Context : Observations of soft X-ray transients in quiescence suggest the existence of heat sources in the crust of accreting neutron stars .
Heat is thought to be released by electroweak and nuclear processes triggered by the burying of ashes of X-ray bursts .

Aims : The heating is studied using a fully quantum approach taking consistently into account nuclear shell effects .

Methods : We have followed the evolution of ashes made of ^ { 56 } Fe employing the nuclear energy-density functional theory .
Both the outer and inner crusts are described using the same functional , thus ensuring a unified and thermodynamically consistent treatment .
To assess the role of the neutron-matter constraint , we have employed the set of accurately calibrated Brussels-Montreal functionals BSk19 , BSk20 , and BSk21 and for comparison the SLy4 functional .

Results : Due to nuclear shell effects , the fully accreted crust is found to be much less stratified than in previous studies .
In particular , large regions of the inner crust contain clusters with the magic number Z = 14 .
The heat deposited in the outer crust is tightly constrained by experimental atomic mass data .
The shallow heating we obtain does not exceed 0.2 MeV and is therefore not enough to explain the cooling of some soft X-ray transients .
The total heat released in the crust is very sensitive to details of the nuclear structure and is predicted to lie in the range from 1.5 MeV to 1.7 MeV .

Conclusions : The evolution of an accreted matter element and therefore the location of heat sources are governed to a large extent by the existence of nuclear shell closures .
Ignoring these effects in the inner crust , the total heat falls to \sim 0.6 MeV .
The neutron-matter constraint is also found to play a key role .
The large amount of heat obtained by Steiner et al .
( 2012 ) could thus be traced back to unrealistic neutron-matter equations of state .