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This article appeared in a journal published by Elsevier. The attached
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Author's personal copy

Computational and Theoretical Chemistry 979 (2012) 1–9

Contents lists available at SciVerse ScienceDirect

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

Isomerization energies of tetrahedranes to 1,3-cyclobutadienes: A challenge
for theoretical methods
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 4 September 2011
Received in revised form 15 October 2011
Accepted 15 October 2011
Available online 25 October 2011
Keywords:
Tetrahedranes
1,3-Cylobutadienes
Isomerization energies
Theoretical methods

a b s t r a c t
The gas phase (298.15 K, 1 atm) isomerization energies (DisomE(g)) of various tetra-substituted (hydro,
chloro, bromo, methyl, ethynyl, cyano, tert-butyl, and tetrakis(trimethylsilyl)) tetrahedranes to their
corresponding 1,3-cyclobutadienes were investigated with a broad range of model chemistries (Hartree–Fock, density functional, Moller–Plesset perturbation, composite, coupled cluster, and quadratic
configuration interaction methods) and Pople-/Ahlrichs-/Dunning-type basis sets. Substantial model
chemistry dependent DisomE(g) variability was found for all tetrahedrane/1,3-cyclobutadiene derivatives.
Basis set influences on DisomE(g) variability were modest and less influential than the choice of model
chemistry. Several density functionals previously found to provide excellent DisomE(g) prediction performance for a broad range of small and large organic compounds demonstrated poor capability when
applied to the tetrahedrane/1,3-cyclobutadiene isomerizations.
Ó 2011 Elsevier B.V. All rights reserved.

Theoretical treatments of isomerization energies (DisomE) for organic compounds have come under scrutiny since the discovery
that commonly used density functional theory (DFT) methods do
not accurately describe the thermodynamic properties of many
important intramolecular rearrangements [1–14]. While the current focus of DisomE benchmarking efforts is the extension to large
organic compounds (e.g., the ISOL database developed by Huenerbein et al. [2] and subsequently examined by other groups [6,14]),
there may still remain small organic isomerization systems for
which even the more modern density functionals are challenged.
For example, tetrahedrane (Fig. 1) and its derivatives have received
substantial theoretical and experimental attention over the past
several decades due to their interesting bonding arrangements,
high strain energies, and unusual gas phase acid–base behavior,
as well as their possible practical applications in high energy materials and nanotechnology [15–64]. While several substituted tetrahedrane derivatives have been synthesized [65–79], experimental
characterization of the parent system has not been reported. Concerted isomerizations of tetrahedranes to 1,3-cyclobutadienes are
symmetry forbidden, but homolytic cleavage of the carbon–carbon
single bonds in the tetrahedron frame to yield intermediate bicyclobutyl radicals are symmetry allowed [80].
In the current study, we examine the ability of a broad suite of
computational methods at various levels of theory (Hartree–Fock,
density functional, Moller–Plesset perturbation, composite,
⇑ Corresponding author. Tel.: +1 306 690 0573.
E-mail address: rayne.sierra@gmail.com (S. Rayne).
2210-271X/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved.
doi:10.1016/j.comptc.2011.10.017

coupled cluster, and quadratic configuration interaction) to predict
gas phase (298.15 K, 1 atm) isomerization energies (DisomE(g)) for
the intramolecular rearrangement of tetra-substituted tetrahedranes to the corresponding 1,3-cyclobutadienes (Fig. 2). Our efforts
focused on the tetrahydro (i.e., parent system), tetrachloro, tetrabromo, tetramethyl, tetraethynyl, tetracyano, tetra-tert-butyl, and
tetrakis(trimethylsilyl) derivatives as they encompass a range of
electron-withdrawing and releasing substituents with and without
steric congestion, impart minimal conformational complexity, and
two of the compounds (tetra-tert-butyltetrahedrane [66] and
tetrakis(trimethylsilyl)tetrahedrane [68]) have been successfully
synthesized. Both the tetrafluorotetrahedrane and tetrafluoro1,3-cyclobutadiene compounds yield converged geometries with
one or more imaginary frequencies using a number of theoretical
methods (particularly composite methods, which are employed
for reference DisomE(g) calculations). Thus, these molecules were
excluded from further consideration. All calculations employed
Gaussian 09 [81]. Molecular structures were visualized using Gabedit 2.2.12 [82] and Avogadro 1.01 (http://avogadro.openmolecules.net/). Except where noted otherwise, all compounds
converged absent imaginary frequencies.
Using single point energy calculations with the Ahlrichs-type
TZVP [83,84] basis set on B3LYP/6-31G(d) [85–96,96] optimized
geometries (frequency calculations at this level of theory were also
conducted to ensure an absence of imaginary frequencies), a wide
range of model chemistry dependent DisomE(g) were obtained
(Table 1). Gaussian-4 (G4) [97] calculations were completed on all
compounds except the tetra-tert-butyl and tetrakis(trimethylsilyl)

Author's personal copy

2

S. Rayne, K. Forest / Computational and Theoretical Chemistry 979 (2012) 1–9

Fig. 1. Three- and two-dimensional representations of tetrahedrane.

Fig. 2. General isomerization reaction for tetra-substituted tetrahedranes to the
corresponding 1,3-cyclobutadienes.

derivatives due to computational expense, and are taken as the reference DisomE(g) at near thermochemical accuracy [51,97–100] for
comparison. Because of the excellent agreement between the
B3LYP (mean signed deviation [MSD] = 1.1 kJ/mol; mean absolute
deviation [MAD] = 1.9 kJ/mol; and root mean squared deviation
[RMSD] = 2.2 kJ/mol), mPW3LYP (MSD = 1.4, MAD = 2.0, and
RMSD = 2.4 kJ/mol), and X3LYP (MSD = 0.7, MAD = 1.7, and
RMSD = 2.0 kJ/mol) DFT methods and the G4 reference DisomE(g)
data for the tetrahydro, tetrachloro, tetrabromo, tetramethyl,
tetraethynyl, and tetracyano derivatives, as well as the good agreement between the MP2 and G4 results for these compounds
(MSD = 3.0, MAD = 7.6, and RMSD = 8.7 kJ/mol), these DFT/MP2
methods are collectively taken as the reference DisomE(g) for the tetra-tert-butyltetrahedrane ( 1.2 to 2.0 kJ/mol) and tetrakis(trimethylsilyl)tetrahedrane (19.6 to 32.3 kJ/mol) isomerizations.
A significant number of prior theoretical DisomE(g) estimates
have been reported for the parent tetrahedrane/1,3-cyclobutadiene
system at various levels of theory, as well as a small number of
previous DisomE(g) estimates for the tetramethyl, tetracyano, tetra-tert-butyl and tetrakis(trimethylsilyl) systems (Table 2). Our
reference values are in excellent agreement with prior DFT/MP2/
composite method estimates for these DisomE(g). A tentative experimental DisomE(g) value for tetra-tert-butyltetrahedrane of
about +10 kJ/mol has been proposed in the literature [101], in good
agreement with our reference value range.
Large DisomE(g) ranges (DisomE(g),max DisomE(g),min) among the
105 model chemistries considered are evident for the tetrahydro
(187.4 kJ/mol), tetrachloro (109.9 kJ/mol), tetrabromo (606.6 kJ/
mol), tetramethyl (184.6 kJ/mol), tetraethynyl (175.5 kJ/mol), tetracyano (184.2 kJ/mol), tetra-tert-butyl (217.9 kJ/mol), and tetrakis(trimethylsilyl) (249.7 kJ/mol) reactions. The high DisomE(g)
range for the tetrabromo derivatives is due to the DisomE(g) obtained using the PM3 (+355.5 kJ/mol) and PDDG (+348.5 kJ/mol)
semiempirical methods. Absent these two methods, the DisomE(g)
range among all other levels of theory for the tetrabromo derivatives is reduced to 117.3 kJ/mol, consistent with that obtained for
the tetrachloro counterpart. The source of the PM3 and PDDG
method discrepancies for the tetrabromo derivative DisomE(g) versus other theoretical methods is not the use of B3LYP/6-31G(d)
geometries, as full optimization and frequency calculations at the
respective semiempirical levels of theory still yield anomalously
high DisomE(g) of + 231.5 (PM3) and + 245.4 (PDDG) kJ/mol,
respectively.
With the G4 data as reference, MPn (n = 3–4), coupled cluster
(CCD, CCSD, and CCSD(T)), and quadratic configuration interaction
(QCISD and QCISD(T)) methods tend to underestimate DisomE(g)

(i.e., overestimate the exothermicity) of the tetra-substituted tetrahedrane to 1,3-cyclobutadiene isomerizations, whereas the M05
and M06 series of Minnesota hybrid density functionals overestimate the DisomE by a significant margin. The poor performance of
the M062X functional is of note, with MSD, MAD, and RMSD of
54.8, 54.8, and 55.1 kJ/mol relative to the reference G4 data, as this
functional has been shown to perform well for other isomerization
reactions [3,5,6,10,14,102]. The unusual M062X results are not due
to the use of B3LYP/6-31G(d) geometries, as calculations at the
M062X/6-31G(d)//M062X/6-31G(d) level on the tetrahydro, tetrachloro, tetramethyl, tetraethynyl, and tetracyano systems yield
similarly large DisomE(g) deviations from the G4 data
(MSD = MAD = RMSD = 65.1 kJ/mol; note that the tetrabromotetrahedrane failed to converge at the M062X/6-31G(d)//M062X/631G(d) level, and is thus omitted from the statistical comparison),
and as discussed below, basis set size effects on DisomE(g) are
minimal.
The B2PLYPD (MSD = 3.1, MAD = 3.1, and RMSD = 3.5 kJ/mol)
and mPW2PLYPD (MSD = 2.1, MAD = 2.1, and RMSD = 2.7 kJ/
mol) functionals perform well for DisomE(g) estimates relative to
the G4 data, which – in light of the good performance of these
functionals for large organic compounds [2] (and the weak performance of the M062X functional herein) – probably moves these
double hybrid methods (which combine exact HF exchange with
an MP2-like correlation to a DFT calculation and contain an empirical dispersion correction) to the top status for general studies into
isomerization thermodynamics. The dispersion corrections (from
Schwabe and Grimme [103]) on these functionals, as expected,
have only a small effect on the DisomE(g) for the less sterically
hindered tetrahydro, tetrahalo, tetramethyl, tetraethynyl, and tetracyano derivatives (raising the DisomE(g) by about 1–2 kJ/mol),
but a modest effect on the DisomE(g) for the tetra-tert-butyltetrahedrane and tetrakis(trimethylsilyl)tetrahedrane derivatives (raising the DisomE(g) by about 5–7 kJ/mol, and improving the
agreement with the reference data).
Using a representative subset of the theoretical methods (HF,
B2PLYPD, B3LYP, B97D, CAM-B3LYP, CCD, CCSD, CCSD(T), LC-wPBE,
M062X, MP2, MP3, MP4(D), MP4(DQ), MP4(SDQ), MP4(SDTQ),
mPW2PLYPD, QCISD, QCISD(T), and wB97XD), DisomE(g) calculations were also conducted at the x/6-31G(d)//B3LYP/6-31G(d), x/
6-311++G(d,p)//B3LYP/6-31G(d) [88–94,96,104–108], and x/6311++G(3df,2pd)//B3LYP/6-31G(d)
[88–94,96,104–108]
(MPn
(n = 3–4), coupled cluster, and quadratic configuration interaction
calculations were omitted at this last level due to computational
expense) levels of theory to examine the effects of basis set size
and to compare Pople- and Ahlrichs-type basis sets (Table 3). We
find little basis set effect among the various isomerization reaction
energies, with intramethod basis set dependent DisomE(g) variability generally on the order of several kJ/mol up to about 10 kJ/
mol. Only modest differences between the Pople- and Ahlrichstype basis sets were observed. Calculations were also conducted
at the B3LYP/cc-pVDZ//B3LYP/6-31G(d) [109–112] and B3LYP/ccpVTZ//B3LYP/6-31G(d) [109–112] levels using Dunning’s correlation consistent double- and triple-zeta quality basis sets (Table
4). The DisomE(g) obtained with the Dunning-type basis sets were
in good agreement with the Pople- and Ahlrichs-type basis set results using this density functional: cc-pVDZ vs. TZVP [MSD = 3.3,
MAD = 3.3, and RMSD = 3.9 kJ/mol); cc-pVDZ vs. 6-31G(d)
[MSD = -3.7, MAD = 5.6, and RMSD = 5.9 kJ/mol); cc-pVDZ vs. 6311++G(d,p) [MSD = 0.9, MAD = 2.2, and RMSD = 2.8 kJ/mol); ccpVDZ vs. 6-311++G(3df,2pd) [MSD = -2.8, MAD = 4.4, and
RMSD = 5.7 kJ/mol); cc-pVTZ vs. TZVP [MSD = 3.7, MAD = 3.8, and
RMSD = 4.6 kJ/mol); cc-pVTZ vs. 6-31G(d) [MSD = -3.3, MAD = 5.3,
and RMSD = 6.6 kJ/mol); cc-pVTZ vs. 6-311++G(d,p) [MSD = 1.3,
MAD = 1.8, and RMSD = 2.5 kJ/mol); and cc-pVTZ vs. 6311++G(3df,2pd) [MSD = -2.3, MAD = 2.3, and RMSD = 2.6 kJ/mol).

Author's personal copy

3

S. Rayne, K. Forest / Computational and Theoretical Chemistry 979 (2012) 1–9

Table 1
Gas phase (298.15 K, 1 atm) isomerization energies (DisomE(g)) for various tetrasubstituted tetrahedranes to the corresponding 1,3-cyclobutadienes at the x/TZVP//B3LYP/631G(d) level of theory using a range of semiempirical, Hartree–Fock, DFT, composite, coupled cluster, and quadratic configuration interaction methods. Values are in kJ/mol.
Negative DisomE(g) signify the 1,3-cyclobutadiene structure is more thermodynamically stable than the tetrahedrane geometry.
Method

AM1
PM3
HFB
QCISD(T)
CCSD(T)
QCISD
MP4(SDTQ)
CCSD
PM6
BPL
MP4(D)
MP4(SDQ)
BVWN5
B98
CCD
BVWN
BMK
MP4(DQ)
MP3
TPSSLYP1W
HF
mPWLYP1W
B971
PDDG
mPWLYP
BV5LYP
BLYP
G1
mPWLYP1M
PBELYP1W
G3MP2
B2PLYP
G3MP2B3
G3
mPW2PLYP
G3B3
B2PLYLPD
mPW1LYP
mPW2PLYPD
B1LYP
tHCTHhyb
G4MP2
G2
MP2
G2MP2
G4
W1BD
CBS-Q//B3
B3LYP
mPW3LYP
X3LYP
CBS-APNO
BHandHLYP
MOHLYP2
CAM-B3LYP
wB97XD
VSXC
BP86
CBS-4M
BVP86
PBE1W
MOHLYP
B97D
BPKZB
BPBE
B3P86
BTPSS
B3PW91
mPW3PBE
M06HF
TPSSh

Ref.

[113–115]
[116,117]
[118]
[119–121]
[119,122–126]
[119]
[127,128]
[122–126]
[129]
[118,130]
[127]
[127]
[118,131]
[132,133]
[122,123]
[118,131]
[134]
[127]
[135,136]
[137]
[137]
[138]
[11,139–142]
[86,87]
[86,87,118,131]
[86,87,118]
[143]
[144]
[137]
[145]
[146]
[147]
[148]
[149]
[147]
[103,146]
[86,87,150]
[103,149]
[86,87,151,152]
[153]
[154]
[155]
[156–160]
[161]
[97]
[162–164]
[165–172]
[85–87]
[173]
[174]
[165–172]
[86,87,118,175–177]
[178]
[179]
[180]
[181]
[118,182]
[165–172]
[118,131,182]
[137]
[144]
[183]
[118,184]
[118,185,186]
[85,182]
[118,187]
[85,188–190]
[150,185,186]
[191]
[187]

Substituent
AH

ACl

ABr

ACH3

AC„CH

AC„CN

AC(CH3)3

ASi(CH3)3

192.9
165.2
146.0
138.8
138.6
131.6
131.1
130.8
128.1
128.0
128.0
127.5
127.3
127.2
126.9
125.1
124.2
124.0
123.2
120.6
119.3
118.5
118.4
118.2
117.2
117.1
117.1
116.6
115.7
115.7
113.4
112.7
112.3
111.4
111.1
110.8
110.5
109.7
109.5
109.5
109.2
109.0
108.9
108.6
107.9
107.3
107.0
106.5
105.8
105.5
105.1
104.2
102.4
98.0
93.4
93.4
93.0
86.5
86.5
85.8
84.9
82.8
81.4
78.9
78.4
78.3
77.1
76.1
74.5
74.2
73.9

273.0
232.0
276.8
264.7
264.2
255.9
262.9
254.6
238.2
262.7
256.5
254.7
262.1
261.2
252.2
260.4
245.4
250.5
252.8
256.7
241.8
259.1
254.1
219.8
258.6
257.3
257.3
243.2
256.2
256.8
246.2
251.3
245.4
243.4
249.7
243.0
249.2
247.4
248.1
246.3
246.6
244.9
242.0
251.0
242.5
244.0
c/e
n/cb
244.5
244.9
244.1
n/c
237.0
231.6
229.5
230.9
257.6
233.5
215.3
232.9
232.0
224.4
227.9
225.4
225.0
222.8
224.7
219.5
219.1
203.2
218.0

237.5
355.5
251.1
237.3
236.6
228.4
236.1
226.9
212.3
238.5
228.6
227.3
238.0
239.1
224.2
236.5
226.2
222.5
224.2
232.2
213.1
235.8
232.0
348.5
235.3
233.9
233.9
213.9
232.6
233.2
221.1
226.4
218.7
218.4
224.7
216.3
223.9
222.9
222.9
221.8
225.4
220.0
214.6
224.2
214.2
218.6
c/e
216.5
220.4
220.8
220.0
n/c
211.5
204.6
204.3
206.2
241.0
211.5
192.7
210.9
209.3
199.7
203.4
202.8
202.6
200.0
202.2
196.1
195.8
193.5
194.1

232.6
210.6
174.2
159.6
159.5
153.2
153.4
152.5
181.7
157.9
152.4
150.6
157.2
162.3
149.6
155.3
153.1
147.8
149.8
149.8
147.6
154.9
154.3
183.9
154.3
152.5
152.5
144.2
152.6
152.4
146.0
144.6
145.7
141.6
144.1
141.8
143.7
146.2
143.4
144.7
144.7
146.1
143.4
135.0
142.5
142.7
c/e
139.1
141.8
142.9
141.9
139.0
137.6
122.5
130.9
131.0
151.5
125.4
111.1
124.7
124.3
115.9
120.7
116.0
115.8
117.0
115.6
113.4
113.2
108.7
107.9

257.6
232.9
221.2
189.0
188.8
177.0
183.7
176.2
197.6
206.2
180.6
173.8
205.6
202.9
173.5
203.8
184.7
170.3
175.2
199.4
174.9
201.4
195.0
207.7
200.7
199.4
199.4
175.2
197.7
198.8
179.4
181.6
181.8
173.4
180.2
176.3
180.8
186.5
179.6
185.4
187.2
185.0
175.5
164.8
175.5
179.8
c/e
176.6
183.6
183.9
183.1
n/c
173.1
173.5
162.4
162.2
186.5
172.4
159.2
171.8
171.0
164.2
169.3
163.4
163.4
159.1
162.6
155.7
155.2
137.5
154.5

251.2
234.3
207.0
180.0
179.9
168.5
175.5
167.7
196.0
191.6
172.6
166.0
190.9
188.2
165.5
189.1
171.9
162.4
166.1
184.8
162.7
185.9
180.1
207.9
185.1
183.9
183.9
169.4
182.3
183.2
171.7
169.2
169.8
167.2
167.7
165.9
168.3
171.6
167.0
170.6
171.9
169.3
167.9
156.5
167.4
165.7
c/e
162.9
168.5
168.7
167.9
161.9
158.9
160.1
149.8
149.7
167.0
156.0
135.7
155.4
154.9
149.5
152.8
147.7
147.6
143.4
146.8
140.5
139.9
124.6
139.5

117.9
115.7
24.0
c/ea
c/e
c/e
c/e
c/e
79.5
13.2
c/e
c/e
12.2
21.4
c/e
11.3
21.5
c/e
c/e
18.4
26.9
18.6
14.4
84.0
19.2
17.7
17.7
c/e
15.9
11.7
c/e
7.5
c/e
c/e
5.1
c/e
14.1
3.6
9.9
2.4
8.7
c/e
c/e
1.7
c/e
c/e
c/e
c/e
1.3
2.0
1.2
c/e
11.1
58.0
10.9
10.7
7.2
2.1
48.6
3.1
11.7
41.5
6.9
17.1
15.1
16.5
17.2
23.9
24.3
26.4
22.7

116.4
120.2
2.7
c/e
c/e
c/e
c/e
c/e
62.1
11.8
c/e
c/e
12.7
1.2
c/e
14.1
18.5
c/e
c/e
14.5
34.8
5.2
4.5
121.0
4.6
7.5
7.5
c/e
7.4
8.1
c/e
18.2
c/e
c/e
19.0
c/e
10.8
17.6
13.6
20.0
14.4
c/e
c/e
32.3
c/e
c/e
c/e
c/e
21.7
19.6
21.0
c/e
30.2
77.4
30.7
20.3
61.7
30.4
91.0
31.4
35.0
66.1
29.2
46.9
46.1
43.0
47.3
51.5
51.0
36.4
59.2

(continued on next page)

Author's personal copy

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S. Rayne, K. Forest / Computational and Theoretical Chemistry 979 (2012) 1–9

Table 1 (continued)
Method

Ref.

BKCIS
mPW1PW91
O3LYP
OLYP
mPW1PBE
TPSS1KCIS
mPW1KCIS
B972
HSE03
HSE1PBE
HSE06
HCTH/147
wB97X
PBE0
M052X
PBEh1PBE
HFS
HCTH/93
tHCTH
BHandH
mPWKCIS1K
B1B95
mPW1B95
XAlpha
mPWB1K
M062X
M06
LC-wPBE
wB97
HCTH/407
M06L
OPBE
OTPSS
M05

[118,192–195]
[150,188–190]
[86,87,196]
[86,87,197,198]
[150,185,186]
[199]
[200]
[201]
[202–208]
[202–208]
[202–208]
[138,209,210]
[211]
[185,186,212]
[213]
[214]
[175–177]
[138,209,210]
[153]
[86,87,131,175–177]
[200]
[151]
[150,151]
[175–177]
[173]
[102]
[102]
[215–218]
[211]
[138,209,210]
[102]
[185,186,197,198]
[187,197,198]
[219]

Substituent
AH

a
b

72.5
72.2
71.0
70.4
70.0
67.7
67.1
66.3
65.5
65.4
65.4
65.3
65.3
65.1
65.1
64.2
64.0
63.9
62.8
60.8
58.0
55.9
55.1
52.4
50.7
47.2
42.4
41.4
39.9
38.0
33.4
31.5
30.2
5.5

ACl

ABr

ACH3

AC„CH

AC„CN

AC(CH3)3

ASi(CH3)3

220.9
216.0
214.5
215.4
214.2
212.7
214.6
211.1
211.6
211.7
211.7
214.1
204.5
211.0
210.9
210.2
222.4
210.8
211.9
208.9
202.7
200.9
200.7
213.3
195.0
195.2
199.3
178.9
178.4
191.9
195.6
183.0
182.7
166.9

198.3
192.3
190.0
191.2
190.6
188.5
191.3
187.0
188.2
188.3
188.3
190.9
179.5
187.5
190.2
186.6
201.4
187.1
188.6
185.7
178.1
177.1
176.8
193.1
170.6
172.5
168.0
152.7
153.8
167.9
164.4
159.6
159.2
133.8

111.9
110.4
106.4
105.2
108.4
103.0
107.9
103.3
105.4
105.6
105.6
103.4
104.7
105.1
106.3
104.3
115.5
99.0
99.9
107.2
98.3
93.9
94.3
104.7
89.7
89.2
90.1
79.8
78.6
78.7
79.4
68.7
68.5
48.0

158.5
151.4
152.0
154.4
149.4
148.2
150.2
146.1
146.7
146.8
146.8
151.4
130.3
145.6
141.1
144.7
157.1
147.7
149.2
140.1
134.8
133.1
132.5
147.4
125.2
119.3
118.9
103.1
100.4
126.6
116.8
118.7
117.9
82.1

142.4
136.3
137.2
139.3
134.3
133.1
134.5
130.7
130.9
131.0
131.0
134.9
118.5
130.2
126.0
129.2
139.1
131.9
132.5
124.0
120.0
118.5
117.9
129.0
111.1
105.8
103.0
93.5
89.6
109.8
100.7
103.1
102.3
67.0

24.8
27.9
50.5
52.5
30.0
32.5
33.6
41.8
31.9
31.8
31.9
46.7
34.9
33.8
34.7
33.2
8.7
55.1
43.4
27.6
49.9
38.8
39.5
19.0
47.2
45.0
52.3
62.3
56.3
87.4
56.1
88.2
89.9
100.0

51.1
54.9
75.0
78.0
57.4
64.6
57.2
65.7
57.3
56.8
56.9
67.7
45.0
57.9
51.3
58.1
27.4
78.1
72.4
46.7
71.5
66.1
65.2
40.0
72.1
63.9
61.6
82.3
62.0
101.2
81.6
118.0
119.1
128.7

Not completed due to computational expense.
Failed to converge.

Table 2
Prior theoretical estimates for gas phase (298.15 K, 1 atm) isomerization energies (DisomE(g)) of various tetrasubstituted tetrahedranes to the corresponding 1,3-cyclobutadienes.
Values are in kJ/mol.
Derivative

DisomE(g)

Level of theory

Refs.

Tetrahydro

49.0
85.8
95.8
98.7
100.4
101.7 to 113.8
101.7
101.9
105.3
105.8
108.8
108.8
108.8
109.2
109.6
111.7
113.4
113.8
113.9
115.5
116.3
116.7
120.1
120.5
120.5
122.6
129.2
130.5
130.5

SVWN/6-311G(2d,2p)
MP2/CBSB3
MP2/6-311G⁄⁄
B3LYP/6-311G⁄⁄
MP2/6-31G(d0 )
HF/DFT
B3LYP/6-31G(d)
B3LYP/6-31G(d)
B3LYP/6-311 + G(d,p)//6-31G(d)
STO-3G
CCSD(T)/cc-pVTZ
CBS-Q
G2
B3LYP/6-311G(2d,2p)
DZP CISD//6-31G⁄ MP2
SCF/DZ + D
6-31G⁄ SCF//6-31G⁄ SCF
6-31G⁄//4-31G
6-31G⁄
DZP SCF//6-31G⁄ MP2
6-31G⁄ MP2//6-31G⁄ MP2
HF/6-31G(d0 )
BLYP/6-311G(2d,2p)
DZP CIDVD//6-31G⁄ MP2
CEPA/DZ + D
MP4SDQ/CBSB4
QCISD(T)/6-31G(d)//B3LYP/6-31G(d)
CCSD(T)/cc-pVDZ//B3LYP/6-311G⁄⁄
CCSD(T)/cc-pVDZ

[220]
[220]
[68]
[221]
[220]
[35]
[68]
[222]
[222]
[223]
[221]
[220]
[26]
[220]
[224]
[15]
[224]
[225]
[223]
[224]
[224]
[220]
[220]
[224]
[15]
[220]
[222]
[221]
[221]

Author's personal copy

5

S. Rayne, K. Forest / Computational and Theoretical Chemistry 979 (2012) 1–9
Table 2 (continued)
Derivative

DisomE(g)

Level of theory
QCISD(T)/6-31+(d )
MRMP2//CASSCF
6-31G⁄
SCF/MB
4-31G
4-31G
SCF/DZ
CEPA/MB
CEPA/DZ
SCF-CI
SCF-MO
HF/DFT
B3LYP/6-31G(d)
B3LYP/6-31G⁄
MRMP2//CASSCF
B3LYP/6-311 + G(d,p)//6-31G(d)
HF/DFT
B3LYP/6-31G(d)
B3LYP/6-31G(d)
B3LYP/6-31G(d)

133.5
134.0
138.5
172.4
177.8
201.3
214.2
228.4
259.8
294.1
352.3
131.4 to 140.6
131.4
163.2
9.2
1.2
0.8 to +36.0
5.0
6.8
36.8

Tetramethyl
Tetracyano
Tetra-tert-butyl

Tetrakis(trimethylsilyl)

Refs.
0

[220]
[226]
[223]
[15]
[223]
[223]
[15]
[15]
[15]
[227]
[228,229]
[35]
[68]
[230]
[231]
[222]
[35]
[68]
[222]
[68]

Table 3
Gas phase (298.15 K, 1 atm) isomerization energies (DisomE(g)) for various tetrasubstituted tetrahedranes to the corresponding 1,3-cyclobutadienes at the x/y//B3LYP/6-31G(d)
level of theory using a range of model chemistries and Pople-type basis sets. Values are in kJ/mol and are presented within each cell for basis set identification as y = 6-31G(d)/6311++G(d,p)/6-311++G(3df,2pd). Negative DisomE(g) signify the 1,3-cyclobutadiene structure is more thermodynamically stable than the tetrahedrane geometry.
Method

QCISD(T)
CCSD(T)
QCISD
CCSD
MP4(SDTQ)
MP4(SDQ)
CCD
MP4(D)
MP4(DQ)
HF
MP3
B2PLYLPD
mPW2PLYLPD
B3LYP
MP2
wB97XD
CAM-B3LYP
B97D
M062X
LC-wPBE
a
b

Substituent
AH

ACl

ABr

ACH3

AC„CH

AC„CN

AC(CH3)3

ASi(CH3)3

129.2/ 129.2/
c/ea
128.9/ 129.0/
c/e
122.2/ 122.7/
c/e
121.1/ 121.9/
c/e
120.9/ 121.0/c/
e
117.4/ 118.5/
c/e
117.2/ 117.5/
c/e
116.9/ 118.6/
c/e
113.6/ 114.8/
c/e
113.3/ 118.2/
113.8
111.7/ 114.9/
c/e
104.8/ 106.7/
98.5
103.8/ 106.0/
98.0
101.9/ 105.1/
101.3
99.0/ 98.5/
80.6
91.2/ 93.8/
89.2
89.1/ 93.0/
89.2
76.3/ 77.9/
72.6
43.1/ 45.2/
40.3
37.9/ 40.8/
36.5

251.0/n/cb/c/e

239.8/ 223.1/
c/e
239.1/ 222.4/
c/e
231.7/ 215.1/
c/e
229.9/ 213.4/
c/e
238.4/ 221.2/
c/e
230.5/ 213.6/
c/e
226.8/ 210.1/
c/e
230.7/ 214.1/
c/e
225.2/ 208.3/
c/e
216.6/ 209.1/
204.1
226.7/ 211.2/
c/e
226.8/ 216.3/
211.9
225.8/ 215.4/
211.1
224.3/ 216.5/
213.6
225.3/ 208.3/
199.8
212.2/ 204.0/
201.1
207.7/ 200.8/
197.5
206.6/ 197.0/
192.8
178.0/ 168.8/
163.8
156.3/ 149.4/
145.1

147.8/ 149.1/
c/e
147.5/ 149.0/
c/e
142.0/ 143.2/
c/e
141.1/ 142.6/
c/e
141.5/ 142.4/
c/e
139.3/ 140.5/
c/e
137.7/ 139.3/
c/e
139.6/ 141.9/
c/e
135.7/ 137.4/
c/e
136.8/ 144.2/
140.5
136.6/ 140.6/
c/e
132.3/ 138.7/
133.8
131.9/ 138.5/
133.7
131.3/ 139.5/
136.2
121.0/ 124.0/
114.7
123.6/ 130.3/
126.9
120.0/ 128.9/
125.5
109.6/ 115.8/
111.3
78.8/ 85.3/
80.7
69.8/ 77.1/
73.8

184.7/ 180.7/
c/e
184.4/ 180.5/
c/e
172.5/ 169.3/
c/e
171.6/ 168.5/
c/e
178.6/ 175.1/
c/e
169.2/ 166.0/
c/e
168.4/ 165.5/
c/e
175.1/ 172.7/
c/e
165.1/ 162.2/
c/e
167.8/ 171.0/
167.8
169.6/ 168.2/
c/e
174.3/ 176.2/
174.3
172.9/ 175.1/
173.1
177.4/ 180.3/
177.7
157.9/ 157.0/
155.2
158.3/ 160.8/
158.2
155.5/ 159.4/
156.7
162.3/ 163.9/
159.8
111.5/ 115.4/
110.5
96.1/ 99.2/
96.3

178.2/ 175.3/
c/e
178.0/ 175.1/
c/e
166.2/ 163.7/
c/e
165.4/ 162.9/
c/e
173.3/ 170.9/
c/e
163.6/ 161.1/
c/e
162.7/ 160.4/
c/e
169.9/ 168.1/
c/e
159.7/ 157.3/
c/e
155.6/ 159.3/
154.8
163.3/ 162.2/
c/e
163.6/ 165.7/
161.1
162.0/ 164.3/
159.8
163.2/ 166.4/
163.1
153.5/ 152.3/
144.0
146.1/ 148.9/
145.4
144.0/ 147.7/
144.5
145.8/ 148.4/
143.5
98.5/ 102.2/
96.6
86.6/ 90.3/
86.6

c/e

c/e

c/e

c/e

c/e

c/e

c/e

c/e

c/e

c/e

c/e

c/e

c/e

c/e

c/e

c/e

c/e

c/e

36.1/30.1/
33.8
c/e

45.2/40.9/
51.9
c/e

1.6/ 8.0/
5.3
2.5/ 4.2/
1.4
6.9/ 1.1/
3.0
19.9/16.2/c/
e
18.1/10.6/
14.1
19.5/11.5/
15.1
17.1/9.5/
14.7
53.6/49.7/
52.5
72.3/64.0/
67.1

22.8/19.3/
31.6
25.5/21.9/
33.9
31.0/26.1/
36.6
48.9/48.6/
c/e
28.8/22.7/
34.2
40.4/34.6/
45.2
39.5/35.7/
47.4
72.7/67.6/
79.5
91.6/83.9/
95.5

250.4/n/c/c/e
243.0/n/c/c/e
241.6/n/c/c/e
248.7/ 246.0/
c/e
241.6/ 239.2/
c/e
238.8/n/c/c/e
242.4/ 240.0/c/
e
237.0/ 234.5/
c/e
232.1/ 238.9/
234.0
238.9/ 237.4/
c/e
237.5/ 241.5/
237.5
236.5/ 240.8/
236.8
234.4/ 241.3/
237.9
236.3/ 233.8/
227.0
223.4/ 230.3/
227.1
219.0/ 226.8/
223.3
217.0/ 222.3/
217.1
184.1/ 191.4/
185.9
168.7/ 176.7/
172.1

Not completed due to computational expense.
Either the tetrahedrane or cyclobutadiene structure failed to converge.

Author's personal copy

6

S. Rayne, K. Forest / Computational and Theoretical Chemistry 979 (2012) 1–9

Table 4
Gas phase (298.15 K, 1 atm) isomerization energies (DisomE(g)) for various tetrasubstituted tetrahedranes to the corresponding 1,3-cyclobutadienes at the B3LYP/y//
B3LYP/6-31G(d) level of theory using the cc-pVDZ and cc-pVTZ Dunning-type basis
sets. Values are in kJ/mol. Negative DisomE(g) signify the 1,3-cyclobutadiene structure
is more thermodynamically stable than the tetrahedrane geometry.
Substituent

cc-pVDZ

cc-pVTZ

H
Cl
Br
CH3
C„CH
C„CN
C(CH3)3
Si(CH3)3

104.3
239.7
215.9
137.6
183.1
167.1
1.6
23.5

102.9
241.7
216.2
137.9
180.1
165.7
2.2
32.0

In conclusion, the isomerization reactions of tetrahedranes to
1,3-cyclobutadienes present a challenge to most theoretical methods. These systems represent a class of small organic molecule
rearrangements whose thermodynamics are poorly described by
many computational approaches. The choice of model chemistry
generally exerts a substantially larger influence on the tetrahedrane/1,3-cyclobutadiene DisomE(g) than does choice of basis set.
Future theoretical developments should incorporate tetrahedrane/1,3-cyclobutadiene rearrangements as part of the thermochemical benchmarking exercises.
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.

Appendix A. Supplementary material
Supplementary data associated with this article can be found, in
the online version, at doi:10.1016/j.comptc.2011.10.017.
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