General recurrence formulas for molecular integrals over Cartesian Gaussian functions

Obara, Shigeru; Saika, A.

doi:10.1063/1.455717

Cited by 131 publications

(101 citation statements)

References 15 publications

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“…The bra orbital in eq A16, 〈φ bν Π j*i (r Rj -R bRj )| is also a Gaussian orbital with a higher angular momentum and the overlap S is therefore calculated using a Gaussian routine with the recurrence formulas. 107 …”

Section: Discussionmentioning

confidence: 99%

Collective Solvent Coordinates for the Infrared Spectrum of HOD in D₂O Based on an ab Initio Electrostatic Map

et al. 2004

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An ab initio MP2 vibrational Hamiltonian of HOD in an external electrostatic potential parametrized by the electric field and its gradient-tensor is constructed. By combining it with the fluctuating electric field induced by the D 2 O solvent obtained from molecular dynamics simulations, we calculate the infrared absorption of the O-H stretch. The resulting solvent shift and infrared line shape for three force fields (TIP4P, SPC/E, and SW) are in good agreement with the experiment. A collective coordinate response for the solvent effect is constructed by identifying the main electrostatic field and gradient components contributing to the line shape. This allows a realistic stochastic Liouville equation simulation of the line shapes which is not restricted to Gaussian frequency fluctuations.

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Section: Discussionmentioning

confidence: 99%

Collective Solvent Coordinates for the Infrared Spectrum of HOD in D₂O Based on an ab Initio Electrostatic Map

et al. 2004

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“…Among the most used of these analytical algorithms, we can mention the PopleHehre (PH) one [123], which additionally exploits the fact that for each fourcenter ERI of low angular momentum there is a privileged Cartesian axis system in which many primitive integrals vanish by symmetry; the McMurchie-Davidson (MD) approach [124], which avoids the rotation in PH thus being more efficient for high angular momentum ERIs; the Obara-Saika-Schlegel (OSS) algorithm [125,126]; and a better defined and improved version of it: the Head-Gordon-Pople (HGP) algorithm [127]. Finally, if the moment at which the contraction is handled is chosen dynamically depending on the type of GTO appearing in the ERI, we have the PRISM modifications of MD and HGP: the MD-PRISM [121,128,129] and HGP-PRISM [122] algorithms, as well as a generalization of all the previous methods, called COLD PRISM [131].…”

Section: Modern Developments: An Introduction To Linear-scaling Methodsmentioning

confidence: 99%

A mathematical and computational review of Hartree–Fock SCF methods in quantum chemistry

Echenique¹,

Alonso²

2007

Molecular Physics

104

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We present here a review of the fundamental topics of Hartree-Fock theory in Quantum Chemistry. From the molecular Hamiltonian, using and discussing the Born-Oppenheimer approximation, we arrive to the Hartree and Hartree-Fock equations for the electronic problem. Special emphasis is placed in the most relevant mathematical aspects of the theoretical derivation of the final equations, as well as in the results regarding the existence and uniqueness of their solutions. All Hartree-Fock versions with different spin restrictions are systematically extracted from the general case, thus providing a unifying framework. Then, the discretization of the one-electron orbitals space is reviewed and the Roothaan-Hall formalism introduced. This leads to a exposition of the basic underlying concepts related to the construction and selection of Gaussian basis sets, focusing in algorithmic efficiency issues. Finally, we close the review with a section in which the most relevant modern developments (specially those related to the design of linear-scaling methods) are commented and linked to the issues discussed. The whole work is intentionally introductory and rather self-contained, so that it may be useful for non experts that aim to use quantum chemical methods in interdisciplinary applications. Moreover, much material that is found scattered in the literature has been put together here to facilitate comprehension and to serve as a handy reference.

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“…[43] and can also be calculated from recursion relations. [44] For convenience, we restate the simplified relations for the special cases involving s and p-type GTO's all in terms of the basic quantity ∂S ij…”

Section: Acknowledgmentsmentioning

confidence: 99%

Metrics for measuring distances in configuration spaces

Sadeghi

Ghasemi

Schaefer

et al. 2013

The Journal of Chemical Physics

140

207

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In order to characterize molecular structures we introduce configurational fingerprint vectors which are counterparts of quantities used experimentally to identify structures. The Euclidean distance between the configurational fingerprint vectors satisfies the properties of a metric and can therefore safely be used to measure dissimilarities between configurations in the high dimensional configuration space. We show that these metrics correlate well with the RMSD between two configurations if this RMSD is obtained from a global minimization over all translations, rotations and permutations of atomic indices. We introduce a Monte Carlo approach to obtain this global minimum of the RMSD between configurations.

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General recurrence formulas for molecular integrals over Cartesian Gaussian functions

Cited by 131 publications

References 15 publications

Collective Solvent Coordinates for the Infrared Spectrum of HOD in D₂O Based on an ab Initio Electrostatic Map

Collective Solvent Coordinates for the Infrared Spectrum of HOD in D₂O Based on an ab Initio Electrostatic Map

A mathematical and computational review of Hartree–Fock SCF methods in quantum chemistry

Metrics for measuring distances in configuration spaces

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General recurrence formulas for molecular integrals over Cartesian Gaussian functions

Cited by 131 publications

References 15 publications

Collective Solvent Coordinates for the Infrared Spectrum of HOD in D2O Based on an ab Initio Electrostatic Map

Collective Solvent Coordinates for the Infrared Spectrum of HOD in D2O Based on an ab Initio Electrostatic Map

A mathematical and computational review of Hartree–Fock SCF methods in quantum chemistry

Metrics for measuring distances in configuration spaces

Contact Info

Product

Resources

About

Collective Solvent Coordinates for the Infrared Spectrum of HOD in D₂O Based on an ab Initio Electrostatic Map

Collective Solvent Coordinates for the Infrared Spectrum of HOD in D₂O Based on an ab Initio Electrostatic Map