Andrew G. Ioannou

On the resolution of identity Coulomb energy approximation in density functional theory

The Resolution of the Identity approximation for the Coulomb (RI-J) energy in Density Functional Theory improves the computational efficiency of large-scale calculations but requires the use of a second, or “auxiliary” basis set. We examine the performance of some of the existing auxiliary basis sets with a variety of basis sets and molecules. We determine the accuracy of the RI-J approximation for these basis sets and suggest criteria for the selection of combinations of basis set and auxiliary basis set.

The diagonal born-oppenheimer correction for He2+ and F+H2

Abstract An unrestricted Hartree-Fock evaluation of the diagonal Born-Oppenheimer correction is reported. The correction is calculated for He 2 + and F + H 2 → FH + H. For He 2 + it is found that on addition of the correction the mean deviation of the best theoretical transition energies is increased (when compared with experiment) by the same order of magnitude (0.04 cm −1 ) as the value of the previous mean deviation. The correction increases the barrier height for the F + H 2 reaction by 0.04 kcal mol −1 .

The calculation of frequency-dependent polarizabilities using current density functional theory

Abstract The formalism of Colwell, Handy and Lee for the calculation of frequency-dependent properties using current density functional theory has been implemented using local, non-local or hybrid functionals. This theory has been applied to the calculation of frequency-dependent polarizabilities and dispersion coefficients in a variety of small molecules. The results obtained are in good agreement with experimental data. The effect of the terms which depend upon the current density is found to be small.

A two-centre implementation of the Douglas–Kroll transformation in relativistic calculations

An implementation of the Douglas–Kroll (DK) transformation is described within a new relativistic quantum chemistry code, MAGIC, which performs calculations on systems containing heavy atoms. This method reduces the computational cost in terms of memory requirements that are associated with completeness identities in the DK implementation by factorizing the one-electron matrices into smaller ones that depend only on two atoms at a time. Examples are presented.

An efficient method for calculating effective core potential integrals which involve projection operators

An efficient approach for evaluating effective core potential integrals which involve projection operators has been implemented in the MAGIC quantum chemistry program. The methodology is presented and its performance is examined through illustrative calculations on transition metal and actinide compounds.

MAGIC: an integrated computational environment for the modelling of heavy-atom chemistry

The nuclear industry has enormous challenges to address in understanding its waste products and their safe disposal. It is extremely expensive and difficult to work with such waste products. As computational chemistry has made so many advances in the last 30 years, the question arises as to whether it can start to answer some of the basic questions. It was in this context that British Nuclear Fuels plc approached the quantum chemistry group at the University of Cambridge. After initial considerations, it was decided to write an entirely new quantum chemistry package to address these fundamental problems. The MAGIC program has been written to model as accurately as possible the properties of heavy-atom (in particular, actinide) complexes in realistic environments. Major requirements were the need to include relativistic effects for which several investigations have been carried out by quantum chemists in recent years. A severe difficulty is the high angular momentum of the occupied orbitals in the actinides. It was also believed that it was very important to include the effects of electron correlation. Again much progress has been made by quantum chemists with this problem. Therefore this code was written to take into account all these advances in a simple enough way that calculations on realistic systems are possible. The program is the result of a collaboration between British Nuclear Fuels plc and the University of Cambridge. The program has been developed with a view to making the implementation of new ideas as straightforward as possible. Hence, the code has a simple modular structure. Individual modules may of course be combined in a script to run more complicated procedures, such as a self-consistent field (SCF) procedure. The aim of such an approach is to maximize the time spent in the science compared with that spent interfacing with the computer code. For the end user a simple graphical user interface through Cerius# is provided. Standard features of the input may be selected easily from individual menus for each module. It is also possible to access more advanced features. Comprehensive help facilities are available within the interface. Use of the visualization tools helps not only to see the results of calculations on large molecules more clearly, but also to present them in a concise and clear way. The program has been developed on an SG workstation, but it has been extended to run in parallel on a Cray T3E. This paper is the basic paper which describes in detail the philosophy, science and implementation of the MAGIC project. At the end, sample calculations are reported. Furthermore suggestions are made about how this program may, even at this stage, be used to address problems with actinides in the nuclear industry. In order to place the development of the MAGIC project in context and to make adequate recognition of the contribution of others, this article contains considerable material of a review nature, a brief history of the development of quantum chemistry and density function theory, the treatment of core electrons and relativistic effects, the evaluation of integrals, the treatment of solvent effects and the convergence of the SCF iterations. All are written with calculations on actinide complexes as the ultimate goal.

Time-dependent density functional theory applied to Raman scattering from methane

Abstract The geometric derivatives of the polarizability are related to non-resonance Raman spectra. Although a common approximation is to proceed with the derivatives of the static polarizability, it is important to account for the frequency of the incident photon when calculating such properties as differential Raman cross-sections. We apply the time-dependent coupled current Kohn-Sham theory of Colwell et al. to the Raman scattering from methane. Our results show that it is not untypical for the geometric derivatives of the polarizability to change by ten percent when we move from the static approximation to frequencies that correspond to common exciting lasers.