Calculation of the energy levels of excited vibrational states of the HD16O molecule by summing divergent series of the Rayleigh-Schrödinger perturbation theory. The shift of zero-order levels

We described an improved version of a modified Davidson scheme previously introduced (F. Ribeiro, C. Iung and C. Leforestier, Chem. Phys. Lett.362, 199 (2002)), aimed at computing highly excited energy levels of polyatomic molecules. The key ingredient is a prediagonalization-perturbation step performed on a subspace of a curvilinear normal modes basis set (including diagonal anharmonicities). The efficiency of the method is demonstrated by computing the lowest 350 vibrational states of A′ symmetry of the HFCO molecule. Also shown is the possibility to restrict the calculation to selected energy levels, based on their zero-order description. This State Filtered Diagonalization method is illustrated on a high overtone (7ν5) of the OCF bend, and on the few energy levels (20) which have been experimentally assigned up to 5000 cm -1 of excitation energy.

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Rydberg levels of the sodium atom and the ammonium radical calculated by perturbation theory

Canadian Journal of Physics ◽

10.1139/p84-181 ◽

1984 ◽

Vol 62 (12) ◽

pp. 1336-1346 ◽

Cited By ~ 38

Author(s):

Stephen Havriliak ◽

Thomas R. Furlani ◽

Harry F. King

Keyword(s):

Perturbation Theory ◽

Pair Correlation ◽

Sodium Atom ◽

Zero Order ◽

Basis Set ◽

Core Model ◽

Basis Sets ◽

Order Problem ◽

Ammonium Radical ◽

Schrödinger Perturbation

Rydberg levels of sodium and the ammonium radical have been computed by second-order Rayleigh–Schrödinger perturbation theory with the frozen-core model defining the zero-order problem. Very extensive basis sets are used. From the sodium atom study, we determine the contributions of f- and g-type functions to the pair correlation energies and use this information to correct for basis set deficiencies as well as higher perturbation corrections in the molecular problem. The theory supports Watson's assignment of the Schüler band as being the analogue of the sodium D line, and implies that this is also the most likely assignment of the Schuster band.

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Special invariance properties of the [ N +1/ N ] Padé approximants in Rayleigh-Schrödinger perturbation theory

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1977.0139 ◽

1977 ◽

Vol 356 (1686) ◽

pp. 363-374 ◽

Cited By ~ 79

Keyword(s):

Perturbation Theory ◽

Padé Approximants ◽

Electronic Energy ◽

Zero Order ◽

Expansion Parameter ◽

Pade Approximants ◽

Invariance Properties ◽

Change Of Scale ◽

Shift Of Origin ◽

Schrödinger Perturbation

Padé approximants to the electronic energy of atoms and molecules are investigated by using the expansion parameter of Rayleigh-Schrödinger perturbation theory as a formal variable. These problems are characterized by the fact that the exact Hamiltonian is known and, although the Hamiltonian is split into a zero order and a perturbing part, the exact Hamiltonian is recovered when the expansion parameter equals unity. The present study shows that for these problems the sequence of [ N +1/ N ] Padé approximants is special in that, when the expansion parameter is set equal to unity, the numerical value of each of these approximants is invariant to two modifications in the zero-order Hamiltonian; namely, a change of scale and a shift of origin in the zero-order energy spectrum. This suggests that it is the essence of the exact Hamiltonian which produces the final energy result, rather than the arbitrary scaling of the unperturbed Hamiltonian. This formalism is particularly appropriate for ab initio perturbative calculations, where the variational principle cannot be used to determine optimal values for the scale and shift parameters.

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TEMPERATURE EFFECT ON IMPURITY-BOUND POLARONIC ENERGY LEVELS IN A PARABOLIC QUANTUM DOT IN MAGNETIC FIELDS

International Journal of Modern Physics B ◽

10.1142/s0217979207038447 ◽

2007 ◽

Vol 21 (32) ◽

pp. 5331-5337 ◽

Cited By ~ 10

Author(s):

SHI-HUA CHEN ◽

JING-LIN XIAO

Keyword(s):

Magnetic Field ◽

Perturbation Theory ◽

Binding Energy ◽

Magnetic Fields ◽

Quantum Dot ◽

Temperature Effect ◽

Applied Magnetic Field ◽

Energy Levels ◽

Schrödinger Perturbation ◽

Parabolic Quantum Dot

Energy levels of an impurity atom and its binding energy in a quantum dot with electron–phonon interactions are obtained by the second-order Rayleigh–Schrodinger perturbation theory. The energy correction is expressed as a function of the temperature, the applied magnetic field, and the effective confinement length of the quantum dot. We apply our calculations to GaAs .

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Analytic-continuation approach to the resummation of divergent series in Rayleigh-Schrödinger perturbation theory

Physical Review A ◽

10.1103/physreva.96.062106 ◽

2017 ◽

Vol 96 (6) ◽

Cited By ~ 2

Author(s):

Zsuzsanna É. Mihálka ◽

Péter R. Surján

Keyword(s):

Perturbation Theory ◽

Analytic Continuation ◽

Divergent Series ◽

Schrödinger Perturbation

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A Perturbation Theory for the Population of Atomic Energy Levels in Non-Lte Plasmas

International Astronomical Union Colloquium ◽

10.1017/s025292110010805x ◽

1988 ◽

Vol 102 ◽

pp. 343-347

Author(s):

M. Klapisch

Keyword(s):

Perturbation Theory ◽

Small Parameter ◽

Classification Scheme ◽

Sum Rules ◽

Energy Levels ◽

Natural Classification ◽

Quantum Numbers ◽

Formal Expansion ◽

Atomic Energy Levels ◽

As Effects

AbstractA formal expansion of the CRM in powers of a small parameter is presented. The terms of the expansion are products of matrices. Inverses are interpreted as effects of cascades.It will be shown that this allows for the separation of the different contributions to the populations, thus providing a natural classification scheme for processes involving atoms in plasmas. Sum rules can be formulated, allowing the population of the levels, in some simple cases, to be related in a transparent way to the quantum numbers.

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