intermolecular bonding and vibrations of 2-naphthol· h (0 0) · intermolecular frequency range is...

Intermolecular bonding and vibrations of 2-naphthol· H20 (020) Martin SchUtz, Thomas BUrgi, and Samuel Leutwyler Institut for anorganische, analytische, und physikalische Chemie, Freiestr.3, 3000 Bern 9, Switzerland

Thomas Fischer Interdiszipliniires Projektzentrum fur Supercomputing, Zurich, ETH-Zentrum, 8092 Zurich, Switzerland

(Received 9 February 1993; accepted 13 April 1993)

A combined experimental and theoretical study of the 2-naphthol . H20/D20 system was performed. Two different rotamers of 2-naphthol C2-hydroxynaphthalene, 2HN) exist with the O-H bond in cis- and trans-position relative to the naphthalene frame. Using Hartree-Fock (HF) calculations with the 6-31G(d,p) basis set, fully energy-minimized geometries were computed for both cis- and trans-2HN' H20 of (a) the equilibrium structures with trans-linear H-bond arrangement and Cs symmetry and (b) the lowest-energy transition states for H atom exchange on the H20 subunit, which have a nonplanar C1 symmetry. Both equilibrium and transition state structures are similar to the corresponding phenol' H20 geometries. The H-bond stabilization energies with zero point energy corrections included.are -;:::;5.7 kcallmol for both rotamers, ~2.3 kcallmol stronger than for the water dimer, and correspond closely to the binding energy calculated for phenol' H20 at the same level of theory. Extension ofthe aromatic 1T-system therefore hardly affects the H-bonding conditions. The barrier height to internal rotation around the H-bond only amounts to 0.5 kcallmol. Harmonic vibrational analysis was carried out at these stationary points on the HF/6-31GCd,p) potential energy surface with focus on the six intermolecular modes. The potential energy distributions and M-matrices reflect considerable mode scrambling for the deuterated isotopomers. For the a' intermolecular modes anharmonic corrections to the harmonic frequencies were evaluated. The {32 wag mode shows the largest anharmonic contributions. For the torsional mode T (H20 H-atom exchange coordinate) the vibrational level structure in an appropriate periodic potential was calculated. On the experimental side resonant-two-photon ionization and dispersed fluorescence emission spectra of 2HN . H20 and d-2HN' D20 were measured. A detailed assignment of the bands in the intermolecular frequency range is given, based on the calculations. The predicted and measured vibrational frequencies are compared and differences discussed.

I. INTRODUCTION molecular clusters are of importance also for molecular modeling, molecular simulations and drug design.

Hydrogen-bonding was recognized already long ago as being of fundamental importance for many different phenomena in nature. With the advent of supersonic molecular beam techniques in the past 15 years, it became possible to synthesize isolated hydrogen-bonded clusters. Very low vibra~ional, rotational, and translational temperatures of the corresponding clusters are achievable in supersonic expansions and a variety of different spectroscopic methods can be applied to provide information on the structure and on the potential energy surface (PES) of the cluster near the minimum-energy geometry. On the theoretical side the development of efficient ab initio algorithms together with present computer performances allow for reliable predictions of structures and energetics of large hydrogen-bonded systems. A comparison of theoretical predictions and spectroscopic data is now possible and necessary and leads to a better understanding of hydrogen bonded systems. On the other hand the experimental data are a gauge for the quality of a theoretical method and can be used for the derivation of basis sets tailored to this type of chemical systems. Since ab initio calculations are widely used for the development of reliable model potentials for hydrogen-bonding interactions, ab initio and experimental investigations on

Pure water clusters already have been the subject of both experimental1

- 6 and theoreticaC-ll studies. Especially the water dimer has been theoretically widely explored with a large assortment of ab initio techniques. 12

-18 Since

the increased computational performance today allows for ab initio Hartree-Fock (HF) structural optimizations and second derivative calculations of molecular systems with more than 300 basis functions, larger hydrogen-bonded systems can now be investigated at a reasonable level of theory using double-zeta (DZ) or triple-zeta CTZ) basis sets, augmented by at least one set of polarization functions and some set of diffuse functions. 19

Molecular complexes involving water or ammonia together with an aromatic chromophore are quite attractive systems for the study of hydrogen-bonding for several reasons. (i) Simple aromatic ring systems with substituents such as hydroxy or amino groups can serve as prototypes for structurally related subunits in biomolecules (e.g., proteins). Thus, knowledge of structures and hydrogenbonding strengths for a series of such solute-solvent complexes or clusters with different aromatic solute molecules is of value for a better understanding of, e.g., solvation effects in biomolecules and protein folding to name a few. eii) A manifold of different hydrogen-bonding conditions

J. Chern. Phys. 99 (3), 1 August 1993 0021-9606/93/99(3)/1469/13/$6.00 @ 1993 American Institute of Physics 1469

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1470 SchOlz et 81.: Vibrations of 2-naphthol· H20

can be studied simply by choosing a proper solute molecule (proper substituents) together with an appropriate solvent, ranging from relatively weak (e.g., benzene-water20,21) to strong interactions including proton transfer reactions [e.g., 2-naphthol' (NH3)4 in the electronic excited 8 1 state22,23]. (iii) Molecular clusters containing an aromatic chromophore allow the convenient use of selective laserspectroscopic methods in molecular beam experiments, e.g., resonant two photon ionization (R2PI) and dispersed fluorescence techniques. Some research groups already succeeded in obtaining direct structural information (rotational constants) from such experiments.24,25 Pure water or ammonia clusters are experimentally less accessible. (iv) As already mentioned above, a reasonable ab initio treatment of such systems is feasible today if the ring system is not too large.26-29

The present paper presents work on the 2-naphthol' H20ID20 complexes (2-naphthol: 2-hydroxynaphthalene, 2HN). We report results from both ab initio calculations and vibrationally resolved electronic spectra obtained using R2PI and dispersed fluorescence emission spectroscopy. Minimum-energy structures and results of harmonic and anharmonic vibrational analyses calculated at the HF 6-31G(d,p) level are presented and compared to the experimental data. The transition-state structure and barrier height for the internal rotation of the H20 moiety relative to the naphthol molecule was investigated. The present study is an extension of our work on the phenol· H20ID20 complexes28,29 where we have shown that a HF calculation using the 6-31G(d,p) basis set provides useful results for geometry and intermolecular vibrational frequencies, consistent with the experiment.

II. METHODS

A. Computational procedure

Minimum-energy structures for cis/trans 2HN (cit rotamers of 2HN, see below), H20 and clt-2HN' H20 were computed at the HF 6-31G(d,p) level (230 contracted basis functions) optimizing both inter- and intramolecular degrees of freedom. Convergence of the selfconsistent field (SCF) step was accomplished if the rootmean-square (rms) difference between the density matrix elements in consecutive cycles of the procedure was lower than 1 X 10-10

• In the structural optimization convergence was assumed if the largest component of the nuclear gradient vectors in internal coordinates was less < 2 X 10-6

hartreelbohr (or hartree/rad). Normal coordinate calculations were carried out at the minimum-energy geometries so obtained using analytic second derivatives. The resulting intramolecular vibrational frequencies used to calculate the zero-point energy (ZPE) corrections were scaled by a factor of 0.9 in order to account for the problem of restricted HF theory in describing dissociation and the ensuing overestimation of these frequencies. 3o Intermolecular vibrational frequencies remained unscaled. In our previous study on phenol' H20 (Ph' H20) and d-phenol' D20 (dPh'D20) (Ref. 29) we compared HF 6-31G(d,p) and 6-311+ + (d,p) calculations to each other and also to ex-

perimental data. Only minor differences in the geometrical parameters and in the harmonic frequencies were observed for these two basis sets, both giving results consistent with the experiment. Since anharmonicity was demonstrated to be of importance for several intermolecular modes of Ph . H20, we also evaluated anharmonic frequencies for several of the clt-2HN' H20ID20 intermolecular normal modes using the same one-dimensional approach; 25-40 points were calculated on the ab initio PES as a function of displacement along the corresponding (harmonic) curvilinear normal coordinate Qi in internal, "natural" coordinates. Since normal coordinates are defined only for infinitesimal displacements and therefore are not unique in different coordinate systems, we selected an appropriate set of natural internal coordinates which express local pseudosymmetries31 as the basis for the normal coordinate displacements. In this context "natural" means dominant contributions of as few as possible internal coordinates of the set to an individual normal coordinate, indicated by the potential energy distribution32,33 or the M_matrix.34,35 A sixth order polynomial fit through these ab initio points was used as the potential energy function in the onedimensional vibrational Schr6dinger equation; this was solved numerically with a fourth-order Runge-Kutta integrator varying the energy until the boundary conditions 1/1(Q/) =0 and alaQ;1/1(Q/) =0 were fulfilled at both ends of the wave function 1/1(Qi)'

The transition-state structures (TS) along the intermolecular torsional paths for H -atom exchange on the water molecule were obtained for both rotamers by full optimization to first-order saddle points (one single imaginary frequency). During the optimization procedure an accurate Hessian was mandatory for each optimization step because of the soft modes of the complexes. Analytical second derivatives were calculated for each step, and the optimization procedure converged after - 5-8 steps.

All ab initio calculations were performed using GAUSSIAN 92.36 For normal coordinate analysis and transformation of the vibrational eigenvectors into the basis of the natural, symmetry-adapted internal coordinates we used the MOLVIB program.37

B. Experimental procedure

2HN (Fluka AG, Buchs, Switzerland, puriss, p.a.) was recrystallized once from toluene. Deuterated 2HN was produced by mixing I g of 2HN, dissolved in 10 ml of CH2C12 with 2 ml of D20 (99.8%). After shaking for some minutes the d-2HN containing CH2Cl2 phase was separated from the D20 phase, and the solvent then removed under vacuum. 2HN' H20ID20 complexes were prepared in a supersonic, adiabatic expansion using a 20 Hz pulsed, heatable and magnetically actuated valve with a circular nozzle (diameter D=O.4 mm) and gas pulse widths of 160-250 f.Ls full-width at half-maximum (FWHM). H20 or D20 was added to the neon carrier gas by flowing the carrier gas over a reservoir held at - 20 ·C. 2HN was seeded into the gas mixture by a heated sample holder (70-80 ·C) built into the valve at backing pressures of po= 1.3-2.0 mbar). For the R2PI experiments the exci-

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R

~~"" •.•••• ~3 .... 8 ". 2

..•...

FIG. 1. Definition of structural parameters for cis/trans 2HN' H20. Only the aromatic ring adjacent to the hydroxy group is depicted.

tation laser (Lambda Physik FL 2002/FL 30) operated at a pulse energy of <25 IlJ, the ionization laser (Lambda Physik FL 3002/FL 30) at ;:::: 1000 IlJ. The resulting cluster ions were detected by a linear time-of-flight mass spectrometer. For the dispersed fluorescence experiments the molecular jet was crossed with the excitation laser beam (200 IlJ/pulse) 0.5 cm downstream of the nozzle. The fluorescence emission was collected by a f = 150 mm, 10 cm lens and analyzed in a I m Spex monochromator equipped with a Hamamatsu 928 photomultiplier. A more detailed description of beam apparatus and time-of-flight (TOF) can be found elsewhere.38

III. THEORETICAL RESULTS AND DISCUSSION

A. Calculated geometries

2HN exists as a cis- (c) and a trans- (t) rotamer which differ in the orientation of the O-H bond with respect to the naphthalene frame (Fig. 1).39-41 Comparing the corresponding HF 6-31G(d,p) optimized minimum-energy structures the c-rotamer is predicted to be stabilized by 354 cm- I relative to the t-rotamer in the So electronic ground state. Including ZPE corrections, the energy difference is

TABLE I. Calculated and experimental rotational constants of c/t-2HN and c/t-2HN' H20 (MHz).

Expt. 6-31G(d,p) A (%)

c-2HN A 2849.3 2891.25 1.472b

B 824.7 833.77 1.100b

C 639.8 647.15 1.149b

t-2HN A 2845.1 2889.39 1.557b

B 825.4 834.25 1.072b

C 640.0 647.35 1.148b

c-2HN'HzO A 1747.34 -40c

B 546.08 _35c

C 416.85 _36c

t-2HN'H2O A 2679.40 _7c

B 456.84 _45c

C 390.99 _40c

"From Ref. 41. b A (calculated-experimental) / experimental. c A (complexed-uncomplexed) /uncomplexed.

301 em -1. This is in close agreement with a previous study where a 6-31G(d,p) basis set was applied to 3-21G optimized geometries41 and a relative stabilization of 353 em-I was calculated for the c-rotamer. The barrier height for t ..... c isomerization in the So electronic ground state, obtained from a HF 6-31G(d,p) TS.optimization, amounts to 728 cm- I (702 cm- i with ZPE corrections included). The corresponding barrier height in the S 1 electronic excited state is expected to exceed the ground state counterpart due to the enhanced double-bond character of the c-o bond in the excited state. Table I contains the calculated rotational constants of c/t-2HN together with the experimental values of Ref. 41. The agreement with experiment is less good than for phenol29 with all calculated constants being too large by 1%-1.5%.

The HF 6-31G(d,p) minimum-energy structures of the c/t-2HN' H20 complexes were obtained by full optimization of intra- and intermolecular degrees of freedom with the starting configuration derived from the corresponding Ph . H20 geometry.29 The hydrogen-bonding arrangement is trans-linear, as for (H20}z and Ph' H20, with the plane of the water molecule perpendicular to the aromatic ring system. The relevant structural parameters of the resulting c/t-2HN . H20 geometries, according to Fig. 1, are com-

TABLE II. Structural parameters of the c/t-2HN' H20 complexes, calculated at the HF 6-31G(d,p) level.

c-2HN t-2HN c-2HN'H2O t-2HN·H2O c-2HN'H2O uncompl. t-2HN'H2O uncompl. Ph· H20' (HzOh TSb TSb

'1 (A) 1.343 1.350 1.345 1.352 1.345 1.342 1.343 '2 (A) 0.950 0.943 0.949 0.942 0.949 0.948 0.950 0.948 R (A) 2.901 2.904 2.906 2.980 2.902 2.905 r3 (A) 0.944 0.943 0.944 0.943 0.944 0.944 0.944 0.944 0 1 (deg) 111.52 110.88 111.81 111.10 111.58 105.9 111.80 112.00 A (deg) 115.96 115.75 120.84 120.84 117.70 115.95 119.10 qJ (deg) 2.82 3.37 3.34 5.3 9.04 9.62 {3 (deg) 138.37 135.18 135.79 117.6 138.55 142.06 O2 (deg) 106.89 105.97 106.82 105.97 106.83 106.3 106.68 106.73

"From Ref. 29. bLowest-energy transition state (hydrogen atom exchange on water moiety).

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piled in Table II. The corresponding values of Ph . H20, (H20h and free clt-2HN for the same level of theory are also given in this.table for convenience. Analogous parameters of the c- and t-2HN . H20 isomers are very similar to each other and to those of Ph . H20. Especially the length of the H-bond (0"'0 distance) is almost equal for clt-2HN . H20 and Ph· H20, both being 0.07 A or 2.5% shorter than in the water dimer. The largest discrepancy occurs in the angle cp being for c-2HN' H20 OS or 16% smaller than in t-2HN' H20 or Ph' H20. Therefore the H-bonding arrangement in the 2HN . H20 c-rotamer seems to be slightly more linear compared to the t-rotamer or the Ph . H20 complex. Complexation shortens the C-O bond length by 0.007 A, and increases the O-H bond length by the same amount.

Table I contains the calculated rotational constants of clt-2HN . H20. Complexation of the t-isomer by H20 mainly affects two constants, decreasing Band C by 45% and 40%, respectively, and A only by 7%. In the c-isomer all three constants are affected; A, B, and C decrease by 40%, 35%, and 36%, respectively.

Transition-state structure. The lowest-energy transition state structures and corresponding binding energies of clt-2HN . H20 were also calculated. These first-order saddle points on the PES represent the barriers for hydrogen atom exchange on the H20 subunit comprising torsion of 180· around the hydrogen bond and furthermore, a change in the inclination angle /3 from {3o to 360·-{3o. The HF 6-31G(d,p) structures so obtained are nonplanar configurations with the H20 moiety rotated by ~95° and ~89° for c- and t-2-HN' H20, respectively and the water oxygen atom 0.4 A above the aromatic plane, quite similar to Ph . H20. The structural parameters are given in Table II. The barrier heights are a prerequisite for a quantitative treatment of the level structure of the torsional mode (cf. Sec. III C).

B. Interaction energIes

1. Binding energies

The binding energies of the cit 2HN' H20 complexes were computed as differences of the minimum-energies of the complexes and the corresponding subunits, each fully optimized at the HF level. ZPE corrections were assessed from the harmonic vibrational analysis with intramolecular frequencies scaled by 0.9 and unscaled intermolecular vibrational frequencies. No attempts were made in this study to correct for the basis set superposition error (BSSE) or to estimate the stabilization energy contributions due to correlation. Our recent study on Ph· H20 (Ref. 29) revealed that both BSSE and correlation contributions are not negligible. Nevertheless reliable estimates for binding energies can be obtained at the BSSE uncorrected HF 6-31 G (d,p) level for H -bonded systems of this type due to fortuitous cancellation of the correlation energy contributions with BSSE. Furthermore the 6-31G(d,p) stabilization energy was shown to be ~ 15% larger than the corresponding 6-311 + + G (d,p) result.29

Table III compares the HF 6-31G(d,p) binding energies of

TABLE Ill. Binding energies and barrier heights to internal rotation of c/t-2HN' HzO, phenol' H20 and (H20h, calculated at the HF level using the standard 6-31G(d,p) basis set. All values in em-I.

-De -Do (Et-Ernin). (Et-Emin)O

c-h-2HN . HzO 2568 2005 247 218 t-h-2HN . HzO 2626 2031 293 236 c-d-2HN'DzO 2568 2122 247 222 t-d-2HN . DzO 2626 2156 293 246 phenol' H20 2537 1958 253 216 (HzOh 1938 1184

the clt-2HN' H20 complexes so obtained to the corresponding values of Ph· H20 and (H20h. No significant differences are noted between the two rotamers of 2HN· H20 and between 2HN' H20 and Ph· H20. Thus extension of the 1T-system of the aromatic molecule from phenol to 2HN hardly influences the H-bonding conditions in the corresponding complexes. For both clt-2HN' H20 and Ph· HP the binding energies are ~ 2.2 kcal/mol or 67% higher than the water dimerization energy. The ZPE contribution again is an important correction; as in Ph . H20 it amounts to ~ 30% of the binding energy in clt-2HN' H20, compared to ~60% in case of the water dimer. The binding energy of the deuterated isotopomers is ~ 6% higher compared to the undeuterated species due to lower intermolecular frequencies.

2. Barrier heights

The differences in electronic energies between the nonplanar transition structures shown in Fig. 4 and the corresponding minimum-energy structures amount to 247 cm- 1

(0.71 kcal/mol) for c-2HN' H20 and to 293 cm- 1 (0.84 kcal/mol) for t-2HN' H20. Inclusion of ZPE corrections for the other 3N - 7 vibrations as described above reduces these barrier heights to only 218 cm- I (0.62 kcal/mol) and 236 cm- I (0.68 kcal/mol) for the c- and the t-isomer, respectively. These values are very similar to the corresponding barrier heights obtained for Ph· H20 (253 and 216 cm- I

). Deuteration increases the barrier heights by <4% (cf. Table III).

C. Intermolecular vibrations

Six low-frequency intermolecular modes occur in the 2HN· H20 complexes, the wag mode {31' the rock mode PI' and the H-bond stretch mode (J originate from the three translations; the wag mode{32, the rock mode P2' and the torsional mode around the H-bond axis T from the three rotations of the free water molecule. (J, /31' and /32 are at (in-plane), whereas PI, P2' and Tare a" (out-of-plane) modes.

The normal modes of c-2HN . H20 are shown in perspective views in Fig. 2 together with the corresponding harmonic frequencies; the normal mode diagrams of the t-rotamer are very similar and not given here. A close resemblance to the intermolecular modes of Ph· H20 (Ref. 29) is evident. The intermolecular modes are fairly localized on the H20 moiety, more so for the modes of rotational than for those of translational parentage. The low-


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FIG. 2. Perspective plots of the intermolecular normal vibrations of cis-2HN' H20 (equilibrium structure) together with the corresponding harmonic frequencies. (a) Intermolecular vibrations with translational parentage. (b) Intermolecular vibrations with rotational parentage. The plots were drawn using the SCHAKAL88B program (Ref. 45).

frequency PI and f31 modes also have noticeable motional components on the 2HN frame, due to linear and angular momentum conservation constraints. Unlike Ph· H20, in the 2HN' H20 complexes two intramolecular a" modes originating from the 2HN ring-torsion and "butterfly" modes occur within the intermolecular frequency range.

These two low-frequency intramolecular modes couple with out-of-plane motions of the water molecule, mainly with PI,2 vibrations. Table IV collects the calculated harmonic frequencies, force constants, and reduced masses of the intermolecular modes of c/t-2HN . H20 obtained at the HF 6-31G(d,p) level. As already discussed in our previous work on Ph· H20 (Ref. 29) a harmonic approximation may be inadequate for some of these modes. Obviously, for the torsional mode r describing a movement in a periodic potential with a barrier height of ~2oo cm- I (TS), a harmonic approximation which predicts a fundamental frequency of ;:::;100 cm-1 fails totally. From our experiences on Ph . H20 we expect large anharmonic corrections for f32 and smaller deviations from harmonicity for o'. For a more complete description, one has to consider (a) the anharmonicity of each mode; (b) anharmonic coupling between the modes; and (c) the effects of internal rotational tunneling for the torsional mode r (H20 hydrogen exchange tunneling path). In order to assess the anharmonic vibrational frequencies of the modes /3l> /32' 0', and r of c/t-2HN . H20 we have used the same one-dimensional approaches as for Ph . H20, assuming separability of the vibrational Hamiltonian in the basis of the normal coordinates and, therefore, neglecting (b) (see below).

1. Deutero complexes

~Since isotopic frequency shifts provide additional information which is of use for the interpretation of experimental data, we also have investigated the intermolecular vibrations of the deutero-substituted 2HN-water complexes using the 6-31 G (d,p) minimum-energy structures and force-fields. Table IV compiles harmonic frequencies, force constants, and reduced masses so obtained of the isotopomecs c- and t-d-2HN' D20. The intermolecular mOdes P2' f32, and r with rotational parentage, which have low reduced masses (;:::; 1 amu) show the largest harmonic frequency shifts (-20% to -27%), while for the modes with translational parentage PI' f31, and 0', which also have sizable components of vibrational motion on the aromatic frame, smaller deuteration shifts (-6% to - 7%) occur. An analogous shift pattern was found for Ph· H20/D20.

As in the_ Ph· H20/D20 case, mode scrambling due to deuteration plays an important role for the 2HN' H20/ D20 intermolecular modes. Deuteration not only modifies the reduced masses, but may also affect the shape or direction of the vibrational eigenvectors, implying deviations in the related force constants between the isotopomers. These changes are particularly noticeable for /32' 0', and P2' The wag force constants f fJ

2 increase by almost 100% and 70%

for cis- and trans-, respectively on going from h-2HN . H20 to d-2HN . D20, while the corresponding stretching force constants f cr decrease by ~ 30% and 20% due to mode scrambling (cf. Table IV). Figure 3 compares the 0' and f32 normal mode diagrams of c-h-2HN' H20 and c-d-2HN . D20. Dramatically increased mixing between the pure wag and stretch (natural) coordinates is evident for the deuterated species.

In the MOL VIB program two different methods are implemented to compute the contributions of individual in-



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1474 SchOtz et al.: Vibrations of 2-naphthol . H20

TABLE IV. Calculated harmonic and anharmonic frequencies, force constants, and reduced masses of c/t-h-2HN' H20 and c/t-d-2HN' D20 at the HF level for the 6-3IG(d,p) basis set.

c-h-2HN . H2O c-d-2HN . D20

cis2HN Harm. freq. Anharm. freq. Force constant Red. mass Harm. freq. Anharm. freq. Force constant Red. mass sym/label (em-I) (em-I) (Nm- I) (amu) (em-I) (em-I) (Nm-I) (amu)

a" PI 29.7 0.17 3.18 a' f31 49.1· 48.3 ( 47.5) 0.58 4.10 a" T 102.8 0.69 1.11 a' u 150.9 145.9 (141.1 ) 6.89 5.14 a' f32 210.9 167.8 ( 183.6) 3.42 1.31 a" P2 229.1 3.79 1.23

trans 2HN t-h-2HN . H2O a" PI 24.8 0.14 3.89 a' f31 54.4 54.2 (54.1 ) 0.73 4.18 a" T 108.6 0.75 1.09 a' u 146.5 142.0 (137.8) 6.71 5.31 a' f32 228.5 19"0.8 (194.3) 3.98 1.29 a" P2- 211.0 3.26 1.24

"In parentheses, frequency of 1st overtone minus frequency of fundamental.

ternal coordinates to a normal mode and thus to quantify mode-mixing, the potential energy distribution (PED) analysis32,33 and the M-matrix assignment (MMA) method.34,35 With the set of natural internal coordinates used in this work to estimate anharmonic corrections to the harmonic frequencies (see below), the off-diagonal contributions of the internal force constant matrix F to the normal modes f32 and a were all negligible and only positive diagonal contributions occurred. For the undeuterated clt-h-2HN . H20 complexes the pure stretch component of a amounts to 90%-91 %, and the pure wag component of f32 to -98%. Deuteration leads to considerably enhanced mixing; a consists of -;::::,67% stretch and -;::::,23% wag, f32 of 25% stretch and 71 % wag in the case of c-d-2HN' D20. For the corresponding trans-rotamer the stretch-wag mixing is less pronounced with a consisting of 77% stretch and 12% wag, f32 of 14% stretch and 82% wag. In the MMA method the participation of the jth internal coordi-

(j

FIG. 3. A comparison of normal modes of u and f32 for the undeuterated cis h-2HN . HzO and the deuterated cis d-2HN . D20 complexes, respectively. Note the dramatically increased mixing between the wag and stretch coordinates for the deuterated species.

27.4 0.16 3.70 45.5 44.8 (44.0) 0.58 4.73 76.0 0.77 2.28

139.4 133.0 (126.9) 4.70 4.10 170.7 162.8 (161.2) 6.67 3.89 170.9 4.82 2.80

t-d-2HN' DzO 23.1 0.14 4.49 50.7 49.9 ( 48.9) 0.72 4.77 79.4 0.82 2.21

136.8 132.3 (128.1) 5.24 4.75 182.4 168.9 (164.9) 6.70 3.42 159.2 4.25 2.84

nate to the ith normal mode M .. is calculated as Mij =~k(LjiLk!,jk)l}.,i=Lji(L -1)ij:fA The MMA picture of the wag-stretch mixing is similar to the PED representation; a and f32 are -;::::, 91 % of pure stretch and pure wag quality in the undeuterated case. For the deuterated ciscomplex a comprises 70% stretch and 25% wag, f32 22% stretch and 66% wag. For the deuterated trans-complex, mixing again is less pronounced with a containing 80% stretch and 14% wag, f32 12% stretch and 77% wag.

2. Anharmonic calculation of the fJt, fJ2 wag and the u stretch frequencies

In order to estimate the first-order anharmonic corrections to the intermolecular wag modes f31' f32' and the H-bond stretch mode a we used the following approach: The vibrational Hamiltonian is assumed to be separable in the basis of the (mass weighted) normal coordinates Qi (as the zero-order harmonic Hamiltonian). The first-order vibrational wave function 'l'vib then can be written as a product of one-dimensional wave functions 1{1(Qi) which all are solutions of the corresponding vibrational Schr6dinger equation,

a2/aQf1{1(Qi) +2{E- V(Qi)}1{1(Qi)lfl=o,

where V( Qi) is the anharmonic potential function for finite displacement along the normal coordinate Qi' V(Qi) was determined in our case by 25-40 ab initio single-point calculations with different displacements (in natural coordinates, cf. Sec. II A) from the equilibrium geometry along the normal coordinate Qi' A 6th-order polynomial then was fitted to these points. The vibrational Schr6dinger equation noted above was solved as previously.29

Table IV includes the resulting frequencies of f31, f32 ,

and a for clt-h-2HN' H20 and c/t-d-2HN' D20. The largest anharmonic corrections occur for f32' similar to the Ph· H20 case. For c- and t-h-2HN . H20 the fundamental frequencies are overestimated in the harmonic approximation by 26% and 20%, respectively. For the deuterated



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counterparts this effect is much less pronounced. For cand t-d-2HN . D20 the frequencies of the {32 fundamental decrease only by 5% and 8%, respectively. This difference in behavior between the deuterated and the undeuterated species can be understand in terms of mode scrambling as discussed above. The main contribution to anharmonicity of {32 stems from the wag internal coordinate, while the PES is more harmonic along the stretch coordinate. Since the stretch components in {32 grow while the wag components decrease upon deuteration of the 2HN-water complexes, a decrease in anharmonicity which is more pronounced for the cis- than the trans-rotamer, is expectable.

Smaller anharmonic corrections are apparent for a; these are 3%-3.5% in case of the undeuterated, 3.5%-5% in case of the deuterated complexes. Note that the anharmonic corrections are enhanced for the deutero species, again due to mixing with the wag component.· Only minor deviations from harmonicity (1 %-2 %) occur for {31' We note that consideration of anharmonicity strongly affects the isotopic frequency shifts of {32 decreasing from - 20% (harmonic approximation) to -11.5% and even -3% for the trans- and cis-rotamer, respectively.

3. Anharmonic calculation of 'T' in a periodic potential, rotational tunneling

For an assessment of the torsional levels we applied the same approach as for Ph . H20, again assuming separability of the vibrational Hamiltonian in the basis of the normal-coordinates. The potential energy along T was approximated one-dimensionally by the function V = V2 ( 1 - cos 2¢ ) /2, where V2 denotes the barrier height (transition structure), and ¢, the displacement from equilibrium along T. Insertion of this potential energy function into the corresponding vibrational Schrodinger equation leads to the Mathieu differential equation42 and tabulated solutions can be used.43 The internal rotation constants42 of 2HN' H20 are F(cis) = 14.71 cm- I and FCtrans) = 14.75 cm- I , nearly the same as for Ph·H20(F=14.74 cm- I ).

Because of the close coincidence of both barrier heights and internal rotation constants between Ph· H20 and 2HN . H20, very similar torsional level spacings are obtained. Considering barrier heights between 120 and 200 cm - I, the experimentally observable transitions (cf. Sec. IV) range within 100-150 cm- I [v=2+ <-v =O+(At ..... At)] and 160-190 cm- I [v=2- <-v =0-(A1 .... An] for the undeuterated species. Deutera-tion decreases these frequency ranges to 8a-.-:120 and 100-130 cm- I , respectively. For a full set ofresuIts we refer to Table VI in Ref. 29. Since the effective path for hydrogen exchange on the water molecule comprises movement along both the torsional and the wag coordinates, nonnegligible, anhllrmonic coupling between T and {32 is expected. For a complete treatment of these modes a fully two-dimensional or even a three-dimensional solution of the Schrodinger equation involving also the stretch coordinate is required.

4. Vibrations in the transition structure

The normal modes of the c-2HN' H20 transition structure belonging to the H20 hydrogen exchange path are depicted in Fig. 4, together with the corresponding harmonic frequencies. Since the normal mode diagrams of the t-2HN' H20 transition state are very similar, they are not given here. As in the Ph . H20 case, one-to-one correlations between the normal modes at the minimum and at the saddle point exist. The normal mode of imaginary frequency (isomerization coordinate) is associated with an almost pure torsion of the H20 subunit around the hydrogen bond (94%, MMA), in close correspondence to Tin the equilibrium structure. For the a mode we note large components of intramolecular butterfly character. The MMA reflects a decrease of the intermolecular stretch contribution on going from the equilibrium to the transition structure from 91 % to 69% for cis- and even to 48% for the trans-rotamer. The significantly larger butterfly character of a for trans-, compared to cis can be explained in terms of the position of the H20 moiety relative to the aromatic frame, being an extension of the double-ring in case of the trans-rotamer. Similarly, strong mixing between intermolecular wag and intramolecular ring-torsion occurs for {32' Nevertheless, the frequency of a hardly differs between the equilibrium and the transition structure. For the rocking and wagging mode frequencies the same inversion pattern was found as for Ph· H20 with the rocking frequencies being increased and the wagging frequencies decreased in the transition state; PI increases from 30 to 50 cm -I, P2 from 230 to 266 cm -I, whereas {31 decreases from 49 to 27 cm- I and {32 from 211 to 189 cm- I (cis-rotamer). The behavior of the trans-rotamer is analogous with PI increasing from 25 to 53 cm- I , P2 from 211 to 260 cm-I, {31 decreasing from 54 to 20 cm - \ and {32 decreasing from 229 to 167 cm- I.

IV. EXPERIMENTAL RESULTS AND DISCUSSION

A. R2PI and dispersed fluorescence spectra of h-2HN • H20 and d-2HN· D20 R2PI spectra

The R2PI spectra of h-2HN' H20 (a) and d-2HN' D20 (b) are presented in Fig. 5. The two most intense bands at 30256 and 30535 cm- I in spectrum (a) and at 30273 and 30547 cm- I in spectrum (b) are the origins of the trans- and cis-rotamers, respectively. The corresponding origins in the absorption spectrum of the 2HN monomer at 30 586 and 30 903 cm -I were recently assigned to the trans- and the cis-rotamer, respectively, by Johnson et al.,41 who measured these bands at rotational resolution. Following this work we assign the less intense origin at lower frequency (30 256/30 273 cm -I) to the trans, the more intense origin at higher frequency (30535/ 30547 cm- I) to the cis-rotamer of h-2HN' H20 and d-2HN' D20, respectively. The red shifts due to complexation with water then amount to 8v= -334 em-I (trans) and 8v= -372 cm- I (cis), both similar to Ph· H20 (8v = -353 em-I). The relative intensity of the origins is in qualitative agreement with the relative trans/cis Boltz-


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1476 SchOtz et al.: Vibrations of 2-naphthol' H20

(a)

P2266em·1

/'

ri-C~~Q

/ ~~~~ ~~\'. ·U. l)

't 901 em-1

(b)

FIG. 4. Perspective plots of the intermolecular normal vibrations of the cis-2HN' H20 transition state structure together with the corresponding harmonic frequencies. (a) Intermolecular vibrations with translational parentage. (b) Intermolecular vibrations with rotational parentage.

mann population of 33% at a temperature of ::::80·C (temperature of sample holder), calculated using the HF 6-31G(d,p) minimum-energies of c/t-2HN' H20 (cf. Sec. III B).

o~ cis

o~ trans

•

31000

FIG. 5. R2PI spectra of h-2HN' H20 and d-2HN . DzO in the vicinity of the electronic origins. The inset shows a section of a spectrum of d-2HN'D l O taken at higher laser intensity. Identified intramolecular modes are marked by '. The electronic origins of the d-2HN isotopomer with double deuterated ring and undeuterated hydroxy group in the spectrum of d-2HN' D20 (see text) are marked with an asterisk.

On the blue side of the origins, numerous weaker features appear, which are due to the intermolecular- and some low-frequency, intramolecular ring-skeletal modes of the complexes. Bands belonging to intramolecular modes are marked by a dot in Fig. 5. The two most prominent, intermolecular features in the h-2HN' H20 spectrum lie 147 and 154 cm- i above the trans and cis origins, respectively. Weaker features appear at +53, +59, + 112, + 118, + 126, and + 130 cm- i relative to 08(trans) and at +55, +64, + 132, and +211 cm- i relative to 08(cis). Furthermore, a relatively complicated band structure is observed 295-300 cm- i to the blue ofOg(cis). Frequencies and intensities relative to the corresponding 08 bands are gathered in Table V.

The R2PI spectrum of d-2HN . D20 in Fig. 5 was recorded on the m/ e = 166 amu channel (4 hydrogen atoms of the complex substituted by deuterium). A selective deuteration of the hydroxy group was not possible under our experimental conditions because of the two acidic ring protons adjacent to the hydroxy group. The two weaker bands :::: 15 em -1 to the red of the 08 bands marked with an asterisk are the origins of the complexes with both ring protons substituted by deuterium and undeuterated hydroxy group.

The two strongest bands in the spectrum belonging to



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Schiltz et al.: Vibrations of 2-naphthol . Hp 1477

TABLE V. Experimental intermolecular vibrational frequencies and relative intensities in the So and SI-spectra of h-2HN' H20 and d-2HN·D20.

So (08 excitation)

Assignment

f3i' 2pi' f37. a"

So (og excitation)

f3'{ a" f37. f37. +f3'{ 2a" a" + f37.

f3i' 2pi f37. a' a' + f3i 2f32 2a'

2p; f3'{ f3i+ 2pi 2f3i 2r+' 2r-' f32 a'

h-c-2HN' H2O

Freq. ReI. into

47 3.5 55 1.3

141 3.2 153 2.8

h-t-2HN . H2O

54 8.4 141 8.2 166 12.9 222 1.3 275 1.5 308 1.5

h-c-2HN . H2O

55 10.0 64 5.7

132 7.3 154 22.6 211 2.7 274 1.9 295 2.3

h-t-2HN' H2O

53 4.3 59 9.6

112 2.3 118 3.6 126 7.8

130 5.7 147 24.1

d-c-2HN . DzO

Freq. ReI. into

45 3.4 51 1.9

140 2.5 147 2.5

d-t-2HN . D20

51 4.1 140 10.0 146 17.6 196 1.2

280 2.7

d-c-2HN' D20

51 5.8 56 2.2

129 3.4 149 7.0

288 2.1

d-t-2HN . D 20

55

109 109 124 95

141

4.8

23.0

intermolecular vibrations are located at + 141 and + 149 cm-1 on the blue side of Og(trans) and OgCcis), respectively. These features correspond to the 147/154 cm-1

bands in the h-2HN . H20 spectrum. Other weak features appear at +55 and +212 cm-1 relative to Og(trans) and +51, +56 +129, and +288 cm- 1 relative to OgCcis).

B. Dispersed fluorescence spectra

Figure 6 shows the dispersed fluorescence em1SSIon spectra of h-2HN' H20 obtained by exciting the OgCcis), OgCcis) + 154 cm-1, Og(trans), and Og(trans) + 147 cm-1

bands. Excitation of the OgCcis) band yields two weak dou~ b1ets at 55/47 and at 153/141 cm-1. The weak feature at 306 cm -1 is due to the intramolecular a' double-ring bend mode. The emission spectrum obtained by exciting the Og(trans) band is similar with features at 54, 141, and 166 em -1. Here, both of the higher-frequency bands show a weak splitting of ~ 5 em -1. The intensity of the peaks relative to the corresponding og band is larger in the Og(trans)-, than in the OgCcis) spectrum. In the emission spectrum excited at the OgCcis) + 154 cm- 1 band a short progression of double bands is visible with the first member at 153(141 cm- 1 being strongly enhanced. Since the

t-2HN·H20 " d:

~ ~ +

cd: "

co + '" ~ tl

• d: tl o:i:

'00 ~ ;! .,.

'"

" o:i:

c-2HN·H20 f!l ;! ~ o:i: + +

00 tl

~~ 0

g co .... '" '"

•

600 500 400 300 200 100 0

FIG. 6. Dispersed fluorescence emission spectra of h-2HN . H20. Lowest spectrum, excitation' at 08 (cis) (30 535 em -I), scattered light contribution subtracted from 08 band. Lower middle spectrum, excitation at Og(cis) + 154 em-I, og band uncorrected. Upper middle spectrum, excitation at 08Urans) (30256 em-I), scattered light contribution subtracted from 08 band. Uppermost spectrum, excitation at OgUrans)+147 em-I, og band uncorrected.

higher-frequency peak in the doublet at 153 cm-1 is slightly stronger, we postulate that the So 153 cm -1 level and the S 1 154 em -1 level are corresponding vibrations. A similar pattern results for the ogCtrans) +147 cm- 1 excitation. A short progression of double bands appears with the first member at 141/166 cm- 1 enhanced. Here, the lower-frequency peak at 141 cm-1 is more accentuated and we thus presume that the So 141 cm- 1 level and the S1 state at 147 cm -1 are corresponding vibrations. We note that the peaks are split, as in the og C trans) spectrum.

Figure 7 compares the four emission spectra of c/t-h-2HN· H20 and c/t-d-2HN' D20, all excited at their corresponding electronic origins. The spectrum of c-d-2HN . D20 looks very similar to the spectrum of the undeuterated species with weak double-bands at 51/45 and 147/140 cm- 1. No substantial isotopic shifts occur. In the spectrum of t-d-2HN . D20 a weak feature at 51 cm -1 and a superposition of two peaks, a strong peak at 146 cm- 1

and a weaker peak at 140 cm-1 appear. The 146 cm-1

peak correlates with the 166 em -1 band in the h-2HN • H20 spectrum. This implies an isotopic frequency shift of 20 em-I.


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1478 SchUtz et al.: Vibrations of 2-naphthol· H20

•

•

•

•

•

600 500

o Q) N

t-h-2HN'H2O

" r--o:i:

0

'<1'\ '<I' r r

,1

c-d-2HN·D2O

" <0

o:i:

r 0 <'l I~

c: o:i: '" ;0 to

.r

\/

c: o:i: '" III ~ III \ I

FIG. 7. Dispersed fluorescence emission spectra of cis/trans h-2HN . H20 and d-2HN . D20, excited at the corresponding electronic origins.

c. Stretching vibrations

In analogy to Ph . H20!D20 we assign the most prominent low-frequency vibronic bands in the R2PI spectra to the S 1 state intermolecular stretching modes a' of trans and cis, respectively (h-2HN'H20: +147/+154 cm- I

,

d-2HN'D20: + 1411+ 149 cm- I). The band at 141 cm- I

in the emission spectra of t-2HN' H20, corresponding to the 147 em-I SI state level (see previous section) is thus assigned to the a" So ground-state stretching vibration of trans. Similarly the 153 cm- I band in the c-2HN' H20 emission spectrum, corresponding to the 154 cm- I SI state level must belong to a" of cis. The ab initio calculation indeed predicts a larger a" frequency Va" for cis than for trans. Calculated harmonic and anharmonic frequencies both agree within < 5% with the experimental values (cf. Table IV). The isotopic frequency shifts are only small for both the So and the S I state and are somewhat overestimated by the calculation. Returning to the R2PI spectra in Fig. 5 we note the occurrence of the first overtone of a'(cis) at +298 cm- 1 and +287 cm- 1 for the undeuterated and the deuterated species, respectively; these are in Fermi resonance with the intramolecular a' double-ring bend mode at 307/300 em-I, which is quite prominent in the R2PI spectrum of the cis-monomer. The 2a' (c-h-2HN' H20) feature is weakly split (::=5 em-I), possibly

. due to a splitting of the S I 0 + /0 - torsional tunneling levels (see below). No splitting is observed for 2a'(c-d-2HN·D20).

The relative intensities of corresponding a6 and 08 .bands in the R2PI spectra are a measure for the shortening of the hydrogen bond (AR = R; - R~) due to SI ",-So excitation. In order to assess aR we computed the quotients of the related Franck-Condon factors 1 <1fJa'(v =1) l1fJa"(V=O) 12 and 1 <1fJa'(V=O) l1fJd'(V=O) 12 for a series of different AR values. The wave functions 1fJa(r) were obtained by numerical solution of the onedimensional vibrational Schrodinger equation. The potential functions V" (r) and V' (r) in the related SchrOdinger equation were approximated by Morse-type potentials of the form V"(r) = D~{1 - exp[ - a"(r - R~)]}2 and V'(r) = D;{l - exp[ - a'(r - R;)]}2, where D~ = 2005/2031 cm- I (c/t) is the ab initio binding energy corrected for the ZPE of the remaining 3N-7 modes and D~ equals D:plus the corresponding experimental spectral red shift 8v (372 cm-I for cis, 334 cm- I for trans). The a" and a' parameters were determined so that the experimental frequencies of the a" and a' fundamentals were matched. Correlating the resulting Franck-Condon factor quotients to the related R2PI peak ratios we obtain a AR = -O.13±O.OI A for both c- and t-h-2HN' H20. This corresponds to a H-bond shortening of ::=5% and can be compared to AR values of -0.15 and -0.22 A found for c/t-2HN' NH3 by rotationally resolved fluorescence excitation spectroscopy.25 For the deuterated isotopomers a significant difference in aR is obtained between the two rotamers, with aR = -0.13 A for the trans and only aR = ~0.08 A for the cis rotamer. A possible explanation for this deviation is the larger stretch/wag mixing of cis, compared to trans, predicted by the calculation (cf. Sec. III C). Since transitions to /3~ (wag) states are much weaker than transitions to a' states we presume that increased wag participation in a leads to an intensity loss in the associated a bands. Our simple consideration therefore probably underestimates aR for the c-d-2HN . D20 complex.

D. Wagging vibrations

If Cs symmetry is conserved in both the So and the SI state, only the a' (in-plane) modes can couple with the SI"'-SO, electronic transition. a" (out-of-plane) modes are only allowed as weak overtones or combinations. Besides a the wag modes /31 and [32 are of a' symmetry and thus are expected to appear in the spectra. [31 is clearly identified in the emission spectra of Fig. 6. We assign the more accentuated peak in the low-frequency double-band structure at 47 cm- I (c-h-2HN'H20), 45 cm- I (c-d-2HN'D20), 54 cm- I (t-h-2HN' H20) and 51 cm- 1 (t-d-2HN' D 20) as the respective [31 fundamentals. Both harmonic and anharmonic calculated frequencies agree with the experimental ground-state values to within <4%. The calculation correctly predicts a larger value of v{3~ for trans than for cis.

Isotopic shifts are small for [31 , as also predicted by the calculation.

In the R2PI spectrum of 2HN· H20 a peak at +55


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SchUtz et at.: Vibrations of 2-naphthol . H20 1479

cm- I relative to the Og(cis) band and a short progression in 59 and 118 cm- I originating from Og(trans) are observed. These bands are assigned to the corresponding S I state f3~ wag modes. The related bands in the R2PI spectrum of the deuterated species appear at Og(trans) +55 cm -I and og (cis) + 51 cm -I, implying a small isotopic frequency decrease of :::::4 cm- I.

In the spectra of Ph· H20!D20 the f31 fundamental was not observed either in absorption or in emission. The occurrence of this band in the 2HN· H20!D20 spectra strengthen our previous interpretation of the Ph· H20 spectra.29

For f32 the experimental So and SI state frequencies of Ph· H20 are v{3~ = 146 cm- I and V{32 = 121 cm-I, respec-

tively.29 Since the hydrogen-bonding conditions are similar for 2HN' H20 and Ph· H20 comparable frequencies for 2HN . H20 are expected. We therefore tentatively assign the peak in the R2PI spectrum (Fig. 5) at og ( cis) + 132 cm- 1 and one peak of the doublet at Og(trans) + 126/130 cm -I as (3~ of cis and trans, respectively. The corresponding peaks in the d-2HN' D20 R2PI spectrum appear at Og(cis) + 129 cm- I and Og(trans) +95 cm- I (very weak, more distinct in inset from saturated spectrum). The resulting isotopic shifts of (3~ are -3 cm- I for cis and -33 cm -I for trans, implying a much larger shift for trans, than for cis. The attenuation of the [3~ (trans) band on going from the undeuterated to the deuterated complex is most likely due to a shift out of Fermi resonance with a'. In emission (Fig. 7) the bands at 141 cm- I (c-2HN' H20 spectrum) and 166 em-I (t-2HN' H20 spectrum) are assigned to the corresponding (3; ground-state wag of cis and trans, respectively. In Fig. 7, the corresponding frequencies of the deuterated species V{3" are 140 cm- I (cis) and 146

2

cm -I (trans) implying isotopic frequency shifts of -1 cm-1 for the cis and -20 cm- I for the trans rotamer. Again, the trans rotamer shows a dramatically larger shift than the cis rotamer. The observed differences in isotopic shift agree with the anharmonic frequency calculation (cf. Sec. III C). In the harmonic approximation the predicted frequency shifts amount to -40 and -46 cm- I for cis and trans, respectively. Using the anharmonic approach the shifts decrease to - 5 and - 22 cm - I, in good agreement with the experiment.

For {32' calculated and experimental frequencies do not agree as well as for f31 or a. In the harmonic approximation the {32 ground-state frequencies are overestimated by 40%-50% in the undeuterated case, and 20%-25% in the deuterated case. Using the anharmonic first-order approximation outlined above the calculated [32 frequencies are still too large by 15%-20% in the undeuterated and::::: 15% in the deuterated case. The remaining disagreement between theory and experiment may be caused by the neglect of f32-'T anharmonic coupling, which is expected to be important (cf. sec. III C and Ref. 29). Nevertheless, a substantial improvement over the harmonic approximation was achieved by this simple approach.

Furthermore, from the f3~/og peak intensity ratios the changes in angle [3 (Fig. 1) due to Sl <-So excitation were

estimated for c/t-h-2HN' H20, respectively. The corresponding Franck-Condon factor quotients were evaluated in the harmonic approximation44 for a series of different displacements using the experimental [3; and f32 frequencies and the reduced mass from Table IV. Based on the Huang-Rhys parameters between 0.36 and 0.41 the resulting change of {3 is I Ll{31 = 15 ± 1° for c/t-h-2HN' H20.

E. Rocking vibrations

Both of the rocking mode fundamentals are symmetryforbidden within the SI <-So transition and are only expected as weak sequences, overtones or combinations. The fundamental frequencies predicted by the ab initio calculation are 229/211 cm- I for P2 and 30/25 cm- I for PI (cf. Table IV). The R2PI spectrum of h-2HN . H20 shows a weak band at Og(cis) +64 cm- I on the blue side of f31 (cis) and, furthermore, two weak peaks at Og(trans) +53cm-1

and Og(trans) + 112 cm- I, on the red side of {31 (trans) and 2{31 (trans). Related features also appear in emission. These may possibly be attributed to 2pI (and/or 2PI{3I) borrowing their intensity from {31 (and 2(31) by Fermi resonances. The calculation predicts a higher 2pI than [31 frequency for cis and vice versa for trans, in agreement with our tentative assignment. The isotopic shifts are small (2-3 cm - I) as predicted by the calculation. Experimental and computed (harmonic) frequencies agree within :::::5%. There is no evidence for P2 overtone or combination bands, in absorption, or in emission.

F. Torsional vibrations

According to the selection rules of the torsional mode discussed in Sec. III D of Ref. 29 only transitions with Llv=O, ±2, ... are allowed for 'T within the Sl <-So electronic transition. For barrier heights of 120-180 cm- I the v=2+ <-v=O+ transitions are predicted to lie in the frequency r~nge of 100-135 and 80-115 cm- I for the undeuterated and the deuterated complex, respectively. The corresponding v=2- <-v=O- transitions are expected' at higher frequencies (undeuterated, 155-185 cm- I; deuterated, 100-120 cm- I; cf. Table VI in Ref. 29).

In the R2PI spectrum of h-2HN . H20 an unidentified feature at Og(trans) + 126 cm- I remains. We very tentatively assign this band to the v' =27 <-v" =0+ (At <- At") transition of'T, in Fermi resonance with f32' This implies an S I state barrier height of ::::: 160 cm -I. The corresponding v'= 2-<-v"=0-(A I '<-A I ") transition, predicted at ::::: 172 cm -I is not visible in the spectrum, probably due to lack of intensity gain by Fermi resonance. For the deuterated species a slightly higher barrier is expected (cf. Sec. III C). Assuming a barrier height of :::::170 cm- I the predicted v'=2+ <-v"=O+(At' <-At") and v'=2- <- v"= 0- (AI' <-AI") frequencies are 110 and 120 cm-I, respectively. Two weak bands at Og(trans) + 109 cm- I and Og(trans) + 124 cm- I indeed are apparent in the R2PI spectrum of d-2HN' D20 (see inset), but again the assignments are very tentative. No indications for transitions in 'T

are evident from the dispersed emission spectra.

J. Chem. Phys., Vol. 99, No.3, 1 August 1993


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1480 SchUtz et 81.: Vibrations of 2-naphthol . Hp

G. Tunneling splittings

Weak splittings of the a" and f32 levels are observed in the emission spectra of t-h-2HN . H20. One possible explanation is as sequence bands due to the difference of the 0+ /0- tunnel splitting in the 8 0 and 8, state, respectively. The 0+/0- splitting should be larger in the 8 0 state since the H-bond is longer and the H-bond energy is smaller by ;:::: 1 kcal/ mol (experimental red shift). For the electronic origins this splitting must be small, < 0.5 cm -', jUdging by the observed width and considering the estimated barrier heights of 120-200 cm -I. Since excitation of a increases the vibrationally averaged length of the hydrogen bond and thus decreases the height of the effective barrier to internal rotation, the 0+/0- splitting is expected to increase in excited a states. The splitting of the f32 band in the emission spectrum of t-h-2HN' H20 at 166 cm-' might be expected because f32 is coupled directly to the tunneling coordinate, as. discussed in Sec. III C. Comparing related features in the emission spectra of c- and t-h-2HN . H20, it is noticeable that bands which are clearly split in the trans case show hardly any splitting for cis. This implies a lower effective barrier to internal rotation for trans than for cis, in contradiction to the calculation. Alternatively, since only differences of the 0+/0- splittings in the 8 0 and the 8 1 state are observable in the spectra, a much smaller deviation between the 8 0 and 8, state barrier heights for cis could follow from this finding. As would be expected in this interpretation, no indication for tunnel splitting is evident from the fluorescence emission spectra of the deutero species. Alternatively, Fermi resonances with overtone and/or combination levels of PI' f31' and/or 7 may be invoked to explain these splittings. However, all such interpretations woUld imply considerable anharmonicities for these modes, and no unique interpretation is possible at this stage.

v. CONCLUSIONS

In our previous study on Ph . H20 and its isotopomers it was shown that ab initio calculations using HF theory and a 6-31G(d,p) basis set provide useful results for both structural parameters and force field, which are consistent with the experiment if anharmonic corrections to the force field are included. In this study we extended our investigations to cis and trans 2HN' H20ID20. Geometryoptimizations at the HF 6-31G(d,p) level yield trans-linear hydrogen-bonding arrangements with Cs symmetry as minimum-energy structures for cis and trans, similar to the Ph· H20 structure reported previously. Only small deviations in the structural parameters occur between c- and t-2HN . H20 and between c/t-2HN' HzO and Ph· H20, calculated at the same level of theory. Especially the H-bond distances R are very similar [2.90-2.91 A, 0.07-0.08 A shorter than in (H20}z]. The binding energies, calculated with zero-point energy corrections included, also are comparable for c/t-2HN' H20 and Ph' H20 [;::::5.7 kcal/mol, 2.3 kcal/mol higher than for (HzO}Z]. An enlargement of the aromatic 1T-system therefore has little influence on the H -bond properties.

The transition structures of c/t-2HN . H20 on the H20 hydrogen atom exchange pathway were also explored by full optimization to first-order saddle points on the related HF 6-31G(d,p)PES. As for Ph' H20, nonplanar C1 structures were obtained with the H20 oxygen atom ~0.4 A above the ring plane. The barrier heights to internal rotation with zero-point energy corrections included amount to 170-180 cm - I, again very similar to the corresponding Ph . H20 value.

Furthermore harmonic vibrational analysis using analytic second derivatives of the HF 6-31G(d,p) PES was carried out for the c/t-2HN . HzOID20 minimum-energy and transition structures with main focus on the six intermolecular modes, characterized as an a' H-bond stretch a, an a" H-bond torsion 7, two a' wags f31, f32' and two a" rocks PI> P2 in the Cs symmetry group. Normal mode analysis of the fully deuterated isotopomers reveals that deuteration induces strong changes in the shapes of the vibrational eigenvectors. Especially for a and f32 a large increase in the stretch/wag mixing was noted, which is more pronounced for cis than for trans. For a more quantitative treatment of this mixing we used the PED and M-matrix methods. The resulting participation of pure stretch to a and pure wag to f32 is > 90% in the undeuterated case. For the deuterated cis-isotopomer a comprises 70% stretch and 25% wag, f32 22% stretch and 66% wag, respectively.

For the a' modes a, f31' and f32' which are symmetryallowed in the 80 .-81 electronic transition anharmonic corrections to the harmonic frequencies were evaluated using a relatively simple, one-dimensional approach which neglects anharmonic coupling between modes. The anharmonic corrections so obtained are relatively small for a and f3, but important for f32. The anharmonic vibrational levels for 1" (H20 hydrogen atom exchange coordinate) were computed using a one-dimensional V = V2 (1-cos 2¢) /2 periodic potential and the estimated barrier heights for internal hindered rotation.

On the experimental side, R2PI and dispersed fluorescence emission spectra of 2HN . H20 and d-2HN . D20 in the region of the 08 transitions of 2HN were measured. Most of the bands observed in the spectra could be interpreted based on the calculations and on our previous work on Ph· H20ID20. The H-bond stretch frequencies are similar to Ph· H20 with v~ = 153/141 cm- 1 in the 8 0 and v~ = 154/147 cm-' in the 8 1 state for cis and trans, respectively. We note a slightly larger Va for cis in both electronic states. Bands due to f3" f32, and 2pI also are identified in the spectra. The occurrence of f3, at 50-60 cm- 1 is new, and supports the assignments in our previous Ph· H20/ D 20 study. Some weaker features were tentatively assigned as transitions to overtones of 7.

Experimental and calculated (anharmonic) frequencies agree within 5% for a and f31 and within 15%-20% for f32' The larger discrepancy for f32 is most likely due to disregard of anharmonic coupling between f32, 1", and a in our approach. Nevertheless, a substantial improvement over the harmonic approximation was achieved. Relative tendencies, e.g., va(cis) >va(trans) were correctly pre-


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Schutz et al.: Vibrations of 2-naphthol . H20 1481

dieted. We conclude that ab initio calculations at the HF/ 6-31G(d,p) level are of predictive value for strongly H-bonded complexes, if anharmonic corrections are taken into account.

ACKNOWLEDGMENTS

This work was supported by the Schweizerische Nationalfonds (20-28995.90 and 20-33879.92). T.F. thanks the Swiss Scientific Computer Center for an NEC Research Grant.

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intermolecular bonding and vibrations of 2-naphthol· h (0 0) · intermolecular frequency range is...

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