1. Computational investigation of the relative energies of
naphthalene and C10H8 isomers
Shahbaz Mushtaq and D. Allen Clabo, Jr., Department of Chemistry, Francis Marion University, Florence, SC,
Southeast Regional Meeting of the American Chemical Society, Nashville, TN, October 19, 2014
A common experiment in the Physical Chemistry
laboratory is the determination of the relative energies
of naphthalene and azulene by bomb calorimetry. In
order to develop a complementary computational
experiment, we have surveyed the relative energies
of three C10H8 isomers using a variety of
computational methods to determine what level of
theory achieves both good accuracy and reasonable
calculation times. The project has systematically
examined basis set size, Hartree-Fock and density-
functional theory, and kind of functional. Results are
compared to typical student calorimetry results and
literature values of the relative energies.
Abstract Results
• The energy difference between naphthalene and
azulene is converging to 177-178 kJ/mol.
• literature reference value: 147.7
• calorimetry data: 134.3-143.1
• various computational methods: 134.3-180.7
• some of our remaining error is from using
unscaled vibrational frequencies; some is
from not including electron correlation effects
• The energy difference between naphthalene and
the 3rd isomer seems to be converging to 387-
388 kJ/mol.
• This difference appears not to have been
reported in the literature, so we are
anticipating eventually providing a first good
estimate of this value.
• Given the remaining error in the
naphthalene/azulene energy difference, the
naphthalene/3rd isomer difference seems
likely to be more like ~355 kJ/mol
Many theoretical methods are available to
complement experimental results, to assist in their
interpretation, and to extend reliable data beyond
those that can be measured. These properties,
including relative energies, bond dissociation
energies, and various spectroscopic properties are
readily amenable to calculation using easily
accessible computational packages like
GAUSSIAN09 and its graphical interface GaussView
5.0. Computational chemistry techniques calculate the
optimized geometry of a molecule of interest to find its
total electronic energy and the vibrational frequencies
to find the zero-point energy. We use these data to
determine the relative energies of our molecules of
interest, namely, the isomers of C10H8, including
naphthalene, azulene, and a 3rd isomer at the
Hartree-Fock level of theory with a series of basis
sets.
GaussView 5.0 was used to draw structures of
naphthalene, azulene and a 3rd isomer. Using 32GB
from each of 12 linked processors for a total of
384GB of RAM, calculations were set up using the
Hartree-Fock theory to optimize the geometries and
determine frequencies of the molecules. The
calculations used a variety of split-valence (3-21G, 6-
31G, 6-311+G, etc.) and correlation consistent (cc-
pVxZ and aug-cc-pVxZ) basis sets. The calculation
times were recorded in addition to the HF energy and
ZPE, to assess the practical impact of increased
basis set size in addition to the degree of agreement
with previous experimental and computational
determinations. The final relative energies reported
include both electronic and vibrational zero-point
energies.
Methods
Background
• FMU Ready to Experience Applied Learning
(REAL) program for travel support for S.M.
• FMU Professional Development Committee and
Department of Chemistry for travel support for
D.A.C.
• SC-EPSCoR GEAR:CI Program (South Carolina
Computational Chemistry Consortium (SC4)) for
providing the Gaussian and GaussView software
• NSF EPSCoR RII Track 1 cooperative agreement
awarded to the University of South Carolina for
providing computational resources (Patriot cluster)
C. Salter and J. B. Foresman, J. Chem. Ed.
1998, 75, 1341.
Reference
Future Work
• Scaling ZPEs to give better agreement with
experimental values
• This scaling is needed less at better levels of
theory (e.g., CCSD)
• Inclusion of electron correlation, including
calculations using density functional theory
(B3LYP), perturbation theory (MP2), or coupled-
cluster theory (CCSD)
• MP2 and CCSD calculations require large
amounts of time when using large basis sets
• A practical method should be identified to
complement existing lab experiments
Acknowledgements
Naphthalene Azulene 3rd Isomer
Naphthalene Azulene 3rd Isomer
Basis Set
Computation Time
(dd:hh:mm:ss) BF E (HF) (a.u.)
ZPVE
(kJ/mol)
Computation Time
(dd:hh:mm:ss) BF E (HF) (a.u.)
ZPVE
(kJ/mol) E (rel) (kJ/mol)
Computation Time
(dd:hh:mm:ss) BF E (HF) (a.u.)
ZPVE
(kJ/mol) E (rel) (kJ/mol)
STO-3G 6:52 58 -378.68685 448.5 1:21 58 -378.59837 446.1 229.8 1:6 58 -378.50699 445.0 468.6
3-21G 7:35 106 -381.21581 418.9 3:30 106 -381.13789 411.8 197.4 2:5 106 -381.04322 410.3 444.5
6-31G 6:10 106 -383.22272 420.5 3:50 106 -383.14728 411.9 189.4 2:21 106 -383.05452 412.7 433.7
6-311G 11:33 154 -383.28572 415.8 10:30 154 -383.21193 408.1 186.0 6:17 154 -383.12210 408.4 422.1
6-31G(d) 12:52 166 -383.35505 415.2 8:48 166 -383.28319 410.5 183.9 8:25 166 -383.20149 409.5 397.4
6-31G(d.p) 15:11 190 -383.36936 414.0 14:37 190 -383.29752 409.2 183.7 13:30 190 -383.21594 408.1 396.9
6-311G(d.p) 21:21 228 -383.43422 411.3 31:57 228 -383.36399 406.6 179.6 29:51 228 -383.28322 405.3 390.4
6-311+G(d.p) 55:27 268 -383.43823 411.0 1:07:33 268 -383.36847 406.0 178.1 1:01:30 268 -383.28749 404.7 389.5
6-311+G(2df.2pd) 3:28:58 452 -383.46989 411.4 4:23:12 452 -383.40042 406.8 177.7 4:00:4 452 -383.32030 405.7 387.0
cc-pVDZ 11:30 180 -383.38496 412.0 15:41 180 -383.31483 407.2 179.3 14:48 180 -383.23344 406.1 391.8
cc-pVTZ 2:30:43 412 -383.47796 411.3 3:21:33 412 -383.40810 406.7 178.7 3:20:47 412 -383.32798 405.6 388.0
cc-pVQZ 1:16:13:59 790 -383.50123 411.2 1:23:40:21 790 -383.43154 406.7 178.4 2:03:12:46 790 -383.35135 405.5 387.8
aug-cc-pVDZ 1:42:25 302 -383.39481 411.0 2:26:25 302 -383.32537 405.8 177.1 2:17:30 302 -383.24407 404.7 389.4
aug-cc-pVTZ 20:58:19 644 -383.48074 411.2 1:01:18:8 644 -383.41126 406.5 177.6 1:04:14:30 644 -383.33108 405.5 387.2
aug-cc-pVQZ 15:23:21:31 1168 -383.50217 411.5 17:10:19:33 1168 -383.43259 406.8 177.9 24:17:52:8 1168 -383.35234 405.7 387.5