The Coulomb phase, with its dipolar correlations and pinch-point-scattering patterns, is central to discussions of geometrically frustrated systems, from water ice to binary and mixed-valence alloys, as well as numerous examples of frustrated magnets. The emergent Coulomb phase of lattice-based systems has been associated with divergence-free fields and the absence of long-range order. Here, we go beyond this paradigm, demonstrating that a Coulomb phase can emerge naturally as a persistent fluctuating background in an otherwise ordered system. To explain this behavior, we introduce the concept of the fragmentation of the field of magnetic moments into two parts, one giving rise to a magnetic monopole crystal, the other a magnetic fluid with all the characteristics of an emergent Coulomb phase. Our theory is backed up by numerical simulations, and we discuss its importance with regard to the interpretation of a number of experimental results

Communication: Full dimensional quantum rate coefficients and kinetic isotope effects from ring polymer molecular dynamics for a seven-atom reaction OH + CH4 → CH3 + H2O Potential energy surface for the CH 3 + HBr → CH 4 + Br hydrogen abstraction reaction: Thermal and stateselected rate constants, and kinetic isotope effects A method for projecting chemical reaction surface coordinates from a Hessian in curvilinear internal coordinates has recently been developed. Here we introduce a modification to this approach which allows for analytical evaluation of the necessary coordinate derivatives, thus reducing the number of ab initio calculations required. We apply this method to the determination of spectator mode frequencies and zero-point energies for the series of hydrogen abstraction reactions X + CH 4 → XH+ CH 3 , X = muonium ͑͒, H, D, CH 3 . Comparison of these frequencies with those obtained using rectilinear coordinates allows us to examine how the mass of X affects the coordinate sensitivity of the spectator modes. We carry out two-dimensional quantum reactive scattering calculations for these reactions to highlight instances where the choice of coordinates may have a significant impact on the evaluated thermal rate constants.

We study the reaction Cl + CH(4)--> HCl + CH(3) using a 2-D potential energy surface obtained by fitting a double Morse analytical function to high level (CCSD(T)/cc-pVTZ//MP2/cc-pVTZ)ab initio data. Dynamics simulations are performed in hyperspherical coordinates with the close-coupled equations being solved using R-matrix propagation. Quantum contributions from spectator modes are included via a harmonic zero-point correction to the ab initio data prior to fitting the potential. This is the first time this method has been applied to a heavy-light-heavy reaction and the first time it has been used to study differential cross sections. We find thermal rate constants and state-to-state differential cross sections which are in good agreement with experimental data. We discuss the applicability of our method to the study of kinetic isotope effects (KIEs), which we derive for the CH(4)/CD(4) substitution. The calculated KIE compares favourably with experiment. Finally, we discuss the sensitivity of the results of dynamics simulations on the accuracy of the fitted potential.

We consider the general problem of vibrational analysis at nonglobally optimized points on a reduced dimensional reaction surface. We discuss the importance of the use of curvilinear internal coordinates to describe molecular motion and derive a curvilinear projection operator to remove the contribution of nonzero gradients from the Hessian matrix. Our projection scheme is tested in the context of a two-dimensional quantum scattering calculation for the reaction H + CH(4) --> H(2) + CH(3) and its reverse H(2) + CH(3) --> H + CH(4). Using zero-point energies calculated via rectilinear and curvilinear projections we construct two two-dimensional, adiabatically corrected, ab initio reaction surfaces for this system. It is shown that the use of curvilinear coordinates removes unphysical imaginary frequencies observed with rectilinear projection and leads to significantly improved thermal rate constants for both the forward and reverse reactions.

We present an efficient approach to the determination of two-dimensional potential energy surfaces for use in quantum reactive scattering simulations. Our method involves first determining the minimum energy path (MEP) for the reaction by means of an ab initio intrinsic reaction coordinate calculation. This one-dimensional potential is then corrected to take into account the zero point energies of the spectator modes. These are determined from Hessians in curvilinear coordinates after projecting out the modes to be explicitly treated in quantum scattering calculations. The final (1+1)-dimensional potential is constructed by harmonic expansion about each point along the MEP before transforming the whole surface to hyperspherical coordinates for use in the two-dimensional scattering simulations. This new method is applied to H-atom abstraction from methane, ethane and propane. For the latter, both reactive channels (producing i-C(3)H(7) or n-C(3)H(7)) are investigated. For all reactions, electronic structure calculations are performed using an efficient, explicitly correlated, coupled cluster methodology (CCSD(T)-F12). Calculated thermal rate constants are compared to experimental and previous theoretical results.