A dual-level approach to four-component relativistic density-functional theory

Mizukami, Wataru; Nakajima, Takahito; Hirao, Kimihiko; Yanai, Takeshi

doi:10.1016/j.cplett.2011.04.031

Cited by 3 publications

(6 citation statements)

References 51 publications

(58 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The key results of this work to arrive at an efficient program are intermediate factorization for exchange matrices [Eq. (36)]; simultaneous evaluation of the Gaunt and retardation terms [Eq. (48)]; and realization of a generic program using a simple scheme to evaluate the coefficient of each element [Eqs.…”

Section: Discussionmentioning

confidence: 99%

“…11,[24][25][26][27][28][29][30][31][32] There have also been many studies on fourcomponent density functional theories (DFT). 9,[33][34][35][36] Their computational costs have nonetheless been considered expensive since orbitals are expanded by 4-spinors, which has prompted the development of approximate two-component relativistic theories (some of them are exact for one-electron systems). In this work, however, we demonstrate by developing an efficient algorithm and a parallel program that the fourcomponent Dirac-Fock theories are routinely applicable to 100 atomic systems with a few heavy elements.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Large-scale Dirac–Fock–Breit method using density fitting and 2-spinor basis functions

Kelley

Shiozaki

2013

The Journal of Chemical Physics

View full text Add to dashboard Cite

We present an efficient theory and algorithm for computing four-component relativistic Dirac-Fock wave functions using the Coulomb, Gaunt, and full Breit interactions. Our implementation is based on density fitting, and is routinely applicable to systems with 100 atoms and a few heavy elements. The small components are expanded using 2-spinor basis functions. We show that the factorization of 3-index half-transformed integrals before building Coulomb and exchange matrices is essential for efficient evaluation of the Fock matrix. With the Coulomb interaction, the computational cost for evaluating the Fock operator has been found to be only 70-90 times that in the non-relativistic density-fitted Hartree-Fock method. The prefactors have been 170 and 350-450 for the Gaunt and Breit interactions, respectively. The largest molecule to which we have applied the Dirac-Fock-Coulomb method is an Ac(III) motexafin complex (130 atoms, 556 electrons, 1289 basis functions), for which one self-consistent iteration takes around 1100 s using 1024 CPU cores. In addition, we have found that, while the standard fitting basis sets are accurate for Dirac-Fock-Coulomb calculations, their accuracy is very poor for Dirac-Fock-Gaunt and Breit calculations. We report a prototype of accurate fitting basis sets for these cases.

show abstract

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Large-scale Dirac–Fock–Breit method using density fitting and 2-spinor basis functions

Kelley

Shiozaki

2013

The Journal of Chemical Physics

View full text Add to dashboard Cite

show abstract

“…Further promising DB HF approximations were introduced by Gill et al deriving perturbative corrections that estimate the complete basis set HF energy by diagonalizing the Fock potential from a small basis in a large one. , New DB MP2 methods were also proposed by these authors, where the MOs are obtained from the large basis HF calculation, and the DB approximation is invoked at the integral transformation. , An interesting dual-level DFT approach was published by Nakajima and Hirao, where, in the primary SCF calculation, not only a smaller basis set but also a less sophisticated functional was used . This approach was also extended to time-dependent DFT and relativistic DFT, while Gill and co-workers generalized the method by also applying a cruder quadrature grid at the first SCF run . The DB approximation was used in reduced-scaling correlation methods by Kobayashi and Nakai and Friedrich and Dolg, − and very recently Røeggen and Gao proposed a scheme closely related to the DB approach for the calculation of the correlation energy of molecules and solids .…”

Section: Introductionmentioning

confidence: 99%

“…33,34 An interesting dual-level DFT approach was published by Nakajima and Hirao, where, in the primary SCF calculation, not only a smaller basis set but also a less sophisticated functional was used. 35 This approach was also extended to time-dependent DFT 36 and relativistic DFT, 37 while Gill and co-workers generalized the method by also applying a cruder quadrature grid at the first SCF run. 38 The DB approximation was used in reduced-scaling correlation methods by Kobayashi and Nakai 39 and Friedrich and Dolg, 40−43 and very recently Røeggen and Gao proposed a scheme closely related to the DB approach for the calculation of the correlation energy of molecules and solids.…”

Section: Introductionmentioning

confidence: 99%

Dual Basis Set Approach for Density Functional and Wave Function Embedding Schemes

Hégely

Nagy

Kállay

2018

J. Chem. Theory Comput.

View full text Add to dashboard Cite

A dual basis (DB) approach is proposed which is suitable for the reduction of the computational expenses of the Hartree-Fock, Kohn-Sham, and wave function-based correlation methods. The approach is closely related to the DB approximation of Head-Gordon and co-workers [ J. Chem. Phys. 2006 , 125 , 074108 ] but specifically designed for embedding calculations. The new approach is applied to our variant of the projector-based embedding theory utilizing the Huzinaga-equation, multilevel local correlation methods, and combined density functional-multilevel local correlation approximations. The performance of the resulting DB density functional and wave function embedding methods is evaluated in extensive benchmark calculations and also compared to that of the corresponding embedding schemes exploiting the mixed-basis approximation. Our results show that, with an appropriate combination of basis sets, the DB approach significantly speeds up the embedding calculations, and, for chemical processes where the electronic structure considerably changes, it is clearly superior to the mixed-basis approximation. The results also demonstrate that the DB approach, if integrated with the mixed-basis approximation, efficiently eliminates the major weakness of the latter, and the combination of the DB and mixed-basis schemes is the most efficient strategy to accelerate embedding calculations.

show abstract

“…In practice, the most accurate procedure for treating relativistic effects in molecular systems is through the solution of the Dirac-Coulomb-Breit (DCB) equation 116,138,168,176,189,190,200 . Although recent developments have made it possible to perform self-consistent field 158,188,216,223 , density functional theory 120,182,201,222 , coupled cluster 185,211 , explicitly correlated 125,171,215 and multireference 114,119,139,141,163,208 calculations on the DCB Hamiltonian, these methods remain problematic due to their high computational cost.…”

Section: Introductionmentioning

confidence: 99%

One-Step Treatment of Spin–Orbit Coupling and Electron Correlation in Large Active Spaces

Mussard

Sharma

2017

J. Chem. Theory Comput.

View full text Add to dashboard Cite

In this work we demonstrate that the heat bath configuration interaction (HCI) and its semistochastic extension can be used to treat relativistic effects and electron correlation on an equal footing in large active spaces to calculate the low energy spectrum of several systems including halogen group atoms (F, Cl, Br, I), coinage atoms (Cu, Au), and the neptunyl(VI) dioxide radical. This work demonstrates that despite a significant increase in the size of the Hilbert space due to spin symmetry breaking by the spin-orbit coupling terms, HCI retains the ability to discard large parts of the low importance Hilbert space to deliver converged absolute and relative energies. For instance, by using just over 10 determinants we get converged excitation energies for Au atom in an active space containing (150o,25e) which has over 10 determinants. We also investigate the accuracy of five different two-component relativistic Hamiltonians in which different levels of approximations are made in deriving the one-electron and two-electrons Hamiltonians, ranging from Breit-Pauli (BP) to various flavors of exact two-component (X2C) theory. The relative accuracy of the different Hamiltonians are compared on systems that range in atomic number from first row atoms to actinides.

show abstract

A dual-level approach to four-component relativistic density-functional theory

Cited by 3 publications

References 51 publications

Large-scale Dirac–Fock–Breit method using density fitting and 2-spinor basis functions

Large-scale Dirac–Fock–Breit method using density fitting and 2-spinor basis functions

Dual Basis Set Approach for Density Functional and Wave Function Embedding Schemes

One-Step Treatment of Spin–Orbit Coupling and Electron Correlation in Large Active Spaces

Contact Info

Product

Resources

About