Numerische Berechnung der 2S-Terme von Ortho- und Par-Helium

Hylleraas, Egil A.; Undheim, Bjarne

doi:10.1007/bf01397263

Cited by 530 publications

(204 citation statements)

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“…According to the Hylleraas-Undheim-MacDonald's theorem [22,23], there exists a one-to-one correspondence between the approximate energy levels E i (N ) and the exact levels ǫ i ≡ E i (∞), the i-th approximate level being an upper bound to the i-th exact level. Mathematically the following relations hold:…”

Section: Chh Basismentioning

confidence: 99%

Variational description of the helium trimer using correlated hyperspherical harmonic basis functions

Barletta

Kievsky

2001

Phys. Rev. A

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A variational wave function constructed with correlated Hyperspherical Harmonic functions is used to describe the Helium trimer. This system is known to have a deep bound state. In addition, different potential models predict the existence of a shallow excited state that has been identified as an Efimov state. Using the Rayleigh-Ritz variational principle the energies and wave functions of both bound states have been obtained by solving a generalized eigenvalue problem. The introduction of a suitable correlation factor reduces considerably the dimension of the basis needed to accurately describe the structure of the system. The most recent helium-helium interactions have been investigated.

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Section: Chh Basismentioning

confidence: 99%

Variational description of the helium trimer using correlated hyperspherical harmonic basis functions

Barletta

Kievsky

2001

Phys. Rev. A

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“…is a consequence of the Hylleraas-Undheim theorem (Hylleraas & Undheim 1930). The CSFs of all states are constructed from a common set of one-electron orbitals of the form…”

Section: Theoretical Calculations Of Oscillator Strengths and Transitmentioning

confidence: 99%

The FERRUM Project: Experimental oscillator strengths of the UV 8 multiplet and other UV transitions from the $\mathsf{y^6}$P levels of Fe II

Pickering

Donnelly

Nilsson

et al. 2002

A&A

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Abstract. We report on experimental branching fractions (BFs) for 19 transitions from the three 3d 5 ( 6 S)4s4p( 3 P) y 6 P levels in Fe II, measured in Fourier transform spectra of a Penning discharge lamp and a hollow cathode lamp. The transition wavelengths span the interval between 1600 and 2850 Å. Absolute oscillator strengths ( f -values) have been derived by combining the BFs with experimental radiative lifetimes recently reported in the literature. Theoretical f -values have been calculated using configuration interaction wavefunctions. The new experimental and theoretical f -values are compared with data available in the literature and in databases. The strongest lines measured belong to the UV 8 multiplet of Fe II, which has one ground state transition appearing as a prominent feature at 1608 Å in interstellar spectra. The line is accompanied by a satellite at 1611 Å due to a level mixing, which is discussed in the paper.

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“…A larger configuration space, however, quickly makes the calculation unfeasible, at least for large systems. Note that if convergence is achieved, the computed energies are variational, i. e. they are upper bounds to the exact ones [189,190].…”

Section: (κ)mentioning

confidence: 99%

Variational quantum approaches for computing vibrational energies of polyatomic molecules

2008

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In this article we review state-of-the-art methods for computing vibrational energies of polyatomic molecules using quantum mechanical, variationally-based approaches. We illustrate the power of those methods by presenting applications to molecules with more than four atoms. This demonstrates the great progress that has been made in this field in the last decade in dealing with the exponential scaling with the number of vibrational degrees of freedom. In this review we present three methods that effectively obviate this bottleneck. The first important idea is the n-mode representation of the Hamiltonian and notably the potential. The potential (and other functions) are represented as a sum of terms that depend on a subset of the coordinates. This makes it possible to compute matrix elements, form a Hamiltonian matrix, and compute its eigenvalues and eigenfunctions. Another approach takes advantage of this multimode representation and represents the terms as sum of products. It then exploits the powerful multiconfiguration Hartree time dependent method to solve the time-dependent Schrödinger equation and extract the eigenvalue spectrum. The third approach we present uses contracted basis functions in conjunction with a Lanczos eigensolver. Matrix vector products are done without transforming to a direct-product grid. The usefulness of these methods is demonstrated for several example molecules, e.g., methane, methanol and the Zundel cation.2

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Numerische Berechnung der 2S-Terme von Ortho- und Par-Helium

Cited by 530 publications

References 0 publications

Variational description of the helium trimer using correlated hyperspherical harmonic basis functions

Variational description of the helium trimer using correlated hyperspherical harmonic basis functions

The FERRUM Project: Experimental oscillator strengths of the UV 8 multiplet and other UV transitions from the $\mathsf{y^6}$P levels of Fe II

Variational quantum approaches for computing vibrational energies of polyatomic molecules

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