HF hydrogen fluoride ground state

(I) W2 calculation

(a)
Reference geometry: CCSD(T)/cc-pVQZ (frozen core)
result: rFH=0.916219966 angstrom

(b) SCF and valence correlation
[By the way, in MOLPRO the basis set sequence to use is
basis,avtz,h=vtz
basis,avqz,h=vqz
basis,av5z,h=v5z
]

HF        SCF                  CCSD                 CCSD(T)
A'VTZ   -100.060988366742    -100.341579275615    -100.349049885506
A'VQZ   -100.068558831621    -100.368880314136    -100.377142498905
A'V5Z   -100.070603709694    -100.377963930033
H
A'VTZ     -0.499809811302
A'VQZ     -0.499945568583
A'V5Z     -0.499994535159

F
A'VTZ    -99.402083121383     -99.623349655724     -99.627771310924
A'VQZ    -99.409209020628     -99.647865823389     -99.652845103807
A'V5Z    -99.411197055583     -99.656371164184

Hence we have for H+F -> HF:
          SCF            CCSD-SCF       CCSD(T)-CCSD
A'VTZ     -0.15909543    -0.05932437    -0.00304895
A'VQZ     -0.15940424    -0.06166468    -0.00328290
A'V5Z     -0.15941212    -0.06218611
Infinite  -0.15941233    -0.062733188   -0.003453624

Extrapolating SCF using A+B.C^l is quite easy using
Einfinity=E[5]-(E[5]-E[4])**2/(E[5]-2*E[4]+E[3])
Extrapolating the CCSD correlation contrib.to A+B/l^3 is also quite easy
Einfinity=E[5]+(E[5]-E[4])/((5/4)**3-1)
Extrapolation the (T) contribution, finally (mind the different l values):
Einfinity=E[4]+(E[4]-E[3])/((4/3)**3-1)
(c) core corr. and scalar relativistics

MTsmall (frozen core): !CCSD(T) ENERGY -100.350417320339
MTsmall (all e-):                      -100.408270982486
core corr. energy:                       -0.05785366
ditto for F atom:
MTsmall (frozen core):                  -99.632199243965
MTsmall (all e-):                       -99.689772583788
core corr. energy:                       -0.05757334
core corr contrib to H+F->HF:            -0.00028032
EREL:
HF                                     -0.08686656
H                                      -0.00000653
F                                      -0.08717340
scalar rel. contrib to H+F->HF:         0.00031337

(d) spin-orbit splitting

HF has no 1st order splitting, neither
has H, but F does. From
http://theochem.weizmann.ac.il/~comartin/w1/
F(2P): -0.00061374 hartree, or -134.70 cm-1,
or -0.385 kcal/mol, or -1.61 kJ/mol

so on H+ F -> HF, we have +0.00061374  hartree

(e) Summarizing:

                       hartree       kcal/mol    kJ/mol
SCF                   -0.15941223    -100.033    -418.54
CCSD valence corr     -0.06273319     -39.366    -164.71
(T) valence corr      -0.00345362      -2.167      -9.07
inner-shell corr      -0.00028032      -0.176      -0.74
scalar rel             0.00031337       0.197       0.82
spin-orbit             0.00061374       0.385       1.61
TOTAL                 -0.22495225    -141.160    -590.61

(II) W1 calculation

(a)
The B3LYP/cc-pVTZ reference geometry is
rHF=0.922318 angstrom

(b) SCF and valence correlation
[By the way, in MOLPRO the basis set sequence to use is
basis,avdz,h=vdz
basis,avtz,h=vtz
basis,avqz,h=vqz
]

HF        SCF                  CCSD                 CCSD(T)
A'VDZ   -100.033217463314    -100.259476331568    -100.263637725068
A'VTZ   -100.060807335651    -100.342026467211    -100.349574734903
A'VQZ   -100.068274666759    -100.369044588713
H
A'VDZ     -0.499278403420
A'VTZ     -0.499809811302
A'VQZ     -0.499945568583
F
A'VDZ    -99.377068840448     -99.402083121383     -99.409209020628
A'VTZ    -99.402083121383     -99.623349655724     -99.627771310924
A'VQZ    -99.409209020628     -99.647865823389

Hence we have for H+F -> HF:
          SCF            CCSD-SCF       CCSD(T)-CCSD
A'VDZ    -0.15687022    -0.05564327    -0.00181136
A'VTZ    -0.15891440    -0.05995260    -0.00312661
A'VQZ    -0.15912008    -0.06211312
Infinite -0.15914309    -0.06352963    -0.00361557

Extrapolating SCF using A+B.C^l is quite easy using
ESCF,infinity=E[4]-(E[4]-E[3])**2/(E[4]-2*E[3]+E[2])
Extrapolating the CCSD correlation contrib.to A+B/l^3 is also quite easy
EcorrCCSD,infinity=E[4]+(E[4]-E[3])/((4/3)**3.22 - 1)
Extrapolation the (T) contribution, finally (mind the different l values):
E(T),infinity=E[3]+(E[3]-E[2])/((3/2)**3.22 - 1)
(c) core corr. and scalar relativistics

MTsmall (frozen core): !CCSD(T) ENERGY -100.35038282
MTsmall (all e-):                      -100.40822999
core corr. energy:                       -0.05784716
[note how the slightly different geometry affects the
individual energies but barely affects the difference]
ditto for F atom:
MTsmall (frozen core):                  -99.632199243965
MTsmall (all e-):                       -99.689772583788
core corr. energy:                       -0.05757334
core corr contrib to H+F->HF:            -0.00027382
EREL:
HF                                     -0.08686732
H                                      -0.00000653
F                                      -0.08717340
scalar rel. contrib to H+F->HF:         0.00031261

(d) spin-orbit splitting

HF has no 1st order splitting, neither
has H, but F does. From
http://theochem.weizmann.ac.il/~comartin/w1/
F(2P): -0.00061374 hartree, or -134.70 cm-1,
or -0.385 kcal/mol, or -1.61 kJ/mol

so on H+ F -> HF, we have +0.00061374  hartree

(e) Summarizing:
                       hartree       kcal/mol    kJ/mol
SCF                   -0.15914309    -99.864    -417.83
CCSD valence corr     -0.06352963    -39.865    -166.80
(T) valence corr      -0.00361557     -2.269      -9.49
inner-shell corr      -0.00027382     -0.172      -0.72
scalar rel            +0.00031261      0.196       0.82
spin-orbit            +0.00061374      0.385       1.61
TOTAL                 -0.22563576   -141.589    -592.41