A reformulation of the theory of unimolecular reactions

1978 ◽  
Vol 56 (10) ◽  
pp. 1389-1414 ◽  
Author(s):  
Andrew W. Yau ◽  
Huw O. Pritchard
Keyword(s):  
Energy Levels ◽  
Normal Modes ◽  
Present Theory ◽  
Vibration Energy ◽  
Unimolecular Reactions ◽  
Methyl Isocyanide ◽  
Master Equation Approach ◽  
Microscopic Reaction ◽  
Reaction Processes ◽  
Activated Complex

The theory of unimolecular reactions is reformulated in a way which makes no reference to the concepts of a transition state, a reaction coordinate, or of an activated complex: the present theory is based, instead, on a simple master-equation approach using the estimated positions and lifetimes of the rotation–vibration energy levels of the molecule. The fundamental basis of this reformulation is that the unimolecular rate is derived from the perturbation of the normal modes of internal relaxation of the reactant molecule by the microscopic reaction processes. The thermal decompositions of cyclobutane, cyclopropane, ethyl isocyanide, ethyl chloride, and methyl isocyanide are examined in detail, and it is shown that not only is the present theory much easier to use than is conventional RRKM theory, but also that it gives better results.An Appendix provides a set of algorithms required for these calculations.

The Pressure Dependance of Ion-Molecule Reaction Rate Coefficients: CH3+ + HCN/He

1985 ◽  
Vol 38 (2) ◽  
pp. 231 ◽  
Author(s):  
RG Gilbert ◽  
MJ McEwan
Keyword(s):  
Reaction Rate ◽  
Rate Coefficients ◽  
Molecule Reaction ◽  
Ion Molecule Reactions ◽  
Methyl Isocyanide ◽  
Microscopic Reaction ◽  
Energy Dependent ◽  
Collisional Energy Transfer ◽  
Activated Complex ◽  
Transfer Probability

Illustrative calculations are presented on the application to termolecular ion-molecule reactions of methods recently developed for the study of fall-off effects in neutral thermal unimolecular reactions. The energy-dependent microscopic reaction rate, k(E), is obtained from RRKM theory with activated complex parameters first estimated by using ab initio and spectroscopic data and then refined to yield the appropriate pressure-saturated rate. The collisional energy transfer probability distribution function, P(E,E′), is obtained by fitting the fall-off data, guided by information from trajectory calculations. Overall rate coefficients are computed from accurate solutions to the appropriate integral master equation. The illustrative calculations are for the CH3+ + HCN+He → C2H4N+ +He system. It is shown that pressure-dependent data for ion-molecule systems can yield reliable information on P(E,E′). Collisions with the bath gas (He) are comparatively weak, with the average downward energy transferred per collision being c. 8 kJ mol-1. The product of the reaction before any isomerization can occur is shown to be protonated methyl isocyanide , H3CNCH+.

scholarly journals The ultra-violet spectrum of magnesium hydride. 1.—The band at λ 2430

1929 ◽  
Vol 122 (790) ◽  
pp. 442-455 ◽  
Keyword(s):  
Fine Structure ◽  
General Structure ◽  
Energy Levels ◽  
Visible Region ◽  
Ultra Violet ◽  
Present Theory ◽  
Magnesium Hydride ◽  
Electronic Energy ◽  
Band Spectra ◽  
Electronic Energy Levels

The system of bands in the visible region of the emission spectrum of magnesium hydride is now well known. The bands with heads at λλ 5622, 5211, 4845 were first measured by Prof. A. Fowler, who arranged many of the strongest lines in empirical series for identification with absorption lines in the spectra of sun-spots. Later, Heurlinger rearranged these series in the now familiar form of P, Q and R branches, and considered them, with the OH group, as typical of doublet systems in his classification of the fine structure of bands. More recently, W. W. Watson and P. Rudnick have remeasured these bands, using the second order of a 21-foot concave grating, and have carried out a further investigation of the fine structure in the light of the present theory of band spectra. Their detection of an isotope effect of the right order of magnitude, considered with the general structure of the system, and the experimental work on the production of the spectrum, seems conclusive in assigning these bands to the diatomic molecule MgH. The ultra-violet spectrum of magnesium hydride is not so well known. The band at λ 2430 and the series of double lines in the region λ 2940 to λ 3100, which were recorded by Prof. Fowler in 1909 as accompanying the group of bands in the visible region, appear to have undergone no further investigation. In view of the important part played by hydride band spectra in the correlation of molecular and atomic electronic energy levels, it was thought that a study of these features might prove of interest in yielding further information on the energy states of the MgH molecule. The present paper deals with observations on the band at λ 2430; details of an investigation of the other features of the ultra-violet spectrum will be given in a later communication.

Refined Theory of Damped Axisymmetric Vibrations of Double-Layered Cylindrical Shells

1979 ◽  
Vol 21 (1) ◽  
pp. 33-37 ◽  
Author(s):  
Ŝ. Markuŝ
Keyword(s):  
Outer Layer ◽  
Loss Factor ◽  
Longitudinal Vibration ◽  
Cylindrical Shells ◽  
Strong Dependence ◽  
Normal Modes ◽  
Present Theory ◽  
Damping Capacity ◽  
Refined Theory ◽  
Vibration Modes

The governing differential equations of vibrations of double-layered cylindrical shells are derived from classical thinshell theory. The outer layer of the shell is assumed to be viscoelastic, possessing high damping capacity to control vibrations (loss factor, β = 0.3). Decoupled torsional and coupled radial-longitudinal vibration modes are analysed by the method of ‘damped normal modes’. The present theory refines Kagawa and Krokstad's former analysis (1)‡. The results obtained point to a strong dependence of mechanical losses upon the thickness-to-radius ratio, h1/ R, even in the case of axisymmetric modes. This phenomenon was not recognized in Kagawa-Krokstad's approach.

scholarly journals A variationally computed room temperature line list for AsH3

2019 ◽  
Vol 21 (6) ◽  
pp. 3264-3277 ◽  
Author(s):  
Phillip A. Coles ◽  
Sergei N. Yurchenko ◽  
Richard P. Kovacich ◽  
James Hobby ◽  
Jonathan Tennyson
Keyword(s):  
Room Temperature ◽  
Energy Levels ◽  
Vibration Energy ◽  
Line List ◽  
Temperature Line

Calculations are reported on the rotation–vibration energy levels of the arsine molecule with associated transition intensities.

Rotation-vibration energy levels of CH3

1991 ◽  
Vol 147 (2) ◽  
pp. 541-542 ◽  
Author(s):  
V. S̆pirko ◽  
W.P. Kraemer
Keyword(s):  
Energy Levels ◽  
Vibration Energy

Vibration energy levels of the PH3, PH2D, and PHD2 molecules calculated from high order potential energy surface

2009 ◽  
Vol 130 (24) ◽  
pp. 244312 ◽  
Author(s):  
Andrei V. Nikitin ◽  
Filip Holka ◽  
Vladimir G. Tyuterev ◽  
Julien Fremont
Keyword(s):  
Potential Energy ◽  
Potential Energy Surface ◽  
Energy Surface ◽  
Energy Levels ◽  
High Order ◽  
Vibration Energy

scholarly journals Relative normal modes for nonlinear Hamiltonian systems

2003 ◽  
Vol 133 (3) ◽  
pp. 665-704 ◽  
Author(s):  
Juan-Pablo Ortega
Keyword(s):  
Periodic Orbits ◽  
Energy Levels ◽  
Relative Equilibrium ◽  
Normal Modes ◽  
Hamiltonian Function ◽  
Isotropy Subgroup ◽  
Continuous Symmetry ◽  
Highly Nonlinear ◽  
Spatio Temporal ◽  
Energy And Momentum

An estimate on the number of distinct relative periodic orbits around a stable relative equilibrium in a Hamiltonian system with continuous symmetry is given. This result constitutes a generalization to the Hamiltonian symmetric framework of a classical result by Weinstein and Moser on the existence of periodic orbits in the energy levels surrounding a stable equilibrium. The estimate obtained is very precise in the sense that it provides a lower bound for the number of relative periodic orbits at each prescribed energy and momentum values neighbouring the stable relative equilibrium in question and with any prefixed (spatio-temporal) isotropy subgroup. Moreover, it is easily computable in particular examples. It is interesting to see how, in our result, the existence of non-trivial relative periodic orbits requires (generic) conditions on the higher-order terms of the Taylor expansion of the Hamiltonian function, in contrast with the purely quadratic requirements of the Weinstein–Moser theorem, which emphasizes the highly nonlinear character of the relatively periodic dynamical objects.

Calculation of Rotation–Vibration Energy Levels of the Water Molecule with Near-Experimental Accuracy Based on an ab Initio Potential Energy Surface

2013 ◽  
Vol 117 (39) ◽  
pp. 9633-9643 ◽  
Author(s):  
Oleg L. Polyansky ◽  
Roman I. Ovsyannikov ◽  
Aleksandra A. Kyuberis ◽  
Lorenzo Lodi ◽  
Jonathan Tennyson ◽  
...  
Keyword(s):  
Water Molecule ◽  
Potential Energy ◽  
Potential Energy Surface ◽  
Ab Initio ◽  
Energy Surface ◽  
Energy Levels ◽  
Vibration Energy ◽  
Experimental Accuracy

CALCULATION OF SELECTED HIGHLY EXCITED VIBRATIONAL STATES OF POLYATOMIC MOLECULES BY THE DAVIDSON ALGORITHM

2003 ◽  
Vol 02 (04) ◽  
pp. 609-620 ◽  
Author(s):  
FABIENNE RIBEIRO ◽  
CHRISTOPHE IUNG ◽  
CLAUDE LEFORESTIER
Keyword(s):  
Energy Levels ◽  
Normal Modes ◽  
Chem Phys ◽  
Polyatomic Molecules ◽  
Zero Order ◽  
Basis Set ◽  
Vibrational States ◽  
Diagonalization Method ◽  
Davidson Algorithm ◽  
High Overtone

We described an improved version of a modified Davidson scheme previously introduced (F. Ribeiro, C. Iung and C. Leforestier, Chem. Phys. Lett.362, 199 (2002)), aimed at computing highly excited energy levels of polyatomic molecules. The key ingredient is a prediagonalization-perturbation step performed on a subspace of a curvilinear normal modes basis set (including diagonal anharmonicities). The efficiency of the method is demonstrated by computing the lowest 350 vibrational states of A′ symmetry of the HFCO molecule. Also shown is the possibility to restrict the calculation to selected energy levels, based on their zero-order description. This State Filtered Diagonalization method is illustrated on a high overtone (7ν5) of the OCF bend, and on the few energy levels (20) which have been experimentally assigned up to 5000 cm -1 of excitation energy.

Sign in / Sign up

Export Citation Format

Share Document