Tables of Integrals Useful for the Calculations of Molecular Energies. III

Kotani, Masao; Ishiguro, Eiichi; Hijikata, Katsunori; Nakamura, Tafeashi; Amemiya, Ayao

doi:10.1143/jpsj.8.463

Cited by 74 publications

(61 citation statements)

References 3 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…of the functions enumerated above [9][10][11][12][13][14][15] , but none of these tabulations were extensive enough for our purposes. Practically all of the functions listed above have been computed ab initio from the following formulae 5; 8 -9 -15 :…”

mentioning

confidence: 99%

Interaction of the Vibrational and Electronic Motions in Some Simple Conjugated Hydrocarbons

Liehr¹

1958

Zeitschrift Für Naturforschung A

View full text Add to dashboard Cite

show abstract

mentioning

confidence: 99%

Interaction of the Vibrational and Electronic Motions in Some Simple Conjugated Hydrocarbons

Liehr¹

1958

Zeitschrift Für Naturforschung A

View full text Add to dashboard Cite

show abstract

“…The total spin S in the four electron case can take three distinct values, namely, S = 0 (singlet), 1 (triplet), and 2 (quintet). According to the spin branching diagram the degree of degeneracy that is associated with the singlet, triplet and quintet states is 2, 3 and 1, respectively [35]. The ground state of the four electron case has the configuration (0,0,1,1).…”

Section: Polyad Structurementioning

confidence: 99%

The Energy Level Structure of Low-dimensional Multi-electron Quantum Dots

Sako

Paldus

Diercksen

2009

Advances in Quantum Chemistry

View full text Add to dashboard Cite

A unified characterization of the energy-level structure of quasi-one-dimensional quantum dots is presented based on accurate computational results for the eigenenergies and wave functions, as obtained in previous studies for the case of two and three electrons, and in the present study also for four electrons. In each case the quantum chemical full configuration interaction method is adopted employing Cartesian anisotropic Gaussian basis sets. The energy-level structure is shown to be strongly dependent on the confinement strength ω and can be exemplified by the three qualitatively distinct regimes for large, medium, and small confinement strengths. To characterize the energy-level structure in the large or medium ω and the small ω regimes, the polyad quantum number, as well as its extended version, the extended polyad quantum number have been introduced. The degeneracy of energy levels for different spin states in the small ω regime is shown to be caused by the potential walls of the electron-electron interaction potential within the internal space. A systematic way of obtaining the degeneracy pattern of the energy levels in the small ω regime is also presented. Finally, qualitative differences between the energy-level structure of quasi-one-dimensional and quasi-two-dimensional quantum dots in the small ω regime are briefly discussed by referring to the different structure of their internal spaces.

show abstract

“…With this assumption the explicit form of the spin function for quartet states is written as |ααα . In the case of doublet states, on the other hand, there are two linearly-independent spin functions for the spin state of |S, M = , namely, (3)) and (3)), respectively [43]. The former spin function (denoted hereafter as |a for brevity) is a product of the singlet spin function for the electron pair (2, 3) and the α spin function for the electron 1, and forms the two-electron singlet for the electron pair 2 and 3 denoted above.…”

Section: Interpretation Of Spectramentioning

confidence: 99%

Understanding the spectra of a few electrons confined in a quasi-one-dimensional nanostructure

Sako

Diercksen

2008

J. Phys.: Condens. Matter

View full text Add to dashboard Cite

Abstract. The energy spectra and wave functions of three electrons confined by a quasi-one-dimensional Gaussian potential have been calculated and analyzed for three regimes of the strength of confinement ω z , namely, large (ω z = 5.0), medium (ω z = 1.0) and small (ω z = 0.1) by using the full configuration interaction method. For large and medium ω z the energy spectrum shows a band structure which is characterized by the polyad quantum number v p while for small ω z it is characterized by the extended polyad quantum number v * p . The wave functions of the quartet states have been assigned uniquely by counting the number of nodal planes for the three normal modes, namely, the center-of-mass, permutation and breathing modes. The energy levels for small ω z form nearly degenerate triplets each of which consists of two doublet states and one quartet state. The nodal pattern of their wave functions in this small ω z regime are almost identical to each other except for their phases. The origin of the tripling of energy levels and the similarity of the wave functions for different spin states has been rationalized by using the projection of one-and two-electron potentials onto the internal plane. Effects of anharmonicity in the confining potential on the energy spectra and wave functions have been also examined.

show abstract

Tables of Integrals Useful for the Calculations of Molecular Energies. III

Cited by 74 publications

References 3 publications

Interaction of the Vibrational and Electronic Motions in Some Simple Conjugated Hydrocarbons

Interaction of the Vibrational and Electronic Motions in Some Simple Conjugated Hydrocarbons

The Energy Level Structure of Low-dimensional Multi-electron Quantum Dots

Understanding the spectra of a few electrons confined in a quasi-one-dimensional nanostructure

Contact Info

Product

Resources

About