Time-dependent potential-functional embedding theory

Abstract

We introduce a time-dependent potential-functional embedding theory (TD-PFET), in which atoms are grouped into subsystems. In TD-PFET, subsystems can be propagated by different suitable time-dependent quantum mechanical methods and their interactions can be treated in a seamless, first-principles manner. TD-PFET is formulated based on the time-dependent quantum mechanics variational principle. The action of the total quantum system is written as a functional of the time-dependent embedding potential, i.e., a potential-functional formulation. By exploiting the Runge-Gross theorem, we prove the uniqueness of the time-dependent embedding potential under the constraint that all subsystems share a common embedding potential. We derive the integral equation that such an embedding potential needs to satisfy. As proof-of-principle, we demonstrate TD-PFET for a Na4 cluster, in which each Na atom is treated as one subsystem and propagated by time-dependent Kohn-Sham density functional theory (TDDFT) using the adiabatic local density approximation (ALDA). Our results agree well with a direct TDDFT calculation on the whole Na4 cluster using ALDA. We envision that TD-PFET will ultimately be useful for studying ultrafast quantum dynamics in condensed matter, where key regions are solved by highly accurate time-dependent quantum mechanics methods, and unimportant regions are solved by faster, less accurate methods.

Subsystem density-functional theory as an effective tool for modeling ground and excited states, their dynamics and many-body interactions

“…The formulation of the Runge-Gross theorem in the case of the time-dependent PFET [15] and PDFT [14] theories is different, since there the time evolution is determined by the initial state Ψ 0 and the embedding potential v emb (r, t). In ground state PFET, there is a unique mapping between the total electron density and the embedding potential, as opposed to the external potential in DFT.…”

“…After that, we will discuss the extension of subsystem DFT to the time domain by way of the Mosquera-Jensen-Wasserman theorem [14,15] (i.e., the extension to subsystem DFT of the Runge-Gross theorem [16]). This will provide us with a discussion of the linear-response and the real-time formalisms.…”

“…Currently there are two flavors of subsystem real time TDDFT implementations, with exact embedding theories [14,15] and with FDE [154]. The first implementation of fragment-based TD-PDFT was introduced by Mosequera et al [14], where a formal proof of the unique mapping between the total time dependent density and the time dependent partition potential is given.…”

“…In ground state PFET, there is a unique mapping between the total electron density and the embedding potential, as opposed to the external potential in DFT. The Runge-Gross theorem has been recast using the timedependent embedding potential first by Mosequra et al [14] in the framework of the fragment-based PDFT [14] method, and later by Huang et al [15] in the framework of the TD-PFET method. Both proofs show that if a system, defined at t = 0 by an initial state and an embedding potential v emb (r, t = 0), evolves into two different time-dependent potentials v emb (r, t) and v emb (r, t)…”

“…An Na 4 cluster, consisting of two Na 2 molecules, is a well studied system [15,186,187] which couples strongly at the excitation energy of 2.18 eV. For this purpose, two Na 2 molecules were placed at a distance of 6.6Å.…”