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Progress in the atomic-scale modeling of matter over the past decade has been tremendous. This progress has been brought about by improvements in methods for evaluating interatomic forces that work by either solving the electronic structure problem explicitly, or by computing accurate approximations of the solution and by the development of techniques that use the Born-Oppenheimer (BO) forces to move the atoms on the BO potential energy surface. As a consequence of these developments it is now possible to identify stable or metastable states, to sample configurations consistent with the appropriate thermodynamic ensemble, and to estimate the kinetics of reactions and phase transitions. All too often, however, progress is slowed down by the bottleneck associated with implementing new optimization algorithms and/or sampling techniques into the many existing electronic-structure and empirical-potential codes. To address this problem, we are thus releasing a new version of the i-PI software. This piece of software is an easily extensible framework for implementing advanced atomistic simulation techniques using interatomic potentials and forces calculated by an external driver code. While the original version of the code (Ceriotti et al., 2014) was developed with a focus on path integral molecular dynamics techniques, this second release of i-PI not only includes several new advanced path integral methods, but also offers other classes of algorithms. In other words, i-PI is moving towards becoming a universal force engine that is both modular and tightly coupled to the driver codes that evaluate the potential energy surface and its derivatives., Program summary, Program Title: i-PI, Program Files doi: http://dx.doLorg/10.17632/x792grbm9g.1, Licensing provisions: GPLv3, MIT, Programming language: Python, External routines/libraries: NumPy, Nature of problem: Lowering the implementation barrier to bring state-of-the-art sampling and atomistic modeling techniques to ab initio and empirical potentials programs., Solution method: Advanced sampling methods, including path-integral molecular dynamics techniques, are implemented in a Python interface. Any electronic structure code can be patched to receive the atomic coordinates from the Python interface, and to return the forces and energy that are used to integrate the equations of motion, optimize atomic geometries, etc., Restrictions: This code does not compute interatomic potentials, although the distribution includes sample driver codes that can be used to test different techniques using a few simple model force fields. (C) 2018 Elsevier B.V. All rights reserved.

We present a simple method for the calculation of reaction rates in the Fermi golden-rule limit, which accurately captures the effects of tunnelling and zero-point energy. The method is based on a modification of the recently proposed golden-rule quantum transition state theory (GR-QTST) of Thapa, Fang and Richardson. While GR-QTST is not size consistent, leading to the possibility of unbounded errors in the rate, our modified method has no such issue and so can be reliably applied to condensed phase systems. Both methods involve path-integral sampling in a constrained ensemble; the two methods differ, however, in the choice of constraint functional. We demonstrate numerically that our modified method is as accurate as GR-QTST for the one-dimensional model considered by Thapa and coworkers. We then study a multi-dimensional spin-boson model, for which our method accurately predicts the true quantum rate, while GR-QTST breaks down with an increasing number of boson modes in the discretisation of the spectral density. Our method is able to accurately predict reaction rates in the Marcus inverted regime, without the need for the analytic continuation required by Wolynes theory., 13 pages, 4 figures

We revisit the well-known aqueous ferrous-ferric electron transfer reaction in order to address recent suggestions that nuclear tunnelling can lead to significant deviation from the linear response assumption inherent in the Marcus picture of electron transfer. A recent study of this reaction by Richardson and coworkers has found a large difference between their new path-integral method, GR-QTST, and the saddle point approximation of Wolynes (Wolynes theory). They suggested that this difference could be attributed to the existence of multiple tunnelling pathways, leading Wolynes theory to significantly overestimate the rate. This was used to argue that the linear response assumptions of Marcus theory may break down for liquid systems when tunnelling is important. If true, this would imply that the commonly used method for studying such systems, where the problem is mapped onto a spin-boson model, is invalid. However, we have recently shown that size inconsistency in GR-QTST can lead to poor predictions of the rate in systems with many degrees of freedom. We have also suggested an improved method, the path-integral linear golden-rule (LGR) approximation, which fixes this problem. Here we demonstrate that the GR-QTST results for ferrous-ferric electron transfer are indeed dominated by its size consistency error. Furthermore, by comparing the LGR and Wolynes theory results, we confirm the established picture of nuclear tunnelling in this system. Finally, by comparing our path-integral results to those obtained by mapping onto the spin-boson model, we reassess the importance of anharmonic effects and the accuracy of this commonly used mapping approach., 15 pages, 5 figures

Radical pair recombination reactions are known to be sensitive to extremely weak magnetic fields, and can therefore be said to function as molecular magnetoreceptors. The classic example is a carotenoid-porphyrin-fullerene (C+PF-) radical pair that has been shown to provide a "proof-of-principle" for the operation of a chemical compass [K. Maeda et al., Nature 453, 387 (2008)]. Previous simulations of this radical pair have employed semiclassical approximations, which are routinely applicable to its 47 coupled electronic and nuclear spins. However, calculating the exact quantum mechanical spin dynamics presents a significant challenge, and has not been possible before now. Here we use a recently developed method to perform numerically converged simulations of the C+PF- quantum mechanical spin dynamics, including all coupled spins. Comparison of these quantum mechanical simulations with various semiclassical approximations reveals that, while it is not perfect, the best semiclassical approximation does capture essentially all of the relevant physics in this problem., Comment: 8 pages, 4 figures

We describe a fast implementation of the quasi-centroid molecular dynamics (QCMD) method in which the quasi-centroid potential of mean force is approximated as a separable correction to the classical interaction potential. This correction is obtained by first calculating quasi-centroid radial and angular distribution functions in a short path integral molecular dynamics simulation, and then using iterative Boltzmann inversion to obtain an effective classical potential that reproduces these distribution functions in a classical NVT simulation. We illustrate this approach with example applications to the vibrational spectra of gas phase molecules, obtaining excellent agreement with QCMD reference calculations for water and ammonia and good agreement with the quantum mechanical vibrational spectrum of methane., Comment: 7 pages, 3 figures, and supplementary material

Relaxation processes can have a large effect on the spin selective electron transfer reactions of radical pairs. These processes are often treated using phenomenological relaxation superoperators or with some model for the microscopic relaxation mechanism treated within Bloch-Redfield-Wangsness theory. Here, we demonstrate that an alternative perturbative relaxation theory, based on the Nakajima-Zwanzig equation, has certain advantages over Redfield theory. In particular, the Nakajima-Zwanzig equation does not suffer from the severe positivity problem of Redfield theory in the static disorder limit. Combining the Nakajima-Zwanzig approach consistently with the Schulten-Wolynes semiclassical method, we obtain an efficient method for modeling the spin dynamics of radical pairs containing many hyperfine-coupled nuclear spins. This is then used to investigate the spin-dependent electron transfer reactions and intersystem crossing of dimethyljulolidine-naphthalenediimide (DMJ-NDI) radical ion pairs. By comparing our simulations with experimental data, we find evidence for a field-independent contribution to the triplet quantum yields of these reactions which cannot be explained by electron spin relaxation alone.

Night-migratory songbirds appear to sense the direction of the Earth's magnetic field via radical pair intermediates formed photochemically in cryptochrome flavoproteins contained in photoreceptor cells in their retinas. It is an open question whether this light-dependent mechanism could be sufficiently sensitive given the low-light levels experienced by nocturnal migrants. The scarcity of available photons results in significant uncertainty in the signal generated by the magnetoreceptors distributed around the retina. Here we use results from Information Theory to obtain a lower bound estimate of the precision with which a bird could orient itself using only geomagnetic cues. Our approach bypasses the current lack of knowledge about magnetic signal transduction and processing in vivo by computing the best-case compass precision under conditions where photons are in short supply. We use this method to assess the performance of three plausible cryptochrome-derived flavin-containing radical pairs as potential magnetoreceptors.

Recent developments in path integral methodology have significantly reduced the computational expense of including quantum mechanical effects in the nuclear motion in ab initio molecular dynamics simulations. However, the implementation of these developments requires a considerable programming effort, which has hindered their adoption. Here we describe i-PI, an interface written in Python that has been designed to minimise the effort required to bring state-of-the-art path integral techniques to an electronic structure program. While it is best suited to first principles calculations and path integral molecular dynamics, i-PI can also be used to perform classical molecular dynamics simulations, and can just as easily be interfaced with an empirical forcefield code. To give just one example of the many potential applications of the interface, we use it in conjunction with the CP2K electronic structure package to showcase the importance of nuclear quantum effects in high-pressure water. © 2013 Elsevier B.V. All rights reserved.

Currently the most likely mechanism of the magnetic compass sense in migratory songbirds relies on the coherent spin dynamics of pairs of photochemically formed radicals in the retina. Spin-conserving electron transfer reactions are thought to result in radical pairs whose near-degenerate electronic singlet and triplet states interconvert coherently as a result of hyperfine, exchange, and dipolar couplings and, crucially for a compass sensor, Zeeman interactions with the geomagnetic field. In this way, the yields of the reaction products can be influenced by magnetic interactions a million times smaller than kBT. The question we ask here is whether one can only account for the coherent spin dynamics using quantum mechanics. We find that semiclassical approximations to the spin dynamics of radical pairs only provide a satisfactory description of the anisotropic product yields when there is no electron spin-spin coupling, a situation unlikely to be consistent with a magnetic sensing function. Although these methods perform reasonably well for shorter-lived radical pairs with stronger electron-spin coupling, the accurate simulation of anisotropic magnetic field effects relevant to magnetoreception seems to require full quantum mechanical calculations.

We present a simple interpolation formula for the rate of an electron transfer reaction as a function of the electronic coupling strength. The formula only requires the calculation of Fermi Golden Rule and Born-Oppenheimer rates and so can be combined with any methods that are able to calculate these rates. We first demonstrate the accuracy of the formula by applying it to a one dimensional scattering problem for which the exact quantum mechanical, Fermi Golden Rule, and Born-Oppenheimer rates are readily calculated. We then describe how the formula can be combined with the Wolynes theory approximation to the Golden Rule rate, and the ring polymer molecular dynamics (RPMD) approximation to the Born-Oppenheimer rate, and used to capture the effects of nuclear tunnelling, zero point energy, and solvent friction on condensed phase electron transfer reactions. Comparison with exact hierarchical equations of motion (HEOM) results for a demanding set of spin-boson models shows that the interpolation formula has an error comparable to that of RPMD rate theory in the adiabatic limit, and that of Wolynes theory in non-adiabatic limit, and is therefore as accurate as any method could possibly be that attempts to generalise these methods to arbitrary electronic coupling strengths., Comment: 17 pages, 5 figures

We show that the stochastic Schr\"odinger equation (SSE) provides an ideal way to simulate the quantum mechanical spin dynamics of radical pairs. Electron spin relaxation effects arising from fluctuations in the spin Hamiltonian are straightforward to include in this approach, and their treatment can be combined with a highly efficient stochastic evaluation of the trace over nuclear spin states that is required to compute experimental observables. These features are illustrated in example applications to a flavin-tryptophan radical pair of interest in avian magnetoreception, and to a problem involving spin-selective radical pair recombination along a molecular wire. In the first of these examples, the SSE is shown to be both more efficient and more widely applicable than a recent stochastic implementation of the Lindblad equation, which only provides a valid treatment of relaxation in the extreme-narrowing limit. In the second, the exact SSE results are used to assess the accuracy of a recently-proposed combination of Nakajima-Zwanzig theory for the spin relaxation and Schulten-Wolynes theory for the spin dynamics, which is applicable to radical pairs with many more nuclear spins. An appendix analyses the efficiency of trace sampling in some detail, highlighting the particular advantages of sampling with SU(N) coherent states., Comment: 14 pages, 4 figures

Radical pair recombination reactions are normally described using a quantum mechanical master equation for the electronic and nuclear spin density operator. The electron spin state selective (singlet and triplet) recombination processes are described with a Haberkorn reaction term in this master equation. Here we consider a general spin state selective electron transfer reaction of a radical pair and use Nakajima-Zwanzig theory to derive the master equation for the spin density operator, thereby elucidating the relationship between non-adiabatic reaction rate theory and the Haberkorn reaction term. A second order perturbation theory treatment of the diabatic coupling naturally results in the Haberkorn master equation with an additional reactive scalar electron spin coupling term. This term has been neglected in previous spin chemistry calculations, but we show that it will often be quite significant. We also show that beyond second order in perturbation theory, i.e., beyond the Fermi golden rule limit, an additional reactive singlet-triplet dephasing term appears in the master equation. A closed form expression for the reactive scalar electron spin coupling in terms of the Marcus theory parameters that determine the singlet and triplet recombination rates is presented. By performing simulations of radical pair reactions with the exact Hierarchical Equations of Motion (HEOM) method, we demonstrate that our master equations provide a very accurate description of radical pairs undergoing spin-selective non-adiabatic electron transfer reactions. The existence of a reactive electron spin coupling may well have implications for biologically relevant radical pair reactions such as those which have been suggested to play a role in avian magnetoreception.

We describe a simple quantum mechanical method that can be used to obtain accurate numerical results over long time scales for the spin correlation tensor of an electron spin that is hyperfine coupled to a large number of nuclear spins. This method does not suffer from the statistical errors that accompany a Monte Carlo sampling of the exact eigenstates of the central spin Hamiltonian obtained from the algebraic Bethe ansatz, or from the growth of the truncation error with time in the time-dependent density matrix renormalization group (t-DMRG) approach. As a result, it can be applied to larger central spin problems than the algebraic Bethe ansatz, and for longer times than the t-DMRG algorithm. It is therefore an ideal method to use to solve central spin problems, and we expect that it will also prove useful for a variety of related problems that arise in a number of different research fields., Comment: Article: 5 pages, 5 figures Supplementary material: 15 pages, 6 figures

Glimpsing resonances as F and H 2 react The reaction of fluorine atoms with hydrogen molecules has long provided a window into the subtle effects of quantum mechanics on chemical dynamics. Kim et al. now show that the system still has some secrets left to reveal. The authors applied photodetachment to FH 2 − anions and their deuterated analogs. This allowed them to intercept the reaction trajectory in the middle and thereby uncover unanticipated weakly bound resonances. Theoretical calculations explain these observations and predict additional similar features that have yet to be seen. Science , this issue p. 510

We have used an efficient new quantum mechanical method for radical pair recombination reactions to study the spin-dependent charge recombination along PTZ$^{\bullet+}$--Ph$_n$--PDI$^{\bullet-}$ molecular wires. By comparing our results to the experimental data of E. Weiss {\em et al.} [J. Am. Chem. Soc. {\bf 126}, 5577 (2004)], we are able to extract the spin-dependent (singlet and triplet) charge recombination rate constants for wires with $n=2-5$. These spin-dependent rate constants have not been extracted previously from the experimental data because they require fitting its magnetic field-dependence to the results of quantum spin dynamics simulations. We find that the triplet recombination rate constant decreases exponentially with the length of the wire, consistent with the superexchange mechanism of charge recombination. However, the singlet recombination rate constant is nearly independent of the length of the wire, suggesting that the singlet pathway is dominated by an incoherent hopping mechanism. A simple qualitative explanation for the different behaviours of the two spin-selective charge recombination pathways is provided in terms of Marcus theory. We also find evidence for a magnetic field-independent background contribution to the triplet yield of the charge recombination reaction, and suggest several possible explanations for it. Since none of these explanations is especially compelling given the available experimental evidence, and since the result appears to apply more generally to other molecular wires, we hope that this aspect of our study will stimulate further experimental work., Comment: 12 pages, 10 figures

The radical pair mechanism has been put forward as the basis of the magnetic compass sense of migratory birds. Some of the strongest supporting evidence has come from behavioural experiments in which birds exposed to weak time‐dependent magnetic fields lose their ability to orient in the geomagnetic field. However, conflicting results and scepticism about the requirement for abnormally long quantum coherence lifetimes have cast a shroud of uncertainty over these potentially pivotal studies. Using a recently developed computational approach, we explore the effects of various radiofrequency magnetic fields on biologically plausible radicals within the theoretical framework of radical pair magnetoreception. We conclude that the current model of radical pair magnetoreception is unable to explain the findings of the reported behavioural experiments. Assuming that an unknown mechanism amplifies the predicted effects, we suggest experimental conditions that have the potential to distinguish convincingly between the two distinct families of radical pairs currently postulated as magnetic compass sensors. We end by making recommendations for experimental protocols that we hope will increase the chance that future experiments can be independently replicated.

International audience; We combine classical and ring polymer molecular dynamics simulations with the molecular jump model to provide a molecular description of the nuclear quantum effects (NQEs) on water reorientation and hydrogen-bond dynamics in liquid H2O and D2O. We show that while the net NQEs is negligible in D2O, it leads to a ∼13% acceleration in H2O dynamics compared to a classical description. Large angular jumps exchanging hydrogen-bond partners are the dominant reorientation pathway (just as in a classical description); the faster reorientation dynamics arise from the increased jump rate constant. NQEs do not change the jump amplitude distribution and no significant tunneling is found. The faster jump dynamics are quantitatively related to decreased structuring of the OO radial distribution function when NQEs are included. This is explained, via a jump model analysis, by a competition between the effects of water’s librational and OH stretch mode zero point energies on the hydrogen-bond strength.

This paper summarizes the contributions to the Faraday Discussion on reaction rate theory. The topics range from contemporary usage of transition state theory, including rare event sampling, to instantons and non-adiabatic dynamics.

The diffusion of protons and hydroxide ions along water wires provides an efficient mechanism for charge transport that is exploited by biological membrane channels and shows promise for technological applications such as fuel cells. However, what is lacking for a better control and design of these systems is a thorough theoretical understanding of the diffusion process at the atomic scale. Here we focus on two aspects of this process that are often disregarded because of their high computational cost: the use of first-principles potential energy surfaces and the treatment of the nuclei as quantum particles. We consider proton and hydroxide ions in finite water wires using density functional theory augmented with an apolar cylindrical confining potential. We employ machine learning techniques to identify the charged species, thus obtaining an agnostic definition that takes explicitly into account the delocalization of the charge in the Grotthus-like mechanism. We include nuclear quantum effects (NQEs) through the thermostated ring polymer molecular dynamics method and model finite system size effects by considering Langevin dynamics on the potential of mean force of the charged species, allowing us to extract the same "universal" diffusion coefficient from simulations with different wire sizes. In the classical case, diffusion coefficients depend significantly on the potential energy surface, in particular on how dispersion forces modulate water-water distances. NQEs, however, make the diffusion less sensitive to the underlying potential and geometry of the wire.

The magnetoelectroluminescence of conjugated organic polymer films is widely accepted to arise from a polaron pair mechanism, but their magnetoconductance is less well understood. Here we derive a new relationship between the experimentally measurable magnetoelectroluminescence and magnetoconductance and the theoretically calculable singlet yield of the polaron pair recombination reaction. This relationship is expected to be valid regardless of the mechanism of the magnetoconductance, provided the mobilities of the free polarons are independent of the applied magnetic field (i.e., provided one discounts the possibility of spin-dependent transport). We also discuss the semiclassical calculation of the singlet yield of the polaron pair recombination reaction for materials such as poly(2,5-dioctyloxy-paraphenylene vinylene) (DOO-PPV), the hyperfine fields in the polarons of which can be extracted from light-induced electron spin resonance measurements. The resulting theory is shown to give good agreement with experimental data for both normal (H-) and deuterated (D-) DOO-PPV over a wide range of magnetic field strengths once singlet-triplet dephasing is taken into account. Without this effect, which has not been included in any previous simulation of magnetoelectroluminescence, it is not possible to reproduce the experimental data for both isotopologues in a consistent fashion. Our results also indicate that the magnetoconductance of DOO-PPV cannot be solely due to the effect of the magnetic field on the dissociation of polaron pairs.

Full geometry optimization has been performed within the semiempirical QCFF/PI model for the 1812 fullerene structural isomers of C{sub 60} formed by 12 pentagons and 20 hexagons. All are local minima on the potential energy hypersurface. Correlations of total energy with many structural motifs yield highly scattered diagrams, but some exhibit linear trends. Penalty and merit functions can be assigned to certain motifs: inclusion of a fused pentagon pair entails an average penalty of 111 kJ mol{sup -1}; a generic hexagon triple costs 23 kJ mol{sup -1}; a triple (open or fused) comprising a pentagon between two hexagonal neighbors gives a stabilization of 19 kJ mol{sup -1}. These results can be understood in terms of the curved nature of fullerene molecules: pentagons should be isolated to avoid sharp local curvature, hexagon triples are costly because they enforce local planarity and hence imply high curvature in another part of the fullerene surface, but hexagon-pentagon-hexagon triples allow the surface to distribute steric strain by warping. The best linear fit is found for H, the second moment of the hexagon-neighbor-index signature, which fits the total energies with a standard deviation of only 53 kJ mol{sup -1} and must be minimized for stability; thismore » index too can be interpreted in terms of curvature. 26 refs., 5 figs.« less

We show how the Kubo transform can be inverted in the time domain and then use this result to investigate the sum rule constraints on a Kubo-transformed correlation function c ˜ AB ( t ) = 1 β ∫ 0 β d λ 〈 A ( - i λ ℏ ) B ( t ) 〉 that arise from the values of the static equilibrium properties c AB ( n ) ( 0 ) = [ d n 〈 A ( 0 ) B ( t ) 〉 / d t n ] t = 0 . We find, perhaps not surprisingly, that these sum rules only depend on the behavior of c ˜ AB ( t ) for times on the order of βℏ. The implications of this finding are discussed in light of the recent use of these sum rules to assess the quality of approximate Kubo-transformed correlation functions for liquid hydrogen at 14 K and liquid water at 298 K.

We report the first scattering calculations for the F+H2 reaction based on ab initio potential energy surfaces (PES's) and an exact treatment of spin-orbit and Coriolis coupling. The probability of reaction of F*(2P1/2) is less than 10% of that for F(2P3/2) and the overall features of the scattering are well represented by calculations on the lowest electronic PES. © 1998 American Institute of Physics.

A leapfrog carbon cluster can be constructed geometrically by omnicapping and dualising a polyhedral parent cluster with one third the number of carbon atoms. In this paper the Hückel molecular orbital energy levels of leapfrog fullerenes, and other related leapfrog carbon clusters, are investigated analytically using graph theory. It is proved in particular that all trivalent leapfrog clusters have antibonding lowest unoccupied molecular orbitals (LUMOs), and that all trivalent leapfrog clusters containing at least one ring of r ≠ 3k atoms have bonding highest occupied molecular orbitals (HOMOs). More generally, all trivalent leapfrog clusters have bonding or non-bonding HOMOs. A chemically significant corollary is that all trivalent leapfrog clusters, irespective of their ring counts, are closed shell.

Isotope fractionation between different phases is a subtle but very important phenomenon that is related to the quantum nature of light nuclei, and that has important consequences for geochemistry, hydrology, and biology. Here we present a joint experimental/theoretical investigation of the differential segregation of hydrogen and deuterium at the liquid/vapor interface of mixtures of light and heavy water. We use both vibrational sum-frequency spectroscopy and path integral molecular dynamics simulations to quantitatively assess this phenomenon. The experimental and theoretical results indicate that the last layer of water molecules at the liquid/vapor interface is enriched in hydrogen. We discuss in detail the extent, the physical origin, and the implications of this surface-specific isotope effect. © 2013 American Chemical Society.

Time-dependent wavepacket calculations have been used to simulate the photoelectron spectrum of the FH 2 − anion at the high energy resolution attainable in anion threshold photodetachment experiments, using the new ab initio potential energy surface of Stark and Werner. In addition to the direct scattering F + H 2 hindered-rotor states that have been seen in earlier spectra at lower resolution, the present high-resolution spectra show a distinct set of narrow peaks due to quantum mechanical reactive scattering resonances. These resonances have not been detected previously in any other F + H 2 reactive scattering experiment.

A statistical model based on the quasiclassical trajectory method is presented in this work for atom-diatom insertion reactions. The basic difference between this and the corresponding statistical quantum model (SQM) lies in the fact that trajectories instead of wave functions are propagated in the entrance and exit channels. Other than this the two formulations are entirely similar. In particular, it is shown that conservation of parity can be taken into account in a natural and precise way in the statistical quasiclassical trajectory (SQCT) model. Additionally, the SQCT model complies with the principle of detailed balance and overcomes the problem of the zero point energy in the products. As a test, the model is applied to the H3+ and H+D2 exchange reactions. The excellent agreement between the SQCT and SQM results, especially in the case of the differential cross sections, indicates that the effect of tunneling through the centrifugal barrier is negligible. The effect of ignoring quantum mechanical parity conservation is also investigated.

In this work, we consider the problem of calculating the classical free energies of liquids and solids for molecular models with intramolecular flexibility. We show that thermodynamic integration from the fully-interacting solid of interest to a Debye crystal reference state, with anisotropic harmonic interactions derived from the Hessian of the original crystal, provides a straightforward route to calculating the Gibbs free energy of the solid. To calculate the molecular liquid free energy, it is essential to correctly account for contributions from both intermolecular and intramolecular motion; we employ thermodynamic integration to a Lennard-Jones reference fluid, coupled with direct evaluation of the molecular ro-vibrational partition function. These approaches are used to study the low-pressure classical phase diagram of the flexible q-TIP4P/F water model. We find that, while the experimental ice-I/liquid and ice-III/liquid coexistence lines are described reasonably well by this model, the ice-II phase is predicted to be metastable. In light of this finding, we go on to examine how the coupling between intramolecular flexibility and intermolecular interactions influences the computed phase diagram by comparing our results with those of the underlying rigid-body water model.

The inclusion of Quantum Mechanical (QM) effects such as zero point energy (ZPE) and tunneling in simulations of chemical reactions, especially in the case of light atom transfer, is an important problem in computational chemistry. In this respect, the hydrogen exchange reaction and its isotopic variants constitute an excellent benchmark for the assessment of approximate QM methods. In particular, the recently developed ring polymer molecular dynamics (RPMD) technique has been demonstrated to give very good results for bimolecular chemical reactions in the gas phase. In this work, we have performed a detailed RPMD study of the H + H(2) reaction and its isotopologues Mu + H(2), D + H(2) and Heμ + H(2), at temperatures ranging from 200 to 1000 K. Thermal rate coefficients and kinetic isotope effects have been computed and compared with exact QM calculations as well as with quasiclassical trajectories and experiment. The agreement with the QM results is good for the heaviest isotopologues, with errors ranging from 15% to 45%, and excellent for Mu + H(2), with errors below 15%. We have seen that RPMD is able to capture the ZPE effect very accurately, a desirable feature of any method based on molecular dynamics. We have also verified Richardson and Althorpe's prediction [J. O. Richardson and S. C. Althorpe, J. Chem. Phys., 2009, 131, 214106] that RPMD will overestimate thermal rates for asymmetric reactions and underestimate them for symmetric reactions in the deep tunneling regime. The ZPE effect along the reaction coordinate must be taken into account when assigning the reaction symmetry in the multidimensional case.

We present results of quantum calculations we have performed on the title reaction in order to study its stereodynamics at collision energies of 0.54 and 1.29 eV. Our theoretical model is based on a representation where directional properties are expressed in terms of real rotational polarization moments instead of magnetic quantum numbers. We analyze the physical meaning of rotational polarization moments and show that, when defined as in the present work, these quantities directly describe the reaction stereodynamics in terms of intuitive chemical concepts related to preferences in the reaction mechanism for particular planes and senses of molecular rotation. Using this interpretation, we identify two distinct regimes for the stereodynamics of the title reaction, observed when HD is formed with low or high rotational excitation. We also identify relevant characteristics of both regimes: (i) the existence and location of preferred planes and senses of molecular rotation, (ii) correlations between these preferences, the scattering angle and the reaction probability, and (iii) their dependence on the collision energy. © 1998 American Institute of Physics.

MACROSCOPIC amounts of the two fullerenes C60 and C70 have been available for a year1, and have already had an enormous impact on research in chemistry and physics. Experimentalists are now turning their attention to the higher fullerenes2,3. Qualitative molecular-orbital theory predicts4-6 stability for Cn with n = 60, 70, (72), 76, 78, 84, . . . , of which all but C72 have now been produced by evaporation of graphite1-3, and in general for infinite series of closed-shell neutral fullerenes for n=60 + 6k (k≠1), 70+30k, 84+36k (all )7-9. Recent experimental observations of endohedral LaCn metallofullerenes10 have been rationalized in terms of 'magic numbers' for fullende anions Cn 2-, for which special stability is predicted11 at n=74, 82, 88, . . . ; but the exact extent of charge transfer in these complexes has yet to be determined. Here we present calculations of magic numbers in the fullerenium sequence Cn 2+ (n = 74, 80, (88), 92) and show that the electron count determines stability and the atom count determines structure in all three (neutral, anionic and cationic) series. Stable cations have two carbons more, and stable anions two carbons less, than the corresponding stable neutral cluster. We predict likely structures of the 'magic' cations.

This article describes a quantum mechanical reactive scattering program for atom–diatom chemical reactions that we have written during the past several years. The program uses a coupled-channel hyperspherical coordinate method to solve the Schrodinger equation for the motion of the three nuclei on a single Born–Oppenheimer potential energy surface. It has been tested for all possible deuterium-substituted isotopomers of the H + H 2 , F + H 2 , and Cl + H 2 reactions, and tried and tested potential energy surfaces for these reactions are included within the program as Fortran subroutines.

The celebrated 1985 molecular beam measurements for the F + H2 reaction of Lee and co-workers, consisting of time-of-flight (TOF) spectra and angular distributions (AD) at several collision energies, have been directly simulated using fully resolved differential cross-sections (DCS) obtained in accurate quantum mechanical (QM) and quasi-classical trajectory (QCT) calculations on the most recent ab initio potential energy surface (PES) by Stark and Werner. The simulations performed using the QM calculations show an unprecedentedly good agreement with the experimental results for all final vibrational states of the HF product. In particular, the height of the peak in the experimental laboratory angular distribution corresponding to HF(v′=3) forward scattering is quite well reproduced by the simulation using the QM theoretical data at all three experimental collision energies for both para and normal hydrogen. The most important discrepancies between theory and experiment are found in the HF(v′=3) sideways and backward scattering. The simulations carried out with the QCT data, although accounting correctly for the backward scattering, fail to account for most of the v′ = 3 forward scattering. The analysis performed in this work indicates that an unbiased comparison between theoretical and experimental results in the laboratory frame (as opposed to the center-of-mass frame) is required to assess the quality of a theoretical calculation on a given ab initio PES.

The water molecule, rotationally state selected in the third and fourth OH stretching overtone (‖04〉−, ‖05〉−) and stretch–bend combination (‖04−2〉) levels, has been photodissociated via the A state at λ≂282 nm. The photofragment rotational state distributions, determined by OH(A–X) laser induced fluorescence (LIF), differ from those reported previously by Andresen and co‐workers, in which water was initially prepared in the ‖01〉− level and photodissociated at 193 nm, and from those by Crim and co‐workers, in which H2O was photodissociated via the ‖04〉− level at wavelengths shorter than 282 nm. These differences become more pronounced with increasing angular momentum in the parent water molecule and with an increasing number of quanta in the intermediate OH stretching overtone state. The Franck–Condon theory of Balint‐Kurti, previously employed successfully to account for the product state distributions arising from the 193 nm photodissociation of H2O‖01〉−, qualitatively reproduces the trends observed in the present study if it is assumed that dissociation occurs preferentially from extended RH‐OH configurations of the ‖04〉− and ‖05〉− overtones. The product OH state distributions are thus shown to be sensitive indicators of the bending and rotational motions of H2O(X) in the wide amplitude stretching region of the ground state surface.