On the accuracy of the algebraic approximation in molecular electronic structure calculations: VI. Matrix Hartree - Fock and many-body perturbation theory calculations for the ground state of the water molecule

Moncrieff, David; Wilson, Stephen

doi:10.1088/0953-4075/29/24/009

Cited by 35 publications

(9 citation statements)

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“…Table displays the theoretical total Hartree–Fock (HF) energies obtained with contracted hybrid‐basis set (this work); contracted atom‐optimized basis sets (ADZP and aug‐cc‐pVDZ); and uncontracted molecule‐optimized basis sets . Numerical HF (NHF) results are also shown. The results presented in Table for uncontracted basis sets have the following compositions: i.…”

Section: Resultsmentioning

confidence: 99%

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Molecule‐adapted basis sets optimized with a quantum Monte Carlo method

Arruda

Neto

Campos

et al. 2014

Int J of Quantum Chemistry

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The Monte Carlo simulated annealing method is adapted to optimize correlated Gaussian‐type functions in nonrelativistic molecular environments. Starting from an atom‐centered atomic Gaussian basis set, the uncontracted functions are reoptimized in the molecular environments corresponding to the H2O, CN−, N2, CO, BF, NO+, CO2, and CS systems. These new molecular adapted basis sets are used to calculate total energies, harmonic vibrational frequencies, and equilibrium geometries at a correlated level of theory. The present methodology is a simple and effective way to improve molecular correlated wave functions, without the need to enlarge the molecular basis set. Additionally, this methodology can be used to generate hierarchical sequences of molecular basis sets with increasing size, which are relevant to establish complete basis set limits. © 2014 Wiley Periodicals, Inc.

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Section: Resultsmentioning

confidence: 99%

“…Conversely, universal basis sets, for high‐accuracy molecular applications require the use of high performance computing machines, suitable algorithms, and direct methods. As an example, Moncrieff and Wilson have reduced the computation cost to generate GBSs for some diatomic and triatomic systems, using the even‐tempered scheme.…”

Section: Introductionmentioning

confidence: 99%

Molecule‐adapted basis sets optimized with a quantum Monte Carlo method

Arruda

Neto

Campos

et al. 2014

Int J of Quantum Chemistry

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“…As is commonly known from Gaussian-basis calculations, the basis set convergence of the correlation energy is very slow. 152,[666][667][668][669][670] In fact, the problem appears already for two-electron systems, 671 e.g. in configuration interaction calculations on the 1s 2 state of He as discovered in the late 1970s in seminal work by Silverstone and coworkers.…”

Section: Post-hf Approachesmentioning

confidence: 99%

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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“…The complete basis set (CBS) limit represents the high accuracy, high computational cost limit for basis set selection. Extrapolation to the CBS limit takes advantage of convergence with successively larger basis sets, and aims to eliminate any errors from choice of basis set . Basis set truncation, dual basis approaches, and related extrapolations have also been used to approach the CBS limit.…”

Section: Introductionmentioning

confidence: 99%

Stepwise basis set selection

Zimmerman

2018

J Comput Chem

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The computational cost of quantum chemical methods grows rapidly with increasing level of theory and basis set size. At increasing costs, higher accuracies can be reached, forcing a compromise between cost and accuracy for most molecular systems. Heats of reaction, however, are mostly determined by a subset of atoms that experience significant bonding and/or electronic changes. To exploit this fact, the Stepwise Basis Builder (SBB) algorithm selectively adds basis functions to reactive atoms and maintains small basis sets on spectator atoms. This article introduces the SBB algorithm and how it chooses a basis for each atom, predicts calculation errors, and uses these predicted errors to reach target levels of accuracy. Benchmarks show SBB heats of reaction and activation barriers converge to values consistent with higher-quality calculations using a greatly reduced number of basis functions. V C 2018 Wiley Periodicals, Inc.

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On the accuracy of the algebraic approximation in molecular electronic structure calculations: VI. Matrix Hartree - Fock and many-body perturbation theory calculations for the ground state of the water molecule

Cited by 35 publications

References 70 publications

Molecule‐adapted basis sets optimized with a quantum Monte Carlo method

Molecule‐adapted basis sets optimized with a quantum Monte Carlo method

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

Stepwise basis set selection

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