Many non-linear effects in elasticity, as, e.g., crack-propagation, contact, or friction, take place on different scales, i.e. a micro scale and a macro scale. Whereas the micro-scale is usually bound to the non-linear effect itself, the macro-scale is connected to the response of the bulk of the material. Therefore, often for the numerical simulation of these multi scale effects different simulation techniques on different scales are employed. One possibility is to use molecular dynamics on the microscale and finite elements on the macro-scale. In this case, due to the large differences in the length scale, a sound coupling between the two discretization schemes has to be developed. Here, we present a new scale-transfer operator, which is based on a weak coupling approach. The key idea is to construct the transfer operator between the micro and the macro scale on the basis of weighted local averaging instead of using point wise taken values, which is widely applied. The local weight functions are constructed by assigning a partition of unity to the molecular degrees of freedom. This allows for decomposing the micro scale displacements into a low frequency and a high frequency part by means of a weighted L 2 -projection. Thus, the entire formulation is given in a function space setting.Since our operator is based on a weak formulation of the transfer conditions, quadrature is necessary for the assembling of its algebraic representation. To resolve this quadrature problem, a new methodology has been developed.For the derivation of our new weak coupling approach, in a first step, we follow Hughes et al.[3] by applying scale separation techniques. Starting from a total displacement field ν, we separate the fine scale parts of ν from the coarse scale parts by means of the decompositionsee [3]. Here,ν is the coarse part of the total displacement and ν refers to the fine scale displacements. In our multiscale context, this frequency decomposition is intended to separate the high frequency atomic interactions from the low frequency parts of the solution on the micro scale. Any scale decomposition like (1) has to deal with the difficulty that the atomistic displacements are given as point-values in the "discrete" space R 3N , whereas the macro-scale displacements are usually assumed to be some functions in, e.g., a Sobolev space. Thus, in order to formulate the scale decomposition (1) properly, a suitable space has to be chosen, which contains the atomistic displacements as well as the macro scale displacements. As a matter of fact -at least to our knowledge-in all existing multiscale methods using this decomposition approach, the scale separation is performed in a completely discrete setting. This is possible, if the macro scale displacements are discretized by means of, e.g., finite elements. Then, the discretized displacements can be regarded as an element of R 3N and the scale decomposition (1) can easily be performed. In contrast, our new weak coupling approach provides a scale decomposition of the total displaceme...