You need to slightly modify code of constructing A and B matrices in ESP fitting code (subroutine fitESP in population.f90).
This feature was not directly supported by Multiwfn because ESP fitting charges can always well reproduce dipole moment, therefore imposing this constraint is redundant.

Dear all,

I want to run ESP fitting imposing constraints so that the final charges reproduce the dipole moment. In principle, this is achievable using charge constraints, adding three constraint (one for each cartesian component of the dipole moment) like this:

\sum_i r_{ij} q_{i} = \mu_{j}

where r_{ij} is the j-th component of the position of the i-th atom, q_i is the charge on i-th atom and \mu_j is the j-th component of the dipole moment.

With reference to chapter 3.9.16.1 of the Multiwfn guide, one would need to add atomic coordinates in matrix A and the dipole moment components in matrix B.

Is this achievable in Multiwfn? Can I input values different from 0 and 1 to matrix A?