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

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Resumo

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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Sobre autores

S. Adamson

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

Autor responsável pela correspondência
Email: sergey.o.adamson@gmail.com
Rússia, Moscow

D. Kharlampidi

Moscow State Pedagogical University; RUDN University

Email: sergey.o.adamson@gmail.com
Rússia, 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
Rússia, Moscow; Moscow

Y. Dyakov

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

Email: sergey.o.adamson@gmail.com
Rússia, Moscow

I. Morozov

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

Email: sergey.o.adamson@gmail.com
Rússia, Moscow

O. Olkhov

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

Email: sergey.o.adamson@gmail.com
Rússia, Moscow

I. Rodionov

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

Email: sergey.o.adamson@gmail.com
Rússia, Moscow

I. Rodionova

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

Email: sergey.o.adamson@gmail.com
Rússia, Moscow

I. Stepanov

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

Email: sergey.o.adamson@gmail.com
Rússia, Moscow

D. Shestakov

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

Email: sergey.o.adamson@gmail.com
Rússia, Moscow

M. Golubkov

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

Email: sergey.o.adamson@gmail.com
Rússia, 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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