Efficient Formalism for Large-ScaleAb InitioMolecular Dynamics based on Time-Dependent Density Functional Theory

Abstract

A new "on the fly" method to perform Born-Oppenheimer ab initio molecular dynamics (AIMD) is presented. Inspired by Ehrenfest dynamics in time-dependent density functional theory, the electronic orbitals are evolved by a Schrödinger-like equation, where the orbital time derivative is multiplied by a parameter. This parameter controls the time scale of the fictitious electronic motion and speeds up the calculations with respect to standard Ehrenfest dynamics. In contrast to other methods, wave function orthogonality needs not be imposed as it is automatically preserved, which is of paramount relevance for large scale AIMD simulations.PACS numbers: 71.15.Pd, 31.15.Ew Ab initio molecular dynamics (AIMD) on the ground state Born-Oppenheimer (gsBOMD) potential energy surface for the nuclei has become a standard tool for simulating the conformational behaviour of molecules, bioand nano-structures and condensed matter systems from first principles [1]. However, gsBOMD (in the DFT [2] picture) requires that the Kohn-Sham (KS) energy functional be minimized for each value of the nuclei positions. As this minimization can be very demanding, Car and Parrinello (CP) [3] proposed an elegant and efficient "on the fly" scheme in which the KS orbitals are propagated with a fictitious dynamics that mimics gsBOMD. The CP method has had a tremendous impact in many scientific areas [4,5]. Nevertheless, the numerical cost of AIMD hinders the application of the method to large scale simulations, such as those of interest in biochemistry or material science. Recently, new methods that allow larger systems and longer simulation times to be studied have been reported [6], but the cost associated with the wave function orthogonalization is still a potential bottleneck for both gsBOMD and CP.Time-dependent density functional theory (TDDFT) [7,8] has been for a long time recognized as an orthogonalization-free alternative for both ground state [9] and excited state AIMD. In its simplest implementation, Ehrenfest TDDFT, the ions are treated classically following electronic Hellmann-Feynman forces. For systems where the gap between the ground and the first excited state is large, Ehrenfest tends to gsBOMD and can mimic adiabatic dynamics [1]. However, the rapid movement of the electrons in TDDFT requires the use of a very small time step, which, in many occasions, renders its numerical application non-practical [10].In this letter, we borrow some of the ideas of CP and introduce a new TDDFT Ehrenfest dynamics that reduces the cost of AIMD simulations while keeping the accuracy of the results in tolerable levels, similar to CP. The whole scheme can be obtained from the following Lagrangian (atomic units are used throughout this paper):whereI M IṘI ·Ṙ I is the kinetic energy of the nuclei, M I their masses and E the KS energy. Note that the major modification with respect to TDDFT is the scaling of the electronic velocities by a parameter µ (TDDFT is recovered when µ = 1). We show in what follows that, in the µ → 0 limit, the trajectories ...

Application of compressed sensing to the simulation of atomic systems

“…The adiabatic MD calculations are performed from first principles using the modified Ehrenfest method (29,30) with an ionic timescale factor (μ) of 30 for Na 2 and 5 for benzene. The systems are given initial velocities equivalent to 300 K and the MD is performed at constant energy.…”

Ab initioelectronic stopping power and threshold effect of channeled slow light ions inHfO2

“…The collision behaviors of intruding ions with the host nuclei and electrons are characterized by the Ehrenfest coupled electron-ion dynamics combined with timedependent density-functional theory (ED-TDDFT) [29][30][31][32][33][34].…”

Analog of Rabi oscillations in resonant electron-ion systems

“…By means of Eqs. (18), (19), and (21), one can write down the matrix elements of the expanded Hamiltonian in Eq. (17) as…”

“…8,10,21 Nevertheless, ED remains computationally appealing because it does not require the explicit knowledge of the adiabatic PESs, i.e., a costly diagonalization of H e at each time-step is avoided. Therefore, in contrast with other schemes, ED can be employed to simulate large atomic systems, 19 including metals. 33 …”

“…6 Including electronic transitions and-possibly classical-atomic motion in a consistent 7,8 and computationally effective molecular dynamics scheme has been the object of intense theoretical and computational investigations during the last decades. [9][10][11][12][13][14][15][16][17][18][19] In the surface hopping algorithm 10 -and similar approaches 12,14,18 that treat atomic evolution classicallyvertical electronic transitions are included in a stochastic way. By averaging over a large ensemble of such stochastic quantum-classical evolutions, one obtains a reliable approximation to the quantum electron-ion 20 dynamics.…”