Alternative linear-scaling methodology for the second-order Møller-Plesset perturbation calculation based on the divide-and-conquer method

Kobayashi, Masato; Imamura, Yutaka; Nakai, Hiromi

doi:10.1063/1.2761878

Cited by 149 publications

(126 citation statements)

References 93 publications

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“…Including the exact exchange as in B3LYP leads a formal scaling as N 4 , whereas including the PT2 term leads to a formal scaling as N 5 , just as for MP2. Linear scaling methods have been developed for MP2 (37)(38)(39) that dramatically accelerate calculations for large molecules, and we expect that these can be used with XYG3. See SI for additional information …”

Section: Discussionmentioning

confidence: 99%

Doubly hybrid density functional for accurate descriptions of nonbond interactions, thermochemistry, and thermochemical kinetics

Zhang

Goddard

2009

Proc. Natl. Acad. Sci. U.S.A.

358

428

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We develop and validate a density functional, XYG3, based on the adiabatic connection formalism and the Gö rling-Levy couplingconstant perturbation expansion to the second order (PT2). XYG3 is a doubly hybrid functional, containing 3 mixing parameters. It has a nonlocal orbital-dependent component in the exchange term (exact exchange) plus information about the unoccupied KohnSham orbitals in the correlation part (PT2 double excitation). XYG3 is remarkably accurate for thermochemistry, reaction barrier heights, and nonbond interactions of main group molecules. In addition, the accuracy remains nearly constant with system size.Becke 3-parameter hybrid functional combined with Lee-Yang-Parr correlation functional ͉ density functional theory ͉ generalized gradient approximation ͉ local density approximation ͉ mean absolute deviation D ensity functional theory (DFT) has revolutionized the role of theory by providing accurate first-principles predictions of critical properties for applications in physics, chemistry, biology, and materials science (1). Despite dramatic successes, there remain serious deficiencies, for example, in describing weak interactions (London dispersion), which are so important to the packing of molecules into solids, the binding of drug molecules to proteins, and the magnitude of reaction barriers. We propose here a DFT functional that dramatically improves the accuracy for these properties by including the role of the virtual (unoccupied) states.Solution of the Schrödinger equation leads to the wavefunction, (r 1 , r 2 , …, r N ) (2), which depends on the 3N space coordinates and N spin coordinates of N-electrons in the system. Solving for such a wavefunction usually starts with the HartreeFock (HF) mean field description involving N self-consistent 1-particle spin-orbitals (in a Slater determinant), which is then used as the basis for expanding the wavefunction in a hierarchy of excited N-electron configurations, by using methods referred to as Møller-Plesset theory (e.g., MP2, MP3, MP4), couplecluster theory (e.g., CCSD(T)), and quadratic configuration interaction theory (e.g., QCISD(T)), etc. These methods are ab initio but suffer from problems of slow convergence with the size of the basis sets and the configuration expansion lengths, preventing scaling to large systems.In contrast, DFT is formulated in terms of the 1-particle density, (r), depending on only 3 spatial coordinates rather than 3N, as the fundamental quantity (3, 4). This dramatically simplifies the process of calculating the structures and properties. However, the exact form of the functional, whose solution will lead to the correct density, is not known. Even so, there has been an evolution of successively better approximations to this functional, that has already provided quite good accuracy for many problems (5-15).Perdew (16) has formulated the hierarchy of DFT approximations as a ''Jacob's ladder'' rising from the ''earth of Hartree'' to the ''heaven of chemical accuracy.'' The first rung of this ladder is the local (s...

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Section: Discussionmentioning

confidence: 99%

Doubly hybrid density functional for accurate descriptions of nonbond interactions, thermochemistry, and thermochemical kinetics

Zhang

Goddard

2009

Proc. Natl. Acad. Sci. U.S.A.

358

428

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“…This is equivalent to solving the Green function method. 32,33 The DC method for electronic structure calculation, [34][35][36] which divides the total system into subsystems and allocates buffer region for each subsystem, reduced the scaling of computational time to quasilinear. The second formula is expressed as the sum-over-state, as follows:…”

Section: Theoretical Calculationmentioning

confidence: 99%

Near-infrared absorption of π-stacking columns composed of trioxotriangulene neutral radicals

et al. 2017

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A long-wavelength photoabsorption of organic molecules has been noticed because of the potential as materials. In addition to the extension of π conjugation, molecular aggregation has been utilized to realize the elongation of absorption wavelength. We report strong near-infrared absorptions of trioxotriangulene neutral radicals in the crystalline state and large-scale theoretical calculations of the radical assemblies interpreting the mechanism of optical properties. Polarized absorption spectra and X-ray diffraction of the crystals clarified that an unusual π-stacking column consisting of π-dimers is key for this absorption. Quantum chemical calculations based on time-dependent density functional theory revealed that the π-dimer shows an electronic transition between frontier orbitals generated by strong coupling of the delocalized singly occupied orbitals of monomers. The interdimer interaction of transition dipole moments, which are parallel to the column, elucidated the increase of absorption wavelength. The divide-andconquer Green function method enabled the large-scale time-dependent density functional theory calculation up to a 60mer, where the maximum number of atoms is 4380, reproducing the near-infrared absorptions of trioxotriangulene crystals. The present method to investigate the mechanism of the long-wavelength photoabsorption is useful for developing organic materials consisting of stable neutral radicals.

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“…395 The first buffer region surrounding each subsystem includes the calculation of the correlation energy, while the second layer buffer only performs a HartreeÀFock calculation. This scheme effectively exploits the local nature of electron correlation and provides additional reductions in the computational effort for correlated calculations.…”

Section: Systematic Fragmentation Methodsmentioning

confidence: 99%

Fragmentation Methods: A Route to Accurate Calculations on Large Systems

et al. 2011

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Theoretical chemists have always strived to perform quantum mechanics (QM) calculations on larger and larger molecules and molecular systems, as well as condensed phase species, that are frequently much larger than the current state-of-the-art would suggest is possible. The desire to study species (with acceptable accuracy) that are larger than appears to be feasible has naturally led to the development of novel methods, including semiempirical approaches, reduced scaling methods, and fragmentation methods. The focus of the present review is on fragmentation methods, in which a large molecule or molecular system is made more computationally tractable by explicitly considering only one part (fragment) of the whole in any particular calculation. If one can divide a species of interest into fragments, employ some level of ab initio QM to calculate the wave function, energy, and properties of each fragment, and then combine the results from the fragment calculations to predict the same properties for the whole, the possibility exists that the accuracy of the outcome can approach that which would be obtained from a full (nonfragmented) calculation. It is this goal that drives the development of fragmentation methods. Disciplines Chemistry CommentsReprinted (adapted) with permission from Chemical Reviews 112 (2012): 632,

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Alternative linear-scaling methodology for the second-order Møller-Plesset perturbation calculation based on the divide-and-conquer method

Cited by 149 publications

References 93 publications

Doubly hybrid density functional for accurate descriptions of nonbond interactions, thermochemistry, and thermochemical kinetics

Doubly hybrid density functional for accurate descriptions of nonbond interactions, thermochemistry, and thermochemical kinetics

Near-infrared absorption of π-stacking columns composed of trioxotriangulene neutral radicals

Fragmentation Methods: A Route to Accurate Calculations on Large Systems

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