## Dr Simon Banks

#### Quantum Reaction Dynamics

Our research covers two broad areas spanning the boundary between chemistry and physics. One of these areas is the theoretical treatment of chemical reaction dynamics, using methods developed in collaboration with the group of David Clary at the University of Oxford. Our approach belongs to the family of reduced dimensionality techniques, designed to facilitate quantum dynamical modelling of polyatomic reactions with many degrees of freedom.

We perform high level ab initio calculations in order to develop accurate potential energy surfaces in a reduced number of dimensions. This is typically *d*=2, with the focus on the bonds being broken and formed in the reaction. Expressing the potential in hyperspherical coordinates allows us to run quantum scattering simulations using *R*-matrix propagation techniques in a straightforward manner. A key component of such a method lies in treating the spectator degrees of freedom (those not explicitly included in the quantum simulations) as accurately as possible. We have recently developed a method which allows for the zero point energies of these modes to be accurately calculated using a projection operator expressed in curvilinear (generally valence bond) coordinates. This leads to a much greater degree of accuracy relative to using rectilinear (Cartesian) coordinates and has been shown to have a significant impact on the quality of the kinetic data one obtains^{2,3}

We are currently extending our approach to include non-adiabatic electronic transitions^{4} and to deal with larger, biomolecular systems.

*Figure 1.** Schematic representation of an X+CH*_{4}* system. The degrees of freedom r*_{1}* and r*_{2}* are those treated explicitly in our reduced dimensionality studies.*

#### Critical Phenomena and Low Dimensional Magnetism

My work in the field is focused on the *2dXY* model of magnetism, which has a rich critical low temperature phase, and analogous models of one dimensional spin chains with long range interactions. This work examines the consequences of criticality, in which interactions across all length scales influence the behaviour. The current focus is on the observation of Kosterlitz-Thouless transitions in novel 1*d* systems and the link between critical phenomena and 1/*f* noise.

#### Highly Frustrated Magnetism

A frustrated system is one in which not all interactions can be simultaneously satisfied. A simple example is three antiferromagnetically coupled magnetic moments (or "spins") placed on a triangle. The first two are easily placed but the third can not be simultaneously antiferromagnetically aligned (that is, aligned antiparallel) to both the others and the system is therefore "frustrated". Frustration occurs throughout many branches of science but is particularly well described within a magnetic framework. The phenomenon leads to wealth of interesting properties such as degenerate ground states and (when coupled with disorder) glassiness.

We have recently been interested in the coupling of frustration with constrained random disorder. We have focused on constraining the ion placement in binary pyrochlores (lattices of corner sharing tetrahedra populated with two type of magnetic ion) and observing the effect that varying the positional constraints has on the magnetic order in the system. Working with Steve Bramwell (of UCL Physics and the London Centre for Nanotechnology) and Mark Harris (University of Oxford) we have demonstrated that certain constraints can lead to novel magnetic behaviour including the emergence of a "semi spin liquid" phase in which spins exhibiting long range antiferromagnetic order also display spin liquid like behaviour in their transverse components. We have also identified a spin liquid phase that stable to *T*=0, which may shed some light on the magtic behaviour of inverse spinel ferrites and a family of magnetic pyrochlore fluorides exemplified by CsNiCrF_{6}.

*Figure 2.** Numerically evaluated structure factor, S(Q), in the [h,h,l] reciprocal space plane for magnetic scattering from CsNiCrF*_{6}* with "ice-rules" ordering of the magnetic ion.*

### Selected Publications

- "Temperature dependent fluctuations in the two-dimensional
*XY*model" S. T. Banks and S. T. Bramwell,*J. Phys. A***38**, 5603 (2005) - "Chemical reaction surface vibrational frequencies evaluated in curvilinear internal coordinates: Application to H+CH
_{4}→H_{2}+CH_{3}" S. T. Banks and D. C. Clary,*J. Chem. Phys*.**130**, 024106 (2009). - "An improved treatment of spectator mode vibrations in reduced dimensional quantum dynamics: Application to the hydrogen abstraction reactions μ+CH
_{4}, H+CH_{4}, D+CH_{4}and CH_{3}+CH_{4}"S. T. Banks, C. S. Tautermann, S. M. Remmert and D. C. Clary,*J. Chem. Phys.***131**, 044111 (2009) - "Reduced dimensionality spin-orbit dynamics of CH
_{3}+ HCl ⇌ CH_{4}+ Cl on ab initio surfaces" Sarah M. Remmert, Simon T. Banks, Jeremy N. Harvey, Andrew J. Orr-Ewing, and David C. Clary,*J. Chem. Phys.***134**, 204311 (2011)