Distributed Gaussian basis sets: a comparison with finite difference Hartree–Fock calculations for potential energy curves of H<sub>2</sub>, LiH and BH

Glushkov, V. N.; Kobus, Jacek; Wilson, Stephen

doi:10.1088/0953-4075/41/20/205102

Cited by 13 publications

(18 citation statements)

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“…Отметим, что, несмот-ря на простоту таких функций, они оказались полезными при расчетах состояний -симметрии ряда малых моле-кул: H 2 , НеН, ВеН и ВН. Значения энергии ХФ в таких оптимизированных базисах отличаются от ХФ-предела лишь на десятые доли микрохартри (µ hartree) [3,4]. Как отмечалось, нами рассматривались два типа бази-сов.…”

Section: алгоритм и обсуждение результатов расчетаunclassified

“…Для фиксированного межъядерного расстояния строим начальное приближение для параметров базиса, ς p и Z p . Для этого используется так называемая ан-гармоническая модель для построения дистрибутивных базисов [4].…”

Section: алгоритм и обсуждение результатов расчетаunclassified

“…Тогда можно ожидать, что после-довательность увеличивающихся по размеру базисов обеспечивает сходимость значений искомой величины к пределу полного базиса. Например, для энергии ХФ такая последовательность оптимальных базисов строит-ся минимизацией частного Релея по параметрам бази-са [1][2][3][4]. Базис, оптимальный для энергии корреляции во втором порядке многочастичной теории возмущений, может быть выбран путем минимизации функционала Хиллераса [5].…”

Section: Introductionunclassified

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О Выборе Дистрибутивного Базиса В Расчетах Дипольных Моментов Перехода В Однодетерминантном Приближении

Глушков¹,

Фесенко²

2018

Журнал Технической Физики

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Section: алгоритм и обсуждение результатов расчетаunclassified

Section: Introductionunclassified

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О Выборе Дистрибутивного Базиса В Расчетах Дипольных Моментов Перехода В Однодетерминантном Приближении

Глушков¹,

Фесенко²

2018

Журнал Технической Физики

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“…can be very useful [96,97] in terms of economy and accuracy of computation. Different parameters α k and β k can be used for the ground (k = 0) and excited (k = 1) states.…”

Section: Distributed Gaussian Basis Sets For Ground and Excited Statesmentioning

confidence: 99%

“…α k and β k can be taken to be functions of m. In 1979, it was established [42] that for atoms well-defined schemes can be constructed such that even-tempered basis sets approach a complete set in the limit of large m and, therefore, the Hartree-Fock limit is approached. It has been shown [96,97] that an anharmonic model can be profitably used to distribute the basis functions along the internuclear axis in diatomic molecules. In the present study, we used a series of anharmonic distributions with shifted origins to generate subsets of functions centred on regularly spaced points lying on the straight line passing through the two nuclei.…”

Section: Distributed Gaussian Basis Sets For Ground and Excited Statesmentioning

confidence: 99%

The Coulson–Fischer wave functions for the ground and excited states of H₂and HeH⁺: parametrisation using distributed Gaussian basis sets

Glushkov

Wilson

2014

Molecular Physics

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Coulson-Fischer wave functions are used to determine complete potential energy curves for the X 1 + g ground state of the H 2 molecule and for the first excited state EF 1 + g having the same symmetry. The Coulson-Fischer orbitals are parametrised by expansion in distributed Gaussian basis sets of s-type functions. The exponents of the Gaussian functions are generated by using an even-tempered prescription. An anharmonic model is used to locate the basis functions along the internuclear axis. Sequences of basis sets are used to reduce the basis set truncation error to the sub-μhartree level. Equations are derived to determine the generalised Coulson-Fischer orbitals for the excited state which ensure that orthogonality conditions with respect to the ground state are satisfied. Potential energy curves are also calculated using smaller basis sets for which both exponents and basis function positions are determined by invoking the variation principle. The results of calculations for the isoelectronic heteronuclear HeH + ion are also reported. The potential energy curves obtained in the present study are compared with literature values for both H 2 and HeH + .

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A review on non‐relativistic, fully numerical electronic structure calculations on atoms and diatomic molecules

Lehtola

2019

Int J of Quantum Chemistry

102

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The need for accurate calculations on atoms and diatomic molecules is motivated by the opportunities and challenges of such studies. The most commonly used approach for all-electron electronic structure calculations in general-the linear combination of atomic orbitals (LCAO) method-is discussed in combination with Gaussian, Slater a.k.a. exponential, and numerical radial functions. Even though LCAO calculations have major benefits, their shortcomings motivate the need for fully numerical approaches based on, for example, finite differences, finite elements, or the discrete variable representation, which are also briefly introduced. Applications of fully numerical approaches for general molecules are briefly reviewed, and their challenges are discussed. It is pointed out that the high level of symmetry present in atoms and diatomic molecules can be exploited to fashion more efficient fully numerical approaches for these special cases, after which it is possible to routinely perform allelectron Hartree-Fock and density functional calculations directly at the basis set limit on such systems. Applications of fully numerical approaches to calculations on atoms as well as diatomic molecules are reviewed. Finally, a summary and outlook is given.atomic calculations, density functional theory, diatomic calculations, fully numerical electronic structure theory, Hartree-Fock | INTRODUCTIONThanks to decades of development in approximate density functionals and numerical algorithms, density functional theory [1,2] (DFT) is now one of the cornerstones of computational chemistry and solid-state physics. [3][4][5] Since atoms are the basic building block of molecules, a number of popular density functionals [6][7][8][9][10] have been parametrized using ab initio data on noble gas atoms; these functionals have been used in turn as the starting point for the development of other functionals. A comparison of the results of density-functional calculations to accurate ab initio data on atoms has, however, recently sparked controversy on the accuracy of a number of recently published, commonly used density functionals. [11][12][13][14][15][16][17][18][19][20][21] This underlines that there is still room for improvement in DFT even for the relatively simple case of atomic studies.The development and characterization of new density functionals require the ability to perform accurate atomic calculations. Because atoms are the simplest chemical systems, atomic calculations may seem simple; however, they are in fact sometimes surprisingly challenging. For instance, a long-standing discrepancy between the theoretical and experimental electron affinity and ionization potential of gold has been resolved only very recently with high-level ab initio calculations. [22] Atomic calculations can also be used to formulate efficient starting guesses for molecular electronic structure calculations via either the atomic density [23,24] or the atomic potential as discussed in Ref. [25].

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Distributed Gaussian basis sets: a comparison with finite difference Hartree–Fock calculations for potential energy curves of H₂, LiH and BH

Cited by 13 publications

References 78 publications

О Выборе Дистрибутивного Базиса В Расчетах Дипольных Моментов Перехода В Однодетерминантном Приближении

О Выборе Дистрибутивного Базиса В Расчетах Дипольных Моментов Перехода В Однодетерминантном Приближении

The Coulson–Fischer wave functions for the ground and excited states of H₂and HeH⁺: parametrisation using distributed Gaussian basis sets

A review on non‐relativistic, fully numerical electronic structure calculations on atoms and diatomic molecules

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Distributed Gaussian basis sets: a comparison with finite difference Hartree–Fock calculations for potential energy curves of H2, LiH and BH

Cited by 13 publications

References 78 publications

О Выборе Дистрибутивного Базиса В Расчетах Дипольных Моментов Перехода В Однодетерминантном Приближении

О Выборе Дистрибутивного Базиса В Расчетах Дипольных Моментов Перехода В Однодетерминантном Приближении

The Coulson–Fischer wave functions for the ground and excited states of H2and HeH+: parametrisation using distributed Gaussian basis sets

A review on non‐relativistic, fully numerical electronic structure calculations on atoms and diatomic molecules

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Product

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Distributed Gaussian basis sets: a comparison with finite difference Hartree–Fock calculations for potential energy curves of H₂, LiH and BH

The Coulson–Fischer wave functions for the ground and excited states of H₂and HeH⁺: parametrisation using distributed Gaussian basis sets