Ein neuer Doppelprojektor

Preuss, E.

doi:10.1016/s0371-1951(56)80077-5

Cited by 5 publications

(5 citation statements)

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“…(15s7p)/[4s3p] for Na and (19s11p)/[5s4p] for Cl. The p functions were constructed from Gaussian lobes [16] which yield an approximate form of Cartesian-type basis functions. The number of basis functions per unit cell was 30.…”

Section: Calculations and Resultsmentioning

confidence: 99%

A Hartree–Fock ab initio band-structure calculation employing Wannier-type orbitals

Albrecht

Shukla

Dolg

et al. 1998

Chemical Physics Letters

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An ab initio Wannier-function-based approach to electronic groundstate calculations for crystalline solids is outlined. In the framework of the linear combination of atomic orbitals method the infinite character of the solid is rigorously taken into account. The Hartree-Fock groundstate energy, cohesive energy, lattice constant and bulk modulus are calculated in a fully ab initio manner as it is demonstrated for sodium chloride, NaCl, using basis sets close to the Hartree-Fock limit. It is demonstrated that the Hartree-Fock band-structure can easily be recovered with the current approach and agrees with the one obtained from a more conventional Bloch-orbital-based calculation. It is argued that the advantage of the present approach lies in its capability to include electron correlation effects for crystalline insulators by means of well-established quantum chemical procedures.

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Section: Calculations and Resultsmentioning

confidence: 99%

A Hartree–Fock ab initio band-structure calculation employing Wannier-type orbitals

Albrecht

Shukla

Dolg

et al. 1998

Chemical Physics Letters

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“…Moreover, it is interesting to note that the standard GLOS [28] provide the best results for such cases: for the CO (CdU) and M,04 (Td) species, there are 21,494 and 14,306 integrals to be computed over GLOS, against 23,678 and 15,132 for the AGLOS or CGTOS basis sets, respectively.…”

Section: Sample Calculations and Discussionmentioning

confidence: 99%

On the use of spatial symmetry in atomic‐integral calculations: An efficient permutational approach

Rouzo¹

1979

Int J of Quantum Chemistry

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AbstractsThe minimal number of independent nonzero atomic integrals that occur over arbitrarily oriented basis orbitals of the form % ( r ) . Yl,(n) is theoretically derived. The corresponding method can be easily applied to any point group, including the molecular continuous groups C,, and Dmh. O n the basis of this (theoretical) lower bound, the efficiency of the permutational approach in generating sets of independent integrals is discussed. It is proved that lobe orbitals are always more efficient than the familiar Cartesian Gaussians, in the sense that GLOS provide the shortest integral lists. Moreover, it appears that the new axial GLOS often lead to a number of integrals, which is the theoretical lower bound previously defined. With AGLOS, the numbers of two-electron integrals to be computed, stored, and processed are divided by factors 2.9 (NH,), 4.2 (C5Hs), and 3.6 (C&) with reference to the corresponding CGTOS calculations. Remembering that in the permutational approach, atomic integrals are directly computed without any four-indice transformation, it appears that its utilization in connection with AGLOS provides one of the most powerful tools for treating symmetrical species.Le nornbre minimal d'inttgrales atomiques indtpendantes et non nulles qui apparaissent entre des orbitales d e base d e la forme % ( I ) . Y,,@) et ayant des orientations arbitraires, est dtrivt thtoriquement. La rnithode correspondante peut h e aistment appliqute a n'importe quel groupe ponctuel, y compris les groupes moltculaires continus C,, et Dmh. A partir de cette borne inferieure thtorique, I'efficacitb d e la mtthode permutationnelle de gintration des ensembles d'inttgrales independantes, est discutte. O n dtmontre que les orbitales "lobes" sont toujours plus efficaces que les Gaussiennes Carttsiennes, dans la mesure ou les premieres fournissent les listes d'inttgrales les plus courtes. D e plus, il apparait que les nouvelles fonctions "axiales" (AGLO) conduisent souvent a un nombre d'inttgrales qui est la borne thtorique infirieure difinie plus haut. Avec les AGLOS, les nombres d'inttgrales bitlectroniques qui doivent &tre calcultes, conservtes et utilisies par la suite, sont divists par des facteurs de 2.9 (NH3). 4.2 (C5Hs), et 3.6 (C6H6) par rapport aux calculs correspondants effectuts avec des gaussiennes cartisiennes. Si I'on se souvient que dans I'approche permutationnelle les inttgrales atomiques sont calcultes directement, sans aucune transformation quatre indices, il apparait que I'utilisation de cette mtthode avec des fonctions de base de type AGLO, constitue un des outils les plus puissants permettant d e traiter les rnoltcules symttriques.

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“…For a charge distribution of the type lP a {l){a/ax)lPb{l), it is convenient to define a new function, (10) where 110 ml, nt, 1 2 , m2, n2 are even positive integers or zero and the x component of Gab is denoted as…”

Section: A Operator P2qmentioning

confidence: 99%

Relativistic integrals over Breit–Pauli operators using general Cartesian Gaussian functions. I. One-electron interactions

Chandra

Buenker

1983

The Journal of Chemical Physics

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Comment on: ''Relativistic integrals over Breit-Pauli operators using general Cartesian Gaussian functions''Cartesian Gaussian functions are employed to derive general expressions for integrals over all one-electron operators of the .Breit-Pauli Hamiltonian. It is shown that in atoms of higher atomic number p6, p', ... operators.can ~e Important in determining relativistic corrections to the kinetic energy. All other operators of ~hls Hamlltoman can be expressed as some derivative of l/r. Thus, a general expression is derived for the mtegral over .the. operator (ol/oX ') (em /oym) (on /iJz") (l/r) by employing its Fourier transform. The operator and charge-dlstnbutlOn-dependent parts can be separately identified in the resulting expression and hence for a given charge distribution, integrals over any number of operators that can be expressed in the above form can b~ obtained simultaneously. In addition to nuclear attraction, these operators include the spin-orbit and DarWin ter~s of t~e Breit-Pauli Hamiltonian, as well as the electric field components and their derivatives, and ot~er mteractlOns over operators required in the study of magnetic shieldings. Furthermore, these expressIOns serve as a prototype for more difficult and numerous two-electron integrals, as discussed in the second paper in this series.358

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Ein neuer Doppelprojektor

Cited by 5 publications

References 0 publications

A Hartree–Fock ab initio band-structure calculation employing Wannier-type orbitals

A Hartree–Fock ab initio band-structure calculation employing Wannier-type orbitals

On the use of spatial symmetry in atomic‐integral calculations: An efficient permutational approach

Relativistic integrals over Breit–Pauli operators using general Cartesian Gaussian functions. I. One-electron interactions

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