On the Stability, Electronic Structure, and Nonlinear Optical Properties

ARTICLE pubs.acs.org/JPCA

On the Stability, Electronic Structure, and Nonlinear Optical Properties of HXeOXeF and FXeOXeF Aggelos Avramopoulos,*,† Jiabo Li,‡ Nicole Holzmann,§ Gernot Frenking,§ and Manthos G. Papadopoulos*,† †

Institute of Organic and Pharmaceutical Chemistry, National Hellenic Research Foundation, 48 Vassileos Constantinou Avenue, Athens 116 35, Greece ‡ Accelrys Inc., Telesis Court, San Diego, California 92121, United States § Fachbereich Chemie, Philipps-Universit€at Marburg, Hans-Meerwein-Strasse, D-35032 Marburg, Germany ABSTRACT: The electronic ground state, stability, and linear and nonlinear optical properties of HXeOXeF and FXeOXeF have been studied theoretically by employing complete active space valence bond (CASVB), multistate complete active space perturbation theory (MS-CASPT2), and coupled cluster methods. It is shown that the oxygen inserted between the two Xe atoms significantly modifies the ground-state electronic configuration of the formed derivative by increasing the closed-shell contribution (σ2) and removing the diradicaloid character observed in HXe2F. The electronic charge distribution has been analyzed by employing the atoms-in-molecules (AIM) method. The dissociation channels of HXeOXeF and FXeOXeF have been studied in detail. It was found that these compounds are metastable, protected by substantial energy barriers and, thus, they can be prepared under appropriate conditions. Both two- and three-body dissociation reactions have been considered. The effects of inserting O in HXe2F and substituting H (HXeOXeF) by F, leading to FXeOXeF, on the energy barriers are discussed. The significant effects of the inserted oxygen on the polarizability and even more on the first hyperpolarizability have been computed and rationalized.

I. INTRODUCTION In 2001, Christe noted that: “noble gas chemistry is still full of surprises and may signal the beginning of a renaissance in this field”. Indeed, the pioneering work of several groups (e.g., R€as€anen and co-workers,1
3 Gerber and co-workers2
5) gave many surprising results. Recently, Jimenez-Halla et al.6 considered whether it is possible to synthesize a neutral noble gas compound containing an Ng
Ng (Ng = Ar, Kr, Xe) bond. They performed a theoretical study of H
Ng
Ng
F and noted that, although two noble gas atoms are unlikely to engage in bonding, as their valence shells are filled, a large number of molecules of the type H
Ng
Y (where Y is an electronegative atom or group) can form in which the intramolecular interactions lead to a covalent bond between hydrogen and the Ng and an ionic bond between HNg+ and Y
. Jimenez-Halla et al.6 found that HXeXeF could be observed in a low-temperature xenon matrix, because of its substantial activation barrier [13.1 kcalmol
1 at CCSD(T)/ aug-cc-pVTZ]. We recently reported a study on the electronic structure of H
Ng
Ng
F, employing ab initio complete active space valence bond (CASVB) and multistate complete active space perturbation theory (MS-CASPT2) methods.7 Both levels of theory indicated the diradicaloid character of the HNg2F ground state, increasing in the order Ar > Kr > Xe. A very significant effect of Xe on the linear and nonlinear optical (L&NLO) properties was also been reported. r 2011 American Chemical Society

This work proposes two novel Xe derivatives, HXeOXeF and FXeOXeF, with respect to which we consider the following questions: (a) How do oxygen and the extra fluorine atom, by which hydrogen has been substituted, affect the electronic structure and the diradical character, in particular? (b) Are these derivatives stable enough to be observed experimentally? (c) What are the L&NLO properties of the proposed structures? How does oxygen affect these properties? The working hypothesis on which this study was based is that substitution of H by the electronegative F is likely to stabilize HXeOXeF and FXeOXeF. Developing materials with large NLO properties and discovering the mechanisms and factors that lead to these properties is of great significance because of the large number of applications of such materials.8
10 In previous articles, we have discussed the conditions under which one or more noble gas atoms can lead to very large NLO properties.7,11
13 Here, we consider how the properties of a xenon derivative involving two Xe atoms (e.g., H
Xe
Xe
F) can be affected by an oxygen atom that interrupts the direct interaction of the Xe atoms (Xe
O
Xe). Received: April 28, 2011 Revised: July 2, 2011 Published: July 27, 2011 10226

dx.doi.org/10.1021/jp203961k | J. Phys. Chem. A 2011, 115, 10226–10236

The Journal of Physical Chemistry A This work provides new physical insight into how to stabilize Xe derivatives and the mechanisms to affect their polarization properties.

II. LITERATURE SURVEY In the past, it was believed and rationalized in terms of the octet rule that the noble gas atoms were inert (nonreactive). However, in 1933, Pauling14 suggested that noble gas atoms could participate in chemical bonds, and he discussed some specific examples such as XeF6. This prediction was made with the aid of ratios of ionic radii. In 1962, Bartlett reported that the reaction of xenon (gas) with PtF6 (vapor; powerful oxidant and fluorinator) produced Xe+PtF6
(yellow-red solid).15 This was the first noble gas derivative and demonstrated the correctness of Pauling’s prediction. Bartlett’s discovery initiated an intensive focus on research in noble gas chemistry. Among the recent important developments in noble gas chemistry, one might note the following: (i) Fluorine-free organoxenon derivatives (e.g., HXeCCH, HXeCCXeH)16,17 have been synthesized. (ii) HNgY compounds have also been the synthesized and characterized.18 More than 20 molecules belonging to this family have been prepared, the most notable case of which is HArF (argon fluorohydride). The preparation of this derivative involves photolysis of hydrogen fluoride in a solid argon matrix.1 The authors noted that this is the first experimentally observed covalent neutral condensed-phase argon derivative. (iii) X-ray crystal structures have been obtained for the [Xe3OF3][PnF6] salts, where Pn = As, Sb, which contain the Z-shaped FXeOXeFXeF+ cation, and [H3O][PnF6] 3 2XeF2 in which the XeF2 molecules interact with H3O+ cations.19 HXeOXeH has been prepared by UV photolysis of H2O in solid Xe and subsequent annealing at 40
45 K,2 with IR spectroscopy used for identification. It has been reported that HXeOXeH is metastable with respect to H2O + 2Xe (global energy minimum) and HXeOH + Xe, but it is stabilized by an energy barrier.2 It has been suggested that HXeOXeH2 might be relevant to the geochemical “missing Xe” problem (the relative depletion of Earth’s atmospheric Xe in comparison with the solar abundance).20 Pettersson et al.3 reported the synthesis of HXeOH in a lowtemperature Xe matrix. The preparation of this derivative involves, in addition to Xe, the naturally abundant H2O. The kinetic stabilities of HXeOH and HXeOXeH were studied using the CASPT2 and MRCI methods.21 The decomposition paths, transition states, and rates of dissociation as a function of temperatures were computed. The synthesis and identification of HXeO (2Σ) has been reported, and it is considered that this radical is formed in the reaction H + Xe + O (1D).22 In addition to the Xe derivatives that are related to the present study, a large number of compounds involving xenon have been synthesized and characterized.23
27 III. COMPUTATIONAL METHODS III.1. VB Computations. A series of valence bond computations were performed to analyze the charge distribution and to comment on the bonding scheme of the AXeOXeF compounds, where A = H, F. The employed methodology has already been applied successfully for the discussion of the electronic structures of HXe2F7 and HXeC2H.28 All VB calculations were performed

ARTICLE

Table 1. Structure Weights Calculated from VB Calculations of Xe Derivatives: HXeOXeF, FXeOXeF, and HXeOXeH VB structure

HXeOXeF

FXeOXeF

HXeOXeH

X Xe O Xe Y (I)

0.082

0.115

0.133

X
Xe+ O
Xe Y (II) X Xe O
Xe+
Y (III)

0.224 0.084

0.146 0.146

0.216 0.216

X
Xe+
O
Xe Y (IV)

0.026

0.103

0.048

X Xe O
Xe+ Y
(V)

0.120

0.103

0.048

X
Xe+
O
Xe+ Y
(VI)

0.034

0.083

0.009

X
Xe+
O
Xe+
Y) (VII)

0.046

0.148

0.123

X
Xe+ O

Xe+ Y
(VIII)

0.350

0.149

0.123

X
Xe+O2
Xe+
Y (IX)

0.033

0.006

0.082

using VB2000, version 2.5,29
31 with VB orbital localization enhancement.30 For the Xe derivatives HXeOXeF and FXeOXeF, nine VB structures were included in the VB calculations. The MP2/aug-cc-pVDZ-optimized geometry and 3-21G* basis set were used. It was shown in our previous study7 that the VB structure weights are not sensitive to the basis set selection; thus, all VB calculations in this work were performed with the 3-21G* basis set. The nine VB structures are listed in Table 1. Eight electrons in six VB orbtials were used to describe the sigma bonding of the molecules. The oxygen atom in the middle contributes two VB orbitals, and each of the remaining four atoms contributes one; the three atoms of the XeOXe unit contribute six electrons (each atom contributes two), and the other two atoms contribute another two electrons. The multipleVB-structure VBSCF calculations29 usually lead to localized VB orbitals. The localization-enhanced option was used for the current VB calculations to ensure more localization of optimized VB orbitals and reduce the ambiguity of VB structure weights.30 Localization enhancement was achieved by optimization of VB orbitals with a delocalization penalty. The default penalty weight was used. III.2. AIM Calculations. We also analyzed the electronic charge distribution with the Atoms-In-Molecules (AIM) method,32 which was performed at the MP2/aug-cc-pVDZ level of theory with a locally modified version of the AIMPAC program package.33 III.3. Dissociation Reactions. A molecule of the type HNgY can dissociate by two reaction channels:21,34,35 HNgY f Ng þ HY HNgY f H þ Ng þ Y It has been found in several cases that the barrier for the first reaction, two-body dissociation (2B), is significantly higher than that for the second reaction, three-body dissociation (3B).21 For example, for HXeCCH, the barrier for the first reaction is 2.1 eV, whereas the barrier for the second reaction is 0.98 eV.5 In the dissociation reactions considered here, both 2B and 3B channels have been considered to check the applicability of the above finding to HXeOXeF and HXeOXeF. The decompositions of HXeOXeF and FXeOXeF were studied by employing the CASSCF/CASPT236,37 method with the ANO-RCC relativistic basis set,37 contracted to Xe[7s6p4d], F[5s3p1d], and H[3s1p]. We used an active space involving 12 electrons distributed in 12 orbitals. The accuracy of the CASPT2 method depends on the proper selection of the active space.21,38 It has been shown that a small number of active orbitals is 10227

dx.doi.org/10.1021/jp203961k |J. Phys. Chem. A 2011, 115, 10226–10236

The Journal of Physical Chemistry A

ARTICLE

Figure 1. Optimized structures of species involved in the dissociation of HXeOXeF. Bond lengths are given in angstroms, and angles in degrees.

sufficient to describe the 3B dissociation process of HXeOH.21 The active space employed in the present study is large enough to safeguard the accuracy of the computed barriers. It has been found that the selected space provided reliable results for the electronic configuration of HNg2F, where Ng = Ar, Kr, Xe.7 Gerber et al.4,5,21 showed that, for the decomposition reactions of several noble gas derivatives (e.g., HXeOH, HXeOXeH, HXeCCH), multireference methods (e.g., MR-CI, CASSCF/ CASPT2) are necessary. The size consistency of multireference second-order perturbation theory (MRPT2) was discussed by Rintelman et al.39 They found that the magnitude of error in size consistency in MRPT depends on the implementation and that CASPT2 (as implemented in MOLCAS37) is “very close to being size-consistent”.39 In this work, we employed multistate CASPT2 (MS-CASPT2), which uses single-state CASPT2 (SS-CASPT2) as a reference. This procedure makes the SS-CASPT2 states interact, leading to orthogonal states and wave functions. The latter are named perturbatively modified complete active space configuration interaction (PMCAS-CI) wave functions.40
42 Thus, we have two sets of results available: CASSCF wave functions

with CASPT2 energies and PMCAS-CI wave functions with MSCASPT2 energies. In the final calculations, we ran state-average (SA) CASSCF calculations, considering the two states (one of which is the ground state) and then applied MS-CASPT2. The MOLCAS suite of programs was used for the CASPT2 calculations.37 The employed multireference methods are particularly suitable for 3B dissociations. The zero-point-energy (ZPE) correction was also taken into account. The Douglas
Kroll procedure was used for the relativistic effects.37 Intrinsic reaction coordinate (IRC) calculations43 were performed using MS-CASPT2 methods. MP2 was also employed for some 2B dissociations. The transition states were also studied using the synchronous transit-guided quasi-Newton method.44,45 III.4. Computation of the Linear and Nonlinear Properties. When a molecule is set in a uniform static electric field F, its energy, E, can be expanded as46 1 1 1 E ¼ E0
μi Fi
Rij Fi Fj
βijk Fi Fj Fk
γijkl Fi Fj Fk Fl
::: 2 6 24 ð1Þ 10228

dx.doi.org/10.1021/jp203961k |J. Phys. Chem. A 2011, 115, 10226–10236

The Journal of Physical Chemistry A

ARTICLE

Figure 2. Optimized structures of species involved in the dissociation of FXeOXeF. Bond lengths are given in angstroms, and angles in degrees.

where E0 is the field-free energy of the atom or the molecular system; Fi, Fj, Fk, and Fl are the field components; and μi, Rij, βijk, and γijkl are the tensor components of the dipole moment, linear dipole polarizability, and first and second hyperpolarizabilities, respectively. Summation over repeated indices is implied. The average isotropic polarizability is given by R¼

∑

1 aii 3 i ¼ x, y, z

ð2Þ

When the direction of the z Cartesian axis is collinear with the dipole-moment axis, the average value of the β tensor is given by β¼

∑

3 β 5 i ¼ x, y, z zii

ð3Þ

By employing the finite-difference method, the components of the dipole moment (μz), polarizability (Rii) and first hyperpolarizability (βzii), were obtained as the first-, second-, and thirdorder derivatives, respectively, of the field-dependent energy. The Romberg approach47 was employed to safeguard the numerical stability of the results and to remove higher-order contaminations. A number of field strengths of the magnitude 2mF, where m = 1, 2, 3, 4, and a base field (F) of 0.0008 au were

used. For all reported computations in this study, the z coordinate axis coincides with the dipole-moment axis. The geometries used for the computation of the L&NLO properties were optimized with the MP2/aug-cc-pVDZ method. The dipole moment and (hyper)polarizabilities were computed by employing a series of methods, namely, HF, MP2, CCSD, and CCSD(T),48 with the aug-cc-pVXZ basis sets, where X = D, T.49 It is known that CCSD(T), in connection with a suitable basis set, is one of the most accurate methods for the computation of the L&NLO properties of the ground states of molecules. For Xe, we used a pseudopotential whose reliability for the computation of (hyper)polarizabilities has been documented.50 The NBO (natural bond orbital)51 charges for HXeOXeH, HXeOXeF, and FXeOXeF were computed at the CCSD/aug-cc-pVDZ level of theory. Software. Gaussian 03 software52 was employed for all optimization and (hyper)polarizabiliy computations. MOLCAS37 was used for the MS-CASPT2 computations.

IV. RESULTS AND DISCUSSION IV.1. Electronic Structure. Geometry Optimization. In Figures 1 and 2, the transition structures and the stationary points produced 10229

dx.doi.org/10.1021/jp203961k |J. Phys. Chem. A 2011, 115, 10226–10236

The Journal of Physical Chemistry A

ARTICLE

from the dissociation of HXeOXeF and FXeOXeF are presented. For the computation of the equilibrium structures of these derivatives, we used the CASPT2/ANO, CCSD/aug-cc-pVDZ, and MP2/aug-cc-pVDZ methods, which are frequently used for the optimization of such compounds.2,4,5,21,53 All other structures were computed with the CASPT2/ANO approach only. As reported in ref 53, in the study of HNgFNgH+, the computation of the equilibrium geometries is less sensitive to the theoretical method and basis set. Borocci et al.53 found that the differences in bond lengths between the aug-cc-pVDZ and aug-cc-pVTZ basis sets amounted to only 0.02
0.04 Å. Both CASPT2 and CCSD gave very similar results for the equilibrium structure of HXeOXeF (Figure 1). The H
Xe length is similar to those computed by Khriachtchev et al.2 and Tsivion et al.21 for HXeOXeH and by Jimenez-Halla et al.6 for HXe2F. The angle — Xe
O
Xe (138.2) of HXeOXeF is smaller than that of HXeOXeH.2,21 In parentheses, the value reported in ref 2 obtained employing the CCSD/6-311++G(2d,2p) method is given. The Xe
O bond in ref 2 (2.149 Å; CCSD) is smaller than that computed for O
XeH with the methods we employed. The 2B and 3B transition structures have significant differences. The F
Xe distance of FXeOXeF is slightly smaller than that of HXeOXe. The Xe
F distance of this derivative (2.04 Å; CCSD/aug-cc-pVDZ) is close to the Xe
F bond length of FXeF (2.03 Å; RHF/LANL2DZ).54 VB Calculations. The weights of the nine VB structures are given in Table 1 for three molecules. In structure I, there is no charge transfer between atoms; in structures II, III, and V, two atoms are involved in the charge transfer; in structures IV and IX, three atoms are involved; and in structures VI
VIII, four atoms participate in the charge transfer. The first structure (I) makes similar contributions (∼8
13%) to all three considered derivatives (Table 1). For FXeOXeF, we observed that structures I
VIII make comparable contributions; the contribution for IX is negligible. For HXeOXeF, structures II and VIII contribute more than 57% to the VB wave function. A strong covalent bond

Figure 3. VB orbitals of HXeOXeF plotted with different colors (or color pairs). The overlapping of the VB orbitals shows some extent of bonding.

is formed between H and the positively charged Xe. Covalent bonding can be seen from the VB orbital plotting. All six VB orbitals are plotted in Figure 3. From left to right, the atoms are H, Xe, O, Xe, and F. The O is on the middle top. The orbitals are plotted with different colors (or color pairs). All six orbitals show some extent of bonding overlapping with neighboring atoms. The VB orbital on H is more or less like a 1s orbital (orange color), and it overlaps with the VB orbital on the first Xe atom, which is very similar to a 4p orbital (red/blue) of Xe. The two VB orbitals on oxygen (red/blue and orange/purple) are similar to sp3-hybridized orbitals pointing to the two Xe atoms. The orbital of the second Xe atom (orange/purple) is quite similar to that of the first Xe. The last VB orbital on F is an sp-hybridized orbital bonding to the neighbor Xe. The bonding characteristics of the VB orbitals are also consistent with the structure weights given in Table 2. The molecule shows a significant amount of charge transfer from Xe to O and F. Because of the charge transfer, various bonding structures are possible. The orbitals were plotted with Discovery Studio Visualizer, version 2.5.55 The VB orbitals as shown in Figure 3 also indicate good overlap between the neighboring atoms. For completeness, we note that the electronic structure that emerges from Table 1 is quite different from the results for H
Ng
Ng
F in our previous study,7 where the H
Ng
Ng
F family was found to show strong diradical characteristics. AIM Calculations. Figure 4 shows contour line plots of the Laplacian distribution r2F(r) of H
Xe
O
Xe
F and F
Xe
O
Xe
F. The information that is provided by the shape of the plots nicely complements the information about the bonding situation that is given by the VB calculations. For HXeOXeF, there is an area of charge concentration [r2F(r) < 0, solid lines] between the hydrogen atom and the xenon atom on the left-hand side that is typical for a covalent hydrogen
xenon bond. The xenon atoms exhibits areas of charge depletion in the valence region [r2F(r) > 0, dotted lines], whereas oxygen and fluorine have circular regions of charge concentration. The Laplacian distribution suggests a description of the bonding situation in terms of (HXe)+, O
, Xe+, and F
ions that is in agreement with the most important VB structure (Table 1). The Laplacian distribution for FXeOXeF exhibits the expected features, where negatively charged fluorine and oxygen atoms are bonded to positively charged xenon. MS-CASPT2 Calculations. We first compare the electronic structure of HXe2F with that of HXeOXeF (Table 2). The configuration of the ground state of HXeXeF is given by 58% (σ)2 + 35% (σσ*). The 21Σ+ excited state lies 0.114 au (3.099 eV) above the ground state and is described by 34% (σ)2 +58% (σσ*). The configuration of the ground state of HXeOXeF is given by 87.1% (σ)2 + 1.0% (σσ*), and the first excited state, given by 6.0% (σ)2 +80.1% (σσ*), lies 0.140 au (3.81 eV) above the ground state. It is observed that the contribution of σ2 to the

Table 2. Description of the Ground-State (G) and First Excited-State (E) Configurations of Some Xe Derivativesa system

configuration

first excited state (eV)

ΔEb (kcal/mol)

HXeOXeH

77.0% (σ2) + 9% (σσ*)c (G) [68% (σσ*) + 7% (σ2)] (E)

5.05


69.6 (70)

HXeXeF

58% (σ2) + 35% (σσ*)c (G) [34% (σ)2 + 58% (σσ*)] (E)

3.09


28.7 (96)

HXeOXeF

87.1% (σ2) (G) [80.1% (σσ*) + 6% (σ2)] (E)

3.81


76.5 (90)

FXeOXeF

76.5% (σ2) + 10% (σσ*) (G) [62.7% (σσ*) + 9% (σ2)] (E)

5.20


78.4 (85)

a MSCASPT2 (two roots) method used, with the 4440/12 active space. All computations performed using the ANO basis set. b ΔE = E(singlet)
E(triplet). Percentage of diradical character (σσ*) of the triplet state in parentheses. c HOMO f LUMO.

10230

dx.doi.org/10.1021/jp203961k |J. Phys. Chem. A 2011, 115, 10226–10236

The Journal of Physical Chemistry A

ARTICLE

Table 3. NBO Charge Distribution of Various Xe Derivatives Computed at the CCSD Level of Theorya,b molecule HXeOXeF Hc

FXeOXeF


0.04

HXeOXeH
0.13
0.10d

0.00d


0.18e
0.16f Xe
(F)c F Xe
(H)c

1.04

1.09

0.53d

0.69d


0.69


0.63


0.49d


0.39d

0.76

1.09

0.71

0.63d

0.69d

0.46d 0.896e 0.85f

O


1.07


0.91


1.17


0.68d


0.59d


0.72d
1.43e
1.46f

a

Basis set of aug-cc-pVDZ. For Xe, an effective core potential of 28 electrons was used.49 b MP2/aug-cc-pVDZ-optimized geometry used. c X
(Y), where X denotes the atom bonded to Y. d CASVB method. e Reference 2. f Reference 21.

Table 4. Energy Barriers (kcal/mol) for the 2B and 3B Decomposition Pathways of HXeOXeF and HXeOXeFa energyb

HXeOXeF

FXeOXeF

E1 E2

14.9 25.5

49.5 40.5

E3

90.3

32.1

E4

50.1

30.1

E5

31.9

13.2

E6

20.1

11.1

ΔEc

17.3

33.07

Figure 4. Contour line diagrams of the Laplacian distributions r2F(r) of (a) H
Xe
O
Xe
F and (b) F
Xe
O
Xe
F. Solid lines indicate areas of charge concentration [r2F(r) < 0], whereas dotted lines show areas of charge depletion [r2F(r) > 0]. The thick solid lines connecting the atomic nulei are the bond paths. The thick solid lines separating the atomic basins indicate the zero-flux surfaces crossing the molecular plane.

Method: CASSCF/CASPT2 (ANO). A space of 12 electrons distributed in 12 orbitals was used. b See Figures 5 and 6 for the definition of Ei, i = 1
6. c ΔE = E(A + Xe + OXeF)
E(AXeOXeF), where A = H, F. Method: CCSD(T)/aug-cc-pVDZ.

ground-state configuration is 58% and 87.1% for HXeXeF and HXeOXeF, respectively. Thus, oxygen increases the closed-shell character of the ground state and reduces this character in the first excited state. A small decrease of the σ2 contribution was observed upon substituting H by F. It is known56 that the lowest singlet
triplet gap provides an indication of the diradical character of a system. The triplet state lies 1.25 eV (28.7 kcal/mol) higher in energy than the singlet ground state of HXe2F. The corresponding difference for HXeOXeF is 3.81 eV (76.5 kcal/mol). The computations of this paragraph were performed at the PMCAS-CI/MS(2)-CASPT2/ ANO level of theory. Wirz57 suggested that a diradical is “a molecular entity whose lowest singlet and triplet state energies do not differ by much more than kT, say, 2 kcal mol
1. The expression ‘biradicaloid’ would then extend this range to, say, 24 kcal mol
1”. According to this definition, HXe2F is diradicaloid,

but oxygen (HXeOXeH, HXeOXeF, FXeOXeF) removes the diradical or diradicaloid character. The results in Table 2 show that σ2 contributes 77
87% to the ground-state configurations of HXeOXeH, HXeOXeH, and FXeOXeF. The first excited state has a very pronounced σσ* contribution (63
80%). The presence of oxygen leads to a higher-lying first excited state and a higher triplet state. Thus, the first excited state lies at 3.09 and 3.81 eV for HXe2F and HXeOXeF, respectively. A similar energy gap (difference between the ground and the first excited state) is observed for HXeOXeH and FXeOXeF. NBO Analysis. The NBO (natural bond orbital) charge distribution was computed using the CCSD/aug-cc-pVDZ method. The geometries of the considered species were computed at the same level (Table 3). Hydrogen atoms bonded to Xe in HXeOXeH and HXeOXeF carry small negative charges,

a

10231

dx.doi.org/10.1021/jp203961k |J. Phys. Chem. A 2011, 115, 10226–10236

The Journal of Physical Chemistry A

ARTICLE

Figure 5. Dissociation paths for HXeOXeF calculated at the CASPT2/ANO level.


0.13 and
0.04 e, respectively. In all cases, the electronegative elements (O, F) have large negative charges (Table 3). The charge of O atom varies from
0.9 to
1.2 e, whereas the charge of F varies from
0.6 to
0.7 e The charges computed by the CASVB and CCSD method show similar trends for the studied species (Tables 2 and 4). The NBO charge of Xe (1.08 e; Table 4) for FXeOXeF is smaller than that of Xe for FXeF (1.306 e; Mulliken, RHF/LANL2DZ).54 The two xenon atoms in HXe2F have a total charge of 0.91 e.6 In HXeOXeH, HXeOXeF, and FXeOXeF, the total charges of the xenon atoms are 1.42, 1.80, and 2.16 e, respectively. Thus, the positive charge of the xenon atoms increases with the electronegativity of the atoms bonded to them. IV.2. Dissociation Channels. Dissociation of HXeOXeF. The two-body (2B) and three-body (3B) dissociation reactions of HXeOXeF have transition states that are 14.9 and 25.5 kcal/mol, respectively, above the equilibrium structure (first transition state, TS1). Thus, the dissociation will proceed through the 2B reaction

respectively (second transition state, TS2). Thus, dissociation of HOXeF will follow the reaction HOXeF f HO þ Xe þ F The dissociation was studied by the CASPT2/ANO method, taking into account the zero-point energy (ZPE). The geometric elements of the various transition structures are given in Figure 1. It was confirmed that the transition states have one imaginary frequency. Reactants and products were connected through IRC calculations. It was found that the 3B dissociation of HXeOXeH has a barrier of 9.2 kcal/mol.21 Thus, replacement of one H by F leads to an increase of the barrier by 16.3 kcal/mol. JimenezHalla et al.6 found that the 2B dissociation of HXe2F (Xe + HXeF) has a barrier of 13.1 kcal/mol, computed with the CCSD(T)/aug-cc-pVTZ method. The 2B dissociation of HXeOXeF has a barrier of 14.9 kcal/mol (Table 4). HXeOXeF is a local minimum and is higher in energy than HOF + 2Xe and other dissociation products (Figure 5) EðHXeOXeFÞ
EðHOF þ 2XeÞ ¼ 125:4 kcal=mol

HXeOXeF f Xe þ HOXeF The 2B and 3B dissociation reactions of HOXeF have transition states that have barrier heights of 50.1 and 31.9 kcal/mol,

EðHXeOXeFÞ
EðOH þ F þ 2XeÞ ¼ 85:2 kcal=mol 10232

dx.doi.org/10.1021/jp203961k |J. Phys. Chem. A 2011, 115, 10226–10236

The Journal of Physical Chemistry A

ARTICLE

Figure 6. Dissociation paths for FXeOXeF, calculated at the CASPT2/ANO level.

EðHXeOXeFÞ
EðH þ Xe þ OXeFÞ ¼
15:3 kcal=mol

EðHXeOXeFÞ
EðOF þ H þ 2XeÞ ¼ 9 kcal=mol

above barrier heights were computed with the CASPT2/ANO method. FXeOXeF has a higher energy than the dissociation products 2Xe + FOF

Thus, HXeOXeF is metastable, protected by a high-energy barrier. However, HXeOXeF is lower in energy than H + F + O + 2Xe EðHXeOXeFÞ
EðH þ F þ 2Xe þ OÞ ¼
45:1 kcal=mol

A metastable derivative, such as HXeOXeF, can be prepared provided that there is a protecting barrier of appropriately high 2 energy to prevent its dissociation to species of lower energy. Dissociation of FXeOXeF. The 2B and 3B dissociation reactions of FXeOXeF have barrier heights of 49.5 and 40.5 kcal/mol, respectively (Table 4, Figure 6). Thus, FXeOXeF will dissociate as FXeOXeF f Xe þ F þ OXeF The 2B and 3B dissociation reactions of OXeF have barriers of 30.1 and 13.2 kcal/mol, respectively. Thus, OXeF will follow the dissociation channel

EðFXeOXeFÞ
EðFOF þ 2XeÞ ¼ 22:8 kcal=mol However, FXeOXeF has a lower energy with respect to a series of dissociation products EðFXeOXeFÞ
Eð2F þ 2Xe þ OÞ ¼
52:9 kcal=mol EðFXeOXeFÞ
EðOF þ 2Xe þ FÞ ¼
42:9 kcal=mol EðFXeOXeFÞ
EðF þ Xe þ OXeFÞ ¼
32:1 kcal=mol FXeOXeF is a local minimum, and thus, it is metastable. Its dissociation is prevented by high-energy barrier(s). Lundell et al.58 noted that all of the experimentally observed rare gas hydrides, HRgY, where Y represents an electronegative fragment, lie below the limit H + Rg + Y. This remark is confirmed by our data, as

OXeF f O þ Xe þ F The configurations of the transition structures are given in Figure 2. Tsivion and Gerber21 noted that this reaction proceeds by a collinear dissociation of OXeF into radical fragments. The

ΔE ¼ EðA þ Xe þ OXeFÞ
EðAXeOXeFÞ where A = H, F. ΔE for HXeOXeF is 17.3 kcal/mol [CCSD(T)/ aug-cc-pVDZ; Table 4]. The corresponding ΔE value for FXeOXeF is 33.07 kcal/mol. Both HXeOXeF and FXeOXeF 10233

dx.doi.org/10.1021/jp203961k |J. Phys. Chem. A 2011, 115, 10226–10236

a Property values computed using the aug-cc-pVTZ basis set; corresponding values computed using the aug-cc-pVDZ basis set in parentheses . b For Xe, a small core pseudopotential (core of 28 electrons) was employed.49 The MP2/aug-cc-pVDZ geometry was employed for the computations. c Values in au. d Dipole moment directed along the Z axis. e ii: xx, yy, zz.


89


1180 (
648)
128 (
121)


1720
49
88
1800
63
1490 8


63
93
1910


1345 (
932)
247 (
235)
791 (
740)


49

β


847 (
1051)


1010 (
680) (
5) (
4)


458 (
343)


1232 (
811)
136 (
139)
615 (
563)


12


112
32


230
56


920
129


10
230


24
1200
306


55
12


43


290


630


85

59


4


8


190


1540

120

βziie

66.38

90.48 (88.72) 107.34 (105.79) 92.79 (91.50) 90.64 (89.20) 107.27 (106.67) 90.32 (89.44) 86.45 (83.33) 88.35 (87.60) 108.49 (105.80) 92.47 (90.74) 104.49 (103.35) 84.59 (83.52)

144.57 71.43

ARTICLE

R

49.34 67.30

159.81 74.96

54.45 48.34

65.47 154.96

65.71 52.57

74.10 66.81 157.96 77.30

49.59 67.99 55.42 61.37 51.21

61.65

3.460 (3.504) 47.84 1.299 (1.310) 190.82 μ zd Riie

45.57

0.623 (0.642) 155.72 2.747 (2.740) 51.19 0.987 (0.985) 192.62 0.650 (0.667) 158.12 2.956 (2.935) 50.30 1.076 (1.064) 195.15 0.615 (0.623) 142.96 2.635 (2.601) 51.46

F/F H/F H/H F/F H/F H/H property

A/B

HF

0.705 (0.727) 0.974 (0.986) 157.85 192.77

H/F H/F

A/B A/B

H/H

CCSD MP2

method

Table 5. Dipole Moments, Polarizabilities, and First Hyperpolarizabilities of AXeOXeB, A = H, F; B = H, Fa
c

F/F

H/H

A/B

CCSD(T)

F/F

The Journal of Physical Chemistry A

have substantial activation barriers and thus could be observed in a low-temperature Xe matrix.16 IV.3. L&NLO Properties. The linear and nonlinear optical properties of H(F)XeOXeH(F) are presented in Table 5. The results were computed using the HF, MP2, CCSD, and CCSD(T) methods with the aug-cc-pVXZ basis sets, where X = D, T.49 Dipole Moments. Of the three considered molecules, HXeOXeF has the largest dipole moment, and for this molecule, we also observed the largest effect of electron correlation [CCSD(T)/augcc-pVTZ]. The effects of oxygen are shown by comparing the dipole moment of HXe2F7 with that of HXeOXeF: μz(HXe2F)
μz(HXeOXeF) = 3.788
2.740 au = 1.048 au. These values were computed at the CCSD(T)/aug-cc-pVDZ level. Polarizabilities. Correlation has a rather small effect on the average polarizability value (R) of HXeOXeH and FXeOXeF. For example, for HXeOXeH, we observed R[CCSD(T)]
R(HF) = 2.44 au [CCSD(T)/aug-cc-pVTZ]. The corresponding effect on HXeOXeF is 8.2 au. Insertion of oxygen noticeably decreases Rzz. It is observed that Rzz(HXe2F)
Rzz(HXeOXeF) = 420.43
159.35 au = 261.08 au. These values were computed at the CCSD(T)/aug-cc-pVDZ level. First Hyperpolarizabilities. The effect of correlation is particularly significant for β of HXeOXeH and FXeOXeF. The small value of β for FXeOXeF is noted. It is observed that |βzzz(HXe2F)|
|βzzz(HXeOXeF)| = 11040
1420 au = 9620 au, computed at the CCSD(T)/aug-cc-pVDZ level. Thus, insertion of oxygen markedly reduces β. The basis set has a larger effect on β of HXeOXeF. The difference β(aug-cc-pVTZ)
β(aug-ccpVDZ) is
532,
52, and
7 au for HXeOXeF, HXeOXeH, and FXeOXeF, respectively. The present results clearly show the great effect of oxygen on the dipole moments and (hyper)polarizabilities. Thus, a mechanism for tuning the properties of Xe derivatives is demonstrated. Interpretation of the Results. In this section, we explain the very remarkable effect on βzzz of inserting oxygen between the Xe atoms by employing a two-state model (TSM) based on the sumover-states (SOS) approach,59 which was shown to explain qualitatively several first hyperpolarizability results.7,60,61 This model assumes that the main contribution to βzzz originates from the lowest symmetry-allowed electronic transition βzzz ð0Þ∞

3ðμe
μg Þμge 2 ðΔEÞ2

ð4Þ

where μe and μg are the excited- and ground-state dipole moments, respectively; μge is the transition dipole moment; and ΔE is the transition energy. For HXeOXeF, the necessary data associated with the lowest low-lying allowed transition were computed at the MS-CASPT2(4440/12) method with the ANO basis set. The transition dipole moment (TDM) was computed at the PMCAS-CI level, whereas the excitation energies were computed at the MS-CASPT2 level. It was found that, for HXeOXeF, the ground-state dipole moment is 2.758 au (4.719 au), the excited-state dipole moment is 0.497 au (2.325 au), the transition dipole moment is
1.51 au (
4.19 au), and the transition energy is 0.230 au (0.107 au). The corresponding data for HXe2F are given in parentheses.7 Thus, insertion of oxygen leads to decreases of |μe
μg| and |μge| and an increase of ΔE. The above features explain why insertion of oxygen in HXe2F (HXeOXeF) leads to a reduction of |β|. 10234

dx.doi.org/10.1021/jp203961k |J. Phys. Chem. A 2011, 115, 10226–10236

The Journal of Physical Chemistry A

V. CONCLUSIONS The stability, electronic structure, and L&NLO properties of HXeOXeH, HXeOXeF, and FXeOXeF were studied using the CASVB, MS-CASPT2, and coupled cluster methods. AIM calculations were performed. A covalent bond between H and Xe of HXeOXeF was found. The AIM results are in agreement with the valence bond data, suggesting the description of (H
Xe)+O
Xe+F
for the bonding scheme. Comparison of the results for HXe2F and HXeOXeF reveals that oxygen increases the closed-shell character of the ground state and reduces this character in the first excited state. It was found that HXe2F is a diradicaloid, but oxygen removes this character in HXeOXeH, HXeOXeF, and FXeOXeF. A detailed study of the dissociation channels of HXeOXeF and FXeOXeF showed that these species are metastable, protected by substantial energy barriers, particularly FXeOXeF. Thus, they can be prepared under appropriate conditions. We considered both two- and three-body dissociation reactions. However, in most, but not all, cases, the latter involve a lower-energy activation barrier. Comparison of the dissociation channels of HXeOXeF and FXeOXeF shows that substitution of H by F leads to a very significant increase of the energy barrier. We believe that the findings of our computations could motivate experimentalists to prepare stable derivatives containing two noble gas atoms. Insertion of oxygen in HXe2F (HXeOXeF) leads to a significant reduction of the dipole moments and the (hyper)polarizabilities. In particular, it was found that βzzz(HXe2F) is 7.7 times larger than βzzz(HXeOXeF) [CCSD(T)/aug-cc-pVDZ]. This result was interpreted by a two-state model. ’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected] (A.A.), [email protected] (M.G.P.).

’ ACKNOWLEDGMENT The research leading to these results received funding from the European Union’s Seventh Framework Programme (FP7REGPOT-2009-1) under Grant 245866. Support is also acknowledged from the High-Performance Computing Infrastructure for South East Europe’s Research Communities (HPSEE), a project cofunded by the European Commission (under Contract 261499) through the Seventh Framework Programme. ’ REFERENCES (1) Khriachtchev, L.; Pettersson, M.; Runeberg, N.; Lundell, J.; R€as€anen, M. Nature 2000, 406, 874. (2) Khriachtchev, L.; Isokoski, K.; Cohen, A.; R€as€anen, M.; Gerber, R. B. J. Am. Chem. Soc. 2008, 130, 6114. (3) Pettersson, M.; Khriachtchev, L.; Lundell, J.; R€as€anen, M. J. Am. Chem. Soc. 1999, 121, 11904. (4) Chaban, G. M.; Lundell, J.; Gerber, R. B. Chem. Phys. Lett. 2002, 364, 628. (5) Tsivion, E.; Zilberg, S.; Gerber, R. B. Chem. Phys. Lett. 2008, 460, 23. (6) Jimenez-Halla, C. O. C.; Fernandez, I; Frenking, G. Angew. Chem., Int. Ed. 2009, 48, 366. (7) Avramopoulos, A.; Serrano-Andres, L.; Li, J.; Papadopoulos, M. G. J. Chem. Theory Comput. 2010, 6, 3365. (8) Heath, J. R.; Ratner, M. A. Phys. Today 2003, 43, 56. (9) Hide, F.; Diaz-Garcia, M. A.; Schwartz, B. J.; Heeger, A. J. Acc. Chem. Res. 1997, 30, 430.

ARTICLE

(10) Painelli, A. Terenzianni, F. In Non-linear Optical Properties of Matter: From Molecules to Condensed Phases; Papadopoulos, M. G., Sadlej, A. J., Leszczynski, J., Eds.; Springer: Dordrecht, The Netherlands, 2006; p 251. (11) Holka, F.; Avramopoulos, A.; Loboda, O.; Kell€o, V.; Papadopoulos, M. G. Chem. Phys. Lett. 2009, 472, 185. (12) Avramopoulos, A.; Serrano-Andres, L.; Li, J.; Reis, H.; Papadopoulos, M. G. J. Chem. Phys. 2007, 127, 214102. (13) Avramopoulos, A.; Reis, H.; Li, J.; Papadopoulos, M. G. J. Am. Chem. Soc. 2004, 126, 6179. (14) Pauling, L. J. Am. Chem. Soc. 1933, 55, 1895. (15) Bartlett, N. Proc. Chem. Soc. London 1962, 218. (16) Khriachtchev, L.; Tanskanen, H.; Lundell, J.; Pettersson, M.; Kiljunen, H.; R€as€anen, M. J. Am. Chem. Soc. 2003, 125, 4696. (17) Feldman, V. I.; Sukhov, F. F.; Orlov, A. Y.; Tyulpina, I. V. J. Am. Chem. Soc. 2003, 125, 4698. (18) Pettersson, M.; Lundell, J.; R€as€anen, M. Eur. J. Inorg. Chem. 1999, 729. (19) Gerken, M.; Moran, M. D.; Mercier, H. P. A.; Pointner, B. E.; Schrobilgen, G. J.; Hoge, B.; Christe, K. O.; Boatz, J. A. J. Am. Chem. Soc. 2009, 131, 13474. (20) Caldwell, W. A.; Nguyen, J. H.; Pfrommer, B. G.; Mauri, F.; Louie, S. G.; Jeanloz, R. Science 1977, 277, 930. (21) Tsivion, E.; Gerber, R. B. Chem. Phys. Lett. 2009, 482, 30. (22) Khriachtchev, L.; Pettersson, M.; Lundell, J.; Tanskanen, H.; Kiviniemi, T.; Runeberg, N.; R€as€anen, M. J. Am. Chem. Soc. 2003, 125, 1454. (23) Stein, L.; Morris, J. R.; Downs, A. J.; Minihan, A. R. J. Chem. Soc., Chem. Commun. 1978, 502. (24) Drews, T.; Seppelt, K. Angew. Chem., Int. Ed. Engl. 1977, 36, 273. (25) Brock, D. S.; Bilir, V.; Mercier, H. P. A.; Schrobilgen, G. J. J. Am. Chem. Soc. 2007, 129, 3598. (26) Seppelt, K.; Lentz, D. Prog. Inorg. Chem. 1982, 29, 167. (27) Frohn, H.
J.; Klose, A.; Henkel, G. Angew. Chem., Int. Ed. 1993, 32, 99. (28) Avramopoulos, A.; Serrano-Andres, L.; Li, J.; Reis, H.; Papadopoulos, M. G. J. Chem. Phys. 2007, 127, 214102. (29) Li., J.; McWeeny, R. Int. J. Quantum Chem. 2002, 89, 208. (30) Li, J.; Duke, B. J.; Klap€otke, T. M.; McWeeny, R. J. Theor. Comput. Chem. 2008, 7, 853. (31) Li, J.; Duke, B. J.; McWeeny, R. VB2000, version 2.5; SciNet Technologies: San Diego, CA, 2011; available at http://www.vb2000. net (accessed March, 2011). VB2000 is an ab initio program for general valence bond calculations. It is available as a stand-alone package and also an extension of GAMESS(US). The Windows version of GAMESS also has a built-in VB2000 extension. (32) Bader, R. F. W. Atoms in Molecules: A Quantum Theory; Oxford University Press: Oxford, U.K., 1990. (33) (a) AIMPAC, http://www.chemistry.mcmaster.ca/aimpac (accessed March, 2011). (b) Krapp, A. University of Oslo, Department of Chemistry, Centre for Theoretical and Computational Chemistry, N-0315 Oslo, Norway. Unplublished, 2010. (34) Chaban, G. M.; Lundell, J.; Gerber, R. B. Chem. Phys. Lett. 2002, 364, 628. (35) Takayanagi, T.; Wada, A. Chem. Phys. Lett. 2002, 352, 91. (36) (a) Andersson, K.; Malmqvist, P.-Å.; Roos, B. O. J. Chem. Phys. 1992, 96, 1218. (b) Roos, B. O.; Andersson, K.; F€ulscher, M. P.; Malmqvist, P.-Å.; Serrano-Andres, L.; Pierloot, K.; Merchan, M. Adv. Chem. Phys. 1996, 93, 219. (37) Aquilante, F.; De Vico, L.; Ferre, N.; Ghigo, G.; Malmqvist, P-.A.; Pedersen, T.; Pitonak, M.; Reiher, M.; Roos, B. O.; SerranoAndres, L.; Urban, M.; Veryazov, V.; Lindh, R. J. Comput. Chem. 2010, 31, 224. (38) Azizi, Z.; Roos, B. O.; Veryazov, V. Phys. Chem. Chem. Phys. 2006, 8, 2727. (39) Rintelman, J. M; Adamovic, I.; Varganov, S.; Gordon, M. S. J. Chem. Phys. 2005, 122, 44105. 10235

dx.doi.org/10.1021/jp203961k |J. Phys. Chem. A 2011, 115, 10226–10236

The Journal of Physical Chemistry A

ARTICLE

(40) Finley, J.; Malmqvist, P-Å; Roos, B. O.; Serrano-Andres, L. Chem. Phys. Lett. 1998, 288, 299. (41) Serrano-Andres, L.; Merchan, M.; Lindh, R. J. Chem. Phys. 2005, 122, 104107. (42) Merchan, M. L. Serrano-Andres, L. Ab Initio Methods for Excited States. In Computational Photochemistry; Olivucci, M., Ed.; Elsevier; Amsterdam, 2005; pp 35
91. (43) Fukui, K. Acc. Chem. Res. 1981, 14, 363. (44) Peng, C.; Schlegel, H. B. Isr. J. Chem. 1993, 33, 449. (45) Peng, C.; Ayala, P. Y.; Schlegel, H. B.; Frisch, M. J. J. Comput. Chem. 1996, 17, 449. (46) Buckingham, A. D. Adv. Chem. Phys. 1967, 12, 107. (47) Davis, P. J. Rabinowitz, P. Numerical Intergration; Blaisdell: London, 1967. (48) Bartlett, R. J. In Modern Electronic Structure Theory ; Yarkony, D. R., Ed.; World Scientific; Singapore, 1995; Vol. 2, p 1047. (49) Peterson, K. A.; Figgen, D.; Goll, E.; Stoll, H.; Dolg, M. J. Chem. Phys. 2003, 119, 11113. (50) Jansik, B; Schimmelpfennig, B; Norman, P; Mochizuki, Y.; Luo, .; Ågren, H. J. Phys. Chem. A 2002, 106, 395. (51) Reed, A. E.; Curtiss, L. A.; Weinhold, F. Chem. Rev. 1988, 88, 899. (52) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; Nakatsuji, H.; Caricato, M.; Li, X.; Hratchian, H. P.; Izmaylov, A. F.; Bloino, J.; Zheng, G.; Sonnenberg, J. L.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Vreven, T.; Montgomery, J. A., Jr.; Peralta, J. E.; Ogliaro, F.; Bearpark, M.; Heyd, J. J.; Brothers, E.; Kudin, K. N.; Staroverov, V. N.; Kobayashi, R.; Normand, J.; Raghavachari, K.; Rendell, A.; Burant, J. C.; Iyengar, S. S.; Tomasi, J.; Cossi, M.; Rega, N. ; Millam, J. M.; Klene, M.; Knox, J. E.; Cross, J. B.; Bakken, V.; Adamo, C; Jaramillo, J.; Gomperts, R. E.; Stratmann, O.; Yazyev, A. J.; Austin, R.; Cammi, C.; Pomelli, J. W.; Ochterski, R.; Martin, R. L.; Morokuma, K.; Zakrzewski, V. G.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Dapprich, S.; Daniels, A. D.; Farkas, O.; Foresman, J. B.; Ortiz, J. V.; Cioslowski, J.; Fox, D. J. Gaussian 09, revision A.02; Gaussian, Inc.: Wallingford, CT, 2009. (53) Borocci, S.; Bronzolino, N.; Giordani, M.; Grandinetti, F. J. Phys. Chem. A 2010, 114, 7382. (54) Frohn, H-J; Theissen, M. Angew. Chem., Int. Ed. 2000, 39, 4591. (55) Discovery Studio Visualizer, version 2.5; Accelrys Inc: San Diego, CA, 2010. (56) Bachler, V.; Olbrich, G.; Neese, F.; Wieghardt, K. Inorg. Chem. 2002, 41, 4179. (57) Wirz, J. Pure Appl. Chem. 1984, 56, 1289. (58) Lundell, J.; Khriachtchev, L.; Pettersson, M.; R€as€anen, M. Chem. Phys. Lett. 2004, 388, 228. (59) Oudar, L.; Chemla, D. S. J. Chem. Phys. 1977, 66, 2664. (60) Serrano-Andres, L.; Pou-Amerigo, R.; F€ulscher, M. P.; Borin, A. C. J. Chem. Phys. 2002, 117, 1649. (61) Chen, W.; Li, Z. R.; Wu, D.; Li, R. Y.; Sun, C. C.; Gu, F. L.; Aoki, Y. J. Am. Chem. Soc. 2006, 128, 1072.

10236

dx.doi.org/10.1021/jp203961k |J. Phys. Chem. A 2011, 115, 10226–10236