The high accuracy extrapolated ab initio thermochemistry (HEAT) protocol is applied to compute the total atomization energy (TAE) and the heat of formation of benzene. Large-scale coupled-cluster calculations with more than 1500 basis functions and 42 correlated electrons as well as zero-point energies based on full cubic and (semi)diagonal quartic force fields obtained with the coupled-cluster singles and doubles with perturbative treatment of the triples method and atomic natural orbital (ANO) triple- and quadruple-zeta basis sets are presented. The performance of modifications to the HEAT scheme and the scaling properties of its contributions with respect to the system size are investigated. A purely quantum-chemical TAE and associated conservative error bar of 5463.0 ± 3.1 kJ mol−1 are obtained, while the corresponding 95% confidence interval, based on a statistical analysis of HEAT results for other and related molecules, is ± 1.8 kJ mol−1. The heat of formation of benzene is determined to be 101.5 ± 2.0 kJ mol−1 and 83.9 ± 2.1 kJ mol−1 at 0 K and 298.15 K, respectively.
REFERENCES
1.
A. D.
Boese
, M.
Oren
, O.
Atasoylu
, J. M. L.
Martin
, M.
Kállay
, and J.
Gauss
, J. Chem. Phys.
120
, 4129
(2004
).2.
A.
Tajti
, P. G.
Szalay
, A. G.
Császár
, M.
Kállay
, J.
Gauss
, E. F.
Valeev
, B. A.
Flowers
, J.
Vázquez
, and J. F.
Stanton
, J. Chem. Phys.
121
, 11599
(2004
).3.
Y. J.
Bomble
, J.
Vázquez
, M.
Kállay
, C.
Michauk
, P. G.
Szalay
, A. G.
Császár
, J.
Gauss
, and J. F.
Stanton
, J. Chem. Phys.
125
, 064108
(2006
).4.
A.
Karton
, E.
Rabinovich
, J. M. L.
Martin
, and B.
Ruscic
, J. Chem. Phys.
125
, 144108
(2006
).5.
A.
Karton
, P. R.
Taylor
, and J. M. L.
Martin
, J. Chem. Phys.
127
, 064104
(2007
).6.
M. E.
Harding
, J.
Vázquez
, B.
Ruscic
, A. K.
Wilson
, J.
Gauss
, and J. F.
Stanton
, J. Chem. Phys.
128
, 114111
(2008
).7.
D.
Feller
, K. A.
Peterson
, and D. A.
Dixon
, J. Chem. Phys.
129
, 204105
(2008
).8.
Note that in thermochemistry, all quoted uncertainties should represent best estimates of 95% confidence intervals, i.e., there is one chance in 20 that the correct value lies outside the given confidence interval.
9.
D.
Feller
and D. A.
Dixon
, J. Phys. Chem. A
103
, 6413
(1999
).10.
D. A.
Dixon
, D.
Feller
, and K. A.
Peterson
, J. Chem. Phys.
115
, 2576
(2001
).11.
D.
Feller
, D. A.
Dixon
, and J. S.
Francisco
, J. Phys. Chem. A
107
, 1604
(2003
).12.
D.
Feller
and D. A.
Dixon
, J. Phys. Chem. A
107
, 9641
(2003
).13.
D.
Feller
and D. A.
Dixon
, J. Phys. Chem. A
107
, 10419
(2003
).14.
B. A.
Flowers
, P. G.
Szalay
, J. F.
Stanton
, M.
Kállay
, J.
Gauss
, and A. G.
Cászár
, J. Phys. Chem. A
108
, 3195
(2004
).15.
M. S.
Schuurman
, W. D.
Allen
, P. V. R.
Schleyer
, and H. F.
Schaefer
III, J. Chem. Phys.
122
, 104302
(2005
).16.
M. E.
Harding
, J.
Gauss
, K.
Pflüger
, and H.-J.
Werner
, J. Phys. Chem. A
111
, 13623
(2007
).17.
M. E.
Harding
, J.
Gauss
, K.
Pflüger
, and H.-J.
Werner
, J. Phys. Chem. A
112
, 5024
(2008
).18.
G.
Czakó
, B.
Nagy
, G.
Tasi
, A.
Somogyi
, J.
Šimunek
, J.
Noga
, B. J.
Braams
, J. M.
Bowman
, and A. G.
Császár
, Int. J. Quantum. Chem.
109
, 2393
(2009
).19.
A. C.
Simmonett
, H. F.
Schaefer
III, and W. D.
Allen
, J. Chem. Phys.
130
, 044301
(2009
).20.
M. E.
Varner
, M. E.
Harding
, J.
Vázquez
, J.
Gauss
, and J. F.
Stanton
, J. Phys. Chem. A
113
, 11238
(2009
).21.
J.
Vázquez
, M. E.
Harding
, J.
Gauss
, and J. F.
Stanton
, J. Phys. Chem. A
113
, 12447
(2009
).22.
D.
Feller
and K. A.
Peterson
, J. Chem. Phys.
131
, 154306
(2009
).23.
D.
Feller
, K. A.
Peterson
, and D. A.
Dixon
, J. Phys. Chem. A
114
, 613
(2010
).24.
N. S.
Shuman
, M.
Johnson
, W. R.
Stevens
, M. E.
Harding
, J. F.
Stanton
, and T.
Baer
, J. Phys. Chem. A
114
, 10016
(2010
).25.
B.
Nagy
, J.
Csontos
, M.
Kállay
, and G.
Tasi
, J. Phys. Chem. A
114
, 13213
(2010
).26.
J.
Csontos
, Z.
Rolik
, S.
Das
, and M.
Kállay
, J. Phys. Chem. A
114
, 13093
(2010
).27.
W. R.
Stevens
, B.
Ruscic
, and T.
Baer
, J. Phys. Chem. A
114
, 13134
(2010
).28.
J. M. L.
Martin
and G.
de Oliveira
, J. Chem. Phys.
111
, 1843
(1999
).29.
D.
Feller
and D. A.
Dixon
, J. Phys. Chem. A
104
, 3048
(2000
).30.
S.
Parthiban
and J. M. L.
Martin
, J. Chem. Phys.
115
, 2051
(2001
).31.
A.
Kamir
, I.
Kaminker
, and J. M. L.
Martin
, J. Phys. Chem. A
113
, 7610
(2009
).32.
M. V.
Roux
, M.
Temprado
, J. S.
Chickos
, and Y.
Nagano
, J. Phys. Chem. Ref. Data
37
, 1855
(2008
).33.
T. H.
Dunning
Jr., J. Chem. Phys.
90
, 1007
(1989
).34.
R. A.
Kendall
, T. H.
Dunning
Jr., and R. J.
Harrison
, J. Chem. Phys.
96
, 6796
(1992
).35.
D. E.
Woon
and T. H.
Dunning
Jr., J. Chem. Phys.
103
, 4572
(1995
).36.
D.
Feller
, J. Chem. Phys.
96
, 6104
(1992
).37.
K.
Raghavachari
, G. W.
Trucks
, J. A.
Pople
, and M.
Head-Gordon
, Chem. Phys. Lett.
157
, 479
(1989
).38.
T. H.
Dunning
Jr., and K. A.
Peterson
, J. Chem. Phys.
117
, 10548
(2002
).39.
T.
Helgaker
, W.
Klopper
, H.
Koch
, and J.
Noga
, J. Chem. Phys.
106
, 9639
(1997
).40.
J.
Noga
and R. J.
Bartlett
, J. Chem. Phys.
86
, 7041
(1987
).41.
Y. J.
Bomble
, M.
Kállay
, J.
Gauss
, and J. F.
Stanton
, J. Chem. Phys.
123
, 054101
(2005
).42.
M.
Kállay
and J.
Gauss
, J. Chem. Phys.
123
, 214105
(2005
).43.
I. M.
Mills
, in Modern Spectroscopy: Modern Research
, edited by K. N.
Rao
and C. W.
Matthews
(Academic
, New York
, 1972
), p. 115
.44.
W.
Klopper
, J. Comput. Chem.
18
, 20
(1997
).45.
C.
Michauk
and J.
Gauss
, J. Chem. Phys.
127
, 044106
(2007
).46.
J. L.
Tilson
, W. C.
Ermler
, and R. M.
Pitzer
, Comput. Phys. Commun.
128
, 128
(2000
).47.
R. M.
Pitzer
, private communication to P. G. Szalay (see Ref. 2).48.
L.
Pacios
and P. A.
Christiansen
, J. Chem. Phys.
82
, 2664
(1985
).49.
J.
Gauss
, A.
Tajti
, M.
Kállay
, J. F.
Stanton
, and P. G.
Szalay
, J. Chem. Phys.
125
, 144111
(2006
).50.
CFOUR, coupled-cluster techniques for computational chemistry, a quantum-chemical program package by
J. F.
Stanton
, J.
Gauss
, M. E.
Harding
, P. G.
Szalay
with contributions from A. A.
Auer
, R. J.
Bartlett
, U.
Benedikt
, C.
Berger
, D. E.
Bernholdt
, Y. J.
Bomble
, L.
Cheng
, O.
Christiansen
, M.
Heckert
, O.
Heun
, C.
Huber
, T.-C.
Jagau
, D.
Jonsson
, J.
Jusélius
, K.
Klein
, W. J.
Lauderdale
, D. A.
Matthews
, T.
Metzroth
, D. P.
O’Neill
, D. R.
Price
, E.
Prochnow
, K.
Ruud
, F.
Schiffmann
, W.
Schwalbach
, S.
Stopkowicz
, A.
Tajti
, J.
Vázquez
, F.
Wang
, J. D.
Watts
and the integral packages MOLECULE (J.
Almlöf
and P. R.
Taylor
), PROPS (P. R.
Taylor
), ABACUS (T.
Helgaker
, H. J. Aa.
Jensen
, P.
Jørgensen
, and J.
Olsen
), and ECP routines by A. V.
Mitin
and C. van
Wüllen
. For the current version; see http://www.cfour.de.51.
M. E.
Harding
, T.
Metzroth
, J.
Gauss
, and A. A.
Auer
, J. Chem. Theory Comput.
4
, 64
(2008
).52.
E.
Prochnow
, M.
Harding
, and J.
Gauss
, J. Chem. Theory Comput.
6
, 2339
(2010
).53.
J.
Vázquez
, D. R.
Price
, M. E.
Harding
, P. G.
Szalay
, J.
Gauss
, and J. F.
Stanton
(unpublished).54.
55.
M.
Kállay
and P. R.
Surján
, J. Chem. Phys
115
, 2945
(2001
).56.
M.
Kállay
and M. E.
Harding
, “Parallel version of the string-based general coupled-cluster program MRCC
” (2006
); see http://www.mrcc.hu.57.
58.
R. J.
Bartlett
and G. D.
Purvis
, Int. J. Quantum Chem.
14
, 561
(1978
).59.
J. F.
Stanton
, J.
Gauss
, J. D.
Watts
, and R. J.
Bartlett
, J. Chem. Phys.
94
, 4334
(1991
).60.
± 0.02 kJ mol−1 refers to the numerical uncertainty of the
$\Delta E_{\rm CCSD(T)}^{\infty }$
contribution: modifying the estimate of the CCSD(T)/(aug)-pwCV5Z correlation energy by ± 3 μEh in the two-point extrapolation (Ref. 39) leads to a change of less than ± 0.02 kJ mol−1, which reflects the maximum effect of the 0.01 kJ mol−1 numerical uncertainty of the CCSD(T)/(aug)-cc-pwCV5Z energy on the extrapolated CCSD(T) correlation energy.61.
The fc-CCSDT/cc-pVQZ calculation required two weeks of wall clock time on a node featuring two quad core Intel W5590 processors running at 3.33 GHz, 144 GB of main memory and 16 striped 64 GB solid state disks.
62.
Each node was equipped with a single core AMD64 3500+ processor, 4 GB of main memory, and two striped 160 GB SATA disks.
63.
S.
Thorwirth
, M. E.
Harding
, D.
Muders
, and J.
Gauss
, J. Mol. Spectrosc.
251
, 220
(2008
).64.
J. F.
Stanton
and J.
Gauss
, Chem. Phys. Lett.
276
, 70
(1997
).65.
J.
Almlöf
and P. R.
Taylor
, J. Chem. Phys.
86
, 4070
(1987
).66.
D. A.
Matthews
, J.
Vázquez
, and J. F.
Stanton
, Mol. Phys.
105
, 2659
(2007
).67.
I. M.
Konen
, E. X. J.
Li
, M. I.
Lester
, J.
Vázquez
, and J. F.
Stanton
, J. Chem. Phys.
125
, 074310
(2006
).68.
J. M. L.
Martin
, P. R.
Taylor
, and T. J.
Lee
, Chem. Phys. Lett.
275
, 414
(1997
).69.
J. M. L.
Martin
, T. J.
Lee
, P. R.
Taylor
, and J.-P.
François
, J. Chem. Phys.
103
, 2589
(1995
).70.
J.
Vázquez
, M. E.
Harding
, and J. F.
Stanton
(unpublished).71.
The evaluation of one perturbation of the second derivatives at the CCSD(T) level scales with N7, where N represents the size of the system. The number of perturbations itself is also directly proportional to the size of the system and the number of required second derivative computations for the numerical evaluation of the cubic and semi-diagonal quartic force constant depends as well on N. This leads to an overall scaling of N9.
72.
J.
Vázquez
and J. F.
Stanton
(unpublished).73.
These calculations were carried out on a 22 node cluster, which was simultaneously used for other purposes as well. The cluster nodes were equipped with two dual core Intel Xeon 5160 processors running at 2.93 GHz, 32 GB RAM, and 8 striped 320 GB SATA disks.
74.
A.
Tajti
, P. G.
Szalay
, and J.
Gauss
, J. Chem. Phys.
127
, 014102
(2007
).75.
The propargyl radical, C3H3, would be another potential candidate to be considered in the size extensivity analysis. However, at present neither the experimental nor the theoretical estimates of its TAE are as accurate as the ones for CH, acetylene, and benzene discussed in this work. See Ref. 21 for details.
76.
S. A.
Kucharski
and R. J.
Bartlett
, Theor. Chim. Acta
80
, 387
(1991
).77.
78.
Given that the total theoretical error estimates for 3 noninteracting acetylenes is about 2–3 times that of 6 noninteracting methylidyne molecules, one might think that this indicates a trend and therefore the error estimate for benzene should be 2–3 times that of 3 noninteracting acetylenes. However, this is clearly inconsistent with the scaling observed for the individual contributions (compare Table VI).
79.
The error estimates for the heat of reaction of C6H6 → 3 C3H3 amount to +0.11, +0.41, and −0.05 kJ mol−1 for
$E_{\rm HF}^{\infty }$
, $\Delta E_{\rm CCSD(T)}^{\infty }$
, and ΔECCSDT, respectively. The corresponding values for the reaction to six methylidyne molecules are +0.12, −1.70, and −0.88 kJ mol−1. The difference between the extrapolated (cc-pVTZ and cc-pVQZ) and the unextrapolated result (cc-pVQZ) was used to estimate the error in the ΔECCSDT contribution80.
This most recent value for the heat of formation of carbon (711.38 ± 0.06 kJ mol−1) (Ref. 27) compares well with the CODATA value of 711.19 ± 0.45 kJ mol−1 (Ref. 81) published more than 20 years ago and is a significant improvement with respect to values used in previous applications of the HEAT scheme 711.79 ± 0.21 kJ mol−1 and 711.58 kJ mol−1, compare, e.g., Refs. 2, 3, 8, 16, 21, and 24.
81.
J. D.
Cox
, D. D.
Wagman
, and V. A.
Medvedev
, CODATA Key values for Thermodynamics
(Hemisphere Publishing Corp
., New York
, 1984
).82.
M. W.
Chase
Jr., “NIST-JANAF Thermochemical Tables
,” J. Phys. Chem. Ref. Data
4th. ed., Monographic No. 9
(American Institute of Physics
, Melville, NY
, 1998
).83.
84.
The temperature correction was also estimated using harmonic frequencies calculated using the fc-CCSD(T) method and the ANO1, cc-pVXZ (X = T,Q) basis sets as well as the ae-CCSD(T)/cc-pVXZ (X = T,Q) levels of theory. All determined values lie within a range of 0.2 kJ mol−1.
85.
N. M.
Laurendeau
, Statistical Thermodynamics: Fundamentals and Applications
(Cambridge University Press
, New York
, 2005
).86.
L.
Goodman
, A. G.
Ozkabak
, and S. N.
Thakur
, J. Phys. Chem.
95
, 9044
(1991
).87.
G. H.
Hess
, Pogg. Ann.
47
, 210
(1839
).88.
G. H.
Hess
, Pogg. Ann.
50
, 385
(1840
).89.
S. E.
Wheeler
, K. N.
Houk
, P.
Schleyer
, and W. D.
Allen
, J. Am. Chem. Soc.
131
, 2547
(2009
).90.
W.
Klopper
, F. R.
Manby
, S.
Ten-no
, and E. F.
Valeev
, Int. Rev. Phys. Chem.
25
, 427
(2006
).91.
T. B.
Adler
, G.
Knizia
, and H.-J.
Werner
, J. Chem. Phys.
127
, 221106
(2007
).92.
J.
Noga
, S.
Kedžuch
, J.
Šimunek
, and S.
Ten-no
, J. Chem. Phys.
128
, 174103
(2008
).93.
A.
Köhn
, J. Chem. Phys.
130
, 131101
(2009
).94.
W.
Klopper
, R. A.
Bachorz
, C.
Hättig
, and D. P.
Tew
, Theor. Chem. Acc.
126
, 289
(2010
).95.
A.
Köhn
, J. Chem. Phys.
133
, 174118
(2010
).© 2011 American Institute of Physics.
2011
American Institute of Physics
You do not currently have access to this content.
