Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userFast real-time time-dependent density functional theory calculations with the parallel transport gauge
294
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
Real-time time-dependent density functional theory (RT-TDDFT) is known to be hindered by the very small time step (attosecond or smaller) needed in the numerical simulation due to the fast oscillation of electron wavefunctions, which significantly limits its range of applicability for the study of ultrafast dynamics. In this paper, we demonstrate that such oscillation can be considerably reduced by optimizing the gauge choice using the parallel transport formalism. RT-TDDFT calculations can thus be significantly accelerated using a combination of the parallel transport gauge and implicit integrators, and the resulting scheme can be used to accelerate any electronic structure software that uses a Schrodinger representation. Using absorption spectrum, ultrashort laser pulse, and Ehrenfest dynamics calculations for example, we show that the new method can utilize a time step that is on the order of $10sim 100$ attoseconds in a planewave basis set, and is no less than $5sim 10$ times faster when compared to the standard explicit 4th order Runge-Kutta time integrator. Thanks to the significant increase of the size of the time step, we also demonstrate that the new method is more than 10 times faster in terms of the wall clock time when compared to the standard explicit 4th order Runge-Kutta time integrator for silicon systems ranging from 32 to 1024 atoms
rate research
Read More
We present a new method to accelerate real time-time dependent density functional theory (rt-TDDFT) calculations with hybrid exchange-correlation functionals. For large basis set, the computational bottleneck for large scale calculations is the application of the Fock exchange operator to the time-dependent orbitals. Our main goal is to reduce the frequency of applying the Fock exchange operator, without loss of accuracy. We achieve this by combining the recently developed parallel transport (PT) gauge formalism and the adaptively compressed exchange operator (ACE) formalism. The PT gauge yields the slowest possible dynamics among all choices of gauge. When coupled with implicit time integrators such as the Crank-Nicolson (CN) scheme, the resulting PT-CN scheme can significantly increase the time step from sub-attoseconds to 10-100 attoseconds. At each time step $t_{n}$, PT-CN requires the self-consistent solution of the orbitals at time $t_{n+1}$. We use ACE to delay the update of the Fock exchange operator in this nonlinear system, while maintaining the same self-consistent solution. We verify the performance of the resulting PT-CN-ACE method by computing the absorption spectrum of a benzene molecule and the response of bulk silicon systems to an ultrafast laser pulse, using the planewave basis set and the HSE functional. We report the strong and weak scaling of the PT-CN-ACE method for silicon systems ranging from 32 to 1024 atoms, with up to 2048 computational cores. Compared to standard explicit time integrators such as the 4th order Runge-Kutta method (RK4), the PT-CN-ACE can reduce the Fock exchange operator application by nearly 70 times, thus reduce the overall wall clock time time by 46 times for the system with 1024 atoms. Hence our work enables hybrid functional rt-TDDFT calculations to be routinely performed with a large basis set for the first time.
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.
Linear-response time-dependent density-functional theory (TDDFT) can describe excitonic features in the optical spectra of insulators and semiconductors, using exchange-correlation (xc) kernels behaving as $-1/k^{2}$ to leading order. We show how excitons can be modeled in real-time TDDFT, using an xc vector potential constructed from approximate, long-range corrected xc kernels. We demonstrate for various materials that this real-time approach is consistent with frequency-dependent linear response, gives access to femtosecond exciton dynamics following short-pulse excitations, and can be extended with some caution into the nonlinear regime.
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.
Time-dependent density-functional theory (TDDFT) is a computationally efficient first-principles approach for calculating optical spectra in insulators and semiconductors, including excitonic effects. We show how exciton wave functions can be obtained from TDDFT via the Kohn-Sham transition density matrix, both in the frequency-dependent linear-response regime and in real-time propagation. The method is illustrated using one-dimensional model solids. In particular, we show that our approach provides insight into the formation and dissociation of excitons in real time. This opens the door to time-resolved studies of exciton dynamics in materials by means of real-time TDDFT.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
