Heat transport through model molecular junctions: A multilayer multiconfiguration time-dependent Hartree approach Kirill A. Velizhanin a , Haobin Wang a, * , Michael Thoss b a Department of Chemistry and Biochemistry, MSC 3C, New Mexico State University, Las Cruces, NM 88003, USA b Department of Chemistry, Technical University of Munich, 85748 Garching, Germany article info Article history: Received 8 April 2008 In final form 19 May 2008 Available online 24 May 2008 abstract A numerically exact approach is proposed to study heat transport through a molecular junction that is coupled to two phonon reservoirs at different temperatures. Within a spin-boson type model, the junc- tion is represented by a two level subsystem and the phonon reservoirs are described by two indepen- dent harmonic baths. Quantum simulations of the thermal flux (heat current) are performed employing the multilayer multiconfiguration time-dependent Hartree theory. Results for the transient and stationary heat current are discussed for different physical regimes. Furthermore, the validity of Red- field theory, as an example of an approximate approach applicable for weak system–bath coupling, is examined using the proposed numerically exact approach. Ó 2008 Elsevier B.V. All rights reserved. 1. Introduction As part of the effort to search for new nano-size electronic de- vices, the study of electrical conductance properties in molecular wires has attracted much attention recently. A relevant question is whether the heat generated in such processes can be released quickly and efficiently. It has been shown experimentally [1] that the localized Joule heating, produced by electric current, can cause a substantial temperature increase within a molecule–metal con- tact and can thus affect the stability of a molecular junction. There- fore, efficient heat transport away from the junction is an important factor that needs to be taken into account when design- ing practical nano-electronics devices. In macroscopic solids heat can be carried away from the junc- tion by electrons and/or phonons. While in metals heat flow is dominated by electrons, in insulators heat is transported solely by phonons. In this Letter we consider the latter case. This form of heat transport has been the focus of extensive theoretical re- search. Both classical [2–5] and quantum mechanical [6–8] ap- proaches have been used to study the properties of phononic heat transport in different regimes. Some of the studies suggested possible realization of new nano-devices such as a thermal rectifier [6,7], a molecular heat pump [8], and thermal logic gates [5]. Among these, the experimental realization of the predicted ther- mal rectifier has been demonstrated very recently [9]. The previous theoretical work provides valuable insight into heat transport processes through molecular junctions. However, the approximate nature of the theories restricts their applicability to certain physical regimes. For example, classical approaches are not able to describe quantum effects. Redfield theory [10,11], which was applied in Refs. [6–8], is based on perturbation theory and, therefore, only applicable if the coupling between the molec- ular states and the phonon bath is sufficiently weak. This may not be the case in realistic situations. The purpose of this work is to present a method that goes beyond perturbation theory in the weak coupling limit by employing the recently developed multi- layer multiconfiguration time-dependent Hartree theory [12]. This allows us to study heat transport through model molecular junc- tions in a broader physical regime, and also provide theoretical benchmarks for developing approximate theories to treat such processes. The remaining part of the Letter is organized as follows. Section 2 discusses the model and observables of interest for studying heat transport through molecular junctions, and the quantum dynamics method used in the simulation. Section 3 presents the results from the quantum simulation and the comparisons with the Redfield theory. Section 4 concludes. In this short communication, we focus on the outline of the methodology and present some illustrative applications. A more detailed discussion of the physics of the prob- lem will be the subject of a future publication. 2. Theory 2.1. Model Following the work of Segal and Nitzan [6,7] we use a spin-bo- son type model to describe phononic heat transport through a nanojunction. Within this model, two states of the junction mole- cule are taken into account, which are coupled to two phonon 0009-2614/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2008.05.065 * Corresponding author. E-mail address: haobin@nmsu.edu (H. Wang). Chemical Physics Letters 460 (2008) 325–330 Contents lists available at ScienceDirect Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett