the isomerization process can be mainly described by the diradical rather than the zwitterion.     

Vibrational and rotational energy transfer upon molecular collisions

The cross section of the rotational and vibrational energy transfer is derived by using the first Born approximation which quantizes the translational motion of the colliding particles. The theory developed here integrates the intermolecular potential V(R) over all regions of the internuclear distance R by obtaining a Fourier transform of V(R). This differs from previous semiclassical (impact-parameter) treatments which either considered the short-range repulsive interaction or expanded V(R) into a long-range multipole expansion. The cross section obtained here is expressed in a very simple algebraic expression which can be readily calculated. This will be illustrated by examples of CO₂(001)+N₂(υ=0)=CO₂(000)+N₂(υ=1)+18.6 cm^?1 and CO(υ=1)+CO(υ=1)=CO(υ=0)+CO(υ=2)+27 cm^?1. Calculations have been made both for the exothermic and for the endothermic reactions. The comparison of the present results with experimental results as well as with previously calculated results will be discussed.     

Partitioning of methyl internal rotational barrier energy of thioacetaldehyde

The nature of methyl internal rotational barrier in thioacetaldehyde has been investigated by relaxation effect, natural bond orbital (NBO) analysis and Pauling exchange interactions. The true experimental barrier can be obtained by considering fully relaxed rotation. Nuclear-electron attraction term is a barrier forming term in the fully relaxed rotation, but it appears as an antibarrier for rigid rotation. It is seen that during methyl rotation, the torsional mode is coupled with the aldehydic hydrogen out-of-plane wagging motion. Natural bond orbital analysis shows that the principal barrier forming term originates from the C-C bond. The lengthening of the C-C bond is explained by considering charge transfer interaction between several bonding and antibonding orbitals in the C-C bond region, which leads to higher bonding overlap for the eclipsed conformer compared to the staggered conformer. S-C(σ)/C^me-Hp and C-H_ald/C_me-H_op interactions appear to be the main barrier-forming Pauling exchange terms but have less contribution to make to the barrier compared to the C-C bond interaction.     

Constant energy partitioning in the photoionization of NO and O2

Published data on the photoelectron spectra of NO and O₂ are analyzed, and the energy distributions are found to have averages proportional to the available energy. Hence, vibration takes a constant fraction of the energy. Average distributions are found as a function of the fraction of available energy.     

Determination of the rotational energy barriers of atropisomeric polychlorinated biphenyls

A spectrophotometric method for the simultaneous determination of Co, Cu, and Fe in ternary mixtures by means of 1,10-phenanthroline as a complexing agent was developed. The influence of chemical variables affecting the analytical reaction was evaluated. A principal component regression procedure was used to assess spectrophotometric data obtained from nineteen calibration solutions. The method was validated by applying it to the analysis of synthetic mixtures over the concentration ranges 0–407 μmol Co/L, 0–189 μmol Cu/L, and 0–143 μmol Fe/L. It was also successfully employed for the analysis of two cobalt magnetic alloys. The relative errors in the determinations were less than 7% in most cases.     

Direct measurement of single and ensemble average particle-surface potential energy profiles

This work involves the development of a novel technique that integrates total internal reflection and video microscopy methods to simultaneously measure single particle and ensemble average particle-surface interactions. For the 2 mum silica colloids and glass coverslip used in this study, particle size polydispersity is found to be a dominant factor in determining the distribution of single particle profiles about ensemble average profiles. In conjunction with this observation, chemical and physical nonuniformity are not evident in any of our measurements even with sensitivity to interactions on the order of kT. One advantage of using ensemble averaging in conjunction with time averaging is the ability to dramatically decrease the time required to measure average particle-wall interactions which scales inversely with interfacial particle concentration. A number of experimental issues are addressed in the development of this technique including (1) combining single particle distribution functions, (2) statistical sampling of distribution functions using both time and ensemble averaging, and (3) correcting overlapping scattering signals between adjacent particles. The capabilities of the ensemble averaging technique are also demonstrated to provide unique measurements of particle-surface interactions in metastable systems by selecting only height excursions of levitated particles when calculating potentials. Ultimately, this new technique provides several important advantages over single particle measurements, which provides a foundation for measuring interactions in increasingly complex interfacial systems.     

Electronic effect on the rotational energy of a diatomic molecule

The rotational hamiltonian for a diatomic molecule has been rederived from the total classical hamiltonian. This procedure directly introduces the effect of electronic motion which is ordinarily neglected in zero-order approximation. Kronig's rotational hamiltonian is discussed and shown to be an approximation of our findings. Our general result is then specialized to ¹Σ states, and the theory tested by calculating the observed fractional discrepancy between the experimentally determined H³⁵Cl energy level constant Y₀₂ and its predicted value from Dunham's theory. When all corrections are summed, the results are in good agreement with experiment.