## 1 Introduction  
Colloidal nanometric metallic and semi conducting quantum dots (QDs) have long been used as versatile building blocks for assembling dimers and larger extended arrays [1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14]. Among possible building blocks, isolated CdSe QDs were extensively studied [15; 16; 17; 18; 19]. Driven by the possible applications to lasing, sensing, light harvesting, and information processing, they have recently received renewed attention focusing on understanding the role of the fine structure coupling [20; 21; 22; 23; 24], electronic and vibrational coherences [25; 26; 27; 28; 29; 30; 31; 32] and coupling to biexcitons [33; 34; 35; 36; 37], electron transport in arrays [38; 39; 40; 41], and the possibility of engineering ultrafast energy transfer between a donor and an acceptor dot [10; 11]. We focus in this paper on investigating theoretically coherent energy and charge transfer in ensembles of small (2 to 4 nm diameter) heterodimers and homodimers of CdSe QDs. The inevitable inherent size distribution of colloidal QDs leads to a distribution in electronic properties (exciton energies and wave functions and their couplings). For homodimers, where the dots are of equal mean radius, all excitonic bands of the two QDs make the dimer overlap. In the heterodimers, the sizes of the two QDs are tuned so that specific excitonic bands overlap, which favors efficient interdot coupling between those bands. Investigating the effects resulting from the size dispersion in the two dots that constitute a dimer is the main motivation of this paper. The size effects on the optical properties of isolated nanocrystals were characterized early on [6; 17; 18; 42; 43; 44]. A wide variety of theoretical approaches have been proposed to investigate the electronic properties of QDs of several hundreds to thousands of atoms [45; 46]. Solid-state all atom density functional theory (DFT) computations have been implemented with adequate pseudo potentials using a direct diagonalization (DD) method [47; 48; 49]. One can also use the semi-empirical tight-binding (TB) atomistic approach based on a parametrized near neighbor Hamiltonian and a reduced number of basis orbitals to obtain electron and hole particles energies and wave functions [50; 51; 52]. For smaller dots, the exciton-phonon coupling has been investigated using a tight-binding surface-hoping approach [53; 27; 54]. For larger quantum dots in the range of 2 to 4 nm in diameter, parametrized model Hamiltonians based on the effective mass theory (EMA, single or multiband) and the **k.p** method [18; 55; 56; 57; 58] provide valuable insights. The values of the parameters are determined by fitting experimental properties, in general, optical properties, or by extrapolating values obtained from atomic scale computations. While isolated CdSe QDs have been the subject of intensive research, up to now, only few modeling studies of dimers have been reported. They have mostly relied on the EMA model owing to the increased complexity and heavy computational cost of atomistic approaches for dimers [59; 60; 61; 62; 63]. Below, we use the EMA-**k.p** methodology [55] to describe the level structure of isolated 2 to 4 nm CdSe QDs and build an excitonic Hamiltonian for dimers. This approach allows computing the optical response of a large ensemble of QD dimers, taking into account the static disorder arising from the size dispersion in the optical response [26; 28; 64; 65]. This inherent static disorder is typical of colloidal QDs and not present in ensembles of molecules that are only subject to the dynamical disorder induced by interactions with the environment. We specifically report on the fast tens of femtosecond charge migration and coherent energy transfer for ensembles of QD dimers excited by sequences of femtosecond laser pulses.