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Erratum: A coupled cluster approach with triple excitations [J. Chem. Phys. 81, 5906
(1984)]
Y. S. Lee, S. A. Kucharski, and Rodney J. Bartlett
Citation: The Journal of Chemical Physics 82, 5761 (1985);
View online: https://doi.org/10.1063/1.448990
View Table of Contents: http://aip.scitation.org/toc/jcp/82/12
Published by the American Institute of Physics
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Letters to the Editor
TABLEL:iF /(NkT) = [F(hcp) - F (fcc))/(NkT) for different shapes ofthe
periodic box (Nx X Ny X N z ) at density P = 0.7778 Po. v.,... is the largest
cube confined within the periodic box. The first four lines and the last two
lines are due to Refs. I and 2. respectively.
NxXNyXN.
1
2
3
4
5
6
8X12X 12
6X 8X 12
4X 6X 6
3X 4X 6
2X 2X 6
IX 2X 6
i1F/(NkT)
- 0.0015(18)"
0.0024(17)
0.0040(34)
0.0071(47)
0.021(5)
0.025(3)
v~a!
v~a!
0.0015
0.0036
0.0122
0.0288
0.1497
0.7778
0.0099
0.0203
0.0536
0.1022
0.2843
0.1955
In Vmax
"The numbers in brackets are the uncertainties of the last (two) digits.
mining an assumed finite-size effect. Vmax is the volume of
the largest cube (in units of the hard-sphere diameter) confined within the periodic box. Linear fits in V';;-..! and
v.;;;.! In Vmax were proposed in Ref. 1. Both fits could not be
excluded from a statistical point of view. Table I shows that
i = 5 and especially i = 6 extend the range of V,;;-..! appreciably so that a simple linear fit in V';;-..! seems doubtful then.
This is not the case for v';;-..! In Vmax ' Indeed, a X 2 test (at 5%
level) shows that for a linear fit in v';;-..!, i = 6 cannot be in-
5761
cluded, whereas all values can be used for the other fit mentioned. The corresponding results for the thermodynamic
limit (v,;;-..!-o) are
v';;-..! extrapolation: t1f/(kT) = 0.0005 ± 0.0012,
(3a)
v.;;;.! In Vmax extrapolation: t1f/(kT) = - 0.0010 ± 0.0013.
(3b)
This is consistent with Ref. 1. One may interpret Eqs. (3a)
and (3b) and Table I in the following way: The fcc structure is
more stable than the hcp structure as long as the periodic box
is very small. With increasing size of the box, the difference
in free energy per particle decreases, so that it is not clear if
the limiting value t1fis slightly positive or negative (or even
zero). Thus the stability offcc and hcp hard-sphere crystals is
again uncertain due to Ref. 1. Since t1fis so small, it is advisable to consider also the influence of crystal defects which
may playa decisive role for the stability of hard-sphere solids
close to melting.
'D. Frenkel and A. J. C. Ladd. J. Chem. Phys. 81. 3188 (1984).
2K. W. Kratky. Chern. Phys. 57, 167 (1981).
3B.J. Alder. D. A. Young, M. R. Mansigh. andZ. W. Salsburg.J. Comput.
Phys. 7. 361 (1971).
ERRATA
Erratum: A coupled cluster approach with triple excitations
[J. Chem. Phys. 81, 5906 (1984)]
Y. S. Lee, S. A. Kucharski, and R. J. Bartlett
Quantum Theory Project. University ofFlorida. Gainesville, Florida 3261 1
In Table I of our recent paper which details the 47 explicit spin-orbital expressions in the triple-excitation cluster
equation for the CCSDT model, there is one sign error and a
factor of 1/2 missing from four terms. The first expression in
the fourth line should be positive while the last two terms in
the table and the first two on line 12 should be preceded by a
factor of 1/2. With these changes, this very complicated table has been verified to be correct, and may be used for
further implementation of the full CCSDT equations.
J. Chern. Phys .• Vol. 82. No. 12. 15 June 1985
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