Chemical Physics Letters 585 (2013) 37–41
Contents lists available at ScienceDirect
Chemical Physics Letters
journal homepage: www.elsevier.com/locate/cplett
Which isomeric form of formaldehyde dimer is the most
stable – a high-level coupled-cluster study
Grygoriy A. Dolgonos
Computational Centre of Chizevsky’s Regional Scientific Library, 24 V. Perspektyvna str., Kirovograd 25006, Ukraine
a r t i c l e
i n f o
Article history:
Received 24 July 2013
In final form 17 August 2013
Available online 23 August 2013
a b s t r a c t
Frozen-core and all-electron CCSD(T) calculations have been performed in order to derive accurate geometrical characteristics as well as dimerization energies of the two lowest-lying isomers of formaldehyde
dimer (H2CO)2: dimer I (Cs) and dimer II (C2h). Contrary to early MP2 calculations, it has been unambiguously determined on the basis of CCSD(T) complete-basis-set extrapolations that dimer I is the true global-minimum structure, which lies 0.3–0.4 kcal/mol lower in energy than the dimer II structure at 0 K.
The obtained equilibrium geometries and dimerization energies can serve as a benchmark for testing
the performance of other, less computationally demanding methods.
Ó 2013 Elsevier B.V. All rights reserved.
1. Introduction
Weak interactions in molecular systems are known to play a
significant role in stabilizing of many chemically and biologically
relevant systems [1–3]. In particular, C–H O interactions involving formyl hydrogen atoms have recently attracted much attention
due to their role in crystal packing [4], in stabilizing and designing
supramolecular systems [5,6], in molecular recognition [7] and
even in selectivity control of organic reactions [8]. The strength
of C–H O interactions typically lies midways between that of systems with strong hydrogen bonds and of systems stabilized by
nonbonding van der Waals interactions and is generally in the
range of 2.4–2.8 kcal/mol per one C–H O interaction involving
formyl hydrogen donor [9]. This strength is however sufficient to
perturb the equilibrium geometries of interacting monomers in
such a way that C–H bond lengths become shorter whereas carbonyl C@O bonds lengthen, which can easily be detected spectroscopically. This shortening of C–H bond lengths and,
consequently, a blue shift of corresponding C–H stretching vibrational frequency makes C–H O interactions completely different
from their conventional hydrogen-bonded (e.g., O–H O) counterparts [10,11] (although examples of blue-shifting bifurcated O–
H O hydrogen bonds are also known [12]). Nevertheless, these
interactions belong formally to the framework of hydrogen bonds
due to similar driving forces involved in their formation [10,13].
Formaldehyde dimers represent one of the simplest examples
which involve C–H O interactions. Theoretical investigations predict an existence of two lowest-energy isomers of (CH2O)2 [14–18].
The first isomer of Cs symmetry (hereafter referred to as: dimer I)
has a perpendicular arrangement of oppositely oriented CH2O
monomers leading to only one C–H O contact whereas the secE-mail address: dolgonos@gmail.com
0009-2614/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved.
http://dx.doi.org/10.1016/j.cplett.2013.08.073
ond isomer (hereafter called dimer II) is characterized by a completely planar arrangement of all atoms leading to C2h symmetry
and, consequently, to the appearance of two C–H O contacts (Figure 1). Only the first isomer has been detected experimentally by
means of microwave spectroscopy [19]. However, on the theoretical side it has not been unambiguously determined up to now
which one of these two isomers is energetically the most stable.
Leaving aside historically first but the least accurate Hartree–
Fock and semiempirical calculations, early MP2 results of Ford
and Glasser [14] indicated that dimer I should be the lowest-energy structure according to the uncorrected MP2/6-31++G⁄⁄ energies, but the stability order has reversed after including
corrections for the basis-set incompleteness (basis set superposition error or BSSE) and for the zero-point energy (ZPE). As pointed
out by Hermida–Ramón and Ríos [15], although the reported by
Ford and Glasser [14] dimerization energies were inconsistent with
their total MP2 energies, the stability trend remained the same if
the correct values of dimerization energies of both dimers were obtained – the dimer II was by approximately 0.1 kcal/mol more stable than the dimer I at 0 K. According to MP2/6-31++G (2d,2p)
results of Hermida–Ramón and Ríos [15], the BSSE-only corrected
value of dimerization energy of dimer I lies by 0.62 kcal/mol lower
in energy than that of dimer II. A similar dimerization energy difference of 0.66 kcal/mol in favor of dimer I has been recently reported by Holt et al. [16] on the basis of MP2/ANO-L calculations
(where ANO-L stands for the large (-L) version of generally contracted Atomic Natural Orbital (ANO) basis sets [20]). On the other
hand, single-point calculations at the coupled-cluster level of theory including single, double and quasiperturbative triple excitations (CCSD(T)) of Smith et al. [17] combined with the ZPE
corrections calculated at the MP2 level resulted in numerically
equal total energies of both dimers. In addition, ZPE-only corrected
dimerization energies obtained with MP2/6-311++G⁄⁄ led to only a
38
G.A. Dolgonos / Chemical Physics Letters 585 (2013) 37–41
H3 H
4
C2
O2
H1
H1
O1
C1
C1
H2
O1
H2
Dimer I (Cs)
limit using a scheme of Peterson et al. [33] that relies on the usage
of a mixed exponential/Gaussian formula:
O2
H4
C2
σ
ðX1Þ
EX ¼ ECBS þ be
H3
σ
Dimer II (C2h)
Figure 1. Schematic view of the two most stable structures of (CH2O)2. Atom
numbering follows that of Ford and Glasser [14].
slight stabilization of dimer I compared to dimer II (by 0.16 kcal/
mol) [21]. These findings clearly indicate an importance of ZPE correction on the resulting stability order of formaldehyde dimers
since most of electron-correlation methods typically yield dimer I
as the most stable isomer on the basis of respective uncorrected total energies [14–18].
Since these two dimers can serve as benchmark structures for
testing other, less computationally demanding approaches (i.e.,
for testing the performance of different DFT functionals) it is essential that the geometric and energetic properties of these systems
are very accurately determined. Recent attempts in this direction
have been made by Remya et al. [22] who assessed the accuracy
of many DFT functionals against reference CCSD/aug-cc-pVTZ
geometry and dimerization energy of the dimer II reported earlier
by Mackie and DiLabio [23]. The latter authors also investigated
the effects of basis set size and electron correlation at MP2, CCSD
and CCSD(T) levels on the dimerization energies of ten weakly
bound systems including the formaldehyde dimer II and proposed
a composite scheme to accurately calculate these energetic properties. Only very recently, Řezáč et al. [24] performed composite
CCSD(T) complete basis set (CBS) extrapolations to yield accurate
dimerization energy of dimer I (as a part of their set of 24 model
complexes) and estimated the effects of core-valence, relativistic
and higher-order excitations on its value. However, the very
important ZPE correction was not considered in their study [24].
Hence, one can conclude that the accurate data for both dimers
evaluated using the same high-level model chemistry are still missing in the literature. Therefore, the main aim of this Letter is not
only to report accurate geometries and CBS-extrapolated CCSD(T)
values of dimerization energies for these two dimers but also to
consider, at the highest possible level of theory, the effects of the
most significant ZPE and anharmonicity as well as core-valence
corrections on the resulting values.
2. Methodology and computational details
Geometries of formaldehyde dimers (dimer I and dimer II) and
formaldehyde molecule itself have been fully optimized at the frozen-core CCSD(T) level of theory [25–28] employing Dunning’s
augmented correlation-consistent polarized valence basis sets,
aug-cc-pVXZ (X = T, Q, 5). [29,30] To estimate the influence of
core-valence correlation effects, analogous geometry optimizations
have been also performed at the CCSD(T) level with all electrons
correlated (denoted hereafter as ae-CCSD(T)) but with nonaugmented, weighted core-valence basis sets, cc-pwCVXZ (X = T, Q,
5) for carbon and oxygen atoms [31]. The choice of this family of
basis sets is based on the fact that the ae-CCSD(T)/CBS extrapolated
equilibrium geometries of H2CO molecule are more accurate and
close to experimental values than those obtained after CCSD(T)/
CBS extrapolations using aug-cc-pVXZ basis sets (cf. Ref. [32]).
On the other hand, analogous ae-CCSD(T) calculations with the
use of aug-cc-pwCVXZ (X > 4) basis sets are still beyond the reach
of today’s computational resources.
In all cases, CCSD(T) total energies for the optimized structures
have been further extrapolated to the complete-basis-set (CBS)
2
þ ceðX1Þ ;
where EX and ECBS are the total energies for a given basis set (with its
cardinal number X defined as previously) and for the CBS, respectively; b and c are fitting parameters. This formula has been shown
by Feller et al. [34] to yield very accurate CBS atomization energies
of small molecules, especially, in the case of a small range of considered cardinal numbers X (i.e., up to 5). For a more detailed discussion on the performance of different high-quality ab initio
approaches to obtain accurate thermochemical and spectroscopic
properties of molecules the interested reader is referred to recent
reviews [35–37].
Dimerization energy DE of a given dimer at the CBS limit has
been defined in a standard way as ECBS ðdimerÞ 2 ECBS ðH2 COÞ.
Harmonic vibrational frequencies have been calculated with
CCSD(T)/aug-cc-pVQZ and with ae-CCSD(T)/cc-pwCVQZ model
chemistries for the respectively optimized geometries, from which
the corresponding zero-point energies (ZPEH) were obtained. The
ZPE correction to dimerization energy, DZPEH, has been calculated
then as ZPEH ðdimerÞ 2 ZPEH ðH2 COÞ. Since obtained this way harmonic ZPEs are generally larger than the real ones (and traditionally require a scaling factor for a given model chemistry to be
employed), an explicit calculation of anharmonicity corrections
to ZPEH has been performed instead based on the formula:
ZPE ¼ 0:5 ðZPEH þ ZPEF Þ þ v0 0:25 X
vii ;
where ZPEH and ZPEF represent harmonic and fundamental zeropoint energies, respectively, and v0 and vii are anharmonic constants [38,39]. Anharmonic corrections to ZPEH, Danharm have been
obtained as a difference ZPE-ZPEH at the frozen-core second-order
Møller–Plesset (MP2) [40] level of theory utilizing the aug-cc-pVTZ
basis set. Consequently, anharmonicity correction to dimerization
energy, DDanharm is defined as a difference Danharm (dimer) 2Danharm (H2CO).
As demonstrated by Feller et al. [32] for the case of formaldehyde molecule, anharmonicity corrections evaluated with MP2
are quite insensitive to the basis set size and agree within 0.01–
0.05 kcal/mol with those obtained using either CCSD(T) quartic
force fields [41] or with those based on variational vibrational
computations [42]. Therefore, the usage of MP2/aug-cc-pVTZ model chemistry for anharmonicity correction determination in this
work is well justified.
Finally, the corrected dimerization energies DEcorr of both dimers
have been obtained as a sum: DE + DZPEH + DDanharm + BSSE,
where the last (BSSE) term is applied only in the case of calculations
with finite basis sets and vanishes upon estimating the CBS extrapolated values.
Calculations of MP2/aug-cc-pVTZ anharmonic corrections have
been performed using the GAUSSIAN 09 suite of programs [43]
whereas all other calculations have been performed with the MOLPRO [44] software package.
3. Results and discussion
3.1. Equilibrium geometries
Tables 1 and 2 contain the equilibrium geometric parameters of
dimer I and dimer II, respectively, obtained with different MP2 and
coupled-cluster approaches. According to the present frozen-core
and all-electron CCSD(T) results with quintuple-zeta basis sets,
the C@O bond lengths in both dimers become longer than that in
the isolated monomer – by 0.003 and 0.004 Å for the dimer I and
dimer II, respectively. These findings are in agreement with
39
G.A. Dolgonos / Chemical Physics Letters 585 (2013) 37–41
Table 1
Geometric characteristics of optimized dimer I structure of (CH2O)2 obtained with electron-correlation methods.
a
b
c
Model chemistry/geometric
parameter
ae-CCSD(T)/ccpwCV5Za
CCSD(T)/aug-ccpV5Zb
Composite CCSD(T)/CBS
[24]
Earlier MP2 data
6-31++G⁄⁄
[14]
6-31++G (2d,2p)
[15]
6-311++G⁄⁄
[21]
r(C1O1)
r(C1H1)
r(C1H2)
a(H1C1O1)
a(H2C1O1)
a(H1C1H2)
r(C2O2)
r(C2H3)=r(C2H4)
a(H3C2O2)=a(H4C2O2)
a(H3C2H4)
r(H1 O2)
r(C2 O1)
1.207
1.099
1.099
121.3
121.1
117.6
1.207
1.098
121.8
116.4
2.391
2.718
1.210
1.101
1.100
121.3
121.1
117.6
1.210
1.100
121.8
116.4
2.380
2.708
1.211
1.102
1.101
121.3
121.1
117.6
1.211
1.101
121.8
116.4
2.383
2.709
1.226
1.096
1.096
121.3
121.1
117.5
1.226
1.096
121.8
116.4
2.434c
2.741
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
1.215
1.103
–
2.406
2.702
2.480
–
ae-CCSD(T)/cc-pwCV5Z equilibrium geometry of CH2O is characterized by r(CO) = 1.204 Å, r(CH) = 1.100 Å and by angle(HCO) = 121.7°.
CCSD(T)/aug-cc-pV5Z equilibrium geometry of CH2O is characterized by r(CO) = 1.207 Å, r(CH) = 1.102 Å and by angle(HCO) = 121.7°.
The original value of 2.831 Å reported by Ford and Glasser [14] is incorrect.
Table 2
Geometric characteristics of optimized dimer II structure of (CH2O)2 obtained with electron-correlation methods.
a
b
Model chemistry/geometric
parameter
ae-CCSD(T)/ccpwCV5Za
CCSD(T)/aug-ccpV5Zb
CCSD/aug-ccpVTZ [23]
r(C1O1) = r(C2O2)
r(C1H1) = r(C2H3)
r(C1H2) = r(C2H4)
a(H1C1H2) = a(H3C2H4)
a(H1C1O1) = a(H3C2O2)
a(H2C1O1) = a(H4C2O2)
r(O1 H4) = r(O2 H2)
1.208
1.100
1.098
117.5
121.0
121.4
2.465
1.211
1.102
1.099
117.6
121.0
121.4
2.461
1.208
1.101
1.098
117.4
121.1
121.4
2.512
Earlier MP2 data
6-31++G⁄⁄
[14]
6-31++G (2d,2p)
[15]
6-311++G⁄⁄/aug-cc-pVTZ /aug-ccpVQZ [21]
1.226
1.098
1.095
117.6
121.1
121.3
2.535
–
–
–
–
–
–
2.530
1.216/–/–
1.101/–/–
–
–
–
–
2.579/2.491/2.483
See also the footnote a to Table 1.
See also the footnote b to Table 1.
previously reported MP2 data [14,21]. One can also see in Tables 1
and 2 that the lowest value of the bond length is given normally by
the ae-CCSD(T) approach and the largest one – by MP2 with a
double-zeta 6-31++G⁄⁄ basis set. In the case of dimer II, the
ae-CCSD(T)/cc-pwCV5Z C@O bond length value fortuitously coincide with the CCSD/aug-cc-pVTZ one reported by Mackie and DiLabio [23].
Interestingly, the C–H bond lengths which involve H atoms not
participating in the formation of a C–H O contact in dimer I demonstrate a shortening of about 0.002 Å, which is slightly larger
(though by not more than 0.001 Å) than the bond length shortening observed for the C–H bond forming the C–H O contact. On the
contrary, the respective C–H bond lengths containing noninteracting with the other monomer H atoms in dimer II remain rather unchanged whereas the C–H bonds involved in the formation of C–
H O contacts become by 0.002–0.003 Å shorter than those of a
free CH2O molecule. Almost identical MP2 values corresponding
to the bond length shrinking in the latter case have been also reported earlier in the literature [14,21]. Typically, the smallest values of C–H bond lengths are obtained with the MP2/6-31++G⁄⁄
model chemistry and the largest ones – with either MP2/6311++G⁄⁄ (for dimer I) or with CCSD(T)/aug-cc-pV5Z (for dimer
II). One notices again in Table 2 that the corresponding bond length
values obtained with the ae-CCSD(T)/cc-pwCV5Z model chemistry
and with the CCSD/aug-cc-pVTZ one are in excellent agreement
with each other. On the other hand, the C@O and C–H bond distances for the dimer I (Table 1) obtained with the composite
CCSD(T)/CBS approach by Řezáč et al. [24] are typically by 0.001
Å larger than the CCSD(T)/aug-cc-pV5Z ones obtained in this work
and correspond roughly to the current CCSD(T)/aug-cc-pVQZ values (not shown in Table 1) .
The most sensitive parameters to the model chemistry
employed are the intermolecular O H and C O distances in both
dimers. As can be inferred from Tables 1 and 2, the MP2 usually
overestimates the values of O H distances – unless the basis set
of (at least) a quadruple-zeta quality has been utilized (as has been
investigated in detail for the dimer II by Kovács et al. [21]). All
CCSD(T) approaches generally agree within 0.011 Å with each
other – leading to ae-CCSD(T)/cc-pwCV5Z values which are slightly
larger than those obtained with the frozen-core CCSD(T). However,
the CCSD/aug-cc-pVTZ value [23] of the O H distances in dimer II
is by 0.05 Å larger than those predicted by CCSD(T) approaches employed in this work. Interestingly, the C O nonbonded distance in
dimer I calculated by Hermida-Ramón and Ríos using MP2/631++G (2d,2p) model chemistry [15] lies very close to the CCSD(T)
ones although the MP2 values with smaller, double-zeta quality
basis set of Ford and Glasser [14] are much larger. As in the case
of O H distances, an agreement within 0.01 Å for the C O distance type has been found for all considered CCSD(T) approaches.
HCO bond angles in dimer I for the perpendicularly oriented
monomer whose hydrogen atoms do not form the C–H O contacts have been found to be larger by only 0.1° compared to the
same angle in CH2O but these angles in the other monomer exhibit
a decrease by 0.6° and 0.4° for the angles containing C–H O noninteracting and interacting H atoms, respectively. In dimer II all
HCO bond angles lie in the same plane leading to only two distinct
HCO angle types and, according to both CCSD(T) approaches, the
respective decrease in their values equals to 0.7° and 0.3° for the
40
G.A. Dolgonos / Chemical Physics Letters 585 (2013) 37–41
Table 3
Dimerization energies (in kcal/mol) of the two lowest-lying formaldehyde dimers calculated with electron-correlation methods.
Model chemistry/energetic
characteristic
ae-CCSD(T)/
CBSa
CCSD(T)/
CBS
Composite CCSD(T)/
CBS [24]
Dimer I
DE
BSSE
DZPEH
DDanharm
DEcorr
4.43
0.00
1.51b
0.21c
3.13
4.48
0.00
1.52d
4.55, 4.47e
0.00
–
–
–
Dimer II
DE
BSSE
DZPEH
DDanharm
DEcorr
3.58
0.00
1.05b
0.16c
2.69
3.68
0.00
0.96d
3.17
2.88
–
–
–
–
–
CCSD/aug-ccpVTZ [23]
–
–
–
–
3.66f
0.36f
–
–
–
Earlier MP2 data
6-31++G⁄⁄
[14]
6-31++G
(2d,2p) [15]
6-311++G⁄⁄ / aug-cc-pVTZ / augcc-pVQZ [21]
4.40g
1.07
1.37
–
1.96
–
–
–
–
3.68h,i
2.53j/–/–
–
–
–
–
3.66g
0.78
0.85
–
2.03
–
–
–
–
3.06h,i
2.37j/2.92j/2.82j
0.75/0.41/0.19
Taken from MP2/6-31++G⁄⁄
–
1.62/2.51/2.63
a
Using core-valence cc-pwCVXZ (X = T, Q, 5) basis sets.
Calculated with ae-CCSD(T)/cc-pwCVQZ.
c
Calculated with MP2/aug-cc-pVTZ.
d
Calculated with CCSD(T)/aug-cc-pVQZ.
e
Including core-valence, relativistic and quadruple-excitation corrections.
f
For a detailed analysis of the influence of single-point MP2, CCSD and CCSD(T) calculations as well as aug-cc-pV(D,T,Q)Z basis sets on resulting dimerization energies see
Ref. [23].
g
Since the reported by Ford and Glasser [14] dimerization energies were in error, the recalculated values based on total MP2 energies from Table 2 of their paper [14] are
shown here.
h
BSSE-corrected value only (no DZPE reported).
i
Slightly smaller absolute BSSE-corrected values (3.35 and 2.69 kcal/mol for dimer I and dimer II, respectively) have been calculated with MP2/ANO-L by Holt et al. [16].
j
Corrected for ZPE (obtained with MP2/6-31++G⁄⁄) but not corrected for BSSE value.
b
angles not involving and involving hydrogen atoms of C–H O
contacts, respectively. The bond angle values obtained with the
considered electron-correlated methods generally agree with each
other within 0.2°.
3.2. Dimerization energies
Table 3 summarizes the uncorrected and corrected values of
dimerization energies obtained with different electron-correlation
methods. Uncorrected DE values extrapolated using ae-CCSD(T)
and CCSD(T) methods agree within 0.05 and 0.1 kcal/mol for dimer
I and dimer II, respectively. This energy difference cannot be attributed to the core-valence contribution alone since the basis sets
used for respective geometry optimizations are different. The
core-valence contribution to DE is supposed to be much smaller
(i.e., 0.004 kcal/mol for dimer I [24]). Indeed, if one performs
geometry optimizations using ae-CCSD(T) and CCSD(T) using the
same cc-pwCV5Z basis set in both cases, the core-valence contribution becomes equal only to +0.02 kcal/mol (dimer I) and +0.01 kcal/
mol (dimer II).
It should be mentioned that the composite CCSD(T)/CBS DE value of 4.55 kcal/mol obtained by Řezáč et al. [24] for the dimer I
lies slightly lower in energy than the corresponding current CBS
value, being midway between our CCSD(T)/aug-cc-pVQZ and
CCSD(T)/aug-cc-pV5Z results, on account of different optimized
geometrical parameters obtained for the dimer I with the composite and conventional CCSD(T) methodologies (see also Section 3.1)
Nevertheless, an inclusion of core-valence, relativistic and quadruple-excitation corrections to the composite CCSD(T)/CBS DE value
brings the dimerization energy by 0.08 kcal/mol up [24] leading
to a better agreement with the current results. Somehow surprisingly, the (recalculated) MP2 values of uncorrected DE of Ford
and Glasser [14] for both dimer I and dimer II agree very well with
the current CCSD(T)/CBS results due to a fortuitous cancellation of
errors. However, MP2 values of dimerization energies corrected for
the BSSE and for the DZPE become, in general, much smaller in
absolute values than those obtained with high-level CCSD(T)/CBS
approaches. In a similar manner the uncorrected DE value of
3.66 kcal/mol obtained with CCSD/aug-cc-pVTZ model chemistry
for dimer II [23] agrees perfectly (within 0.1 kcal/mol) with the
current (ae-)CCSD(T)/CBS uncorrected values since the effects
associated with BSSE and with an inclusion of perturbative triple
excitations on the resulting CCSD/aug-cc-pVTZ dimerization energy almost completely cancel out.
After inclusion of all significant corrections to DE, the CCSD(T)/
CBS corrected values (DEcorr) for dimer I and dimer II at 0 K were
found to be 3.17 and 2.88 kcal/mol, respectively, i.e. the dimer
I is now by 0.29 kcal/mol more stable than the dimer II. Corresponding core-valence ae-CCSD(T)/CBS results yield even better
stabilization of the dimer I versus dimer II – by 0.44 kcal/mol.
Therefore, it is unlikely that the usage of other extrapolation
schemes or the inclusion of other correction types (i.e., higher order correlation, relativistic or diagonal Born–Oppenheimer corrections) could invert the stability order in favor of dimer II.
It is also desirable to include the present high-level energetic
and geometric characteristics of both dimer I and dimer II into
the benchmark sets (like the A24 set [24]) to test the performance
of different density-functional theory (DFT) functionals (and other
computational approaches). This will definitely help to elucidate
the predicted differences in the location of both stationary points
on the formaldehyde dimer potential energy surface. For instance,
according to the recent M062X/6-311++G(3df,3pd) results [4],
dimerization energies (corrected for BSSE only) resulted in a more
pronounced stabilization of the dimer I (5.09 kcal/mol) over the
dimer II (3.73 kcal/mol) indicating that the former dimer is probably less accurately described with this model chemistry than the
latter. Therefore, a more extended DFT benchmark study than already available [22] is still needed before recommending a particular group of DFT functionals to investigate the properties of
structurally similar (but larger) structures.
4. Conclusions
Accurate geometric and energetic characteristics of the two
lowest-lying isomers of formaldehyde dimer, dimer I of Cs
G.A. Dolgonos / Chemical Physics Letters 585 (2013) 37–41
symmetry and dimer II of C2h symmetry, have been calculated
employing high-level CCSD(T) computations with CBS extrapolations. In agreement with earlier MP2 calculations, both dimers
have been found to exhibit C@O bond length elongation (by
0.003–0.004 Å) and shrinking of most C–H bonds (up to 0.003 Å)
compared to a free formaldehyde molecule. Nonbonded C O
and O H distances in both dimers agree within 0.011 Å depending on whether core correlation is, or is not, taken into account
in respective (ae-)CCSD(T) geometry optimizations. After including
the very important ZPE and anharmonicity corrections, the calculated ae-CCSD(T)/CBS (CCSD(T)/CBS) dimerization energies are
equal, correspondingly, to 3.13 (3.17) kcal/mol for dimer I and
2.69 (2.88) kcal/mol for dimer II, indicating that dimer I is the
true global-minimum structure on the potential-energy surface.
Much less significant corrections to dimerization energies (including higher order correlation, relativistic or diagonal Born–Oppenheimer corrections) seem unlikely to invert the obtained stability
order. It is recommended to include both formaldehyde dimeric
structures in reference datasets and in benchmark studies of other
methods to be able to choose the most appropriate (but less expensive) model chemistry suitable for an accurate description of this
type of weakly bound complexes.
Acknowledgments
The author gratefully acknowledges the hospitality of the Bremen Center for Computational Materials Science (Bremen, Germany) and the use of its computational facilities at the early
stage of this work.
Appendix A. Supplementary data
Supplementary data associated with this article can be found, in
the online version, at http://dx.doi.org/10.1016/j.cplett.2013.
08.073.
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