Laplace transform techniques in Mo/ller–Plesset perturbation theory

Häser, Marco; Almlöf, Jan

doi:10.1063/1.462485

Cited by 279 publications

(201 citation statements)

References 21 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.

345

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.

345

428

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“…24 An additional, and more important benefit of using this scaled opposite-spin (SOS) approach over SCS- 4 as opposed to ~N 5 ) through the use of a Laplace transform. 25,26 This low-scaling characteristic allows SOS-CIS(D) to be applied to calculations on larger molecules than CIS(D) itself.…”

Section: Introductionmentioning

confidence: 99%

Scaled Second-Order Perturbation Corrections to Configuration Interaction Singles: Efficient and Reliable Excitation Energy Methods

2007

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“…6,7 During the past decades, several groups have contributed to improving this situation and to extending the applicability of MP2 in various ways. 8 Several approaches have been proposed in order to reduce the formal O(N 5 ) scaling and they can be classified as Laplacetransformed MP2, [9][10][11][12][13][14][15][16] local MP2 (LMP2), [17][18][19][20][21][22][23][24][25][26] and stochastic [27][28][29][30] methods, while explicitly correlated schemes can be used for accelerating the convergence of the MP2 energy with respect to basis set size (F12-MP2). [31][32][33] Furthermore, the Resolution of Identity (RI) [34][35][36][37][38][39][40][41][42] approximation, sometimes referred as Density Fitting (DF), has shown to greatly speed up the evaluation of the MP2 energy giving almost a order of magnitude reduction of the computational cost without significant loss of accuracy.…”

Section: Introductionmentioning

confidence: 99%

Forces and stress in second order Møller-Plesset perturbation theory for condensed phase systems within the resolution-of-identity Gaussian and plane waves approach

Ben

Hutter

VandeVondele

2015

The Journal of Chemical Physics

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The forces acting on the atoms as well as the stress tensor are crucial ingredients for calculating the structural and dynamical properties of systems in the condensed phase. Here, these derivatives of the total energy are evaluated for the second-order Møller-Plesset perturbation energy (MP2) in the framework of the resolution of identity Gaussian and plane waves method, in a way that is fully consistent with how the total energy is computed. This consistency is non-trivial, given the different ways employed to compute Coulomb, exchange, and canonical four center integrals, and allows, for example, for energy conserving dynamics in various ensembles. Based on this formalism, a massively parallel algorithm has been developed for finite and extended system. The designed parallel algorithm displays, with respect to the system size, cubic, quartic, and quintic requirements, respectively, for the memory, communication, and computation. All these requirements are reduced with an increasing number of processes, and the measured performance shows excellent parallel scalability and efficiency up to thousands of nodes. Additionally, the computationally more demanding quintic scaling steps can be accelerated by employing graphics processing units (GPU's) showing, for large systems, a gain of almost a factor two compared to the standard central processing unit-only case. In this way, the evaluation of the derivatives of the RI-MP2 energy can be performed within a few minutes for systems containing hundreds of atoms and thousands of basis functions. With good time to solution, the implementation thus opens the possibility to perform molecular dynamics (MD) simulations in various ensembles (microcanonical ensemble and isobaric-isothermal ensemble) at the MP2 level of theory. Geometry optimization, full cell relaxation, and energy conserving MD simulations have been performed for a variety of molecular crystals including NH3, CO2, formic acid, and benzene. The forces acting on the atoms as well as the stress tensor are crucial ingredients for calculating the structural and dynamical properties of systems in the condensed phase. Here, these derivatives of the total energy are evaluated for the second-order Møller-Plesset perturbation energy (MP2) in the framework of the resolution of identity Gaussian and plane waves method, in a way that is fully consistent with how the total energy is computed. This consistency is non-trivial, given the different ways employed to compute Coulomb, exchange, and canonical four center integrals, and allows, for example, for energy conserving dynamics in various ensembles. Based on this formalism, a massively parallel algorithm has been developed for finite and extended system. The designed parallel algorithm displays, with respect to the system size, cubic, quartic, and quintic requirements, respectively, for the memory, communication, and computation. All these requirements are reduced with an increasing number of processes, and the measured performance shows excellent parallel scala...

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Laplace transform techniques in Mo/ller–Plesset perturbation theory

Cited by 279 publications

References 21 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

Scaled Second-Order Perturbation Corrections to Configuration Interaction Singles: Efficient and Reliable Excitation Energy Methods

Forces and stress in second order Møller-Plesset perturbation theory for condensed phase systems within the resolution-of-identity Gaussian and plane waves approach

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