Comparative Study of Empirical Internuclear Potential Functions

Steele, D.; Lippincott, Ellis R.; Vanderslice, Joseph T.

doi:10.1103/revmodphys.34.239

Cited by 367 publications

(129 citation statements)

References 36 publications

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“…[4]) potentials represent a second class of potentials [4] accurate over a wider range of distances. Quantum chemists [5,6,7,8,9] have derived a third class that reproduce spectroscopic and thermodynamic data with impressive fidelity.…”

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confidence: 99%

Rydberg–London potential for diatomic molecules and unbonded atom pairs

Cahill

Parsegian

2004

The Journal of Chemical Physics

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We propose and test a pair potential that is accurate at all relevant distances and simple enough for use in large-scale computer simulations. A combination of the Rydberg potential from spectroscopy and the London inverse-sixth-power energy, the proposed form fits spectroscopically determined potentials better than the Morse, Varnshi, and Hulburt-Hirschfelder potentials and much better than the Lennard-Jones and harmonic potentials. At long distances, it goes smoothly to the correct London force appropriate for gases and preserves van der Waals's "continuity of the gas and liquid states," which is routinely violated by coefficients assigned to the Lennard-Jones 6-12 form.There are at least three classes of interatomic potentials. Commercial codes use the Lennard-Jonesand harmonicforms, which are accurate near the minimum at r = r 0 . But this first class of potentials may be too simple for complex materials away from from equilibrium.(β = (κr 2 0 − 1)/(2r 2 0 )), and Hulburt-Hirschfelder [3][4]) potentials represent a second class of potentials [4] accurate over a wider range of distances. Quantum chemists [5,6,7,8,9] have derived a third class that reproduce spectroscopic and thermodynamic data with impressive fidelity. But the potentials of this class involve many parameters and may be too cumbersome for use in large-scale simulations.We propose and test a formthat is nearly as accurate as the class-3 potentials but simpler than many class-2 potentials. It is a combination of the Rydberg formula used in spectroscopy and , and e = 47.6Å 12 ) (solid, red) fits the RKR spectral points for the ground state of molecular hydrogen (pluses, blue) and gives the correct London tail for r > 3Å. The Lennard-Jones VLJ (dashes, green) and harmonic VH (dots, magenta) forms fit only near the minimum.the London formula for pairs of atoms. In Eq.(6), the terms involving a, b, and c were proposed by Rydberg [10] to incorporate spectroscopic data, but were largely ignored until recently [11,12]. The constant d = C 6 is the coefficient of the London tail. The new term e r −6 cures the London singularity. As r → 0, V (r) → a, finite; as r → ∞, V (r) approaches the London term, V (r) → −d/r 6 = −C 6 /r 6 . In a perturbative analysis [13], the a, b, c terms arise in first order, and the d term in second order.To test whether the hybrid V (r) can represent covalent bonds far from equilibrium, we used Gnuplot [14] to fit Eq.(6) to empirical potentials for molecular H 2 , N 2 , and

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confidence: 99%

Rydberg–London potential for diatomic molecules and unbonded atom pairs

Cahill

Parsegian

2004

The Journal of Chemical Physics

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“…Furthermore, force constants obtained from numerical fits of ab initio potential energy data will not be used, but instead an empirical function for the potential energy curve will be employed. The reason for this choice is that there exist [2,34,45] several well-known analytic functions that can accurately represent potential energy curves for most diatomic molecules. Such functions cannot be employed in truly ab initio work, since their forms depend parametrically upon experimentally measured spectroscopic constants.…”

Section: Numerical Results and Analysismentioning

confidence: 99%

Symbolic derivation of high-order Rayleigh-Schroedinger perturbation energies using computer algebra: Application to vibrational-rotational analysis of diatomic molecules

Herbert

1997

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“…Here the vibrational level ν is displaced from the bottom of the potential well byhω, which is defined as [30] hω =hω e ν + 1 2 −hω e χ e ν + 1…”

Section: Theoretical Modelmentioning

confidence: 99%

Femtosecond wave-packet dynamics in cesium dimers studied through controlled stimulated emission

et al. 2010

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We study the dynamics of wave packets in cesium dimers using a femtosecond-controlled pump-probe technique. We implement configurations with one pulse (pump) or two pulses (pump and control) to produce vibrational wave packets on the electronic excited state. The transmission of an additional, variable-delay probe pulse is measured to monitor the time evolution of the wave packets. In the case of the pump-control-probe configuration, a superposition of two independent wave packets is observed. In order to elucidate the observed experimental data, we develop a theory based on the Liouville equation for the density matrix associated with the Franck-Condon factors. Both the numerical and analytical calculations are in good agreement with our experimental results.

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Comparative Study of Empirical Internuclear Potential Functions

Cited by 367 publications

References 36 publications

Rydberg–London potential for diatomic molecules and unbonded atom pairs

Rydberg–London potential for diatomic molecules and unbonded atom pairs

Symbolic derivation of high-order Rayleigh-Schroedinger perturbation energies using computer algebra: Application to vibrational-rotational analysis of diatomic molecules

Femtosecond wave-packet dynamics in cesium dimers studied through controlled stimulated emission

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