The application of numerical inversion of the laplace transform to calculate the density of molecular states

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To estimate the rate constants of monomolecular reactions using quasi-equilibrium statistical theory, information on the density of discrete states of molecules is required. In the present work, a new approach to calculating the density of discrete states of stable molecules and transition complexes is proposed, which is based on the numerical inversion of the Laplace transform. To test the method, the calculations of model systems including H₂O, NH₃, CD4 and с-C₃H₆ molecules were carried out. It is shown that at energies less than 200 kcal/mol, the relative error in calculating the density of discrete states does not exceed 0.5%. The results obtained by this method can be used, for instance, to estimate the rate constants of reactions involving organic radicals formed in the troposphere and tropopause.

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作者简介

S. Adamson

Semenov Federal Research Center for Chemical Physics, Russian Academy of Sciences

编辑信件的主要联系方式.
Email: sergey.o.adamson@gmail.com
俄罗斯联邦, Moscow

D. Kharlampidi

Moscow State Pedagogical University; RUDN University

Email: sergey.o.adamson@gmail.com
俄罗斯联邦, Moscow; Moscow

G. Golubkov

Semenov Federal Research Center for Chemical Physics, Russian Academy of Sciences; National Research Center “Kurchatov Institute”

Email: sergey.o.adamson@gmail.com
俄罗斯联邦, Moscow; Moscow

Y. Dyakov

Semenov Federal Research Center for Chemical Physics, Russian Academy of Sciences

Email: sergey.o.adamson@gmail.com
俄罗斯联邦, Moscow

I. Morozov

Semenov Federal Research Center for Chemical Physics, Russian Academy of Sciences

Email: sergey.o.adamson@gmail.com
俄罗斯联邦, Moscow

O. Olkhov

Semenov Federal Research Center for Chemical Physics, Russian Academy of Sciences

Email: sergey.o.adamson@gmail.com
俄罗斯联邦, Moscow

I. Rodionov

Semenov Federal Research Center for Chemical Physics, Russian Academy of Sciences

Email: sergey.o.adamson@gmail.com
俄罗斯联邦, Moscow

I. Rodionova

Semenov Federal Research Center for Chemical Physics, Russian Academy of Sciences

Email: sergey.o.adamson@gmail.com
俄罗斯联邦, Moscow

I. Stepanov

Semenov Federal Research Center for Chemical Physics, Russian Academy of Sciences

Email: sergey.o.adamson@gmail.com
俄罗斯联邦, Moscow

D. Shestakov

Semenov Federal Research Center for Chemical Physics, Russian Academy of Sciences

Email: sergey.o.adamson@gmail.com
俄罗斯联邦, Moscow

M. Golubkov

Semenov Federal Research Center for Chemical Physics, Russian Academy of Sciences

Email: sergey.o.adamson@gmail.com
俄罗斯联邦, Moscow

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2. Fig. 1. Dependence of the root-mean-square error σ(W) for the H₂O molecule on the ratio Eₘₐₓ/Eᵤ.

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3. Fig. 2. Dependence of the lower values ​​of the function W(E ) for the H₂O molecule on the ratio Eₘₐₓ/Eᵤ: circles correspond to energy E = 5 kcal/mol; squares – E = 10 kcal/mol; diamonds – E =15 kcal/mol.

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4. Fig. 3. Dependence of the relative calculation error DW/W(E ) on the energy E for model systems: circles — H₂O molecule; squares — NH₃; diamonds — CD4; triangles — c-C₃H₆.

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