Six-dimensional ab initio potential energy surfaces for H3O+ and NH3: Approaching the subwave number accuracy for the inversion splittings

Comparison of classical and ab initio simulations of hydronium and aqueous proton transfer

Proton transport in aqueous systems occurs by making and breaking covalent bonds, a process that classical force fields cannot reproduce. Various attempts have been made to remedy this deficiency, by valence bond theory or instantaneous proton transfers, but the ability of such methods to provide a realistic picture of this fundamental process has not been fully evaluated. Here we compare an ab initio molecular dynamics (AIMD) simulation of an excess proton in water to a simulation of a classical H3O+ in TIP3P water. The energy gap upon instantaneous proton transfer from H3O+ to an acceptor water molecule is much higher in the classical simulation than in the AIMD configurations evaluated with the same classical potential. The origins of this discrepancy are identified by comparing the solvent structures around the excess proton in the two systems. One major structural difference is in the tilt angle of the water molecules that accept an hydrogen bond from H3O+. The lack of lone pairs in TIP3P produces a tilt angle that is too large and generates an unfavorable geometry after instantaneous proton transfer. This problem can be alleviated by the use of TIP5P, which gives a tilt angle much closer to the AIMD result. Another important factor that raises the energy gap is the different optimal distance in water-water vs H3O+-water H-bonds. In AIMD the acceptor is gradually polarized and takes a hydronium-like configuration even before proton transfer actually happens. Ways to remedy some of these problems in classical simulations are discussed.

A convenient set of vibrational coordinates for 2D calculation of the tunneling splittings of the ground state and some excited vibrational states for the inversion motion in H3O+, H3O-, and H3O

Splitting of the ground state and some excited symmetric bending vibrational states due to inversion tunneling of the oxygen atom in the H₃O⁺, H₃O^- ions and in the H₃O radical are analyzed by numerically solving the vibrational Schrödinger equation of restricted (2D) dimensionality. As two vibrational coordinates, we used 1) the distance of the oxygen atom from the plane of a regular triangle formed by three hydrogen atoms and 2) a symmetry coordinate composed of three distances between chemically non-bonded hydrogen atoms. The kinetic energy operator in this case takes the simplest form. The 2D potential energy surface (PES) in the given coordinates was calculated for H₃O⁺ at the CCSD(T)/aug-cc-pVTZ and CCSD(T)-F12/cc-pVTZ-F12 levels of theory. The same 2D PES for the H₃O^- anion and H₃O radical were calculated at the CCSD(T)/aug-cc-pVQZ, CCSD(T)/d-aug-cc-pVQZ and UCCSD(T)/aug-cc-pVQZ, UCCSD(T)/d-aug-cc-pVQZ levels of theory, respectively. The tunneling splittings were calculated for the cations H₃¹⁶O⁺, D₃¹⁶O⁺, T₃¹⁶O⁺, H₃¹⁸O⁺, D₃¹⁸O⁺, T₃¹⁸O⁺. The tunneling splittings for the H₃O^-, D₃O^-, T₃O^- anions and H₃O, D₃O, T₃O radicals were calculated for the first time. The results of calculations demonstrate good agreement with experimental values of the tunneling splittings in the ground state and in some excited vibrational states of the H₃¹⁶O⁺ and D₃¹⁶O⁺ cations.

Wavepacket dynamical study of H-atom tunneling in catecholate monoanion: the role of intermode couplings and energy flow

We present a study of H-atom tunneling in catecholate monoanion through wavepacket dynamical simulations. In our earlier study of this symmetrical double-well system [Phys. Chem. Chem. Phys., 2022, 24, 10887], a limited number of transition state modes were identified as being important for the tunneling process. These include the imaginary frequency mode Q₁, the CO scissor mode Q₁₀, and the OHO bending mode Q₂₉. In this work, starting from non-stationary initial states prepared with excitations in these modes, we have carried out wavepacket dynamics in two and three dimensional spaces. We analyse the dynamical effects of the intermode couplings, in particular the role of energy flow between the studied modes on H-atom tunneling. We find that while Q₁₀ strongly modulates the donor-acceptor distance, it does not exchange energy with Q₁. However, excitation in Q₂₉ or Q₁ does lead to rapid energy exchange between these modes, which modifies the tunneling rate at early times.

Molecular origins of asymmetric proton conduction in the influenza M2 channel

The M2 proton channel of influenza A is embedded into the viral envelope and allows acidification of the virion when the external pH is lowered. In contrast, no outward proton conductance is observed when the internal pH is lowered, although outward current is observed at positive voltage. Residues Trp41 and Asp44 are known to play a role in preventing pH-driven outward conductance, but the mechanism for this is unclear. We investigate this issue using classical molecular dynamics simulations with periodic proton hops. When all key His37 residues are neutral, inward proton movement is much more facile than outward movement if the His are allowed to shuttle the proton. The preference for inward movement increases further as the charge on the His37 increases. Analysis of the trajectories reveals three factors accounting for this asymmetry. First, in the outward direction, Asp44 traps the hydronium by strong electrostatic interactions. Secondly, Asp44 and Trp41 orient the hydronium with the protons pointing inward, hampering outward Grotthus hopping. As a result, the effective barrier is lower in the inward direction. Trp41 adds to the barrier by weakly H-bonding to potential H+ acceptors. Finally, for charged His, the H3O+ in the inner vestibule tends to get trapped at lipid-lined fenestrations of the cone-shaped channel. Simulations qualitatively reproduce the experimentally observed higher outward conductance of mutants. The ability of positive voltage, unlike proton gradient, to induce an outward current appears to arise from its ability to bias H3O+ and the waters around it toward more H-outward orientations.

How the Zundel (H5O2+) Potential Can Be Used to Predict the Proton Stretch and Bend Frequencies of Larger Protonated Water Clusters

From a series of seminal experiments on the IR spectra of protonated water clusters and associated theoretical analyses, it is clear that the energies and spectral features of the proton stretch and bend modes are very sensitive functions of the cluster size. Here we show that this dynamic range can be understood by examining the sensitivity of these modes in the potential of the Zundel cation, H₅O₂⁺, as the separation of the two water monomers is varied. As this distance increases, the proton increasingly localizes on a monomer, and this is encoded in the IR spectrum of the proton vibrational modes. The quantitative predictions from this simple correlation are verified for the H₇O₃⁺ and H₉O₄⁺ clusters, for which new benchmark harmonic frequencies are reported. The predictions are also in good accord with trends seen experimentally and previous calculations for these and five other clusters, including H⁺(H₂O)₂₁.

Towards black-box calculations of tunneling splittings obtained from vibrational structure methods based on normal coordinates

Multidimensional potential energy surfaces obtained from explicitly correlated coupled-cluster calculations and further corrections for high-order correlation contributions, scalar relativistic effects and core-correlation energy contributions were generated in a fully automated fashion for the double-minimum benchmark systems OH3(+) and NH3. The black-box generation of the potentials is based on normal coordinates, which were used in the underlying multimode expansions of the potentials and the μ-tensor within the Watson operator. Normal coordinates are not the optimal choice for describing double-minimum potentials and the question remains if they can be used for accurate calculations at all. However, their unique definition is an appealing feature, which removes remaining errors in truncated potential expansions arising from different choices of curvilinear coordinate systems. Fully automated calculations are presented, which demonstrate, that the proposed scheme allows for the determination of energy levels and tunneling splittings as a routine application.

On the protonation of water

Dissociative photoionization onsets of water and water dimer, measured by Imaging Photoelectron Photoion Coincidence (iPEPICO) Spectroscopy, are used in a floating thermochemical cycle to determine the proton affinity of water with unprecedented accuracy, as confirmed by state-of-the-artab initioquantum-chemical calculations.

Thermochemistry of ammonium nitrate, NH₄NO₃, in the gas phase

Hildenbrand and co-workers have shown recently that the vapor above solid ammonium nitrate includes molecules of NH₄NO₃, not only NH₃ and HNO₃ as previously believed. Their measurements led to thermochemical values that imply an enthalpy change of D₂₉₈ = 98 ± 9 kJ mol⁻¹ for the gas-phase dissociation of ammonium nitrate into NH₃ and HNO₃. Using updated spectroscopic information for the partition function leads to the revised value of D₂₉₈ = 78 ± 21 kJ mol⁻¹ (accompanying paper in this journal, Hildenbrand, D. L., Lau, K. H., and Chandra, D. J. Phys. Chem. B 2010, DOI: 10.1021/jp105773q). In contrast, high-level ab initio calculations, detailed in the present report, predict a dissociation enthalpy half as large as the original result, 50 ± 3 kJ mol⁻¹. These are frozen-core CCSD(T) calculations extrapolated to the limiting basis set aug-cc-pV∞Z using an anharmonic vibrational partition function and a variational treatment of the NH₃ rotor. The corresponding enthalpy of formation is Δ(f)H₂₉₈°(NH₄NO₃,g) = −230.6 ± 3 kJ mol⁻¹. The origin of the disagreement with experiment remains unexplained.

Tunneling dynamics and spectroscopic parameters of monodeuterated hydronium, H(2)DO(+), from a combined analysis of infrared and sub-millimeter spectra

The infrared laser direct absorption spectrum of H(2)DO(+) in the OH stretching region was reported quite recently revealing large amplitude tunneling dynamics. The large rotational constants make the jet-cooled spectrum relatively sparse at low rotational temperatures and assignments thus challenging. Transitions were assigned through ground state combination differences, with additional tentative assignments made via comparison of predicted/observed spectra. More recently, 9 rotation-inversion transitions were recorded in the sub-millimeter (sub-mm) region, which yielded tunneling splittings and rotational constants differing slightly from IR results. This has prompted the present reinvestigation of the H(2)DO(+) spectra, which now takes full advantage of the combined data from both studies. While previous analyses considered each tunneling state as independent and non-interacting, the present analysis is based on a tunneling-Hamiltonian model for the well studied, isoelectronic NH(2)D molecule, modified to account for the larger tunneling splitting. The combined analysis revealed rotational interaction between tunneling states as well as between the two OH stretching modes and permitted a substantial number of new assignments to be made, including one sub-millimeter transition while only few IR assignments had to be corrected or omitted. It leads to improvement in parameters for both the ground as well as for the OH stretching states of this important molecular ion, which reproduce the assigned lines within experimental uncertainties, provides guidance, e.g., for the spectral search in the OD stretch region, and yields deeper insight into the tunneling dynamics.

Orthogonal coordinates and hyperquantization algorithm. The NH3 and H3O+ umbrella inversion levels

In order to describe the umbrella inversion mode, which is characteristic of AB(3)-type molecules, we have introduced an alternative hyperspherical coordinate set based on a parametrization of Radau-Smith orthogonal vectors and have considered constraints which allow us to enforce the C(3v) symmetry. Structural properties and electronic energies at equilibrium and barrier configurations have been obtained at MP2 and CCSD(T) levels of theory. Energy profiles have been calculated using the CCSD(T) method with an aug-cc-pVQZ basis set. The NH(3) and H(3)O(+) umbrella inversion levels are obtained by the hyperquantization algorithm for a one-dimensional calculation, using a specially defined hyperangle as the inversion coordinate. The results are compared with experimental and theoretical energy levels, in particular, with those obtained by calculations based on two-dimensional models. The emerging picture of the umbrella inversion based on this hyperangular coordinate compares favorably with respect to the usual valence-type description.

Microwave spectrum of the HD2O+ ion: inversion-rotation transitions and inversion splitting

Inversion-rotation spectral lines of the dideuterated hydronium ion, HD2O+, have been observed by a source-modulation millimeter- to submillimeter-wave spectrometer. The ion was generated by a hollow-cathode discharge in a gas mixture of D2O and H2O in a free-space cell. Ten inversion-rotation lines were measured precisely for the lowest pair of inversion doublets in the frequency region from 380 to 730 GHz. The observed lines include the most astronomically important transitions, 0(00) (-)-1(10)+ for the para species at 380 538.031(32) MHz and 1(01) (-)-1(11)+ for the ortho species at 728 420.189(34) MHz, which could be used as a radio astronomical probe investigating interstellar chemistry of deuterium fractionation. An analysis of the measured lines has yielded the rotational constants in the ground doublet states and the inversion splitting. The inversion splitting in the ground state was determined to be 808 866(34) MHz, that is, 26.980 87(113) cm(-1), where the numbers in parentheses give uncertainties estimated from the Jacobian matrix of the assumed centrifugal distortion constants. The determined inversion splitting is off by -0.51 cm(-1) from the predicted value of 27.49 cm(-1) by Rajamaki et al. using high-order coupled cluster ab initio calculation [J. Chem. Phys. 118, 10929 (2003)], and by -0.0510 cm(-1) from the observed value of 27.0318(72) cm(-1) by Dong et al. using high-resolution jet-cooled infrared spectroscopy [J. Chem. Phys. 122, 224301 (2005)] beyond the quoted uncertainty.

Microwave spectrum of the H2DO+ ion: inversion-rotation transitions and inversion splitting

Inversion-rotation spectral lines of the monodeuterated hydronium ion, H(2)DO(+), have been observed by a source-modulation spectrometer in the millimeter- to submillimeter-wave region. The ion was generated by a hollow-cathode discharge in a gas mixture of H(2)O and D(2)O. Nine inversion-rotation lines were measured precisely for the lowest pair of inversion doublets in the frequency region from 210 to 720 GHz. The measured lines were analyzed to derive rotational constants in the inversion-doublet states and inversion splitting. The inversion splitting in the ground state was determined to be 1,215,866(410) MHz, that is, 40.5569(137) cm(-1), where the numbers in parentheses give probable uncertainties estimated from the Jacobian matrix of the assumed centrifugal distortion constants of the inversion-doublet states. The determined inversion splitting is off by -0.58 cm(-1) from the predicted value of 41.14 cm(-1) by Rayamaki et al. using high-order coupled cluster ab initio calculations [J. Chem. Phys. 118, 10929 (2003)], and by 0.039 cm(-1) from the observed value of 40.518(10) cm(-1) by Dong and Nesbitt using high-resolution jet-cooled infrared spectroscopy [J. Chem. Phys. 125, 144311 (2006)] beyond the quoted uncertainty. The most astronomically important transition 0(00)(-)-1(0)(+) for the ortho species was measured at 673,257.024(31) MHz, which could be used as a radioastronomical probe investigating interstellar chemistry of deuterium fractionation in space.

Photoionization-induced dynamics of ammonia: ab initio potential energy surfaces and time-dependent wave packet calculations for the ammonia cation

An analytical anharmonic six-dimensional three-sheeted potential energy surface for the ground and first excited states of the ammonia cation has been developed which is tailored to model the ultrafast photoinduced dynamics. Selected ab initio cuts, obtained by multireference configuration interaction calculations, have been used to determine the parameters of a diabatic representation for this Jahn-Teller and pseudo-Jahn-Teller system. The model includes higher-order coupling terms both for the Jahn-Teller and for the pseudo-Jahn-Teller matrix elements. The relaxation to the ground state is possible via dynamical pseudo-Jahn-Teller couplings involving the asymmetric bending and stretching coordinates. The photoelectron spectrum of NH3 and the internal conversion dynamics of NH3+ have been determined by wave packet propagation calculations employing the multiconfigurational time-dependent Hartree method. Three different time scales are found in the dynamics calculations for the second absorption band. The ultrafast Jahn-Teller dynamics of the two excited states occurs on a 5 fs time scale. The major part of the internal conversion to the ground state takes place within a short time scale of 20 fs. This fast internal conversion is, however, incomplete and the remaining excited state population does not decay completely even within 100 fs.

Structure and Raman Spectrum of Clavulanic Acid in Aqueous Solution

The calculation of the vibrational Raman spectrum of enzyme-bound beta-lactamase inhibitors may be of help to understand the mechanisms responsible for bacterial drug resistance. Here, we present a study of the solvation structure and the vibrational properties of clavulanate, an important beta-lactamase inhibitor, in aqueous solution as obtained from full quantum and hybrid empirical/quantum molecular dynamics simulations at ambient conditions. The analysis of the vibrational density of states indicates that hybrid empirical/quantum mechanical simulations are able to properly describe the vibrational levels of clavulanate in solution. In addition, we propose a computationally efficient protocol to calculate the vibrational Raman effect for large solute molecules in water, which is able to faithfully reproduce the experimentally recorded clavulanate Raman spectrum and discloses the possibility to employ hybrid simulations to assign the experimental Raman spectra of inhibitors bound to beta-lactamases.

Jet cooled spectroscopy of H2DO+: Barrier heights and isotope-dependent tunneling dynamics from H3O+ to D3O+

The first high resolution spectroscopic data for jet cooled H2DO+ are reported, specifically via infrared laser direct absorption in the OH stretching region with a slit supersonic jet discharge source. Transitions sampling upper (0-) and lower (0+) tunneling states for both symmetric (nu1+ <-- 0+, nu1- <-- 0-, and nu1- <-- 0+) and antisymmetric (nu3+ <-- 0+ and nu3- <-- 0-) OH stretching bands are observed, where +/- refers to wave function reflection symmetry with respect to the planar umbrella mode transition state. The spectra can be well fitted to a Watson asymmetric top Hamiltonian, revealing band origins and rotational constants for benchmark comparison with high-level ab initio theory. Of particular importance are detection and assignment of the relatively weak band (nu1- <-- 0+) that crosses the inversion tunneling gap, which is optically forbidden in H3O+ or D3O+, but weakly allowed in H2DO+ by lowering of the tunneling transition state symmetry from D(3h) to C(2v). In conjunction with other H2DO+ bands, this permits determination of the tunneling splittings to within spectroscopic precision for each of the ground [40.518(10) cm(-1)], nu1 = 1 [32.666(6) cm(-1)], and nu3 = 1 [25.399(11) cm(-1)] states. A one-dimensional zero-point energy corrected potential along the tunneling coordinate is constructed from high-level ab initio CCSD(T) calculations (AVnZ, n = 3,4,5) and extrapolated to the complete basis set limit to extract tunneling splittings via a vibrationally adiabatic treatment. Perturbative scaling of the potential to match splittings for all four isotopomers permits an experimental estimate of DeltaV0 = 652.9(6) cm(-1) for the tunneling barrier, in good agreement with full six-dimensional ab initio results of Rajamaki, Miani, and Halonen (RMH) [J. Chem. Phys. 118, 10929 (2003)]. (DeltaV0 (RMH) = 650 cm(-1)). The 30%-50% decrease in tunneling splitting observed upon nu1 and nu3 vibrational excitations arises from an increase in OH stretch frequencies at the planar transition state, highlighting the transition between sp2 and sp3 hybridizations of the OHD bonds as a function of inversion bending angle.

Inversion vibration of PH3+(X2A2") studied by zero kinetic energy photoelectron spectroscopy

We report the first rotationally resolved spectroscopic studies on PH3+(X2A2") using zero kinetic energy photoelectron spectroscopy and coherent VUV radiation. The spectra about 8000 cm(-1) above the ground vibrational state of PH3+(X2A2") have been recorded. We observed the vibrational energy level splittings of PH3+(X2A2") due to the tunneling effect in the inversion (symmetric bending) vibration (nu2+). The energy splitting for the first inversion vibrational state (0+/0-) is 5.8 cm(-1). The inversion vibrational energy levels, rotational constants, and adiabatic ionization energies (IEs) for nu2+ = 0-16 have been determined. The bond angles between the neighboring P-H bonds and the P-H bond lengths are also obtained using the experimentally determined rotational constants. With the increasing of the inversion vibrational excitations (nu2+), the bond lengths (P-H) increase a little and the bond angles (H-P-H) decrease a lot. The inversion vibrational energy levels have also been calculated by using one dimensional potential model and the results are in good agreement with the experimental data for the first several vibrational levels. In addition to inversion vibration, we also observed firstly the other two vibrational modes: the symmetric P-H stretching vibration (nu1+) and the degenerate bending vibration (nu4+). The fundamental frequencies for nu1+ and nu4+ are 2461.6 (+/-2) and 1043.9 (+/-2) cm(-1), respectively. The first IE for PH3 was determined as 79670.9 (+/-1) cm(-1).

Abnormal inversion splitting in NH2D: rotational analysis of the nu5 bending vibrational band system

A high-resolution Fourier transform infrared spectrum of the nu(5) bending vibrational band system region of the partially deuterated ammonia molecule NH(2)D has been measured and rotationally analyzed. The spectrum consists of strong a-type transitions between the states of same vibrational symmetry and weaker c-type transitions between the states of different vibrational symmetry. The Hamiltonian model used includes interaction terms between the rotational states of both upper and lower inversion doublets. The vibrational term values for the symmetric and the antisymmetric component of the upper-inversion doublet are 1,605.637 965(620) cm(-1) and 1,590.993 82(100) cm(-1), respectively, where the numbers in parentheses are one-standard deviations in the least significant digit. These figures are close to the corresponding values 1,605.62 cm(-1) and 1,590.72 cm(-1) obtained recently from results based on high-level ab initio calculations. The order of the vibrational term values is abnormal in the ammonia family, as typically the symmetric state is lower in wavenumber than the antisymmetric one.

Direct calculation of coupled diabatic potential-energy surfaces for ammonia and mapping of a four-dimensional conical intersection seam

We used multiconfiguration quasidegenerate perturbation theory and the fourfold-way direct diabatization scheme to calculate ab initio potential-energy surfaces at 3600 nuclear geometries of NH3. The calculations yield the adiabatic and diabatic potential-energy surfaces for the ground and first electronically excited singlet states and also the diabatic coupling surfaces. The diabatic surfaces and coupling were fitted analytically to functional forms to obtain a permutationally invariant 2 x 2 diabatic potential-energy matrix. An analytic representation of the adiabatic potential-energy surfaces is then obtained by diagonalizing the diabatic potential-energy matrix. The analytic representation of the surfaces gives an analytic representation of the four-dimensional conical intersection seam which is discussed in detail.

Potential-energy surface for the electronic ground state of NH3 up to 20000cm−1 above equilibrium

Ab initio coupled cluster calculations with single and double substitutions and a perturbative treatment of connected triple excitations [CCSD(T)] with the augmented correlation-consistent polarized valence triple-zeta aug-cc-pVTZ basis at 51 816 geometries provide a six-dimensional potential-energy surface for the electronic ground state of NH3. At 3814 selected geometries, CBS+ energies are obtained by extrapolating the CCSD(T) results for the aug-cc-pVXZ(X=T,Q,5) basis sets to the complete basis set (CBS) limit and adding corrections for core-valence correlation and relativistic effects. CBS** ab initio energies are generated at 51,816 geometries by an empirical extrapolation of the CCSD(T)/aug-cc-pVTZ results to the CBS+ limit. They cover the energy region up to 20,000 cm-1 above equilibrium. Parametrized analytical functions are fitted through the ab initio points. For these analytical surfaces, vibrational term values and transition moments are calculated by means of a variational program employing a kinetic-energy operator expressed in the Eckart-Sayvetz frame. Comparisons against experiment are used to assess the quality of the generated potential-energy surfaces. A "spectroscopic" potential-energy surface of NH3 is determined by a slight empirical adjustment of the ab initio potential to the experimental vibrational term values. Variational calculations on this refined surface yield rms deviations from experiment of 0.8 cm-1 for 24 inversion splittings and 0.4 (3.0) cm-1 for 34 (51) vibrational term values up to 6100 (10,300) cm-1.

Large amplitude quantum mechanics in polyatomic hydrides. I. A particles-on-a-sphere model for XHn

A framework is presented for converged quantum mechanical calculations on large amplitude dynamics in polyatomic hydrides (XH(n)) based on a relatively simple, but computationally tractable, "particles-on-a-sphere" (POS) model for the intramolecular motion of the light atoms. The model assumes independent two-dimensional (2D) angular motion of H atoms imbedded on the surface of a sphere with an arbitrary interatomic angular potential. This assumption permits systematic evolution from "free rotor" to "tunneling" to "quasi-rigid" polyatomic molecule behavior for small, but finite, values of total angular momentum J. This work focuses on simple triatom (n=2) and tetratom (n=3) systems as a function of interatomic potential stiffness, with explicit consideration of H2O, NH3, and H3O+ as limiting test cases. The POS model also establishes the necessary mathematical groundwork for calculations on dynamically much more challenging XH(n) species with n>3 (e.g., models of CH5+) where such a reduced dimensionality approach offers prospects for being quantum mechanically tractable at low J values (i.e., J=0, 1, 2) characteristic of supersonic jet expansion conditions.

Supersonically cooled hydronium ions in a slit-jet discharge: High-resolution infrared spectroscopy and tunneling dynamics of HD2O+

Jet-cooled high-resolution infrared spectra of partially deuterated hydronium ion (HD2O+) in the O-H stretch region (nu3 band) are obtained for the first time, exploiting the high ion densities, long absorption path lengths, and concentration modulation capabilities of the slit-jet discharge spectrometer. Least-squares analysis with a Watson asymmetric top Hamiltonian yields rovibrational constants and provides high level tests of ab initio molecular structure predictions. Transitions out of both the lower (nu3(+)<--0(+)) and the upper (nu3(-)<--0(-)) tunneling levels, as well as transitions across the tunneling gap (nu3(-)<--0(+)) are observed. The nu3(-)<--0(+) transitions in HD2O+ acquire oscillator strength by loss of D(3h) symmetry, and permit both ground-state-[27.0318(72) cm(-1)] and excited-state-[17.7612(54) cm(-1)]-tunneling splittings to be determined to spectroscopic precision from a single rovibrational band. The splittings and band origins calculated with recent high level ab initio six-dimensional potential surface predictions for H3O+ and isotopomers [X. C. Huang, S. Carter, and J. M. Bowman, J. Chem. Phys. 118, 5431 (2003); T. Rajamaki, A. Miani, and L. Halonen, J. Chem. Phys. 118, 10929 (2003)] are in very good agreement with the current experimental results.

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.