Comparison of the Morse and Deng-Fan potentials for X-H bonds in small molecules

Rong, Zimei; Kjaergaard, Henrik G.; Sage, Martin L.

doi:10.1080/0026897031000137706

Cited by 88 publications

(93 citation statements)

References 36 publications

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“…Several other potentials are been used as alternatives and their performances have been compared with the Morse potential [43,[46][47][48][49][50][51][52][53][54][55][56]. For examples, Kratzer and pseudoharmonic potentials which have known exact solutions like in the Coulomb and harmonic oscillator model potentials [31,45,[57][58][59][60][61].…”

Section: Introductionmentioning

confidence: 99%

Exact solutions of the Schrödinger equation for the pseudoharmonic potential: an application to some diatomic molecules

Oyewumi

Sen

2012

J Math Chem

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For arbitrary values n and quantum numbers, we present the solutions of the 3-dimensional Schrödinger wave equation with the pseudoharmonic potential via the SU (1, 1) Spectrum Generating Algebra (SGA) approach. The explicit bound state energies and eigenfunctions are obtained. The matrix elements r 2 and r d dr are obtained (in a closed form) directly from the creation and annihilation operators. In addition, by applying the Hellmann-Feynman theorem, the expectation values of r 2 and p 2 are obtained. The energy states, the expectation values of r 2 and p 2 and the Heisenberg uncertainty products (HUP) for set of diatomic molecules (CO, NO, O 2 , N 2 , CH, H 2 , ScH) for arbitrary values of n and quantum numbers are obtained. The results obtained are in excellent agreement with the available results in the literature. It is also shown that the HUP is obeyed for all diatomic molecules considered.

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Section: Introductionmentioning

confidence: 99%

Exact solutions of the Schrödinger equation for the pseudoharmonic potential: an application to some diatomic molecules

Oyewumi

Sen

2012

J Math Chem

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“…Donaldson et al 45 compute f 20 ϭ5.96ϫ10 at the QCISD/6-311ϩ ϩG(2d,2p) level using an empirical Deng-Fan potential, and f 20 ϭ6.05ϫ10 Ϫ7 using a Morse oscillator approach. 46 The results of both the anharmonic and Morse oscillator approaches for HOONO are given in Table IV. The difference in the anharmonic and Morse oscillator results indicate the accuracy of modeling transitions in the lowest vibrational levels.…”

Section: Calculated Transition Strengths Of Cis-cis and Trans-perpmentioning

confidence: 99%

Cis-cis and trans-perp HOONO: Action spectroscopy and isomerization kinetics

Fry

Nizkorodov

Okumura

et al. 2004

The Journal of Chemical Physics

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The weakly bound HOONO product of the OHϩNO 2 ϩM reaction is studied using the vibrational predissociation that follows excitation of the first OH overtone (2 1 ). We observe formation of both cis-cis and trans-perp conformers of HOONO. The trans-perp HOONO 2 1 band is observed under thermal ͑223-238 K͒ conditions at 6971 cm Ϫ1 . We assign the previously published ͑warmer temperature͒ HOONO spectrum to the 2 1 band at 6365 cm Ϫ1 and 2 1 -containing combination bands of the cis-cis conformer of HOONO. The band shape of the trans-perp HOONO spectrum is in excellent agreement with the predicted rotational contour based on previous experimental and theoretical results, but the apparent origin of the cis-cis HOONO spectrum at 6365 cm Ϫ1 is featureless and significantly broader, suggesting more rapid intramolecular vibrational redistribution or predissociation in the latter isomer. The thermally less stable trans-perp HOONO isomerizes rapidly to cis-cis HOONO with an experimentally determined lifetime of 39 ms at 233 K at 13 hPa ͑in a buffer gas of predominantly Ar͒. The temperature dependence of the trans-perp HOONO lifetime in the range 223-238 K yields an isomerization barrier of 33Ϯ12 kJ/mol. New ab initio calculations of the structure and vibrational mode frequencies of the transition state perp-perp HOONO are performed using the coupled cluster singles and doubles with perturbative triples ͓CCSD͑T͔͒ model, using a correlation consistent polarized triple basis set ͑cc-pVTZ͒. The energetics of cis-cis, trans-perp, and perp-perp HOONO are also calculated at this level ͓CCSD͑T͒/ cc-pVTZ͔ and with a quadruple basis set using the structure determined at the triple basis set ͓CCSD͑T͒/cc-pVQZ//CCSD͑T͒/cc-pVTZ͔. These calculations predict that the anti form of perp-perp HOONO has an energy of ⌬E 0 ϭ42.4 kJ/mol above trans-perp HOONO, corresponding to an activation enthalpy of ⌬H 298 ‡0 ϭ41.1 kJ/mol. These results are in good agreement with statistical simulations based on a model developed by Golden, Barker, and Lohr. The simulated isomerization rates match the observed decay rates when modeled with a trans-perp to cis-cis HOONO isomerization barrier of 40.8 kJ/mol and a strong collision model. The quantum yield of cis-cis HOONO dissociation to OH and NO 2 is also calculated as a function of photon excitation energy in the range 3500-7500 cm Ϫ1 , assuming D 0 ϭ83 kJ/mol. The quantum yield is predicted to vary from 0.15 to 1 over the observed spectrum at 298 K, leading to band intensities in the action spectrum that are highly temperature dependent; however, the observed relative band strengths in the cis-cis HOONO spectrum do not change substantially with temperature over the range 193-273 K. Semiempirical calculations of the oscillator strengths for 2 1 (cis-cis HOONO) and 2 1 (trans-perp HOONO) are performed using ͑1͒ a one-dimensional anharmonic model and ͑2͒ a Morse oscillator model for the OH stretch, and ab initio dipole moment functions calculated using Becke, Lee, Yang, and Parr density functional theory ͑B3LYP͒,...

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“…Codriansky et al [27] studied the eigenvalues and eigenfunctions of the generalized Morse potential for the case of l ¼ 0 by using SO (2, 1) algebra method. Rong et al [28] investigated the XAH stretching motion in small molecules by using the generalized Morse potential model. By using the conventional approximation scheme [6] to deal with the centrifugal term, Dong and Gu [12] studied approximately the bound state solutions of the Schrö dinger equation with the generalized Morse potential (1).…”

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confidence: 99%

Approximate solutions of the Schrödinger equation with the generalized Morse potential model including the centrifugal term

Zhang

Jia

2011

Int J of Quantum Chemistry

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By using a new improved approximation scheme to deal with the centrifugal term, we solve approximately the Schrö dinger equation with the generalized Morse potentials for the arbitrary angular momentum values. The bound state energy spectra and the unnormalized radial wave functions have been approximately obtained by using the basic concept of the supersymmetric shape invariance formalism and the function analysis method. The numerical experiments show that our approximate results are in better agreement with those obtained by using the numerical integration approach than the approximate results obtained by using the conventional approximation scheme to deal with the centrifugal term. We also calculate the rotational transition frequencies for HF molecule and compare them with the experimental data.

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Comparison of the Morse and Deng-Fan potentials for X-H bonds in small molecules

Cited by 88 publications

References 36 publications

Exact solutions of the Schrödinger equation for the pseudoharmonic potential: an application to some diatomic molecules

Exact solutions of the Schrödinger equation for the pseudoharmonic potential: an application to some diatomic molecules

Cis-cis and trans-perp HOONO: Action spectroscopy and isomerization kinetics

Approximate solutions of the Schrödinger equation with the generalized Morse potential model including the centrifugal term

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