Showing papers on "Vibrational partition function published in 2020"
TL;DR: In this article, the energy spectra of the improved deformed exponential-type potential model were obtained using the Greene-Aldrich approximation scheme and an appropriate coordinate transformation, and analytical expressions of the vibrational partition function and other thermodynamic functions were derived by employing the Poisson summation formula.
Abstract: Within the framework of non-relativistic quantum mechanics, the ro-vibrational energy spectra of the improved deformed exponential-type potential model are obtained using the Greene-Aldrich approximation scheme and an appropriate coordinate transformation. With the help of the energy spectra, analytical expressions of the vibrational partition function and other thermodynamic functions are derived by employing the Poisson summation formula. These thermodynamic functions are studied for the electronic states of hydrogen dimer, carbon monoxide, nitrogen dimer and lithium hydride diatomic molecules, as they vary with temperature and upper bound vibration quantum number.
26 citations
TL;DR: In this article, the effect of quantum correction on the vibrational partition function was calculated by using improved Rosen-Morse potential for Cs 2 molecules and the related thermodynamics properties, i.e. vibrational mean energy, vibrational specific heat and vibrational free energy, were derived.
25 citations
TL;DR: In this paper, the Dirac equation was solved using modified factorization method with hyperbolic Poschl-Teller potential model and the eigenfunction for this potential has been obtained in terms of hypergeometric function.
Abstract: We solved the Dirac equation using modified factorization method with hyperbolic Poschl–Teller potential model. Relativistic and non-relativistic ro-vibrational energy spectra were obtained and numerical solutions for four diatomic molecules $$\left( {{\text{HCl}},\;{\text{H}}_{2} ,\;{\text{CO}}\;{\text{and}}\;{\text{LiH}}} \right)$$
obtained also. The eigenfunction for this potential has been obtained in terms of hypergeometric function. The energy variations with different potential parameters and quantum numbers of the hyperbolic Poschl–Teller potential are also plotted. In addition, we evaluate the vibrational partition function and other thermodynamic properties such as vibrational internal energy, vibrational free energy, vibrational entropy and vibrational specific heat capacity, in terms of temperature and upper bound vibration quantum number. Our results are consistent with those found in the available literature.
22 citations
Posted Content•
TL;DR: In this paper, the energy spectra of the improved deformed exponential-type potential model were obtained using the Greene-Aldrich approximation scheme and an appropriate coordinate transformation, and analytical expressions of the vibrational partition function and other thermodynamic functions were derived by employing the Poisson summation formula.
Abstract: Within the framework of non-relativistic quantum mechanics, the ro-vibrational energy spectra of the improved deformed exponential-type potential model are obtained using the Greene-Aldrich approximation scheme and an appropriate coordinate transformation. With the help of the energy spectra, analytical expressions of the vibrational partition function and other thermodynamic functions are derived by employing the Poisson summation formula. These thermodynamic functions are studied for the electronic states of hydrogen dimer, carbon monoxide, nitrogen dimer and lithium hydride diatomic molecules, as they vary with temperature and upper bound vibration quantum number.
12 citations
TL;DR: In this article, the authors derived the vibrational partition function using improved energy spectrum obtained recently via the path integral formalism and computed the thermodynamic properties of O2 and H2 molecules, for a multi-parameter exponential-type potential describing the internal vibration.
10 citations
TL;DR: The present article demonstrates how to combine improved theoretical methods to provide rate constants in cases where experimental data are uncertain or missing and studies the reaction in the high-pressure limit using multifaceted variable-reaction-coordinate variational transition-state theory (VRC-VTST) at the outer transition state and reaction-path variational Transition state theory at the inner turning point.
Abstract: Barrierless unimolecular association reactions are prominent in atmospheric and combustion mechanisms but are challenging for both experiment and kinetics theory. A key datum for understanding the pressure dependence of association and dissociation reactions is the high-pressure limit, but this is often available experimentally only by extrapolation. Here we calculate the high-pressure limit for the addition of a chlorine atom to acetylene molecule (Cl + C2H2→C2H2Cl). This reaction has outer and inner transition states in series; the outer transition state is barrierless, and it is necessary to use different theoretical frameworks to treat the two kinds of transition state. Here we study the reaction in the high-pressure limit using multifaceted variable-reaction-coordinate variational transition-state theory (VRC-VTST) at the outer transition state and reaction-path variational transition state theory (RP-VTST) at the inner turning point; then we combine the results with the canonical unified statistical (CUS) theory. The calculations are based on a density functional validated against the W3X-L method, which is based on coupled cluster theory with single, double, and triple excitations and a quasiperturbative treatment of connected quadruple excitations [CCSDT(Q)], and the computed rate constants are in good agreement with some of the experimental results. The chlorovinyl (C2H2Cl) adduct has two isomers that are equilibrium structures of a double-well C≡C–H bending potential. Two procedures are used to calculate the vibrational partition function of chlorovinyl; one treats the two isomers separately and the other solves the anharmonic energy levels of the double well. We use these results to calculate the standard-state free energy and equilibrium constant of the reaction.
8 citations
TL;DR: The vibrational partition function is calculated with classical method of integration over the whole phase space for the ground electronic state of the carbon monoxide molecule with main focus on temperature 5000K-20000K which is common in hypersonic flows of gases and plasmas.
Abstract: 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.
8 citations
01 Jun 2020
TL;DR: In this paper, a screened modified Krazer potential and the newly proposed NUFA method were used to obtain the energy spectrum and the corresponding wave function for selected diatomic molecules.
Abstract: In this work, we proposed a screened modified Krazer potential and use the newly proposed by Analysis (NUFA) method to obtain the energy spectrum and the corresponding wave function. With the obtained energy spectrum, we studied the numerical results for some selected diatomic molecules and our results are in good agreement with other analytical method. We also evaluated the vibrational partition function for , and diatomic molecules via the Euler–Maclaurin approach and other thermodynamic functions such as free energy, entropy, mean energy and specific heat Capacity. The expectations values of and are also calculated numerically for different diatomic molecules using the normalized wave function for the two low lying states corresponding to the ground and first excited states. Our numerical results for the selected diatomic molecules validate the Heisenberg uncertainty relation, .
6 citations
05 May 2020
TL;DR: In this article, the authors determined the rotational vibrational (RV) partition function from the energy eigenvalues obtained for the attractive radial potential plus class of Yukawa potential (ARPCYP) via asymptotic iteration method (AIM).
Abstract: We determined the rotational vibrational (RV) partition function from the energy eigenvalues obtained for the attractive radial potential plus class of Yukawa potential (ARPCYP) via asymptotic iteration method (AIM). From these eigenvalue spectrum and RV partition functions, we obtained various thermodynamical properties such as vibrational mean energy (U)and vibrational mean free energy (F).
3 citations
TL;DR: The complementarity of the harmonic oscillator and classical integration over the phase space approaches is investigated for the CO and H2+ molecules showing that those two approaches are complementary in the sense that they smoothly overlap.
Abstract: The vibrational and rovibrational partition functions of diatomic molecules are considered in the regime of intermediate temperatures. The low temperatures are those at which the harmonic oscillator approximation is appropriate, and the high temperatures are those at which classical partition function (with Wigner–Kirkwood correction) is applicable. The complementarity of the harmonic oscillator and classical integration over the phase space approaches is investigated for the CO and H2+ molecules showing that those two approaches are complementary in the sense that they smoothly overlap.
3 citations
TL;DR: In this article, the explicit expression of the vibrational partition function for the modified Poschl-Teller plus Woods-Saxon potential has been presented in a closed-form.
Abstract: The explicit expression of the vibrational partition function for the modified Poschl–Teller plus Woods–Saxon potential has been presented in a closed-form. The analytical expression for the vibrational mean energy have also been calculated were other thermodynamic functions like the vibrational specific heat, free energy, and the entropy for the gallium nitride wurtzite crystal structure have been determined in details. The dependence of these functions on the potential parameters has also been discussed in detail. By using the ground state energy and the probability density, the behaviours of some theoretic quantities (Shannon entropy and Fisher information entropy) have also been calculated and analyzed graphically as a function of the potential parameters.
TL;DR: In this article, a statistical thermodynamic model for the vibrational partition function with separated stretching and bending is developed, and the model is studied on the example of a CO molecule for temperature up to 20,000 K with the aim to describe efficient dissociation by deposition of energy mainly to the stretching modes of vibration.
Abstract: The statistical thermodynamic model for the vibrational partition function with separated stretching and bending is developed. The model is studied on the example of $$\hbox {CO}_{2}$$ molecule for temperature up to 20,000 K with the aim to describe efficient dissociation by deposition of energy mainly to the stretching modes of vibration. The observed separation of bending mode at lower temperatures suggest that it is possible to construct such kinetic model of plasma in which the high vibrational temperature of stretching and the low vibrational temperature of bending are obtained resulting in an efficient dissociation. In particular, the proposed model is extended to ideal-gas version where all the interactions between atoms are taken into account. The idea behind such approach is to eliminate contributions to partition functions stemming from non-interacting dissociated fragments of the molecule. The application areas of such partition functions are discussed and the full vibrational partition functions based on that model are compared with the known data.