General complex rotated finite-element method for predissociation studies of diatomic molecules: An application on the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>1</mml:mn><mml:mtext>–</mml:mtext><mml:mn>6</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mmultiscripts><mml:mi>Σ</mml:mi><mml:mi>g</mml:mi><mml:mo>+</mml:mo><mml:mprescripts /><mml:none /><mml:mn>1</mml:mn></mml:mmultiscripts></mml:mrow></mml:math>states

Andersson, Stefan; Elander, Nils

doi:10.1103/physreva.69.052507

Cited by 10 publications

(5 citation statements)

References 41 publications

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“…At the same time, most of the outer-well state energies (below the barrier) can be accurately computed without considering delocalization to the inner well. This behaviour was pointed out already several times in the literature [12][13][14][15][16], and we have also checked it for every rovibrational state by solving the rovibrational Schrödinger equation with different [R min , R max ] intervals. In particular, we obtained the (adiabatic) inner-well state energies (below the barrier) with an accuracy better than 0.01 cm −1 even if we used the restricted, [R min , R max ] = [6,20] bohr, interval.…”

supporting

confidence: 68%

“…Finally, we mention that Andersson and Elander [15], by extending earlier work of Yu and Dressler [21], solved the coupled-state equations, including the coupling of the six lowest-energy 1 Σ + g states, and studied also the outer-well region of H H. They found that it was necessary to include all six 1 Σ + g states to converge the H vibrational energies better than 0.1 cm −1 whereas the 15th and 16th vibrational states (v = 14 and 15 in Table I) changed by 0.12 and 24.11 cm −1 between the fiveand six-state treatment. Although their computed values are off by 10-35 cm −1 from experiment, probably due to the fact that they used less accurate potential energy curves, their results seem to underline the general observation that the many-state Born-Oppenheimer (BO) expansion converges relatively slowly when one aims to achieve spectroscopic accuracy.…”

mentioning

confidence: 92%

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Non-adiabatic mass correction for excited states of molecular hydrogen: Improvement for the outer-well HH¯ 1Σg+ term values

Ferenc

Mátyus

2019

The Journal of Chemical Physics

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The mass-correction function is evaluated for selected excited states of the hydrogen molecule within a single-state non-adiabatic treatment. Its qualitative features are studied under the avoided crossing of the EF with the GK state and also for the outer well of the HH state. For the HH state, a negative mass correction is obtained for the vibrational motion near the outer minimum, which accounts for most of the deviation between experiment and earlier theoretical work. * Electronic address: matyus@chem.elte.hu This work represents the first steps towards a fully coupled non-adiabatic calculation of the EF -GK-HH-etc. singlet-gerade manifold of H 2 including the formerly neglected mass-correction terms which appear in the multi-state effective non-adiabatic Hamiltonian recently formulated [1]. Relying on the condition of adiabatic perturbation theory [2] that the electronic band must be separated from the rest of the electronic spectrum by a finite gap over the relevant dynamical range, already a single-state treatment delivers insight into the extremely rich non-adiabatic dynamics of electronically excited hydrogen. Motivated by these ideas and after careful inspection of the singlet gerade manifold (Figure 1), we have selected the lowerenergy region of the EF and the outer well of the HH state, often labelled withH, for a single-state non-adiabatic study. Concerning the computational methodology, we used the QUANTEN computer program [3-6] to accurately solve the electronic Schrödinger equation for the selected states using floating, explicitly correlated Gaussian functions. The mass-correction functions were also computed with QUANTEN according to the procedure described in Refs. [5, 6]. The resulting non-adiabatic corrections to the (effective) vibrational and rotational mass are shown in Figures 2 and 3. These numerical examples shed light on qualitative properties of the mass-correction functions, which can be understood by remembering the appearance of the R a reduced resolvent in the masscorrection tensor of the selected a electronic state [1, 2],Note that this is the Cartesian form of the tensor, and the general transformation of the KEO, including also the coordinate-dependent M aa,ij elements, to arbitrary curvilinear coordinates has been worked out in Ref. [5]. From this general expression, the specific results for a diatomic molecule with spherical polar coordinates, giving rise to the vibrational and rotational corrections, were derived and used in Refs. [5,6]. The single-state non-adiabatic mass-correction term has been discovered-and rediscovered several times in the past and has been used for the ground electronic state of diatomics [6,7,[7][8][9], for an approximate treatment of the water molecule

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supporting

confidence: 68%

mentioning

confidence: 92%

Non-adiabatic mass correction for excited states of molecular hydrogen: Improvement for the outer-well HH¯ 1Σg+ term values

Ferenc

Mátyus

2019

The Journal of Chemical Physics

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“…This makes the value of the Morse potential smaller than that from the experiments in the region of large r. Based on these, many works have been tried to improve it, at the same time, some new potential functions have been suggested [1,6,9,[18][19][20][21][22][23][24][25][26][27][28][29][30].…”

Section: Introductionmentioning

confidence: 99%

Analytic Quantum Mechanics of Diatomic Molecules with Empirical Potentials

2005

Phys. Scr.

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The Schrödinger equations of diatomic molecules with empirical potential functions are solved approximately by means of the hypergeometric series method. The potential functions may fit the experimental Rydberg-Klein-Rees curve more closely than the Morse function. Rigorous solutions of Schrödinger equations are also obtained with a similar method for zero total angular momentum. The eigenfunctions of diatomic molecules, expressed in terms of Jacobi polynomial, are employed as the orthonormal basis sets, and analytic expressions of matrix elements for the position and momentum operators are given in closed form.

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“…20 An alternative first principles calculation of the singlet-g levels was reported by Andersson and Elander. 21 In a recent experimental study the level energies of many bound quantum states of singlet-g symmetry below the n = 2 dissociation limit were determined at very high precision, 22 with absolute reference to the ground state. 23,24 To assist the discussion the calculated BornOppenheimer potential energy curves of all relevant states of singlet character and gerade symmetry in the region below and above the n = 2 limit [25][26][27] are displayed in Fig.…”

Section: Introductionmentioning

confidence: 99%

Spectral identification of diffuse resonances in H2 above the n = 2 dissociation limit

Ivanov¹,

Lange²,

Ubachs³

2011

The Journal of Chemical Physics

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The resonance structure in molecular hydrogen above the n = 2 dissociation limit is experimentally investigated in a 1 XUV + 1 VIS coherent two-step laser excitation process, with subsequent ionization of H(n = 2) products. Diffuse spectral features exhibiting widths of several cm −1 in the excitation range of 118 500-120 500 cm −1 are probed. Information on angular momentum selection rules for parallel and crossed polarizations, combination differences, the para-ortho distinction, extrapolation from rovibrational structure in the bound region below the n = 2 threshold, and mass-selective detection of H

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General complex rotated finite-element method for predissociation studies of diatomic molecules: An application on the(1–6)Σg+1states

Cited by 10 publications

References 41 publications

Non-adiabatic mass correction for excited states of molecular hydrogen: Improvement for the outer-well HH¯ 1Σg+ term values

Non-adiabatic mass correction for excited states of molecular hydrogen: Improvement for the outer-well HH¯ 1Σg+ term values

Analytic Quantum Mechanics of Diatomic Molecules with Empirical Potentials

Spectral identification of diffuse resonances in H2 above the n = 2 dissociation limit

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