Occupied-Orbital Fast Multipole Method for Efficient Exact Exchange Evaluation

Le, Hai-Anh; Shiozaki, Toru

doi:10.1021/acs.jctc.7b00880

Cited by 7 publications

(3 citation statements)

References 49 publications

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“…In addition, RHF based on the fast multipole methods (FMM) including exact exchange is implemented for systems larger than a few hundreds of atoms. 6 MP2 is implemented as a post-HF method to account for dynamical electron correlation. The programs for computing analytical nuclear gradients for RHF, UHF, ROHF, and MP2 are available, all of which are efficiently parallelized.…”

Section: Single-reference Modelsmentioning

confidence: 99%

“…The pilot KS‐DFT code is also implemented using Libxc, but it is neither efficient nor of production quality; we are hereby soliciting future collaboration for improving the DFT code. In addition, RHF based on the fast multipole methods (FMM) including exact exchange is implemented for systems larger than a few hundreds of atoms . MP2 is implemented as a post‐HF method to account for dynamical electron correlation.…”

Section: Program Featuresmentioning

confidence: 99%

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BAGEL: Brilliantly Advanced General Electronic‐structure Library

Shiozaki

2017

WIREs Comput Mol Sci

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On behalf of the development team, I review the capabilities of the Brilliantly Advanced General Electronic-structure Library (BAGEL) program package in this article. BAGEL is a newly developed full-fledged program package for electronic-structure computation in quantum chemistry, which is released under the GNU General Public License with many contributions from the developers. The unique features include analytical CASPT2 nuclear energy gradients and derivative couplings, relativistic multireference wave functions based on the Dirac equation, and implementations of novel electronic structure theories. All of the programs are efficiently parallelized using both threads and MPI processes. We also discuss the code generator SMITH3, which has been used to implement some of the programs in BAGEL. The developers' contributions are listed at the end of the main text.

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Section: Single-reference Modelsmentioning

confidence: 99%

Section: Program Featuresmentioning

confidence: 99%

BAGEL: Brilliantly Advanced General Electronic‐structure Library

Shiozaki

2017

WIREs Comput Mol Sci

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188

204

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“…Throughout the past few decades, there has been extensive methodological developments to optimize its evaluation using a range of approaches varying in complexity, sophistication and accuracy. It is worthwhile mentioning some of the notable ones, such as pseudo-spectral scheme using Gaussian basis functions, multipole accelerated algorithm, LinK, truncated or short-range exchange kernels with/without the use of resolution-of-theidentity (RI) approximation, chain-of-sphere exchange based on quadrature, auxiliary density matrix, plane-wave basis functions, metropolis stochastic, pair-atomic RI, adaptively compressed exchange operator, density fitting with local domains, real-space with projection operators, rigorous integral screening, occupied-orbital fast multipole [24][25][26][27][28][29][30][31][32] , etc. The HF exchange energy density can be represented as,…”

Section: Introductionmentioning

confidence: 99%

Efficient HF exchange evaluation through Fourier convolution in Cartesian grid for orbital-dependent density functionals

Ghosal

Mandal

Roy

2019

The Journal of Chemical Physics

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We present a purely numerical approach in Cartesian grid, for efficient computation of Hartree-Fock (HF) exchange contribution in the HF and density functional theory models. This takes inspiration from a recently developed algorithm [Liu et al., J. Chem. Theor. Comput. 13, 2571]. A key component is the accurate evaluation of electrostatic potential integral, which is the rate-determining step. This introduces the Fourier convolution theorem in conjunction with a range-separated Coulomb interaction kernel. The latter is efficiently mapped into real grid through a simple optimization procedure, giving rise to a constraint in the range-separated parameter.The overall process offers logarithmic scaling with respect to molecular size. It is then extended towards global hybrid functionals such as B3LYP, PBE0 and BHLYP within pseudopotential Kohn-Sham theory, through an LCAO-MO ansatz in Cartesian grid, developed earlier in our laboratory. For sake of comparison, a parallel semi-numerical approach has also been worked out that exploits the familiar Obara-Saika recursion algorithm. An excellent agreement between these two routes is demonstrated through total energy and orbital energy in a series of atoms and molecules (including 10 πelectron molecules), employing an LANL2DZ-type basis function. A critical analysis of these two algorithms reveals that the proposed numerical scheme could lead to very attractive and competitive scaling. The success of our approach also enables us for further development of optimally tuned range-separated hybrid and hyper functionals.

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CASSCF linear response calculations for large open-shell molecules

Helmich‐Paris

2019

The Journal of Chemical Physics

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The complete active space self-consistent-field (CASSCF) linear response method for the simulation of ultraviolet-visible (UV/Vis) absorption and electronic circular dichroism (ECD) spectra of large open-shell molecules is presented. By using a one-index transformed Hamiltonian, the computation of the most time-consuming intermediates can be pursued in an integral-direct fashion, which allows us to employ the efficient resolution-of-the-identity and overlap-fitted chain-of-spheres approximation. For the iterative diagonalization, pairs of Hermitian and anti-Hermitian trial vectors are used which facilitate, on the one hand, an efficient solution of the pair-structured generalized eigenvalue problem in the reduced space, and on the other hand, make the full multiconfigurational random phase approximation as efficient as the corresponding Tamm-Dancoff approximation. Electronic transitions are analyzed and characterized in the particle-hole picture by natural transition orbitals that are introduced for CASSCF linear response theory. For a small organic radical, we can show that the accuracy of simulated UV/Vis absorption spectra with the CASSCF linear response approach is significantly improved compared to the popular state-averaged CASSCF method. To demonstrate the efficiency of the implementation, the 50 lowest roots of a large Ni triazole complex with 231 atoms are computed for the simulated UV/Vis and ECD spectra.

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Occupied-Orbital Fast Multipole Method for Efficient Exact Exchange Evaluation

Cited by 7 publications

References 49 publications

BAGEL: Brilliantly Advanced General Electronic‐structure Library

BAGEL: Brilliantly Advanced General Electronic‐structure Library

Efficient HF exchange evaluation through Fourier convolution in Cartesian grid for orbital-dependent density functionals

CASSCF linear response calculations for large open-shell molecules

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