Generalized approximation to the reaction path: the formic acid dimer case

A set of mass-weighted internal coordinates was derived and applied to the double proton transfer reaction in the formic acid dimer (FAD). The coordinate set was obtained starting from the Hirschfelder "mobile" by an optimization procedure consisting of a sequence of kinematic rotations. In FAD, the optimization procedure leads to three coordinates that do change significantly along the reaction path. These coordinates span the reaction space, whereas the remaining modes are treated in a harmonic approximation. The effect that the dimer dissociative motion has on the ground and excited vibrational states dynamics was explored. In the frequency region corresponding to the symmetric OH-stretch vibration four doublets have been identified with splittings of 2.76, 0.07, 0.60, and 4.03 cm(-1).     

Vibrational relaxation and coupling of two OH-stretch oscillators with an intramolecular hydrogen bond

We studied the vibrational dynamics of the OH-stretch oscillators of an alcohol with two vicinal OH groups using femtosecond midinfrared pump-probe spectroscopy. The absorption spectrum of pinacol (2,3-dimethyl-2,3-butanediol) in CDCl3 shows two OH-stretch peaks belonging to hydrogen bonded and free OH groups. The anharmonicities of the hydrogen-bonded and free OH-stretch vibrations are 180 and 160 cm(-1), respectively. The lifetime T1 of the OH-stretch vibration is found to be 3.5 +/- 0.4 ps for the hydrogen bonded and 7.4 +/- 0.5 ps for the free OH group. We observed sidebands in the transient spectra after excitation of the bonded OH group, which we attribute to a progression in a low-frequency hydrogen-bond mode. The sideband is redshifted 60 cm(-1) with respect to the 0 --> 1 transition. Due to the coupling between the two OH groups and the presence of the sidebands, simultaneous excitation of both OH-stretch vibrations leads to oscillations on the pump-probe signal with frequencies of 40 and 60 cm(-1).     

Full-dimensional quantum calculations of ground-state tunneling splitting of malonaldehyde using an accurate ab initio potential energy surface

Quantum calculations of the ground vibrational state tunneling splitting of H-atom and D-atom transfer in malonaldehyde are performed on a full-dimensional ab initio potential energy surface (PES). The PES is a fit to 11 147 near basis-set-limit frozen-core CCSD(T) electronic energies. This surface properly describes the invariance of the potential with respect to all permutations of identical atoms. The saddle-point barrier for the H-atom transfer on the PES is 4.1 kcalmol, in excellent agreement with the reported ab initio value. Model one-dimensional and "exact" full-dimensional calculations of the splitting for H- and D-atom transfer are done using this PES. The tunneling splittings in full dimensionality are calculated using the unbiased "fixed-node" diffusion Monte Carlo (DMC) method in Cartesian and saddle-point normal coordinates. The ground-state tunneling splitting is found to be 21.6 cm(-1) in Cartesian coordinates and 22.6 cm(-1) in normal coordinates, with an uncertainty of 2-3 cm(-1). This splitting is also calculated based on a model which makes use of the exact single-well zero-point energy (ZPE) obtained with the MULTIMODE code and DMC ZPE and this calculation gives a tunneling splitting of 21-22 cm(-1). The corresponding computed splittings for the D-atom transfer are 3.0, 3.1, and 2-3 cm(-1). These calculated tunneling splittings agree with each other to within less than the standard uncertainties obtained with the DMC method used, which are between 2 and 3 cm(-1), and agree well with the experimental values of 21.6 and 2.9 cm(-1) for the H and D transfer, respectively.     

Intramolecular proton transfer in malonaldehyde: accurate multilayer multi-configurational time-dependent Hartree calculations

Full-dimensional (multilayer) multi-configurational time-dependent Hartree calculations studying the intramolecular proton transfer in malonaldehyde based on a recent potential energy surface (PES) [Wang et al., J. Chem. Phys. 128, 224314 (2008)] are presented. The most accurate calculations yield a ground state tunneling splitting of 23.8 cm(-1) and a zero point energy of 14,678 cm(-1). Extensive convergence tests indicate an error margin of the quantum dynamics calculations for the tunneling splitting of about 0.2 cm(-1). These results are to be compared with the experimental value of the tunneling splitting of 21.58 cm(-1) and results of Monte Carlo calculations of Wang et al. on the same PES which yielded a zero point energy of 14,677.9 cm(-1) with statistical errors of 2-3 cm(-1) and a tunneling splitting of 21.6 cm(-1). The present data includes contributions resulting from the vibrational angular momenta to the tunneling splitting and the zero point energy of 0.2 cm(-1) and 2.4 cm(-1), respectively, which have been computed using a perturbative approach.     

The ground-state tunneling splitting of various carboxylic acid dimers

Carboxylic acid dimers in gas phase reveal ground-state tunneling splittings due to a double proton transfer between the two subunits. In this study we apply a recently developed accurate semiclassical method to determine the ground-state tunneling splittings of eight different carboxylic acid derivative dimers (formic acid, benzoic acid, carbamic acid, fluoro formic acid, carbonic acid, glyoxylic acid, acrylic acid, and N,N-dimethyl carbamic acid) and their fully deuterated analogs. The calculated splittings range from 5.3e-4 to 0.13 cm(-1) (for the deuterated species from 2.8e-7 to 3.3e-4 cm(-1)), thus indicating a strong substituent dependence of the splitting, which varies by more than two orders of magnitude. One reason for differences in the splittings could be addressed to different barriers heights, which vary from 6.3 to 8.8 kcal/mol, due to different mesomeric stabilization of the various transition states. The calculated splittings were compared to available experimental data and good agreement was found. A correlation could be found between the tunneling splitting and the energy barrier of the double proton transfer, as the splitting increases with increased strength of the hydrogen bonds. From this correlation an empirical formula was derived, which allows the prediction of the ground-state tunneling splitting of carboxylic acid dimers at a very low cost and the tunneling splittings for parahalogen substituted benzoic acid dimers is predicted.     

Unimolecular processes in CH2OH below the dissociation barrier: O-H stretch overtone excitation and dissociation

The OH-stretch overtone spectroscopy and dynamics of the hydroxymethyl radical, CH(2)OH, are reported in the region of the second and third overtones, which is above the thermochemical threshold to dissociation to H+CH(2)O (D(0)=9600 cm(-1)). The second overtone spectrum at 10 484 cm(-1) is obtained by double resonance IR-UV resonance enhanced multiphoton ionization (REMPI) spectroscopy via the 3p(z) electronic state. It is rotationally resolved with a linewidth of 0.4 cm(-1) and displays properties of local-mode vibration. No dissociation products are observed. The third overtone spectra of CH(2)OH and CD(2)OH are observed at approximately 13 600 cm(-1) by monitoring H-atom photofragments while scanning the excitation laser frequency. No double resonance REMPI spectrum is detected, and no D fragments are produced. The spectra of both isotope analogs can be simulated with a linewidth of 1.3 cm(-1), indicating dissociation via tunneling. By treating the tunneling as one dimensional and using the calculated imaginary frequency, the barrier to dissociation is estimated at about 15 200 cm(-1), in good agreement with theoretical estimations. The Birge-Sponer plot is linear for OH-stretch vibrations 1nu(1)-4nu(1), demonstrating behavior of a one-dimensional Morse oscillator. The anharmonicity parameter derived from the plot is similar to the values obtained for other small OH containing molecules. Isomerization to methoxy does not contribute to the predissociation signal and the mechanism appears to be direct O-H fission via tunneling. CH(2)OH presents a unique example in which the reaction coordinate is excited directly and leads to predissociation via tunneling while preserving the local-mode character of the stretch vibration.     

Molecular structure and OH-stretch spectra of liquid water surface

Molecular dynamics simulations are used to investigate typical coordination shells of molecules in the liquid water surface, for two potential energy surfaces. The major undercoordinated species found in the surface include three-coordinated H2O with either a dangling-H or a dangling-O atom and two-coordinated H2O with one hydrogen bond via H, and another via O. Vibrational signatures of the different coordinations are calculated. The 3400 cm(-1) band in the surface sum frequency generation (SFG) spectrum is assigned to four-coordinated molecules within the surface layer. The low-frequency wing of the OH-stretch band, near 3200 cm(-1) in the SFG spectrum, is proposed to be due to collective excitations of a relatively small number of intermolecularly coupled O-H bond vibrations.     

The all-Cartesian reaction plane Hamiltonian: formulation and application to the H-atom transfer in tropolone

In this work we present an all-Cartesian reaction surface approach, where the large amplitude coordinates span the so-called reaction plane, that is, the unique plane defined by the two minima and the saddle-point structure of an isomerization reaction. Orthogonal modes are treated within harmonic approximation which gives the total Hamiltonian an almost separable form that is suitable for multidimensional quantum dynamics calculations. The reaction plane Hamiltonian is constructed for the H-atom transfer in tropolone as an example for a system with an intramolecular O...H-O hydrogen bond. We find ground-state tunneling splittings of 3.5 and 0.16 cm(-1) for the normal and deuterated species, respectively. We calculated infrared-absorption spectra for a four-dimensional model focusing on the low-frequency region. Here, we identify a reaction mode which is closely connected to the tautomerization that is reflected in the increase of tunneling splitting to 18 cm(-1) upon excitation.     

Application of Schrödinger equation to study the tunnelling dynamics of proton transfer in the hydrogen bond of 2,5-dinitrobenzoic acid: proton T1 T1rho, and deuteron T1 relaxation methods

Temperature measurements of proton T1 (24.7 MHz), deuteron (deuterated hydroxyl group) T1 (55.2 MHz), and proton T1(rho) (B1 = 9 G) spin-lattice relaxation times of 2,5-dinitrobenzoic acid have been performed. An analysis of present experimental data together with previously published proton T1 (55.2 MHz) data has revealed the following molecular motions: proton/deuteron transfer in the hydrogen bond and two-site hopping of the whole dimer. It is shown that the proton-transfer dynamics are characterized by two correlation times tau(ov) and tau(tu), describing two fundamentally different motional processes, namely, thermally activated jumps over the barrier and tunneling through the barrier. The temperature dependence of 1/tau(tu) is the solution of Schr?dinger's equation, which also yields the temperature T(tun), where begins the tunnel pathway for proton transfer. A new equation for the spectral density function of complex motion consisting of the three motions is derived. The third motion (two-site hopping of the whole dimer characterized by tau(lib) correlation time) is responsible for a proton T1(rho) minimum in high temperatures, just below the melting point. Such a minimum is not reached by T1 temperature dependencies. The minimum of T1(rho) assigned to the classical hopping of a hydrogen-bonded proton occurs in the same low-temperature regime in which the flattening of the temperature dependencies of T1 points to the dominance of incoherent tunneling. This experimental fact denies the known theories predicting the intermediate temperature regime where a smooth transition between classical and quantum tunneling dynamics is expected. The fit of the derived theoretical equations to the experimental data T1(rho) and T1 is satisfactory. The correlation times obtained for deuterons indicate deuteron-transfer dynamics much slower than proton-transfer dynamics. It is concluded that the classical proton transfer takes place over the whole temperature regime, while the incoherent tunneling occurs below 46.5 (hydrogen) or 87.2 K (deuterium) only.     

A unique vibrational signature of rotated water monolayers on Pt(111): predicted and observed

Six H-bonds in the periodic di-interstitial structure that accounts for scanning tunneling microscope images of "√37" and "√39" wetting layers on Pt(111) are some 0.2 A? shorter than H-bonds are in ice Ih. According to a broadly obeyed correlation, this density functional theory result implies a stringent test of the di-interstitial motif, namely the presence of an OH-stretch band red-shifted from that of ice Ih by more than 1000 cm(-1). Infrared absorption spectra satisfy the test, in showing a feature centered at about 1965 cm(-1), which grows in as deposited water orders.     

Role of OH-stretch/torsion coupling and quantum yield effects in the first OH overtone spectrum of cis-cis HOONO

A joint theoretical and experimental investigation is undertaken to study the effects of OH-stretch/HOON torsion coupling and of quantum yield on the previously reported first overtone action spectrum of cis-cis HOONO (peroxynitrous acid). The minimum energy path along the HOON dihedral angle is computed at the coupled cluster singles and doubles with perturbative triples level with correlation consistent polarized quadruple zeta basis set, at the structure optimized using the triple zeta basis set (CCSD(T)/cc-pVQZ//CCSD(T)/cc-pVTZ). The two-dimensional ab initio potential energy and dipole moment surfaces for cis-cis HOONO are calculated as functions of the HOON torsion and OH bond length about the minimum energy path at the CCSD(T)/cc-pVTZ and QCISD/AUG-cc-pVTZ (QCISD-quadratic configuration interaction with single and double excitation and AUG-augmented with diffuse functions) level of theory/basis, respectively. The OH-stretch vibration depends strongly on the torsional angle, and the torsional potential possesses a broad shelf at approximately 90 degrees , the cis-perp conformation. The calculated electronic energies and dipoles are fit to simple functional forms and absorption spectra in the region of the OH fundamental and first overtone are calculated from these surfaces. While the experimental and calculated spectra of the OH fundamental band are in good agreement, significant differences in the intensity patterns are observed between the calculated absorption spectrum and the measured action spectrum in the 2nu(OH) region. These differences are attributed to the fact that several of the experimentally accessible states do not have sufficient energy to dissociate to OH+NO(2) and therefore are not detectable in an action spectrum. Scaling of the intensities of transitions to these states, assuming D(0)=82.0 kJ/mol, is shown to produce a spectrum that is in good agreement with the measured action spectrum. Based on this agreement, we assign two of the features in the spectrum to Deltan=0 transitions (where n is the HOON torsion quantum number) that are blue shifted relative to the origin band, while the large peak near 7000 cm(-1) is assigned to a series of Deltan=+1 transitions, with predominant contributions from torsionally excited states with substantial cis-perp character. The direct absorption spectrum of cis-cis HOONO (6300-6850 cm(-1)) is recorded by cavity ringdown spectroscopy in a discharge flow cell. A single band of HOONO is observed at 6370 cm(-1) and is assigned as the origin of the first OH overtone of cis-cis HOONO. These results imply that the origin band is suppressed by over an order of magnitude in the action spectrum, due to a reduced quantum yield. The striking differences between absorption and action spectra are correctly predicted by the calculations.     

Microwave and UV excitation spectra of 4-fluorobenzyl alcohol at high resolution. S0 and S1 structures and tunneling motions along the low frequency -CH2OH torsional coordinate in both electronic states

Rotationally resolved electronic spectra of several low frequency vibrational bands that appear in the S(1) ← S(0) transition of 4-fluorobenzyl alcohol (4FBA) in the collision-free environment of a molecular beam have been observed and assigned. Each transition is split into two or more components by the tunneling motion of the attached -CH(2)OH group. A similar splitting is observed in the microwave spectrum of 4FBA. Analyses of these data show that 4FBA has a gauche structure in both electronic states, but that the ground state C(1)C(2)-C(7)O dihedral angle of ～60° changes by ～30° when the photon is absorbed. The barriers to the torsional motion of the attached -CH(2)OH group are also quite different in the two electronic states; V(2) ～ 300 cm(-1) high and ～60° wide in the S(0) state, and V(2) ～ 300 cm(-1) high and ～120° wide (or V(2) ～ 1200 cm(-1) high and ～60° wide) in the S(1) state. Possible reasons for these behaviors are discussed.     

A study of the mode-selective trans--cis isomerization in HONO using ab initio methodology

Ab initio calculations on the six-dimensional cis--trans double minimum potential energy surface of the electronic ground state of the HONO molecule were performed using a coupled cluster approach. An analytic fit to the data points was established. The interconversion barrier was calculated to be 4105 cm(-1). The nuclear motion problem was solved variationally using a full six-dimensional Hamiltonian in internal coordinates. The eigenstates up to about 3650 cm(-1) were tentatively assigned by harmonic quantum numbers. The assignment was based on the mean values of the internal coordinates of the six-dimensional eigenfunctions and on a comparison of the eigenenergies with those calculated by second-order perturbation theory from a full quartic force field in dimensionless normal coordinates. In cold matrices the trans- and the cis-OH nu(1) stretching modes and the first trans- and cis-NO 2nu(2) stretching overtones lead to isomerization. In the isolated molecule these modes (J=0) were found to be entirely localized. However, several overtones of the nu(4) ONO bending and nu(5) N-O stretching, which are close in energy to the OH stretch and combined with the torsional mode, were found to be strongly cis-trans delocalized.     

Spectroscopic, magnetochemical, and crystallographic study of cesium iron phosphate hexahydrate: characterization of the electronic structure of the iron(II) hexa-aqua cation in a quasicubic environment

Spectroscopic, magnetochemical, and crystallographic data are presented for CsFe(H2O)6PO4, a member of a little-known isomorphous series of salts that facilitates the study of hexa-aqua ions in a quasicubic environment. Above 120 K, the deviations from cubic symmetry are minimal, as shown by the first example of an iron(II) M?ssbauer spectrum that exhibits no measurable quadrupole splitting. Two crystallographically distinct [Fe(OH2)6]2+ complexes are identified from inelastic neutron-scattering (INS) experiments conducted between 2 and 15 K. The data are modeled with the ligand-field Hamiltonian, H = lambdaL? + betaB(kL + 2?) + Delta(tet){Lz2 - (1/3)L(L + 1)} + Delta(rhom){Lx2 - Ly2}, operating in the ground-term (5)T(2g) (Oh) basis. An excellent reproduction of INS, M?ssbauer, HF-EPR, and magnetochemical data are obtained in the 2 and 15 K temperature regimes with the following parameters: lambda = -80 cm(-1); k = 0.8; site A Delta(tet) = 183 cm(-1), Delta(rhom)= 19 cm(-1); site B Delta(tet) = 181 cm(-1), Delta(rhom)= 12 cm(-1). The corresponding zero-field-splitting (ZFS) parameters of the conventional S = 2 spin Hamiltonian are as follows: site A D = 12.02 cm(-)(1), E = 2.123 cm(-1); site B D = 12.15 cm(-1), E = 1.37 cm(-1). A theoretical analysis of the variation of the energies of the low-lying states with respect to displacements along selected normal coordinates of the [Fe(OH2)6]2+, shows the zero-field splitting to be extremely sensitive to small structural perturbations of the complex. The expressions derived are discussed in the context of spin-Hamiltonian parameters reported for the [Fe(OH2)6]2+ cation in different crystalline environments.     

Vibrational analysis of the H5O2+ infrared spectrum using molecular and driven molecular dynamics

Standard molecular and driven molecular dynamics are used to analyze prominent spectral features in the H5O2+ infrared spectrum. In the driven method, the molecular Hamiltonian is augmented with a time-dependent term, mu x epsilon(0) sin(omegat), where mu is the dipole moment of H5O2+, epsilon0 is the electric field, and omega is the frequency. The magnitude of the electric field determines whether the driving is mild (the harmonic limit) or strong (anharmonic motion and mode coupling). We analyze the spectrum in the wavenumber range from 600 to 1900 cm(-1), where recent experimental measurements are available for H5O2+. On the basis of the simulations, we have assigned the broad feature around 1000 cm(-1) to the proton transfer coupled with the torsion motion. Intense absorption near 1780 cm(-1) is assigned to the H2O monomer bend coupled with proton transfer.     

Structure of protonated carbon dioxide clusters: infrared photodissociation spectroscopy and ab initio calculations

The infrared photodissociation spectra (IRPD) in the 700 to 4000 cm(-1) region are reported for H+ (CO2)n clusters (n = 1-4) and their complexes with argon. Weakly bound Ar atoms are attached to each complex upon cluster formation in a pulsed electric discharge/supersonic expansion cluster source. An expanded IRPD spectrum of the H+ (CO2)Ar complex, previously reported in the 2600-3000 cm(-1) range [Dopfer, O.; Olkhov, R.V.; Roth, D.; Maier, J.P. Chem. Phys. Lett. 1998, 296, 585-591] reveals new vibrational resonances. For n = 2 to 4, the vibrational resonances involving the motion of the proton are observed in the 750 to 1500 cm(-1) region of the spectrum, and by comparison to the predictions of theory, the structure of the small clusters are revealed. The monomer species has a nonlinear structure, with the proton binding to the lone pair of an oxygen. In the dimer, this nonlinear configuration is preserved, with the two CO2 units in a trans configuration about the central proton. Upon formation of the trimer, the core CO2 dimer ion undergoes a rearrangement, producing a structure with near C2v symmetry, which is preserved upon successive CO2 solvation. While the higher frequency asymmetric CO2 stretch vibrations are unaffected by the presence of the weakly attached Ar atom, the dynamics of the shared proton motions are substantially altered, largely due to the reduction in symmetry of each complex. For n = 2 to 4, the perturbation due to Ar leads to blue shifts of proton stretching vibrations that involve motion of the proton mostly parallel to the O-H+-O axis of the core ion. Moreover, proton stretching motions perpendicular to this axis exhibit smaller shifts, largely to the red. Ab initio (MP2) calculations of the structures, complexation energies, and harmonic vibrational frequencies are also presented, which support the assignments of the experimental spectra.     

Free-jet rotational spectrum and tunneling motion of difluoromethane...xenon

The rotational spectra of three isotopologues of difluoromethane...xenon have been investigated by free-jet millimeter-wave absorption spectroscopy. Only mu(c)-type transitions have been observed, all of them evenly split due to the internal motion of Xe relative to the difluoromethane moiety. The vibrational splitting, 39.1(3) MHz, has been used to estimate the tunneling barrier, V(2) = 109 cm(-1). Information on the dissociation energy has been deduced from centrifugal distortion effects (E(B) = 1.8 kJ mol(-1)). The xenon atom lies in the sigma(v) symmetry plane of difluoromethane containing the hydrogen atoms, at an r(0) distance of 3.816 A from its center of mass (cm), and forms a Xe-cm-C r(0) angle of 118 degrees . The observed conformation is in agreement with the minimum found with a distributed polarizability model.     

Determination of the proton tunneling splitting of the vinyl radical in the ground state by millimeter-wave spectroscopy combined with supersonic jet expansion and ultraviolet photolysis

The vinyl radical in the ground vibronic state produced in a supersonic jet expansion by 193 nm excimer laser photolysis of vinyl bromide was investigated by millimeter-wave spectroscopy. Due to the proton tunneling, the ground state is split into two components, of which the lower and higher ones are denoted as 0+ and 0-, respectively. Eight pure rotational transitions with Ka = 0 and 1 obeying a-type selection rules were observed for each of the 0+ and 0- states in the frequency region of 60-250 GHz. Tunneling-rotation transitions connecting the lower (0+) and upper (0-) components of the tunneling doublet, obeying b-type selection rules, were also observed in the frequency region of 190-310 GHz, including three R- and six Q-branch transitions. The observed frequencies of the pure rotational and tunneling-rotation transitions were analyzed by using an effective Hamiltonian in which the coupling between the 0+ and 0- states was taken into account. A set of precise molecular constants was obtained. Among others, the proton tunneling splitting in the ground state was determined to be DeltaE0 = 16,272(2) MHz. The potential barrier height was estimated to be 1580 cm(-1) from the proton tunneling splitting, by an analysis using a detailed one-dimensional model. The spin-rotation and hyperfine interaction constants were also determined for the 0+ and 0- states together with the off-diagonal interaction constants connecting the 0+ and 0- states, epsilonab + epsilonba for the spin-rotation interaction and Tab for the hyperfine interaction of the alpha (CH) proton. The hyperfine interaction constants, due to the alpha proton and the beta (CH2) protons, are consistent with those derived from electron spin resonance studies.     

Internal motions in a complex consisting of a rare gas atom and a C2v molecule: theoretical formulations and their applications to Fourier transform microwave spectra of Ne-dimethyl ether and Ar-dimethyl ether

The internal motion of the rare gas atom, i.e., the relative motion of the two constituents, in a complex shown in the title was discussed by paying special attention to its effect on the rotational motion of the complex in order to extract as much precise information on this motion as possible from the observed rotational spectra. We have set up two theoretical formulations. One is based on a coordinate axis system attached to the C2v molecule, but its origin is floating with the motion of the rare gas atom, while keeping the orientation parallel to the original C2v molecule-fixed coordinate system. The second approach starts with counting the number of equivalent potential minima, which are well separated from the others by high potential barriers, and then collects all permutation-inversion operations, which transform the system from one minimum to another, to set up a group appropriate for the complex. By using the symmetry properties thus derived, a phenomenological Hamiltonian is set up to fit the observed spectra. The two formulations result in alike rotational energy matrices, and we have applied them to analyze the internal motions in the two complexes of present concern: neon-dimethyl ether (Ne-DME) and argon-dimethyl ether (Ar-DME). Some of the transitions observed by the present study exhibited additional splittings, which were interpreted as due to an internal rotation of the methyl groups in DME and were analyzed by the second formulation. For Ar-DME the splittings appeared only in high-K transitions, yielding the V3 potential barrier to be 778(1) cm(-1), whereas those observed for Ne-DME were ascribed to the effects of the CH3 internal rotation on the inversion splitting.     

Vibrations in the B4 rhombic structure

A double minimum six-dimensional potential energy surface (PES) is determined in symmetry coordinates for the most stable rhombic (D2h) B4 isomer in its 1Ag electronic ground state by fitting to energies calculated ab initio. The PES exhibits a barrier to the D4h square structure of 255 cm(-1). The vibrational levels (J=0) are calculated variationally using an approach which involves the Watson kinetic energy operator expressed in normal coordinates. The pattern of about 65 vibrational levels up to 1600 cm(-1) for all stable isotopomers is analyzed. Analogous to the inversion in ammonia-like molecules, the rhombus rearrangements lead to splittings of the vibrational levels. In B4 it is the B1g (D4h) mode which distorts the square molecule to its planar rhombic form. The anharmonic fundamental vibrational transitions of 11B4 are calculated to be (splittings in parentheses): G(0)=2352(22) cm(-1), nu1(A1g)=1136(24) cm(-1), nu2(B1g)=209(144) cm(-1), nu3(B2g)=1198(19) cm(-1), nu4(B2u)=271(24) cm(-1), and nu5(Eu)=1030(166) cm(-1) (D4h notation). Their variations in all stable isotopomers were investigated. Due to the presence of strong anharmonic resonances between the B1g in-plane distortion and the B2u out-of-plane bending modes, the higher overtones and combination levels are difficult to assign unequivocally.