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Register a new userPredictive Mixing for Density Functional Theory (and other Fixed-Point Problems)
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Authors
Laurence Marks
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Density functional theory calculations use a significant fraction of current supercomputing time. The resources required scale with the problem size, internal workings of the code and the number of iterations to convergence, the latter being controlled by what is called mixing. This note 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 Multisecan
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The Breit correction, the finite-light-speed correction for the Coulomb interaction of the electron-electron interaction in $ O left( 1/ c^2 right) $, is introduced to density functional theory (DFT) based on the non-relativistic reduction with the local density approximation. Using this newly developed relativistic DFT, it is found that the possible outer-most electron of lawrencium atom is the $ p $ orbital instead of the $ d $ orbital, which is consistent with the previous calculations based on wave-function theory. A possible explanation of the anomalous behavior of its first ionization energy is also given. This DFT scheme provides a practical calculation method for the study of properties of super-heavy elements.
Imaginary-time time-dependent Density functional theory (it-TDDFT) has been proposed as an alternative method for obtaining the ground state within density functional theory (DFT) which avoids some of the difficulties with convergence encountered by the self-consistent-field (SCF) iterative method. It-TDDFT was previously applied to clusters of atoms where it was demonstrated to converge in select cases where SCF had difficulty with convergence. In the present work we implement it-TDDFT propagation for {it periodic systems} by modifying the Quantum ESPRESSO package, which uses a plane-wave basis with multiple $boldsymbol{k}$ points, and has the options of non-collinear and DFT+U calculations using ultra-soft or norm-conserving pseudo potentials. We demonstrate that our implementation of it-TDDFT propagation with multiple $boldsymbol{k}$ points is correct for DFT+U non-collinear calculations and for DFT+U calculations with ultra-soft pseudo potentials. Our implementation of it-TDDFT propagation converges to the exact SCF energy (up to the decimal guaranteed by double precision) in all but one case where it converged to a slightly lower value than SCF, suggesting a useful alternative for systems where SCF has difficulty to reach the Kohn-Sham ground state. In addition, we demonstrate that rapid convergence can be achieved if we use adaptive-size imaginary-time-steps for different kinetic-energy plane-waves.
Real-time time-dependent density functional theory (rt-TDDFT) with hybrid exchange-correlation functional has wide-ranging applications in chemistry and material science simulations. However, it can be thousands of times more expensive than a conventional ground state DFT simulation, hence is limited to small systems. In this paper, we accelerate hybrid functional rt-TDDFT calculations using the parallel transport gauge formalism, and the GPU implementation on Summit. Our implementation can efficiently scale to 786 GPUs for a large system with 1536 silicon atoms, and the wall clock time is only 1.5 hours per femtosecond. This unprecedented speed enables the simulation of large systems with more than 1000 atoms using rt-TDDFT and hybrid functional.
Reliable and robust convergence to the electronic ground state within density functional theory (DFT) Kohn-Sham (KS) calculations remains a thorny issue in many systems of interest. In such cases, charge sloshing can delay or completely hinder the convergence. Here, we use an approach based on transforming the time-dependent DFT equations to imaginary time, followed by imaginary-time evolution, as a reliable alternative to the self-consistent field (SCF) procedure for determining the KS ground state. We discuss the theoretical and technical aspects of this approach and show that the KS ground state should be expected to be the long-imaginary-time output of the evolution, independent of the exchange-correlation functional or the level of theory used to simulate the system. By maintaining self-consistency between the single-particle wavefunctions and the electronic density throughout the determination of the stationary state, our method avoids the typical difficulties encountered in SCF. To demonstrate dependability of our approach, we apply it to selected systems which struggle to converge with SCF schemes. In addition, through the van Leeuwen theorem, we affirm the physical meaningfulness of imaginary time TDDFT, justifying its use in certain topics of statistical mechanics such as in computing imaginary time path integrals.
We extend density functional perturbation theory for lattice dynamics with fully relativistic ultrasoft pseudopotentials to magnetic materials. Our approach is based on the application of the time-reversal operator to the Sternheimer linear system and to its self-consistent solutions. Moreover, we discuss how to include in the formalism the symmetry operations of the magnetic point group which require the time-reversal operator. We validate our implementation by comparison with the frozen phonon method in fcc Ni and in a monatomic ferromagnetic Pt wire.
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