Do Traditional, Chlorine-shared, and Ion-pair Halogen Bonds Exist

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Do Traditional, Chlorine-shared, and Ion-pair Halogen Bonds Exist? An ab Initio Investigation of FCl:CNX Complexes Janet E. Del Bene,*,† Ibon Alkorta,‡ and Jose´ Elguero‡ Department of Chemistry, Youngstown State UniVersity, Youngstown, Ohio 44555, United States, and Instituto de Quı´mica Me´dica, CSIC, Juan de la CierVa, 3, E-28006 Madrid, Spain ReceiVed: October 27, 2010

Ab initio MP2/aug′-cc-pVTZ calculations have been carried out to determine the structures, binding energies, and bonding of complexes FCl:CNX, with X ) CN, NC, NO2, F, CF3, Cl, Br, H, CCF, CCH, CH3, SiH3, Li, and Na. Equation-of-motion coupled cluster calculations have also been carried out to determine the coupling constants 1J(F-Cl), 1XJ(Cl-C), and 2XJ(F-C) across these halogen bonds. As the strength of the base is systematically increased, the nature of the halogen bond changes from traditional, to chlorine-shared, to ionpair. The type of halogen bond present in a complex can be readily determined from its structure, binding energy, AIM bonding analyses, and spin-spin coupling constants. Coupling constants across halogen bonds are compared with corresponding coupling constants across traditional, proton-shared, and ion-pair hydrogen bonds. Introduction Although halogen bonds (X-bonds) have been known for over a half century, there has been a resurgence of interest in these bonds over the past decade.1-39 In his recent article,25 Legon reviewed the gas-phase structures and binding energies of complexes with intermolecular halogen bonds, and compared them with corresponding properties of complexes with hydrogen bonds. Legon’s work prompted us to investigate halogen bonds involving a series of nitrogen bases.40 In that study, we examined Cl transfer across the F-Cl · · · N halogen bond in F-Cl · · · NH3, and observed that there is no contraction and subsequent expansion of the F-N distance as the transfer takes place. This behavior is quite different from that observed for proton transfer across an F-H · · · N hydrogen bond, in which case the F-N distance in a traditional (normal) hydrogen bond initially decreases along the proton-transfer coordinate, exhibits a minimum for a quasi-symmetric proton-shared hydrogen bond, and then increases to some extent as an ion-pair hydrogen bond is formed.41 However, in an ongoing study of ternary complexes with CNH and its derivatives as bases, we observed some unusual results for complexes with FCl as the Lewis acid. This led us to ask whether or not neutral complexes with F-Cl · · · C bonds can be stabilized by traditional, chlorine-shared, and ionpair halogen bonds. If so, what are the structural, energetic, and coupling constants characteristics that distinguish each type, and how do these compare with traditional, proton-shared, and ionpair hydrogen bonds. In this paper we present our responses to these inquiries.

CH3, SiH3, Li, and Na. Monomers and complexes were first optimized at second-order Møller-Plesset perturbation theory (MP2)42-45 with the 6-31+G(d,p) basis set.46-49 Vibrational frequencies were computed to establish that each of the optimized structures is a local minimum on its potential surface. These structures were subsequently fully reoptimized at MP2 using the aug′-cc-pVTZ basis set, which is the Dunning aug-cc-pVTZ50,51 basis with diffuse functions removed from H. Geometry optimization and frequency calculations were carried out with the Gaussian 03 suite of programs.52 The halogen bonds in these complexes have also been analyzed using the atoms in molecules (AIM) theory.53 This analysis was carried out with the AIMPAC program.54 Spin-spin coupling constants for the monomers FCl, ClCN, ClCNH+, and FCl:CNX complexes with X ) CN, NC, NO2, F, CF3, Cl, H, CCF, CCH, CH3, and Li were computed using the equation-of-motion coupled cluster singles and doubles (EOM-CCSD) method in the CI(configuration interaction)-like approximation,55,56 with all electrons correlated. For these calculations, the Ahlrichs57 qzp basis set was placed on 13C, 15 N, and 19F atoms, and the qz2p basis set on 35Cl. A previously developed corresponding basis set with the same number of functions as the qzp basis was placed on 7Li.58 The Dunning cc-pVDZ basis50,51 was placed on H atoms. Coupling constants were evaluated as a sum of four terms, namely, the paramagnetic spin-orbit (PSO), diamagnetic spin-orbit (DSO), Fermi-contact (FC), and spin-dipole (SD).59 The coupling constant calculations were carried out using ACES II60 on the IBM 1350 cluster (Glenn) at the Ohio Supercomputer Center.

Methods

Results and Discussion

For this study, binary complexes have been constructed with FCl as the Lewis acid and substituted CNH molecules as the electron-donor Lewis bases. The bases may be represented as CNX, with X ) CN, NC, NO2, F, CF3, Cl, Br, H, CCF, CCH,

Structures and Binding Energies. Table 1 presents MP2/ aug′-cc-pVTZ distances and binding energies for 14 neutral complexes FCl:CNX. All of these have linear F-Cl · · · C halogen bonds. The majority have C∞V symmetry except for three with C3V symmetry (FCl:CNCH3, FCl:CNCF3, FCl:CNSiH3) and one with C2V symmetry (FCl:CNNO2). In Table 1 the complexes are arranged into three sections according to increasing binding energy.

* To whom correspondence should be addressed. E-mail: jedelbene@ ysu.edu. † Youngstown State University. ‡ Instituto de Quı´mica Me´dica.

10.1021/jp110295n  2010 American Chemical Society Published on Web 11/16/2010

Ab Initio Investigation of FCl:CNX Complexes

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TABLE 1: MP2/aug′-cc-pVTZ Distances (R, Å) and Binding Energies (∆E, kJ/mol) for Neutral Complexes with F-Cl · · · C Halogen Bondsa monomer/complex R(F-C) R(F-Cl) R(F-Cl) - R(Cl-C)

∆E

FCl:CNCN FCl:CNNC FCl:CNNO2 FCl:CNF

4.133 4.116 4.085 4.124

1.666 1.668 1.674 1.670

-0.801 -0.780 -0.737 -0.783

22.91 24.62 24.97 25.87

FCl:CNCF3 FCl:CNCl FCl:CNBr FCl:CNH FCl:CNCCF FCl:CNCCH FCl:CNCH3 FCl:CNSiH3

3.560 3.603 3.598 3.587 3.577 3.571 3.612 3.587

1.864 1.854 1.867 1.875 1.877 1.878 1.888 1.903

0.167 0.106 0.134 0.165 0.178 0.185 0.165 0.219

34.61 37.54 45.11 45.44 48.67 48.70 59.11 64.65

FCl:CNLi FCl:CNNa

3.660 3.687

1.976 2.003

0.292 0.318

121.07 139.73

a Distances in reference monomers: F-Cl ) 1.638 Å; Cl-C in ClCN ) 1.631 Å.

The first section of Table 1 consists of complexes with strong electron-withdrawing groups that make CNX a weak base. These complexes have low binding energies that range from 23 to 26 kJ/mol, and relatively long F-C distances near 4.1 Å. The F-Cl bonds are slightly elongated relative to isolated F-Cl, and the Cl-C distances are much longer than the Cl-C distance in ClCN. As a result, the quantity [R(F-Cl) - R(Cl-C)] is negative. The structural characteristics of these complexes are similar to those of complexes stabilized by traditional hydrogen bonds. Thus, complexes FCl:CNX with X ) CN, NC, NO2, and F are stabilized by traditional halogen bonds. In order of increasing binding energy, the complex that follows FCl:CNF is FCl:CNCF3. This complex is structurally quite different from FCl:CNF, but shares similar structural and energetic characteristics with the complexes in the second section, where X ) CF3, Cl, Br, H, CCF, CCH, CH3, and SiH3. These CNX molecules are stronger bases, and their complexes with FCl have relatively short F-C distances that range from 3.56 to 3.61 Å. The shortening of the F-C distance occurs as the F-Cl bond lengthens to between 1.85 and 1.90 Å. This implies that the Cl-C distance shortens, as is also evident from the values of [R(F-Cl) - R(Cl-C)], which are now positive and range from 0.1 to 0.2 Å. The structural characteristics of these complexes are typical of those associated with protonshared hydrogen bonds, which suggests that these complexes are stabilized by chlorine-shared halogen bonds. As expected, the binding energies of these complexes are greater than those of complexes with traditional halogen bonds, and range from 35 to 65 kJ/mol. The final section of Table 1 consists of only two complexes, FCl:CNLi and FCl:CNNa. CNLi and CNNa are very strong bases, and their complexes with FCl have high binding energies of 121 and 140 kJ/mol, respectively. The F-C distances in these complexes are somewhat elongated relative to complexes with chlorine-shared bonds. In addition, the quantity [R(F-Cl) R(Cl-C)] has increased to 0.3 Å. Relative to isolated ClCN, the Cl-C distance has increased from 1.631 to 1.684 Å. Thus, these complexes have the structural and energetic characteristics of complexes with ion-pair hydrogen bonds and can be classified as complexes stabilized by ion-pair halogen bonds. All of the complexes in Table 1 are neutral complexes, and being able to subdivide them into those with traditional, chlorineshared, and ion-pair halogen bonds is a result of varying the strength of the CNX base. It is possible to further extend both

Figure 1. The Steiner-Limbach relationship applied to the FCl:CNX halogen-bonded complexes. r1 ) R(F-Cl); r2 ) R(Cl-C); r1 + r2 ) R(F-C).

ends of the spectrum of binding energies of complexes in Table 1 by allowing the base to be charged. Thus, the cationic complex FCl:CNNH3+ has a very weak (5 kJ/mol) traditional halogen bond. The F-C distance of 4.454 Å is the longest distance among all of the complexes, and the F-Cl distance of 1.639 Å is essentially the same as the distance in the FCl monomer. The difference between the F-Cl and Cl-C distances is -1.176 Å. The ion-pair complexes at the other end of the scale can be extended by introducing a negative charge on the base. FCl: CN- has an extremely large binding energy of 475 kJ/mol. Among the ion-pair complexes it has the longest F-C distance of 3.880 Å, and a short Cl-C distance of 1.666 Å, which is only 0.035 Å longer than the Cl-C distance in the neutral molecule ClCN, and 0.041 Å longer than the distance in ClCNH+. As expected, the difference between the F-Cl and Cl-C distances has increased to 0.548 Å. The two interatomic distances F-Cl (r1) and Cl-C (r2) for the FCl:CNX complexes have been correlated using the SteinerLimbach relationship originally developed for hydrogen-bonded systems.61

(r1 + r2) ) 2r02 + (r1 - r2) + 2b ln[1 + exp{(r01 - r02 - r1 + r2)/b}] where (r1 + r2) is the F-C distance, and b is an adjustable parameter. The fitted reference values of r01 and r02 are 1.666 and 1.651 Å, respectively, which are near the values for isolated FCl and ClCN (1.638 and 1.631 Å, respectively). The SteinerLimbach plot for FCl:CNX complexes in Figure 1 has a correlation coefficient of 0.994. Results of AIM Analyses. Further support for the evolution of halogen bond type in these complexes comes from the results of the AIM analyses, which are given in Table S1 of the Supporting Information. The AIM analyses characterize the F-Cl and Cl-C interactions involved in the halogen bond in terms of the electron density at each bond critical point (bcp), and the sign of the Laplacian at that point. In all cases, one interaction has a negative Laplacian at the bcp indicating a covalent interaction, while the other has a positive Laplacian characteristic of a weak intermolecular interaction. As expected, the Laplacians change sign as the type of halogen bond changes. In addition, the electron density at the F-Cl bond critical points decrease with increasing F-Cl distance, while the electron density at the Cl-C bond critical points increase with

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TABLE 2: Spin-Spin Coupling Constants 1J(F-Cl), 1X J(Cl-C), and 2XJ(F-C) (Hz) for F-Cl · · · C Halogen Bonds in Complexes FCl:CNX monomer/complex

1

J(F-Cl)

1X

J(Cl-C)

2X

J(F-C)

FCl FCl:CNNH3+ FCl:CNCN FCl:CNNC FCl:CNNO2 FCl:CNF

798.0 746.5 720.2 718.0 717.6 727.8

47.7 105.7 114.6 120.5 122.1

8.4 82.0 93.9 101.0 94.7

FCl:CNCF3 FCl:CNCl FCl:CNH FCl:CNCCF FCl:CNCCH FCl:CNCH3

539.0 576.5 554.9 540.3 536.1 562.2

-62.6 -36.4 -63.0 -68.5 -70.6 -63.5

413.3 422.0 396.8 406.7 407.5 385.6

FCl:CNLi FCl:CN-

508.8 338.4

-80.2 -76.8

289.9 134.8

decreasing Cl-C distance as the nature of the halogen bond changes from traditional to chlorine-shared to ion-pair. Exponential relationships with correlation coefficients of 0.999 exist between corresponding F-Cl and Cl-C densities and distances, in agreement with trends previously associated with intermolecular interactions.62 Spin-Spin Coupling Constants. Spin-spin coupling constants 1J(F-Cl), 1XJ(Cl-C), and 2XJ(F-C) for complexes FCl: CNX are reported in Table 2. The components of these coupling constants are given in Table S2 of the Supporting Information. 1 J(F-Cl). Table 2 indicates that 1J(F-Cl) in complexes FCl: CNX decreases relative to the FCl monomer. However, the extent of this decrease depends on the nature of the halogen bond. Thus, 1J(F-Cl) decreases from 800 Hz in FCl to between 720 and 750 Hz for complexes with tradition halogen bonds. A further and more dramatic decrease is found for complexes stabilized by chlorine-shared halogen bonds, for which 1J(F-Cl) varies between 535 and 575 Hz. A further decrease to 510 Hz occurs for the ion-pair complex FCl:CNLi. The negatively charged complex FCl:CN- has 1J(F-Cl) equal to 340 Hz. Figure 2 illustrates the distance dependence of 1J(F-Cl) and the clustering of coupling constants arising from the same type of halogen bond. The correlation coefficient of the trendline is 0.98. The data of Table S2 in the Supporting Information show how the components of 1J(F-Cl) vary with halogen-bond type. For FCl and complexes with traditional halogen bonds, 1J(F-Cl) is dominated by a large and positive PSO term, followed by a

Figure 2.

1

J(F-Cl) vs R(F-Cl) for FCl and complexes FCl:CNX.

Figure 3.

2X

J(F-C) vs R(F-Cl) for complexes FCl:CNX.

smaller but very significant positive contribution from the SD term. The FC term is negative and has the smallest absolute value among these three terms. The DSO term makes no contribution to 1J(F-Cl). There is a dramatic change in the relative contributions of the PSO, FC, and SD terms for complexes with chlorine-shared halogen bonds. For these, all three terms are positive, but it is the FC term that is the dominant term. The PSO and SD terms make much smaller but non-neglible contributions to 1J(F-Cl). All three terms remain positive but decrease in complexes with ion-pair halogen bonds, thereby accounting for the decrease in 1 J(F-Cl) in going from chlorine-shared to ion-pair halogen bonds. 1X J(Cl-C). For FCl:CNX complexes with traditional halogen bonds, 1XJ(Cl-C) is positive, equal to the FC term, and varies from 50 to 120 Hz. In contrast, for complexes with chlorineshared and ion-pair halogen bonds, 1XJ(Cl-C) is negative, is dominated by a negative FC term, and receives smaller negative contributions from the PSO and SD terms. 1XJ(Cl-C) varies from -35 to -70 Hz in complexes with chlorine-shared halogen bonds, and is approximately -80 Hz for ion-pair halogen bonds. These values are consistent with the negative values for the onebond C-Cl coupling constant for ClCN (-52 Hz) and ClCNH+ (-65 Hz). Since the magnetogyric ratios of 13C and 35Cl are positive, the reduced coupling constant 1K(Cl-C) is negative, and thus in violation of the Dirac Vector Model, which states that reduced one-bond coupling constants are positive. This is often the case when the coupled atoms have lone pairs of electrons.63,64 2X J(F-C). The two-bond coupling constant 2XJ(F-C) is always positive because the PSO, FC, and SD terms are always positive, with the FC term dominant. However, there are significant changes in this coupling constant as the type of halogen bond changes. 2XJ(F-C) for traditional halogen bonds varies from 10 to 100 Hz. The PSO, SD, and FC terms all increase in complexes with chlorine-shared halogen bonds, and 2X J(F-C) increases dramatically, varying from 380 to 420 Hz. In complexes with ion-pair halogen bonds, 2XJ(F-C) then decreases to 290 Hz for FCl:CNLi and 135 Hz for FCl:CN-, as all of the terms decrease relative to their values for chlorineshared halogen bonds. However, they are greater than the corresponding terms for traditional halogen bonds. Figure 3 illustrates that as a function of the F-Cl distance, values of 2X J(F-C) cluster according to halogen-bond type. 2XJ(F-C) increases upon going from traditional to chlorine-shared halogen

Ab Initio Investigation of FCl:CNX Complexes bonds for which it has its maximum values, and it then decreases as ion-pair halogen bonds are formed. The value of 2XJ(F-C) for FCl:CNLi also supports the classification of the halogen bond in this complex as an ion-pair halogen bond. Coupling Across Halogen Bonds versus Hydrogen Bonds. How does the variation in one- and two-bond coupling constants across halogen bonds compare with the variation in these coupling constants across hydrogen bonds? 1 J(X-H) and 1J(F-Cl). Both one-bond coupling constants decrease in absolute value as the corresponding distances increase, although in some complexes with X-H · · · Y hydrogen bonds, 1J(X-H) may initially increase before decreasing.65 Whether 1J(X-H) goes to 0 Hz or changes sign at long X-H distances depends on the nature of X and Y. For an X-H-Y hydrogen bond, the reduced coupling constants 1K(X-H) are always positive, as are the reduced coupling constants 1K(F-Cl), since the magnetogyric ratio of 19F is also positive. 1h J(H-Y) and 1XJ(Cl-C). If proton-transfer occurs in a neutral X · · · H · · · Y hydrogen-bonded complex, 1hJ(H-Y) increases in absolute value as the X-H distance increases and the proton approaches Y. For a traditional hydrogen bond, the reduced coupling constant 1hK(H-Y) is negative.65 In contrast, 1X K(Cl-C) for a traditional halogen bond is positive. As proton transfer occurs in a hydrogen-bonded complex, 1hK(H-Y) changes sign and becomes positive. Of course, in an ion-pair, 1h K(H-Y) becomes 1K(Y-H), and the reduced one-bond coupling constant involving H is positive. 1XJ(Cl-C) also changes sign as a traditional halogen bond becomes a chlorineshared halogen bond, but the reduced coupling constant 1X K(Cl-C) is negative. Note that values of 1K(Cl-C) for ClCN and ClCNH+ are also negative. 2h J(X-Y) and 2XJ(F-C). In a very early experimental investigation of spin-spin coupling constants in the FH:collidine complex, Limbach and co-workers observed that although both 1 J(F-H) and 1hJ(H-N) change as a function of temperature, 2h J(F-N) remains essentially constant.66,67 Our theoretical study of a model hydrogen-bonded system FH:NH3 provided an explanation of the experimental data by illustrating the variation in 1J(X-H), 1hJ(H-Y), and 2hJ(X-Y) as proton transfer occurs.68 Subsequently, we demonstrated that two-bond coupling constants 2hJ(X-Y) across X-H-Y hydrogen bonds exhibit maximum absolute values for complexes having proton-shared hydrogen bonds.65 The plot in Figure 3 of 2XJ(F-C) as a function of the F-Cl distance is similar to the curve that shows the variation in 2hJ(F-N) as a function of the F-H distance. Conclusions An ab initio study has been carried out to investigate the halogen-bonded complexes FCl:CNX, with X ) CN, NC, NO2, F, CF3, Cl, Br, H, CCF, CCH, CH3, SiH3, Li, and Na. The results of this study support the following statements. (1) Systematically changing the strength of the base in these complexes leads to changes in the nature of the halogen bond. FCl:CNX complexes in which CNX is a weak base are stabilized by traditional halogen bonds. Increasing the base strength leads to complexes with chlorine-shared halogen bonds, and further increasing the strength of the base produces complexes stabilized by ion-pair halogen bonds. (2) Traditional halogen bonds have long F-C distances, F-Cl distances that are somewhat elongated relative to the FCl monomer, and relatively small binding energies. Chlorine-shared halogen bonds have short F-C distances and longer F-Cl distances, with increased binding energies. Ion-pair halogen bonds have F-C distances that are longer than chlorine-shared

J. Phys. Chem. A, Vol. 114, No. 49, 2010 12961 bonds, relatively short C-Cl and long F-Cl distances, and very large binding energies. (3) Electron densities at F-Cl and Cl-C bond critical points and signs of the Laplacians at these points are indicative of the changing nature of the halogen bonds. (4) EOM-CCSD spin-spin coupling constants 1J(F-Cl), 1X J(Cl-C), and 2XJ(F-C) vary with halogen-bond type. (a) 1J(F-Cl) decreases as the F-Cl distance increases in going from traditional to chlorine-shared to ion-pair halogen bonds. The variation of 1J(F-Cl) with the F-Cl distance is similar to the variation of 1J(X-H) as a function of the X-H distance in complexes with X-H-Y hydrogen bonds. (b) 1XJ(Cl-C) is positive for traditional halogen bonds, and becomes negative in chlorine-shared and ion-pair bonds. Thus, the sign of the corresponding reduced coupling constant also changes from positive to negative. In contrast, 1hK(H-Y) is negative for traditional halogen bonds, and becomes positive as proton transfer occurs. (c) Both 2XJ(F-C) and 2hJ(X-Y) exhibit maximum absolute values for chlorine-shared halogen bonds and proton-shared hydrogen bonds, respectively. The corresponding reduced coupling constants are positive. Acknowledgment. Thanks are due to the Ohio Supercomputer Center for continuing support of this research. We also thank the Ministerio de Ciencia e Innovacio´n (Project No. CTQ2009-13129-C02-02), the Spanish MEC (CTQ2007-62113), and the Comunidad Auto´noma de Madrid (Project MADRISOLAR2, ref S2009/PPQ-1533) for continuing support. Thanks are given to the CTI (CSIC) for an allocation of computer time. Supporting Information Available: Data from the AIM analyses, and the PSO, DSO, FC, and SD components of coupling constants. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Alkorta, I.; Rozas, I.; Elguero, J. J. Phys. Chem. A 1998, 102, 9278. (2) Ouvard, C.; Le Questel, J.-Y.; Berthelot, M.; Laurence, C. Acta. Crystallogr. Sect. B 2003, B59, 512. (3) Karpfen, A. Theor. Chem. Acc. 2003, 110, 1. (4) Auffinger, P.; Hays, F. A.; Westhof, E.; Ho, P. S. Proc. Natl. Acad. Sci. 2004, 101, 16789. (5) Glaser, R.; Chen, N.; Wu, H.; Knotts, N.; Kaupp, M. J. Am. Chem. Soc. 2004, 126, 4412. (6) Wang, W.; Wong, N.-B.; Zheng, W.; Tian, A. J. Phys. Chem. A 2004, 108, 1799. (7) Berski, S.; Ciunik, Z.; Drabent, K.; Latajka, Z.; Panek, J. J. Phys. Chem. B 2004, 108, 12327. (8) Metrangolo, P.; Neukirch, H.; Pilati, T.; Resnati, G. Acc. Chem. Res. 2005, 38, 386. (9) Zou, J.-W.; Jiang, Y.-J.; Guo, M.; Hu, G.-X.; Zhang, B.; Liu, H.C.; Yu, Q.-S. Chem.sEur. J. 2005, 11, 740. (10) Zou, J.-W.; Lu, Y.-X.; Yu, Q.-S.; Zhang, H.-X.; Jiang, Y.-J. Chin. J. Chem. 2006, 24, 1709. (11) Grabowski, S. J.; Bilewicz, E. Chem. Phys. Lett. 2006, 427, 51. (12) Aakero¨y, C. B.; Desper, J.; Helfrich, B. A.; Metrangolo, P.; Pilati, T.; Resnati, G.; Stevenazzi, A. Chem. Commun. 2007, 4236. (13) Lu, Y.-X.; Zou, J.-W.; Yu, Q.-S.; Jiang, Y.-J.; Zhao, W.-N. Chem. Phys. Lett. 2007, 449, 6. (14) Lu, Y.-X.; Zou, J.-W.; Wang, Y.-H.; Yu, Q.-S. Int. J. Quantum Chem. 2007, 107, 1479. (15) Aakeroy, C. B.; Fasulo, M.; Schultheiss, N.; Desper, J.; Moore, C. J. Am. Chem. Soc. 2007, 129, 13772. (16) Riley, K. E.; Merz, K. M., Jr. J. Phys. Chem. A. 2007, 111, 1688. (17) Alkorta, I.; Solimannejad, M.; Provasi, P.; Elguero, J. J. Phys. Chem. A. 2007, 111, 7154. (18) Lu, Y.-X.; Zou, J.-W.; Wang, Y.-H.; Jiang, Y.-J.; Yu, Q.-S. J. Phys. Chem. A. 2007, 111, 10781. (19) Palusiak, M.; Grabowski, S. J. Struc. Chem. 2007, 18, 859. (20) Voth, A. R.; Hays, F. A.; Ho, P. S. Proc. Natl. Acad. Sci. U.S.A. 2007, 104, 6188.

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