On the equivalence of LIST and DIIS methods for convergence acceleration

Garza, Alejandro J.; Scuseria, Gustavo E.

doi:10.1063/1.4919283

Cited by 9 publications

(21 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Some algorithms deal with them as a least-squares problem while others use a Taylor seriesherein I will use the latter. As has been demonstrated previously by several authors, the approaches are nominally identical (e.g., refs , , , − ) but differ in important implementation details. Dropping the ( r , R ) notation for brevity, and using ρ n and R n to describe the density and positions respectively for iteration n and Δ( ρ n , R n ) for a change in the density and positions, this suggests a standard Newton algorithm using a vector/matrix representation: where H n is the inverse of the Jacobian B n for the change in density/pseudogradients with density/atomic positions.…”

Section: Linear Mixing Methodsmentioning

confidence: 65%

Predictive Mixing for Density Functional Theory (and Other Fixed-Point Problems)

Marks

2021

J. Chem. Theory Comput.

View full text Add to dashboard Cite

Density functional theory calculations use a significant fraction of current supercomputing time. The resources required scale with the problem size, the internal workings of the code, and the number of iterations to convergence, with the latter being controlled by what is called “mixing”. This paper describes a new approach to handling trust regions within these and other fixed-point problems. Rather than adjusting the trust region based upon improvement, the prior steps are used to estimate what the parameters and trust regions should be, effectively estimating the optimal Polyak step from the prior history. Detailed results are shown for eight structures using both the “good” and “bad” multisecant versions as well as the Anderson method and a hybrid approach, all with the same predictive method. Additional comparisons are made for 36 cases with a fixed algorithm greed. The predictive method works well independent of which method is used for the candidate step, and it is capable of adapting to different problem types particularly when coupled with the hybrid approach.

show abstract

Section: Linear Mixing Methodsmentioning

confidence: 65%

Predictive Mixing for Density Functional Theory (and Other Fixed-Point Problems)

Marks

2021

J. Chem. Theory Comput.

View full text Add to dashboard Cite

show abstract

“…We remark that the gauge-invariance property is what distinguishes the PC-DIIS method from other acceleration schemes such as the RMM-DIIS method . The PC-DIIS method can also be viewed as a generalized formulation of the C-DIIS method with its residual weighted by the gauge-fixing matrix . We demonstrate that the PC-DIIS method can be viewed as an extension of an iterative eigensolver for nonlinear problems.…”

Section: Introductionmentioning

confidence: 90%

“…6 The PC-DIIS method can also be viewed as a generalized formulation of the C-DIIS method with its residual weighted by the gauge-fixing matrix. 36 We demonstrate that the PC-DIIS method can be viewed as an extension of an iterative eigensolver for nonlinear problems. The PC-DIIS method is well suited for accelerating Hartree−Fock and hybrid functional Kohn−Sham density functional theory calculations.…”

Section: Introductionmentioning

confidence: 95%

Projected Commutator DIIS Method for Accelerating Hybrid Functional Electronic Structure Calculations

Lin

Yang

2017

J. Chem. Theory Comput.

View full text Add to dashboard Cite

The commutator direct inversion of the iterative subspace (commutator DIIS or C-DIIS) method developed by Pulay is an efficient and the most widely used scheme in quantum chemistry to accelerate the convergence of self consistent field (SCF) iterations in Hartree-Fock theory and Kohn-Sham density functional theory. The C-DIIS method requires the explicit storage of the density matrix, the Fock matrix and the commutator matrix. Hence the method can only be used for systems with a relatively small basis set, such as the Gaussian basis set. We develop a new method that enables the C-DIIS method to be efficiently employed in electronic structure calculations with a large basis set such as planewaves for the first time. The key ingredient is the projection of both the density matrix and the commutator matrix to an auxiliary matrix called the * To whom correspondence should be addressed

show abstract

“…For more information on recently suggested Fock matrix extrapolation techniques, I refer to Refs. and references therein.…”

Section: Lcao Approachesmentioning

confidence: 99%

A review on non‐relativistic, fully numerical electronic structure calculations on atoms and diatomic molecules

Lehtola

2019

Int J of Quantum Chemistry

102

View full text Add to dashboard Cite

The need for accurate calculations on atoms and diatomic molecules is motivated by the opportunities and challenges of such studies. The most commonly used approach for all-electron electronic structure calculations in general-the linear combination of atomic orbitals (LCAO) method-is discussed in combination with Gaussian, Slater a.k.a. exponential, and numerical radial functions. Even though LCAO calculations have major benefits, their shortcomings motivate the need for fully numerical approaches based on, for example, finite differences, finite elements, or the discrete variable representation, which are also briefly introduced. Applications of fully numerical approaches for general molecules are briefly reviewed, and their challenges are discussed. It is pointed out that the high level of symmetry present in atoms and diatomic molecules can be exploited to fashion more efficient fully numerical approaches for these special cases, after which it is possible to routinely perform allelectron Hartree-Fock and density functional calculations directly at the basis set limit on such systems. Applications of fully numerical approaches to calculations on atoms as well as diatomic molecules are reviewed. Finally, a summary and outlook is given.atomic calculations, density functional theory, diatomic calculations, fully numerical electronic structure theory, Hartree-Fock | INTRODUCTIONThanks to decades of development in approximate density functionals and numerical algorithms, density functional theory [1,2] (DFT) is now one of the cornerstones of computational chemistry and solid-state physics. [3][4][5] Since atoms are the basic building block of molecules, a number of popular density functionals [6][7][8][9][10] have been parametrized using ab initio data on noble gas atoms; these functionals have been used in turn as the starting point for the development of other functionals. A comparison of the results of density-functional calculations to accurate ab initio data on atoms has, however, recently sparked controversy on the accuracy of a number of recently published, commonly used density functionals. [11][12][13][14][15][16][17][18][19][20][21] This underlines that there is still room for improvement in DFT even for the relatively simple case of atomic studies.The development and characterization of new density functionals require the ability to perform accurate atomic calculations. Because atoms are the simplest chemical systems, atomic calculations may seem simple; however, they are in fact sometimes surprisingly challenging. For instance, a long-standing discrepancy between the theoretical and experimental electron affinity and ionization potential of gold has been resolved only very recently with high-level ab initio calculations. [22] Atomic calculations can also be used to formulate efficient starting guesses for molecular electronic structure calculations via either the atomic density [23,24] or the atomic potential as discussed in Ref. [25].

show abstract

On the equivalence of LIST and DIIS methods for convergence acceleration

Abstract: Self-consistent field extrapolation methods play a pivotal role in quantum chemistry and electronic structure theory. We, here, demonstrate the mathematical equivalence between the recently proposed family of LIST methods [Wang et al., J. Chem. Phys. 134, 241103 (2011)

Cited by 9 publications

References 22 publications

Predictive Mixing for Density Functional Theory (and Other Fixed-Point Problems)

Predictive Mixing for Density Functional Theory (and Other Fixed-Point Problems)

Projected Commutator DIIS Method for Accelerating Hybrid Functional Electronic Structure Calculations

A review on non‐relativistic, fully numerical electronic structure calculations on atoms and diatomic molecules

Contact Info

Product

Resources

About