We report the electronic spectrum of the prototypical ruthenium coordination complex Ru(bpy)32+ (bpy = 2, 2′-bipyridine) by messenger tagging with N2 in a cryogenic ion trap and photodissociation spectroscopy of mass selected Ru(bpy)32+ ⋅ N2 ions. We observe individual electronic bands and groups of bands with unprecedented detail, particularly in the usually unresolved metal-to-ligand charge transfer region of the spectrum. By comparing our experimental results with time-dependent density functional theory, both with and without spin-orbit interaction [Heully et al., J. Chem. Phys. 131, 184308 (2009)], we are able to assign the spectrum of the isolated ion.

Ruthenium polypyridine complexes constitute an important group of organometallic compounds with many applications, from light harvesting dyes to redox catalysts.1–6 Arguably the most prototypical complex in this group is the Ru(bpy)32+ ion (Figure 1). The ground state of this ion is a singlet state with D3 symmetry. Its absorption spectrum shows several pronounced bands that have been attributed to metal-to-ligand charge transfer (MLCT) states in the visible, followed by weak bands of metal centered or MLCT character in the near UV and ligand centered π–π* transitions at higher energies.7,8 In room temperature solutions, these transitions are very broad, mostly featureless peaks, and it is expected that these bands are composed of several unresolved electronic transitions. The visible spectral region in aqueous solution at room temperature shows two partially resolved peaks at ca. 431 nm (23 200 cm−1) and 452 nm (22 100 cm−1). In the spectra of crystals at cryogenic temperatures, these bands are sharper, but interaction with the crystal lattice shifts the spectrum.9,10 In solutions, these peaks show a weak dependence on solvent polarity, which has sparked a debate in the literature whether the MLCT excited states are initially delocalized over the complex, or whether interaction with the solvent induces an instantaneous localization onto one bpy ligand.11–15 The former (preserving D3 symmetry) could be characterized by the formal structure [Ru3+(bpyδ−)3], the latter (with C2 symmetry) by [Ru3+(bpy)2(bpy)].

FIG. 1.

Structure of Ru(bpy)32+.

FIG. 1.

Structure of Ru(bpy)32+.

Close modal

Strong spin-orbit interaction in Ru complexes is expected to influence the absorption spectrum of Ru(bpy)32+, and recent computational work on the MLCT region16 lends guidance on how the calculated electronic structure is changed compared to a treatment without spin-orbit interaction. Experimentally, spin-orbit effects in the spectrum of Ru(bpy)32+ are challenging to characterize due to the lack of spectroscopic detail in the spectra of solutions, interaction with the solvent, or—for crystal spectra—with the ionic environment of the crystal.

Spectroscopy of mass selected ions in vacuo is ideally suited to approach such questions. Transition metal polypyridine complexes in vacuo were first studied by Posey and coworkers.17,18 Experiments on mass selected Ru(bpy)32+ and its solvent adducts by Brøndsted Nielsen and coworkers19,20 showed that attaching a single acetonitrile molecule to the complex did not significantly shift the MLCT band envelope in the visible spectral region, suggesting that the excited state is initially delocalized. This interpretation is consistent with earlier condensed phase work by McCusker and coworkers who found that the initial excitation leads to a delocalized state, followed by solvent reorganization and localization.15 

A lack of better resolved spectra has long hampered the interpretation and assignments of the spectrum of Ru(bpy)32+, and has prevented a comparison between excited state calculations and experiment beyond a very coarse level. One reason for the significant spectral congestion in the singlet MLCT band of this ion is that Ru complexes exhibit very strong spin-orbit coupling, leading to ultrafast intersystem crossing (τ < 30 fs) into the triplet manifold,21 which results in strong lifetime broadening (estimated >170 cm−1). However, recent work on other mass selected Ru polypyridine complexes22,23 showed that electronic bands can still be partially resolved in vacuo in some cases. Another source of spectral congestion is the temperature of the complexes under study. Finally, interactions with the chemical environment (solution or crystal lattice) can introduce significant congestion as well as solvatochromic shifts to the spectrum. Advances in the cryogenic preparation of ions24–30 have opened an avenue to suppress hot bands and exclude solvatochromic effects. In this paper, we present a low temperature electronic absorption spectrum of Ru(bpy)32+ and use it to compare with time-dependent density functional theory (TDDFT) calculations in unprecedented detail. We show that our experimental low-temperature data approach the resolution limit one can expect to reach for Ru(bpy)32+, and the remaining widths are intrinsic, caused by lifetime broadening and congested Franck-Condon progressions in the electronic bands.

Our experimental setup has been described in detail previously.31 Briefly, Ru(bpy)32+ gas phase ions were produced via electrospray ionization from a 0.2 mM solution of Ru(bpy)3Cl2 in a 9:1 mixture of methanol and water. All chemicals were commercially obtained and used without further purification. The ions passed through a desolvation capillary and a skimmer, and were accumulated for 100 ms in a linear octupole ion trap at ca. 10−2 mbar pressure. After the accumulation period, the ions were ejected as an ion bunch into a series of octupole ion guides and passed through several differential pumping stages into a cryogenic 3D quadrupole ion trap held at 25 K. Here, they were allowed to interact with N2 buffer gas for 95 ms. Weakly bound clusters of the form Ru(bpy)32+ ⋅ (N2)n were formed by condensation of N2 molecules onto the trapped ions (see Figure 2). The trapped ions were then accelerated in a Wiley-McLaren time-of-flight mass spectrometer. The binding energy of bpy ligands in the complex is calculated to be ca. 4 eV. In order to record one-photon photodissociation spectra, the tagged complex Ru(bpy)32+ ⋅ N2 was mass-selected and irradiated by tunable pulsed radiation from an optical parametric converter system in the region 354–670 nm (bandwidth 5 cm−1). If a photon is absorbed by a target ion, the energy of the absorbed photon will be converted into vibrational energy of the ion and eventually cause unimolecular dissociation to yield bare Ru(bpy)32+ ions. Fragment and parent ions were mass-analyzed by a reflectron which acts as a secondary mass spectrometer. The flight time between irradiation and reflectron was of the order of 15 μs. Photodissociation spectra were recorded by monitoring the intensity of the Ru(bpy)32+ fragment as a function of photon energy. The ion trap was operated at 10 Hz repetition rate while the laser was triggered at 5 Hz, allowing back-ground subtraction for each data point. The fragment ion yield was normalized to the photon fluence, measured by monitoring the laser intensity using a pyroelectric joulemeter. The full spectrum was composed of several sections corresponding to the tuning ranges of the light source with different crystal configurations. Different pulse energies were available in different spectral regions, resulting in a lower signal-to-noise ratio in some parts of the UV. Data in each section were averaged over several scans taken on multiple days to increase the signal-to-noise ratio and ensure reproducibility.

The aqueous absorption spectrum was obtained for a 25 μM solution of Ru(bpy)3Cl2 in distilled water. The spectra were taken using a Varian Cary 500 Scan UV-visible-NIR spectrometer (version 8.01) with a 5 mm path length, 10 cm−1 step size, 1 nm resolution, and an integration time of 0.1 s. The data were baseline-corrected using a distilled water sample.

FIG. 2.

Time-of-flight trace of Ru(bpy)32+ ⋅ (N2)n. Brackets indicate the isotope pattern for each cluster size.

FIG. 2.

Time-of-flight trace of Ru(bpy)32+ ⋅ (N2)n. Brackets indicate the isotope pattern for each cluster size.

Close modal

The ground state geometries of Ru(bpy)32+ and Ru(bpy)32+ ⋅ N2 were calculated using density functional theory32 (DFT, B3LYP functional33,34) with def2-TZVP basis sets35 for all atoms. Singlet excitation energies were calculated by TDDFT36–38 with the same basis sets and functionals. In the case of bare Ru(bpy)32+, the complex was held in D3 symmetry, whereas the spectra of N2 adducts were calculated without symmetry restrictions. All computations were performed using the Turbomole program suite.39 

Since the binding energy of a bpy ligand to Ru(bpy)32+ is rather high (calculated to be ca. 4 eV), it is impossible to induce photodissociation from absorption of a single photon in the MLCT band region. However, this problem can be circumvented using messenger tagging spectroscopy. In the present case, we use Ru(bpy)32+ ⋅ N2 as a parent ion and monitor the loss of the N2 messenger, i.e., we measure the yield of Ru(bpy)32+ originating from Ru(bpy)32+ ⋅ N2 as a function of photon energy, following the reaction

Ru(bpy)32+N2ωRu(bpy)32++N2.
(1)

Figure 3 shows the photodissociation spectrum of Ru(bpy)32+ ⋅ N2, obtained by monitoring the loss of N2 from the parent ion, which is the only significant fragment channel, even in the UV. The two features that are barely resolved in aqueous solution at ca. 22 100 cm−1 (452 nm) and 23 200 cm−1 (431 nm) are now two very clear, well resolved bands peaking at (23 160 ± 50) cm−1 (432 nm, feature IV) and (24 660 ± 50) cm−1 (405 nm, feature V). There are several shoulders at lower energies (features I–III, the onset of the spectrum is at 18 700 cm−1), as well as a shoulder at (26 230 ± 50) cm−1 (feature VI). Towards higher photon energies, weak, broad bands (VII, VIII) are observed around 29 500 cm−1 and 32 000 cm−1, followed by a very intense band (IX) at (36 100 ± 50) cm−1.

FIG. 3.

Photodissociation action spectrum of Ru(bpy)32+ ⋅ N2 at 25 K trap temperature (top) compared to the UV/vis absorption spectrum of an aqueous solution of Ru(bpy)3Cl2 (25 μM). The data points in the photodissociation spectrum are raw data; the full line is a 30-point adjacent average. The vertical columns in the top panel represent oscillator strengths calculated from TDDFT in the present work, and their energies are shifted by 800 cm−1 to the blue. Distinct features are labeled by roman numerals as discussed in the text.

FIG. 3.

Photodissociation action spectrum of Ru(bpy)32+ ⋅ N2 at 25 K trap temperature (top) compared to the UV/vis absorption spectrum of an aqueous solution of Ru(bpy)3Cl2 (25 μM). The data points in the photodissociation spectrum are raw data; the full line is a 30-point adjacent average. The vertical columns in the top panel represent oscillator strengths calculated from TDDFT in the present work, and their energies are shifted by 800 cm−1 to the blue. Distinct features are labeled by roman numerals as discussed in the text.

Close modal

Assuming D3 symmetry, electric dipole selection rules allow A2 and E transitions. We have performed calculations based on time-dependent density functional theory (TDDFT, see Sec. II) to aid in interpreting the spectrum (see Table I and supplementary material). The calculated energies are somewhat too low, and the low energy transitions in the MLCT region of the spectrum are not well represented by this simple approach. However, the overall calculated and observed patterns are in reasonable agreement, and shifting the bands by 800 cm−1 to the blue in order to roughly capture the most intense bands allows assigning the dominant features, particularly in the UV. The literature generally agrees that the transitions in the region of features I–VI are predominantly of MLCT character.8 We will discuss the lower energy bands I–V separately below (see text and Table II), and use our simple TDDFT calculations only for features IV and higher. We can identify the two intense bands IV and V as E transitions, while feature VI is tentatively assigned to an A2 transition.

The assignment of features VII and VIII has been ambiguous in the previous literature. Based on molecular orbital arguments, Meyer and coworkers assigned feature VII to an MLCT transition,7 but others speculated that features in this region could be metal centered transitions.8 Our TDDFT calculations identify both features as predominantly of MLCT character (see supplementary material). Feature VII seems to be a single electronic band with E symmetry, while feature VIII consists of a group of unresolved bands, where the most intense band is also of E symmetry. Finally, the most intense feature in the spectrum (IX) can be attributed mostly to two unresolved intense transitions of π–π character, one of A2 symmetry and one of E symmetry.

The MLCT band of Ru(bpy)32+ in the visible spectral region has been investigated by several authors using excited state calculations (see Refs. 8 and 16 and references therein). One of the most comprehensive studies is a paper by Heully et al.,16 who used TDDFT calculations including spin-orbit coupling. They also provide a clear discussion of the effect of the spin-orbit operator on the ground and excited states in the MLCT band region. The three highest occupied orbitals in the D3 ground state of Ru(bpy)32+ are d orbitals on the metal atom, two of e symmetry and one of a1 symmetry. Only those will be significantly affected and mixed by the (atomic) spin-orbit operator, since the spin-orbit splittings on the ligand centered virtual orbitals are expected to be small.

TABLE I.

Energies, E, and oscillator strengths, f, for selecteda calculated dipole allowed excited states (TDDFT without spin-orbit interaction, this work) compared to experimentally observed features.

TDDFTExperimental
StateE (cm−1)fE (cm−1)Featureb
2E 22 429 1.7 × 10−2 23 160 IV 
3E 23 507 2.0 × 10−1 24 660 
3A2 27 014 6.8 × 10−3 26 230 VI 
4E 28 516 2.0 × 10−2 29 500 VII 
9E 31 659 1.5 × 10−1 32 000 VIII 
14E 36 066 4.2 × 10−1 36 100 IX 
8A2 36 783 7.6 × 10−1 
TDDFTExperimental
StateE (cm−1)fE (cm−1)Featureb
2E 22 429 1.7 × 10−2 23 160 IV 
3E 23 507 2.0 × 10−1 24 660 
3A2 27 014 6.8 × 10−3 26 230 VI 
4E 28 516 2.0 × 10−2 29 500 VII 
9E 31 659 1.5 × 10−1 32 000 VIII 
14E 36 066 4.2 × 10−1 36 100 IX 
8A2 36 783 7.6 × 10−1 
a

See the supplementary material for additional calculated transitions.

b

Note that we do not assign features I–III based on our simple calculations (see text and Table II).

Figure 4 shows the low energy MLCT portion of the experimental photodissociation spectrum in greater detail in comparison with the calculations by Heully et al.16 as well as our own. In general, the calculated oscillator strengths for the lower energy transitions relative to the most intense MLCT features are too low by a factor of 10–100, compared to the experiment. Note that possible distortions of the experimental relative intensities due to photon emission cannot account for this discrepancy (see the discussion below). Assuming that the true onset of the spectrum is not too weak to be experimentally observed, the calculated transitions by Heully et al.16 are about 800 cm−1 too low in energy, but the pattern of excited states fits otherwise rather well with the experimentally observed spectrum. This behavior is similar to that of our own simple TDDFT calculations.

The lowest energy feature in the experimental spectrum (I) is rather weak and has an onset at ca. 18 700 cm−1. It rises to a shoulder at 18 900 cm−1 with a plateau that continues until the photodissociation yield steps up again. We consider only singlet excited states, since direct transitions into the triplet manifold are electric dipole forbidden, and are likely to have lower absorption cross sections than the singlet transitions. We assign feature I to the lowest three dipole allowed states calculated by Heully et al.16 The band we observe is probably dominated by the 2E′ transition (based on oscillator strength, see Table II). We note that the S1 state may be slightly lower than 18 700 cm−1, based on the difference of 200 cm−1 between the S1 state as calculated by Heully et al. (1A2′), and we assign the more intense 2E′ state to the observed feature beginning at 18 700 cm−1. Feature II, beginning at 20 100 cm−1, has some substructure and extends up to 21 200 cm−1. It can be assigned to a combination of the 3A2′ and 6E′ states. A shoulder at 21 900 cm−1 (III) is consistent with the 8E′ state, and the two most intense features in the MLCT region can be easily assigned to the 11E′ (IV) and 12E′ states (V). Clearly, spin-orbit splitting needs to be taken into account to correctly describe the onset of the electronic spectrum, since our simple TDDFT calculations are unable to account for the lower energy portion of the MLCT region, especially features I and II. Unfortunately, no assignment from spin-orbit corrected calculations is available for the higher energy features.

The two main peaks in the visible MLCT band show considerable shifts compared to solutions. Features IV and V are shifted by −1060 cm−1 and −1460 cm−1 in aqueous solution, respectively, and their relative intensities also change. The different solvatochromic shifts for the two features as well as the difference in relative intensities may be attributed to increased intensity of hot bands, as the overview spectrum reported by Brondsted Nielsen and co-workers19,20 suggests a profile similar to the solution spectra. Hot bands will change the overall peak shapes and can lead to a skewed band profile of the two blurred peaks in solution.

FIG. 4.

Photodissociation action spectrum of Ru(bpy)32+ ⋅ N2 at 25 K trap temperature (top) compared to the calculated spectrum of Ru(bpy)32+ (bottom). The data points in the photodissociation spectrum are raw data, the full blue line is a 30-point adjacent average. Roman numerals describe individual features as discussed in the text. The full grey line is the absorption spectrum in aqueous solution as shown in Figure 3, scaled to have the same MLCT peak intensity as the photodissociation spectrum. The calculated transitions (bottom panel) are displayed as columns (full: Ref. 16; open: this work), and the wavenumber scale for the calculated spectrum is graphically offset by 800 cm−1 compared to the experimental spectrum to allow easier comparison and assignment. Note the logarithmic scale for the oscillator strength.

FIG. 4.

Photodissociation action spectrum of Ru(bpy)32+ ⋅ N2 at 25 K trap temperature (top) compared to the calculated spectrum of Ru(bpy)32+ (bottom). The data points in the photodissociation spectrum are raw data, the full blue line is a 30-point adjacent average. Roman numerals describe individual features as discussed in the text. The full grey line is the absorption spectrum in aqueous solution as shown in Figure 3, scaled to have the same MLCT peak intensity as the photodissociation spectrum. The calculated transitions (bottom panel) are displayed as columns (full: Ref. 16; open: this work), and the wavenumber scale for the calculated spectrum is graphically offset by 800 cm−1 compared to the experimental spectrum to allow easier comparison and assignment. Note the logarithmic scale for the oscillator strength.

Close modal
TABLE II.

Calculated dipole allowed excited states including spin-orbit interaction16 and experimentally observed features in the visible MLCT region.

Calculated (Heully et al.16)Experimental (this work)
StateaE (cm−1)fE (cm−1)Featureb
1A2′ 18 065 2 × 10−6   
2E′ 18 242 1.3 × 10−3 18 900 
3E′ 18 478 3.8 × 10−4   
2A2′ 19 197 2.2 × 10−7   
3A2′ 19 487 6 × 10−4   
4E′ 19 714 1.7 × 10−5 20 100 II 
6E′ 20 007 8.4 × 10−4   
8E′ 20 827 9.6 × 10−4   
5A2 20 844 2.9 × 10−4 21 900 III 
9E′ 21 004 1.3 × 10−5   
6A2′ 21 842 6.8 × 10−5   
11E′ 22 015 1.3 × 10−2 23 160 IV 
12E′ 23 411 1 × 10−1 24 660 
Calculated (Heully et al.16)Experimental (this work)
StateaE (cm−1)fE (cm−1)Featureb
1A2′ 18 065 2 × 10−6   
2E′ 18 242 1.3 × 10−3 18 900 
3E′ 18 478 3.8 × 10−4   
2A2′ 19 197 2.2 × 10−7   
3A2′ 19 487 6 × 10−4   
4E′ 19 714 1.7 × 10−5 20 100 II 
6E′ 20 007 8.4 × 10−4   
8E′ 20 827 9.6 × 10−4   
5A2 20 844 2.9 × 10−4 21 900 III 
9E′ 21 004 1.3 × 10−5   
6A2′ 21 842 6.8 × 10−5   
11E′ 22 015 1.3 × 10−2 23 160 IV 
12E′ 23 411 1 × 10−1 24 660 
a

The state designation follows that given in Ref. 16. Calculated values shown in bold are assigned to the corresponding experimentally observed features.

b

See Figures 3 and 4.

It is, of course, a valid question whether the presence of the N2 tag significantly changes the electronic spectrum. Previous work by Brøndsted Nielsen and coworkers established that the presence of an acetonitrile molecule does not have a significant effect on the room temperature spectrum of Ru(bpy)32+.20 Since the binding energy of the N2 tag to Ru(bpy)32+ (calculated to be ca. 50 meV) is certainly much smaller than that of acetonitrile (which has a sizeable electric dipole moment), we can assume that the presence of the N2 tag will not have a significant effect on the spectrum. Exploratory TDDFT calculations for states up to 30 000 cm−1 for complexes with and without N2 tagging confirm that the effects of an N2 tag on the overall pattern of the electronic spectrum are negligible (see the supplementary material).

In addition, it is an important question whether the relative intensities in the spectrum resemble those in the absorption spectrum of the parent ion, or whether the photodissociation cross section is significantly different from the photoabsorption cross section. While we do not expect any kinetic shift effects associated with a finite survival probability of the Ru(bpy)32+ ⋅ N2 parent ion, photon emission as a viable competing channel cannot be ruled out as quickly. The large spin-orbit coupling in Ru complexes leads to ultrafast intersystem crossing into the triplet manifold, followed by fast internal conversion into the lowest triplet state, T1. The quantum yield for phosphorescence into the electronic ground state is ca. 0.4,8 with a phosphorescence lifetime of several μs in a glassy matrix8 at 77 K and 600 ns in room temperature aqueous solution.40 While phosphorescence from Ru(bpy)32+ has not been observed in vacuo so far, we assume that the phosphorescence lifetime in a low temperature glassy solution can serve as an estimate for its upper limit in the gas phase. Since the time scale for electronic relaxation into the T1 state is likely to be short compared to the phosphorescence lifetime, the energy difference between the absorbed photon energy and the T1 state is stored in vibrational energy. If this energy difference is sufficiently large, one can expect that the time scale for the loss of the weakly bound N2 tag is comparable with or even shorter than the phosphorescence lifetime. Heully et al. calculated the T1 state to be at 17 830 cm−1,16 but their calculated singlet states are ca. 800 cm−1 lower than the lowest energy feature in our experimental results (see below), so we tentatively assume it to be at ca. 18 500 cm−1. The N2 tag is bound by ca. 400 cm−1. Consequently, the loss of N2 after intersystem crossing into the triplet manifold (but before relaxation into the electronic ground state) would only be feasible above ca. 19 000 cm−1 photon energy, and the photodissociation signal may be somewhat suppressed by phosphorescence at such low photon energies. However, this suppression cannot be greater than the phosphorescence quantum yield of the ion, and it is unlikely to change much within a given electronic absorption band. At photon energies thousands of cm−1 above the triplet state, we assume that N2 loss will be the dominant relaxation channel, since it is likely to be faster than photon emission. In addition, phosphorescence may end in higher vibrational levels on the electronic ground state surface, and N2 loss could be possible even after phosphorescence due to the low binding energy of the N2 tag.

Summarizing, we have presented the photodissociation spectrum of Ru(bpy)32+ ⋅ N2in vacuo, prepared in a cryogenic ion trap at 25 K trap temperature. We place the lowest singlet excited state (1A2′) at (18 500 ± 200) cm−1, and we can assign the observed electronic bands in unprecedented detail by comparison with theoretical data. We conclusively show that spin-orbit coupling needs to be taken into account in order to represent the onset of the spectrum in the visible spectral region. We assign the most dominant bands in the near UV to MLCT transitions, clarifying the somewhat ambiguous assignments in the earlier literature.

Solvatochromic effects can be excluded due to the absence of perturbations by solvent molecules. The low temperature in our experiment minimizes hot bands, and the use of N2 tagging does not significantly shift the electronic spectrum. The strong spin-orbit coupling in this complex limits the excited state lifetime, and the resulting lifetime broadening (>170 cm−1, estimated from τ < 30 fs21) thus precludes the resolution of any further structure in the spectrum. The experimental spectrum reported here therefore represents the intrinsic absorption spectrum of Ru(bpy)32+.

See the supplementary material for the full comparison of calculated dipole allowed excited states without spin-orbit interaction and experimentally observed features, comparison of TDDFT calculations for Ru(bpy)32+ and Ru(bpy)32+ ⋅ N2, selected calculated electronic transition energies, oscillator strengths, and orbitals contributing to these transitions.

We gratefully acknowledge funding from the National Science Foundation through Grant No. CHE-1361814 for student support and through the NSF AMO Physics Frontier Center at JILA (No. PHY-1125844) for instrument development.

1.
T. J.
Meyer
,
Acc. Chem. Res.
22
,
163
(
1989
).
2.
F.
Liu
,
J. J.
Concepcion
,
J. W.
Jurss
,
T.
Cardolaccia
,
J. L.
Templeton
, and
T. J.
Meyer
,
Inorg. Chem.
47
,
1727
(
2008
).
3.
D. R.
Weinberg
,
C. J.
Gagliardi
,
J. F.
Hull
,
C. F.
Murphy
,
C. A.
Kent
,
B. C.
Westlake
,
A.
Paul
,
D. H.
Ess
,
D. G.
McCafferty
, and
T. J.
Meyer
,
Chem. Rev.
112
,
4016
(
2012
).
4.
B.
Kumar
,
M.
Llorente
,
J.
Froehlich
,
T.
Dang
,
A.
Sathrum
, and
C. P.
Kubiak
,
Annu. Rev. Phys. Chem.
63
,
541
(
2012
).
5.
D. J.
Wasylenko
,
R. D.
Palmer
, and
C. P.
Berlinguette
,
Chem. Commun.
49
,
218
(
2013
).
6.
L.
Zayat
,
O.
Filevich
,
L. M.
Baraldo
, and
R.
Etchenique
,
Philos. Trans. R. Soc., A
371
,
20120330
(
2013
).
7.
E. M.
Kober
and
T. J.
Meyer
,
Inorg. Chem.
21
,
3967
(
1982
).
8.
A.
Juris
,
V.
Balzani
,
F.
Barigelletti
,
S.
Campagna
,
P.
Belser
, and
A.
von Zelewsky
,
Coord. Chem. Rev.
84
,
85
(
1988
).
9.
F.
Felix
,
J.
Ferguson
,
H. U.
Güdel
, and
A.
Ludi
,
Chem. Phys. Lett.
62
,
153
(
1979
).
10.
F.
Felix
,
J.
Ferguson
,
H. U.
Güdel
, and
A.
Ludi
,
J. Am. Chem. Soc.
102
,
4096
(
1980
).
11.
E. M.
Kober
,
B. P.
Sullivan
, and
T. J.
Meyer
,
Inorg. Chem.
23
,
2098
(
1984
).
12.
P. J.
Carroll
and
L. E.
Brus
,
J. Am. Chem. Soc.
109
,
7613
(
1987
).
13.
H.
Yersin
and
D.
Braun
,
Coord. Chem. Rev.
111
,
39
(
1991
).
14.
D.
Braun
,
P.
Huber
,
J.
Wudy
,
J.
Schmidt
, and
H.
Yersin
,
J. Phys. Chem.
98
,
8044
(
1994
).
15.
N. H.
Damrauer
,
G.
Cerullo
,
A.
Yeh
,
T. R.
Boussie
,
C. V.
Shank
, and
J. K.
McCusker
,
Science
275
,
54
(
1997
).
16.
J.-L.
Heully
,
F.
Alary
, and
M.
Boggio-Pasqua
,
J. Chem. Phys.
131
,
184308
(
2009
).
17.
T. D.
Burns
,
T. G.
Spence
,
M. A.
Mooney
, and
L. A.
Posey
,
Chem. Phys. Lett.
258
,
669
(
1996
).
18.
T. G.
Spence
,
T. D.
Burns
,
G. B.
Guckenberger
, and
L. A.
Posey
,
J. Phys. Chem. A
101
,
1081
(
1997
).
19.
M. B. S.
Kirketerp
and
S. B.
Nielsen
,
Int. J. Mass Spectrom.
297
,
63
(
2010
).
20.
M. H.
Stockett
and
S. B.
Nielsen
,
J. Chem. Phys.
142
,
171102
(
2015
).
21.
S.
Yoon
,
P.
Kukura
,
C. M.
Stuart
, and
R. A.
Mathies
,
Mol. Phys.
104
,
1275
(
2006
).
22.
S.
Xu
and
J. M.
Weber
,
J. Phys. Chem. A
119
,
11509
(
2015
).
23.
S.
Xu
,
J. E. T.
Smith
, and
J. M.
Weber
,
J. Phys. Chem. A
120
,
2350
(
2016
).
24.
K. R.
Asmis
,
N. L.
Pivonka
,
G.
Santambrogio
,
M.
Brümmer
,
C.
Kaposta
,
D. M.
Neumark
, and
L.
Wöste
,
Science
299
,
1375
(
2003
).
25.
O. V.
Boyarkin
,
S. R.
Mercier
,
A.
Kamariotis
, and
T. R.
Rizzo
,
J. Am. Chem. Soc.
128
,
2816
(
2006
).
26.
X. B.
Wang
and
L. S.
Wang
,
Rev. Sci. Instrum.
79
,
073108
(
2008
).
27.
M. Z.
Kamrath
,
R. A.
Relph
,
T. L.
Guasco
,
C. M.
Leavitt
, and
M. A.
Johnson
,
Int. J. Mass Spectrom.
300
,
91
(
2011
).
28.
A. B.
Wolk
,
C. M.
Leavitt
,
E.
Garand
, and
M. A.
Johnson
,
Acc. Chem. Res.
47
,
202
(
2014
).
29.
E. M.
Duffy
,
B. M.
Marsh
, and
E.
Garand
,
J. Phys. Chem. A
119
,
6326
(
2015
).
30.
J. G.
Redwine
,
Z. A.
Davis
,
N. L.
Burke
,
R. A.
Oglesbee
,
S. A.
McLuckey
, and
T. S.
Zwier
,
Int. J. Mass Spectrom.
348
,
9
(
2013
).
31.
S.
Xu
,
S.
Gozem
,
A. I.
Krylov
,
C. R.
Christopher
, and
J.
Mathias Weber
,
Phys. Chem. Chem. Phys.
17
,
31938
(
2015
).
32.
R. G.
Parr
and
W.
Yang
,
Density-Functional Theory of Atoms and Molecules
(
Oxford University Press
,
New York
,
1989
).
33.
A. D.
Becke
,
Phys. Rev. A
38
,
3098
(
1988
).
34.
C. T.
Lee
,
W. T.
Yang
, and
R. G.
Parr
,
Phys. Rev. B
37
,
785
(
1988
).
35.
F.
Weigend
and
R.
Ahlrichs
,
Phys. Chem. Chem. Phys.
7
,
3297
(
2005
).
36.
R.
Bauernschmitt
and
R.
Ahlrichs
,
Chem. Phys. Lett.
256
,
454
(
1996
).
37.
R.
Bauernschmitt
,
M.
Häser
,
O.
Treutler
, and
R.
Ahlrichs
,
Chem. Phys. Lett.
264
,
573
(
1997
).
38.
F.
Furche
,
J. Chem. Phys.
114
,
5982
(
2001
).
39.
R.
Ahlrichs
,
M.
Bär
,
M.
Häser
,
H.
Horn
, and
C.
Kölmel
,
Chem. Phys. Lett.
162
,
165
(
1989
).
40.
C.
Creutz
,
M.
Chou
,
T. L.
Netzel
,
M.
Okumura
, and
N.
Sutin
,
J. Am. Chem. Soc.
102
,
1309
(
1980
).

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