Tunneling splittings in vibrational spectra of non-rigid molecules

Tunneling splittings using modified WKB method in Cartesian coordinates: The test case of vinyl radical

Modified WKB theory for calculating tunneling splittings in symmetric multi-well systems in full dimensionality is re-derived using Cartesian coordinates. It is explicitly shown that the theory rests on the wavefunction that is exact for harmonic potentials. The theory was applied to calculate tunneling splittings in vinyl radical and some of its deuterated isotopologues in their vibrational ground states and the low-lying vibrationally excited states and compared to exact variational results. The exact results are reproduced within a factor of 2 in most states. Remarkably, all large enhancements of tunneling splittings relative to the ground state, up to three orders in magnitude in some excited mode combinations, are well reproduced. It is also shown that in the asymmetrically deuterated vinyl radical, the theory correctly predicts the states that are localized in a single well and the delocalized tunneling states. Modified WKB theory on the minimum action path is computationally inexpensive and can also be applied without modification to much larger systems in full dimensionality; the results of this test case serve to give insight into the expected accuracy of the method.

MC-QTAIM analysis reveals an exotic bond in coherently quantum superposed malonaldehyde

The proton between the two oxygen atoms of the malonaldehyde molecule experiences an effective double-well potential in which the proton's wavefunction is delocalized between the two wells. Herein we employ a state-of-the-art multi-component quantum theory of atoms in molecules partitioning scheme to obtain the molecular structure, i.e. atoms in molecules and bonding network, from the superposed ab initio wavefunctions of malonaldehyde. In contrast to the familiar clamped-proton portrayal of malonaldehyde, in which the proton forms a hydrogen basin, for the superposed states the hydrogen basin disappears and two novel hybrid oxygen-hydrogen basins appear instead, with an even distribution of the proton population between the two basins. The interaction between the hybrid basins is stabilizing thanks to an unprecedented mechanism. This involves the stabilizing classical Coulomb interaction of the one-proton density in one of the basins with one-electron density in the other basin. This stabilizing mechanism yields a bond foreign to the known bonding modes in chemistry.

Vibrational Tunneling Spectra of Molecules with Asymmetric Wells: A Combined Vibrational Configuration Interaction and Instanton Approach

A combined approach that uses the vibrational configuration interaction (VCI) and semiclassical instanton theory was developed to study vibrational tunneling spectra of molecules with multiple wells in full dimensionality. The method can be applied to calculate low-lying vibrational states in the systems with an arbitrary number of minima, which are not necessarily equal in energy or shape. It was tested on a two-dimensional double-well model system and on malonaldehyde, and the calculations reproduced the exact quantum mechanical (QM) results with high accuracy. The method was subsequently applied to calculate the vibrational spectrum of the asymmetrically deuterated malonaldehyde with nondegenerate vibrational frequencies in the two wells. The spectrum is obtained at a cost of single-well VCI calculations used to calculate the local energies. The interactions between states of different wells are computed semiclassically using the instanton theory at a comparatively negligible computational cost. The method is particularly suited to systems in which the wells are separated by large potential barriers and tunneling splittings are small, for example, in some water clusters, when the exact QM methods come at a prohibitive computational cost.

Theoretical Study of Proton Tunneling in the Imidazole-Imidazolium Complex

Proton tunneling in the hydrogen-bonded imidazole–imidazolium complex ion has been studied theoretically. Ab initio CASSCF/6-311++G(d,p) calculations concerning geometry optimization and vibrational frequencies have been carried out for equilibrium and transition state structures of the system. Two-dimensional double-well model potentials were constructed on the basis of ab initio results and used to analyze the proton dynamics in the hydrogen bond and the influence of the excitation of low-frequency hydrogen-bond vibrations on the proton tunneling splittings. The energy of tunneling-split vibrational sublevels of the high-frequency tunneling mode have been calculated for its ground and first excited vibrational state for the series of excitations of the coupled low-frequency intramolecular hydrogen-bond modes. The promoting and suppressing effect of the low-frequency modes on the proton splittings was shown in the ground and first excited vibrational state of the tunneling mode. The vibrational sublevels form the two separate semicontinuous bands between which the absorption transitions may occur. This mechanism explains the experimentally observed splitting and doublet-component broadening of the high-frequency N–H stretching infrared (IR) absorption band.

Tunneling splittings of vibrationally excited states using general instanton paths

A multidimensional semiclassical method for calculating tunneling splittings in vibrationally excited states of molecules using Cartesian coordinates is developed. It is an extension of the theory by Mil'nikov and Nakamura [J. Chem. Phys. 122, 124311 (2005)] to asymmetric paths that are necessary for calculating tunneling splitting patterns in multi-well systems, such as water clusters. Additionally, new terms are introduced in the description of the semiclassical wavefunction that drastically improves the splitting estimates for certain systems. The method is based on the instanton theory and builds the semiclassical wavefunction of the vibrationally excited states from the ground-state instanton wavefunction along the minimum action path and its harmonic neighborhood. The splittings of excited states are thus obtained at a negligible added numerical effort. The cost is concentrated, as for the ground-state splittings, in the instanton path optimization and the hessian evaluation along the path. The method can thus be applied without modification to many mid-sized molecules in full dimensionality and in combination with on-the-fly evaluation of electronic potentials. The tests were performed on several model potentials and on the water dimer.

Selective photoisomerisation of 2-chloromalonaldehyde

Isomerization of 2-chloromalonaldehyde (2-ClMA) is explored giving access to new experimental data on this derivative of malonaldehyde, not yet studied much. Experiments were performed isolating 2-ClMA in argon, neon, and para-hydrogen matrices. UV irradiation of the matrix samples induced isomerization to three open enolic forms including two previously observed along with the closed enolic form after deposition. IR spectra of these specific conformers were recorded, and a clear assignment of the observed bands was obtained with the assistance of theoretical calculations. UV spectra of the samples were measured, showing a blue shift of the π^* ← π absorption with the opening of the internal hydrogen bond of the most stable enol form. Specific sequences of UV irradiation at different wavelengths allowed us to obtain samples containing only one enol conformer. The formation of conformers is discussed. The observed selectivity of the process among the enol forms is analyzed.

2-Chloromalonaldehyde, a model system of resonance-assisted hydrogen bonding: vibrational investigation

The chelated enol isomer of 2-chloromalonaldehyde (2-ClMA) is experimentally characterized for the first time by IR and Raman spectroscopies. The spectra are obtained by trapping the molecule in cryogenic matrices and analyzed with the assistance of theoretical calculations. Experiments were performed in argon, neon and para-hydrogen matrices. The results highlight puzzling matrix effects, beyond site effects, which are interpreted as due to a tunneling splitting of the vibrational levels related to the proton transfer along the internal hydrogen bond (IHB). 2-ClMA is thus one of the very few molecules in which the H tunneling has been observed in cryogenic matrices. The comparison with its parent molecule (malonaldehyde) shows experimentally and theoretically the weakening of the IHB upon chlorination, with a reduced cooperative effect in the resonance assisted hydrogen bond. In addition, the Cl substitution induces an important stabilization of two open enol conformers. These two open forms appear in the spectra of as-deposited samples, meaning that, in contrast with other well-studied molecules of the same family (β-dialdehydes and β-diketones), they are present in the gas phase at room temperature.

Finding Chemical Reaction Paths with a Multilevel Preconditioning Protocol

Finding transition paths for chemical reactions can be computationally costly owing to the level of quantum-chemical theory needed for accuracy. Here, we show that a multilevel preconditioning scheme that was recently introduced (Tempkin et al. J. Chem. Phys.2014, 140, 184114) can be used to accelerate quantum-chemical string calculations. We demonstrate the method by finding minimum-energy paths for two well-characterized reactions: tautomerization of malonaldehyde and Claissen rearrangement of chorismate to prephanate. For these reactions, we show that preconditioning density functional theory (DFT) with a semiempirical method reduces the computational cost for reaching a converged path that is an optimum under DFT by several fold. The approach also shows promise for free energy calculations when thermal noise can be controlled.

Measurement of proton tunneling in short hydrogen bonds in single crystals of 3,5 pyridinedicarboxylic acid using nuclear magnetic resonance spectroscopy

In this Letter, we present NMR spin-lattice and relaxometry data for proton transfer in one of the shortest known N-H⋯O hydrogen bonds in a single crystal of 3,5 pyridinedicarboxylic acid (35PDCA). It is widely believed that proton transfer by quantum tunneling does not occur in short hydrogen bonds since the ground state energy level lies above the potential barrier, yet these data show a temperature independent, proton tunneling rate below 77 K and a clear deviation from classical dynamics below 91 K. This study therefore suggests that proton tunneling occurs in all hydrogen bonds at low temperature and the crossover temperature to classical hopping must be determined when evaluating whether proton tunneling persists at higher temperature, for example in enzyme catalysis under physiological conditions.

Where are Protons and Deuterons in KH p D1 – p CO3? A Neutron Diffraction Study

The crystals of potassium hydrogen carbonate (KHCO3) and the KDCO3 analogue are isomorphous. They are composed of hydrogen or deuterium bonded centrosymmetric dimers (HCO3 –)2 or (DCO3 –)2. The space group symmetry of KH p D1 – p CO3 (p ≈ 0.75) determined with neutron diffraction is identical to those of KHCO3 and KDCO3. This is at variance with a random distribution of H and D nuclei. These crystals are macroscopic quantum systems in which protons or/and deuterons merge into macroscopic states.

The Intramolecular Hydrogen-Bond in Malonaldehyde as Seen by Infrared Spectroscopy. A Four-Dimensional Model Study

The infrared spectrum of the O–H–O fragment of malonaldehyde is studied using a four-dimensional model. This comprises the OH stretching and the two OH bending vibrations as well an O–O ring deformation mode under the assumption of overall Cs symmetry. The full anharmonic potential energy and dipole moment surfaces are calculated using density functional theory and the respective vibrational eigenvalue problem is solved by an iterative Lanczos method. Fundamental and combination transitions are discussed for the normal species and the symmetrically deuterated isotopomer. Special emphasis is paid to the OH/OD stretching region which reveals the signatures of strong mode mixing what renders a simple assignment in terms of fundamental transitions difficult. In addition results for hot transitions are presented which show a rather different OH/OD band due to the topology of the potential energy surface. The influence of H atom tunneling on the spectrum is briefly addressed employing an alternative three-dimensional model which takes into account the in-plane H atom motion as well as the O–O distance.

Combining the nuclear-electronic orbital approach with vibronic coupling theory: calculation of the tunneling splitting for malonaldehyde

The nuclear-electronic orbital (NEO) method is combined with vibronic coupling theory to calculate hydrogen tunneling splittings in polyatomic molecules. In this NEO-vibronic coupling approach, the transferring proton and all electrons are treated quantum mechanically at the NEO level, and the other nuclei are treated quantum mechanically using vibronic coupling theory. The dynamics of the molecule are described by a vibronic Hamiltonian in a diabatic basis of two localized nuclear-electronic states for the electrons and transferring proton. This ab initio approach is computationally practical and efficient for relatively large molecules, and the accuracy can be improved systematically. The NEO-vibronic coupling approach is used to calculate the hydrogen tunneling splitting for malonaldehyde. The calculated tunneling splitting of 24.5 cm(-1) is in excellent agreement with the experimental value of 21.6 cm(-1). This approach also enables the identification of the dominant modes coupled to the transferring hydrogen motion and provides insight into their roles in the hydrogen tunneling process.

Real-time observation of intramolecular proton transfer in the electronic ground state of chloromalonaldehyde: Anab initiostudy of time-resolved photoelectron spectra

The authors report on studies of time-resolved photoelectron spectra of intramolecular proton transfer in the ground state of chloromalonaldehyde, employing ab initio photoionization matrix elements and effective potential surfaces of reduced dimensionality, wherein the couplings of proton motion to the other molecular vibrational modes are embedded by averaging over classical trajectories. In the simulations, population is transferred from the vibrational ground state to vibrationally hot wave packets by pumping to an excited electronic state and dumping with a time-delayed pulse. These pump-dump-probe simulations demonstrate that the time-resolved photoelectron spectra track proton transfer in the electronic ground state well and, furthermore, that the geometry dependence of the matrix elements enhances the tracking compared with signals obtained with the Condon approximation. Photoelectron kinetic energy distributions arising from wave packets localized in different basins are also distinguishable and could be understood, as expected, on the basis of the strength of the optical couplings in different regions of the ground state potential surface and the Franck-Condon overlaps of the ground state wave packets with the vibrational eigenstates of the ion potential surface.

The ground state tunneling splitting and the zero point energy of malonaldehyde: A quantum Monte Carlo determination

Quantum dynamics calculations of the ground state tunneling splitting and of the zero point energy of malonaldehyde on the full dimensional potential energy surface proposed by Yagi et al. [J. Chem. Phys. 1154, 10647 (2001)] are reported. The exact diffusion Monte Carlo and the projection operator imaginary time spectral evolution methods are used to compute accurate benchmark results for this 21-dimensional ab initio potential energy surface. A tunneling splitting of 25.7+/-0.3 cm-1 is obtained, and the vibrational ground state energy is found to be 15 122+/-4 cm-1. Isotopic substitution of the tunneling hydrogen modifies the tunneling splitting down to 3.21+/-0.09 cm-1 and the vibrational ground state energy to 14 385+/-2 cm-1. The computed tunneling splittings are slightly higher than the experimental values as expected from the potential energy surface which slightly underestimates the barrier height, and they are slightly lower than the results from the instanton theory obtained using the same potential energy surface.

Quantum Tunneling in the Midrange Vibrational Fundamentals of Tropolone

The Fourier transform infrared spectrum of tropolone(OH) vapor in the 1175-1700 cm(-1) region is reported at 0.0025 and 0.10 cm(-1) spectral resolutions. The 12 vibrational fundamentals in this region of rapidly rising vibrational state density are dominated by mixtures of the CC, CO, CCH, and COH internal coordinates. Estimates based on the measurement of sharp Q branch peaks are reported for 11 of the spectral doublet component separations DS(v) = |Delta(v) +/- Delta(0)|. Delta(0) = 0.974 cm(-1) is the known zero-point splitting, and three a(1) modes show tunneling splittings Delta(v) approximately Delta(0), four b(2) modes show splittings Delta(v) approximately 0.90Delta(0), and the remaining four modes show splittings Delta(v) falling 5-14% from Delta(0.) Significantly, the splitting for the nominal COH bending mode nu(8) (a(1)) is small, that is, 10% from Delta(0). Many of the vibrational excited states demonstrate strong anharmonic behavior, but there are only mild perturbations on the tautomerization mechanism driving Delta(0). The data suggest, especially for the higher frequency a(1) fundamentals, the onset of selective intramolecular vibrational energy redistribution processes that are fast on the time scale of the tautomerization process. These appear to delocalize and smooth out the topographical modifications of the zero-point potential energy surface that are anticipated to follow absorption of the nu(v) photon. Further, the spectra show the propensity for the Delta(v) splittings of b(2) and other complex vibrations to be damped relative to Delta(0).

Time-resolved photoelectron spectroscopy of proton transfer in the ground state of chloromalonaldehyde: Wave-packet dynamics on effective potential surfaces of reduced dimensionality

We report on a simple but widely useful method for obtaining time-independent potential surfaces of reduced dimensionality wherein the coupling between reaction and substrate modes is embedded by averaging over an ensemble of classical trajectories. While these classically averaged potentials with their reduced dimensionality should be useful whenever a separation between reaction and substrate modes is meaningful, their use brings about significant simplification in studies of time-resolved photoelectron spectra in polyatomic systems where full-dimensional studies of skeletal and photoelectron dynamics can be prohibitive. Here we report on the use of these effective potentials in the studies of dump-probe photoelectron spectra of intramolecular proton transfer in chloromalonaldehyde. In these applications the effective potentials should provide a more realistic description of proton-substrate couplings than the sudden or adiabatic approximations commonly employed in studies of proton transfer. The resulting time-dependent photoelectron signals, obtained here assuming a constant value of the photoelectron matrix element for ionization of the wave packet, are seen to track the proton transfer.

Isoelectronic Homologues and Isomers: Tropolone, 5-Azatropolone, 1-H-Azepine-4,5-dione, Saddle Points, and Ions

Computational studies of 12 64-electron homologues and isomers of tropolone in the S(0) electronic ground state are reported. Three minimum-energy structures, tropolone (Tp), 5-azatropolone (5Azt), and 5-H-5-azatropolonium (5AztH(+)), have an internal H-bond and planar C(s)) geometry, and three, tropolonate (TpO(-)), 5-azatropolonate (5AzO(-)), and 1-H-azepine-4,5-dione (45Di), lack the H-bond and have twisted C(2) geometry. All 6 substances have an equal double-minimum potential energy surface and a saddle point with planar C(2)(v) geometry. The energy for the gas-phase isomerization reaction 45Di --> 5Azt is near +4 kJ mol(-1) at the MP4(SDQ)/6-311++G(df,pd)//MP2/6-311++G(df,pd) (energy//geometry) theoretical level and around -20 kJ mol(-1) at lower theoretical levels. The dipole moments computed for 45Di and 5Azt are 9.6 and 2.1 D, respectively, and this large difference contributes to MO-computed free energies of solvation that strongly favor--as experimentally observed--45Di over 5Azt in chloroform solvent. The MO-computed energy for the gas-phase protonation reaction 45Di + H(+) --> 5AztH(+) is -956.4 kJ mol(-1), leading to 926.8 kJ mol(-1) as the estimated proton affinity for 45Di at 298 K and 1 atm. The intramolecular dynamical properties predicted for 5Azt and 5AztH(+) parallel those observed for tropolone. They are therefore expected to exhibit spectral tunneling doublets. Once they are synthesized, they should contribute importantly to the understanding of multidimensional intramolecular H transfer and dynamical coupling processes.

Quantum-instanton evaluation of the kinetic isotope effects

A general quantum-mechanical method for computing kinetic isotope effects is presented. The method is based on the quantum-instanton approximation for the rate constant and on the path-integral Metropolis-Monte Carlo evaluation of the Boltzmann operator matrix elements. It computes the kinetic isotope effect directly, using a thermodynamic integration with respect to the mass of the isotope, thus avoiding the more computationally expensive process of computing the individual rate constants. The method should be more accurate than variational transition-state theories or the semiclassical instanton method since it does not assume a single tunneling path and does not use a semiclassical approximation of the Boltzmann operator. While the general Monte Carlo implementation makes the method accessible to systems with a large number of atoms, we present numerical results for the Eckart barrier and for the collinear and full three-dimensional isotope variants of the hydrogen exchange reaction H + H2 --> H2 + H. In all seven test cases, for temperatures between 250 and 600 K, the error of the quantum instanton approximation for the kinetic isotope effects is less than approximately 10%.

Infrared Spectroscopy of the Intramolecular Hydrogen Bond in Acethylacetone: A Computational Approach

The intramolecular hydrogen bond in the enol-acethylacetone (ACAC) is investigated by performing reduced-dimensional quantum calculations. To analyze the shared proton vibrations, two sets of coordinates were employed: normal mode coordinates describing the motion in the vicinity of the most stable configuration, and internal coordinates accounting for the double minimum proton motion. It is proved that the extreme broadness of the OH-stretch band in ACAC is a consequence of the coexistence of two enol-ACAC structures: the global minimum and the transition state for rotation of the distal methyl group. Further, a ground-state tunneling splitting of 116 cm(-1) is found, and it is shown that the inclusion of the kinematic coupling is mandatory when treating large-amplitude proton motion. In the OH-stretch direction a splitting of 853 cm(-1) was predicted.

The ground state tunneling splitting of malonaldehyde: Accurate full dimensional quantum dynamics calculations

Benchmark calculations of the tunneling splitting in malonaldehyde using the full dimensional potential proposed by Yagi et al. are reported. Two exact quantum dynamics methods are used: the multiconfigurational time-dependent Hartree (MCTDH) approach and the diffusion Monte Carlo based projection operator imaginary time spectral evolution (POITSE) method. A ground state tunneling splitting of 25.7+/-0.3 cm(-1) is calculated using POITSE. The MCTDH computation yields 25 cm(-1) converged to about 10% accuracy. These rigorous results are used to evaluate the accuracy of approximate dynamical approaches, e.g., the instanton theory.