Charge-conserving integral approximations for ab initio quantum chemistry

Wilhite, D. L.; Euwema, R. N.

doi:10.1016/0009-2614(73)80513-5

Cited by 52 publications

(10 citation statements)

References 8 publications

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“…The error involved in using (12) for the evaluation of the integral (y,kZ) can be estimated from: We can derive (13) starting from the follow- a point with coordinates A,, A,, and A,, the function is multipled by a factor (x -Ax).…”

Section: The Expansion Of a Product Of Two Gaussiansmentioning

confidence: 99%

Ab initio calculations on large molecules: The multiplicative integral approximation

1988

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In the multiplicative integral approximation (MIA), two-electron integrals are evaluated using an expansion of a product of two Gaussians in terms of auxiliary functions. An estimator of the error introduced by the approximation is incorporated in the self-consistent field (SCF) calculations and the integrals for which the error estimate is larger than a preset value are systematically corrected. In this way the results of a MIA-assisted calculation have the same accuracy as a conventional calculation. The full exploitation of the expansion technique while constructing the Fock-matrix allows important time savings. Results are presented for a number of test cases.

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Section: The Expansion Of a Product Of Two Gaussiansmentioning

confidence: 99%

Ab initio calculations on large molecules: The multiplicative integral approximation

1988

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“…In the scheme of Wilhite and Euwema [7], the basis set is the usual set f. The same integrals (ijlkiy are evaluated as in our scheme for a given threshold. Overlap, kinetic, and nuclear attraction integrals for weakly related pairs are also neglected.…”

Section: Calculations and Discussionmentioning

confidence: 99%

“…Otherwise, the pair (i, j ) is called a strongly related pair and XI is set at the original overlap integral S,,. This partitioning of orbital pairs was proposed by Wilhite and Euwema [7].…”

Section: Methodsmentioning

confidence: 95%

Test of an integral approximation scheme based on semiorthogonalized orbitals in LCAO SCF MO CI calculations of naphthalene

Kashiwagi

Takada

1977

Int J of Quantum Chemistry

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AbstractsAb inirio LCAO SCF MO CI calculations of naphthalene are carried out with a minimal basis set to test an integral approximation scheme proposed in a previous paper. When 71.3 and 53.0% of the two-electron integrals are neglected, the errors in the SCF total energy are only -0.0534 and -0.0006 a x , respectively. In the latter case, the maximum absolute errors of the orbital energy and the gross AO population are 0.007 a.u. and 0.001, respectively. Even in the former case the errors of the excitation energies are less than 0.0004 a x . Errors of oscillator strengths are also examined and are found to be tolerably small. LcAo-scF-MO-CI-Berechnungen von ab-initio-Typ sind fur Naphtalin mit einem Minimalbasissatz ausgefuhrt worden um ein in einem friiheren Artikel von einem der Verfasser eingefuhrtes Naherungsverfahren fur Integrale zu testen. Wenn 71.3 und 53.0% bzw. der Zweielektronenintegrale vernachlassigt werden, sind die Fehler in der Gesamtenergie nur -0.0534 und -0.0006 at.E. Im zweiten Fall sind die maximalen Absolutfehler der Orbitalenergien und der "gross AO population" 0.007 at.E. und 0.001, bzw. Sogar im ersten Fall sind die Fehler in den Anregungsenergien kleiner als 0.0004 at.E. Fehler in Oszillatorenstarken sind auch untersucht worden; sie haben sich ziemlich klein erwiesen.

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“…The characters ,y*(R) of the [T(R)I2 matrix are easily expressed in terms of ,yl(R) [14] X 2 ( R 1 = t[x: ( R )+ X I @ ' 11 (3 ) so that [rI2 can be solved like r (Eq. (1)).…”

Section: Minimal Number Of Independent Nonzero Atomic Integralsmentioning

confidence: 99%

“…Several efficient methods are now available and allow for the detection, before their actual calculations, of integrals that are smaller than a given threshold and whose computation (and eventually storage) can consequently be avoided. For Gaussian-type orbitals (GTO), it has been proposed to replace contracted functions [2] and distributions [3] by single GTOS, chosen by least-squares procedures, in order to get a fast estimation of the integral magnitude. Effective testing algorithms are available for Gaussian-lobe orbitals (GLO) [ 1,4].…”

Section: Introductionmentioning

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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Charge-conserving integral approximations for ab initio quantum chemistry

Cited by 52 publications

References 8 publications

Ab initio calculations on large molecules: The multiplicative integral approximation

Ab initio calculations on large molecules: The multiplicative integral approximation

Test of an integral approximation scheme based on semiorthogonalized orbitals in LCAO SCF MO CI calculations of naphthalene

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

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