Calculated and Experimental Structures of the p-Difluorobenzene

Characterization of Photoinduced Electron Transfer in Jet-Formed Acceptor−Donor Complexes. 1. Isomeric Forms of Complexes of Anthracene with Aniline...
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J. Phys. Chem. 1995, 99, 5848-5860

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Calculated and Experimental Structures of the p-Difl~orobenzene-(H20)~=1-3 Clusters in Their Different Electronic States and Inference for the Ionic Nucleophilic Substitution V. Brenner,*J S. Martrenchard-Barra,' P. Millie,? C. Dedonder-Lardeux,' C. Jouvet,' and D. SolgadP CEA-CE Saclay, DSMLDRECAM/SPAM, 91191 Gif sur Yvette, France, Luboratoire de Photophysique Moleculaire du CNRS, Universitk Paris-Sud, 91405 Orsay, France Received: November 15, 1994; In Final Form: January 24, 1995@

The equilibrium geometries and corresponding binding energies of the different electronic states (ground, excited and ionic) of p-difluorobenzene-(H20),=1-3 clusters have been determined using a semiempirical perturbation exchange theory model for intermolecular interactions. The theoretical results correctly reproduce the spectroscopic properties of these clusters and allow interpretation of experimental observations. The calculated energetics can then be compared to experimental results in order to understand the role of the cluster size in the ionic nucleophilic substitution reaction.

Introduction Molecular clusters produced in supersonic jet experiments can be used as microsystems to study chemical reactivity at the simplest level, particularly photochemical reactions. The environmental effects, i.e., the solvent, is modeled by adding molecules one by one to the cluster. The stoichiometry of the cluster can be determined by mass spectrometry with soft ionization (here resonant-enhanced multiphoton ionization). The geometry of the reactive partners before excitation or ionization is well-defined since the temperature in the supersonic expansion is very low (a few degrees K). However, this geometry is not always easy to obtain experimentally and several isomers can coexist in the expansion and the determination of the different structures needs accurate calculations. Following the pioneering work of Brutschy and co-workers on chemical reactions in ionic benzene derivatives clustered with NH3 or CH30H,' we have reported a detailed study of the nucleophilic substitution of ionic p-difluorobenzene (PDFB) by water leading to ionic solvated p-fluorophenoL2 The experiments indicate that at least three water molecules are necessary to induce the chemical reaction. We have proposed a kinetic scheme where the role of the water cluster is to enable a proton transfer, this effect being related to the proton affinity of the solvent which increases with the cluster size. However, the energetics of the system cannot be deduced directly from the experiment. Accurate calculations are necessary to determine the binding energies and structures of the small p-difluorobenzene-water clusters in the ground, excited, and ionic states. From these calculations, it will be possible to build the thermodynamical diagram of the reaction and to test whether the mechanism previously proposed is consistent with the calculated geometries. The challenge is to find a model for intermolecular interactions with sufficient complexity to reflect the observed properties of the different electronic states of clusters, and at the same time which allows an almost exhaustive exploration of the potential energy surfaces in order to be sure to find all the significant isomers. Consequently, only semiempirical methods can be easily applied. This paper presents semiempirical calculations on the ground, excited, and ionic state DSM/DRECAM/SPAM.

* Universit6 Paris-Sud.

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Abstract published in Advance ACS Absrracts, March 15, 1995.

of PDFB(H20),,1-3 clusters (equilibrium geometries and interaction energies) in comparison with new experimental results. Experimental Section We have already presented in ref 2 a detailed study on PDFB(HzO), clusters obtained by resonance-enhanced two photon ionization. The main results will be summarized in this section together with new experimental data on the rotational contours. Neutral clusters in the jet are excited to the S1 state and then ionized by a second photon. The resulting ions are detected by time of flight mass spectrometry. Excitation spectra for each cluster size can be obtained by recording the ion current at each mass peak as a function of the first wavelength (hvl). In onecolor two-photon ionization, some excess energy can be imparted to the ionic system and two decay processes can occur: evaporation of one water molecule or chemical reaction leading to fluorophenol+. Thus, the excitation spectra of a precursor to a reaction product will not always be detected at its mass but may be detected at the mass of the fragment. As we will see, this may lead to difficulties in the interpretation of the spectra which cannot always be elucidated by two color ionization. Calculations, however, may be useful to assign the spectra. I. Excitation Spectra. The spectra of the 1-1 and 1-2 clusters in the vicinity of 0; band under low partial pressure of water conditions in the 36 800-37 800 cm-I range are presented in Figure 1. Assignment of these spectra has been partly done in ref 2: the vibrational bands correspond essentially to four intramolecular vibrations of PDFB in this energy region: the two intense correspond to the 0; and 5; and the two weaker ones to 8; and 6; transitions, shifted by complexation. As can be seen in Figure la, at the mass peak corresponding to 1-1 cluster (Le., PDFB(H2O)), two series of structured vibronic bands are observed. One of them is also observed at the mass of 1-2 cluster and is thus assigned to the evaporation of one water molecule from the 1-2 precursor. The other vibronic progression is assigned to the 1-1 cluster. This cluster also evaporates one water molecule when the vibronic band 5; is excited. Through a two-color experiment, it has been shown that this fragmentation occurs in the excited state and an evaluation of the binding energy of PDFB(H20) neutral cluster has been deduced from the fragmentation limit and the known

0022-3654/95/2099-5848$09.00/0 0 1995 American Chemical Society

Structure of PDFB-(HZO)~=~-~ Clusters

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1

1

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reactive isomer

m

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1

400

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I

600

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I

800

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I

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1000

1: 0

cm-’ Figure 1. Excitation spectra of PDFB(H20) and PDFB(H20)z clusters. Energies are given with respect to the SI SO 0; transition of free

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PDFB (36 838 cm-’). The most important vibronic bands are labeled and van der Waals modes are marked with an asterisk. (a) Spectrum recorded at the 1- 1 cluster mass peak: bands marked with # belong to the 1-2 cluster (which has evaporated one molecule of water in the ionic state). (b) Spectrum recorded at the 1-2 mass peak. Two progressions are observed, one corresponding to the “structured isomer” and the other broad one to the “reactive isomer” (see text).

TABLE 1: Experimental Data (cm-l) on PDFB(H,O), Clusters evaporation of the threshold binding energy ground excited SI SO ionization of one water clusters state state transition threshold molecule 1-1 975 f 12 8 0 6 f 12 169 72450f50 1-2 271 72400f50 73756f50 structured

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adiabatic ionization potential of PDFB, the binding energy of PDFB(H2O) being 975 f 12 cm-L.2 Other weak bands appear in the 1- 1 mass selected excitation spectrum (asterisks in Figure la)): they have been assigned to van der Waals intermolecular PDFB-H20 elongation, but these progressions are very short, indicating small variation of equilibrium geometry between ground and excited states. Similar van der Waals vibrations appear also for the 1-2 structured cluster. The shifts of the electronic transition of PDFB(H20), clusters are presented in Table 1. For both 1- 1 and “1-2 structured” clusters, the main absorption is blue-shifted as compared to the bare molecule. At the mass peak corresponding to 1-2 cluster, besides the “structured” blue-shifted bands described above, a broad feature, which starts at =-100 cm-l and presents a maximum shifted by 180 cm-’ with respect to the bare molecule, appears for each

most intense vibronic band of p-difluorobenzene. This broad band can be assigned either to a cluster with two water molecules (Le., belongs to a second 1-2 isomer) or to a cluster with three water molecules which evaporates one water molecule in the ionic state. It should be noticed that these broad bands do not appear at the mass of the 1-1 cluster. To choose between both hypotheses above, we have varied the water partial pressure in the expansion and we have seen that the broad band increases with respect to the narrow band as the amount of water increases. One cannot immediately deduce from this experiment that broad bands belong to a larger cluster (i.e., 1-3). But, if the broad bands belong to a second isomer of the 1-2 cluster, it should be very different from the first one (no more structure in the absorption, different shift of the transition, and larger binding energy since it does not evaporate a water molecule) so that the expansion conditions could favor one of these isomer^.^ The most important point is that this broad band appears also in the excitation spectrum recorded at the mass of the chemical reaction product (p-fluorophenol-H20)+ whereas the structured band does not. It is then very important to know which is the size of this cluster giving the broad band excitation fingerprint (1-2) or (1-3) to determine the number of molecules necessary to induce the nucleophilic substitution reaction. Calculation of interaction energies and electronic shifts will help us to interpret the spectra. In the discussion, the structured features will be called “1-2 structured isomer” and the broad band “reactive cluster”. It should be noticed that the spectrum observed at the mass of PDFB(H20)3+ cluster exhibits other broad bands whose red tail is also red-shifted which are slightly different from the previous ones. These bands belong to either the 1-3 or the 1-4 cluster and most probably to the superposition of both. 11. Ionization and Evaporation Thresholds. Two-color experiments have been performed to gain insight on the energetics of the system: (1) The ionization thresholds of 1- 1 and 1-2 structured clusters are listed in Table 1. It must be stated that, since the geometry of neutral and ionic clusters may be noticeably different, the measured vertical threshold may be higher than the adiabatic ionization potential. (2) The fragmentation threshold PDFB(H20)z 2hv PDFB(H20)2+ PDFB(H20)+ H20 is also given in Table 1. 111. Rotational Contours. The rotational contour of the 0; vibronic band of the bare molecule, and those of the 1- 1 and 1-2 structured isomer as well as the one of some associated van der Waals vibrational modes have been recorded, the SI SO transition being excited by an excimer pumped dye laser with a Fabry-Perot intracavity etalon enabling a resolution of 0.08 cm-I. They are displayed in Figures 2-4. For the bare molecule, since 2hv: is lower than the ionization threshold, the rotational contour was obtained by laser induced fluorescence whereas for the clusters they were obtained using one-color two-photon REMPI excitation spectra. Experimental contours will be compared with simulations using ASYROT code4 starting from the calculated geometries presented in the next section in order to test the validity of the calculations first and then to see how many isomers are formed for each size of clusters (Le., are the vdW mode attributed bands really associated to the most important vibronic progression or are they in fact a new progression corresponding to another isomer?). At first, we have simulated the contour of the 0; vibronic band of the bare molecule, for which rotational constants are known in ground and excited state5(see Table 2). The transition moment is perpendicular to the fluorine axis; thus the contour

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5850 J. Phys. Chem., Vol. 99, No, 16, 1995 100-

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experimental contour

J -2

0

2

4

cm-‘

J\

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Figure 3. Rotational contours of the 0; band of PDFB(H20) cluster. (a) Experimental contour. Simulated contours with the same constants in excited and ground state (see Table 2): (b) isomer 1, bla type; (c) isomer 2, a type; (d) isomer 3, c type; (e) isomer 1 with optimized constants in excited state.

20

P

0

-4

-2

0

2

4

Figure 2. Rotational contours of the 0; band of free PDFB molecule: (a) experimental contour and (b) simulated b type contour (see text and Table 2). corresponds to a b type. A very good agreement between experimental contour and simulation is obtained with a temperature of 5 K (see Figure 2). For both 1-1 and 1-2 complexes, no striking difference has been observed between contour recorded on the 0; band and on the vdW modes. This seems to validate this last assumption of van der Waals mode attribution and shows that only one kind of isomer is formed in the jet for both 1-1 and 1-2 complexes. Furthermore, the shape of the contour looks like the one of the bare molecule (no Q branch) which seems to be characteristic of a b type transition. Theoretical Section

I. Methodology. I. 1. Intermolecular Interactions. We have used the semiempirical method initially developed by Claverie et al.,637based on the “exchange perturbation theory”. At the second order of this treatment, the interaction energy is obtained as a sum of four terms: electrostatic, polarization, dispersion, and short-range repulsion. Each contribution is expressed by simplified analytical formulas which give a reliable description of interactions for all intermolecular distances: (i) The electrostatic term is calculated as the sum of multipole-multipole interactions. The set of multipoles of each molecular subunit (a monopole, a dipole, and a quadrupole on each atom and one point per chemical bond) is obtained by the procedure developed by Vigne-Maeder et aL8 From the exact multipolar multicentric development of the electron distribution derived from the wave function of each molecular subunit, a

simplified representation of the multipole distribution is generated through a systematic procedure of the reduction of the number of centers. The wavefunction is obtained by an ab initio SCF or (SCF f CI) calculation. (ii) The polarization energy is the sum of the polarization energies of each molecular subunit due to the electric field created by the multipoles of all the other molecular subunits. A detailed study of the effects of the basis set and intramolecular correlation on the interaction energy and its minima has shown that the multipole distribution of molecular subunits, involved in the calculation of the electrostatic and polarization terms, must be derived from a correlated wave function within at least a double zeta plus polarization basis set.9 (iii) The dispersion and repulsion terms are sums of atomatom terms. In the repulsion term, the influence on the van der Waals radius of the electronic population variation of each atom is taken into account. According to the “charge” carried by the atom and its number of valence electrons, a corrective factor diminishes or increases the repulsion term; i.e., the van der Waals radius of the atoms is decreased if the “charge” is positive and increased if the “charge” is negative. Recently, a comparison between results obtained by the method of Claverie and by ab initio calculation^^^^^ has allowed us to determine the more appropriate definition of these “charges”, Le., the charges of the multipole distribution. This correction, rather small in most cases, becomes noticeable for the hydrogen atom. The standard definition must be modified in the case of systems involving intermolecular hydrogen bonds. Indeed, the polarization terms of order n ( n > 3) and the term of polarization exchange,“ not taken into account in the method of Claverie since they are negligible for usual equilibrium distances, become important in this particular case. Then, to take into account these terms, the repulsion term is reduced using more important charges, i.e., the charges of the multipole distribution before the reduction

Structure of PDFB-(H20),=1-3 Clusters

J. Phys. Chem., Vol. 99, No. 16, 1995 5851

1 .o

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with some modification^.'^-'^ In particular, we have to determine the correct electronic structure of the excited or ionic molecular subunit to obtain a corresponding satisfactory electronic density. Moreover, supplementary terms appear in the interaction energy, Le., the "excitonic" type term corresponding to the interaction between (A*-B,) and (A-B*,B,-l) for the excited state and the term corresponding to the interaction between (A+-Bn) and (A-B,+B,-l) for the ionic state. The semiempirical parameters are unchanged. These modifications have already been tested and validated. For complexes of 1and 2-cyanonaphthalene with water or acetonitrile,12the calculations reproduce satisfactorily the number of isomers observed in the excitation spectrum and the shift (blue shift as well as red shift) of their electronic transition relative to that of the uncomplexed molecule. Furthermore, this method have been used to explain the stability of small doubly-charged p difluorobenzene clusters13 and to demonstrate for the first time the stability of the ion-neutral [C&-iso-C3H7+] and [C&I7+C&] c~mplexes.'~ 1.2. Geometries, Bases, and Multipole Distributions. The neutral experimental geometry of the p-difl~orobenzene'~ is used for both ground, excited, and ionic state. This assumption is justified by the fact that the variations of geometry for the excited and ionic state are small and lead to quasi-identical interaction energies in the clusters. The p-difluorobenzene multipole distributions in these different electronic states derive from correlated wave functions. The different correlated wave functions are determined for a 6-31G** basis set (6-31G basis set of Pople16 plus one set of polarization functions F( 1.62), C(0.63), and H(0.80)) by the following procedure: As a valence CASSCF calculation (CASSCF, complete active space self-consistent field) in the (a n)system is untractable, we have first performed a CASSCF calculation in the n system of the different electronic states. We thus obtain, for the different electronic states, a good description of the molecular n orbitals and of the variation of the doubly occupied bonding and nonbonding a molecular orbitals. Second, we have used the P A 0 method (PAO, polarized atomic orbitals)17 to obtain the antibonding a molecular orbitals of the different electronic states. Third, we have performed, for the different electronic states, a configuration interaction calculation including, in the (a -k n)system, all mono- and diexcitation with respect to the preponderant configuration and in the n system, all excitations. Finally, from each configuration interaction matrix, the natural orbitals of the different electronic states and their occupation numbers are determined.'* Such calculations allow us to obtain correlated wave functions which take into account the major part of the intramolecular nondynamical correlation (around 95% for the system n and 60-70% for the system a) and to have a balanced representation of the ground, excited, and ionic states. Moreover, they correctly reproduce the excitation energy and the ionization potential of the p-difluorobenzene. The calculated values are 40 300 cm-' for the excitation energy and 70 610 cm-' for the ionization potential and the experimental values are 36 838 cm-l 19 and 73 871 cm-I?O respectively. The uncertainty in our theoretical values is about 0.4 eV, an acceptable value in view of the size of the system. For the determination of the ionization potential of the benzene, Taheshitazl has obtained similar uncertainty using a single and double excitation configuration interaction calculation. For the water molecule, the experimental geometry has been taken from the ref 11. The basis set is a (8s4p/4s) basis set obtained by a contraction of the van Duijneveltd (14s7p/lOs)

+

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0.4

0.2

0 . 0 1 ' ' -4

"

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L

"

0

'

'

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I

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cm-' Figure 4. Rotational contours of the 0; band of PDFB(H20)z cluster: (a) experimental contour, (b) coplanar isomer (l),simulated b/a type contour, and (c) stacked isomer (2), simulated c/a type contour.

of the numbers of centers. In this way, a geometry close to the experimental one is obtained for the water dimer (see paragraph II.2.a). The dispersion component includes terms up to C1dRi)O. Added to this term is an exchange dispersion contribution which also takes into account the influence on the van der Waals radius of the electronic population variation of each atom. All the semiempirical parameters involved in these terms have been determined in order to reproduce results obtained on small systems by both supermolecule and symetry-adapted perturbation theory methods.' This method and all semiempirical parameters are suited for the study of clusters in their ground electronic state. This method can be applied to excited and ionic electronic states

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TABLE 2: Rotational Constants (cm-’) Used in the Simulations ground state PDFB PDFB(H20) PDFB(H20)z

isomer 1 isomer 2 isomer 3 coplanar isomer 1 stacked isomer 2

A”

B”

C”

A’

B’

C’

type of contour

0.1881 0.09705 0.0457 0.6452 0.06744 0.03664

0.04764 0.09005 0.0401 0.0365 1 0.01781 0.02993

0.03801 0.025 13 0.02 157 0.03092 0.01413 0.02015

0.17623 0.09005

0.04787 0.02513

0.03764 0.02126

b b/a = 4.85 a

primitive set22to which two sets of polarization functions are added (O(1.5, 0.35) and H(1.4, 0.25)). As the water molecule is a system with a small number of electrons, the multipole distribution is generated from the correlated wave function obtained by a valence CASSCF calculation. The value of the dipole moment of the water molecule, 1.81 D, calculated from this multipole distribution is in very good agreement with the experimental value, 1.855 D.23 1.3. Characterization of the Potential Energy Su@aces (PESs). For every cluster studied in their different electronic states, we have determined the equilibrium geometries using a nonlocal method. This method is an extension of the simulated annealing method to complicated PESs involving many minima and allows the determination of the most significant isomers. Moreover, it gives information about their relative probability of formation, i.e., the width of the attractive area of the corresponding minima.12 These results are significant when the probability of formation is governed by thermodynamic factors and does not obviously reproduce processes which are only dynamic. When the clusters present isomers with similar interaction energy, we have calculated the isomerization barriers using the method developed by Liotard et al.24325to find transition states that we adapted to our systems. For the excited and ionic states of the clusters, we also performed direct interaction energy calculations from the equilibrium geometries determined for the ground state in order to obtain the shifts of the SI SO transition in the cluster relative to the bare p-difluorobenzene (Franck-Condon excitation) and the vertical ionization potential of the clusters. It is important to point out that for the systems studied here, the “excitonic” type terms which appear for the excited and ionic states are negligible and are not taken into account in the calculation of the interaction energy. These approximations are justified by (i) the first excited state of the water molecule being much higher in energy than that of the p-difluorobenzene and (ii) the ionization potential of water and that of p-difluorobenzene being very different. The validity of these approximations will be confirmed by the good agreement between the experimental and theoretical results. 11. Ground State. For all clusters, several isomers are found. According to the number of water molecules, we have observed evolutionary changes in their number and structures. In the 1- 1 cluster, only one isomer is preferentially obtained. It displays a coplanar structure and results from specific interactions. For the 1-2 cluster, a coplanar isomer is also found: the two water molecules form a dimer and interact specifically with the fluorine and hydrogen atoms of the p-difluorobenzene to obtain a cyclic structure. However, we have determined another isomer with very similar interaction energy but with strongly different geometry: a stacked structure where the two water molecules form a dimer but do not interact specifically with atoms of the p-difluorobenzene. In the 1-3 cluster, six isomers which can be divided in two families are found: the stacked structures where the three molecules are above the plane of the p-difluorobenzene and form a trimer and

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excited state

C

b/a = 3.35 c/a = 3.60

0

0

(c)

Figure 5. Isomers of the ground state of the PDFB(H20) clusters: (a) isomer 1, (b) isomer 2, and (c) isomer 3.

the “peripheral” structures where the water trimer is close to one of the fluorine atoms with one or two water molecules in the plane of the p-difluorobenzene. It is important to point out that the number of isomers, the order of stability, and the global geometries are unchanged whatever the definition of charges used to correct the repulsion term, the standard definition or the definition specific to systems involved intermolecular hydrogen bonds. Indeed, only the absolute value of the interaction energy and the characteristic distances are modified. 11.1. PDFB(H20). The interaction energy of the most stable isomer is equal to -2.89 kcal/mol (1). This isomer corresponds to a coplanar structure with an 0-H bond of the water molecule in the plane of the p-difluorobenzene molecule (see Figure 5a)). The distance between the oxygen atom and an hydrogen atom in a-position of the fluorine atom is 2.391 %i and the distance between an hydrogen atom of the water molecule and the fluorine atom is 2.578 A. It is important to note that these distances are intermediate between the intermolecular hydrogen bond lengths and the usual equilibrium distances of the van der Waals clusters mainly bound by dispersive forces. Two other equilibrium geometries, a coplanar structure, 2 (Figure 5b), and a stacked structure, 3 (Figure 5c), are found. However, their interaction energies are significantly smaller: -2.29 kcaVmol for the coplanar structure and -2.08 kcaumol for the stacked structure. The probability of formation of these different isomers determined by the simulated annealing method is 76% for the most stable coplanar structure, 13% for the second coplanar structure, and 11% for the stacked structure. The probability of formation of the two less stable structures is not equal to zero, although the difference in energy with the most stable isomer is relatively important. This can be explained by the widths of the attractive areas corresponding t o the two less stable isomers which are larger than that corresponding to the most stable isomer. The analysis of the terms involved in the interaction energy shows that the electrostatic contribution is prominent in the two coplanar isomers: 94% of the interaction energy for the most

Structure of PDFB-(H20),=1-3 Clusters stable isomer and 85% for the second coplanar isomer. On the other hand, in the stacked isomer, this term represents only 37% of the interaction energy. Moreover, without taking into account the dispersion term (the corresponding result is comparable to a calculation at the (SCFSBSSE) level in the supermolecule method), this isomer is not stable whereas the two coplanar isomers are already stable at this level: 0.15 kcal/mol for the stacked isomer, -1.11 kcaYmol for the most stable coplanar isomer and -1.18 kcdmol for the second coplanar isomer. It is important to note that the contribution of the dispersive forces is more important in the most stable coplanar isomer than in the second coplanar isomer. In the coplanar isomers, the major part of the electrostatic contribution is given by the monopole-monopole term (80%). The monopole carried by the fluorine atoms of the p-difluorobenzene is strongly negative (-0.24 au) as well as the monopole carried by the oxygen atom of the water (-0.14 au) whereas the monopole carried by the hydrogen atoms is strongly positive (0.47 au) as well as that carried by the p-difluorobenzene hydrogen atoms (0.36 au). Consequently, as the intermolecular distances seem to show it, the two coplanar isomers result from specific interactions between these different atoms. The calculations show that one isomer, 1, is preferentially obtained for ground state of the 1-1 cluster and that its equilibrium geometry results from specific interactions: (i) between one of the fluorine atoms of the p-difluorobenzene and one of the hydrogen atoms of the water, (ii) between a hydrogen atom in a-position of the fluorine atom in the p-difluorobenzene and the oxygen atom of the water. We have evidenced here the specificity of p-difluorobenzene as compared to benzene. Indeed, for benzene clustered with one water molecule, we have performed similar calculations26 and only one equilibrium geometry has been determined. This structure, with an interaction energy of -3.30 kcaYmo1, is a stacked structure which retains the 6-fold symmetry of benzene with the oxygen atom on the 6-fold axis, the distance between the centers of mass of the two molecules being equal to 3.168 A. Consequently, the equilibrium geometry of the benzene clustered with one water molecule corresponds to that of the less stable isomer determined for the paradifluorobenzene clustered with one water molecule (Figure 5c). These results are in good agreement both with ab initio calculations and experimental results. Indeed, the ab initio calculations predict a structure similar to ours with a centerof-mass separation in the range 3.21-3.33 A (ref 27 and reference therein) and an interaction energy in the range 3.04.0 kcavmol. In the same way, the experimental structure places the water molecule's center of mass on or very near the 6-fold axis, the center-of-mass separation being 3.329 A for ref 28a, 3.347 f 0.005 A for ref 28b, and 3.32 f 0.07 8, for ref 27. The difference between clusters with benzene and p-difluorobenzene can be partly explained by the modification of the multipole distribution induced in the p-difluorobenzene by the fluorine atom. For example, in the p-difluorobenzene, the monopoles carried by the hydrogen atoms increase about 20%. The difference between the calculated structure of the 1-1 cluster with benzene and p-difluorobenzene is a confirmation of the well-balanced representation of the different contributions to the interaction energy in our approach as proved by the good agreement with the experiment (see Discussion). 11.2. PDFB(H20)2. ( a ) The Water Dimer. The equilibrium geometry determined for the water dimer corresponds to a structure where one hydrogen atom of a molecule interacts strongly with the oxygen atom of the second water molecule (ROO= 2.927 A, 8 d = 9", and 8, = 101'; see Figure 6). Its interaction energy is equal to -4.53 kcaYmo1. Many ab initio

J. Phys. Chem., Vol. 99, No. 16, I995 5853

Figure 6. Equilibrium geometry of the water dimer.

calculations have been performed for this dimer. However, Szalewics et al.29reported that, even in considering only highlevel calculations, the interaction energy varies from -4.10 to -6.10 kcal/mol for similar equilibrium geometries always involving an intermolecular hydrogen bond. For example, Frish et u ~ . , ~ Owith a MP2/6-3 1l++G(2d,2p) optimization calculation, have found a structure similar to our structure (Roo = 2.91 1 A, 8 d = 4S0, and 8, = 123.2') and have shown that the interaction energy varies from -4.5 to -5.4 kcal/mol according to whether the basis set superposition error (BSSE) is taken into account or not. The range of the interaction energy has been determined up to the Mp4/6-31lG++G(3d,3dp)//MP2/6-311G++G(2d,2p) level and, even at this highest level of theory, it is still important: 4.6-5.3 kcal/mol. More recently, Smith et ai?1have calculated at the MP4/6-31l++G(2df,2p)//MW6-3 1lG++G(d,p) level a similar range of the interaction energy: 4.4-5.4 kcal/ mol. The experimental equilibrium geometry of the water dimer is now well e~tablished~~ and the values of the different parameters are similar to the theoretical values: ROO= 2.976 A, 8 d = 2 f lo', and ea= 123 f 10'. On the other hand, the experimental value of the dissociation energy has not yet been determined with the same precision: 3.59 f 0.5 kcaVm01.~~ Furthermore, to compare this value with the theoretical value, the zero-point vibrational energy (ZPVE) contribution must be added. Curtis et al. have calculated this contribution from the intermolecular vibrational frequencies obtained for a 4-3 1G basis set SCF calculation and have found then an interaction energy of -5.4 f 0.7 kcal/mol. In conclusion, the problem of the determination of the equilibrium geometry of the water dimer seems definitively solved but there is still an ambiguity concerning interaction energy. Consequently, we can assume that our approach allows to correctly reproduce the equilibrium geometry of the water dimer and to obtain a satisfactory evaluation of its interaction energy. (b) The 1-2 Cluster. We have found two isomers with very similar interaction energy, -8.88 and -8.86 kcdmol, but with strongly different geometries (Figure 7). The coplanar isomer (1) corresponds to a cyclic structure. There is formation of a water dimer, and each molecule of water interacts strongly with the molecule of p-difluorobenzene. The oxygen atom of one of the water molecules has a specific interaction with one of the hydrogen atoms in a-position of the fluorine atom (2.261 A). One of the hydrogen atoms bonded to this oxygen forms a intermolecular hydrogen bond with the oxygen atom of the second water molecule (1.961 A) (see paragraph II.2.a for details on the isolated water dimer). Finally, one of the hydrogen atoms of the second water molecule is close to the fluorine atom (2.404 A), The second isomer (2) corresponds to a stacked structure where the two water molecules form a dimer: the distance between the oxygen atom of one of the water molecules and one of the hydrogen atoms of the other water molecule is equal to 1.983 A. The two water molecules are above the plane of the molecule of p-difluorobenzene and do not interact specifically with atoms of the latter. The probability of formation of this isomer given by the method for finding minima is equal to that of the coplanar isomer.

5854 J. Phys. Chem., Vol. 99, No. 16, 1995

4:

Brenner et al.

=Y

-

co)

b

(b) (a Figure 7. Isomers of the ground state of PDFE!(H20)2 cluster: (a) coplanar isomer (1)and (b, c) stacked isomer (2).

TABLE 3: Decomposition of the Interaction Energy (kcaVmo1) of the Two Isomers of the 1-2 Cluster ~~

isomers

interaction

---

~~

~

electrostatic repulsion dispersion total

Coplanar (1) PDFB H20 -2.43 PDFB H20 -1.58 H20 H20 -6.21 total -10.22 stacked (2) PDFB H20 -1.73 PDFB H20 -1.06 -6.07 H20 H20 total -8.86

-

(4

Figure 8. Equilibrium geometries (a-d) of the water trimer.

1.82 0.91 4.63 7.36 1.21 1.47 4.36 7.04

-1.36 -0.96 -2.10 -4.42 -1.38 -1.94 -2.07 -5.39

-1.97 -1.63 -3.68 -7.28 -1.90 -1.53 -3.78 -7.21

polarization -1.60

-1.65

The analysis of the decomposition of the interaction energy for these two isomers shows that their stability is due to two different effects (see Table 3). For the two isomers, there is formation of a water dimer since the interaction energies between the two water molecules excluding the polarization term are similar to that of the isolated dimer (-3.81 kcdmol). Moreover, the electrostatic term of the interaction energy of the isolated dimer is equal to -6.03 kcaVmol, a similar value to those of the electrostatic terms between the two water molecules in the two isomers. The total electrostatic term of the coplanar isomer is more important than that of the stacked isomer. In this latter, the electrostatic term is principally due to the electrostatic interaction between the two water molecules whereas for the coplanar isomer the specific interactions between each water molecule and one atoms of the p-difluorobenzene must be added. On the other hand, as the dispersive forces are generally in favor of stacked structures, the dispersion contributions between the two water molecules and the p-difluorobenzene are more important in the stacked isomer than in the coplanar isomer. Consequently, these two effects compensate one for each other and the two isomers have similar interaction energy with two different geometries. Many other isomers have been found for this cluster. We can distinguish two families. For the first family, the interaction is on the average equal to -7.30 kcdmol. The two water molecules always form a dimer but only one of the molecules interacts strongly with the p-difluorobenzene. For example, one of these isomers corresponds to the most stable coplanar isomer of the 1- 1 cluster to which one water molecule, not interacting with the p-difluorobenzene, is added. In the second family, the isomers correspond to the association between the two coplanar structures of the 1-1 cluster, without formation of a water dimer. The interaction energy of these isomers is on the average equal to -5.00 kcal/mol. All these isomers are significantly

TABLE 4: Decomposition of the Interaction Energy (kcaymol) of the Different Isomers of the Water TrimeP isomer 1 E

H20-H20 H2OeH20 H20 H20 polarization total

-

a

do^

don

-3.65 2.005 -3.16 2.047 -3.64 2.006 -2.72 -13.17

isomer 2

isomer 3

isomer 4

E doH -3.18 2.038 0.44 -3.88 2.043 -3.18 2.038 -3.85 2.017 0.51 -3.18 2.038 -3.85 2.017 -3.88 2.043 -2.61 - 1.20 -0.83 -12.15 -8.46 -8.08 E

don

E

don

(A) is the length of the different hydrogen bonds.

less stable than the coplanar and stacked isomers and then chat be considered as significant minima on the potential energy surface of this cluster. In conclusion, the calculations predict two stable isomers with similar interaction energy and probability of formation but with strongly different geometries. The isomerization barrier has been calculated and we have found a value of 0.25 kcdmol. Consequently, we can assume that the process of isomerization can not occur in the supersonic expansion. 11.3. PDFB(H20)j. (a) The Water Trimer. We have found four equilibrium geometries for the water trimer (Figure 8). The two most stable isomers, -13.17 kcaVmol (Figure 8a) and -12.15 kcdmol (Figure 8b), are cyclic and maximize the interaction between the three water molecules (Table 4). For the most stable isomer (Figure 8a), two molecules are equivalent and interact strongly with the third molecule, the interaction between the two equivalent molecules being all the same important. In fact, the three oxygen atoms form an isosceles triangle: the 0-0 distances are R1 = 2.926 8, and R2.3 = 2.897 A. In the second isomer (Figure 8b), the three molecules are equivalent and the three oxygen atoms form an equilateral triangle (R1,2,3 = 2.923 8,). The two others isomers are much less stable, -8.46 kcaVmol (Figure 8c) and -8.08 kcal/mol (Figure 8d) and correspond to open-chain structures where one water molecule interacts strongly with the two other molecules, the interaction between these two molecules being repulsive (Table 4). These results are in relatively good agreement with other theoretical investigations on the water trimer. All the calculation^^^^^^ agree that the lowest energy structure of the water trimer is a hydrogen-bonded ring in which the three 0- - -H-0 atoms are not aligned and two of the free hydrogens lie above the ring and one below giving rise to a chiral structure. The equilibrium 0-0 bond lengths have a wide range of values. The three oxygen atoms form an isosceles triangle (R = 2.802.97 8, for the long bond and R = 2.79-2.96 8, for the two short bonds) except in ref 35 in which all 0-0 separations are equal to 2.80 8,. Recently, two experimental s t ~ d i e s by ~~,~~ FIRVRTS (far-infrared laser vibration-rotation tunneling spectroscopy) have confirmed that the water trimer has a cyclic chiral structure and Pugliano and Saykally deduced that the 0-0

J. Phys. Chem., Vol. 99, No. 16, 1995 5855

Structure of PDFB-(H20),=1-3 Clusters

TABLE 6: Decomposition of the Interaction Energy (kcavmol) of the “Peripheral” Isomers of the 1-3 Clustel“

TABLE 5: Decomposition of the Interaction Energy (kcaVmo1) of the Stacked Isomers of the 1-3 Clustel“ IS 1

----

PDFB PDFB PDFB H20 H20

H20

E H20 H20

H2O

H20 H20 H20

polarization total

doH

IS2

-0.95 - 1.46 - 1.63 -3.69 2.053 -3.07 2.038 -3.06 1.969 -3.28 - 17.68

IS3

OH

E

IS4

doH

-1.63

-1.10 -1.33 -1.55 -3.66 2.071 -3.11 2.034 -3.58 1.963 -3.34 -17.67

-1.11 -0.89 -3.62 1.971 -3.03 2.033 -3.66 2.068 -3.23 - 17.23

(A) is the length of the different hydrogen bonds.

n

----

PDFB PDFB PDFB H20 H20 H20

E H20 H20

H20 H20 H20

H20 polarization total a

doH

IS5

OH

-1.44 -0.48 -1.70 -2.98 2.028 -3.57 1.962 -3.61 2.065 -3.16 -16.94

IS6

E doH -0.90 -1.53 -0.44 -3.69 2.055 -3.60 1.991 -3.10 2.009 -3.22 -16.48

E doH -1.93 0.35 -1.47 -3.14 2.102 -3.55 1.944 -3.65 2.028 -3.07 -16.46

(A) is the length of the different hydrogen bonds.

n

“

6

(4 0 Figure 9. Stacked isomers of the ground state of the PDFB(H20h cluster: (a, b) IS1, (c, d) IS2, and (e, f) IS3.

separations were unequal with two of the 0-0 distances equal to 2.97 8, and the third one shorter at 2.94 A; the quoted error bar was f0.03 A. (b) The 1-3 Cluster. We have found six equilibrium geometries where the three water molecules form a trimer: the three intermolecular distances 0 - H are on the average equal to 2.000 8, and then they are similar to those involved in the isolated water trimer (see paragraph II.3.a for details on the isolated trimer). All these structures have the same probability of formation and their interaction energies are similar. Indeed, the most stable structure has an interaction energy equal to -17.68 kcdmol and the less stable structure has an interaction energy equal to - 16.46 kcdmol. We distinguish two families. For the first family (Table 5, Figure 9), the stacked structures, the water trimer is above the plane of the p-difluorobenzene and, according to its position, the interaction energy is not very different: -17.68 kcdmol for the most stable structure (IS1, Figure 9a,b), -17.67 kcaVmol for the second structure (IS2, Figure 9c,d), and -17.23 kcdmol for the third structure (IS3, Figure 9e,f). In the second family (Table 6 and Figure lo), the “peripheral” structures, the water trimer is close to one of the fluorine atoms of the p-difluorobenzene and one or two water molecules are in its plane. The interaction energy of the

Figure 10. “Peripheral” isomers of the ground state of the PDFB(H20)3

cluster: (a, b) IS4, (c, d) IS5, and (e, f) IS6.

structure presented in the Figure 10a,b is equal to - 16.94 kcaV mol (IS4), that of the structure presented in the Figure 10c,d is equal to -16.48 kcdmol (IS5), and finally that of the structure presented in the Figure 10e,f is equal to - 16.46 kcaVmol (IS6). As for the 1-2 cluster, many other equilibrium geometries have been found for the 1-3 cluster. Some of them (interaction energy of on the average -13.80 kcdmol) correspond to stacked structures where the three water molecules, which are above the plane of the p-difluorobenzene, have the configuration of one of the less stable isomer of the isolated trimer. Others (interaction energy on the average -12.00 kcdmol) correspond to the association between one of the most stable isomers of the 1-2 cluster and one of the most stable isomers of the 1-1 cluster. Finally, we have found equilibrium geometries (interaction energy on the average -8.00 kcdmol) which correspond to the association between three isomers of the 1-1 cluster. However, all these isomers are significantly less stable than the first six isomers presented above and then cannot be considered as significant minima on the potential energy surface of this clusters. In conclusion, the calculations predict several stable structures with similar interaction energy: the stacked structure (IS1, IS2,

5856 J. Phys. Chem., Vol. 99, No. 16, 1995

Brenner et al.

IS3) and the “peripheral” structures (IS4, IS5, IS6). Unfortunately, we have not be able to determine the different isomerization barriers between the six isomers. In. Shifts of the SI SOElectronic Transition of the p-Difluorobenzene. 111.1. The Electronic Excited State of the 1-1 Cluster. As shown by the annealing probability of formation and by energetics, only one isomer is likely to be formed in the jet: the coplanar isomer 1. Starting from the equilibrium geometry of the ground state, we have calculated the interaction energy in the frst electronic excited state (vertical excitation). The interaction energy is equal to -2.57 kcdmol and then less important than that of the ground state. Consequently, the shift of the vertical S I SOelectronic transition of the p-difluorobenzene in the cluster relative to the bare molecule is 112 cm-’ toward the blue. Starting from this geometry and performing a local optimization on the excited state PESs, we obtain a minimum very close to the equilibrium geometry of the ground state. Moreover, if we perform the global determination of the equilibrium geometries of the excited state, the most stable isomer corresponds to this structure. This indicates that there are no changes in the geometry between the ground and excited state. The analysis of the decomposition of the interaction energy of this coplanar geometry shows that the energy variation between the ground and excited state is due to the variation of the electrostatic term. Indeed, the interaction energy is decreased by 0.32 kcdmol (variation from -2.89 to -2.57 k c d mol) whereas the electrostatic term diminishes by 0.38 k c d mol (variation from -2.70 to -2.32 kcdmol). This lowering of the electrostatic term corresponds to the lowering of the monopole-monopole term. Comparing the p-difluorobenzene multipole distribution in the ground and excited states shows that the monopoles carried by the heavy atoms (C, F) have decreased in absolute value whereas the monopoles of the hydrogen atoms are unchanged. Consequently, the blue shift results mainly from the variation of the monopole on the fluorine atom. In conclusion, the shift of the SI SOelectronic transition of the p-difluorobenzene in the cluster relative to the bare molecule is 112 cm-l toward the blue and there are no significant changes in the geometry between the ground and excited states. 111.2. The Electronic Excited State of the 1-2 Cluster. With the geometries of the two most stable isomers of the ground state, we have calculated the interaction energies in the excited state: -8.37 kcal/mol for the coplanar isomer (1) and -8.10 kcal/mol for the stacked isomer (2). The shifts of the S1 SO electronic transition of the p-difluorobenzene in the cluster relative to the bare molecule for these two isomers are then toward the blue but the shift is more important for the stacked isomer, +266 cm-’, than for the coplanar isomer, +178 cm-l. These two isomers lead to shifts which are larger than that calculated for the 1- 1 cluster. The local optimization of these two geometries shows that they correspond to minima on the potential energy surface of the excited state. Indeed, the optimized geometries and the corresponding interaction energies (-8.38 kcdmol for the coplanar isomer and -8.23 kcdmol for the stacked isomer) are very close to those reached by vertical excitation. Moreover, if we perform a global determination of the equilibrium geometries of the excited state, the two most stable isomers correspond to these two equilibrium geometries. Thus, as for the 1- 1 cluster, there are no significant changes in the geometry of these two isomers between the ground and the excited state. The isomerization barrier between

-

-

+

+

TABLE 7: Interaction Energy (kcaUmol) of the Six Stable Isomers of the 1-3 Clusters in the Excited State and Corresponding Shift (cm-’) of the Electronic Transition SI

-

S R

IS 1 IS2 IS3 IS4

IS5 IS6

interaction energy

shift

-16.92 -16.91 -16.70 -16.50 -16.13 -16,12

+266 +262 +189 +154 +122 +120

these two isomers has been calculated and we have found the same value as that of the ground state (0.25 kcdmol). 111.3. The Electronic Excited State of the 1-3 Cluster. From the geometries of the six stable isomers predicted for the ground state (IS1 -IS6), we have calculated the interaction energies in the excited state. The value of the different interaction energies and the calculated shifts of the S1 SO electronic transition are reported in the Table 7. All these isomers lead to blue shifts but the order of magnitude differs from the stacked isomers to the “peripheral” isomers. Indeed, the three stacked isomers (IS1, IS2, IS3) lead to shifts (+189 to +266 cm-l) which are larger than that calculated for the 1-1 cluster (+112 cm-l) whereas the three “peripheral” isomers (IS4, IS5, IS6) lead to shifts (120-154 cm-l) which are similar to that of the 1-1 cluster. The optimization of these six geometries shows that they correspond to minima on the potential energy surface of the excited state. Indeed, during the optimization, the interaction energies increase of 0.08 kcal/mol on the average and there are no significant changes between the optimized geometries and the starting geometries. Moreover, when we have determined the equilibrium geometries of the excited state, we have found that these six isomers correspond to the most stable isomers. IV. The Ionization Potentials. In this section, the results concerning the 1-3 cluster are not presented. Indeed, as for the ground and excited states, we have determined for the ionic state many equilibrium geometries close in energy (on the average -27.50 kcal/mol) and the choice between them is not obvious considering the lack of experimental informations for this cluster. For 1-1 and 1-2 clusters, we have determined the adiabatic and the vertical ionization potential from

-

where E(PDFB(H,O)J is the stabilization energy of the equilibrium geometry of the ground state and E ~ D ~ + ( H is , othe ) J stabilization energy of the ionic state calculated at the ground-state equilibrium geometry (vertical ionization potential) or at the equilibrium geometry of the ionic state (adiabatic ionization potential). It is obvious that these two values only differ when there is an important change in geometry between the ground and the ionic state. N.I. The 1-1 Cluster. From the coplanar equilibrium geometry of the ground and excited state, we have determined for the ionic state an interaction energy of -4.29 kcdmol. The vertical ionization potential is then 73 383 cm-l. If we optimize this structure, there are important changes in the geometry and the corresponding interaction energy increase to -10.15 kcaY mol. This locally optimized geometry also corresponds to the most stable isomer found in the global determination of the equilibrium geometries of the ionic state. The calculated adiabatic ionization potential is then 71 333 cm-’. The equilibrium geometry of the ionic state corresponds to a coplanar structure where the oxygen atom of the water molecule interacts strongly with two hydrogen atoms of the p-difluorobenzene (see Figure 11). In fact, this structure is similar to

J. Phys. Chem., Vol. 99, No. 16, 1995 5857

Structure of PDFB-(H20),=1-3 Clusters

0

Figure 11. Most stable isomer of the ionic state of the PDFB(H20) cluster. d = 2.389 A.

0

of formation of these two isomers given by the method for finding minima are similar. The isomerization barrier is equal to 2.39 kcal/mol. Consequently, it is not obvious to choose between these two structures. Anyway, the adiabatic ionization potential does not differ strongly whatever the isomer is considered and it is nearly equal to 70 000 cm-l. Discussion In this section, the theoretical and experimental results are compared and we will see that the calculated equilibrium geometries and the corresponding interaction energies of the different electronic state of the PDFB(H20),=1-3 clusters allow a clarification of the experimental observations. I. The 1-1 Cluster. The calculations show that a coplanar isomer is preferentially obtained for the ground state. The following experimental and calculated data can be compared: 1. The calculated interaction energy is 1011 cm-l, in good agreement with the experimental binding energy, 975 cm-l. In the calculations, the ZPVE (zero-point vibrational energy) is not taken into account and the interaction energy is then overestimated since calculations give De and experiment DO. 2. The calculated equilibrium geometries are the same in the ground and in the excited state, which corresponds to a wellstructured spectra with short van der Waals progression as observed. 3. The calculated shift is +112 cm-' (toward the blue) instead of 169 cm-' experimentally determined. 4. The measured ionization threshold (72450 cm-') lies between the calculated adiabatic (71 333 cm-') and vertical (73 383 cm-') ones. Indeed, the theoretical vertical threshold is obtained by calculating the potential energy of the ionic cluster at the equilibrium geometry of the ground state. This does not take into account the extension of the vibrational wave function. Classically, this effect means that the experimental measurement of the threshold allows to explore a portion of the neutral potential from which the vertical ionization potential may be lower than at the equilibrium geometry. Therefore, the measured vertical ionization threshold is expected to be smaller than the calculated one, but in any case higher than the adiabatic one, as obtained. Using ASYROT-PC program: simulation of the rotational contour of the 1-1 cluster has been done, starting from the calculated geometries in the ground and excited states. For the 1-1 cluster, we have supposed that the transition moment stays perpendicular to the fluorines axis. Preliminary simulations at 5 K have been undertaken with the same rotational constants for excited state than in the ground state. Indeed, the equilibrium geometries of the 1-1 cluster are the same but the geometry of the p-difluorobenzene is weakly modified between the ground and the excited state. Simulations are presented for each of the three calculated isomers in Figure 3 and constants are listed Table 2. For the first coplanar isomer, the contour is a mixed type b and a (see Figure 3b), for the second one a pure a type (see Figure 3c), and for the stacked isomer a pure c type (see Figure 3d). As can be easily seen, only the first coplanar isomer can reproduce experimental results. To improve the simulation for the first coplanar isomer (water in the plane), we have taken into account the deformation of the p-difluorobenzene in the excited state (the C-F bond is shortened by 0.032 and the angle of the benzene ring (CCF-C) is increased by 2.4°)38 to calculate the rotational constants of the cluster (see Table 2). A good agreement between simulation and experiment is thus obtained (see Figure 3e).

+

(b)

Figure 12. Most stable isomers (a, b) of the ionic state of the PDFB(H20)2 cluster.

that of the second isomer determined for the ground state (Figure 5b) but the distance between the oxygen atom and the two hydrogen is shorter, 2.389 A as compared to 2.678 A. These differences between the ground and the ionic state can be explained by the modification of the multipoles on the fluorine atom in the multipole distribution of the ionic state whereas the multipoles of the hydrogen atoms do not vary so much. For example, the monopole carried by the fluorine atom strongly decreases (55%) whereas that carried by the hydrogen atoms weakly increase (20%). Consequently, the specific electrostatic interactions involving the fluorine atom in the ground state are weakened in the ionic state and the system adopts preferentially a structure involving specific electrostatic interactions between the hydrogen atoms of the p-difluorobenzene and the oxygen atom of the water molecule. N.2. The 1-2 Cluster. From the two equilibrium geometries of the ground and excited state, we have determined for the ionic state an interaction energy of -7.70 kcal/mol for the stacked isomer (2) and -11.53 kcaVmol for the coplanar isomer (1). The vertical ionization potential is then 74 277 cm-' for the stacked isomer and 72 944 cm-' for the coplanar isomer. If we optimize these two structures, there are important changes in the geometry and the equilibrium geometries obtained from these two structures correspond to a water dimer with one molecule in the plane of the p-difluorobenzene and one above this plane. Moreover, using the method for finding minima, we have determined two coplanar equilibrium geometries close in energy. The most stable isomer, with an interaction energy of - 19.97 kcaYmo1, results from specific interactions between a water molecule and two hydrogen atoms of the p-difluorobenzene (Figure 12a). On the contrary, the second isomer, -19.84 kcal/mol, corresponds to the association of the most stable isomer of the ionic state of the 1-1 cluster and the two water molecules do not interact (Figure 12b). The probabilities

5858 J. Phys. Chem., Vol. 99, No. 16, 1995 In conclusion, the calculations show for the ground and excited state the preponderance of one isomer with the water molecule lying in the plane of the benzene ring and an important change in the geometry in the ionic state. The theoretical data concerning this isomer are in agreement with the experimental ones. Furthermore, as predicted by the annealing proportions, only one isomer is obtained in the supersonic expansion. 11. The 1-2 Cluster. In the experimental section we have shown that two kinds of features are observed at the mass corresponding to the 1-2 cluster. The structured one, blueshifted with respect to the bare molecule, appears both at mass of 1-2 and 1- 1 clusters and is attributed to a first isomer of PDFB(H20)z. The other one, broad and less blue-shifted, could be either a second isomer of PDFB(H20)2 or the 1-3 cluster, undergoing evaporation in the ionic state. It has been called "reactive cluster" since it leads to the formation of fluorophenol(HzO)+ product in the ionic state. 11.1. The Broad Band Reactive Cluster. The broad bands observed at the 1-2+ mass peak will be showed to belong to the 1-3 precursor. Indeed, the hypothesis of a second isomer of 1-2 cluster can be ruled out by the following arguments. If these broad bands correspond to an other isomer of 1-2 cluster, one must point out that it does not fragment in the ionic state to give 1- 1 cluster even if the 5; vibration is excited whereas "1 -2 structured" complex does it already by excitation of the 0; band. Thus, the binding energy of the nonstructured isomer 0 is at least 2[5i,,t,,so - Oosmc ,,I Le., ca. 1600 cm-I more than the structured one. From comparison with calculations on 1-2 neutral clusters (see Theoretical Section, paragraph II.2.b)), it results that the broad features would belong to one of the most stable isomers (with an interaction energy of 3080 cm-': the coplanar isomers 1 or the stacked isomer 2 (Figure 7)) with a water dimer linked to the p-difluorobenzene) and the structured features will be attributed to less stable isomers, made of two separated water molecules linked to the p-difluorobenzene in two different sites ( ~ 1 7 5 0cm-'). However, this assumption does not enable to reproduce experimental results. 1. For the most stable (3080 cm-') calculated isomers (coplanar and stacked), the calculated shifts (+266 and 178 cm-l) are larger than the one calculated for the 1-1 cluster (+I12 cm-'). However, the broad band has its maximum at the same position than the 1-1 cluster and extends far in the red. 2. Furthermore, experimental variation of water partial pressure in the expansion showing that the structured isomer appears at lower concentration that the reactive one seems to indicate that the broad band belong to a larger cluster ruling out directly the assumption of two isomers for the 1-2 clusters. However, these pressure effects are not always unambigous and one could propose that the complex appearing at higher pressure is a 1-2 isomer also, more bond than the structured one (see above) but with a very small attraction valley. Since it is not the case, one can be confident that reactive isomer is not the more stable 1-2 cluster and thus the broad band must be due to the 1-3 cluster. 11.2. The Structured 1-2 Cluster. Before assigning the structure of the 1-2 cluster, the following comments on our previous paper can be made: Experimentally, the dissociation threshold of 1-2 cluster leading to 1-1 cluster has been found to be 73 756 cm-'.* A binding energy of 2280 cm-' in the PDFB(H20)2 cluster has been evaluated as the difference between this appearance potential and the experimental ionization threshold (72 450 cm-', assuming that this potential is the adiabatic one) of the

Brenner et al. 1- 1 cluster plus the binding energy of the 1- 1 complex (Ebind. = 975 cm-'). This value of 2280 cm-' is anomalously small as compared to the calculated interaction energy (3080 cm-' for both isomers). This can be understood if we consider that the measured ionization threshold of the 1-1 cluster is not the adiabatic one. This implies that there is an important change in geometry between neutral and ionic states as evidenced by the calculations. For the 1-1 cluster, the calculations lead to an adiabatic ionization potential of 71 330 cm-'. It results that the calculated energy for evaporation of one water molecule in the 1-2 cluster is 71 330 3080 - 1011 cm-' = 73 399 cm-l in relatively good agreement with the experimental value of 73 756 cm-'. The calculations predict two stable isomers (a coplanar 1 and a stacked 2 structure) with the same interaction energy and probability of formation. From the calculated geometries in both the ground and excited state, one can simulate the rotational contour of both isomers (see Figure 4;the rotational constants are listed in Table 2). It can be seen that they both have a very characteristic contour: the coplanar isomer is a mixed b and a type contour whereas the stacked isomer is a mixed a and c type. As for the 1-1 cluster, we have recorded the rotational contour of the band 0; as well as other bands represented with an asterisk in Figure l b of the 1-2 cluster. As one can easily see, only the coplanar isomer (l),with the two water molecules in the plane of the p-difluorobenzene, enables to reproduce quite well the experimental contours of the 0; band. Moreover, the stacked isomer (2) which should be easy to differentiate from the coplanar isomer by its narrow Q branch in the rotational contour is not found (bands with an asterisk are effectively van der Waals modes associated to the 0; band and not isomers of the 1-2 cluster). Therefore, it seems reasonable to assign the well-structured spectrum to the coplanar isomer (1). The stacked isomer (2) does not seem to be present in the expansion, although the two isomers are predicted isoenergetic by the calculation for which the uncertainties in the relative interaction energies can be evaluated to f 0 . 2 kcdmol. Thus, we have to explain this apparent disagreement between calculations and experiment: One can understand the absence of the stacked isomer in the expansion if one assumes that the formation process is a sequential process, the 1-2 cluster being formed by the addition of a water molecule on the 1- 1 cluster and not by the addition of a water dimer on the free molecule. The geometry of the 1-2 coplanar isomer is obtained by adding a water molecule to the 1-1 cluster in the plane of the benzene ring, whereas the 1-2 stacked isomer requires a strong movement of the molecules from a site where the molecules are close to the F atom to a site where the molecules are above the cycle. Such a reorganization will require a lot more energy than the simple addition process and may be quite improbable if the formation process is sequential. By the calculations, the isomerization barrier between the coplanar and stacked isomer of the 1-2 cluster is about 126 K, a nonnegligible value. The assumption of a sequential formation process is validated by the vapor pressure and the ratio of the two flux: water in He and p-difluorobenzene in He. The concentration of water in the carrier gas is 40 times less than the one of p-difluorobenzene and thus a p-difluorobenzene-water meeting is much more likely than a water-water one. The calculated shift of the SI SO electronic transition for the coplanar and the stacked isomers are respectively 178 and 266 cm-', compared to the experimental value of 271 cm-'. Consequently, the theoretical value in best agreement with the

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J. Phys. Chem., Vol. 99, No. 16, 1995 5859

Structure of PDFB-(H20)n=1-3 Clusters experimental one is the one obtained for the stacked isomer, which is inconsistent with the results obtained for the rotational contours. However, there is very good agreement of the theoretical and experimental results for the 1- 1 cluster, although the calculated shift is underestimated. This may also be true for the 1-2 coplanar isomer (similar position of water molecules in the plane); thus 178 cm-l is a lower limit of the shift and this value cannot be used to rule out the isomer 1. The choice of the coplanar isomer is confirmed by the analysis of the theoretical and experimental results obtained for the ionic state. The measured ionization threshold for the 1-2 cluster is equal to 72 400 cm-’, a value a little smaller than to the one obtained for the 1-1 cluster (72 450 cm-I). The theoretical vertical ionization potential are respectively 72 944 cm-’ for the coplanar isomer and 74 277 cm-’ for the stacked isomer, the value being 73 383 cm-’ for the 1-1 cluster. Thus, the difference between the theoretical vertical ionization potentials of the 1- 1 and 1-2 clusters which is more consistent with the experiment is the value obtained when we consider the coplanar isomer. In conclusion, the broad features belong more likely to the 1-3 cluster and only one isomer corresponding to the structured 1-2 cluster can be detected in our experimental conditions: the proposed calculated structure is the coplanar isomer (1). 11.3. The 1-3 Cluster. From the discussion above, the broad “reactive bands” are assigned to the 1-3 cluster. These bands present a maximum shifted by 180 cm-’ toward the blue with respect to the bare molecule. The measured maximum for the 1-3 cluster, smaller than the shift measured for the 1-2 cluster (27 1 cm-’), is in fact similar to the one of the 1- 1 cluster (169 cm-’). With the calculations, we have determined for the 1-3 clusters two families of isomers having nearly the same interaction energy: the stacked isomers (IS1, IS2, and IS3) and the “peripheral” isomers (IS4, IS5, and IS6). The stacked isomers lead to calculated blue shifts (189 to 266 cm-’) which are larger than those calculated for the 1- 1 cluster (calculated 112 cm-’). In contrast, the “peripheral” isomers lead to shifts (120 to 154 cm-’) comparable to the calculated one for the 1-1 cluster. We thus think that this three isomers are responsible for the observed band. This assignment will be consistent with the sequential formation process since the “peripheral” isomers could be easily obtained from the coplanar isomer of the 1-2 cluster whereas the stacked isomers may be more easily obtained from the stacked isomer of the 1-2 cluster which has not been observed. The excited-state equilibrium geometries of the “peripheral” isomers are quite similar to those of the ground state, and therefore one should expect as previously a well-structured spectrum for the 1-3 cluster. However, as we have observed for example in the case of Hgz-Solv, where Solv is water or the temperature of the clusters increases as the cluster size increases due to the heat condensation released in the expansion. Such an effect together with the higher density of low vibrational modes for large clusters may explain the structureless observed spectrum and in this case justify the comparison between calculated vertical transition and the maximum-and not the red beginning of the vibronic bands of the 1-3 clusters. Furthermore, the coexistence of many isomers of the same type can also contribute to the observed broadening. 11.4. Back to the Reactivity. With the new experimental and theoretical results, we can now get more precision on the ionic nucleophilic substitutionchemical reaction. At first, we strongly asserted that three water molecules are necessary to induce the chemical reaction. From the new energetical values for PDEB(H20), clusters, one can build the thermodynamical diagram

7.5~10‘ PDFB’

VIP-

alp.. . . . . . . .

. . ..

R.T.

-.. -

~~

Figure 13. Energetic diagram of PDFB(H20),,,0-3 and fluorophenol(H20)n=0,1clusters in their ground and ionic states. Binding energies with respect to bare molecule and ionic p-difluorobenzene are those

calculated in the text. The relative position between reactants and products is evaluated using experimental ionization potentials of the p-difluorobenzene and the fluorophenoland enthalpy of formation (see ref 2 and references therein). For the PDFB(H20),=0-3+ clusters, the energy range between the two continuous lines corresponds to the energy domain reacted in one-color two-photon excitation spectra presented in Figure 1. Two-color experiments results: VIP is the vertical ionization potential, aIP is the adiabatic ionization potential, and RT is the reaction threshold. of the reaction (Figure 13). As can be seen in this diagram, the reaction channel is already open in the 1- 1 cluster but is not observed, neither for the 1-2 cluster. It is interesting to note in this diagram that for three water molecules, the channel PDFB(H20)3+ fluorophenol+ 2H20 HF becomes energetically closed due to the stabilization by solvation of the reactive cluster PDEB(H20)3. The product of the reaction is then fluorophenol(H20)+ and not bare fluorophenol+ in agreement with the observed mass spectrum where the fluorophenol(H20)+ signal is much more intense than the bare fluorophenol+ one. Kinetic reasons have to be proposed to explain why 1-1 and 1-2 cluster do not react. If the mechanism of X abstraction seems to be well as passing through an addition u complex, the HX elimination process is still subject to discussions. We recently performed energetic and kinetic measurement^^^ on 1- 1 chlorofluorobenzene-ammonia ionic reactive complex which lead us to propose a mechanism for HX elimination passing through the same sigma complex. However, in the present case when simple C-X bond breaking is energetically closed, and it is particularly the case with a strong C-F bond, a new exit channel can be considered with solvent participation. It involves a proton transfer from the water molecule linked to the u complex to the rest of the cluster, creating thus a kind of chain between F and OH through the water cluster which helps to break the C-F bond, allowing the formation of HF. In this

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5860 J. Pliys. Chem.)\Vol. 99, No. 16, 1995 TABLE 8: Measured or Calculated42Proton Affinities (kcaVmol) for Small Ammonia, Methanol, and Water Clusters clusters

proton affinities

NH3 (NH3)2 CH30H (CH30H)z HzO (Hz0)z

-206 -227 -182 -21 1 -167 -195 -206

case, the limiting step is the proton transfer to the water cluster which depends on its proton affinity. This has been also shown for other reactions on other aromatic fluoro compounds where two molecules of methanol or ammonia' enabled the nucleophilic substitution. Table 8 shows the measured or calculated4* proton affinities for small ammonia, methanol, and water clusters. One can remark that three water molecules are necessary to get the same proton affinity as the methanol dimer, providing a good correlation between proton affinities of solvent clusters and experimental results on nucleophilic substitution efficiency. One can add that the proposed geometry of a water trimer bound to the p-difluorobenzene chromophore is consistent with the proposed mechanism. Conclusion The semiempirical method of Claverie has been applied to

PDFB(H20),=1-3clusters in their different electronic states in order to determine their equilibrium geometries and the corresponding interaction energies. The theoretical results reflect very well the observed spectroscopic properties of these clusters. One interesting aspect is that the annealing procedure gives more isomers than observed, which has been interpreted with a sequential formation process of the clusters in the supersonic expansion. From the calculated energetics, it has been possible to show that the role of the cluster size in the ionic nucleophilic substitution is dual: as the cluster size increases, its lowers the proton-transfer barrier enabling the reaction to occur from n = 3 molecules but it also closes the simplest exit channel: the formation of the unsolvated product. Acknowledgment. Thanks are due to 0. Benoist d'Azy for her help in the installation of ASYROT-PC and to M. C. Cossart for fruitful discussions on the interpretation of rotational contours. The authors also thank E. Chaput and R. Richter for their help in getting the experimental data and performing the rotational simulations. Helpful discussions have also been carried on reaction mechanisms with B. Bigot and R. Botter. References and Notes (1) (a) Brutschy, B. J . Phys. Chem. 1990, 94, 8637. (b) Riehn, C.; Lahmann, C.; Brutschy, B. J . Phys. Chem. 1992, 95, 3626. (2) Martrenchard, S.; Jouvet, C.; Lardeux-Dedonder, C.; Solgadi, D. J . Phys. Chem. 1991, 95, 9186 and references therein. (3) Fuke, K.; Kaya, K. J . Phys. Chem. 1989, 93, 614. (4) ASYROT PC: Judge, H. Comput. Phys. Commun. 1987,47, 361.

Brenner et al. (5) Vitas, T.; Hollas, J. M. Mol. Phys. 1970, 18, 793. (6) Claverie, P. In Intermolecular Interactions from Diatomics to Biopolymers; Pullman, B.; Ed.; Wiley: New York, 1978. (7) Hess, 0.; Caffarel, M.; Langlet, J.; Caillet, J.; Huiszoon, C.; Claverie, P. In Proceedings of the 44th International meeting Modelling of Molecular Structures and Properties in Physical Chemistry and Biophysics, Nancy, France 11-15, Sept 1989; Rivail, J. L., Ed.; Elsevier: Amsterdam, 1990. (8) Vigne-Maeder, F.; Claverie, P. J . Chem. Phys. 1988, 88, 4934. (9) Brenner, V.; Millib, Ph. 2.Phys. D 1994, 30, 327. (10) Brenner, V. Thesis, University of Orsay (Paris XI), France, 1993. (11) Hess, 0.;Caffarel, C.; Huiszoon, C.; Claverie, P. J. Chem. Phys. 1990, 92, 6049. (12) Brenner, V.; Zehnacker, A.; Labmani, F.; Millib, Ph. J. Phys. Chem. 1993, 97, 10570. (13) Brenner, V.; Martrenchard, S.; Millit, Ph.; Jouvet, C.; LardeuxDedonder, C.; Solgadi, D. Chem. Phys. 1992, 162, 303. (14) Berthomieu, D.; Brenner, V.; Ohanessian, G.; Denhez, J. P.; Millit, Ph.; Audier, H. E. J . Am. Chem. SOC.1993, 115, 2505. (15) Bowen, H. J. M.; Donohue, J.; Jenkin, D. J.; Kennard, 0.;Wheatle, P. J.; Whiffen, D. J. Table of Interatomic Distances and Configurations in Molecules and Ions; The Chemical Society, Barlington House: London, 1958; W.l. (16) Hehre, W. J.; Steward, R. F.; Pople, J. A. J. Am. Chem. SOC.1969, 51, 2657. (17) Pemot, P. Thesis, University of Pierre et Marie Curie (Paris VI), France, 1984. (18) Hurley, A. C. In Introduction of the Electron Theory of Small Molecules; Academic Press: New York, 1976. (19) Knight, A. E. M.; Kable, S. H. J . Chem. Phys. 1989, 89, 7139. (20) Tsuchiya, Y.; Fuji, M.; Ito, M. Chem. Phys. Len. 1990, 168, 173. (21) Takeshita, K. J . Chem. Phys. 1994, 101, 2192. (22) van Duijneveltdt, F. B. IBM Research Report, RJ945, 1971. (23) Handbook of Chemistry and Physics, 62nd ed.; Weast, R. C., Ed.; CRC Press: Boca Raton, FL, 1981-1982. (24) Liotard, D.; Penot, J. P. In Numerical Methods in the Study of Critical Phenomena; Della, J., Ed.; Springer-Verlag: Berlin, 1981. (25) Liotard, D. Int. J . Quantum Chem. 1992, 44, 723. (26) Cannet, I. private communication. (27) Goth, A. J.; Zwier, T. S. J. Chem. Phys. 1992, 96, 3388. (28) (a) Gutowsky, H. S.; Emilsson,T.; Arunan, E. J . Chem. Phys. 1993, 99, 4883. (b) Suzuki, S.; Green, P. G.; Bumgamer, R. E.; Dagupta, S.; Goddard III,W. A.; Blake, G. A. Science 1992, 257, 942. (29) Szalewiz, K.; Cole, S. J.; Kolos, W.; Bartlett, R. J. J . Chem. Phys. 1988, 89, 3663. (30) Frish, M. J.; Del Bene, J. E.; Bingley, J. S.; Schaefer 111, H. F. J . Chem. Phys. 1986, 84, 2279. (31) Smith, B. J.; Swanton, D. J.; Pople, J. A,; Schaefer III, H. F.; Radom, L. J . Chem. Phys. 1990, 92, 1240. (32) Odutola, J. A.; Dyke, T. R. J . Chem. Phys. 1980, 72, 5063. (33) Curtis, L. A.; Frurip, D. J.; Blander, M. J . Chem. Phys. 1979, 71, 2703. (34) (a) Schiitz, M.; Biirgi, T.; Leutwyler, S.J . Chem. Phys. 1993, 99, 5228. (b) M6, 0.; Yfiez, M.; Elguero, J. J . Chem. Phys. 1992, 97, 6628. (c) Honegger, E.; Leutwyler, S. J . Chem. Phys. 1988, 88, 2582. (d) Kistnrnacher,H.; Lie, G. C.; Popkie, H.; Clementi, E. J . Chem. Phys. 1974, 61,546. (c) Owicki, J. C.; Shipman, L. L.; Scheraga, H. A. J . Phys. Chem. 1975, 79, 1794. (35) Xantheas, S. S.; Dunning Jr., T. H. J . Chem. Phys. 1993,98,8037. (36) Liu, K.; Elrod, M. J.; Loeser, J. G.; Gruzan, J. D.; Pugliano, N.; Brown, M.; Saykally, R. J. Faraday Discuss. 1994, 96, OOO. (37) Pugliano, N.; Saykally, R. J. Science 1992, 257, 1937. (38) Callomon, J. H.; Dum, T. M.; Mills, I. M. Philos. Trans. R. SOC. 1966, A 259, 499. (39) Martrenchard-Barra, S.; Jouvet, C.; Lardeux-Dedonder, C.; Solgadi, D. to be published. (40) Lardeux-Dedonder, C.;Martrenchard-Barra,S.; Jouvet, C.; Solgadi, D.; Amar, F. Laser Chem. 1994, 14, 61. (41) Shaik, S. S.; Pross, A. J . Am. Chem. Soc. 1989, 111,4306. (42) Wanna, J.; Menapace, J. A.; Bemstein, E. R. J . Chem. Phys. 1986, 85, 1795. JP94305 1P