An improved eigenvalue corrector formula for solving the Schrödinger equation for central fields

Cooley, James W.

doi:10.1090/s0025-5718-1961-0129566-x

Cited by 409 publications

(320 citation statements)

References 7 publications

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“…In CASSCF, the active space was composed by the valence molecular orbitals (MOs) of N 2 to which we added one σ g and one π g MOs for better relaxation of the wavefunctions of the N 2 electronic states whose configurations differ in their σ π orbital occupations. We used an active space larger than the valence and a diffuse basis set in order to well describe any possible The nuclear motion problem was solved using the method of Cooley [29]. The spectroscopic constants discussed below were obtained using the derivatives at the minimum energy distances and standard perturbation theory.…”

Section: Methodsmentioning

confidence: 99%

Valence–Rydberg electronic states of N₂: spectroscopy and spin–orbit couplings

Hochlaf

Ndome

Hammoutène

et al. 2010

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

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Using an ab initio methodology, we compute the potential energy curves and the spinorbit coupling integrals of the N 2 electronic states located in the 0-120000 cm -1 energy domaine.In our analysis, we focus mostly on those located outside the Franck-Condon regio n accessible from the ground state of N 2 i.e. the two strongly bound states 1 3 Σ g -and 1 1 Γ g , and the weakly bound state 2 3 Σ g -, in addition to several repulsive states. We characterize them spectroscopically and we compute their spin-orbit couplings to the close lying singlets, triplets and quintets. This work completes our knowledge on the electronic states of N 2 that may be important intermediates during N + N collisions and for the dynamics of the N 2 singlets and triplets and quintets VUV photodissociation.

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Section: Methodsmentioning

confidence: 99%

Valence–Rydberg electronic states of N₂: spectroscopy and spin–orbit couplings

Hochlaf

Ndome

Hammoutène

et al. 2010

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

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“…The wave functions were obtained numerically using the standard Numerov method [26,27,28] with a step size of 0.001 a 0 over internuclear distances 0.1 < R < 200 a 0 .…”

Section: Photodissociation Approachmentioning

confidence: 99%

Rovibrationally resolved photodissociation of SH⁺

McMillan¹,

Shen²,

McCann³

et al. 2016

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

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Abstract. Photodissociation cross sections for the SH + radical are computed from all rovibrational (RV) levels of the ground electronic state X 3 Σ − for wavelengths from threshold to 500Å. The five electronic transitions,treated with a fully quantum-mechanical two-state model, i.e. no non-adiabatic coupling between excited states was included in our work.. The photodissociation calculations incorporate adiabatic potentials and transition dipole moment functions computed in the multireference configuration interaction approach along with the Davidson correction (MRCI+Q), but adjusted to match available experimental molecular data and asymptotic atomic limits. Local thermodynamic equilibrium (LTE) photodissociation cross sections were computed which assume a Boltzmann distribution of RV levels in the X 3 Σ − molecular state of the SH + cation. The LTE cross sections are presented for temperatures in the range 1000-10,000 K. Applications of the current photodissociation cross sections to interstellar gas, photon-dominated regions, and stellar atmospheres are briefly discussed.

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“…In TROVE, the primitive vibrational basis set is represented by a symmetrized product of six one-dimensional vibrational functions φn 1 (r ℓ 1 ), φn 2 (r ℓ 2 ), φn 3 (r ℓ 3 ), φn 4 (θ ℓ 1 ), φn 5 (θ ℓ 2 ), and φn 6 (τ ), where ni denotes the associated local mode vibrational quanta, {r ℓ 1 , r ℓ 2 , r ℓ 3 , θ ℓ 1 , θ ℓ 2 } are linearized versions (Yurchenko et al 2007;Bunker & Jensen 1998) of the coordinates {rCO, rCH 1 , rCH 2 , θOCH 1 , and θOCH 2 }, respectively, and τ is the dihedral angle between the OCH1 and OCH2 planes. The functions φn i (qi) are obtained by solving the corresponding 1D Schrödinger equation (Yurchenko et al 2007) for the vibrational motion associated with the corresponding coordinate qi ∈ {r ℓ 1 , r ℓ 2 , r ℓ 3 , θ ℓ 1 , θ ℓ 2 , τ }, with the other coordinates held fixed at their equilibrium values, where the Numerov-Cooley method (Noumerov 1924;Cooley 1961) is used. The direct product of the 1D basis functions is contracted using the polyad condition:…”

Section: Variational Computationmentioning

confidence: 99%

ExoMol line lists – VIII. A variationally computed line list for hot formaldehyde

Al-Refaie

Yachmenev

Tennyson

et al. 2015

Monthly Notices of the Royal Astronomical Society

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A computed line list for formaldehyde, H 2 12 C 16 O, applicable to temperatures up to T = 1500 K is presented. An empirical potential energy and ab initio dipole moment surfaces are used as the input to nuclear motion program TROVE. The resulting line list, referred to as AYTY, contains 10.3 million rotational-vibrational states and around 10 billion transition frequencies. Each transition includes associated Einstein-A coefficients and absolute transition intensities, for wavenumbers below 10 000 cm −1 and rotational excitations up to J = 70. Room-temperature spectra are compared with laboratory measurements and data currently available in the HITRAN database. These spectra show excellent agreement with experimental spectra and highlight the gaps and limitations of the HITRAN data. The full line list is available from the CDS database as well as at www.exomol.com.

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An improved eigenvalue corrector formula for solving the Schrödinger equation for central fields

Cited by 409 publications

References 7 publications

Valence–Rydberg electronic states of N₂: spectroscopy and spin–orbit couplings

Valence–Rydberg electronic states of N₂: spectroscopy and spin–orbit couplings

Rovibrationally resolved photodissociation of SH⁺

ExoMol line lists – VIII. A variationally computed line list for hot formaldehyde

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An improved eigenvalue corrector formula for solving the Schrödinger equation for central fields

Cited by 409 publications

References 7 publications

Valence–Rydberg electronic states of N2: spectroscopy and spin–orbit couplings

Valence–Rydberg electronic states of N2: spectroscopy and spin–orbit couplings

Rovibrationally resolved photodissociation of SH+

ExoMol line lists – VIII. A variationally computed line list for hot formaldehyde

Contact Info

Product

Resources

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Valence–Rydberg electronic states of N₂: spectroscopy and spin–orbit couplings

Valence–Rydberg electronic states of N₂: spectroscopy and spin–orbit couplings

Rovibrationally resolved photodissociation of SH⁺