Sayan Bhowmik, Andrew J. Medford, Phanish Suryanarayana
We present an accurate and efficient framework for real-space Hubbard-corrected density functional theory. In particular, we obtain expressions for the energy, atomic forces, and stress tensor suitable for real-space finite-difference discretization, and develop a large-scale parallel implementation. We verify the accuracy of the formalism through comparisons with established planewave results. We demonstrate that the implementation is highly efficient and scalable, outperforming established planewave codes by more than an order of magnitude in minimum time to solution, with increasing advantages as the system size and/or number of processors is increased. We apply this framework to examine the impact of exchange-correlation inconsistency in local atomic orbital generation and introduce a scheme for optimizing the Hubbard parameter based on hybrid functionals, both while studying TiO$_2$ polymorphs.
Clara Iglesias-Tesouro, Valentin de la Rubia, Alessio Monti
et al.
In this work, we propose to use the Reduced-Basis Method (RBM) as a model order reduction approach to solve Maxwell's equations in electromagnetic (EM) scatterers based on plasma to build a metasurface, taking into account a parameter, namely, the plasma frequency. We build up the reduced-order model in an adaptive fashion following a greedy algorithm. This method enables a fast sweep over a wide range of plasma frequencies, thus providing an efficient way to characterize electromagnetic structures based on Drude-like plasma scatterers. We validate and test the proposed technique on several plasma metasurfaces and compare it with the finite element method (FEM) approach.
Jacob A. Blackmore, Philip D. Gregory, Jeremy M. Hutson
et al.
We present a computer program to calculate the quantised rotational and hyperfine energy levels of $^{1}Σ$ diatomic molecules in the presence of dc electric, dc magnetic, and off-resonant optical fields. Our program is applicable to the bialkali molecules used in ongoing state-of-the-art experiments with ultracold molecular gases. We include functions for the calculation of space-fixed electric dipole moments, magnetic moments and transition dipole moments.
Computation of derivatives (gradient and Hessian) of a fidelity function is one of the most crucial steps in many optimization algorithms. Having access to accurate methods to calculate these derivatives is even more desired where the optimization process requires propagation of these calculations over many steps, which is in particular important in optimal control of spin systems. Here we propose a novel numerical approach, ESCALADE (Efficient Spin Control using Analytical Lie Algebraic Derivatives) that offers the exact first and second derivatives of the fidelity function by taking advantage of the properties of the Lie group of $2\times 2$ Hermitian matrices, $\mathrm{SU}(2)$, and its Lie algebra, the Lie algebra of skew-Hermitian matrices, $\mathfrak{su}(2)$. A full mathematical treatment of the proposed method along with some numerical examples are presented.
We present a software to simulate the propagation of positive streamers in dielectric liquids. Such liquids are commonly used for electric insulation of high-power equipment. We simulate electrical breakdown in a needle-plane geometry, where the needle and the extremities of the streamer are modeled by hyperboloids, which are used to calculate the electric field in the liquid. If the field is sufficiently high, electrons released from anions in the liquid can turn into electron avalanches, and the streamer propagates if an avalanche meets the Townsend-Meek criterion. The software is written entirely in Python and released under an MIT license. We also present a set of model simulations demonstrating the capability and versatility of the software.
We propose a wave operator method to calculate eigenvalues and eigenvectors of large parameter-dependent matrices, using an adaptative active subspace. We consider a hamiltonian which depends on external adjustable or adiabatic parameters, using adaptative projectors which follow the successive eigenspaces when the adjustable parameters are modified. The method can also handle non-hermitian hamiltonians. An iterative algorithm is derived and tested through comparisons with a standard wave operator algorithm using a fixed active space and with a standard block-Davidson method. The proposed approach is competitive, it converges within a few dozen iterations at constant memory cost. We first illustrate the abilities of the method on a 4-D coupled oscillator model hamiltonian. A more realistic application to molecular photodissociation under intense laser fields with varying intensity or frequency is also presented. Maps of photodissociation resonances of H${}_2^+$ in the vicinity of exceptional points are calculated as an illustrative example.
Zdeněk Mašín, Jakub Benda, Jimena D. Gorfinkiel
et al.
UKRmol+ is a new implementation of the UK R-matrix electron-molecule scattering code. Key features of the implementation are the use of quantum chemistry codes such as Molpro to provide target molecular orbitals; the optional use of mixed Gaussian -- B-spline basis functions to represent the continuum and improved configuration and Hamiltonian generation. The code is described, and examples covering electron collisions from a range of targets, positron collisions and photionisation are presented. The codes are freely available as a tarball from Zenodo.
This paper provides the first ab-initio on-the-fly example of using the Quasi-Diabatic (QD) scheme for non-adiabatic simulations with diabatic dynamics approaches. The QD scheme provides a seamless interface between diabatic quantum dynamics approaches and {\it adiabatic} electronic structure calculations. It completely avoids additional theoretical efforts to reformulate the equation of motion from diabatic to adiabatic representation, or construct global diabatic surfaces. This scheme enables many recently developed diabatic quantum dynamics approaches for ab-inito on-the-fly simulations, providing the non-adiabatic community a wide variety of approaches (such as the real-time path integral method and symmetric quasi-classical approach) beyond the well-explored methods (like trajectory surface-hopping or ab-initio multiple-spawning). The QD scheme also enables using realistic test cases (like ethylene photodynamics) that go beyond simple model systems to assess the accuracy and limitation of recently developed quantum dynamics approaches.
In this paper we test two strategies to improving the accuracy of machine-learning potentials, namely adding more fitting parameters thus making use of large volumes of available quantum-mechanical data, and adding a charge-equilibration model to account for ionic nature of the SiO2 bonding. To that end, we compare Moment Tensor Potentials (MTPs) and MTPs combined with the charge-equilibration (QEq) model (MTP+QEq) fitted to a density functional theory dataset of alpha-quartz SiO2-based structures. In order to make a meaningful comparison, in addition to the accuracy, we assess the uncertainty of predictions of each potential. It is shown that adding the QEq model to MTP does not make any improvement over the MTP potential alone, while adding more parameters does improve the accuracy and uncertainty of its predictions.
An optimization problem has been formulated to find a resonant current extremizing various antenna parameters. The method is presented on, but not limited to, particular cases of gain $G$, quality factor $Q$, gain to quality factor ratio $G/Q$, and radiation efficiency $η$ of canonical shapes with conduction losses explicitly included. The Rao-Wilton-Glisson basis representation is used to simplify the underlying algebra while still allowing surface current regions of arbitrary shape to be treated. By switching to another basis generated by a specific eigenvalue problem, it is finally shown that the optimal current can, in principle, be found as a combination of a few eigenmodes. The presented method constitutes a general framework in which the antenna parameters, expressed as bilinear forms, can automatically be extremized.
Studying single-particle dynamics over many periods of oscillations is a well-understood problem solved using symplectic integration. Such integration schemes derive their update sequence from an approximate Hamiltonian, guaranteeing that the geometric structure of the underlying problem is preserved. Simulating a self-consistent system over many oscillations can introduce numerical artifacts such as grid heating. This unphysical heating stems from using non-symplectic methods on Hamiltonian systems. With this guidance, we derive an electrostatic algorithm using a discrete form of Hamilton's Principle. The resulting algorithm, a gridless spectral electrostatic macroparticle model, does not exhibit the unphysical heating typical of most particle-in-cell methods. We present results of this using a two-body problem as an example of the algorithm's energy- and momentum-conserving properties.
Amartya S. Banerjee, Phanish Suryanarayana, John E. Pask
Pulay's Direct Inversion in the Iterative Subspace (DIIS) method is one of the most widely used mixing schemes for accelerating the self-consistent solution of electronic structure problems. In this work, we propose a simple generalization of DIIS in which Pulay extrapolation is performed at periodic intervals rather than on every self-consistent field iteration, and linear mixing is performed on all other iterations. We demonstrate through numerical tests on a wide variety of materials systems in the framework of density functional theory that the proposed generalization of Pulay's method significantly improves its robustness and efficiency.
Taking advantage of the flexibility of the variational method with coordinate transformations, we derive a self-consistent set of equations of motion from a discretized Lagrangian to study kinetic plasmas using a Fourier decomposed cylindrical coordinate system. The phase-space distribution function was reduced to a collection of finite-sized macro-particles of arbitrary shape moving on a virtual Cartesian grid. However, the discretization of field quantities was performed in cylindrical coordinates and decomposed into a truncated Fourier series in angle. A straightforward finite element interpolation scheme is used to transform between the two grids. The equations of motion were then obtained by demanding the action be stationary. The primary advantage of the variational approach is preservation of Lagrangian symmetries. In the present case, this leads to exact energy conservation, thus avoiding possible difficulties with grid heating.
Since the kinetic and the potential energy term of the real time nonlinear Schrödinger equation can each be solved exactly, the entire equation can be solved to any order via splitting algorithms. We verified the fourth-order convergence of some well known algorithms by solving the Gross-Pitaevskii equation numerically. All such splitting algorithms suffer from a latent numerical instability even when the total energy is very well conserved. A detail error analysis reveals that the noise, or elementary excitations of the nonlinear Schrödinger, obeys the Bogoliubov spectrum and the instability is due to the exponential growth of high wave number noises caused by the splitting process. For a continuum wave function, this instability is unavoidable no matter how small the time step. For a discrete wave function, the instability can be avoided only for $\dt k_{max}^2{<\atop\sim}2 π$, where $k_{max}=π/Δx$.