Research in the Manby group is focused on the development of new methods in electronic structure theory and quantum chemistry. Our main projects are summarized below. Electronic structure method development is performed mostly in the Molpro quantum chemistry package, of which I am a contributing author.

The Ornstein-Zernike equation relates the concept of direct correlation (the correlations between two particles at a time) to that of full correlation (which includes all of the higher-order effects of interpair correlations). It was developed, amazingly, in 1914, as a means to describe the long-range correlations in fluids near their critical point. We have recently discovered that the approach can be used to include interpair correlations in electronic structure theory, and this provides an alternative to coupled-cluster theory as a means of going beyond simple pair-theories of electron correlation .

A new method for treating electron correlation in crystalline systems has been introduced in collaboration with Mike Gillan at UCL. The method simply combines binding energies of a series of (no more than four) different finite clusters, in such a way that the vertex, edge and surface contributions cancel out. This then produces an estimate of the cohesive energy of the bulk. Surface and edge energies can also be extracted. For lithium hydride essentially perfect agreement is found with experiment for cohesive energy , lattice parameter and bulk modulus .

High accuracy in the correlation energy is only worth while if one can converge the HF energies to high accuracy as well. This has proven immensely challenging , and has led to a major investment of effort in this direction in many groups around the world.

We have recently learnt more about the workings of the method by comparison with the incremental scheme for solid neon ; and we have begun to compute surface properties, eg for lithium hydride and fluoride .

New work in the group is under way to treat molecular solids through embedded many-body expansions

We are looking at new methods for the simulation of water clusters and — ultimately — liquids . The aim is to combine the hierarchies of approximation that have proven so successful for gas-phase problems with a many-body expansion of the energy of the liquid. We aim to acheive specified (eg MP2/aug-cc-pVTZ) levels of theory for the periodic liquid. The computational cost of the approach is of course very high compared to simple model potentials but the approach has several advantages:

• Ab initio, so no reparameterization needed for different systems
• Multiresolution in a length-scale sense, rather than a position sense, so all molecules are treated on the same footing, but all interactions are not
• Multiresolution in terms of order: two-body effects can be treated more accurately than the smaller three-body effects

By using a combination of local and density fitting (DF) methods it has been possible to develop extremely efficient electronc correlation methods for treating large molecules . These methods are particularly attractive as they combine the benefits of the local methods (low scaling with respect to system size) and density fitting approximations (low prefactor and lower scaling with respect to basis set size) into a single method. The DF-LMP2 method proved to be so efficient that the Hartree-Fock calculation became a serious bottle-neck. We now have DF-HF , DF-LMP2 gradients , and DF-LCCSD(T) . It is now possible to treat the electronic structure of even quite large molecules using high-level methods in triple- and quadruple-zeta basis sets. Such methods can also be applied in studying enzyme catalysis with unprecedented accuracy. They can also be combined with explicitly correlated methods to give dramatically improved basis-set convergence (see below).

New work in the group, and in collaboration with Prof Garnet Chan, Cornell and Prof Yuki Kurashige, IMS, is focussed on using tensor factorizations as an approah to building automatically local correlation methods .

Expanding wavefunctions in products of orbitals has been a profoundly successful strategy in quantum chemistry. Nevertheless, the approach is not perfect because the description of the correlation cusp converges only very slowly with respect to the size of the basis set used. One solution to this problem is to use wavefunctions that depends explicitly on inter-electronic distances.

Methods of this kind — explicitly correlated methods — have the technical setback of many-electron integrals, which are both hard to compute individually and very numerous. These can however be avoided by the use of resolutions of the identity (RIs).

I have worked on a number of ways of improving the currently available explicitly correlated methods, including: the use of density fitting to make things more efficient and more accurate ; the development of methods that use local approximations ; the investigation of alternatives to the commonly used linear-r₁₂ ansatz . For a review of this field, see , and for an attempt to set out MP2-F12 theory without approximations (other than RI) see .

This project started off as a collaboration with ClearSpeed Technology plc. We investigated the fine-scale parallelization of density functional theory (DFT) on multi-core processors . ClearSpeed's CSX600 processor (left) consists of around 200 small processor elements capable of delivering around 50 Gflop performance with very low power consumption. We have developed a purely grid-based Coulomb method, and this combined with conventional DFT quadrature leads to an algorithm that can be efficiently parallelized on this type of architecture. We are also investigating other multicore architectures, including GPUs and commodity multicore processors . This activity contributes to our efforts to perform DFT QM/MM free energy calculations for biological problems, and is also supported by computer time from our Advanced Computing Research Centre.

I have interest (current or past) in all sorts of other projects, a selection of which are listed below.

• Effective treatment of solvation
• Embedding schemes
• QM/MM methodology an applications
• Time-dependent electronic structure theory
• Extraction of correlation energies from intracule-like objects
• DFT methodology
• Optimal control theory
• Automatic code generation for integrals and density functionals
• Efficient evaluation of molecular integrals (can be tedious, but very important!)
• Computation of hyperfine interactions

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