Analytic gradients in the random-phase approximation

081101-4 Rekkedal et al. J. Chem. Phys. 139, 081101(2013)
TABLE I. Equilibrium distances (r e ,inÅ)andbindingenergies(E, in
meV) for RG dimers in the aug-cc-pV5Z basis without counterpoise correction.
DFT results from Ref. 18, referenceresultsfromRef.24.
He 2 Ne 2 Ar 2
r e E r e E r e E
vdW-DF 2.82 6.6 3.07 14.1 3.92 23.1
vdW-DF2 2.75 2.8 2.95 9.2 3.75 18.3
PBE-D3 2.66 5.7 3.01 9.9 3.88 15.3
revPBE-D3 2.90 3.0 3.20 5.6 3.93 12.8
B97D-D3 3.01 0.8 3.33 4.3 3.99 11.3
rVV10 2.92 0.9 3.01 5.6 3.73 13.9
MP2 3.07 0.61 3.15 3.12 3.63 27.43
dRPA 3.13 0.46 3.14 3.10 3.72 21.96
SOSEX 3.13 0.45 3.17 2.51 3.78 16.32
Reference 2.97 0.95 3.09 3.65 3.76 12.35
with (selected) results of Tran and Hutter in Table I and
compared with accurate reference values. The accuracy of
dRPA/SOSEX is similar to that of MP2 for equilibrium distances
and binding energies of the RG dimers, with SOSEX
increasing the difference between dRPA and MP2. Equilibrium
distance errors from dRPA and SOSEX are less than 5%,
while binding energy errors range from 15% to almost 100%.
None of the DFT methods in the table are consistently better
than dRPA/SOSEX, and none can be considered highly accurate
relative to CCSD(T), which agrees with the reference
values within 0.5% for distances and 3% for energies of the
RG dimers. 25
III. CONCLUDING REMARKS
We have presented an implementation of analytic molecular
gradients using the Lagrangian approach for the dRPA
and SOSEX methods. Our pilot implementation scales with
system size M as O(M 6 ), which may be reduced using the
techniques of linear-scaling CC theories. The importance
of selecting the proper stabilizing solution to the dRPA
CARE has been highlighted. Illustrative calculations indicate
that dRPA and SOSEX deliver an accuracy on par with
MP2. SOSEX does not always improve the agreement with
MP2.
ACKNOWLEDGMENTS
This work was supported by the Research Council of
Norway (RCN) through CoE Grant No. 179568/V30, by the
Norwegian Supercomputing Program (Grant No. NN4654K),
and by the European Research Council under the European
Union Seventh Framework Program through the Advanced
Grant ABACUS, ERC Grant Agreement No. 267683.
A.M.T. was supported by the RCN (Grant No. 197446/V30)
and a Royal Society university research fellowship. S.C.
was supported by the Italian Ministero dell’Istruzione,
dell’Università e della Ricerca (MIUR), PRIN2009 Grant No.
2009C28YBF_001.
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