The Experts below are selected from a list of 609 Experts worldwide ranked by ideXlab platform
H Guerin - One of the best experts on this subject based on the ideXlab platform.
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the exact classical vibrational Rotational Partition Function for the woolley potential calculations of the equilibrium constants for the formation of ar ar and mg mg
Journal of Physics B, 1992Co-Authors: H GuerinAbstract:Exact analytical expressions are derived for the classical vibrational-Rotational Partition Function and for the number of vibrational-Rotational energy levels of the one-constant Woolley potential, which can be viewed as a deformed Lennard-Jones (12, 6) potential. These expressions are then used first to fit the Woolley potential to accurate analytic potentials of Ar2 and Mg2 by matching the total number of vibrational-Rotational energy levels and, secondly, to calculate the corresponding classical equilibrium constants for the formation of these two molecules. The results are in excellent agreement with the exact classical and quantum-mechanical equilibrium constants calculated from the accurate analytic potentials by Dardi and Dahler (1990) with a maximum error of 4% for Ar2 and 2% for Mg2. In particular, they are in much better agreement than those calculated from various Lennard-Jones (12, 6) potentials.
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Exact classical vibrational-Rotational Partition Function for Lennard-Jones and Morse potentials
Journal of Physics B: Atomic Molecular and Optical Physics, 1992Co-Authors: H GuerinAbstract:Exact analytical expressions for the classical vibrational-Rotational Partition Function of the Lennard-Jones (m, n) and Morse potentials are derived. The values obtained from such expressions are compared to accurate evaluations of the corresponding quantum-mechanical Partition Function for the LJ (10, 6) and Morse potentials. Both sets of values are found to be in close agreement over a wide range of temperatures.
R Gijbels - One of the best experts on this subject based on the ideXlab platform.
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the Rotational Partition Function of the symmetric top and the effect of k doubling thereon
Chemical Physics Letters, 1991Co-Authors: Jan M L Martin, Jeanpierre Francois, R GijbelsAbstract:Abstract McDowell's earlier derivation of the Partition Function for a nonrigid symmetric top has been extended with a fourth-order correction for centrifugal distortion and correction terms for K doubling. Comparison with direct numerical summation (including K -doubling effects) indicates that the inclusion of the fourth-oder term is necessary to ensure high accuracy in the computed enthalpy Function and heat capacity above 2000 K, as well as that the effect of K doubling is very small at practical temperatures. The only effect of any practical importance is that of d 2 for molecules with fourfold symmetry: the present approximate expressions represent this effect quite well.
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on the effect of centrifugal stretching on the Rotational Partition Function of an asymmetric top
Journal of Chemical Physics, 1991Co-Authors: Jan M L Martin, Jeanpierre Francois, R GijbelsAbstract:Correction terms (up to third order in temperature) for the effect of centrifugal distortion on the Rotational Partition Function of linear molecules, spherical, symmetric, and asymmetric tops are evaluated by means of the classical Partition Function. It is shown that for the linear, spherical, and symmetric cases, the expressions thus obtained differ from the exact quantum expressions only in the absence of a very small constant correction term. It is then proposed that the Partition Function for a nonrigid asymmetric top, for which no exact expression has as yet been derived, be evaluated as the product of Watson’s asymptotic expansion for the rigid rotor and the centrifugal correction factor derived in the present work. Numerical comparison with direct numerical summation shows that, even for troublesome cases, this approximation holds very well even at 2000 K. Similar performance is observed for the heat content Function, except for pathological cases at high temperatures. In the rigid‐rotor case, Watson’s asymptotic series holds very well. As an example application, pilot calculations have been performed on the thermodynamic Functions of water and formaldehyde. The present method yields Functions in excellent agreement with those obtained by direct rovibrational summation, whereas computer‐time requirements are reduced by 3 or 4 orders of magnitude.
Jan M L Martin - One of the best experts on this subject based on the ideXlab platform.
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the Rotational Partition Function of the symmetric top and the effect of k doubling thereon
Chemical Physics Letters, 1991Co-Authors: Jan M L Martin, Jeanpierre Francois, R GijbelsAbstract:Abstract McDowell's earlier derivation of the Partition Function for a nonrigid symmetric top has been extended with a fourth-order correction for centrifugal distortion and correction terms for K doubling. Comparison with direct numerical summation (including K -doubling effects) indicates that the inclusion of the fourth-oder term is necessary to ensure high accuracy in the computed enthalpy Function and heat capacity above 2000 K, as well as that the effect of K doubling is very small at practical temperatures. The only effect of any practical importance is that of d 2 for molecules with fourfold symmetry: the present approximate expressions represent this effect quite well.
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on the effect of centrifugal stretching on the Rotational Partition Function of an asymmetric top
Journal of Chemical Physics, 1991Co-Authors: Jan M L Martin, Jeanpierre Francois, R GijbelsAbstract:Correction terms (up to third order in temperature) for the effect of centrifugal distortion on the Rotational Partition Function of linear molecules, spherical, symmetric, and asymmetric tops are evaluated by means of the classical Partition Function. It is shown that for the linear, spherical, and symmetric cases, the expressions thus obtained differ from the exact quantum expressions only in the absence of a very small constant correction term. It is then proposed that the Partition Function for a nonrigid asymmetric top, for which no exact expression has as yet been derived, be evaluated as the product of Watson’s asymptotic expansion for the rigid rotor and the centrifugal correction factor derived in the present work. Numerical comparison with direct numerical summation shows that, even for troublesome cases, this approximation holds very well even at 2000 K. Similar performance is observed for the heat content Function, except for pathological cases at high temperatures. In the rigid‐rotor case, Watson’s asymptotic series holds very well. As an example application, pilot calculations have been performed on the thermodynamic Functions of water and formaldehyde. The present method yields Functions in excellent agreement with those obtained by direct rovibrational summation, whereas computer‐time requirements are reduced by 3 or 4 orders of magnitude.
Marcin Buchowiecki - One of the best experts on this subject based on the ideXlab platform.
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vibrational Partition Function for the multitemperature theories of high temperature flows of gases and plasmas
Journal of Physical Chemistry A, 2020Co-Authors: Marcin BuchowieckiAbstract:The vibrational Partition Function is calculated using the classical method of integration over the whole phase space. The calculations were done for the ground electronic state of a carbon monoxide molecule. The main focus is on temperature in the range 5000-20 000 K, which is common in hypersonic flows of gases and plasmas. The method presented here, because of the exclusion of the noninteracting part of canonical Partition Function according to the ideas of T.L. Hill, is applicable at temperatures of tens of thousands of Kelvins, where the standard expression for the vibrational Partition Function fails. At lower temperatures (here 1000-6000 K), the correct quantum results can be obtained with the help of Wigner-Kirkwood expansion. The influence of vibrations on the Rotational Partition Function by bond-length elongation is examined, and the results are compared with the exact ro-vibrational Partition Function.
Jeanpierre Francois - One of the best experts on this subject based on the ideXlab platform.
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the Rotational Partition Function of the symmetric top and the effect of k doubling thereon
Chemical Physics Letters, 1991Co-Authors: Jan M L Martin, Jeanpierre Francois, R GijbelsAbstract:Abstract McDowell's earlier derivation of the Partition Function for a nonrigid symmetric top has been extended with a fourth-order correction for centrifugal distortion and correction terms for K doubling. Comparison with direct numerical summation (including K -doubling effects) indicates that the inclusion of the fourth-oder term is necessary to ensure high accuracy in the computed enthalpy Function and heat capacity above 2000 K, as well as that the effect of K doubling is very small at practical temperatures. The only effect of any practical importance is that of d 2 for molecules with fourfold symmetry: the present approximate expressions represent this effect quite well.
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on the effect of centrifugal stretching on the Rotational Partition Function of an asymmetric top
Journal of Chemical Physics, 1991Co-Authors: Jan M L Martin, Jeanpierre Francois, R GijbelsAbstract:Correction terms (up to third order in temperature) for the effect of centrifugal distortion on the Rotational Partition Function of linear molecules, spherical, symmetric, and asymmetric tops are evaluated by means of the classical Partition Function. It is shown that for the linear, spherical, and symmetric cases, the expressions thus obtained differ from the exact quantum expressions only in the absence of a very small constant correction term. It is then proposed that the Partition Function for a nonrigid asymmetric top, for which no exact expression has as yet been derived, be evaluated as the product of Watson’s asymptotic expansion for the rigid rotor and the centrifugal correction factor derived in the present work. Numerical comparison with direct numerical summation shows that, even for troublesome cases, this approximation holds very well even at 2000 K. Similar performance is observed for the heat content Function, except for pathological cases at high temperatures. In the rigid‐rotor case, Watson’s asymptotic series holds very well. As an example application, pilot calculations have been performed on the thermodynamic Functions of water and formaldehyde. The present method yields Functions in excellent agreement with those obtained by direct rovibrational summation, whereas computer‐time requirements are reduced by 3 or 4 orders of magnitude.
