Ultraviolet Photodepletion Spectroscopy of Dibenzo-18-Crown-6-Ether

Jul 23, 2010 - Chang Min Choi, Jun Ho Lee, Yong Hun Choi, Hwan Jin Kim, and Nam Joon Kim* .... chungbuk.ac.kr (N. J. K.), [email protected] (J. H...
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J. Phys. Chem. A 2010, 114, 11167–11174

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Ultraviolet Photodepletion Spectroscopy of Dibenzo-18-Crown-6-Ether Complexes with Alkaline Earth Metal Divalent Cations† Chang Min Choi, Jun Ho Lee, Yong Hun Choi, Hwan Jin Kim, and Nam Joon Kim* Department of Chemistry, Chungbuk National UniVersity, Chungbuk 361-763, Korea

Jiyoung Heo* Department of Applied Chemistry, Kyung Hee UniVersity, Yongin, 446-701, Korea ReceiVed: March 26, 2010; ReVised Manuscript ReceiVed: July 7, 2010

Ultraviolet photodepletion spectra of dibenzo-18-crown-6-ether complexes with alkaline earth metal divalent cations (A2+-DB18C6, A ) Ba, Sr, Ca, and Mg) were obtained in the gas phase using electrospray ionization quadrupole ion-trap reflectron time-of-flight mass spectrometry. Each spectrum exhibits the lowest energy absorption band in the wavenumber region of 35 400-37 800 cm-1, which is tentatively assigned as the origin of the S0-S1 transition of A2+-DB18C6. This origin band shows a red shift as the size of the metal dication increases from Mg2+ to Ba2+. The binding energies of the metal dications to DB18C6 at the S0 state were calculated at the lowest energy structures optimized by the density functional theory and employed with the experimental energies of the origin bands to estimate the binding energies at the S1 state. We suggest that the red shifts of the origin bands arise from the decrease in the binding energies of the metal dications at the S1 state by nearly constant ratios with respect to the binding energies at the S0 state, which decrease with increasing size of the metal dication. This unique relationship of the binding energies between the S0 and S1 states gives rise to a linear correlation between the relative shift of the origin band of A2+-DB18C6 and the binding energy of the metal dication at the S0 state. The size effects of the metal cations on the properties of metal-DB18C6 complex ions are also manifested in the linear plot of the relative shift of the origin band as a function of the size to charge ratio of the metal cations, where the shifts of the origin bands for all DB18C6 complexes with alkali and alkaline earth metal cations are fit to the same line. Introduction Crown ethers are one of the most well-known host molecules and have the ability to bind ions selectively. Since the first discovery in 1967,1 crown ethers have drawn much attention from many researchers for their potential usages as phasetransfer reagents, fluoroionophores, nanoswitches, isotope separators, ion transporters through membranes, and as simple model systems for understanding noncovalent interactions in host-guest complexes.2-6 Despite such a wide variety of applications of crown ethers, the origin of their selectivity in binding has not been completely understood on a microscopic level. This situation is partly because the selectivity of crown ethers has been largely observed and studied in solution phase where the interaction between the crown ether and the metal cation cannot be isolated from other interactions, especially with solvent molecules. Disregarding those solvent effects, it was believed that the selectivity of crown ethers for metal cations in aqueous solution stemmed from the size-relationship between the metal cation and the cavity of a crown ether.6,7 However, the results of theoretical and experimental studies in the gas phase8-11 demonstrated that the selective behavior of crown ethers in aqueous solution was not from the size-relationship but from the balance of all of the noncovalent interactions among species present in the solution.12-14 This explicitly shows the importance of the gas-phase studies †

Part of the “Klaus Mu¨ller-Dethlefs Festschrift”. * To whom correspondence should be addressed. E-mail: namjkim@ chungbuk.ac.kr (N. J. K.), [email protected] (J. H.).

revealing intrinsic properties of molecules and ions in understanding the selective behavior of crown ethers. Only with the knowledge of the intrinsic properties it is possible to understand the effects of the solvent and thereby the properties in solution phase. Over the last two decades crown ethers complexed with metal cations have been intensively studied in the gas phase using mass spectrometry and laser spectroscopy.8,10,11,15-19 The laser spectroscopic studies on crown ether complexes are of critical importance for the development of crown-ether based fluoroionophores3,4 or supramolecular photonic devices.20,21 By employing various laser spectroscopic techniques, the geometric and electronic structures of benzo-18-crown-6 (B18C6), dibenzo18-crown-6 (DB18C6), benzo-15-crown-5 (B15C5), and their hydrated complexes produced in a supersonic jet were investigated.15-17 Lisy and co-workers18,19 produced hydrated or argon-tagged alkali metal ion-crown ether complexes by the collision of the metal ion with a neutral molecular beam of crown ether clusters and studied those complex ions using a combination of infrared predissociation spectroscopy and density functional theory (DFT). We also investigated DB18C6 complexes with alkali metal cations (M+-DB18C6, M ) Cs, Rb, K, Na, and Li) produced by electrospray ionization (ESI) using ultraviolet (UV) photodepletion spectroscopy.22 The application of laser spectroscopic techniques on the ions produced by ESI has now become a powerful tool to study nonvolatile and largesized ions in the gas phase.23,24 Herein, we turned our attention to DB18C6 complexes with alkaline earth metal divalent cations (A2+-DB18C6, A ) Ba,

10.1021/jp1027299  2010 American Chemical Society Published on Web 07/23/2010

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Sr, Ca, and Mg). It is well-known that DB18C6 has strong and selective binding affinity to alkaline earth metal dications as well as to alkali metal cations. The stability constants of DB18C6 complexes with alkaline earth metal dications were determined in aqueous solution and the order of binding selectivity was reported as Ba2+ > Sr2+> Ca2+.25 However, this order turned out to be the opposite to the theoretical selectivity order in the gas phase.26 Moreover, it was predicted that the selectivity order in aqueous solution would be recovered by hydration with at least six water molecules. However, the studies on A2+-DB18C6 have been very limited compared with those on M+-DB18C6. No spectroscopic studies on A2+-DB18C6 have been performed in the gas phase, as far as we know. In this paper, as a continuing effort of elucidating intrinsic properties of metal-DB18C6 complex ions, with emphasis on the effects of a size or a charge state of the metal cation, we investigated A2+-DB18C6 in the gas phase by a combination of UV photodepletion spectroscopy and DFT. The origin bands of the S0-S1 transition for A2+-DB18C6 were observed in the photodepletion spectra and exhibited red shifts as the size of the metal dication in A2+-DB18C6 increased from Mg2+ to Ba2+. The reason for this size effect was elucidated from the binding energies of the metal dications to DB18C6 at the S0 and S1 states and the properties of the molecular orbitals involved in the S0-S1 transition, which were estimated theoretically using DFT and time-dependent density functional theory (TDDFT). Experimental Section The experimental apparatus is a typical quadrupole ion-trap reflectron time-of-flight (QIT-reTOF) mass spectrometer with an ESI source. The details of the experimental setup were described elsewhere22,27 and only a brief description is given below. DB18C6, MgCl2, CaCl2, and BaCl2 were purchased from Sigma-Aldrich and Sr(NO3)2 was from Fluka. All of the chemicals were used without further purification. Each powder sample was dissolved in methanol at a concentration of 200 µM. The DB18C6 solution was then mixed with one of the alkaline earth metal solutions to produce A2+-DB18C6. The mixed solution was electrosprayed into ion droplets through a nozzle floated to a voltage of +2.0 kV. The ion droplets were desolvated while passing through a heated capillary and entered a QIT through a skimmer. Each end-cap electrode of the QIT has a hole for ion beams to enter and exit, and the ring electrode has holes for laser beams. For ion storage, a radio frequency signal was applied to the ring electrode with both end-caps grounded. The QIT was cooled down to ∼150 K by attaching a coldfinger of a liquid nitrogen reservoir on top of it. After 47 ms of ion accumulation, the broadband stored waveform inverse Fourier transform (SWIFT) pulses were applied to the exit end-cap of the QIT for isolation of A2+-DB18C6 from other residual ions.28,29 At 12 ms after the SWIFT pulses, the frequency-doubled output of a dye laser pumped by the third harmonic of an Nd:YAG laser was irradiated onto the isolated A2+-DB18C6 in the QIT. A positive DC pulse was then applied to the entrance end-cap to extract all of the ions in the QIT out to a reflectron TOF mass spectrometer for mass analysis. The extracted ions were reflected in the reflectron and then detected with a microchannel plate (MCP). The photodepletion spectra were obtained by recording the photodepletion yield (Ipd) as a function of the laser wavelength. The photodepletion yield was given by

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Ipd )

Ioff - Ion Ioff

(1)

where Ion and Ioff were the ion intensities of A2+-DB18C6 measured with and without irradiating laser pulses, respectively. The slope of the plot of log(Ipd) versus log(laser power) was measured to be ∼1.0, indicating that the photodepletion of A2+-DB18C6 was a single-photon process. The photodepletion spectra were normalized with the laser power as a function of wavelength. Computational Methods The initial conformations of A2+-DB18C6 for geometry optimization were found by the conformational search using a Metropolis Monte Carlo method with the AMBER* force field in the Macromodel package (Schrodinger, Inc., Portland OR). From this search, only the conformations within the energy of 20 kJ/mol were selected and fully optimized by a series of theoretical calculations at the HF/3-21G, HF/6-31G, and B3LYP/ 6-31G levels. Then, the local minima within the energy of 8.4 kJ/mol (2.0 kcal/mol) after those optimizations were further optimized at the B3LYP/6-31+G(d) level. The single-point energies of these optimized structures were also calculated at the MP2/6-31+G(d) level. In all of those calculations, the Los Alamos effective-core potential (LANL2DZ) was employed for the atoms of Ca, Sr, and Ba. No imaginary vibrational frequency was found from the vibrational analysis for all of the optimized structures at the B3LYP/6-31+G(d) level. Among the local minima optimized at the B3LYP/6-31+G(d) level, only the conformations within the energy of 3.0 kJ/mol were selected for estimating their singlet excitation energies and metal binding energies. The excitation energies to the S1 state were predicted using TDDFT at the same level of theory. The binding energy of the metal dication to DB18C6 at the electronic ground state (BE(S0)) for each conformation was calculated at the B3LYP/6-31+G(d) and the MP2/6-31+G(d)//B3LYP/631+G(d) levels. The binding energy is given by

BE(S0) ) E(A2+ - DB18C6) - {E(A2+) + E(DB18C6)} (2) where E(A2+-DB18C6) and E(DB18C6) are the single-point energies of the optimized structures of A2+-DB18C6 and DB18C6, respectively, with zero-point energy (ZPE) corrections. For the value of E(DB18C6), the energy of the global minimum of bare DB18C6, which has the boat-shaped structure with C2V symmetry, was employed.15 In the ZPE correction, the vibrational frequencies calculated at the B3LYP/6-31+G(d) level were used with a scale factor of 0.98. The counterpoise method for the correction of the basis set superposition error was employed in both the B3LYP and MP2 calculations.30 The calculations of HF, B3LYP, and MP2 were all carried out using the GAUSSIAN 03 package.31 Results Mass and Photodepletion Spectra. Figure 1 shows the mass spectra of A2+-DB18C6 obtained using the QIT-reTOF mass spectrometer with SWIFT pulses applied on the ion trap. Only the signals of A2+-DB18C6 are observed in the mass spectra, which is different from the case of M+-DB18C6 where the

Photodepletion Dibenzo-18-crown-6-ether Complexes

Figure 1. Mass spectra of (a) Ba2+-, (b) Sr2+-, (c) Ca2+-, and (d) Mg2+-DB18C6. The asterisks in trace (a) represent the ion signals of Ba+ and BaOH+, which are likely to be impurities present in the solution.

Figure 2. Mass spectra of A2+-DB18C6 obtained by subtracting the ion signals without laser pulses from those with laser pulses irradiated onto the complex ions in the QIT. The asterisks in traces (b) and (c) represent the ion signals of SrOH+ and CaOH+, respectively. See the text for details.

fragment ions of alkali metal cations from metastable dissociation were detected along with the parent ion in the mass spectra.22 Figure 2 is the difference mass spectra obtained by subtracting the ion signals measured without laser pulses from those with laser pulses irradiated onto the ions in the QIT. The negative signals, therefore, represent the depleted parent ion intensities, and the positive signals represent the intensities of the fragment ions produced by photoinduced dissociation (PID) of the parent ions. It is found that the PID of A2+-DB18C6 produces A+ rather than A2+ as the fragment ion. The absence of the fragment

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Figure 3. The photodepletion spectra of A2+-DB18C6 in the gas phase. The gas-phase spectra are overlapped with the corresponding absorption spectra in methanol.

A2+ is attributed to the larger binding energy of A2+ to DB18C6 than the one-photon energy of laser pulses used for the PID (270 nm, 4.59 eV). The binding energies of A2+ are estimated to be in the range of 5.57-13.3 eV, as described later in this section. As a mechanism for the generation of the fragment A+, we suggest the dissociation involving the charge reduction through an electron-transfer. The same mechanism was also proposed for the dissociation of hydrated, multiply charged transition metal ions.32 In this mechanism, upon irradiation of UV laser pulses A2+-DB18C6 is excited to the S1 state that arises from the ππ* transition of the benzene moieties. The electron in the π* orbital is then transferred to A2+, possibly through a barrier formed by the crossing of the potential energy surfaces between the S1 and the charge transfer state, producing a charge-reduced complex of A+-DB18C6+. This complex is very unstable due to the coulomb repulsion and dissociates into the fragment ions of A+ and DB18C6+. The counterpart DB18C6+ was indeed observed along with the fragment A+ in the difference mass spectra (not shown here). The fragment AOH+ (A ) Sr and Ca), however, is more likely to be from PID of (A:H2O)2+-DB18C6,33 where a monohydrated alkali earth metal dication (A2+(H2O)) is bound to the cavity of DB18C6, rather than from PID of A2+DB18C6. This is supported by the observation that the relative intensity of AOH+ to that of A+ in the mass spectra decreases as the relative intensity of (A:H2O)2+-DB18C6 to that of A2+-DB18C6 decreases. (A:H2O)2+-DB18C6 is generated along with A2+-DB18C6 by electrospray ionization of the methanol solution mixed with ACl2 (or A(NO3)2), DB18C6, and a trace of H2O, and could not be removed completely from the QIT with the isolating SWIFT pulses. Figure 3 shows the photodepletion spectra of A2+-DB18C6 in the wavenumber region of 35 400-37 800 cm-1 (282-265 nm). The UV absorption spectra of A2+-DB18C6 in methanol are also overlapped on the corresponding photodepletion spectra. We assume that the excitation energy dependence of the

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TABLE 1: The Energies and Widths of the Lowest-energy Peaks Observed in the Photodepletion Spectra of A2+-DB18C6a lowest-energy peak Ba2+ Sr2+ Ca2+ Mg2+ a

energy

width

relb

36714 ( 10 36825 ( 7 36951 ( 7 37127 ( 7

340 ( 30 300 ( 20 300 ( 20 270 ( 20

-413 -302 -176 0

Units in cm-1. b Relative energy.

photodepletion yields results mainly from the energy dependence of molecular absorption coefficients.34,35 Because no other bands were observed below 35 400 cm-1, the lowest-energy bands in the photodepletion spectra were assigned tentatively as the origins of the S0-S1 transition. However, considering the broad band widths and the ion temperature of 150 K, we cannot completely rule out the possibility that some hot vibronic bands or the origins from multiple conformations may also contribute to the assigned origin band. We also surmise that the large rise to the blue of the assigned origin band is a vibronic band as the

case in M+-DB18C6, though the unambiguous assignment is not possible at this stage. The energies and widths of the origin bands determined by fitting the photodepletion spectra to Gaussian functions are listed in Table 1. The origin bands exhibit the red shifts as the size of the metal dication bound to DB18C6 increases. However, this trend is much less clear in the UV absorption spectra obtained in methanol. It is also found that the origin bands of A2+-DB18C6 are at the bluer wavelengths than those of M+-DB18C6. Although the origin band of Ba2+-DB18C6 is slightly red-shifted by 71 cm-1, the origin bands of the other A2+-DB18C6s are all blue-shifted by 40-342 cm-1 from that of Li+-DB18C6, which is at the bluest wavelength among those of M+-DB18C6s. We also note that the lowest-energy absorption bands in the solution-phase spectra are all red-shifted from the origin bands of the corresponding photodepletion spectra. Those red-shifts are typical and can be explained by more stabilization of the electronic excited state than that of the ground state by solvation of A2+-DB18C6. Geometries and Binding Energies. Figure 4 shows the lowest energy conformations of A2+-DB18C6 optimized at the

Figure 4. The optimized structures of (a) C2V and (b) Cs conformations of Ba2+-DB18C6, (c) C2V and (d) Cs conformations of Sr2+-DB18C6, (e) C2 conformation of Ca2+-DB18C6, and (f) D2 and (g) C1 conformations of Mg2+-DB18C6 at the B3LYP/6-31+G(d) level. Top views are on the left and side views on the right. The lengths are in Å and the angles in degrees.

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TABLE 2: Relative Energies, Gibbs Free Energies, and Singlet Excitation Energies of A2+-DB18C6 B3LYPa Ba

2+

Sr2+ Ca2+ Mg2+

MP2b

S0-S1c

sym

∆Ed

∆Ge

∆E

∆G

absf

relg

C2V Cs C2V Cs C2 D2 C1

0.00 0.54 0.00 1.53

0.00 -0.50 0.00 0.30

0.00 -9.32 0.00 -6.35

0.00 -10.69 0.00 -7.59

0.00 2.42

0.00 4.11

0.00 -6.68

0.00 -4.99

33810 35849 33611 35926 39108 42124 42236

-8426 -6387 -8625 -6310 -3128 -112 0

a B3LYP/6-31+G(d). b MP2/6-31+G(d)//B3LYP/6-31+G(d). c Singlet excitation energies in cm-1 estimated using TDDFT at the B3LYP/ 6-31+G(d) level. d Relative energies in kJ/mol without the zeropoint-energy correction. e Gibbs free energies in kJ/mol at 150 K. f Absolute energies. g Relative energies.

B3LYP/6-31+G(d) level. The energies and Gibbs free energies of the conformations are listed in Table 2. Two different conformations were predicted as the local minima for Ba2+-, Sr2+-, and Mg2+-DB18C6 within the relative energy of 3 kJ/mol, whereas a single conformation was predicted for Ca2+-DB18C6. The C2V and Cs conformations of Ba2+- and Sr2+-DB18C6 are boat-shaped structures similar to the global minimum of bare DB18C6. However, the C2 conformation of Ca2+-DB18C6 is a twisted boat-shaped structure, and the D2 and C1 conformations of Mg2+-DB18C6 are the “folded” structures where the oxygen atoms coordinate Mg2+ in a quasioctahedral arrangement. The large distortion from the boat-shaped structure upon complexation with Ca2+ or Mg2+ can be attributed to the smaller radii of the metal dications compared to the cavity size of DB18C6, as pointed out previously.22 It was proposed that the metal dications with the smaller radii draw the six oxygen atoms around the cavity in DB18C6 toward them. This makes the distances between the metal dication and the oxygen atoms (M-O) shorter than those in the boat-shaped structure, and the resulting steric effects among the oxygen atoms lead to the twisted geometry. For the conformations of Ca2+-, Sr2+-, and Ba2+-DB18C6, both the average M-O distance and the angle between the two benzene-ring moieties increase from 2.46 Å to 2.82 Å and from 111° to 140°, respectively, as the size of the metal dication increases. It is conceivable that the lowest energy structure of Ba2+-DB18C6 is the boat-shaped structure with C2V symmetry as that of K+-DB18C6, considering that the radius of Ba2+ (1.35 Å) is very close to that of K+ (1.38 Å) and hence to the cavity size of DB18C6.36-38 However, the energy of the C2V conformation is predicted to be higher by 9.32 kJ/mol than that of the Cs at the MP2 level. The discrepancy in the prediction

of the lowest-energy structure between the B3LYP and MP2 calculations was also reported previously and attributed to the difference in handling dispersive interaction.39 As the case of Ba2+-DB18C6, the orders of the lowest energy structures of Sr2+-DB18C6 and Mg2+-DB18C6 predicted by the B3LYP and MP2 are different. In the B3LYP, the C2V and D2 conformations are the lowest energy structures for Sr2+and Mg2+-DB18C6, respectively, whereas in the MP2, the Cs and C1 conformations become their respective global minimum structures. The energy difference between those two conformations for each of Ba2+-, Sr2+-, and Mg2+-DB18C6 is in the range of 0.54-2.42 kJ/mol and 6.35-9.32 kJ/mol at the B3LYP and the MP2 level, respectively. With such small energy differences as well as the disagreement in the predictions between the B3LYP and MP2, it is difficult to determine which one of those two conformations is the global minimum at this stage. With near coincidence of the radii between Ca2+ (1.00 Å) and Na+ (1.02 Å) the lowest energy structure of Ca2+-DB18C6 is very similar to that of Na+-DB18C6, though the average M-O and the angle between the two benzene ring of Ca2+-DB18C6 (2.46 Å and 111°) are a little larger than those of Na+-DB18C6 (2.44 Å and 99°).22 This similarity in the structures between Ca2+- and Na+-DB18C6, along with the similarity between Ba2+- and K+-DB18C6, indicates that the global minimum structures of DB18C6 complexes with metal cations are strongly influenced by the size of the metal cation and a little affected by the charge state of the metal cation. However, it should be noted that the effects of the charge state are somewhat included in the ionic radii of the metal cations. Despite roughly the same size of Mg2+ (0.72 Å) to that of + Li (0.76 Å), the lowest energy structures of Mg2+-DB18C6 are quite different from that of Li+-DB18C6. Although the former are the folded structures, the latter is a twisted boatshaped structure. This discrepancy is also true of the structures of 18C6 complexes with Mg2+ and Li+. It was reported that the geometry optimization of Mg2+-18C6 starting from the global minimum of the twisted boat shaped structure of Li+-18C6 reverted to the folded structure.26 Likewise, the local minimum of Mg2+-DB18C6 having the twisted boat-shaped structure like the Li+-DB18C6 is predicted to be higher in energy by 9.15 kJ/mol than the folded D2 conformation of Mg2+-DB18C6 at the B3LYP/6-31+G(d) level. The reasons for adopting the folded structures of Mg2+DB18C6 may be the followings: First, the radius of Mg2+ is smaller than that of Li+. Note that the ratio of radii between Mg2+ and Li+ is only 0.95 and smaller than the ratios of 0.98 between Ca2+ and Na+, or between Ba2+ and K+. Second, the binding energy of the dication is much higher than that of the monocation with the same size. Therefore, the stronger attractive force with Mg2+ brings the oxygen atoms in DB18C6 much

Figure 5. Pictorial representations of HOMO and LUMO of Ca2+-DB18C6.

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TABLE 3: Binding Energies of the Metal Dications in A2+-DB18C6 at the S0 and S1 Statesa Ba2+

sym

method

BE(S0)b

BE(S1)c

ratiod

differencee

C2V

MP2f B3LYPg MP2 B3LYP MP2 B3LYP MP2 B3LYP MP2 B3LYP MP2 B3LYP MP2 B3LYP

537.2 591.6 545.7 592.0 649.8 707.1 656.4 706.7 768.3 821.8 1280.6 1254.5 1287.0 1251.3

524.9 579.3 533.4 579.7 636.2 693.5 642.8 693.1 753.2 806.7 1263.4 1237.3 1269.8 1234.1

0.977 0.979 0.977 0.979 0.979 0.981 0.979 0.981 0.980 0.982 0.987 0.986 0.987 0.986

12.3 12.3 12.3 12.3 13.6 13.6 13.6 13.6 15.1 15.1 17.2 17.2 17.2 17.2

Cs Sr2+

C2V Cs

Ca2+

C2

Mg2+

D2 C1

a Units in kJ/mol. b Theoretical binding energies of the metal dications at the S0 state. c Binding energies of the metal dications at the S1 state. d Ratios of the binding energies at the S1 state to those at the S0 state. e Differences in the binding energies between the S0 and the S1 state in kJ/mol. f MP2/6-31+G(d)//B3LYP/6-31+G(d). g B3LYP/6-31+G(d).

Figure 6. Schematic energy diagram illustrating the red shift of the origin band of the S0-S1 transition for A2+-DB18C6 with increasing size of the metal dication. AS2+ and AL2+ represent the small- and largesized metal dications, respectively. BE(S0) and BE(S1) represent the binding energies of the metal dication at the S0 and the S1 state, respectively. R is the ratio of BE(S1) to BE(S0) and nearly constant for all A2+-DB18C6s.

similar size. For instance, the binding energies of Ba2+ and Ca2+ are about 2.5 times larger than those of K+ and Na+, respectively. The binding energy at the S1 state is given by

BE(S1) ) BE(S0) + ∆EDB18C6 - ∆EA2+-DB18C6 closer to the metal dication, forming the more distorted, folded structure than the twisted boat-shape one. The excitation energies to the S1 state for the conformations in Figure 4 were calculated using TDDFT and listed in Table 2. The calculated excitation energies do not agree well with the experimental values. However, excluding the value of the C2V conformation of Sr2+-DB18C6, the red shifts of the experimental excitation energies of A2+-DB18C6 with increasing size of the metal dication from Mg2+ to Ba2+ are well reproduced in the theoretical values. This reproduction of the experimental red shifts by theory may indicate that the lowest energy structures of A2+-DB18C6 predicted by DFT coincide well with those present in the QIT under our experimental conditions. The large deviation of the theoretical excitation energies from the experimental energies can be attributed to the charge-transfer failure of TDDFT. It has been pointed out that TDDFT gives substantial errors for charge transfer (CT) states.40 Although the S1 state of A2+-DB18C6 is not a charge-transfer state, it may have some charge-transfer character arising from the strong electrostatic interactions between A2+ and the DB18C6 backbone. It is also worth noting that the curve crossing between the S1 state and the charge-transfer state was suggested to play a role in the PID of A2+-DB18C6 in the previous section. The TDDFT calculations predict that the excitation to the S1 state of A2+-DB18C6 arises mainly from the π-π* transition of the benzene moieties. The pictorial representations for the highest occupied (HOMO) and the lowest unoccupied molecular orbital (LUMO) of Ca2+-DB18C6 are shown in Figure 5. Those for the other A2+-DB18C6s are in the Supporting Information. The binding energies of alkali earth metal dications to DB18C6 at the electronic ground state were calculated at the lowest-energy conformations and listed in Table 3. The binding energy decreases as the radius of the metal dication increases from Mg2+ to Ba2+, consistent with the previous results.22,26 The decrease in the binding energy of larger metal dications can be attributed to their longer M-O distances in the complexes, which reduce the strength of the electrostatic interactions between the metal dication and the oxygen atoms in the DB18C6 backbone. It is also found that the binding energy of A2+ to DB18C6 is more than two times stronger than that of M+ of a

(3)

where BE(S1) and BE(S0) are the binding energies of the metal dication at the S1 and S0 states, respectively; and ∆EDB18C6and ∆EA2+-DB18C6 are the excitation energies to the origin bands of the S0-S1 transition for bare DB18C6 and A2+-DB18C6, respectively. The values of BE(S1) in Table 3 were calculated using the experimental values from the literature15 and the energies of the origin bands in the photodepletion spectra (Figure 3), respectively. Discussion The most interesting feature in the photodepletion spectra of A2+-DB18C6 is that the origin bands are red-shifted as the radius of a metal dication bound to DB18C6 increases from Mg2+ to Ba2+. The similar type of red-shift with increasing size of the metal cation was also observed in the photodepletion spectra of M+-DB18C6.22 The rearrangement of eq 3 gives

∆EA2+-DB18C6 - ∆EDB18C6 ) BE(S0) - BE(S1)

(4)

Thus, the origin-band shift between A2+-DB18C6 and bare DB18C6 equals the difference in the binding energies between the S0 and the S1 state. Therefore, the red-shift of the origin band for the larger-sized metal dication implies that the difference between BE(S0) and BE(S1) of A2+-DB18C6 decreases as the size of A2+ increases. To quantify variations of the binding energies at the S0 and the S1 state for different metal dications, we calculated the binding energies at the S0 state using DFT and then estimated the binding energies at the S1 state by eq 3 (Table 3). The BE(S0) as well as its difference from BE(S1) decreases from Mg2+- to Ba2+-DB18C6. However, the ratios BE(S1)/BE(S0) are nearly constant in the range of 0.98-0.99. On the basis of those binding energies at the S0 and S1 states, we suggest that the reason for the red-shift of the origin band for A2+-DB18C6 with increasing size of the metal dication is that the binding energies at the S1 state decrease less than those at the S0 with increasing size of the metal dication in such a way that the ratio of the S1 state binding energy to the S0 is nearly constant for all of the complex ions (Figure 6).

Photodepletion Dibenzo-18-crown-6-ether Complexes

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TABLE 4: Contributions of 2p Oxygen Orbitals in A2+-DB18C6 to the Normalized Electron Densities in HOMO and LUMO Ba2+ C2V HOMO LUMO ratioa a

Sr2+ Cs

-2

6.8 × 10 2.0 × 10-5 2.9 × 10-4

C2V -2

6.1 × 10 1.4 × 10-5 2.3 × 10-4

Ca2+ Cs

-2

7.3 × 10 3.5 × 10-5 4.8 × 10-4

Mg2+

C2 -2

2.5 × 10 2.2 × 10-5 8.8 × 10-4

D2 -2

3.5 × 10 4.6 × 10-5 1.3 × 10-3

C1 -2

6.1 × 10 2.7 × 10-4 4.4 × 10-3

5.9 × 10-2 3.7 × 10-4 6.3 × 10-3

Relative ratios of the contributions in LUMO to those in HOMO (≡LUMO/HOMO).

The nearly constant decreasing ratios of BE(S1) to BE(S0) were also reported for M+-DB18C6. The reason for the constant ratios was explained by almost constant decrease in the contribution of 2p orbitals of the six oxygen atoms, which were assumed to act as electron donors in the electrostatic interactions with the metal cations, to the electron density of an overall MO upon excitation from HOMO to LUMO.22 Likewise, the contributions of the 2p orbitals of the six oxygen atoms in A2+-DB18C6 were calculated from the MO coefficients of HOMO and LUMO, and listed in Table 4. The relative ratios of the contributions of the 2p orbitals in LUMO to those in HOMO for all A2+-DB18C6s are in the order of magnitude of 10-3-10-4 as the case for M+-DB18C6 and increase slightly with decreasing size of the metal dication, which may reflect the increasing ratio of BE(S1) to BE(S0) for the smaller metal dications. Although the ratios for A2+-DB18C6 are not as constant as those for M+-DB18C6, considering their small orders of magnitude, we suggest that the ratios of the 2p orbital contributions between HOMO and LUMO largely support the nearly constant ratios between BE(S1) and BE(S0) of A2+-DB18C6. By including R (≡BE(S1)/BE(S0)) in eq 4, the origin-band shift of A2+-DB18C6 from bare DB18C6 is modeled by

∆EA2+-DB18C6 - ∆EDB18C6 ) BE(S0) - BE(S1) ) BE(S0) × (1 - R) (5) With almost constant values of R for all A2+-DB18C6s, this model assumes a linear relation between the origin-band shift and the value of BE(S0). The linear relation is shown in the plot of Figure 7a. The linearity, however, is somewhat worse than that in the same plot of M+-DB18C6.22 This is due to a little larger value of R for Mg2+-DB18C6 compared with those for the other A2+-DB18C6s. This deviation may result from the structural difference of Mg2+-DB18C6 from those of the other A2+-DB18C6s. Note that although the lowest energy conformations of A2+-DB18C6 (A ) Ba, Sr, and Ca) are basically the boat-shaped structures, those of Mg2+-DB18C6 are the folded structures. Interestingly, however, the better linearity is achieved for all A2+-DB18C6s, even including the results of all M+DB18C6s,22 when the relative shift of the origin band is plotted as a function of ri/z, where ri is an ionic radius of the metal cation in Å and z is its charge state (Figure 7b). The correlation coefficient of the plot is -0.98. Because the binding energy of the metal cation to DB18C6 decreases with increasing value of ri and decreasing value of z, the ratio ri/z can be regarded as proportional to the reciprocal of BE(S0). Conclusions DB18C6 complexes with alkaline earth metal dications have been studied in the gas phase using a combination of UV photodepletion spectroscopy and DFT. The red shifts of the origin bands of the S0-S1 transition for the complex ions were

Figure 7. Plots of (a) the relative shift of the origin-band for A2+-DB18C6 from that for bare DB18C6, ∆EA2+-DB18C6 - ∆EDB18C6, as a function of the binding energy of the metal dication at the S0 state and (b) the relative shift of the origin band for A2+- and M+-DB18C6 as a function of the size to charge ratio of the metal cation.

observed in the photodepletion spectra as the size of the metal dication increased from Mg2+ to Ba2+. The binding energies of A2+ to DB18C6 at the S0 state were calculated at the optimized geometries of A2+-DB18C6 by DFT. It was found that the lowest energy conformations of A2+-DB18C6 were largely influenced by the ionic radius of the metal dication. For instance, DB18C6 complexes with Ca2+ and Na+, whose radii are close to each other, have the similar twisted boat-shaped structures. Moreover, the complexes with Ba2+ and K+, both of which have radii close to the cavity size, adopt the boat-shaped structures. With the calculated binding energies of the metal dications at the S0 state, the binding energies at the S1 state were estimated from the experimental energies of the origin bands of the S0-S1 transition. On the basis of those binding energies at the S0 and S1 states, we suggested that the red shifts of the origin bands arise from nearly constant decrease of the S1 state binding energy from the S0 state binding energy that decreases with increasing size of the metal dication. Those constant decreasing ratios of the binding energies between the S1 and the S0 state lead to a linear correlation between the relative shift of the origin band for A2+-DB18C6 and the binding energy of the metal dication at the S0 state. This finding of the linear correlation may enable us to extract valuable information about the binding energies of the metal cations to DB18C6 from the spectral shifts in the

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gas-phase absorption spectra of DB18C6 complexes. More interesting correlation was also found between the relative shifts of the origin bands for all A2+- and M+-DB18C6s and the size to charge ratio of the metal cations. Further studies are under way to investigate whether those types of correlations can be found in the gas-phase or even in the solution-phase absorption spectra of other crown ether complexes as well. Acknowledgment. This work was supported by the research grant of the Chungbuk National University in 2008. The authors thank Professor Mino Yang in Chungbuk National University for valuable discussion. Supporting Information Available: Pictorial representations for HOMOs and LUMOs of A2+-DB18C6. This information is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Pedersen, C. J. J. Am. Chem. Soc. 1967, 89, 7017. (2) Basilio, N.; Garcia-Rio, L.; Mejuto, J. C.; Perez-Lorenzo, M. J. Org. Chem. 2006, 71, 4280. (3) Bourson, J.; Pouget, J.; Valeur, B. J. Phys. Chem. 1993, 97, 4552. (4) Wang, Z.; Chang, S. H.; Kang, T. J. Spectrochim. Acta A 2008, 70, 313. (5) Horwitz, E. P.; Dietz, M. L.; Fisher, D. E. SolVent Extr. Ion Exch. 1991, 9, 1. (6) Gokel, G. W.; Leevy, W. M.; Weber, M. E. Chem. ReV. 2004, 104, 2723. (7) Izatt, R. M.; Bradshaw, J. S.; Nielsen, S. A.; Lamb, J. D.; Christensen, J. J.; Sen, D. Chem. ReV. 1985, 85, 271. (8) Chu, I.-H.; Zhang, H.; Dearden, D. V. J. Am. Chem. Soc. 1993, 115, 5736. (9) Anderson, J. D.; Paulsen, E. S.; Dearden, D. V. Int. J. Mass Spectrom. 2003, 227, 63. (10) Maleknia, S.; Brodbelt, J. J. Am. Chem. Soc. 1992, 114, 4295. (11) More, M. B.; Ray, D.; Armentrout, P. B. J. Am. Chem. Soc. 1999, 121, 417. (12) Feller, D. J. Phys. Chem. A 1997, 101, 2723. (13) Grootenhuis, P. D. J.; Kollman, P. A. J. Am. Chem. Soc. 1989, 111, 2152. (14) Glendening, E. D.; Feller, D.; Thompson, M. A. J. Am. Chem. Soc. 1994, 116, 10657. (15) Kusaka, R.; Inokuchi, Y.; Ebata, T. Phys. Chem. Chem. Phys. 2007, 9, 4452. (16) Shubert, V. A.; Muller, C. W.; Zwier, T. S. J. Phys. Chem. A 2009, 113, 8067. (17) Shubert, V. A.; James III, W. H.; Zwier, T. S. J. Phys. Chem. A 2009, 113, 8055. (18) Rodriguez, J. D.; Vaden, T. D.; Lisy, J. M. J. Am. Chem. Soc. 2009, 131, 17277.

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