Ab initio calculations of the total dielectronic recombination (DR) ra
te coefficient for Ar-like tungsten (W56+) are performed using the rel
ativistic HULLAC code package based on the parametric potential method
. The high efficiency of HULLAC compared to other codes enables us to
perform extensive DR calculations for highly complex atomic systems su
ch as Ar-like tungsten. The present work provides a general procedure
for computing the DR rate coefficients for multielectron high-Z ions.
This procedure is applicable to DR computations for other Ar-like ions
, as well as for ions in neighboring isoelectronic sequences. In the p
resent work level-by-level calculations are performed for evaluating t
he contributions to DR through all the relevant K-like autoionizing in
ner-shell excited configuration complexes: 3p(5)4ln'l' (4 less than or
equal to n'less than or equal to 17), 3s3p(6)4ln'l' (4 less than or e
qual to n'less than or equal to 12), 3p(5)3dn'l' (8 less than or equal
to n'less than or equal to 18), 3s3p(6)3dn'l' (7 less than or equal t
o n'less than or equal to 18), 2p(5)3s(2)3p(6)3dn'l', II (3 less than
or equal to n'less than or equal to 8), 2s2p(6)3s(2)3p(6)3dn'l' (3 les
s than or equal to n'less than or equal to 5), and 3p(5)5l5l'. in addi
tion, extrapolation methods are developed to calculate the contributio
ns of even higher n' complexes along each complex series. In the case
of 3p(5)3dn'l', the usual complex-by-complex extrapolation method base
d on the n'(-3) scaling law is found to be inaccurate; thus, a more de
tailed level-by-level procedure is discussed. All calculations are car
ried out assuming no electron collisions occur after the initial elect
ron capture. Although the dominant DR contributions come from 3p(5)4ln
'l' and 3p(5)3dn'l', the contributions of the other complex series can
not be neglected. A comparison between the present results and the Bur
gess-Merts (BM) approximation shows that at low electron temperatures
the BM approximation greatly underestimates the DR rate coefficients,
whereas at high electron temperatures this approximation is fairly goo
d.