Performance of Density Functional Theory and

Article
pubs.acs.org/JPCA
Performance of Density Functional Theory and Relativistic Effective
Core Potential for Ru-Based Organometallic Complexes
Selvarengan Paranthaman,†,‡,⊥ Jiwon Moon,§,⊥ Joonghan Kim,*,§ Dong Eon Kim,‡,∥ and Tae Kyu Kim*,†
†
Department of Chemistry and Chemical Institute for Functional Materials, Pusan National University, Busan 609-735, Republic of
Korea
‡
Max Planck Center for Attosecond Science, Pohang 790-784, Republic of Korea
§
Department of Chemistry, The Catholic University of Korea, Bucheon 420-743, Republic of Korea
∥
Department of Physics and Center for Attosecond Science and Technology, POSTECH, Pohang 790-784, Republic of Korea
S Supporting Information
*
ABSTRACT: Herein a performance assessment of density functionals used for
calculating the structural and energetic parameters of bi- and trimetallic Ru-containing
organometallic complexes has been performed. The performance of four popular
relativistic effective core potentials (RECPs) has also been assessed. On the basis of the
calculated results, the MN12-SX (range-separated hybrid functional) demonstrates
good performance for calculating the molecular structures, while MN12-L (local
functional) performs well for calculating the energetics, including that of the Ru−Ru
bond breaking process. The choice of appropriate density functional is a crucial factor
for calculating the energetics. The LANL08 demonstrates the lowest performance of
the RECPs for calculating the molecular structures, especially the Ru−Ru bond length.
■
INTRODUCTION
In recent decades, Ru-based organometallic complexes have
attracted special attention from researchers due to their
applications in catalysis and dye-sensitized solar cells
(DSSCs).1−5 In addition, Ru−carbonyl clusters such as
Ru3(CO)12 are of interest because of their catalytic properties
and as a precursor for the synthesis of organometallic
complexes containing Ru−Ru bonds.6 Their properties are
directly related to the Ru−Ru interactions, and consequently
on the Ru−Ru bond length and Ru−Ru bond energy. The Ru−
Ru bond length is readily measured by X-ray crystallography,
but measuring the Ru−Ru bond energy is a more difficult task.
Theoretical predictions of the molecular properties of organometallic complexes are usually performed using density
functional theory (DFT) because of its robustness with a low
computation time.7−14 However, different exchange-correlation
functionals can give varying results, creating difficulty when
studying these complexes. Therefore, the benchmark studies of
exchange-correlation functionals used for calculating the
molecular properties of the organometallic complexes have
been extensively studied. Most of these studies considered
small complexes containing only one transition metal.
However, a benchmark study of exchange-correlation functionals for bi- or trimetallic compounds is still lacking.
Narendrapurapu et al. investigated the performance of DFT
functionals of metal−metal and metal−carbon bond distances
in carbonyl complexes of first-row transition metals carbonyl
complexes (e.g., Mn2(CO)10) with the all-electron correlation© 2016 American Chemical Society
consistent (cc) basis sets; the M06-L functional worked well for
predicting metal−metal bond distances.12 This kind of study
should be expanded to second-row transition metal complexes
containing metal−metal bonds. Recent systematic studies for
assessing the performance of the DFT functional to predict the
molecular structure of two Ru-containing organometallic
complexes are reported.15−17 However, the compounds in
these studies contain the bridged oxygen between two Ru
atoms; the extension of their results to bi- and trimetallic
compounds, which has a Ru−Ru bond, is still questionable.
Recently, Laury and Wilson assessed the performance of 22
density functionals combined with the relativistic effective core
potential (RECP) for studying small complexes of second-row
transition metals complexes.13 They suggested that the doublehybrid functionals that mix the second-order Møller−Plesset
perturbation theory (MP2), B2GP-PLYP and mPW2-PLYP,
performed well for calculating the enthalpies of formation when
compared with experimental data. However, using doublehybrid functionals for studying organometallic complexes can
be questionable due to their expensive computation time than
other DFT functionals. Therefore, using these methods is
limited to only small transition metal complexes. Hence it is
necessary to find a suitable DFT functional with lower
computational cost to study these organometallic systems.
Received: January 20, 2016
Revised: March 17, 2016
Published: March 17, 2016
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the cc-pVTZ-PP (ECP28MDF); the valence basis set of the
dhf-TZVPP is reoptimized using the segmented contraction.
Therefore, the performance of the dhf-TZVPP may be almost
equivalent to that of the cc-pVTZ-PP.
The single-point energy calculations were performed using
the coupled-cluster singles and doubles, including the
perturbative corrections for triple excitations, CCSD(T) for
CO, Ru(CO)4, Ru(CO)5, and Ru3(CO)12 molecules to
examine accurate energetics. The CCSD(T) calculations were
performed on the optimized structure using MN12-SX/dhfTZVPP because it gave the smallest mean absolute deviation
(MAD) for the Ru−Ru bond lengths. The dhf-TZVPP and
def2-TZVPP were used for Ru and main group atoms (C and
O) in the CCSD(T) calculations, respectively. All DFT and
CCSD(T) calculations were performed using the Gaussian09
program.40
Additionally, in the bi- or trimetallic system, the neardegeneracy effect is not negligible. Therefore, in principle, a
multireference-based method is needed to calculate the
molecular properties; however, using that method is practically
impossible for bi- or trimetallic complexes with large ligands.
Therefore, using DFT methods is essential, which makes
finding suitable exchange-correlation functionals necessary.
Most benchmark studies have been focused on assessing the
performance of exchange-correlation functionals for calculating
the molecular properties. Since Ru is a heavy element,
considering relativistic effects is also crucial for predicting the
molecular properties of its complexes. The scalar relativistic
effect can be readily considered using RECP, and various
RECPs are available for Ru. Therefore, the calculation of
molecular properties of Ru-containing organometallic complexes can be performed using a robust combination of
exchange-correlation functionals with RECPs.
In the present study, we performed systematic assessment of
DFT functionals combined with four popular RECPs for
predicting the Ru−Ru, Ru−C, Ru−N, and Ru−S bond lengths
and additionally for calculating the energetics of Ru-containing
organometallic complexes. A total of 80 models of chemistry (=
20 exchange-correlation functionals × 4 RECPs) are examined
in this work. To the best of our knowledge, this is the first
assessment of the performance of RECPs for calculating the
molecular properties of Ru-containing organometallic complexes. This work will provide a reference for further
development of new exchange-correlation functionals and
guidance for selecting a reasonable combination of exchangecorrelation functional and RECP.
■
RESULTS AND DISCUSSION
A. Bond Lengths. Six molecules, Ru 2 , Ru(CO) 5 ,
Ru 3 (CO) 1 2 , [Ru 2 ( CO) 6 (μ-SCH 2 CH 2 S)], [Ru(bpy)
(CO)2(COOCH3)]2, and trans-[Cp2Ru2(CO)4], were optimized using 20 DFT functionals with four RECPs (total of 80
models of chemistry), and their molecular structures are shown
in Figure 1. Figure 1 shows that all the molecules except
Ru(CO)5 contain Ru−Ru bonds. In addition, [Ru(bpy)
(CO)2(COOCH3)]2 contains the bipyridine (bpy) ligand that
is often used for the design of an efficient DSSC.41,42 The Ru−
S bond is also important due to the recent demonstration of
■
COMPUTATIONAL DETAILS
The molecular structures of the Ru containing organometallic
complexes were optimized using 20 exchange-correlation
functionals, BLYP,18,19 BP86,18,20 BPW91,18,21 BE,22,23 N12,24
M06-L, 25 M11-L, 26 TPSS, 27 MN12-L, 28 B3LYP, 19,29
B3P86, 20,29 B3PW91, 21,29 PBE0, 30 M06, 31 TPSSh, 32
ωB97X,33 ωB97XD,34 M11,35 N12-SX,36 and MN12-SX.36
The harmonic vibrational frequency calculations were performed to identify the minimum energy structure. For all atoms
except Ru, the second generation default bases and triple-ζ
valence with heavily polarized basis functions (def2-TZVPP)
were used. The validation of def2-TZVPP basis sets for the
main group atoms has been examined via calculating the
molecular properties of the CO molecule and comparing with
experimental data.37−39 These results are summarized in Table
S1 in the Supporting Information. Four popular RECPs
(CRENBL, def2-TZVPP, dhf-TZVPP, and LANL08) were
employed for Ru to consider the scalar relativistic effects. These
four RECPs have the same core size of 28-electron, small-core
RECPs. The basis sets of def2-TZVPP and dhf-TZVPP for the
valence electrons (16 electrons) of Ru are [6s4p3d2f1g] and
[6s5p3d2f1g], respectively. On the other hand, the valence
basis sets of both CRENBL and LANL08 are [5s5p4d]. A
direct comparison of the four RECPs is difficult because the
valence basis sets of CRENBL and LANL08 do not have
polarization functions. Therefore, [2f1g] functions from def2TZVPP were augmented to the valence basis sets of CRENBL
and LANL08. Thereby the level of the valence basis sets of the
four RECPs is similar to each other. The RECP with the cc
triple-ζ valence basis set, cc-pVTZ-PP, was not used for Ru due
to the computation cost. However, we note that the
pseudopotential part of the dhf-TZVPP is the same as that of
Figure 1. Optimized molecular structures of Ru contained complexes
(a) Ru 2 , (b) Ru(CO) 5 , (c) Ru 3 (CO) 12 , (d) [Ru 2 (CO) 6 (μSCH2CH2S)], (e) [Ru(bpy)(CO)2(COOCH3)]2, and (f) trans[Cp2Ru2(CO)4].
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photoisomerization of the Ru−S bond containing organometallic complexes.43 In summary, the molecules examined in
this study are structurally similar to recently popular organometallic complexes. Since all the molecules except Ru2 have
been well characterized by X-ray crystallography, the calculated
bond lengths can be readily compared with those of
experimental values.44−49 For Ru2, the result of recent highlevel ab initio calculations (the second-order multiconfigurational perturbation theory, CASPT2) has been considered as a
reference value.50 The optimized geometrical parameters of the
molecular structures are summarized in Tables S2−S7 in the
Supporting Information. We have considered 31 bond lengths,
including Ru−Ru (5 bonds), Ru−C (17 bonds), Ru−S (1
bond), and Ru−N (8 bonds) for assessing the performance of
DFT functionals in this study. The mean absolute deviations
(MADs) of the Ru−X (X= C, N, and S), Ru−Ru, and all bond
lengths, with respect to the respective experimental values, are
shown in Figure 2a, 2b, and 2c, respectively. For clarity the
MADs of the Ru−Ru and Ru−X (X= C, N, and S) were split
between the figures due to the significance of the Ru−Ru bond
of the organometallic complexes.
First, the scales of the vertical axes in Figure 2a and 2b are
evidently different; the MADs of the Ru−Ru bonds are much
larger than those of the Ru−X bonds. This result clearly
demonstrates the error source of all bond lengths (see Figure
2c) originates from the Ru−Ru bond length. This implies that
theoretical description of the Ru−Ru bond of organometallic
complexes is a difficult task. As seen in Figure 2c, the BLYP
shows the worst performance in calculating the bond lengths; it
seriously overestimates the Ru−Ru and the Ru−X bond lengths
(see Tables S2−S7 in the Supporting Information). Therefore,
it is strongly not recommended for calculating the molecular
structures of Ru-containing organometallic complexes. The
B3LYP, a hybrid version of BLYP, also gives poor performance.
This is demonstrated by an overestimation of the Ru−Ru bond
lengths, shown in Figure 2b and Tables S2−S7 in the
Supporting Information. Additionally, B3LYP gave the poorest
results of the Ru−Ru bond lengths among the hybrid DFT
functionals. Although the B3LYP is the most popular DFT
functional, the results calculated by B3LYP are not promising.
Caution should therefore be exercised when using B3LYP for
the Ru−Ru bonds containing organometallic complexes. As
shown in Figure 2b, the new Minnesota hybrid functionals
(M11, N12-SX, and MN12-SX) show good results for the Ru−
Ru bond lengths. Especially, M11 and MN12-SX, which give
the smallest MAD of the Ru−Ru bond lengths. The MADs of
the Ru−Ru bond lengths calculated using the ωB97X and
ωB97XD functionals are slightly larger than those of new
Minnesota hybrid functionals. The MADs of ωB97X and
ωB97XD in Figure 2a show that the inclusion of the empirical
dispersion interaction improves the description of the Ru−X
bond lengths slightly. However, the same effect is not observed
on the Ru−Ru bond length (see Figure 2b), indicating that the
dispersion interaction on the Ru−Ru bond is negligible.
Figure 2b shows that hybrid functionals are in general slightly
better than their counterpart, generalized gradient approximation (GGA) or meta-GGA functionals, according to the
small MAD (e.g., PBE vs PBE0). As shown in Tables S4−S7 in
the Supporting Information, the hybrid functionals predict
shorter Ru−Ru bond lengths than those calculated by their
counterpart GGA or meta-GGA functionals, leading to the
smaller MAD value. It is well-known that the Hartree−Fock
(HF) method tends to underestimate the bond lengths of
Figure 2. MAD of the calculated (a) Ru−C, Ru−S, and Ru−N bond
lengths (total 31 bonds), (b) Ru−Ru bond lengths (total 5 bonds),
and (c) all bond lengths. Vertical dashed line separates hybrid
functionals from pure DFT functionals.
molecular structures. Therefore, mixing some amount of HF
exchange (i.e., hybrid functional) also tends to give a shorter
bond length. Similar results can be found in recent theoretical
investigations on Ru2 and Os2.50,51
Figure 2 demonstrates the LANL08 RECP has poor
performance for calculating the structural parameters;
LANL08 overestimates all bond lengths compared with the
reference values (see Tables S2−S7 in the Supporting
Information). This observation correlates with the results of
the recent study on the performance of DFT and MP2 methods
for determining the structural parameters of Ru-containing
organometallic complexes. 52 This study showed that
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LANL2DZ RECP was inadequate for predicting the structural
parameters. It is noteworthy that the pseudo-potential part of
LANL08 is the same as that of LANL2DZ. Therefore, the
LANL08 performance is similar to LANL2DZ. In addition,
LANL2DZ shows poor performance in calculating the bond
lengths and vibrational frequencies of MX (M = Zn, Cd; X = S,
Se, Te) quantum dots.53 According to these results, LANL08
(and LANL2DZ) is not recommended for calculating the
structural parameters of organometallic complexes. Other
RECPs give similar results; no RECP gave a remarkably small
MAD. In summary, with the exception of LANL08, recently
developed Minnesota functionals with RECPs (especially
MN12-SX) are recommended for predicting the molecular
structure of Ru-containing organometallic complexes.
B. Energetics. The performance of exchange-correlation
functionals for calculating the energetics of Ru-containing
organometallic complexes was assessed. The experimental bond
dissociation energy (BDE) of Ru−CO in Ru(CO)5 was
selected as the reference value. To the best of our knowledge
the BDE of the Ru−Ru bond is not available in the literature,
with the exception of Ru2 (see ref 50, references therein).
However, we replace the experimental value of BDE of Ru2 as
the recent multireference configuration interaction including
the Davidson correction (MRCI+Q) result because of the
discrepancy (see ref 50 for the details). To circumvent the lack
of experimental data for the BDE of the Ru−Ru bond, we
calculate the reaction energies for two reactions (eqs 1 and 2)
using the high-level CCSD(T) method (CCSD(T)/dhfTZVPP//MN12-SX/dhf-TZVPP). It should be noted that
some DFT functionals are more accurate than CCSD(T) for
calculating the dissociation energy of 3d transition metal
containing diatomic molecules.54 However, Ru is a 4d transition
metal and Ru3(CO)12, Ru(CO)5, and Ru(CO)4 in eqs 1 and 2
are well described by a single reference method. For example,
the BDE (D0) of Ru(CO)5 (Ru(CO)5 → Ru(CO)4 + CO)
calculated by CCSD(T)/dhf-TZVPP//MN12-SX/dhf-TZVPP
(ZPEs calculated by MN12-SX/dhf-TZVPP are used) is 28.6
kcal/mol, which is very close to the experimental value (27.6 ±
0.4 kcal/mol; see Table S3 in the Supporting Information) even
if it is obtained by single-point calculations. Therefore, it is
readily expected that reaction energies of eqs 1 and 2 calculated
by CCSD(T)/dhf-TZVPP//MN12-SX/dhf-TZVPP will be
reasonably close to the true values.
Ru3(CO)12 + 3CO → 3Ru(CO)5
(1)
Ru3(CO)12 → 3Ru(CO)4
(2)
Figure 3. MAD of the calculated (a) three energetic parameters (BDE
of Ru2, reaction energy of Ru3(CO)12 + 3CO → 3Ru(CO)5 (eq 1),
and reaction energy of Ru3(CO)12 → 3Ru(CO)4 (eq 2)) and (b) four
energetic parameters (BDE of the Ru−CO in Ru(CO)5, BDE of Ru2,
reaction energy of Ru3(CO)12 + 3CO → 3Ru(CO)5 (eq 1), and
reaction energy of Ru3(CO)12 → 3Ru(CO)4 (eq 2)). Vertical dashed
line separates hybrid functionals from pure DFT functionals.
M06-L and MN12-L show large deviations from the reference
values. Especially, N12, which shows almost 40 kcal/mol
deviation. The MN12-L, a recently developed local DFT
functional, demonstrates the best performance for the
energetics, with M06-L closely following it. However, although
N12 and M11-L are also recently developed local DFT
functionals they demonstrate a large deviation. Especially the
MAD of N12 is comparable with that of BLYP. These results
indicate that local DFT functionals cannot guarantee good
performance for calculating the energetics; therefore, selecting
the DFT functional itself is crucial. Including the exact
exchange energy slightly reduces the MAD. However, the
MAD of M11 is still comparable with that of M11-L. Therefore,
the M11 family functional is not recommended for calculating
the energetics of Ru-containing organometallic complexes. The
variation between ωB97X and ωB97XD indicates that
including empirical dispersion will slightly improve the
prediction of energetic values; however, it is hardly noticeable.
On the basis of the results in Figure 3a, calculating of the
energetics of the Ru−Ru bond by DFT is still a difficult task.
The deviations in M06-L and MN12-L are smaller than those in
other exchange-correlation functionals, but they are still close to
As these two reactions include the Ru−Ru bond breaking
process, they can serve as a model to estimate the BDE of the
Ru−Ru bond. The four energy values (BDE of the Ru−CO in
Ru(CO)5, BDE of Ru2, reaction energies of eqs 1 and 2) are
considered the reference values for assessing exchangecorrelation functionals. The four calculated energy values are
summarized in Tables S2, S3, and S8 in the Supporting
Information, and the calculated MADs with respect to the
reference values are shown in Figure 3. Figure 3a and 3b show
the MADs of three (excluding the BDE of the Ru−CO bond in
Ru(CO)5 from four energetic values) and four energetic values,
respectively. First, the difference between Figure 3a and 3b
shows that the large deviation originates from the energetics of
the Ru−Ru bond. Therefore, the following discussion will focus
on the results in Figure 3a, with the energetics of the Ru−Ru
bond. As can be seen from Figure 3, all DFT functionals except
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10 kcal/mol. In addition, both M06-L and MN12-L predict the
ground state of Ru2 as 7Δu instead of the 5Σg+ state (see Table
S2 in the Supporting Information), although high-level
multireference ab initio calculations such as CASPT2 and
MRCI+Q have predicted the 5Σg+ state as the ground state.50
Table S8 shows that CCSD(T) predicts reaction 1 is
endothermic. However, there is no DFT functional to predict
reaction 1 as endothermic. Therefore, development of a new
exchange-correlation functional giving improved energetics for
the Ru−Ru bond breaking process is necessary. One should be
careful to select the exchange-correlation functional for
calculating the energetics, in particular, the process involving
the Ru−Ru bond breaking. We recommend the MN12-L
functional for calculating the energetics of the Ru−Ru bond
containing organometallic complexes.
Contrary to bond length calculations, LANL08 does not
show poor performance when calculating the bond energy. In
the calculations with local DFT functionals, LANL08 generally
shows the smallest MAD. However, in the calculations with
hybrid DFT functionals, the situation is generally opposite;
LANL08 shows the largest MAD. In addition, MN12-L with
LANL08 shows the smallest MAD, but M06-L with LANL08
shows the largest MAD. A similar situation takes place in the
calculations with the def2-TZVPP; generally, the def2-TZVPP
with local and hybrid DFT functionals shows the largest and
smallest MADs, respectively. Therefore, in energetic calculations, the type of RECP is not a crucial factor, whereas the
type of DFT functional is crucial for calculating the energetics
of Ru-containing organometallic complexes.
■
AUTHOR INFORMATION
Corresponding Authors
*E-mail: [email protected] (T.K.K.).
*E-mail: [email protected] (J.K.).
Author Contributions
⊥
S.P. and J.M. contributed equally to this work.
Notes
The authors declare no competing financial interest.
■
ACKNOWLEDGMENTS
This work was supported by National Research Foundation of
Korea (NRF) grants funded by the Korean government
(MEST and MSIP) (2013R1A1A2009575 and
2014R1A4A1001690). This research was also supported in
part by the Global Research Laboratory Program [Grant No
2009-00439] and the Max Planck POSTECH/KOREA
Research Initiative Program [Grant No 2011-0031558] through
the MEST’s NRF funding. This research was also supported by
Basic Science Research Program through the National Research
Foundation of Korea (NRF) funded by the Ministry of Science,
ICT & Future Planning (NRF-2014R1A1A1007188). This
work was also supported by the National Institute of
Supercomputing and Network/Korea Institute of Science and
Technology Information with supercomputing resources
including technical support (KSC-2015-C1-002).
■
CONCLUSIONS
The performance of DFT functionals for calculating the
structural and energy parameters of bi- and trimetallic Rucontaining organometallic complexes has been investigated.
The DFT functionals examined in this study range from GGA
to hybrid meta-GGA functionals, along with recently developed
Minnesota functionals. In addition, the performance of four
popular RECPs has been assessed. Thereby, a total 80 models
of chemistry were considered in this work. The recently
developed MN12-SX functional performs well for predicting
the structural parameters. For energy parameters, including that
of the Ru−Ru breaking process, the local DFT functional
MN12-L shows the smallest MAD. The M06-L also shows
good performance for calculating energy parameters. The
LANL08 is the lowest performing RECP for calculating the
molecular structures. This result correlates with previous
studies. However, all RECPs show similar performance in
calculating energetics of the Ru containing organometallic
complexes; therefore, when calculating energetics, choosing an
appropriate DFT functional is crucial. Although the MN12-L
gives the best performance for calculating the energetics, the
MAD is over 5 kcal/mol. Therefore, further development of
exchange-correlation functionals is necessary and this work
should be referenced for that purpose.
■
Tables S2 and S3. The optimized structural parameters
of Ru3(CO)12, [Ru2(CO)6(μ-SCH2CH2S)], [Ru(bpy)
(CO)2(COOCH3)]2, and trans-[Cp2Ru2(CO)4] and the
calculated reaction energies of Ru3(CO)12 + 3CO →
3Ru(CO)5 and Ru3(CO)12 → 3Ru(CO)4 are given in
Tables S4−S8 (PDF)
■
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ASSOCIATED CONTENT
* Supporting Information
S
The Supporting Information is available free of charge on the
ACS Publications website at DOI: 10.1021/acs.jpca.6b00654.
The calculated molecular properties of CO are
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