On the Rovibrational Partition Function of Molecular Hydrogen at High Temperatures

Riganelli, António; Prudente, Frederico V.; Varandas, A. J. C.

doi:10.1021/jp011330o

Cited by 23 publications

(23 citation statements)

References 28 publications

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“…2.] For temperatures up to T ≈ 2000 K, the results in this figure are fitted well by When expressed relative to the minimum of the X 1 Σ + g potential energy curve, rather than the lowest ( v = 0, J = 0) rovibrational energy level, the results which we obtained are in excellent agreement with the quantal calculations tabulated by Riganelli, Prudente & Varandas (2001). As may be seen in Fig.…”

Section: Three‐body Recombination Of Hydrogen and Collisional Dissosupporting

confidence: 86%

“…For molecular hydrogen, we calculated the partition function as a function of the kinetic temperature, T, using the rovibrational bound state energies (within the X 1 + g ground electronic state) from Dabrowski (1984); the results of this calculation, and of the corresponding values of the ortho:para H 2 ratio, are shown in Fig. 2. [The results obtained using the H 2 bound state energies from the University of Georgia Molecular Opacity Project (Stancil et al 2002) were indistinguishable from those in When expressed relative to the minimum of the X 1 + g potential energy curve, rather than the lowest (v = 0, J = 0) rovibrational energy level, the results which we obtained are in excellent agreement with the quantal calculations tabulated by Riganelli, Prudente & Varandas (2001). As may be seen in Fig.…”

Section: Three-body Recombination Of Hydrogensupporting

confidence: 81%

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Three-body recombination of hydrogen during primordial star formation

Flower¹,

Harris²

2007

Monthly Notices of the Royal Astronomical Society

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We consider the formation and destruction of H2 and HD during the gravitational contraction of condensations of the primordial gas, which led to the formation of the first generation of stars (Population III stars). The determination of the populations of the bound rovibrational levels of molecular hydrogen is considered in detail. Initially, the rates per unit volume at which these levels are populated and depopulated are not in equilibrium. As the density increases, equilibrium between the rates of population and depopulation is established first, and then the levels gradually thermalize (i.e. their populations tend towards a Boltzmann distribution at the kinetic temperature of the gas), with the lowest energy levels thermalizing first. Ultimately, both the bound and the continuum states thermalize (i.e. attain a Saha distribution), but this process is not complete until densities nH≈ 1013 cm−3 are reached. Using the principle of microscopic reversibility, we derive an expression for the rate coefficient for three‐body recombination of hydrogen which is found to differ significantly from the much used expression of Jacobs et al.

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Section: Three‐body Recombination Of Hydrogen and Collisional Dissosupporting

confidence: 86%

Section: Three-body Recombination Of Hydrogensupporting

confidence: 81%

Three-body recombination of hydrogen during primordial star formation

Flower¹,

Harris²

2007

Monthly Notices of the Royal Astronomical Society

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“…14. In fact, when the temperature is sufficiently high, it is known that the quantum partition function can be usefully approximated by the classical expression 14,28,29 ͑the T dependence is omitted from the notation for simplicity͒…”

Section: B Classical Formulasmentioning

confidence: 99%

Level distributions, partition functions, and rates of chirality changing processes for the torsional mode around O–O bonds

Bitencourt

Ragni

Maciel

et al. 2008

The Journal of Chemical Physics

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In view of the particular attention recently devoted to hindered rotations, we have tested reduced kinetic energy operators to study the torsional mode around the O-O bond for H(2)O(2) and for a series of its derivatives (HOOCl, HOOCN, HOOF, HOONO, HOOMe, HOOEt, MeOOMe, ClOOCl, FOOCl, FOOF, and FOONO), for which we had previously determined potential energy profiles along the dihedral ROOR(') angle [R,R(')=H,F,Cl,CN,NO,Me (=CH(3)), Et (=C(2)H(5))]. We have calculated level distributions as a function of temperature and partition functions for all systems. Specifically, for the H(2)O(2) system we have used two procedures for the reduction in the kinetic energy operator to that of a rigid-rotor-like one and the calculated partition functions are compared with previous work. Quantum partition functions are evaluated both by quantum level state sums and by simple classical approximations. A semiclassical approach, using a linear approximation of the classical path and a quadratic Feynman-Hibbs approximation of Feynman path integral, introduced in previous work and here applied to the torsional mode, is shown to greatly improve the classical approximations. Further improvement is obtained by the explicit introduction of the dependence of the moment of inertia from the torsional angle. These results permit one to discuss the characteristic time for chirality changes for the investigated molecules either by quantum mechanical tunneling (dominating at low temperatures) or by transition state theory (expected to provide an estimate of racemization rates in the high energy limit).

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“…[7][8][9][10] In turn, q vr assumes in classical statistical mechanics the form 1,11 with H CM (q, p) being the classical Hamiltonian, h the Planck constant, n the number of degrees of freedom, q the generalized coordinate vector, and p its conjugate momenta. In turn, the subscript B implies that the hypervolume of integration is restricted to phase space regions corresponding to a bound state situation, i.e., 0 e H CM (q, p) e D e , where D e is the dissociation energy of the molecule 12 (throughout this work we assume as reference energy the minimum of the potential energy surface). A major advantage of the classical approach is the appreciably smaller computational cost in comparison to the quantum one, which allows a treatment of molecular systems with a large number of degrees of freedom.…”

Section: Introductionmentioning

confidence: 99%

Calculation of the Rovibrational Partition Function Using Classical Methods with Quantum Corrections

2001

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The rovibrational partition functions of diatomic molecules are calculated using a classical framework plus quantum, semiclassical, and semiempirical corrections. The most popular methods to calculate such corrections are briefly reviewed and applied to the benchmark H 2 molecule. A novel hybrid scheme is proposed and applied to H 2 , HCl, and ArO. Each method is analyzed with a view to find an economical way to calculate such corrections for polyatomic systems.

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On the Rovibrational Partition Function of Molecular Hydrogen at High Temperatures

Abstract: We report a comparative study of the vibrational and rovibrational partition functions using several quantum and classical statistical mechanics approaches. The calculations refer to H 2 , but the conclusions are anticipated to be valid also for larger systems.

Cited by 23 publications

References 28 publications

Three-body recombination of hydrogen during primordial star formation

Three-body recombination of hydrogen during primordial star formation

Level distributions, partition functions, and rates of chirality changing processes for the torsional mode around O–O bonds

Calculation of the Rovibrational Partition Function Using Classical Methods with Quantum Corrections

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