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Author's personal copy

Computational and Theoretical Chemistry 983 (2012) 69–75

Contents lists available at SciVerse ScienceDirect

Computational and Theoretical Chemistry
journal homepage: www.elsevier.com/locate/comptc

Singlet–triplet excitation energies of naphthyl cations: High level composite
method calculations suggest a singlet ground state
Sierra Rayne a,⇑, Kaya Forest b
a

Chemologica Research, PO Box 74, 318 Rose Street, Mortlach, Saskatchewan, Canada S0H 3E0
Department of Environmental Engineering, Saskatchewan Institute of Applied Science and Technology, Palliser Campus, PO Box 1420, 600 6th Avenue NW, Moose Jaw,
Saskatchewan, Canada S6H 4R4

b

a r t i c l e

i n f o

Article history:
Received 8 September 2011
Received in revised form 1 January 2012
Accepted 1 January 2012
Available online 10 January 2012
Keywords:
Phenyl cation
Naphthyl cations
Ground state multiplicity
Singlet–triplet excitation energy
Comparative theoretical study

a b s t r a c t
Singlet–triplet excitation energies (ES–T) were calculated for the phenyl, 1-naphthyl, and 2-naphthyl cations using a broad range of model chemistries, including semiempirical, Hartree–Fock, density functional,
Moller–Plesset perturbation, composite, coupled cluster, and quadratic configuration interaction methods and various basis sets. Substantial model chemistry dependent ES–T results were obtained for all three
cations with correspondingly minimal basis set size effects. G4/G4MP2 composite method well-to-well
(and adiabatic) ES–T for the phenyl, 1-naphthyl, and 2-naphthyl cations are 101.9/102.3 (101.7/102.0),
20.4/18.8 (19.3/17.8), and 21.6/21.4 (20.8/20.7) kJ/mol, respectively. All composite methods predict a
substantially positive ES–T for the 1- and 2-naphthyl cations, and are in both quantitative and qualitative
disagreement with many other model chemistries (particularly density functionals such as B3LYP) in
estimating both the magnitude and sign of the singlet–triplet excitation energy for the 1- and 2-naphthyl
cations. Composite method approaches suggest both the 1- and 2-naphthyl cations are ground state singlets with sufficiently large ES–T such that the population of the corresponding triplet state should be negligible, and thereby non-observable, where experimental conditions operate under thermodynamic
control.
Ó 2012 Elsevier B.V. All rights reserved.

The mechanistic roles of aryl cations in important organic and
organometallic reactions, as well as fundamental interest in their
structure and energetics, has stimulated substantial experimental
and theoretical study [1–5]. Owing to experimental challenges,
there are limited data available for even the most basic member
of this class. Although the nature of the phenyl cation ground state
is established as a singlet, there appear to be only two widely
varying experimental singlet–triplet excitation energy (ES–T) measurements of +31 and +96 kJ/mol ([6,7] as cited in [8]). No quantitative experimental ES–T measurements are available for the 1- or
2-naphthyl cations, but recently published [9] qualitative spectroscopic evidence (infrared (IR) multiple photon dissociation spectroscopy using both 1- and 2-bromonaphthalene as precursors)
coupled with density functional theory (DFT; B3LYP/6-311++G
(d,p)) level IR spectrum simulations and ES–T calculations collectively suggest a triplet ground state (i.e., ES–T < 0) for one or both
of these cations. With the knowledge that many DFT methods
significantly underestimate the ES–T of polyaromatic systems
[10–14], we undertake herein a broad theoretical investigation
using a number of different model chemistries and basis sets with
the goal of determining the true nature of the naphthyl cation
⇑ Corresponding author. Tel.: +1 306 690 0573.
E-mail address: rayne.sierra@gmail.com (S. Rayne).
2210-271X/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved.
doi:10.1016/j.comptc.2012.01.005

ground states and the magnitude of their singlet–triplet excitation
energies.
Adiabatic singlet–triplet excitation energy (AES–T) calculations
at 298.15 K and 1 atm used Gaussian 09 [15] for the phenyl,
1-naphthyl, and 2-naphthyl cations (Fig. 1) at the B3LYP/6311++G(d,p), B3LYP/TZVP, CBS-4M, CBS-Q//B3, CBS-APNO, G1, G2,
G2MP2, G3, G3MP2, G3B3, G3MP2, G3MP2B3, G4, and G4MP2 levels of theory (Table 1). Molecular structures were visualized using
Gabedit 2.2.12 [16] and Avogadro 1.01 (http://avogadro.openmolecules.net/). The CBS-APNO calculations for the singlet and triplet
forms of all compounds failed to converge, as did the triplet form
for the 1-naphthyl cation at the G1 and G2 levels of theory. The
G4 and G4MP2 level methods are in excellent agreement
that the AES–T for the phenyl cation is about 102 kJ/mol, whereas
the B3LYP/6-311++G(d,p) and B3LYP/TZVP methods both predict
significantly lower AES–T of 84 kJ/mol.
A similar difference is found between the composite method
and B3LYP calculations for the 1- and 2-naphthyl cations, with
the exception that not only are the composite method and B3LYP
results in quantitative disagreement, they are also in qualitative
disagreement. All composite methods predict a substantially positive singlet–triplet energy gap for the 1- and 2-naphthyl cations
with a likely AES–T (based on the G4MP2 and G4 calculations)
between +18 and +21 kJ/mol. Consequently, while lower level

Author's personal copy

70

S. Rayne, K. Forest / Computational and Theoretical Chemistry 983 (2012) 69–75

Fig. 1. Structures of the phenyl (1), 1-naphthyl (2), and 2-naphthyl (3) cations.

Table 1

Adiabatic singlet–triplet excitation energies (AES–T) for the phenyl, 1-naphthyl, and 2-naphthyl cations and spin-conserved isomerization enthalpies (Disom;sc HðgÞ ) between the
1
+
1
+
3
+
3
+
singlet ( 1-Na ? 2-Na ) and triplet ( 1-Na ? 2-Na ) 1- and 2-naphthyl cations at 298.15 K and 1 atm using various Complete Basis Set (CBS) and Gaussian-n (Gn) composite
methods as well as the B3LYP/6-311++G(d,p) and B3LYP/TZVP density functional levels of theory. Values are in kJ/mol.
Level of theory

G1
G2MP2
G2
CBS-Q//B3
G3MP2B3
G3MP2
G3B3
G4MP2
G3
G4
CBS-4M
B3LYP/6-311++G(d,p)
B3LYP/TZVP
a

Refs.

[48]
[47]
[46]
[28–35]
[36]
[45]
[36]
[37]
[44]
[38]
[28–35]
[39,40]
[39–43]



AES–T

Disom;sc HðgÞ

Phenyl

1-Naphthyl

2-Naphthyl

1

113.0
110.7
110.1
106.7
103.6
103.2
102.6
102.0
101.9
101.7
94.9
84.3
84.0

ea
32.9
e
21.4
25.8
26.2
24.1
17.8
23.7
19.3
4.6
1.6
2.6

42.0
39.5
38.2
22.8
27.8
30.4
24.5
20.7
27.1
20.8
6.7
1.1
3.7

1.3
1.8
2.0
4.2
3.9
3.3
4.7
3.0
3.9
3.8
4.6
5.0
6.3

+

1-Na ? 12-Na+

3

1-Na+ ? 32-Na+

e
8.4
e
5.6
5.9
7.4
5.1
5.9
7.4
5.3
6.7
5.5
5.2

Triplet state calculation failed to converge.

B3LYP calculations predict that the 1- and 2-naphthyl cations are
triplet ground states (potentially isoenergetic with the corresponding singlet states), the composite methods clearly predict singlet
ground states with negligible populations of the triplet state due
to large, and positive, AES–T. Spin-conserved isomerization enthal
pies (Disom;sc HðgÞ ) between the singlet (11-Na+ ? 12-Na+) and triplet
(31-Na+ ? 32-Na+) 1- and 2-naphthyl cations were also calculated.

The Disom;sc HðgÞ display little dependence on level of theory, ranging
from 1.3 to 6.3 kJ/mol (11-Na+ ? 12-Na+) and 5.1 to 8.4 kJ/mol (31Na+ ? 32-Na+), suggesting the isomers for each of the singlet and
triplet states are effectively isoenergetic within the expected accuracy of the calculations (i.e., ±4 to 8 kJ/mol), although there appears
to be a modest thermodynamic preference for the respective 1naphthyl isomers.
This discrepancy between high-level composite results and the
DFT-B3LYP AES–T values, and the implications therein for our theoretical understandings of these systems and subsequent interpretations of experimental data, led us to examine the well-to-well
singlet–triplet excitation energies (WWES–T) of these three aryl
cations using a broad range of model chemistries, including calculations with semiempirical, Hartree–Fock (HF), density functional,
Moller–Plesset perturbation, composite, coupled cluster, and quadratic configuration interaction methods at the x/TZVP//B3LYP/
TZVP level of theory (Table 2; semiempirical calculations are at
the x//B3LYP/TZVP level of theory). Analogous to the variation in
model chemistry dependent WWES–T we found for the [n]acenes
and their [4 2] rectangular graphene nanoribbon counterparts
[10,11], similarly wide ranges of WWES–T are observed for the phenyl ( 40.3 [HF] to +113.3 [MP2] kJ/mol), 1-naphthyl ( 113.3 [HF]
to +57.3 [MP2] kJ/mol), and 2-naphthyl ( 115.3 [HF] to +91.3
[MP2] kJ/mol) cations. All composite methods predict a substantially positive WWES–T for the 1- and 2-naphthyl cations, with
likely WWES–T (based on the G4MP2 and G4 calculations) of about

19 to 22 kJ/mol, compared to a G4/G4MP2 estimated phenyl cation
WWES–T of about 102 kJ/mol. The majority of DFT methods agree
with the composite approaches (and the AES–T trends) regarding

Disom;sc HðgÞ , suggesting the 1- and 2-naphthyl cations are approximately isoenergetic with a probable small thermodynamic preference for the respective singlet and triplet 1-naphthyl cations. Of

note are the unusually high Disom;sc HðgÞ predictions for the
3
+
3
+
1-Na ? 2-Na isomerization (on the order of 20–30 kJ/mol) predicted by the MPn methods, compared to the range of about 5–
10 kJ/mol estimated by the composite approaches and the semiempirical, HF, and DFT methods.
The basis set size effects on WWES–T and AES–T estimates for
these molecules appear to be minimal compared to the model
chemistry dependence. WWES–T were calculated using various Pople- (6-311++G(d,p) and 6-311++G(3df,2pd)), Dunning (AUG-ccpVDZ, cc-pVTZ, AUG-cc-pVTZ, and cc-pVQZ), and Ahlrichs (TZVP
and QZVP) type basis sets at the B3LYP/y//B3LYP/TZVP level of theory (Table 3). In all cases, increasing the basis set size (e.g., 6311++G(d,p) ? 6-311++G(3df,2pd), cc-pVTZ ? cc-pVQZ, AUG-ccpVDZ ? AUG-cc-pVTZ, TZVP ? QZVP) increases the WWES–T, but
the total WWES–T range among all basis sets is <8 kJ/mol for all

compounds. The basis set dependence on Disom;sc EðgÞ for the 1and 2-naphthyl cations is negligible (<3 kJ/mol).
A number of ES–T calculations for the phenyl cation have been
published since the early 1970s (Table 4), with estimates ranging
widely between 81.2 and +610.9 kJ/mol. More recent DFT and
higher level calculations have converged on an ES–T range between
about 70 (DFT) and 110 (composite methods) kJ/mol. Our G4 AES–T
of 101.7 kJ/mol is in excellent agreement with the prior G2
(B3LYP, MP2, RCC) ‘‘best estimate’’ of 103.0 kJ/mol by Nicolaides
et al. [8]. With the exception of a single coupled cluster calculation
(CCSD(T)/6-311G⁄⁄//B3LYP/6-31G⁄) on the 1-naphthyl cation
(yielding an ES–T of 13.5 kJ/mol [17]), to the best of our knowledge

Author's personal copy

71

S. Rayne, K. Forest / Computational and Theoretical Chemistry 983 (2012) 69–75

Table 2

Well-to-well singlet–triplet excitation energies (WWES–T) for the phenyl, 1-naphthyl, and 2-naphthyl cations and spin-conserved isomerization energies (Disom;sc EðgÞ ) between the
singlet (11-Na+ ? 12-Na+) and triplet (31-Na+ ? 32-Na+) 1- and 2-naphthyl cations at 298.15 K and 1 atm using various semiempirical, Hartree–Fock, density functional, Moller–
Plesset perturbation, composite, coupled cluster, and quadratic configuration interaction methods at the x/TZVP//B3LYP/TZVP level of theory (semiempirical calculations are at
the x//B3LYP/TZVP level of theory). Values are in kJ/mol.
Level of theory

Refs.

Phenyl
MP2
G1
G2MP2
G2
CBS-Q//B3
BKCIS
G3MP2B3
BPKZB
G3B3
G3MP2
G4MP2
G4
MP4(SDTQ)
G3
BP86
PBE1W
OTPSS
BTPSS
mPWLYP
MOHLYP
PBELYP1W
OPBE
OLYP
mPWLYP1W
BPBE
BV5LYP
BLYP
B1B95
BVP86
HFS
XAlpha
BPL
BVWN
mPW1B95
CBS-4M
HCTH/93
mPWLYP1M
mPW1KCIS
VSXC
HCTH/147
BVWN5
B2PLYP
B2PLYPD
B972
BMK
O3LYP
M06HF
B971
HCTH/407
M06L
B97D
QCISD(T)
CCSD(T)
tHCTHhyb
mPW2PLYPD
mPW2PLYP
B3P86
M06
M052X
B98
mPWB1K
TPSS1KCIS
M062X
B3LYP
tHCTH
mPW3PBE
TPSSLYP1W
mPW3LYP
X3LYP

[49–53]
[48]
[47]
[46]
[28–35]
[54–58]
[36]
[54,59]
[36]
[45]
[37]
[38]
[60,61]
[44]
[54,62]
[63]
[64–66]
[54,66]
[40,41]
[67]
[63]
[64,65,68,69]
[40,41,64,65]
[63]
[54,68,69]
[40,41,54,70]
[40,41,54]
[71]
[54,62,70]
[72–74]
[72–74]
[54,75]
[54,70]
[71,76]
[28–35]
[77–79]
[67]
[80]
[81]
[77–79]
[54,70]
[82]
[82,83]
[84]
[85]
[40,41,86]
[87]
[77]
[77–79]
[88]
[89]
[90–92]
[90,93–97]
[98]
[83,99]
[99]
[39,62]
[88]
[100]
[101,102]
[103]
[104]
[88]
[39–41]
[98]
[68,69,76]
[63]
[103]
[105]



WWES–T

113.3
112.3
110.0
109.4
107.0
106.2
104.0
103.5
103.0
102.5
102.3
101.9
101.6
101.2
100.5
99.7
99.0
98.4
98.3
98.0
97.9
97.8
97.5
97.4
97.3
97.1
97.1
96.1
95.9
95.4
95.2
94.5
94.5
94.4
94.2
93.8
93.8
93.7
93.4
91.4
89.9
89.8
89.7
89.5
89.4
88.9
87.9
87.7
86.6
86.3
86.3
86.2
85.7
85.7
85.2
85.2
84.9
84.6
84.2
83.7
83.4
83.1
82.8
82.8
82.6
82.2
82.0
82.0
81.7

Disom;sc EðgÞ
1-Naphthyl
57.3
ea
33.1
e
22.6
16.3
27.1
14.2
25.4
26.5
18.8
20.4
38.2
24.0
10.9
10.0
12.4
10.0
7.8
11.5
7.8
11.3
9.4
7.3
9.0
7.4
7.4
8.2
7.0
6.4
5.0
7.0
6.8
6.3
4.7
6.8
3.9
4.8
1.0
3.8
3.2
4.5
4.4
1.4
5.9
1.5
17.6
0.1
0.4
1.5
0.3
7.8
7.5
1.5
0.1
0.0
3.3
1.0
1.7
3.6
3.1
3.0
5.6
5.5
2.8
5.1
4.3
6.7
6.8

2-Naphthyl
91.3
42.6
40.0
38.7
23.5
18.2
28.4
15.9
25.2
30.9
21.4
21.6
65.7
27.7
13.1
12.4
13.6
11.8
10.9
13.7
10.9
12.6
11.7
10.4
10.8
10.3
10.3
9.4
9.4
10.8
9.3
9.4
9.2
7.6
7.1
9.2
6.8
6.5
3.6
6.9
5.8
9.4
9.4
3.0
5.5
3.4
19.3
1.7
3.8
0.8
3.1
20.4
20.5
0.9
4.6
4.6
1.7
1.9
2.5
1.6
1.9
1.7
7.4
3.5
0.3
3.5
1.6
4.5
4.7

1

1-Na+ ? 12-Na+

3

1-Na+ ? 32-Na+

2.5
0.9
1.4
1.6
4.7
4.8
4.5
5.1
5.3
2.9
3.2
4.0
3.2
3.5
4.2
3.9
6.9
5.2
2.8
5.0
2.9
6.8
5.1
3.0
5.0
3.3
3.3
5.9
4.2
2.9
3.3
4.3
4.4
5.6
4.3
5.3
3.1
5.0
0.7
4.2
4.3
1.7
0.9
5.5
7.9
5.4
7.5
4.8
4.5
7.1
2.2
4.5
4.4
4.6
1.3
1.9
5.0
5.7
5.9
4.8
6.0
5.7
6.6
4.4
4.7
5.2
4.0
4.0
4.2

31.4
e
8.4
e
5.6
6.7
5.8
6.7
5.0
7.3
5.8
5.2
24.3
7.3
6.4
6.3
8.1
6.9
5.9
7.3
6.0
8.0
7.3
6.0
6.8
6.2
6.2
7.1
6.6
7.2
7.5
6.8
6.8
6.9
6.7
7.7
6.0
6.7
3.3
7.3
7.0
6.6
5.8
7.0
7.4
7.4
9.2
6.6
7.9
6.4
5.6
8.2
8.6
7.0
6.0
6.5
6.7
6.6
6.7
6.8
7.2
7.1
8.5
6.4
7.7
6.9
6.6
6.2
6.3
(continued on next page)

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S. Rayne, K. Forest / Computational and Theoretical Chemistry 983 (2012) 69–75

Table 2 (continued)

a

Level of theory

Refs.

M05
B3PW91
wB97XD
MP4(D)
PBE0
BHandH
TPSSh
CAM-B3LYP
wB97
HSE1PBE
HSE06
mPW1LYP
PBEh1PBE
HSE03
wB97X
B1LYP
mPW1PBE
mPW1PW91
MP4(SDQ)
CCD
mPWKCIS1K
QCISD
MP3
MP4(DQ)
CCSD
LC-wPBE
MOHLYP2
BHandHLYP
HFB
PM6
AM1
PDDG
PM3
HF

[106]
[39,107–109]
[110]
[60]
[68,69,111]
[40,41,70,72–74]
[66]
[112]
[113]
[114–120]
[114–120]
[40,41,76]
[121]
[114–120]
[113]
[40,41,71,122]
[68,69,76]
[76,107–109]
[60]
[93,94]
[80]
[90]
[123,124]
[60]
[93–97]
[125–128]
[129]
[40,41,54,72–74]
[54]
[130]
[131–133]
[134–138]
[139,140]



WWES–T

Disom;sc EðgÞ

Phenyl

1-Naphthyl

2-Naphthyl

1

3

81.5
81.0
80.1
79.7
77.8
77.4
77.2
77.2
76.7
76.7
76.7
76.5
76.4
75.9
75.7
75.6
75.4
74.9
72.5
72.3
71.0
70.6
69.9
69.2
69.0
67.6
60.5
55.1
49.9
45.5
0.5
11.6
11.7
40.3

0.4
5.8
3.6
21.6
9.2
13.1
7.7
8.7
3.2
10.4
10.4
11.4
10.4
11.0
5.8
11.8
10.9
11.3
5.2
11.4
14.9
4.8
7.1
8.0
6.6
11.6
17.4
29.8
27.9
14.3
70.6
87.0
83.4
113.3

1.6
4.3
2.3
49.6
7.6
11.0
6.3
7.4
2.6
8.7
8.7
9.3
8.8
9.4
4.6
9.8
9.4
9.8
24.7
34.2
13.7
6.1
33.6
30.4
3.5
11.8
14.2
28.6
23.2
15.1
68.7
74.6
72.9
115.3

1-Na+ ? 12-Na+

8.2
5.5
5.3
3.5
5.2
4.0
5.9
5.0
5.6
5.0
5.0
4.1
5.2
5.1
5.5
4.5
5.6
5.5
1.3
1.5
5.9
2.1
3.6
1.5
1.6
7.1
5.9
5.3
3.8
8.7
5.7
9.4
5.8
7.3

1-Na+ ? 32-Na+

6.9
7.1
6.6
24.5
6.8
6.1
7.3
6.3
6.2
6.7
6.7
6.2
6.8
6.8
6.7
6.4
7.0
7.0
18.2
21.4
7.1
8.8
22.8
20.9
8.5
7.0
9.1
6.6
8.6
7.8
7.7
2.9
4.7
5.3

Triplet state calculation failed to converge.

Table 3

Well-to-well singlet–triplet excitation energies (WWES–T) and spin-conserved isomerization energies (Disom;sc EðgÞ ) between the singlet (11-Na+ ? 12-Na+) and triplet (31-Na+ ? 32+
Na ) 1- and 2-naphthyl cations at 298.15 K and 1 atm for the phenyl, 1-naphthyl, and 2-naphthyl cations using various Pople–, Dunning, and Ahlrichs type basis sets at the B3LYP/
y//B3LYP/TZVP level of theory. Values are in kJ/mol.
Level of theory

cc-pVQZ
QZVP
AUG-cc-pVTZ
cc-pVTZ
6-311++G(3df,2pd)
TZVP
6-311++G(d,p)
AUG-cc-pVDZ



WWES–T

Disom;sc EðgÞ

Phenyl

1-Naphthyl

2-Naphthyl

1

3

86.7
86.6
86.6
86.5
86.1
82.8
82.4
79.5

0.3
0.4
0.3
0.6
0.9
5.5
5.6
7.7

0.8
0.9
0.8
1.1
1.1
3.5
4.0
5.7

6.4
6.4
6.4
6.5
6.1
4.4
4.7
3.7

5.9
5.9
6.0
6.0
5.9
6.4
6.3
5.8

no prior high level ES–T estimates have been provided for the 1- and
2- naphthyl cations. All prior semiempirical and DFT ES–T estimates
for these molecules suggested either highly (semiempirical) or
modestly (DFT) negative ES–T, in contrast to the substantially positive ES–T presented herein.
Support for the higher accuracy of composite method ES–T calculations is evident in the literature (see, e.g., Refs. [8,18–22]). Both
the CBS-Q//B3 [8] and G3MP2 [21] methods have been validated
against experimental data (and shown to be in excellent agreement), and we have validated herein the G4 method against the
same experimental data employed by Winter and Falvey [22].
Experimental ES–T of 37.7 [23], +238.5 [24], 9.6 [25], and
125.1 [26,27] kJ/mol are available for the parent carbene methylene, difluorocarbene, phenyl carbene, and the parent nitrenium
ion (NHþ
2 ), respectively. The corresponding AES–T/WWES–T at the

1-Na+ ? 12-Na+

1-Na+ ? 32-Na+

B3LYP/TZVP level of 51.5/ 53.4, 216.4/216.5, 25.6/ 23.8, and
142.6/ 140.5 kJ/mol underestimate the experimental values by
between 14 and 22 kJ/mol. In contrast, the G4 AES–T/WWES–T of
36.0/ 36.0, 235.5/235.3, 16.1/ 16.0, and 124.5/ 124.8 kJ/
mol, respectively, are in excellent agreement with the experimental data, with no systematic bias nor absolute deviations greater
than 6.5 kJ/mol.
In conclusion, high-level composite methods (as well as CCSD(T)
and QCISD(T) calculations) are in both quantitative and qualitative
disagreement with many other model chemistries (particularly
density functionals such as B3LYP) in estimating both the magnitude and sign of the singlet–triplet excitation energy for the 1and 2-naphthyl cations. Composite method approaches (including
at the most recent G4 and G4MP2 levels of theory) suggest both
the 1- and 2-naphthyl cations are ground state singlets with

Author's personal copy

S. Rayne, K. Forest / Computational and Theoretical Chemistry 983 (2012) 69–75
Table 4
Prior theoretical estimates in the literature of singlet–triplet excitation energies (ES–T)
for the phenyl, 1-naphthyl, and 2-naphthyl cations. Values are in kJ/mol.
System

Level of theory

ES–T

Refs.

Phenyl

INDO
INDO
EHT
MINDO/2
MINDO/3
G2(B3LYP, MP2, RCC)
MP2/6-31G⁄
G2(B3LYP, MP2, RCC) [Df HðgÞ approach]

610.9
337.7
171.5
142.3
115.5
110.0
108.9
105.0

[141]
[142]
[143]
[144]
[144]
[8]
[145]
[8]

CBS-Q//B3
G2(B3LYP, MP2, RCC) [best estimate]
G2(B3LYP, MP2, RCC) [corrected]
CCSD(T)/6-31 G⁄ + MP2/6-311G(2df,2p)
B3LYP/6-31G(d)
4-31G (corrected)
CNDO/S
CAS-MP2/6-311+G(3df,2p)
B3LYP/6-311+G⁄//B3LYP/6-311+G⁄
FOCI/CEP-31G
B3LYP/cc-pVDZ
B3LYP/6-31G⁄
CCSD(T)/cc-pVDZ//B3LYP/SV
CCSD(T)/MCSCF/cc-pVDZ
CCSD(T)/B3LYP/cc-pVDZ
B3LYP/SV//HF/SV
B3LYP/SV
MC SCF-4-31G//STO-3G
SCF/STO-3G/CI
MCSCF/cc-pVDZ
CASSCF(5,7)/6-31G⁄⁄
PM3
MC SCF-6-31G⁄//STO-3G
MC SCF-STO-3G//STO-3G
4-31G
SCF-3-21G//3-21G
SCF-4-31G//3-21G
SCF-6-31G//3-21G
HF/SV
STO-3G
SCF-STO-3G//STO-3G

104.3
103.0
99.0
94.5
89.1
84.1
83.9
83.0
82.0
79.1
79.1
78.4
78.1
77.8
76.6
68.5
67.4
66.1
58.9
33.9
29.5
25.5
20.5
5.0
31.5
44.4
46.4
49.0
55.2
76.2
81.2

[22]
[8]
[8]
[145]
[146]
[144]
[147]
[8]
[148]
[149]
[150]
[145]
[151]
[150]
[150]
[151]
[151]
[152]
[6]
[150]
[145]
[153]
[152]
[152]
[144]
[152]
[152]
[152]
[151]
[144]
[152]

1-Naphthyl

CCSD(T)/6-311G⁄⁄//B3LYP/6-31G⁄
B3LYP/6-311++G(d,p)
B3LYP/6-311+G⁄//B3LYP/6-311+G⁄
CCSD/6-311G⁄⁄//B3LYP/6-31G⁄
B3LYP/6-311++G(2d,2p)//B3LYP/6-311G(d,p)
B3LYP/6-31G⁄
PM3
INDO/S (CISD)
INDO/S (ROHF)

13.5
0.5
2.5
2.9
4.6
6.8
38.5
52.3
53.1

[17]
[9]
[148]
[17]
[154]
[17]
[153]
[155]
[155]

2-Naphthyl

B3LYP/6-311++G(d,p)
B3LYP/6-311++G(2d,2p)//B3LYP/6-311G(d,p)
B3LYP/6-311+G⁄//B3LYP/6-311+G⁄
PM3
INDO/S (ROHF)
INDO/S (CISD)

0.4
3.8
6.7
33.9
51.9
51.9

[9]
[154]
[148]
[153]
[155]
[155]



sufficiently large ES–T ( +20 kJ/mol) such that the population of the
corresponding triplet state should be negligible, and thereby nonobservable, where experimental conditions operate under thermodynamic control. Future studies of singlet–triplet gaps for organic,
inorganic, and organometallic compounds should include composite method calculations unless computationally prohibitive.

Acknowledgements
This work was made possible by the facilities of the Western
Canada Research Grid (WestGrid: Project 100185), the Shared
Hierarchical Academic Research Computing Network (SHARCNET:
Project sn4612), and Compute/Calcul Canada.

73

Appendix A. Supplementary material
Supplementary data associated with this article can be found, in
the online version, at doi:10.1016/j.comptc.2012.01.005.
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