Electronic wave functions - I. A general method of calculation for the stationary states of any molecular system

Boys, Samuel Francis

doi:10.1098/rspa.1950.0036

Cited by 1,082 publications

(154 citation statements)

References 4 publications

Supporting

Mentioning

149

Contrasting

Unclassified

Order By: Relevance

“…5 STFs behave similarly to hydrogen-like radial functions and are efficient in representing the AOs, but they are difficult to use in calculating threeand four-center two-electron integrals. Boys 6 started to use Gaussian-type orbitals or more properly Gaussian-type functions (GTFs), which differ from the STFs in the exponent term. When the same number of functions are used in linear least-squares fittings, the GTFs are less accurate than the STFs because they decay too fast when compared with the "real" radial functions (e.g., hydrogen-like orbitals).…”

Section: Introductionmentioning

confidence: 99%

Basis Set Exchange: A Community Database for Computational Sciences

Schuchardt

Didier

Elsethagen

et al. 2007

J. Chem. Inf. Model.

2,904

2,028

View full text Add to dashboard Cite

Basis sets are some of the most important input data for computational models in the chemistry, materials, biology, and other science domains that utilize computational quantum mechanics methods. Providing a shared, Web-accessible environment where researchers can not only download basis sets in their required format but browse the data, contribute new basis sets, and ultimately curate and manage the data as a community will facilitate growth of this resource and encourage sharing both data and knowledge. We describe the Basis Set Exchange (BSE), a Web portal that provides advanced browsing and download capabilities, facilities for contributing basis set data, and an environment that incorporates tools to foster development and interaction of communities. The BSE leverages and enables continued development of the basis set library originally assembled at the Environmental Molecular Sciences Laboratory. Disciplines Chemistry CommentsReprinted (adapted) Basis sets are some of the most important input data for computational models in the chemistry, materials, biology, and other science domains that utilize computational quantum mechanics methods. Providing a shared, Web-accessible environment where researchers can not only download basis sets in their required format but browse the data, contribute new basis sets, and ultimately curate and manage the data as a community will facilitate growth of this resource and encourage sharing both data and knowledge. We describe the Basis Set Exchange (BSE), a Web portal that provides advanced browsing and download capabilities, facilities for contributing basis set data, and an environment that incorporates tools to foster development and interaction of communities. The BSE leverages and enables continued development of the basis set library originally assembled at the Environmental Molecular Sciences Laboratory.

show abstract

Section: Introductionmentioning

confidence: 99%

Basis Set Exchange: A Community Database for Computational Sciences

Schuchardt

Didier

Elsethagen

et al. 2007

J. Chem. Inf. Model.

2,904

2,028

View full text Add to dashboard Cite

show abstract

“…The primitive integrals can be evaluated analytically as originally shown by Boys. 12 Since Boys' seminal work, numerous computational approaches have been developed to minimize the effort in this N 4 bottleneck. [13][14][15][16][17] However, even if the most efficient algorithm is being used, the twoelectron integral evaluation phase still takes much of the computation time.…”

Section: Two-electron Repulsion Integralsmentioning

confidence: 99%

Quantum Chemistry on Graphical Processing Units. 2. Direct Self-Consistent-Field Implementation

Ufimtsev

Martı́nez

2009

J. Chem. Theory Comput.

437

455

View full text Add to dashboard Cite

Abstract:Modern videogames place increasing demands on the computational and graphical hardware, leading to novel architectures that have great potential in the context of high performance computing and molecular simulation. We demonstrate that Graphical Processing Units (GPUs) can be used very efficiently to calculate two-electron repulsion integrals over Gaussian basis functionssthe first step in most quantum chemistry calculations. A benchmark test performed for the evaluation of approximately 10 6 (ss|ss) integrals over contracted s-orbitals showed that a naïve algorithm implemented on the GPU achieves up to 130-fold speedup over a traditional CPU implementation on an AMD Opteron. Subsequent calculations of the Coulomb operator for a 256-atom DNA strand show that the GPU advantage is maintained for basis sets including higher angular momentum functions.

show abstract

“…It was already apparent in the 1950s that calculations of polyatomic systems based on Slater-type orbitals would be intractable. The breakthrough occurred when Boys proposed basis functions based on Cartesian Gaussian functions [4]. It was also found that linear combinations of Gaussians, designated as contracted Gaussians, could approximate atomic orbitals with great accuracy.…”

Section: Introductionmentioning

confidence: 99%

Fast calculation of two-electron-repulsion integrals: a numerical approach

Lopes

2017

Theor Chem Acc

View full text Add to dashboard Cite

An alternative methodology to evaluate two-electron-repulsion integrals based on numerical approximation is proposed. Computational chemistry has branched into two major fields with methodologies based on quantum mechanics and classical force fields. However, there are significant shadowy areas not covered by any of the available methods. Many relevant systems are often too big for traditional quantum chemical methods while being chemically too complex for classical force fields. Examples include systems in nanomedicine, studies of metalloproteins, etc. There is an urgent need to develop fast quantum chemical methods able to study large and complex systems. This work is a proof-of-concept on the numerical techniques required to develop accurate and computationally efficient algorithms for the fast calculation of electron-repulsion integrals, one of the most significant bottlenecks in the extension of quantum chemistry to large systems. All concepts and calculations were developed for the three-center integral (p xA p xB |p xC p xC ) with all atoms being carbon. Starting with the analytical formulae, convenient decompositions were tested to provide smooth two-dimensional surfaces that were easily fitted. The approximating algorithm consisted of a multilayered approach based on multiple fittings of two-dimensional surfaces. An important aspect of the new method is its independence on the number of contracted Gaussian primitives. The basis set of choice was STO-6G. In future developments, larger basis sets will be developed. This work is part of a large effort aimed at improving the inadequacies of existing computational chemistry methods, both based on quantum mechanics and classical force fields, in particular in describing large and heterogeneous systems (ex. metalloproteins).

show abstract

Electronic wave functions - I. A general method of calculation for the stationary states of any molecular system

Cited by 1,082 publications

References 4 publications

Basis Set Exchange: A Community Database for Computational Sciences

Basis Set Exchange: A Community Database for Computational Sciences

Quantum Chemistry on Graphical Processing Units. 2. Direct Self-Consistent-Field Implementation

Fast calculation of two-electron-repulsion integrals: a numerical approach

Contact Info

Product

Resources

About