The repulsive interaction of atoms in S states

Buckingham, R. A.

doi:10.1039/tf9585400453

Cited by 79 publications

(23 citation statements)

References 4 publications

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“…In particular, the analytic approximation for the potential curve V (R) = E 1sσg (R) (19) made out the expressions (16) and (7) allows us to calculate the rovibrational energies E νL associated with the bound state 1sσ g for different values of ν and L. It is done by solving the one-dimensional differential equation (25) using the Lagrange-mesh method, see e.g. [12].…”

Section: H + 2 : the Lowest States Potential Curvesmentioning

confidence: 99%

H2+, HeH and H2: Approximating potential curves, calculating r

Olivares-Pilón

Turbiner

2018

Annals of Physics

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Analytic consideration of the Bohr-Oppenheimer (BO) approximation for diatomic molecules is proposed: accurate analytic interpolation for potential curve consistent with its rovibrational spectra is found.It is shown that in the Bohr-Oppenheimer approximation for four lowest electronic states 1sσ g and 2pσ u , 2pπ u and 3dπ g of H + 2 , the ground state X 2 Σ + of HeH and the two lowest states 1 Σ + g and 3 Σ + u of H 2 , the potential curves can be analytically interpolated in full range of internuclear distances R with not less than 4-5-6 figures. Approximation based on matching the Taylor-type expansion at small R and a combination of the multipole expansion with one-instanton type contribution at large distances R is given by two-point Padé approximant. The position of minimum, when exists, is predicted within 1% or better.For the molecular ion H + 2 in the Lagrange mesh method, the spectra of vibrational, rotational and rovibrational states (ν, L) associated with 1sσ g and 2pσ u , 2pπ u and 3dπ g potential curves is calculated. In general, it coincides with spectra found via numerical solution of the Schrödinger equation (when available) within six figures. It is shown that 1sσ g curve contains 19 vibrational states (ν, 0), while 2pσ u curve contains a single one (0, 0) and 2pπ u state contains 12 vibrational states (ν, 0). In general, 1sσ g electronic curve contains 420 rovibrational states, which increases up to 423 when we are beyond BO approximation. For the state 2pσ u the total number of rovibrational states (all with ν = 0) is equal to 3, within or beyond Bohr-Oppenheimer approximation. As for the state 2pπ u within the Bohr-Oppenheimer approximation the total number of the rovibrational bound states is equal to 284. The state 3dπ g is repulsive, no rovibrational state is found.It is confirmed in Lagrange mesh formalism the statement that the ground state potential curve of the heteronuclear molecule HeH does not support rovibrational states.Accurate analytical expression for the potential curves of the hydrogen molecule H 2 for the states 1 Σ + g and 3 Σ + u is presented. The ground state 1 Σ + g contains 15 vibrational states (ν, 0), ν = 0 − 14.In general, this state supports 301 rovibrational states. The potential curve of the state 3 Σ + u has a shallow minimum: it does not support any rovibrational state, it is repulsive. * Electronic address: horop@xanum.uam.mx † Electronic address: turbiner@nucleares.unam.mx

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Section: H + 2 : the Lowest States Potential Curvesmentioning

confidence: 99%

H2+, HeH and H2: Approximating potential curves, calculating r

Olivares-Pilón

Turbiner

2018

Annals of Physics

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“…The most famous of these is the Morse po- tential. Here, however, a more accurate one that has been given by Frost and Buckingham [7] will be used, i.e.,…”

Section: B Isoelectronic Equationsmentioning

confidence: 99%

The variation of spectroscopic properties with numbers of electrons

Laurenzi

Gaylord

1992

Int J of Quantum Chemistry

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A formalism that describes the variation of the spectroscopic properties, D,, R,, and k,, of homonuclear, diatomic molecules, with the number of molecular electrons has been developed. The theory describes the interrelation of these properties and predicts "critical" behavior in sequences of "isonuclear" and neutral molecules. Detailed calculations are possible with the help of experimental data in lieu of a deeper, dynamical theory of molecular behavior with respect to electron number. The present work points the way toward a first-principle's theory. Q 1992 JohnWiley & Sons, Inc.

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“…The key issue in the design of kinetic energy functionals is the incorporation of the atomic shell effect caused by the Pauli exclusion principle . An appropriate model for the Pauli repulsion is mandatory to obtain qualitative correct binding energy curves on bond distortion and thus, such models also find application in semiempirical potential‐energy‐functions . Given that approximations on the exchange‐correlation terms are accepted, the Pauli kinetic energy and the corresponding Pauli potential remain the only unknown quantities for a purely density‐based description of the system .…”

Section: Introductionmentioning

confidence: 99%

“…[25] An appropriate model for the Pauli repulsion is mandatory to obtain qualitative correct binding energy curves on bond distortion and thus, such models also find application in semiempirical potential-energy-functions. [26][27][28][29][30][31] Given that approximations on the exchange-correlation terms are accepted, the Pauli kinetic energy and the corresponding Pauli potential remain the only unknown quantities for a purely density-based description of the system. [32] Properties of the Pauli potential were intensively studied by several authors [33][34][35][36][37][38][39][40] and suitable approximations yielding self-consistent electron densities exhibiting proper atomic shell structure for all atoms in their groundstate were developed.…”

Section: Introductionmentioning

confidence: 99%