Symmetric group approach to configuration interaction methods

Duch, Włodzisław; Karwowski, Jacek

doi:10.1016/0167-7977(85)90001-2

Cited by 144 publications

(54 citation statements)

References 111 publications

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“…No line-up permutations or interaction classes need to be calculated as in SGA. 31 Our implementation can handle arbitrary spin states, excitation levels, and reference configurations, and includes an efficient analytic CI gradient 32 for all semiempirical methods that offer an analytic SCF gradient. 33,34 Efficient gradients are important for locating stationary points [35][36][37][38][39] or conical intersections, 40,41 and for following intrinsic reaction coordinates 42 or general minimum energy paths.…”

Section: Introductionmentioning

confidence: 99%

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Implementation of a general multireference configuration interaction procedure with analytic gradients in a semiempirical context using the graphical unitary group approach

2003

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The graphical unitary group approach has been applied in an efficient implementation of a general multireference configuration interaction (MRCI) method for use with small active molecular orbital spaces in a semiempirical framework. Gradients can be computed analytically for molecular orbitals from a closed-shell or a half-electron open-shell Hartree-Fock calculation. CPU times for single point energy and gradient calculations are reported. The code allows MRCI geometry optimizations of large molecules, as illustrated for the singlet ground state and the four lowest triplet states of fullerene C(76).

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Section: Introductionmentioning

confidence: 99%

“…This is especially important because the Hamiltonian in multireference (MR) CI procedures is very sparse. In the alternative symmetric group approach (SGA), 31 the pre-exclusion of vanishing matrix elements has to be done explicitly. 11 In GUGA, many common intermediates may be reused in different matrix elements.…”

Section: Introductionmentioning

confidence: 99%

Implementation of a general multireference configuration interaction procedure with analytic gradients in a semiempirical context using the graphical unitary group approach

2003

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“…Thus the spin function which forms a two-electron singlet for the electron pairs (1,2) and (2,3) should be coupled with configurations of the type (n a , n a , n b ) and (n a , n b , n b ) since it has to be antisymmetric with respect to the exchange of the electron pairs (1,2) and (2,3). It is convenient to impose on the orbital configuration (n 1 , n 2 , ..., n N ) the restriction that the singly occupied orbitals always precede the doubly occupied [34]. With this restriction the latter two three-electron configurations can be represented by the configuration (n a , n b , n b ).…”

Section: Polyad Structurementioning

confidence: 99%

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

Sako

Paldus

Diercksen

2009

Advances in Quantum Chemistry

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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.

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“…The first inequality, 0 ≤ n 1 < n 2 < n 3 , is imposed in order to remove redundancy in the configurations since permutations of the electron coordinates are performed in the process of antisymmetrization to form configuration state functions. The former configuration is constructed of thee different orbitals and can be coupled both to the two-types of doublet spin functions and the one-type of quartet spin function while the latter configuration has a doubly-occupied orbital and can be coupled only to the one-type of doublet spin function forming a two-electron singlet between the electrons residing in the doubly-occupied orbital [42]. Therefore the lowest energy configuration |1, 0 2 is a doublet state with the polyad quantum number 1 as shown in figure 2.…”

Section: Energy Spectrummentioning

confidence: 99%

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

Sako

Diercksen

2008

J. Phys.: Condens. Matter

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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.

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Symmetric group approach to configuration interaction methods

Cited by 144 publications

References 111 publications

Implementation of a general multireference configuration interaction procedure with analytic gradients in a semiempirical context using the graphical unitary group approach

Implementation of a general multireference configuration interaction procedure with analytic gradients in a semiempirical context using the graphical unitary group approach

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

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