Volume 134, Issue 19, 21 May 2011
Index of content:

The Poisson–Nernst–Planck (PNP) model is based on a meanfield approximation of ion interactions and continuum descriptions of concentration and electrostatic potential. It provides qualitative explanation and increasingly quantitative predictions of experimental measurements for the ion transport problems in many areas such as semiconductor devices, nanofluidic systems, and biological systems, despite many limitations. While the PNP model gives a good prediction of the ion transport phenomenon for chemical, physical, and biological systems, the number of equations to be solved and the number of diffusion coefficient profiles to be determined for the calculation directly depend on the number of ion species in the system, since each ion species corresponds to one Nernst–Planck equation and one positiondependent diffusion coefficient profile. In a complex system with multiple ion species, the PNP can be computationally expensive and parameter demanding, as experimental measurements of diffusion coefficient profiles are generally quite limited for most confined regions such as ion channels, nanostructures and nanopores. We propose an alternative model to reduce number of Nernst–Planck equations to be solved in complex chemical and biological systems with multiple ion species by substituting Nernst–Planck equations with Boltzmann distributions of ion concentrations. As such, we solve the coupled Poisson–Boltzmann and Nernst–Planck (PBNP) equations, instead of the PNP equations. The proposed PBNP equations are derived from a total energy functional by using the variational principle. We design a number of computational techniques, including the Dirichlet to Neumann mapping, the matched interface and boundary, and relaxation based iterative procedure, to ensure efficient solution of the proposed PBNP equations. Two protein molecules, cytochrome c551 and Gramicidin A, are employed to validate the proposed model under a wide range of bulk ion concentrations and external voltages. Extensive numerical experiments show that there is an excellent consistency between the results predicted from the present PBNP model and those obtained from the PNP model in terms of the electrostatic potentials, ion concentration profiles, and current–voltage (I–V) curves. The present PBNP model is further validated by a comparison with experimental measurements of I–V curves under various ion bulk concentrations. Numerical experiments indicate that the proposed PBNP model is more efficient than the original PNP model in terms of simulation time.
 COMMUNICATIONS


Communication: Exploring the reorientation of benzene in an ionic liquid via molecular dynamics: Effect of temperature and solvent effective charge on the slow dynamics
View Description Hide DescriptionThe rotational time correlation function (RTCF) of solute benzene molecules in the ionic liquid (1butyl3methylimidazolium chloride) has been studied using classical molecular dynamics simulation. The effect of solvent charge on the functional form of RTCF was investigated by comparing four force fields for the solvent where the total charge on the anion and the cation was set to ±1e, ±0.7e, ±0.5e, and 0, respectively. For all three charged solventmodels, the RTCF exhibits a longtime tail where the relaxation rate exhibits a significant slowdown. This feature is strengthened by higher solvent charges as well as lower temperatures, indicating the influence of the strong Coulombic fields arising from the solvent charges. The longtime tail is caused by the extraordinarily slow solvent structural relaxation of ionic liquids compared to the time scale of their local vibrational and librational dynamics.

Communication: Probing the entrance channels of the X + CH_{4} → HX + CH_{3} (X = F, Cl, Br, I) reactions via photodetachment of X^{−}–CH_{4}
View Description Hide DescriptionThe entrance channel potentials of the prototypical polyatomic reaction family X + CH_{4} → HX + CH_{3} (X = F, Cl, Br, I) are investigated using anion photoelectron spectroscopy and highlevel ab initioelectronic structure computations. The prereactive van der Waals (vdW) wells of these reactions are probed for X = Cl, Br, I by photodetachmentspectra of the corresponding X^{−}–CH_{4} anion complex. For F–CH_{4}, a spinorbit splitting (∼1310 cm^{−1}) much larger than that of the F atom (404 cm^{−1}) was observed, in good agreement with theory. This showed that in the case of the F–CH_{4} system the vertical transition from the anion ground state to the neutral potentials accesses a region between the vdW valley and transition state of the earlybarrier F + CH_{4}reaction. The doublet splittings observed in the other halogen complexes are close to the isolated atomic spinorbit splittings, also in agreement with theory.

 ARTICLES


Theoretical Methods and Algorithms

Poisson–Boltzmann–Nernst–Planck model
View Description Hide DescriptionThe Poisson–Nernst–Planck (PNP) model is based on a meanfield approximation of ion interactions and continuum descriptions of concentration and electrostatic potential. It provides qualitative explanation and increasingly quantitative predictions of experimental measurements for the ion transport problems in many areas such as semiconductor devices, nanofluidic systems, and biological systems, despite many limitations. While the PNP model gives a good prediction of the ion transport phenomenon for chemical, physical, and biological systems, the number of equations to be solved and the number of diffusion coefficient profiles to be determined for the calculation directly depend on the number of ion species in the system, since each ion species corresponds to one Nernst–Planck equation and one positiondependent diffusion coefficient profile. In a complex system with multiple ion species, the PNP can be computationally expensive and parameter demanding, as experimental measurements of diffusion coefficient profiles are generally quite limited for most confined regions such as ion channels, nanostructures and nanopores. We propose an alternative model to reduce number of Nernst–Planck equations to be solved in complex chemical and biological systems with multiple ion species by substituting Nernst–Planck equations with Boltzmann distributions of ion concentrations. As such, we solve the coupled Poisson–Boltzmann and Nernst–Planck (PBNP) equations, instead of the PNP equations. The proposed PBNP equations are derived from a total energy functional by using the variational principle. We design a number of computational techniques, including the Dirichlet to Neumann mapping, the matched interface and boundary, and relaxation based iterative procedure, to ensure efficient solution of the proposed PBNP equations. Two protein molecules, cytochrome c551 and Gramicidin A, are employed to validate the proposed model under a wide range of bulk ion concentrations and external voltages. Extensive numerical experiments show that there is an excellent consistency between the results predicted from the present PBNP model and those obtained from the PNP model in terms of the electrostatic potentials, ion concentration profiles, and current–voltage (I–V) curves. The present PBNP model is further validated by a comparison with experimental measurements of I–V curves under various ion bulk concentrations. Numerical experiments indicate that the proposed PBNP model is more efficient than the original PNP model in terms of simulation time.

Molecular density functional theory of solvation: From polar solvents to water
View Description Hide DescriptionA classical density functional theory approach to solvation in molecular solvent is presented. The solvation properties of an arbitrary solute in a given solvent, both described by a molecular force field, can be obtained by minimization of a position and orientationdependent freeenergydensity functional. In the homogeneous reference fluid approximation, limited to twobody correlations, the unknown excess term of the functional approximated by the angulardependent direct correlation function of the pure solvent. We show that this function can be extracted from a preliminary MD simulation of the pure solvent by computing the angulardependent pair distribution function and solving subsequently the molecular OrnsteinZernike equation using a discrete angular representation. The corresponding functional can then be minimized in the presence of an arbitrary solute on a threedimensional cubic grid for positions and GaussLegendre angular grid for orientations to provide the solvation structure and freeenergy. This twostep procedure is proved to be much more efficient than direct molecular dynamics simulations combined to thermodynamic integration schemes. The approach is shown to be relevant and accurate for prototype polar solvents such as the Stockmayer solvent or acetonitrile. For water, although correct for neutral or moderately charged solute, it tends to underestimate the tetrahedral solvation structure around Hbonded solutes, such as spherical ions. This can be corrected by introducing suitable threebody correlation terms that restore both an accurate hydration structure and a satisfactory energetics.

Densityfunctional expansion methods: Generalization of the auxiliary basis
View Description Hide DescriptionThe formulation of densityfunctional expansion methods is extended to treat the second and higherorder terms involving the response density and spin densities with an arbitrary singlecenter auxiliary basis. The twocenter atomic orbital products are represented by the auxiliary functions centered about those two atoms, and the mapping coefficients are determined from a local constrained variational procedure. This twocenter variational procedure allows the mapping coefficients to be pretabulated and splined as a function of internuclear separation for efficient look up. The splines of mapping coefficients have a range no longer than that of the overlap integrals, and the auxiliary density appears as a single pointmultipole expansion to all nonoverlapping atoms, thus allowing for the trivial implementation of a linearscaling algorithm. The method is tested using Gaussian multipole expansions, and the effect of angular and radial completeness is explored. Several auxiliary basis sets are parametrized and compared to an auxiliary basis analogous to that used in the selfconsistentcharge densityfunctional tightbinding model, and the method is demonstrated to greatly improve the representation of the density response with respect to a reference expansion model that does not use an auxiliary basis.

Local orbitals by minimizing powers of the orbital variance
View Description Hide DescriptionIt is demonstrated that a set of local orthonormal Hartree–Fock (HF) molecular orbitals can be obtained for both the occupied and virtual orbital spaces by minimizing powers of the orbital variance using the trustregion algorithm. For a power exponent equal to one, the Boys localization function is obtained. For increasing power exponents, the penalty for delocalized orbitals is increased and smaller maximum orbital spreads are encountered. Calculations on superbenzene, C_{60}, and a fragment of the titin protein show that for a power exponent equal to one, delocalized outlier orbitals may be encountered. These disappear when the exponent is larger than one. For a small penalty, the occupied orbitals are more local than the virtual ones. When the penalty is increased, the locality of the occupied and virtual orbitals becomes similar. In fact, when increasing the cardinal number for Dunning's correlation consistent basis sets, it is seen that for larger penalties, the virtual orbitals become more localthan the occupied ones. We also show that the local virtual HF orbitals are significantly more local than the redundant projected atomic orbitals, which often have been used to span the virtual orbital space in local correlated wave function calculations. Our local molecular orbitals thus appear to be a good candidate for local correlation methods.

Analog of Rabi oscillations in resonant electronion systems
View Description Hide DescriptionQuantum coherence between electron and ion dynamics, observed in organic semiconductors by means of ultrafast spectroscopy, is the object of recent theoretical and computational studies. To simulate this kind of quantum coherent dynamics, we have introduced in a previous article [L. Stella, M. Meister, A. J. Fisher, and A. P. Horsfield, J. Chem. Phys.127, 214104 (2007)]10.1063/1.2801537 an improved computational scheme based on Correlated ElectronIon Dynamics (CEID). In this article, we provide a generalization of that scheme to model several ionic degrees of freedom and manybody electronic states. To illustrate the capability of this extended CEID, we study a model system which displays the electronion analog of the Rabi oscillations. Finally, we discuss convergence and scaling properties of the extended CEID along with its applicability to more realistic problems.

Exploring the top and bottom of the quantum control landscape
View Description Hide DescriptionA controlled quantum system possesses a search landscape defined by the target physical objective as a function of the controls. This paper focuses on the landscape for the transition probability P _{ i → f } between the states of a finite level quantum system. Traditionally, the controls are applied fields; here, we extend the notion of control to also include the Hamiltonian structure, in the form of time independent matrix elements. Level sets of controls that produce the same transition probability value are shown to exist at the bottom P _{ i → f } = 0.0 and top P _{ i → f } = 1.0 of the landscape with the field and/or Hamiltonian structure as controls. We present an algorithm to continuously explore these level sets starting from an initial point residing at either extreme value of P _{ i → f }. The technique can also identify control solutions that exhibit the desirable properties of (a) robustness at the top and (b) the ability to rapidly rise towards an optimal control from the bottom. Numerical simulations are presented to illustrate the varied control behavior at the top and bottom of the landscape for several simple modelsystems.

A universal stateselective approach to multireference coupledcluster noniterative corrections
View Description Hide DescriptionA new form of the asymmetric energy functional for multireference coupled cluster (MRCC) theories is discussed from the point of view of an energy expansion in a quasidegenerate situation. The resulting expansion for the exact electronic energy can be used to define the noniterative corrections to approximate MRCC approaches. In particular, we show that in the proposed framework the essential part of dynamic correlation can be encapsulated in the socalled correlation Hamiltonian, which in analogy to the effective Hamiltonian, is defined in the model space (). The proper parametrization of the exact/trial wavefunctions leads to the cancellation of the overlaptype numerators and to a connected form of the correlation Hamiltonian and sizeextensive energies. Within this parametrization, when the trial wavefunctions are determined without invoking a specific form of the MRCC sufficiency conditions, the ensuing correction can be universally applied to any type of the approximate MRCC method. The analogies with other MRCC triples corrections to MRCC theories with singles and doubles (MRCCSD) are outlined. In particular, we discuss the approach, which in analogy to the ΛMkMRCCSD(T) method [F. A. Evangelista, E. Prochnow, J. Gauss, H. F. Schaefer III, J. Chem. Phys.132, 074107 (2010)], introduces an approximate form of the triplyexcited clusters into the effective and correlation Hamiltonians. Since the discussed corrections can be calculated as a sum of independent referencerelated contributions, possible parallel algorithms are also outlined.

Global minimum structures and structural phase diagrams of modified Morse clusters: 11 ≤ N ≤ 30
View Description Hide DescriptionThe energetically favored structures of clusters are determined by the interactions among particles. Using the modified Morse pair potential, which has two parameters that can freely control the interactions at the minimum, short range, and long range, we systematically investigated how the interactions determines the global minimum structures of clusters and gave the structural phase diagram at 0 K for each cluster size at the range 11 ≤ N ≤ 30. Compared to the Morse potential, a number of new structures are found, and some of them are unexpected. The global minimum structures of modified Morse clusters can act as structural bank, which will be helpful in the optimization of certain real clusters.

Using forcematching to reveal essential differences between density functionals in ab initio molecular dynamics simulations
View Description Hide DescriptionThe exchangecorrelation (XC) functional and value of the electronic fictitious mass μ can be two major sources of systematic errors in ab initio CarParrinello Molecular Dynamics (CPMD) simulations, and have a significant impact on the structural and dynamic properties of condensedphase systems. In this work, an attempt is made to identify the origin of differences in liquid water properties generated from CPMD simulations run with the BLYP and HCTH/120 XC functionals and two different values of μ (representative of “small” and “large” limits) by analyzing the effective pairwise atomatom interactions. The forcematching (FM) algorithm is used to map CPMD interactions into nonpolarizable, empirical potentials defined by bonded interactions, pairwise shortranged interactions in numerical form, and Coulombic interactions via atomic partial charges. The effective interaction models are derived for the BLYP XC functional with μ = 340 a.u. and μ = 1100 a.u. (BLYP340 and BLYP1100 simulations) and the HCTH/120 XC functional with μ = 340 a.u. (HCTH340 simulation). The BLYP340 simulation results in overstructured water with slow dynamics. In contrast, the BLYP1100 and HCTH340 simulations both produce radial distribution functions (indicative of structure) that are in reasonably good agreement with experiment. It is shown that the main difference between the BLYP340 and HCTH340 effective potentials arises in the shortranged nonbonded interactions (in hydrogen bonding regions), while the difference between the BLYP340 and BLYP1100 interactions is mainly in the longranged electrostatic components. Collectively, these results demonstrate how the FM method can be used to further characterize various simulation ensembles (e.g., densityfunctional theory via CPMD). An analytical representation of each effective interaction water model, which is easy to implement, is presented.

Two more approaches for generating trajectorybased dynamics which conserves the canonical distribution in the phase space formulation of quantum mechanics
View Description Hide DescriptionWe show two more approaches for generating trajectorybased dynamics in the phase space formulation of quantum mechanics: “equilibrium continuity dynamics” (ECD) in the spirit of the phase space continuity equation in classical mechanics, and “equilibrium Hamiltonian dynamics” (EHD) in the spirit of the Hamilton equations of motion in classical mechanics. Both ECD and EHD can recover exact thermal correlation functions (of even nonlinear operators, i.e., nonlinear functions of position or momentum operators) in the classical, high temperature, and harmonic limits. Both ECD and EHD conserve the quasiprobability within the infinitesimal volume dx _{ t } dp _{ t } around the phase point (x _{ t }, p _{ t }) along the trajectory. Numerical tests of both approaches in the Wigner phase space have been made for two strongly anharmonic model problems and a double well system, for each potential autocorrelation functions of both linear and nonlinear operators have been calculated. The results suggest EHD and ECD are two additional potential useful approaches for describing quantum effects for complex systems in condense phase.

Development of a general timedependent absorbing potential for the constrained adiabatic trajectory method
View Description Hide DescriptionThe constrained adiabatic trajectory method (CATM) allows us to compute solutions of the timedependent Schrödinger equation using the Floquet formalism and Fourier decomposition, using matrix manipulation within a nonorthogonal basis set, provided that suitable constraints can be applied to the initial conditions for the Floquet eigenstate. A general form is derived for the inherent absorbing potential, which can reproduce any dispersed boundary conditions. This new artificial potential acting over an additional time interval transforms any wavefunction into a desired state, with an error involving exponentially decreasing factors. Thus, a CATM propagation can be separated into several steps to limit the size of the required Fourier basis. This approach is illustrated by some calculations for the molecular ion illuminated by a laser pulse.

Exchangecorrelation generalized gradient approximation for gold nanostructures
View Description Hide DescriptionWe compare the performance of different exchangecorrelation functionals, based on the PerdewBurkeErnzerhof (PBE) generalized gradient approximation, for the structural and electronic properties of goldnanostructures. In particular we consider PBEsol (constructed to correctly describe solidstate systems) and PBEint [Phys. Rev. B82, 113104 (2010)10.1103/PhysRevB.82.113104] which was recently introduced for hybrid interfaces and preserves the correct secondorder gradient expansion of exchange energy (as in PBEsol) providing as well a significant nonlocality for higher density variation (as in PBE). We find that the PBEint functional gives a well balanced description of atomization energies, structural properties, energy differences between isomers, and bulk properties. Results indicate that PBEint is expected to be the most accurate functional for medium and large size goldclusters of different shapes.

Zerofield splittings from density functional calculations: Analysis and improvement of known methods
View Description Hide DescriptionSeveral different approaches have been proposed to calculate the zerofield splitting tensor with density functional methods. In this work, our own derivation is presented in some detail, to allow a theoretical analysis and a comparison with other methods [M. R. Pederson and S. N. Khanna, Phys. Rev. B60, 9566 (1999)10.1103/PhysRevB.60.9566; F. Neese, J. Am. Chem. Soc.128, 10213 (2006)10.1021/ja061798a; J. Chem. Phys.127, 164112 (2007)10.1063/1.2772857]. Pederson's method can be improved by properly taking into account the quantum nature of spin when extracting the zero field splitting tensor from the magnetic anisotropy. A closedshell molecule at large distance from an open shell complex will have a spurious contribution to the zerofield splitting tensor calculated with Neese's methods. We thus have analyzed his approach in some detail and found that it can be corrected if one properly transforms the equations used in wave function based theory to a sumoverstates type expression before one interprets it as an energy derivative. If improved along these lines, Neese's and Pederson's methods become identical down to the working equations. The theoretical analysis is illustrated by sample calculations on the wellstudied Mn(III)trisacetylacetonato complex Mn(acac)_{3}, both as an isolated molecule and with a Pd(II) dichloro diammine complex at large distance as an innocent spectator.

Refinement of the experimental energy levels of higher ^{2} D Rydberg states of the lithium atom with very accurate quantum mechanical calculations
View Description Hide DescriptionVery accurate variational nonrelativistic calculations are performed for four higher Rydberg^{2} D states (1s ^{2} nd ^{1}, n = 8, …, 11) of the lithium atom (^{7}Li). The wave functions of the states are expanded in terms of allelectron explicitly correlated Gaussian functions and finite nuclear mass is used. The exponential parameters of the Gaussians are optimized using the variational method with the aid of the analytical energy gradient determined with respect to those parameters. The results of the calculations allow for refining the experimental energy levels determined with respect to the ^{2} S 1s ^{2}2s ^{1} ground state.

Calculating solvation energies by means of a fluctuating charge model combined with continuum solvent model
View Description Hide DescriptionContinuum solvent models have shown to be very efficient for calculating solvation energy of biomolecules in solution. However, in order to produce accurate results, besides atomic radii or volumes, an appropriate set of partial charges of the molecule is needed. Here, a set of partial charges produced by a fluctuating charge model—the atombond electronegativity equalization method model (ABEEMσπ) fused into molecular mechanics is used to fit for the analytical continuum electrostatics model of generalizedBorn calculations. Because the partial atomic charges provided by the ABEEMσπ model can well reflect the polarization effect of the solute induced by the continuum solvent in solution, accurate and rapid calculations of the solvation energies have been performed for series of compounds involving 105 small neutral molecules, twenty kinds of dipeptides and several protein fragments. The solvation energies of small neutral molecules computed with the combination of the GB model with the fluctuating charge protocol (ABEEMσπ/GB) show remarkable agreement with the experimental results, with a correlation coefficient of 0.97, a slope of 0.95, and a bias of 0.34 kcal/mol. Furthermore, for twenty kinds of dipeptides and several protein fragments, the results obtained from the analytical ABEEMσπ/GB model calculations correlate well with those from ab initio and PoissonBoltzmann calculations. The remarkable agreement between the solvation energies computed with the ABEEMσπ/GB model and PB model provides strong motivation for the use of ABEEMσπ/GB solvent model in the simulation of biochemical systems.

Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Transport and dynamic properties of O_{2} ^{+}(X^{2}Π_{g}) in Kr under the action of an electrostatic field: Single or multiple potential energy surface treatment
View Description Hide DescriptionIon transport and dynamic properties are calculated through molecular dynamics simulation of the motion of O_{2} ^{+} in Kr under the action of an electrostatic field. The two lower potential energy surfaces ^{2}A^{″} and ^{2}A^{′} are considered for the interaction of the Π ground state of the ion with a closed shell noble gas. First, we study the reproduction of experimental mobility data through the use of single and multiple potential energy surfaces and establish the contribution of both lower energy states to the interactions. Further, we obtain mean energies and components of the diffusion coefficient parallel and perpendicular to the field, the latter through calculation of the velocity correlation functions. We also calculate components of the angular momentum which provide a measure of the collisional rotational alignment of the ions at high field strength.

Rovibrational eigenenergy structure of the [H,C,N] molecular system
View Description Hide DescriptionThe vibrationalrotational eigenenergy structure of the [H,N,C] molecular system is one of the key features needed for a quantum mechanical understanding of the HCN HNC model reaction. The rotationless vibrational structure corresponding to the multidimensional double well potential energy surface is well established. The rotational structure of the bending vibrational states up to the isomerisation barrier is still unknown. In this work the structure of the rotational states for low and high vibrational angular momentum is described from the ground state up to the isomerisation barrier using hot gas molecular high resolution spectroscopy and rotationally assigned ab initio rovibronic states. For low vibrational angular momentum the rotational structure of the bending excitations splits in three regions. For J < 40 the structure corresponds to that of a typical linear molecule, for 40 < J < 60 has an approximate double degenerate structure and for J > 60 the splitting of the e and f components begins to decrease and the rotational constant increases. For states with high angular momentum, the rotational structure evolves into a limiting structure for v 2 > 7 – the molecule is locked to the molecular axis. For states with v 2 > 11 the rotational structure already begins to accommodate to the lower rotational constants of the isomerisation states. The vibrational energy begins to accommodate to the levels above the barrier only at high vibrational excitations of v 2 > 22 just above the barrier whereas this work shows that the rotational structure is much more sensitive to the double well structure of the potential energy surface. The rotational structure already experiences the influence of the barrier at much lower energies than the vibrational one.

Tunnelling under a conical intersection: Application to the product vibrational state distributions in the UV photodissociation of phenols
View Description Hide DescriptionWhen phenol is photoexcited to its S_{1} (1^{1}ππ*) state at wavelengths in the range 257.403 ≤ λ_{phot} ≤ 275.133 nm the O−H bond dissociates to yield an H atom and a phenoxyl coproduct, with the available energy shared between translation and well characterised product vibration. It is accepted that dissociation is enabled by transfer to an S_{2} (1^{1}πσ*) state, for which the potential energy surface (PES) is repulsive in the O−H stretch coordinate, R _{O–H}. This S_{2} PES is cut by the S_{1} PES near R _{O–H} = 1.2 Å and by the S_{0}ground state PES near R _{O−H} = 2.1 Å, to give two conical intersections (CIs). These have each been invoked—both in theoretical studies and in the interpretation of experimental vibrational activity—but with considerable controversy. This paper revisits the dynamic mechanisms that underlie the photodissociation of phenol and substituted phenols in the light of symmetry restrictions arising from torsional tunnelling degeneracy, which has been neglected hitherto. This places tighter symmetry constraints on the dynamics around the two CIs. The nonrigid molecular symmetry group G _{4} necessitates vibronic interactions by a _{2} modes to enable coupling at the inner, higher energy (S_{1}/S_{2}) CI, or by b _{1} modes at the outer, lower energy (S_{2}/S_{0}) CI. The experimental data following excitation through many vibronic levels of the S_{1} state of phenol and substituted phenols demonstrate the effective role of the ν_{16a} (a _{2}) ring torsional mode in enabling O–H bond fission. This requires tunnelling under the S_{1}/S_{2} CI, with a hindering barrier of ∼5000 cm^{−1} and with the associated geometric phase effect. Quantum dynamic calculations using new ab initio PESs provide quantitative justification for this conclusion. The fates of other excited S_{1} modes are also rationalised, revealing both spectator modes and intramolecular vibrational redistribution between modes. A common feature in many cases is the observation of an extended, oddnumber only, progression in product mode ν_{16a} (i.e., the parent mode which enables S_{1}/S_{2}tunnelling), which we explain as a FranckCondon consequence of a major change in the active vibration frequency. These comprehensive results serve to confirm the hypothesis that O−H fission following excitation to the S_{1} state involves tunnelling under the S_{1}/S_{2} CI—in accord with conclusions reached from a recent correlation of the excited state lifetimes of phenol (and many substituted phenols) with the corresponding vertical energy gaps between their S_{1} and S_{2} PESs.
