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! As atom...Test of relativistic energy correction,
! by the Douglas-Kroll transformation to 3rd order.
!
! the FINAL DK3 energy is -2259.0955118153
! web page says -2259.095511826
! <r(4s)>=1.997, <r(4p)>=2.504 Bohr
!
! convergence of the DK transformation is typical,
! 0th order -2234.2372862734 (non-relativistic)
! 1st order -2264.6131852344
! 2nd order -2258.9450216276
! 3rd order -2259.0955118173
! inf. order -2259.0876044131
! in that 1st order way undershoots, 2nd order comes
! back close, and 3rd order is not insubstantial.
!
! Compare with -2259.456841 which is the point
! nucleus Dirac-Coulomb numerical Hartree-Fock from
! L.Visscher, K.G.Dyall
! At.Data Nucl.Data Tables 67, 207-224(1997),
! noting that the present run does not include any
! relativistic treatment of the 2e- potential.
!
! The Infinite Order Two Component (relwfn=iotc)
! shows the limit of the Douglas-Kroll method,
! and is preferred in practice.
!
! The uncontracted 20s15p9d basis set below is from
! T.Tsuchiya, M.Abe, T.Nakajima, K.Hirao
! J.Chem.Phys. 115, 4463-4472(2001)
! using exponents downloaded from the web page of
! this group at the University of Tokyo. A general
! contraction of this basis can easily be obtained,
! by manipulating the $VEC coefs produced by this run,
! see ~/gamess/tools/dk3.f.
!
! The semicolon divides two lines of input that happen
! to be given on a single physical line of the file.
!
$contrl scftyp=rohf mult=4 relwfn=dk ispher=1 $end
$system timlim=2 mwords=2 $end
$relwfn norder=3 $end
$guess guess=huckel $end
$radial nshell=2 idegsh(1)=1,3 memsh(1)=15, 16,17,18 $end
$data
illustration of 3rd order Douglas-Kroll for As
Dnh 2

Arsenic 33.0
S 1 ; 1 7.2421890D+07 1.0
S 1 ; 1 7.7040750D+06 1.0
S 1 ; 1 1.3365730D+06 1.0
S 1 ; 1 3.0394350D+05 1.0
S 1 ; 1 8.3289250D+04 1.0
S 1 ; 1 2.5994450D+04 1.0
S 1 ; 1 8.9795770D+03 1.0
S 1 ; 1 3.3667950D+03 1.0
S 1 ; 1 1.3464700D+03 1.0
S 1 ; 1 5.6774580D+02 1.0
S 1 ; 1 2.4923080D+02 1.0
S 1 ; 1 1.1199520D+02 1.0
S 1 ; 1 4.6328140D+01 1.0
S 1 ; 1 2.2611220D+01 1.0
S 1 ; 1 1.0910110D+01 1.0
S 1 ; 1 4.5498340D+00 1.0
S 1 ; 1 2.1494630D+00 1.0
S 1 ; 1 1.0337510D+00 1.0
S 1 ; 1 3.0892460D-01 1.0
S 1 ; 1 1.1206710D-01 1.0
P 1 ; 1 4.9515580D+04 1.0
P 1 ; 1 8.4637830D+03 1.0
P 1 ; 1 2.2908560D+03 1.0
P 1 ; 1 7.7965970D+02 1.0
P 1 ; 1 3.0545690D+02 1.0
P 1 ; 1 1.3097990D+02 1.0
P 1 ; 1 5.9698960D+01 1.0
P 1 ; 1 2.8408790D+01 1.0
P 1 ; 1 1.3883000D+01 1.0
P 1 ; 1 6.6102210D+00 1.0
P 1 ; 1 3.0821260D+00 1.0
P 1 ; 1 1.3919830D+00 1.0
P 1 ; 1 4.8254700D-01 1.0
P 1 ; 1 1.9228260D-01 1.0
P 1 ; 1 7.2849660D-02 1.0
D 1 ; 1 7.1896480D+02 1.0
D 1 ; 1 2.0798400D+02 1.0
D 1 ; 1 7.9590850D+01 1.0
D 1 ; 1 3.4514110D+01 1.0
D 1 ; 1 1.5730540D+01 1.0
D 1 ; 1 7.2805600D+00 1.0
D 1 ; 1 3.3000700D+00 1.0
D 1 ; 1 1.4173160D+00 1.0
D 1 ; 1 5.4472730D-01 1.0

$end