Trans influence and substituent effects on the HOMO-LUMO energy gap and Stokes shift in Ru mono-diimine derivatives

Article abstract of DOI:10.1016/j.molstruc.2019.06.005

The ground (S₀) and excited triplet (T₁) electronic states and corresponding optical spectra of a series of cationic complexes [RuH(CO)L(PPh₃)₂]⁺ (L = 2,2′-bipyridyl) (Rubpy), 4,4′-dicarboxylic-2,2′-b

Full text of DOI:10.1016/j.molstruc.2019.06.005

Journal of Molecular Structure 1195 (2019) 620e631
Contents lists available at ScienceDirect
Journal of Molecular Structure
journal homepage: http://www.elsevier.com/locate/molstruc
Trans influence and substituent effects on the HOMO-LUMO energy
gap and Stokes shift in Ru mono-diimine derivatives
a
a
c
a
b
Sanaa AlAbbad , Tova Sardot , Oliko Lekashvili , Daniel Decato , Francesco Lelj ,
a,
**
a, *
J.B. Alexander Ross
Department of Chemistry and Biochemistry, University of Montana, Missoula, MT, 59812, USA
La.M.I. and LaSCAMM, INSTM Sezione Basilicata, Dipartimento di Scienze, Universit aꢀ della Basilicata, Via dell’Ateneo Lucano 10, 85100, Potenza, Italy
Department of Chemistry, Ivane Javakhishvili Tbilisi State University, 1, I. Chavchavadze ave., 0128, Tbilisi, Georgia
, Edward Rosenberg
a
b
c
a r t i c l e i n f o
a b s t r a c t
Article history:
Received 28 November 2018
Received in revised form
The ground (S ) and excited triplet (T ) electronic states and corresponding optical spectra of a series of
0
1
þ
0
0
0
cationic complexes [RuH(CO)L(PPh
idyl(Rudcbpy),bis-4,4 -(N-methylamide)-2,2 -bipyridyl(Rudamidebpy),bis-4,4 -(methyl)-2,2 -bipyr-
3
)
2
]
(L ¼ 2,2 -bipyridyl) (Rubpy), 4,4 -dicarboxylic-2,2 -bipyr-
0
0
0
0
7
May 2019
2þ
2
idyl(RudMebpy),[Ru(CO) dcbpy(PPh
3
)
2
]
(Ru(2CO)dcbpy),and [Ru(H)
2
dcbpy(PPh
3
)
2
]
(Ru(2H)dcbpy)
Accepted 3 June 2019
Available online 10 June 2019
have been studied by combined Density Functional/Time-Dependent Density Functional (DFT/TDDFT)
techniques using different combinations of DFT exchange-correlation functionals and basis sets. PBE0/
0
LANL2DZ provided more accurate geometries to describe S whereas B3LYP/LANL2DZ predicted spectral
Keywords:
energies that correlated better with the available experiment data. The Ru (II) complexes with different
substituents emit photons ranging from 560 to 610 nm in the series RudMebpy, Rubpy, Rudamidebpy,
Rudcbpy. The calculations predicted a maximum emission at about 540 nm for the complex constructed
Ru mono-diimine complexes
Triplet excited state
Stokes shift
HOMO-LUMO energy gap
Trans influence
Density functional theory
from two carbonyl
calculated when two H
between HOMO-LUMO energy gap, Stokes shift, and T
p
-acceptors ligands trans to the dcbpy, while an emission in the far infrared region is
-donor ligands trans to the dcbpy. Our calculation results show correlations
distortion, which reflect the different effects of
s
1
electron-withdrawing and donating groups. We proposed that these correlations can be used to predict
the photophysical properties for new complexes.
©
2019 Elsevier B.V. All rights reserved.
1
. Introduction
properties.
The push-pull from ruthenium as a strong oxidant that donates
an electron from the t g orbital to the bpy low-lying * molecular
orbital, results in a singlet ground-state (S ) to singlet metal-to-
Ruthenium (II) poly-diimine complexes have received signifi-
cant attention in recent years [1e4], particularly in applications
such as dye-sensitized solar cells, artificial photocatalysis, DNA di-
agnostics, and as potential agents for the detection of different
biological analytes of clinical and environmental interest [1,5e12].
2
p
0
1
ligand charge-transfer ( MLCT) transitions. The emission after
1
excitation of the MLCT band has a large Stokes shift, typically on
ꢀ
1
the order of 150 nm or 6000 cm in the visible-to-near IR region of
the spectrum, and has a long decay time, ranging from 100 ns to
0
Additionally, ruthenium diimine (2,2 -bipyridyl) complexes con-
taining hydride, carbonyl and triphenylphosphine (PPh
3
) ligands
10 ms; the Stokes shift and long-lived intensity decay are charac-
3
have been used as catalysts for hydrogenation of unsaturated
organic compounds [13e17]. The importance of these complexes
comes from their unique photophysical and photochemical
teristic of triplet state ( MLCT) emissions [1e4]. Additionally,
ruthenium complexes exhibit reversible redox behavior with
adjustable potentials [18e20].
Tuning the emission wavelength of the transition metals com-
plexes over the visible range is desirable for applications such as
organic light-emitting devices (OLEDs) [21], luminescence-based
sensors [22], and photocatalysis [23]. Therefore, several modifica-
tion strategies have been applied to control the HOMO-LUMO en-
ergy gap: taking advantage of the substituent effects on the ligand
*
Corresponding author. Department of Chemistry, College of Science, Imam
Abdulrahman bin Faisal University, Dammam 31113, Saudi Arabia.
** Corresponding author.
E-mail addresses: sandy.ross@mso.umt.edu (J.B.A. Ross), edward.rosenberg@
mso.umt.edu (E. Rosenberg).
https://doi.org/10.1016/j.molstruc.2019.06.005
0
022-2860/© 2019 Elsevier B.V. All rights reserved.

S. AlAbbad et al. / Journal of Molecular Structure 1195 (2019) 620e631
621
parent by changing the ligand parent entirely or by varying the li-
2. Experimental section
gands trans to the ligand parent [21e27]. For example, tuning
molecular orbital energies with a variety of substituents has been
reported for Ir (III), Pt (II), and dyes for dye-sensitized solar cells
2.1. Preparation of complexes
[
25e27].
Density functional theory (DFT) combined with the time-
It was found that the previously synthesized Rubpy and
Rudcbpy complexes could be made in one step from
dependent DFT (TD-DFT) calculations have been employed to
study the photophysical properties of different transition metal
systems, and the calculated excitation energies agree well with the
experimental data [25,28,29]. This agreement between theory and
experiment demonstrates the power of these calculations to pro-
vide reliable predictions about the nature of the molecular orbitals,
electronic transitions, and conformational changes that can occur
upon excitation. Most previous computational studies have been
limited to the description of the trans-influence, the extent to
which a ligand weakens the bond trans to itself in the equilibrium
ground state of a complex [30], and most have been more con-
cerned with square planar rather than octahedral complexes
3 3
Ru(PPh ) (H)(CO)Cl and the appropriate ligand by following the
method of Malecki and Maro nꢁ [38]. Essentially as previously
described [36], each complex was combined with the appropriate
ligand in equimolar amounts followed by reflux in methanol for 2 h
followed by addition of NH
compounds, Rubpy and Rudcbpy, were isolated as the PF
which after recrystallization gave pale-yellow crystals. The IR, H
4
PF
6
(1.0 g/10 mL solution). The final
6
salts,
1
31
and P NMR data were in agreement with previously published
6
data [36]. This same method, except without addition of NH PF ,
4
was then applied to the synthesis of RudMebpy. This new complex
was isolated as the chloride salt, which after recrystallization gave
1
31
brown crystals. H and P NMR spectra for RudMebpy were ob-
tained on a Varian VNNMRS 500 MHz NMR or a Varian VNNMRS
600 MHz NMR spectrometer. Infrared spectra were obtained on a
Nicolet 100 FT-IR spectrometer. The details are provided in the
supplemental materials.
[
31e35].
The purpose of our study is to extend the previous computa-
tional studies to include octahedral Ru (II) complexes, and thereby
establish, qualitatively, a broader screening protocol for evaluating
the correlation between the HOMO-LUMO energy gap and the
Stokes shift in transition metal complexes. Here, we are investi-
gating the spectroscopic effects of i) different ligands trans to bpy
2.2. Crystal structure analysis for RudMebpy
(
hydride as a good
s
-donor in comparison to carbonyl as a good
p
-
X-ray diffraction data for [RuH(CO)bis-4, 4’-(methyl)bpy(PPh
Cl (Cambridge Crystallographic Data Center Code CCDC 1845877)
were collected at 100 K on a Bruker D8 Venture using MoΚ -radi-
ation (
¼ 0.71073 Å). Data have been corrected for absorption us-
3 2
) ]
acceptor), and ii) introducing different electron-withdrawing or
electron-donating substituents in derivatives of the Ru(bpy)(PPh
moiety.
Our laboratory has been interested in using the photophysical
properties of Ru hydride complexes to study dynamics in biological
membranes and for applications as catalysts and sensors [36,37].
Here, we report computational results for the photophysical, and
photochemical properties of Ru (II) complexes of bpy, carbonyl and
3
)
2
a
l
ing SADABS1 area detector absorption correction program. Using
Olex22, the structure was solved with the SHELXT3 structure so-
lution program using Direct Methods and refined with the SHELXL4
refinement package using least squares minimization. All non-
hydrogen atoms were refined with anisotropic thermal parame-
ters. Hydrogen atoms attached to heteroatoms were found from the
residual density maps, placed, and refined with isotropic thermal
parameters. All other hydrogen atoms in the investigated structure
were located from difference Fourier maps but finally their posi-
tions were placed in geometrically calculated positions, and refined
using a riding model. Isotropic thermal parameters of the placed
hydrogen atoms were fixed to 1.2 times the U value of the atoms
they are linked to (1.5 times for methyl groups). The structure was
found to contain indistinguishable solvent molecules voids within
the lattice. Attempts at modeling this solvent were not able to
produce a suitable model. The SQUEEZE5 routine within PLATON6
was utilized to account for the residual, diffuse electron density and
the model is refined against these data. A total of 185 electrons per
unit cell were corrected. This corresponds to roughly 10 methanol
molecules per unit cell (180 electrons). All calculations and re-
finements were carried out using APEX27, SHELXTL8, Olex2, and
PLATON, (Fig. 2) [39e46]. A comparison between selected experi-
mental and calculated parameters is listed in Table 1.
PPh
3
and their derivatives, which previously have been shown to
display long excited-state lifetimes with high quantum yields
[36,37]. We also report a different synthesis procedure for
[RuH(CO)bpy(PPh ]PF (Rubpy) and [RuH(CO)dcbpy(PPh ]PF
(Rudcbpy) complexes, both of which have been studied previously
3
)
2
6
3
)
2
6
in our laboratory [36,37], as well as synthesis of the new complex
RuH(CO)bis-4, 4’-(methyl)bpy(PPh ]Cl (RudMebpy) (including
spectral data).
[
3 2
)
The good agreement between the experimental data for the
former Ru(II) complexes and these calculations, encouraged us to
extend the study to include theoretical predictions of three other
Ru(II) complexes of interest:[RuH(CO)bis-4,4 -(N-methylamide)
bpy(PPh
0
þ
3
)
2
] (Rudamidebpy),[Ru(H)
2
dcbpy(PPh
(Ru(2CO)dcbpy) (see Fig. 1).
3 2
) ] (Ru(2H)dcbpy),
2
þ
2 3 2
and [Ru(CO) dcbpy(PPh ) ]
2.3. Spectroscopy
Absorption, excitation and emission spectra for Rubpy, Rudcbpy,
and RudMebpy (solution in ethanol) were recorded on a Molecular
Devices Spectra Max M2 (Figs. 3 and 4). It should be noted that the
absorption and emission spectra of Rudcbpy reported here are a
correction of those previously reported by our laboratory [36].
2
2
.4. Computational methods
.4.1. DFT/TDDFT
Fig. 1. Optimized molecular structures of Rubpy and Rudcbpy complexes. Hydrogen
atoms are omitted for clarity.
To select the appropriate functional for describing the

622
S. AlAbbad et al. / Journal of Molecular Structure 1195 (2019) 620e631
Fig. 4. Experimental emission spectra of Rubpy in black (the maximum of emission is
at 593 nm), Rudcbpy in red (the maximum of emission is at 609 nm), and RudMebpy in
blue (the maximum of emission is at 563 nm) in ethanol. The intensity is normalized
for the comparison.
0
Fig. 2. Solid state structure of [RuH(CO)bis-4, 4 -(methyl)bpy(PPh
3 2
) ]Cl, showing the
50% probability thermal ellipsoid and the hydride position, hydrogen atoms omitted
for clarity.
0
in the S state. M06, B2PLYP, and wB97XD were included for better
Table 1.
description of noncovalent interactions. To compare the basis sets,
we employed two commonly used effective core potentials (ECPs)
for Ru: the Los Alamos pseudopotential (LANL2DZ) [54] and the
Stuttgart-Dresden pseudopotential (SDD) [55]. The former are
shape-consistent, have no adjustable parameters, and are derived
by calculation of the spatial distributions of the valence orbital of
the isolated atom. The latter are energy-consistent and include
empirical parameters derived from observable data for a single
atom, such as ionization energy. For all other atoms, we used the 6-
31G* basis set. In addition, to improve the angular description of
the valence orbitals of the central atoms, a one-set-f-polarization
functions (exponent: 1.235) and a one-set-d-polarization functions
Selected bond lengths (Å), bond angles (º), and torsion angles (º) optimized for
RudMebpy in S using B3LYP/LANL2DZ and PBE0/LANL2DZ compared to X-ray data.
0
Experimental
B3LYP
PBE0
Ru-P1
Ru-P2
Ru-N1
Ru-N2
Ru-H
Ru-C
N1-Ru-N2
P1-Ru-P2
N1-C-C-N2
2.353
2.359
2.116
2.179
1.563
1.843
75.688
165.209
2.032
2.448
2.449
2.173
2.246
1.613
1.862
74.544
170.099
1.854
2.391
2.392
2.137
2.198
1.613
1.852
75.413
169.164
1.002
(exponent: 0.371) [56] were added to Ru and to P [57], respectively.
All geometries were optimized, as described below, starting from
the crystal structure of Rubpy (Cambridge Crystallographic Data
ꢀ
Center Code CCDC 704327) [36], neglecting the PF
6
counterion in
the model. The carboxylic groups were added to the 4 and 4’ po-
sitions of the bpy group. The most stable conformation of the
carboxyl groups in S state was determined by scanning the po-
0
tential energy surfaces (PES) as a function of -COOH torsion angle
and optimizing the remaining non-scanned coordinates (relaxed
PES scan). We found that the most stable ground state conforma-
tion has both -COOH groups coplanar with bpy, Ru, carbonyl, and
the hydride (Fig. S1).
To assess the performance of the computations, we used several
statistical measures [58]: the mean error
in the errors std, the mean absolute error Dabs, and the maximum
absolute error max, where the experimental values used for
D, the standard deviation
D
D
1
comparison were taken from the crystal structure of Rubpy. A total
of six Ru-ligand and six P-C bond-lengths, and 15 ligand-Ru-ligand,
six C-P-C, and six C-P-Ru angles were considered. Solvation effects
were modeled by using the “Polarizable Continuum Model” (PCM)
Fig. 3. Experimental absorption spectra of Rubpy (black), Rudcbpy (red), and Rud-
Mebpy (blue) in ethanol. The intensity is normalized for the comparison.
[
59,60] and the Onsager reaction-field model [61]. Normal-mode
analysis confirmed that all optimized geometries were in minima.
From the optimized S , the lowest 22 singlet-singlet transitions,
0
and their corresponding oscillator strengths were determined us-
ing TDDFT in combination with B3LYP/LANL2DZ, B3LYP/LANL2Z
photophysical properties for all complexes, we employed DFT using
six different exchange-correlation potentials: B3LYP [47], PBE0 [48],
CAM-B3LYP [49], M06 [50], B2PLYP coupled with D3 dispersion
correction [51] and hybrid meta-GGA with functional wB97XD [52].
All calculations were performed with the Gaussian 09 suite of
programs [53] to determine the equilibrium structure of Rudcbpy
1
The details of the statistical methods can be found in the supplemented
material.

S. AlAbbad et al. / Journal of Molecular Structure 1195 (2019) 620e631
623
with inclusion of f,d-polarization functions to Ru and P, and M06/
LANL2DZ [62]. B3LYP and M06 generated similar excitation and
absorption spectra that correlated well with the experimental data.
We determined the nature of each band by calculating the orbital
energies and the composition in terms of atom contributions using
electron density difference maps (EDDMs) implemented in
GaussSum 2.2 [63]. A half-width at half-maximum was assigned to
the default value in gaussian (0.4 eV).
3.2. The optimized S
functionals
0
geometry of Rudcbpy and performance of
Table 3 compares selected bond distances and angles from the
experimental data for Rubpy (Cambridge Crystallographic Data
Center Code CCDC 704327) [36] with the calculated values obtained
using B3LYP/LANL2DZ/PCM in ethanol as solvent. The comparison
with the X-ray data could be appropriate because the presence in
the crystal structure of polarizable PF
environment that is far different from a “non-polarizable” one, as in
the gas phase, and better described by some polar media. The
calculations predicted a deviation in the range of 1.20e11.15 p.m. in
the bond length for the different Ru-ligand and a total mean error of
7.07 pm The table also shows the calculated parameters of Rudcbpy
using the same level of theory. Introducing -COOH into the bpy
ligand did not significantly affect the core coordination of the
parent complex (Table S2-S5). For example, the total mean error
associated with the calculated Ru-ligand bond-lengths of Rudcbpy
is 7.14 pm Additionally, the total mean error for the calculated P-C
bond-lengths for Rudcbpy compared to Rubpy differs by 0.09 pm In
the following, we compare the performance of the different com-
binations of density functional/basis set/PCM in terms of the
calculated Ru and P bond-lengths and bond-angles that describe
e
The lowest energy T
geometry using two approaches: the linear-response TDDFT and
the difference in the self-consistent field (SCF) energies of the S
and T spin states ( SCF) [64,65]. The later was used to ensure the
stability of the calculated T states by TDDFT. For both methods, the
spin-unrestricted Kohn-Sham (UKS) orbitals were used. The ana-
lytic gradients and frequencies were calculated for T optimized to
its minimum energy configuration via TDDFT using Gaussian 16
66]. T was modeled using seven different combinations of
methods and basis sets as explained in the discussion. The emission
energies were calculated as the energy difference between S and
with the zero-point (ZP) vibrational energy correction included.
For this, the emission energy was determined as the difference of
the ZP of S and the ZP of T calculated using SCF and TDDFT
approaches.
1
states were optimized starting from the S
0
6
counter ions creates an
0
1
D
1
1
[
1
0
T
1
0
1
D
The data suggested that B3LYP/LANL2DZ/6-31G* is sufficient for
describing the Ru mono-diimine system and its photophysical
properties. Therefore, at lower computational cost, we used this
level of theory to describe the other systems. To model RudMebpy
0
the Rudcbpy S geometry (Fig. 5, Table S2-S5).
The total mean errors of the bond lengths were, on average,
larger for Ru-ligand than for P-C bonds. We noted that in all
methods the maximum error was associated with Ru-N bonds. As
expected, the functionals that were constructed to account for
dispersion (M06, B2PLYPD3, and wB79xD) yielded geometric pa-
rameters that were closest to the crystal structure parameters. The
performance of the different DFT methods followed the ‘Jacobs
ladder’ classification scheme with total mean errors of the bond
lengths decreasing in the series double-hybrid (B2PLYPD3) < meta-
hybrid (M06) < hybrid-GGA (wB79xD) [70]. The methods, however,
show no trend in evaluation of bond-angles. With all methods, the
and Rudamidebpy, the -COOH groups were substituted by -CH
3
and
-
CONHCH , respectively. The Ru(2CO)dcbpy and Ru(2H)dcbpy
3
complexes were modeled starting from the optimized Rudcbpy
ground-state geometry. Energy minima were then obtained by
optimizing all the geometrical parameters.
ꢁ
2.4.2. QTAIM/NBO
Ru bond-angles were smaller (0.01-0.20 ) than in the crystal
To rationalize the effects of the trans influence and substituent
structure of the parent complex Rubpy; the P bond-angles varied
over a range of þ0.02/-0.04 . It should be noted that the PBE0/
ꢁ
groups, we determined the atomic charges of the optimized
structures in the S and T states using two different approaches:
0
1
LANL2DZ performance was superior to B3LYP/LANL2DZ. Both
functionals use a fraction of exact exchange energy, but B3LYP in-
cludes empirical parameters determined from the correlation en-
ergy of the He atom [71]. Additionally, PBE0 performance was
comparable to that of the functionals that include dispersion.
Including the long-range corrected exchange correlation functional
(CAM-B3LYP) provided a better description compared to that ob-
tained with B3LYP alone.
NBO analysis implemented in Gaussian 09 and the quantum theory
of atoms in molecules (QTAIM) implemented in the AIMAll pro-
gram package [67e69]. The wave functions were generated first by
a single-point calculation on the optimized structures of the com-
plexes in S
similar trends for the atomic charge changes between S
Table S1).
0
and T
1
using the UKS orbitals. Both methods provided
0
and T ,
1
(
We found that increasing the basis set size did not provide
significant improvement in the geometric parameters. For instance,
adding f,d-polarization functions slightly decreased the mean error
of the bond-lengths of Ru-ligand, but not of P-C. The performance
of the basis sets that include ECPs is tested with B3LYP and M06
level of theory (Fig. 5, Table S2-S5). The results show better im-
provements in the determination of Ru-ligand bond-lengths using
SDD with both B3LYP and M06 functionals (total mean errors are
5.4 pm and 4.1 pm, respectively) compared to LANL2DZ (7.1 pm and
3
. Results and discussion
3.1. Photophysical properties of RudMebpy
The UVeVis absorption spectra were measured at room tem-
perature in ethanol solution (Fig. 3 and Table 2). Similar to other
octahedral Ru-diimine complexes, a weak and wide absorption
band around 350e500 nm is observed due to MLCT. However, it is
5.5 pm, respectively). However, LANL2DZ provides
description of the bond angles, see Table S4 and S5.
a better
1
blue shifted when compared to that of other complexes (Rubpy and
Rudcbpy) (Fig. 3). The calculations reveal the characterizations of
the strong absorption bands below 350 nm due to several elec-
tronic transitions as we explained latter. The same blue shift was
observed in the emission spectra of RudMebpy at room tempera-
ture (Fig. 4). This is most likely due to the less distortion in the
excited-state of RudMebpy because of the electron-donating
feature of the methyl groups.
0
To determine the S geometry of Rudcbpy, we initially used
functionals that did not include dispersion (i.e., B3LYP, PBE0, and
CAM-B3LYP). The calculations were performed first without sym-
metry constraints and then applied the constraints. In all cases,
there was lack of symmetry in the calculated structure (i.e., C
However, using functionals that include dispersion (i.e., B2PLYPD3,
M06, and wB79xD), S for Rudcbpy was fully optimized with C
symmetry (i.e., the bpy rings were coplanar with Ru, CO, and H),
1
).
0
s

624
S. AlAbbad et al. / Journal of Molecular Structure 1195 (2019) 620e631
Table 2.
Computed absorption, excitation and electronic transitions for complexes using B3LYP/LANL2DZ.
complex
Rubpy
l
absa (nm)
400
l
absb (nm)
l
exit. (nm)
f
major contribution
% composition
character
3 2
Ru,(PPh ) / bpy
394.9
287.0
387.7
288.9
0.06
H / L (95%)
H: Ru 47%, (PPh
L: bpy 96%
3
)
2
46%
2
2
77c
57
0.36
H-1/ Lþ2 (46%)
H-1: Ru 50%, (PPh
Lþ2: Ru 21%, (PPh
Lþ3: (PPh 13%, bpy 85%
3
)
2
45%
3 2
Ru / (PPh )
3 2
)
75%
2
2
85.9
86.7
0.19
0.14
0.13
0.06
H-1/ Lþ3 (34%)
H /Lþ3 (60%)
H /Lþ2 (57%)
H /Lþ3 (57%)
H-1 /Lþ3 (20%)
H/ L (94%)
)
3 2
Ru,(PPh
Ru,(PPh
3
)
)
2
2
/ bpy
/ bpy
3
00c
326.1
3
c
3
3 2
Ru / (PPh )
23.8c
Ru,(PPh
Ru,(PPh
Ru,(PPh
/ bpy
/ bpy
/ dcbpy
3
)
3
)
3
)
2
2
2
Rudcbpy
422
455.3
320.3
446.1
0.09
H: Ru 42%; (PPh
L: bpy 80%, (COOH)
H-15: bpy 81%; (PPh
3
)
2
52%
14%
18%
2
3
2
10
70
309.5
322.5
0.29
0.13
H-15 / L (82%)
H / Lþ3 (55%)
H-1 / Lþ3(19%)
H-3 / L (53%)
H-9 / L (68%)
H-1 /Lþ3 (20%)
H/ L (96%)
3
)
2
3 2 2
bpy,(PPh ) / (COOH)
c
Lþ3: Ru 22%, (PPh
3
)
)
2
73%
43%
Ru / (PPh
Ru / (PPh
3
)
)
2
2
H-1: Ru 54%; (PPh
3
2
3
3
3
49.6
28.5
0.08
0.08
H-3: (PPh
H-9: bpy 14%; (PPh
3
)
2
83%, Ru 12%
85%
Ru, (PPh
(PPh / dcbpy
Ru,(PPh / bpy
Ru, (PPh / dMebpy
3 2
) / dcbpy
3
)
2
3 2
)
3 2
)
RudMebpy
390
390.6
286.4
382.7
290.1
0.07
0.30
H: Ru 50%, (PPh
L: bpy 94%, (CH
H-1: (PPh
Lþ1: Ru 20%, (PPh
H-6: (PPh 34%, bpy 55%, Ru 9%
Lþ2: bpy 88%, (CH 1%
3
)
2
42%
2%
3 2
)
3 2
)
2
90c
H-1/ Lþ1 (46%)
3
)
2
46%, Ru 48%, bpy 8%
75%
3 2
Ru / (PPh )
3 2
)
2
2
95.5
87.1
0.24
0.17
0.13
0.06
H-6/ L (61%)
H-1/ Lþ2(36%)
H/ Lþ1 (64%)
H /Lþ2 (61%)
H-1 /Lþ2 (17%)
3
)
2
Ru, (PPh
Ru, (PPh
3
)
)
2
2
/ dMebpy
/ dMebpy
3 2
)
3
10c
328.3
3
c
Ru / (PPh
3
3 2
)
25.9c
Ru, (PPh ) / dMebpy
3 2
a
Experimental data for Rudcbpy, Rubpy, and RudMebpy from this work.
Calculated absorption.
Excitation observed at the shoulder.
b
c
Table 3.
0 1
Selected bond lengths (Å), bond angles (º), and torsion angles (º) optimized for complexes in S and T using TDDFT in ethanol except for Ru(2H)dcbpy where DSCF data are
reported.
Rubpy
Rudcbpy
B3LYP
Rudamidebpy
RudMebpy
B3LYP
Ru(2H)dcbpy
B3LYP
Ru(2CO)dcbpy
B3LYP
a
S
0
B3LYP
PBE0
B3LYP
PBE0
Ru-P1
Ru-P2
Ru-N1
Ru-N2
Ru-H
2.351
2.349
2.091
2.135
1.623
2.448
2.449
2.174
2.246
1.613
2.392
2.394
2.139
2.196
1.613
2.454
2.453
2.168
2.244
1.610
2.451
2.450
2.169
2.246
1.611
2.448
2.449
2.173
2.246
1.613
2.391
2.392
2.137
2.198
1.613
2.364
2.364
2.152
2.186
1.635,
2.561
2.560
2.160
2.161
1.652
Ru-C
1.816
1.861
1.852
1.865
1.864
1.862
1.852
1.918,
1.919
P1-Ru-P2
N1-Ru-N2
N1-C-C-N2
174.701
75.040
ꢀ2.869
170.034
74.733
0.181
168.952
75.579
0.616
168.954
74.858
ꢀ0.122
169.194
74.772
0.201
170.099
74.544
1.100
169.164
75.413
1.002
160.234
75.801
0.172
176.817
76.650
ꢀ0.112
T
1
Ru-P1
Ru-P2
Ru-N1
Ru-N2
Ru-H
2.414
2.402
2.102
2.097
1.635
2.445
2.518
2.140
2.161
1.627
2.440
2.521
2.137
2.153
1.628
2.408
2.404
2.101
2.089
1.636
2.406
2.406
2.219
2.218
1.604,
2.556
2.557
2.144
2.149
1.630
Ru-C
1.884
1.896
1.895
1.883
1.920,
1.923
P1-Ru-P2
N1-Ru-N2
N1-C-C-N2
142.144
78.876
ꢀ2.769
143.280
77.377
4.195
143.788
77.590
3.189
143.024
78.864
ꢀ2.046
169.175
74.716
0.114
178.093
77.505
ꢀ0.874
*
N1 is trans to CO and N2 is trans to H.
Experimental data taken from Ref. [36].
a
without any constraints and it was true minimum.
To assess solvent effects, we optimized the structure using
B3LYP first in vacuum and then applying the Onsager model [61].
accurately for the solute-solvent interaction [72]. In addition, the
absence of the dispersion correction in these methods affects the
conformation and stability of the system, particularly, the interac-
tion between the phenyl rings.
s
This procedure produced a minimum geometry with C symmetry.
The lower symmetry obtained when using the hybrid functionals
B3LYP, PBE0 and CAM-B3LYP, as described above, is due to the in-
tegral equation approach formalism model (PCM) not accounting
Regardless of the inability of B3LYP/PCM to adequately describe
the geometry of Rudcbpy, it reproduced the experimentally
observed absorption and emission energies at a relatively low

S. AlAbbad et al. / Journal of Molecular Structure 1195 (2019) 620e631
625
combination of Ru dyz
,
p
bpy, and
p
(PPh
3
). The calculations
showed that more than 80% of the electron density of the LUMO in
all ions has * character and is localized on the bpy rings bearing
p
the substituent with a fractional contribution from the Ru dxz
orbital (Fig. 6).
The changes in the relative energies of the frontier molecular
orbitals are based on the different mesomeric effects of the sub-
stituents and are plotted in Fig. 6. Introducing the electron with-
drawing substituents (-COOH), decreased the electron density and
stabilized the LUMO level; the energy is lower by 0.58 eV compared
to that of Rubpy. The weaker negative mesomeric behavior for
3 2
(-CONHCH ) groups also stabilized the LUMO but by 0.35 eV
compared to Rubpy. However, the electron releasing groups (-CH3)
destabilized the LUMO level by only 0.09 eV.
Fig. 5. Mean errors relative to experiment in the calculated Ru bond distances (pm) of
Rudcbpy.
3
.3.2. Trans influence
The following comparisons are made relative to Rudcbpy.
Replacing the carbonyl by hydride increased the
s donation
strength along x and y axes reducing the partial positive charge
over Ru (Table 4). Thus, the increase of the electron density in-
creases the electrostatic repulsion between Ru dx2-y2 orbitals and
the two hydride ions. The Ru-H bond lengths showed the largest
increase (~2.59 pm) compared to the other complexes. The HOMO
orbital is destabilized by 1.54 eV and is 95% Ru dxy. On the other
hand, the Ru-N and Ru-P bond lengths decreased by ~5.76 and
computational cost compared to other methods. Moreover, it has
been reported that the functionals that provide the most precise
geometries, M06-2X, underestimated the triplet gaps of Ru(II)
complexes [73]. With these considerations, we chose B3LYP/
LANL2DZ/6-31G*/PCM to evaluate the conformational changes
and photophysical properties computed for the other compounds.
~
9.02 pm, respectively, suggesting that introducing a s donor
3
3
.3. Ru coordination geometry and molecular orbital energies
ligand will push more electron density toward Ru, thereby
increasing back-bonding from Ru toward other ligands. Addition-
ally, we found that the MLCT band originates from the HOMO-1-
HOMO-2 orbitals, which have been both destabilized by ~1.82 eV.
The HOMO-1 and HOMO-2 orbitals have Ru dxz and dyz contribu-
.3.1. Substituent effects
In general, the deviations of the Ru-ligand bond lengths upon
introducing substituents in Rubpy are not significant (<1.00 pm, see
Table 3). The significant changes are in the electronic distributions
and orbital energies. The negative charges over the bpy and phenyl
rings decreased as the donor strength of the substituents decreased
and the positive charge on the Ru atom increased (Table 4). It
should be noted that the charges on the P atoms did not correlate
well with the expected trends of the substituents, (i.e., larger pos-
itive charge with electron-withdrawing substituents and larger
negative charge with electron-donating substituents). The positive
charge over the P atoms increased in the series: 1.71 e, 1.78 e, 1.80 e
for Rudcbpy, Rubpy, and RudMebpy, respectively.
tions (57%, and 83% respectively) with less
phenyl rings. In addition, the HOMO-1orbital has 17%
p
bonding from the
bonding
p
from dcbpy. The three lowest LUMOs, lying 2.53 eV above the
HOMO, are largely localized on the dcbpy, and have minor Ru dxz
and dyz character. Introducing hydride destabilized the LUMO by
0.64 eV and the charge on the bpy is more negative, ꢀ0.052 e
compared to the Rudcbpy.
Replacing the two hydride ions by two CO
in depopulation of the orbitals between the x and y axes (dxz and
yz), which stabilized the HOMO and LUMO by 0.65 and 0.63 eV,
p-acceptors resulted
d
In general, the atomic contributions to the molecular orbitals are
similar for Ru complexes with different substituents (Tables 2 and
respectively. Consequently, the contributions of the Ru dxz and dyz
to the HOMO orbital are significantly reduced and become smaller
(<10%). The major contribution to the HOMO up to HOMO-3 comes
4
, Fig. 6). In all complexes, more than 90% of the electron density
of the HOMO and HOMO-1 is delocalized between the Ru atom and
the (PPh groups. HOMO and HOMO-1 can be described as a
combination of the Ru dyz orbitals and the bonding orbitals of the
phenyl rings; one phenyl ring from each PPh ligand does not
contribute to the HOMO (Fig. 5). HOMO-2 is Ru dxy with no
from the bonding
p orbitals of the phenyl rings (89%). Introducing
3
)
2
the -acceptors and due to the dicationic nature of the Ru(2CO)
p
p
dcbpy complex, the positive partial charges on the Ru and both P
atoms increased, thereby reducing the back-bonding from Ru to-
ward P atoms, and the Ru-P bond length increased by ~10.0 p.m.
compared to Rudcbpy. The LUMO and LUMOþ1 are mainly
3
contribution from the phenyl rings, while HOMO-3 is
a
Table 4.
The change in the electron density distribution between optimized S
0 1
and T estimated by calculating the partial atomic charges e using QTAIM using B3LYP/LANL2DZ for
Rudcbpy, Rudamidebpy, Ru(2H)dcbpy, and Ru(2CO)dcbpy, and PBE0/LANL2DZ for Rubpy and RudMebpy.
Complex
S
0
T
1
Ru
bpy
Xbpya
2P
Ph
Ru
bpy
Xbpya
2P
Pha
Rubpy
Rudcbpy
Rudamidebpy
RudMebpy
Ru(2H)dcbpy
Ru(2CO)dcbpy
0.639
0.669
0.669
0.626
0.474
0.869
0.064
0.301
0.119
ꢀ0.011
0.123
0.365
e
3.549
3.412
3.411
3.601
3.339
3.461
ꢀ2.906
ꢀ2.764
ꢀ2.777
ꢀ2.969
ꢀ3.075
ꢀ2.418
0.795
0.838
0.845
0.806
0.625
0.885
ꢀ0.561
ꢀ0.197
ꢀ0.386
ꢀ0.573
ꢀ0.257
0.255
e
3.733
3.581
3.574
3.763
3.408
3.486
ꢀ2.722
ꢀ2.558
ꢀ2.583
ꢀ2.782
ꢀ2.972
ꢀ2.287
ꢀ0.386
0.661
0.289
ꢀ0.275
ꢀ0.020
ꢀ0.989
0.081
ꢀ0.353
ꢀ0.399
ꢀ0.067
a
X is the substituent and (Ph) is the phenyl rings for both ligands.

626
S. AlAbbad et al. / Journal of Molecular Structure 1195 (2019) 620e631
Fig. 6. HOMO and LUMO representations of the optimized ground states of the complexes calculated using B3LYP/LANL2DZ. Left: isodensity plots of the frontier orbitals of LUMO of
the complexes arranged as the energies increase along with schematic representation of LUMOs energies. Right: isodensity plots of the frontier orbitals of HOMO of the complexes
arranged as the energies increase along with schematic representation of HOMOs energies.
localized on the dcbpy with a contribution from the antibonding
p
p
*
*
2
CO, while LUMOþ2 has antibonding contribution from Ru d
z
,
phenyl rings, and * CO.
p
3.4. Calculated absorption spectra
TDDFT/B3LYP/LANL2DZ/PCM calculations were employed to
calculate the 22 lowest singlet-singlet transitions starting from the
geometry, optimized in ethanol. In all complexes, two maxima
S
0
are observed in the calculated absorption spectra (Figs. 3 and 7).
The results reveal that the lowest energy band (ꢂ390 nm) is due to
electronic transition from HOMO state to the LUMO state for all
complexes (see Tables 2 and 5). Thus, this band, which is in the
visible region of the spectrum, is the MLCT transition with a
3 2
contribution from (PPh ) that varies from 25% (Ru(2H)dcbpy) to
8
9% (Ru(2CO)dcbpy) (see Table 5). Most notably, our calculations
predicted a forbidden HOMO /LUMO transition in Ru(2H)dcbpy.
The MLCT band for this complex is due to transitions from lower
HOMOs (HOMO-1 to HOMO-3) to the lower LUMOs (LUMO to
LUMOþ3).
Fig. 7. The absorption spectra for the complexes calculated using B3LYP/LANL2DZ. The
intensities are optimized to the highest intensity for each complex.
near-UV region of the experimental spectra is composed of several
The next higher energy absorption maximum observed in the

S. AlAbbad et al. / Journal of Molecular Structure 1195 (2019) 620e631
627
Table 5.
Computed absorption, excitation and electronic transitions for theoretical complexes using B3LYP/LANL2DZ.
complex
l
abs (nm)
l
exit. (nm)
f
major contribution
% composition
character
Ru, (PPh
Rudamidebpy
428.1
420.8
297.2
0.09
H / L (95%)
H: Ru 45%; (PPh
L: bpy 86%; (CONHCH ) 9%
3 2
3
)
2
49%
3
)
2
/ damidebpy
3
20.1
0.19
0.13
0.07
0.07
H-17 / L (31%)
H-17:(PPh
CONHCH
Lþ3: (PPh
3
)
2
46%; bpy 42%;
(PPh ) ,(CONHCH ) / bpy
3 2 3 2
(
) 12%
3 2
3
3
3
24.3
16.9
10.5
H-1 / Lþ3 (17%)
H / Lþ3 (57%)
H-8/ L (27%)
3
)
2
74%; Ru 21%
Ru / (PPh
Ru / (PPh
3
)
)
2
2
H-1:Ru 52%; (PPh
H-8: (PPh 89%
Lþ2: damidebpy 96%
H-13: (CONHCH 41%;
PPh 55%
H-9: (PPh
CONHCH
3 2
) 44%
3
3
)
2
(PPh
Ru, (PPh )
3
)
2
/damidebpy
/ damidebpy
H / Lþ2 (37%)
3 2
H-13 / L (19%)
3
)
2
(PPh
3
3
)
2
2
,(CONHCH
3
)
2
/ bpy
(
3 2
)
H-9 / L (25%)
3
)
)
2
62%; bpy 19%;
17%
(PPh
)
,(CONHCH
3
)
2
/ bpy
(
3
2
3
26.8
0.06
0.20
0.14
0.11
H/ Lþ1 (76%)
3 2
Ru, (PPh ) / damidebpy
Ru(2H)dcbpy
454.6
502.6
H-1 /Lþ1 (97%)
H-1 /Lþ2 (77%)
H-2 /Lþ1 (75%)
H-1: (PPh
3
)
2
25%, Ru 57%, bpy 17%
Ru,(PPh
Ru,(PPh
Ru,(PPh
3
)
2
)
2
)
2
/ dcbpy
/ dcbpy
/ dcbpy
4
4
44.0
57.5
Lþ1: bpy 82%, (COOH)
Lþ2: bpy 93%, (COOH)
2
2
16%
4%
3
3
3 2
H-2: (PPh ) 11%, Ru 83%
5
76.3
0.18
H-1 /L (67%)
Lþ1: bpy 78%, (COOH)
Lþ3: (PPh 91%, Ru 8%
H: Ru 10%, (PPh
2
8%
Ru,(PPh
3
)
2
/ dcbpy
3
57.1
436.0
32.8
360.8
55.2
0.23
0.12
0.34
H-1 /Lþ3 (83%)
H-1 /Lþ3 (83%)
H/ L (99%)
3
)
2
Ru / (PPh
Ru,(PPh / dcbpy
(PPh / (2CO), Ru
3 2
)
3
Ru(2CO)dcbpy
428.5
3
)
2
89%
L: bpy 87%, (COOH) 7%
55%
3 2
)
2
3
341.5
0.99
0.58
H/ Lþ2 (91%)
H/ Lþ2 (92%)
Lþ2: Ru 36%, (PPh
3
)
2
3 2
)
331.9
(2CO) 5%
overlapping bands that are not well resolved (Fig. 3). The calcula-
tions show that these are the intra-ligand * and n- * electronic
transitions of PPh and bpy with the substituents that occur in the
same region. This band is due to excitation either from lower HO-
MOs to LUMO or from HOMO to higher LUMOs (Tables 2 and 5).
Moreover, the calculations reveal that the low-energy side of this
band, which ranges from 300 to 330 nm (Tables 2 and 5), includes
can be studied further by applying combined quantum mechanics/
molecular mechanics (QM/MM) methods.
p
-p
p
3
We also computed the UV/Visible absorption spectra for
Rudcbpy using M06/LANL2DZ and CAM-B3LYP/LANL2DZ (Fig. S3).
Overall, all methods predicted similar shapes for the optical
spectra, and the atomic orbital contributions involved in the exci-
tations. B3LYP and M06 provided comparable excitation energies.
However, a large blue-shift is observed with TDDFT/CAM-B3LYP
(>100 nm). This overestimate of the HOMO-LUMO energy gap
when using CAM-B3LYP combined with PCM has been observed for
other Ru(II) systems [75].
3
MLCT transitions from Ru to both PPh and bpy for all complexes
except Ru(2H)dcbpy and Ru(2CO)dcbpy. The appearance of an
additional near-UV MLCT band (300e350 nm) has also been
observed for other Ru (II) systems [74]. To confirm the theoretical
findings, excitation spectra were measured over the range
3
00e500 nm, and electronic transitions that correspond to the
3.4.1. Substituent effects
predicted MLCT transitions were observed. The molecular orbital
contributions and maxima of the computed absorption spectra and
electronic transitions compared with the corresponding experi-
mental data are listed in Tables 2 and 5. The computational results
agree well with the overall features of the experimentally deter-
mined absorption spectra of Rubpy and RudMebpy (Figs. 3 and 7).
The calculated MLCT band of Rudcbpy is red shifted by ~28 nm
compared with the experimental absorption spectrum which has a
maximum at 422 nm. It should be noted that the calculation does
not take into account the possibility of hydrogen bond formation
with solvent molecules. However, we anticipated that hydrogen
bonding will affect the molecular orbital energies in the Rudcbpy
compared to Rubpy and RudMebpy because of the solvent inter-
action with the carboxylic groups. To test this hypothesis, we
modeled a system with four explicit methanol molecules with their
hydroxyl groups interacting with the carboxylic groups of Rudcbpy.
This interaction elongated the O-H bond length of the -COOH
The shift in the MLCT bands correlated well with the changes in
the conformational and MO energies described above. In the
experimental data, the MLCT band of Rudcbpy was red shifted by
2
2 nm when compared to Rubpy, whereas the MLCT band of Rud-
Mebpy was blue shifted by 14 nm (Fig. 3). The computations using
the continuum model predicted the same trends but different
magnitudes for the shifts. The MLCT band of the Rudcbpy was red
shifted by 60 nm when compared to Rubpy. Converting -COOH to
CONHCH resulted in a smaller red shift of 33 nm, whereas the
3
MLCT band of RudMebpy was blue shifted by 4 nm (Fig. 7).
-
3.4.2. Trans influence
Calculations show that the carbonyl groups in the Ru(2CO)dcbpy
stabilize both HOMO and LUMO, but the overall energy gap in-
creases resulting in a 19 nm blue shift of the MLCT band when
compared to Rudcbpy. In addition, in Ru(2CO)dcbpy, the intra-
ꢁ
groups by 3.70 pm and rotated the eCOOH by ~15 with respect to
the plane of the bpy ring. In addition, the LUMO orbital was
destabilized by 0.10 eV, which blue shifted the MLCT band ~9 nm.
dcbpy
p-
p* transitions are weak while strong electronic excita-
tions from PPh
3
to Ru and CO are observed in the higher energy
bands. Replacing the two carbonyls with hydrides destabilizes all
occupied orbitals and moreover decreases the energy gap causing a
red shift in the MLCT. Interestingly, this band has greater intensity
and is much broader than the MLCT bands of the other complexes.
This is because it is characterized by a larger (97%) weight from a
transition involving HOMO-1 and LUMOþ1with a significant
contribution of orbitals both localized on the bpy ligand (17% and
We then explored the possible effect of the counterion on the
ꢀ
computational results by including PF
6
with the methanol mole-
cules, and the MLCT band was further blue shifted by another
3 nm (Fig. S2). The calculated shift suggests the role of the solvent
and counterion in controlling the HOMO-LUMO energy gap which
1

628
S. AlAbbad et al. / Journal of Molecular Structure 1195 (2019) 620e631
8
2%, respectively). This composition enhances the transition dipole
and also causes a large bathochromic shift in excitation when
compared to the excitation of the other complexes. Notably, it has a
high intensity peak at 455 nm and shoulder at 576 nm.
3.5. Triplet excited-state geometries
The T
1
state geometry was optimized for Rudcbpy using TDDFT/
SCF) with combinations of LANL2DZ,
B3LYP and UKS/B3LYP (
D
Fig. 9. Overlaying S
0 1
and T calculated using B3LYB/UB3LYP, respectively, for Rudcbpy
LANL2DZ(f), and LANL2DZ(f,d), CAM-B3LYP/LANL2DZ, M06/
LANL2DZ, and M06/SDD (Table S6). The corresponding TDDFT and
(left) and Ru(2CO)dcbpy (right).
D
SCF calculations characterized the optimized geometry as a
3
MLCT state. Furthermore, the analysis of the T
showed that the highest singly occupied molecular orbital
HSOMO) centered on the bpy (Fig. 8). To quantify the geometric
changes, we calculated the root-mean-square deviation (RMSD) of
compared to S using the method of Kabsch as implemented in
1
molecular orbital
However, different approaches were required to minimize T1 ge-
ometries of the other complexes. For example, when optimizing
(
Ru(2H)dcbpy T state, TDDFT/B3LYP produced oscillatory minima.
1
This is due to a small HOMO-LUMO gap that caused the states to
T
1
0
cross during the optimization. By using UKS/B3LYP, optimization
was achieved. However, this approach was inadequate for Rubpy
and RudMebpy. Minimization of these complexes was achieved
the Visual Molecular Dynamics (VMD) program [76] (Table S6). All
methods yielded similar pattern of geometric parameter changes in
T
1
using both
DSCF and TDDFT. For example, the difference in the
using the PBE0 level of theory with DSCF and TDDFT. The calculated
RMSD between
B3LYP gave the higher deviation.
Upon excitation, the symmetry and planarity between Ru and
the other ligands are broken and the bpy rings are twisted. The
most significant change is reduction in the bend observed in the P1-
D
SCF and TDDFT is in the range 0.001e0.239; CAM-
RMSD for all minimized geometries correlated well with HOMO-
LUMO gap d the larger energy gap in S0 is accompanied by less
distortion and smaller RMSD in T . The changes between the S and
1
0
optimized T1 geometries, due to the substituent effects and the
trans influence, were evaluated comparing SCF with TDDFT
(Table 3). A comparison of selected parameters, emission energies,
D
ꢁ
Ru-P2 angle for all complexes (24.66e32.25 ). This reduction is
asymmetric and is accompanied by an increase in the distance
between the phenyl rings and bpy, which likely reduces the steric
and RMSD using
Table S7.
DSCF and TDDFT for all complexes is in Fig. 10 and
crowding that could arise from an increase in the p*-LUMO orbital
population on bpy. N1 is trans to CO and N2 is trans to H. Both Ru-N
bonds lengths decrease, but because of the trans influence, Ru-N2
3.5.1. Substituent effects
The T of RudMebpy, which has the largest energy gap, showed
1
decreases the most. The increase of the Ru-P bond length in the
the smaller RMSD while Rudcbpy had the larger RMSD (Fig. 10). As
3
MLCT state, which is observed when using
DSCF with all levels of
explained above for Rudcbpy, the changes in the Ru-ligand bond
lengths for the different substituents show similar trends. Specif-
ically, increases in the Ru-P bond lengths were observed for all
complexes except for one Ru-P bond in Rudamidebpy, and Ru-N
bond lengths decreased with RudMebpy having the shortest Ru-N
bond lengths. This reduction in the Ru-N bond is associated with
greater localization of the electron density on the N atoms
compared to other complexes for which the electron density is
distributed over the entire bpy ring. On the other hand, Ru-H and
Ru-CO bonds lengths in all complexes increased. Moreover, as a
theory, is due to the depopulation of the HOMO orbitals and
reduction of the bond strength. However, the optimized T by
1
TDDFT/B3LYP and TDDFT/CAM-B3LYP predicted an increase of only
one Ru-P bond length. Regardless of the method used, accompa-
nying the electron migration from Ru and PPh to the bpy, there is
3
an overall reduction in CPRu angles and increase in CPC angles. The
changes in the phenyl ring twist angles (Fig. 9) are presumably due
to decreased repulsion between rings that occurs upon electron
ꢁ
migration. The largest twist (30.05 ) is observed for the phenyl
rings that do not contribute to the HOMO.
result of the electron migration, the Ru and PPh charges became
3
The T
1
geometries for Rudamidebpy and Ru(2CO)dcbpy were
more positive. The positive charge on Ru increased the most in the
minimized successfully using TDDFT/B3LYP and UKS/B3LYP.
RudMebpy complex, indicating that more electron density moves
toward bpy. This unexpected trend of increased positive charge on
Ru in T
1
when in the presence of an electron-donating group has
0
been noted previously in platinum(II) biphenyl 2,2 -bipyridine
complexes, where Pt was found to have the largest positive charge
upon binding the strongest electron-donating group (-NH
2
) [25].
Finally, in T , the same change in the relative rotation of the phenyl
1
ꢁ
rings was observed for all complexes, the largest twist being ~41 in
RudMebpy.
3.5.2. Trans influence
1 0 1
The Ru(2H)dcbpy has the smallest S ) S energy gap and its T
shows the largest distortion. By contrast, Ru(2CO)dcbpy has the
largest S ) S energy gap and its T shows the smallest distortion
Fig. 10). The variations in the Ru-ligand bond lengths in T with
respect to S of the two complexes had opposite trends. While the
1
0
1
(
1
0
Ru-P and Ru-N bond lengths increased in Ru(2H)dcbpy, both bond
types decreased in Ru(2CO)dcbpy. In addition, the Ru-CO bond
increased in Ru(2CO)dcbpy while the Ru-H bond length decreased
in Ru(2H)dcbpy (Table 3). There was no change in either the P-Ru-P
1
Fig. 8. HSOMO representation of the T for Rudcbpy derivatives.

S. AlAbbad et al. / Journal of Molecular Structure 1195 (2019) 620e631
629
Fig. 10. The calculated RMSD of T
1
compared to the HOMO-LUMO energy gap for the complexes with respect to the substitutions using TDDFT (a), and trans influence using
D
SCF
(
b). The calculated emission energies using TDDFT compared to the HOMO-LUMO energy gap for the complexes with respect to the substitutions (c), and trans influence using D
SCF
(
d).
bond angle or phenyl ring twist angles in Ru(2CO)dcbpy, while the
ꢁ
P-Ru-P bond angle increased by 9 and the phenyl ring twist angle
ꢁ
changed by 18 in Ru(2H)dcbpy.
3.6. Excitation and emission energies
The
the emission energies, as explained previously. To assess the quality
of the DFT models of the T for Rudcbpy, we compared the exper-
DSCF approach (
1 0
DE ¼ E (T ) - E (S )) was used to calculate
1
imental and calculated emission energies using different methods,
as explained above. In general, including the zero-point energy
vibrational correction yielded emission energies that agreed well
with experiment. We further noted that the emission energies
obtained by TDDFT are comparable to those from
DSCF, and both
B3LYP and M06 provided similar emission energies (Fig. 11). In
addition, CAM-B3LYP overestimated the emission energy (2.36 eV
or 525 nm) when compared to B3LYP (1.94 eV or 639 nm), the latter
which predicted an energy more similar to the experimental value
of 2.04 eV (609 nm). On this basis, we concluded that B3LYP/
1 0 1
Fig. 11. The calculated energy of the optimized T and S at T using different methods
for Rudcbpy.
their relative order (including the parent compound), but not the
absolute energies observed experimentally (Fig. 3), where the
maximum of RudMebpy emission is at 563 nm while that of
Rudcbpy is at 609 nm.
LANL2DZ predicted a reasonable T
set size by adding f and then f,d-polarization functions neither
improved the description of S , as explained earlier, nor the pre-
diction of the T emission energy (Fig. 11).
1
. Moreover, increasing the basis
0
1
Experimentally, the observed Stokes shift is largely determined
The calculated emission energies for Rubpy and RudMebpy us-
ing TDDFT/PBE0/LANL2DZ were also overestimated (2.35 eV
1 1
by the Coulomb energy difference between S and T as well as
contributions from radiationless processes such as vibrational
relaxation with higher quantum yield. Theoretically, we are relating
(
528 nm) and 2.41 eV (514 nm), respectively) compared to the
experimental values (2.09 eV (593 nm) and 2.20 eV (563 nm),
respectively). Nevertheless, all complexes showed the expected
shift that correlated with the HOMO-LUMO gap (Fig. 10). The trend
in the Stokes shifts calculated for the two complexes reproduced
the radiationless processes to the amount of distortion of the T
1
(RMSD). The system that undergoes minimal conformational
reorganization between the two states will emit higher energy
photons. Our calculations estimated Stokes shifts that agreed well

630
S. AlAbbad et al. / Journal of Molecular Structure 1195 (2019) 620e631
with the calculated energy gap and RMSD (Fig. 10). To estimate the
Stokes shift, the molecular orbital energies of each complex were
calculated using the same level of theory at which the emission
energy has been calculated. Because Ru(2H)dcbpy has the smallest
HOMO-LUMO gap compared to Rudcbpy and Ru(2CO)dcbpy, its
emission spectra was shifted to the far infrared (0.88 eV or
Acknowledgements
This work used the Extreme Science and Engineering Discovery
Environment (XSEDE) resource Comet, at the San Diego Super-
computer Center (SDSC) through allocation TG-CHE160010 [80],
supported by the National Science Foundation (ACI-1548562).
Support was also provided by the Molecular Computational Core
Facility, the Macromolecular X-ray Diffraction Core Facility, and the
BioSpectroscopy Core Research Laboratory at the University of
Montana, which all are operated with funds from National In-
stitutes of Health Centers of Biomedical Research Excellence
(CoBRE) Award P20GM103546 to the Center for Biomolecular
Structure and Dynamics and from the University of Montana Vice
President for Research and Creative Scholarship. We also
acknowledge support from National Science Foundation award
(NSF)-MRI CHE-1337908. S. A. acknowledges financial support from
Imam Abdulrahman Bin Faisal University, Saudi Arabia. Finally, we
appreciate that one of the reviewers pointed out a discrepancy
between the electronic spectra of Rudcbpy previously reported [36]
and those we report, which we addressed in the revision.
1409 nm). Comparing complexes with different substituents, the
emission energy was increasingly red shifted with decreasing the
electron-donor strength: RudMebpy (2.41 eV or 514 nm), Rubpy
(
2.35 eV or 528 nm), Rudamidebpy (2.13 eV or 582 nm), and
Rudcbpy (1.94 eV or 639 nm) (Fig. 10). The shifts observed in the
emission spectra of other Ru systems constructed from imidazole,
phenanthroline, and other derivatives with various ligands, are in
accord with our calculations [25e27,77,78]. Furthermore, based on
1
the energy gap law, the rate of the radiationless decay of T will
increase as the energy gap between the two states decreases [79].
Consequently, we predict that Ru(2H)dcbpy should exhibit the
shorter triplet decay time.
4
. Conclusion
Appendix A. Supplementary data
The structural, HOMO-LUMO gap, and spectroscopic properties
of the ground-state singlet and lowest lying triplet excited states of
Supplementary data to this article can be found online at
https://doi.org/10.1016/j.molstruc.2019.06.005.
derivatives of Ru(bpy)(PPh
3
)
2
with different electron-withdrawing
-donor and -acceptor ligands trans
and donor substituents and
s
p
to the bpy have been investigated by combined DFT/TDDFT calcu-
lations. The statistical measurements of the performance of ten
References
combinations DFT/basis sets used to describe S
0
geometry for [(H)
[
[
[
1] J.R. Lakowicz, Principles of Fluorescence Spectroscopy, third ed., Springer,
New York, 2006.
2] B.-Z. Shan, Q. Zhao, N. Goswami, D.M. Eichorn, D.P. Rillema, Coord. Chem. Rev.
þ
Ru(CO)(PPh
scheme and
B2PLYPD3) > meta-hybrid (M06) > hybrid-GGA (PBE0, B3LYP,
3
)
2
(dcbpy)] , followed the ‘Jacobs ladder’ classification
decreased
in
the
series
double-hybrid
211 (2001) 117.
(
3] D.J. Stufkens, A. Vleek, Coord. Chem. Rev. 177 (1998) 127.
CAM-B3LYP, wB79xD) [70]. The PBE0/LANL2DZ performance was
superior compared to that of B3LYP/LANL2DZ. To accurately assess
the symmetry of these systems, it is essential to use methods that
include the dispersion correction. Although B3LYP did not produce
the most accurate geometry for the ground state, it reproduced well
the experimental singlet absorption and triplet emission energies,
which suggests that it will likely yield reliable predictions for the
spectroscopy of other complexes. Also, we have shown with
Rudcbpy that when solvent and counterions are included, the
calculated excitation energies are closer to those observed in the
experimental spectra.
[4] E. Terpetschnig, H.M. Szmacinski, J.R. Lakowicz, Biophysics 68 (1995) 342.
[
[
[
5] A. Hagfeldt, M. Gratzel, Acc. Chem. Res. 33 (2000) 269.
6] A.P. Doherty, M.A. Stanley, D. Leech, J.G. Vos, Anal. Chim. Acta 319 (1996) 111.
7] J.N. Demas, B.A. DeGraff, J Chem. Educ. 74 (1997) 690.
[8] J.K. Barton, A.T. Danishefsky, J.M. Goldberg, J. Am. Chem. Soc. 106 (1984) 2172.
[
9] V. Balzani, C. Alberto, M. Venturi, Nano Today 2 (2007) 18.
[
[
10] M. Gr €a tzel, Nature 414 (2001) 338.
11] Md.K. Nazeeruddin, P. Pechy, T. Renouard, S.M. Zakeeruddin, R. Humphry-
Baker, P. Comte, P. Liska, L. Cevey, E. Costa, V. Shklover, L. Spiccia, G.B. Deacon,
C.A. Bignozzi, M. Gr a€ tzel, J. Am. Chem. Soc. 123 (2001) 1613.
[
12] S.M. Zakeeruddin, Md.K. Nazeeruddin, R. Humphry-Baker, P. P eꢁ chy,
P. Quagliotto, C. Barolo, G. Viscardi, M. Gr €a tzel, Langmuir 18 (2002) 952.
[13] L. Salvi, A. Salvini, F. Micoli, C. Bianchini, W.J. Oberhauser, Organomet. Chem.
692 (2007) 1442.
14] L.C. Po, N.S. Man, G. Jia, Z. Lin, Coord. Chem. Rev. 251 (2007) 2223.
15] Y.C. Jun, Y. Liu, R.J. He, Mol Catal A: Chem. 259 (2006) 17.
16] N.F. Haque, A.J. Lough, R.H. Morris, Inorg. Chim. Acta 361 (2008) 3149.
[17] P. Buskens, D. Giunta, W. Leitner, Inorg. Chim. Acta 357 (2004) 1969.
18] A. Juris, V. Balzani, F. Barigelletti, S. Campagna, P. Belser, A.V. Zelewsky, Coord.
Chem. Rev. 84 (1988) 85.
19] M.A. Haga, M.M. Ali, S. Koseki, K. Fujimoto, A. Yoshimura, K. Nozaki, T. Ohno,
K. Nakajima, D.J. Stufkens, Inorg. Chem. 35 (1996) 3335.
20] R. Gobetto, G. Caputo, C. Garino, S. Ghiani, C. Nervi, L. Salassa, E. Rosenberg,
J.B.A. Ross, G. Viscardi, G. Martra, I. Miletto, M. Milanesio, Eur. J. Inorg. Chem.
[
[
[
The calculations showed that introducing electron-withdrawing
groups stabilizes the bpy
emission spectra to lower energies, and increases the distortion in
the T geometry. The opposite was observed with electron-
donating substituents. The bpy * LUMOs were destabilized, the
absorption and emission spectra shifted to higher energies, and
there was less distortion in the T geometry. In addition, when the
two ligands trans to bpy are strong -donors, the calculated T is
much closer to S , which predicts an unusually red-shifted lumi-
p* LUMOs, shifts the absorption and
[
[
[
1
p
1
s
1
(
2006) 2839.
[21] H. Xia, C. Zhang, X. Liu, S. Qiu, P. Lu, F. Shen, J. Zhang, I. Ma, J. Phys. Chem. B
08 (2004) 3185.
22] Y. Zhang, Z. Liu, K. Yang, Y. Zhang, Y. Xu, H. Li, C. Wang, A. Lu, S. Sun, Sci. Rep.
2015) 5.
0
1
nescence and potentially lower quantum yield. This suggests that to
generate complexes with less red-shifted emission and higher
quantum yields, it is desirable to use weaker electron donors such
[
(
[23] K. Teegardin, J.I. Day, J. Chan, J. Weaver, Org. Process Res. Dev. 20 (2016) 1156.
[24] P.-T. Chou, Y. Chi, M.-W. Chung, C.-C. Lin, Coord. Chem. Rev. 255 (2011) 2653.
25] D.P. Rillema, S.R. Stoyanov, A.J. Cruz, H. Nguyen, C. Moore, W. Huang, K. Siam,
A. Jehan, V. KomReddy, Dalton Trans. 44 (2015) 17075.
[26] J. Frey, B.F.E. Curchod, R. Scopelliti, I. Tavernelli, U. Rothlisberger,
M.K. Nazeeruddin, E. Baranoff, Dalton Trans. 43 (2014) 5667.
as halogens or better
p acceptors.
[
In this computational study, we have examined relationships
between the HOMO-LUMO energy gap and the photophysical
properties for three synthesized and three proposed Ru (II) com-
plexes. In all cases, we observed a general trend: increased HOMO-
LUMO energy gaps correlate with a blue shift in both the excitation
[
[
27] X. Zarate, E. Schott, T. Gomez, R.J. Arratia-Perez, Phys. Chem. 117 (2013) 430.
28] C. Barolo, M.K. Nazeeruddin, S. Fantacci, D.D. Censo, P. Comte, P. Liska,
G. Viscard, P. Quagliotto, F.D. Angelis, S. Ito, M. Graltzel, Inorg. Chem. 45
(2006) 4642.
€
1
and emission energies and less geometric distortion in T . This
[
[
[
29] E. Ronca, F.D. Angelis, S. Fantacci, J. Phys. Chem. C 118 (2014) 17067.
30] A. Pidcock, R.E. Richards, L.M. Venanzi, J. Chem. Soc. A (1966) 1707.
31] P.K. Sajith, C.H. Suresh, Dalton Trans. 39 (2010) 815.
correlation and the computational approach outlined here can be
used to design complexes rationally and screen other organome-
tallic candidates that may have desirable excited-state properties.
[32] A.E. Anastasi, R.J. Deeth, Chem. Theory Comput. 5 (2009) 2339.

S. AlAbbad et al. / Journal of Molecular Structure 1195 (2019) 620e631
631
[
[
33] P.N. Kapoor, R. Kakkar, Theor. Chem. 679 (2004) 149.
34] J. Kuta, J. Wuerges, L. Randaccio, P.M. Kozlowski, J. Phys. Chem. 113 (2009)
1604.
35] L. Rigamonti, A. Forni, M. Manassero, C. Manassero, A. Pasini, Inorg. Chem. 49
2010) 123.
[58] M. Swart, J.G. Snijders, Theor. Chem. Acc. 110 (2003) 34.
[59] S. Miertu ꢂs , E. Scrocco, J. Tomasi, Chem. Phys. 55 (1981) 117.
1
[60] G. Scalmani, M.J. Frisch, J. Chem. Phys. 132 (2010) 114110.
[61] L. Onsager, J. Am. Chem. Soc. 58 (1936) 1486.
[62] E. Runge, E.K.U. Gross, Phys. Rev. Lett. 52 (1984) 997.
[63] N.M. O'Boyle, A.L. Tenderholt, K.M. Langner, J. Comput. Chem. 29 (2008) 839.
[64] T. Ziegler, A. Rauk, E. Baerends, Theor. Chim. Acta 43 (1977) 261.
[65] C. Daul, Int. J. Quantum Chem. 52 (1994) 867.
[
[
[
(
36] A. Sharmin, R.C. Darlington, K.I. Hardcastle, M. Ravera, E. Rosenberg,
J.B.A. Ross, J. Organomet. Chem. 694 (2009) 988.
37] A. Sharmin, L. Salassa, E. Rosenberg, J.B.A. Ross, J.A. Abbott, L. Black
M. Terwilliger, R. Brooks, Inorg. Chem. 52 (2013) 10835.
[66] M.J. Frisch, G.W. Trucks, H.B. Schlegel, G.
E Scuseria, M.A. Robb,
[
[
38] J.G. Malecki, A. Maro nꢁ , Trans. Met. Chem. 37 (2012) 727.
J.R. Cheeseman, G. Scalmani, V. Barone, G.A. Petersson, H. Nakatsuji, X. Li,
M. Caricato, A.V. Marenich, J. Bloino, B.G. Janesko, R. Gomperts, B. Mennucci,
H.P. Hratchian, J.V. Ortiz, A.F. Izmaylov, J.L. Sonnenberg, D. Williams-Young,
F. Ding, F. Lipparini, F. Egidi, J. Goings, B. Peng, A. Petrone, T. Henderson,
D. Ranasinghe, V.G. Zakrzewski, J. Gao, N. Rega, G. Zheng, W. Liang, M. Hada,
M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda,
O. Kitao, H. Nakai, T. Vreven, K. Throssell, J.A. Montgomery Jr., J.E. Peralta,
F. Ogliaro, M.J. Bearpark, J.J. Heyd, E.N. Brothers, K.N. Kudin, V.N. Staroverov,
T.A. Keith, R. Kobayashi, J. Normand, K. Raghavachari, A.P. Rendell, J.C. Burant,
S.S. Iyengar, J. Tomasi, M. Cossi, J. Millam, M. Klene, C. Adamo, R. Cammi,
J.W. Ochterski, R.L. Martin, K. Morokuma, O. Farkas, J.B. Foresman, D.J. Fox,
Gaussian 16, Revision A.03, Gaussian, Inc., Wallingford CT, 2016.
[67] A.E. Reed, L.A. Curtiss, F. Weinhold, Chem. Rev. 88 (1988) 899.
[68] R.F.W. Bader, Atoms in MoleculesdA Quantum Theory, Oxford University
Press, Oxford, UK, 1990.
39] G.M. Sheldrick, G.M., SADABS: Area Detector Absorption Correction, Univer-
sity of G o€ ttingen, Germany, 1996.
[40] O.V. Dolomanov, L.J. Bourhis, R.J. Gildea, J.A.K. Howard, H. Puschmann, J. Appl.
Crystallogr. 42 (2009) 339.
[
[
[
[
[
[
[
[
[
[
[
[
41] G.M. Sheldrick, Acta Crystallogr. A71 (2015) 3.
42] G.M. Sheldrick, Acta Crystallogr. C71 (2015) 3.
43] A.L. Spek, Acta Crystallogr. C71 (2015) 9.
44] A.L. Spek, Acta Crystallogr. D65 (2009) 148.
45] Bruker, APEX2, Bruker AXS Inc., Madison, Wisconsin, USA, 2007.
46] G.M. Sheldrick, Acta Crystallogr. A64 (2008) 112.
47] C. Lee, W. Yang, R.G. Parr, Phys. Rev. B 37 (1988) 785.
48] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865.
49] T. Yanai, D.P. Tew, N.C. Handy, Chem. Phys. Lett. 393 (2004) 57.
50] Y. Zhao, D.G. Truhlar, Theor. Chem. Account. 120 (2008) 215.
51] Y. Zhanga, X. Xua, W.A. Goddard, Proc. Natl. Acad. Sci. U.S.A. 106 (2009) 4963.
52] Y. Minenkov, A. Singstad, G. Occhipinti, V.R. Jensen, Dalton Trans. 41 (2012)
[69] AIMAll (Version 16.01.09), Todd A. Keith, TK Gristmill Software, Overland Park
KS, USA, 2016 (aim.tkgristmill.com).
5
526.
[70] J.P. Perdew, K. Schmidt, in: V. Van Doren, C. Van Alsenoy, P. Geerlings (Eds.),
Density Functional Theory and its Application to Materials, AIP, Melville, NY,
2001.
[
53] M.J. Frisch, G.W. Trucks, H.B. Schlegel, G.
E Scuseria, M.A. Robb,
J.R. Cheeseman, G. Scalmani, V. Barone, B. Mennucci, G.A. Petersson,
H. Nakatsuji, M. Caricato, X. Li, H.P. Hratchian, A.F. Izmaylov, J. Bloino,
G. Zheng, J.L. Sonnenberg, M. Hada, M. Ehara, K. Toyota, R. Fukuda,
J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, T. Vreven,
J.A. Montgomery, J. E Peralta, F. Ogliaro, M. Bearpark, J.J. Heyd, E. Brothers,
K.N. Kudin, V.N. Staroverov, R. Kobayashi, J. Normand, K. Raghavachari,
A. Rendell, J.C. Burant, S.S. Iyengar, J. Tomasi, M. Cossi, N. Rega, J.M. Millam,
M. Klene, J.E. Knox, J.B. Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts,
R.E. Stratmann, O. Yazyev, A.J. Austin, R. Cammi, C. Pomelli, J.W. Ochterski,
R.L. Martin, K. Morokuma, V.G. Zakrzewski, G.A. Voth, P. Salvador,
J.J. Dannenberg, S. Dapprich, A.D. Daniels, O. Farkas, J.B. Foresman, J.V. Ortiz,
J. Cioslowski, D.J. Fox, Gaussian 09, Revision D. 01, Gaussian, Inc., Wallingford
CT, 2013.
[71] D. Coskun, S.V. Jerome, R.A. Friesner, J. Chem. Theory Comput. 12 (2016) 1121.
[72] E. Canc eꢀ s, B.J. Mennucci, Math. Chem. 23 (1998) 309.
[73] A.J. Atkins, F. Talotta, L. Freitag, M. Boggio-Pasqua, L. Gonz aꢁ lez, J. Chem. Theory
Comput. 13 (2017) 4123.
[74] D.W. Thompson, A. Ito, T.J. Meyer, Pure Appl. Chem. 85 (2013) 1257.
[75] G.R. Freeman, J.A.G. Williams, Density functional theory in the design of or-
ganometallics for energy conversion, in: W.Y. Wong (Ed.), Organometallics
and Related Molecules for Energy Conversion. Green Chemistry and Sus-
tainable Technology, Springer, Berlin, Heidelberg, 2015.
[76] W. Humphrey, A. Dalke, K.J. Schulten, Molec. Graphics 4 (1996) 33.
[77] A. Islam, H. Sugihara, L.P. Singh, K. Hara, R. Katoh, Y. Nagawa, M. Yanagida,
Y. Takahashi, S. Murata, H. Arakawa, Inorg. Chim. Acta 322 (2001) 7.
[78] P. Datta, D. Sardar, R. Saha, T.K. Mondal, C. Sinha, Polyhedron 53 (2013) 193.
[79] R. Englman, J. Jortner, Mol. Phys. 18 (1970) 145.
[
[
54] P.J. Hay, W.R.J. Wadt, Chem. Phys. 82 (1985) 299.
55] D. Andrae, U. Haussermann, M. Dolg, H. Stoll, H. Preuss, Theor. Chim. Acta 77
(
1990) 123.
[80] John Towns, Timothy Cockerill, Maytal Dahan, Ian Foster, Gaither Kelly,
Andrew Grimshaw, Victor Hazlewood, Lathrop Scott, Dave Lifka, Gregory
D. Peterson, Ralph Roskies, J. Ray Scott, Nancy wilkins-diehr, "XSEDE: accel-
erating scientific Discovery, Comput. Sci. Eng. 16 (5) (2014) 62e74, https://
doi.org/10.1109/MCSE.2014.80. Sept.-Oct.
[
[
56] A.W. Ehlers, M. Bohme, S. Dapprich, A. Gobbi, A. Hollwarth, V. Jonas,
F.K. Kohler, R. Stegmann, A. Veldkamp, G. Frenking, Chem. Phys. Lett. 208
(
1993) 111.
57] C.E. Check, T.O. Faust, J.M. Bailey, B.J. Wright, T.M. Gilbert, L.S.L. Sunderlin,
Phys. Chem. 105 (2001) 8111.