Long-Range Behavior of Hartree-Fock Orbitals

Handy, Nicholas C.; Marron, Michael T.; Silverstone, Harris J.

doi:10.1103/physrev.180.45

Cited by 236 publications

(121 citation statements)

References 2 publications

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“…Because all of the integrals that arise in Hartree−Fock and traditional post-Hartree−Fock calculations can be reduced 12−27 to elementary functions and error functions, 28 Gaussians are ubiquitous in molecular calculations and have even challenged plane waves in solidstate calculations. 29,30 However, from a theoretical viewpoint, Gaussians are suboptimal for two reasons: they lack a cusp 31 at r = 0, and they decay too fast 32 at large r. The complementary nature of these deficiencies becomes clear if an exponential function (the exact wave function for a hydrogen atom) and a Gaussian (the exact wave function for a harmonic oscillator) are superimposed as shown in Figure 1. The logarithmic transformation that converts the exponential into a straight line converts the Gaussian into a sigmoidal curve that is flat at both ends of the domain.…”

Section: Introductionmentioning

confidence: 99%

Gaussian Expansions of Orbitals

McKemmish

Gill

2012

J. Chem. Theory Comput.

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Using numerical calculations and analytic theory, we examine the convergence behavior of Gaussian expansions of several model orbitals. By following the approach of Kutzelnigg, we find that the errors in the energies of the optimal n-term even-tempered Gaussian expansions of s-type, p-type, and d-type exponential orbitals are ε n s ∼ exp(−π(3n) 1/2 ), ε n p ∼ exp(−π(5n) 1/2 ), and ε n d ∼ exp(−π(7n) 1/2 ), respectively. We show that such "root-exponential" convergence patterns are a consequence of the orbital cusps at r = 0, rather than the over-rapid decay of Gaussians at large r. We find that even-tempered expansions of the cuspless Lorentzian orbital also exhibit root-exponential convergence but that this is a consequence of its fat tail.

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Section: Introductionmentioning

confidence: 99%

Gaussian Expansions of Orbitals

McKemmish

Gill

2012

J. Chem. Theory Comput.

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“…where ↔ α is the polarizability tensor of the ionized system, and v ∞ C is an arbitrary constant, which we take as zero (57,58). Clearly, in both approaches the asymptotic form of the XC potential is dominated by the exchange −1/r behavior.…”

Section: Gks Cmentioning

confidence: 99%

“…Thus, the GKS system has higher kinetic energy than that of the KS system, whereas its XC energy is lower. (58), where ε M (M) is the orbital energy of the highest occupied molecular orbital (HOMO). The arguments of Reference 58 hold for GKS as well.…”

Section: Gks Cmentioning

confidence: 99%

Tuned Range-Separated Hybrids in Density Functional Theory

Baer

Livshits

Salzner

2010

Annu. Rev. Phys. Chem.

747

846

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We review density functional theory (DFT) within the Kohn-Sham (KS) and the generalized KS (GKS) frameworks from a theoretical perspective for both time-independent and time-dependent problems. We focus on the use of range-separated hybrids within a GKS approach as a practical remedy for dealing with the deleterious long-range self-repulsion plaguing many approximate implementations of DFT. This technique enables DFT to be widely relevant in new realms such as charge transfer, radical cation dimers, and Rydberg excitations. Emphasis is put on a new concept of system-specific range-parameter tuning, which introduces predictive power in applications considered until recently too difficult for DFT.

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“…In principle, at large distances the potential should be dominated by the exchange term decaying as −1/r, while the correlation term decays as ≈ −1/r 4 . 32,33 However, for the local density approximation and to a lesser extent for the generalized gradient approximation (GGA), the exchange term decays exponentially. 34 Second, the approximate nature of the exchange term does not cancel the Coulomb interaction of the electron with itself at large r as it is the case for the Hartree-Fock (HF) method (self-interaction error).…”

Section: Optimally Tuned Rangeseparated Functionalsmentioning

confidence: 99%

Tuning Range-Separated Density Functional Theory for Photocatalytic Water Splitting Systems

Bokarev

Grell

Kühn

2015

J. Chem. Theory Comput.

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We discuss the system-specific optimization of long-range separated density functional theory (DFT) for the prediction of electronic properties relevant for a photocatalytic cycle based on an Ir(III) photosensitizer (IrPS). Special attention is paid to the charge-transfer properties, which are of key importance for the photoexcitation dynamics, but and cannot be correctly described by means of conventional DFT. The optimization of the rangeseparation parameter using the ∆SCF method is discussed for IrPS including its derivatives and complexes with electron donors and acceptors used in photocatalytic hydrogen production. Particular attention is paid to the problems arising for a description of medium effects by means of a polarizable continuum model.

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Long-Range Behavior of Hartree-Fock Orbitals

Cited by 236 publications

References 2 publications

Gaussian Expansions of Orbitals

Gaussian Expansions of Orbitals

Tuned Range-Separated Hybrids in Density Functional Theory

Tuning Range-Separated Density Functional Theory for Photocatalytic Water Splitting Systems

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