Energy eigenvalues for Lennard-Jones potentials using the hypervirial perturbative method

Mateo, F.G.; Zúñiga, José; Requena, A.; Hidalgo, Antonio

doi:10.1088/0953-4075/23/16/019

Cited by 12 publications

(3 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…If Eq. ͑9͒ is expanded in a Taylor series, the vibrational energy E l and the mean atomic separation ͗r l ͘ of the motion with the principle quantum number l of this oscillator can be expressed as 27 E l = បͩl + 1 2 ͪ−C e ប 2 2 ͩl+ 1 2 ͪ 2…”

Section: Thermal Expansion and Grüneisen Parametermentioning

confidence: 99%

Structural metrics of high-temperature lattice conductivity

Huang

Kaviany

2006

Journal of Applied Physics

View full text Add to dashboard Cite

An atomic structure-based model for high-temperature lattice conductivity is developed for both compact crystals and cage-bridge crystals. For compact crystals, where long-range acoustic phonons dominate, the Debye temperature T D and Grüneisen parameter ␥ are estimated using interatomic potentials to arrive at the lattice conductivity relation. Under the assumption of homogeneous deformation, T D is estimated according to a simplified force constant matrix and a phenomenological combinative rule for force constants, which is applicable to an arbitrary pair of interacting atoms. Also, ␥ is estimated from a general Lennard-Jones potential form and the combination of the bonds. The results predicted by the model are in close agreement with the experimental results. For cage-bridge crystals, where both short-range acoustic phonons and optical phonons may be important, a simple mean-free path model is proposed: The phonon mean-free path of such a crystal at high temperatures is essentially limited by its structure and is equal to the cage size. This model also shows good agreement with the results of experiments and molecular dynamics simulations. Based on this atomic-level model, the structural metrics of crystals with low or high lattice conductivity are discussed, and some strategies for thermal design and management are suggested.

show abstract

Section: Thermal Expansion and Grüneisen Parametermentioning

confidence: 99%

Structural metrics of high-temperature lattice conductivity

Huang

Kaviany

2006

Journal of Applied Physics

View full text Add to dashboard Cite

show abstract

“…The perturbation method that we employ in this work is the hypervirial treatment, which is based on the combined used of the hypervirial [22,23] and Hellmann-Feynman [24,25] theorems to derive recursion relations which allows us to determine the successive corrections of the energy [26]. This method is well known and has been applied to many quantum eigenvalue problems [23,[27][28][29][30][31][32][33][34][35][36], so we will give here only a brief sketch of its application to the rotating Morse oscillator. A more detailed presentation of the hypervirial perturbation treatment for perturbed Morse oscillators can be found in [30,34].…”

Section: Perturbation Treatmentmentioning

confidence: 99%

An analytical perturbation treatment of the rotating Morse oscillator

Zúñiga

Bastida

Requena

2008

J. Phys. B: At. Mol. Opt. Phys.

View full text Add to dashboard Cite

An analytical perturbation treatment to determine the energy levels of the rotating Morse oscillator is proposed. The method is based on making an exponential expansion of the rotational term about a suitably chosen internuclear distance rb, and on solving the equations obtained in this way using analytic perturbation theory. The value of the parameter rb is chosen as the minimum of the Morse–Pekeris oscillator or as the minimum of the third-order Morse–Pekeris expansion, both of which can be evaluated analytically. The resulting zero-order system is then a modified version of the original Morse–Pekeris oscillator model. The perturbation treatment is carried out using the hypervirial perturbation method and by rearranging the energy corrections in terms of inverse powers of dissociation energy of the zero-order system. The accuracy of the analytical expression derived for the energy levels of the rotating Morse oscillator is checked by making a numerical application to the H2 molecule.

show abstract

“…With p = 6, one gets the LJ( 10,6) potential, which has been considered by Mateo er a/ (1990) wlth p = 1250 and J = 0. it is then particularly easy to calculate in a completely analytical way an accurate approximation of Q, for this potential. In order to get a better idea of the accuracy obtained by this method, we give in table 1 the energies of the rovibrational levels E ; = E , / D of the W(10,6) potential with p = 1250 and j = 2 0 in comparison to the corresponding one-term WKB eigenvalues, which should be very close to the exact ones, since this is the case for j = 0 (Mateo et al 1990). The third reason we use this potential comes from the fact that in order to get an accurate value of Q,, the exact number a, of hound states for each j has to be included in the sum of (1).…”

Section: Numerical Applicationmentioning

confidence: 99%

Exact classical vibrational-rotational partition function for Lennard-Jones and Morse potentials

Guérin¹

1992

J. Phys. B: At. Mol. Opt. Phys.

View full text Add to dashboard Cite

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.

show abstract

Energy eigenvalues for Lennard-Jones potentials using the hypervirial perturbative method

Cited by 12 publications

References 23 publications

Structural metrics of high-temperature lattice conductivity

Structural metrics of high-temperature lattice conductivity

An analytical perturbation treatment of the rotating Morse oscillator

Exact classical vibrational-rotational partition function for Lennard-Jones and Morse potentials

Contact Info

Product

Resources

About