On the Probability Density of the Nuclei in a Vibrationally Excited Molecule

The mechanism of IR multiple photon excitation through the dense manifold of vibrational states, usually called the quasicontinuum, of a vibrationally excited molecule is one of the unresolved issues in the field of laser chemistry. The effects of deuterium substitution on propylene IR multiple photon excitation are used to identify the vibrational modes leading to efficient excitation. Optoacoustic energy deposition data show that for propylene, 3 μm multiple photon excitation occurs most efficiently at the methyl group, and furthermore that efficient methyl group excitation requires the CH group on the adjacent carbon. Thus 3 μm multiple photon excitation of propylene, while involving energy deposition directly into several spatially discrete intramolecular groups, is found to be enhanced by specific intramolecular couplings. Implications of this result for mechanisms of IR multiple photon excitation are discussed.

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MULTISTAGE DEACTIVATION IN THE PHOTOLYSIS OF HEXAFLUOROACETONE

Canadian Journal of Chemistry ◽

10.1139/v64-207 ◽

1964 ◽

Vol 42 (6) ◽

pp. 1345-1354 ◽

Cited By ~ 15

Author(s):

A. N. Strachan ◽

R. K. Boyd ◽

K. O. Kutschke

Keyword(s):

Vibrational Energy ◽

Excited Molecule ◽

Single Step ◽

Inert Gases ◽

Ultraviolet Region ◽

Vibrationally Excited ◽

Vibrational Levels ◽

New Treatments ◽

Lower Group ◽

Vibrational Equilibrium

In principle the vibrationally excited molecule in an upper electronic state, formed by absorption in the ultraviolet region of the spectrum, can attain vibrational equilibrium by two mechanisms. In most discussions of this degradation of vibrational energy it has been considered that the data are represented adequately by a single-step deactivation from high to low vibrational levels rather than by a multistep cascade from one group of vibrational levels to the next lower group. The present work suggests new treatments of the experimental data by which it is possible to distinguish between the single- and the multi-step deactivation processes. It is demonstrated that the literature data on the quantum yield for the decomposition of hexafluoroacetone is better interpreted in terms of a multistep deactivation. Some new data are presented which support this conclusion.Methods to evaluate the efficiencies as deactivating agents of added inert gases are discussed. It is suggested that the deactivation of excited hexafluoroacetone by hydrocarbons might involve chemical rather than, or in addition to, purely physical quenching.

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Nonparametric estimation of the quadratic functional of multimodal probability density

Metrologiya ◽

10.32446/0132-4713.2019-3-17-2910.32446/ ◽

2019 ◽

pp. 17-29

Author(s):

А. V. Lapko ◽

V. A. Lapko

Keyword(s):

Probability Density ◽

Nonparametric Estimation ◽

Quadratic Functional

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Modified algorithm for fast bandwidth selection for kernel estimates of multidimensional probability densities

Izmeritel`naya Tekhnika ◽

10.32446/0368-1025it.2020-11-9-13 ◽

2020 ◽

pp. 9-13

Author(s):

A. V. Lapko ◽

V. A. Lapko

Keyword(s):

Probability Density ◽

Optimal Parameter ◽

Random Variables ◽

Kernel Functions ◽

Independent Random Variables ◽

Functional Dependencies ◽

Approximation Properties ◽

Probability Density Estimation ◽

Multidimensional Probability ◽

Selection Of

An original technique has been justified for the fast bandwidths selection of kernel functions in a nonparametric estimate of the multidimensional probability density of the Rosenblatt–Parzen type. The proposed method makes it possible to significantly increase the computational efficiency of the optimization procedure for kernel probability density estimates in the conditions of large-volume statistical data in comparison with traditional approaches. The basis of the proposed approach is the analysis of the optimal parameter formula for the bandwidths of a multidimensional kernel probability density estimate. Dependencies between the nonlinear functional on the probability density and its derivatives up to the second order inclusive of the antikurtosis coefficients of random variables are found. The bandwidths for each random variable are represented as the product of an undefined parameter and their mean square deviation. The influence of the error in restoring the established functional dependencies on the approximation properties of the kernel probability density estimation is determined. The obtained results are implemented as a method of synthesis and analysis of a fast bandwidths selection of the kernel estimation of the two-dimensional probability density of independent random variables. This method uses data on the quantitative characteristics of a family of lognormal distribution laws.

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