STRUCTURE CALCULATIONS

This application was intended to provide computer access to the RAL CRAY Y-MP8I/8128 to support the development of a novel relativistic molecular electronic structure code being developed within our group. We had considerable experience with using the CRAY up to this time, and our code was being developed with the Y-MP architecture in mind. The application was accepted and the grant of 450 Cray Y-MP8 processor hours was to run for 36 months starting 1 June 1995.

At that stage, we were still developing the algorithms needed, using local Oxford machines, planning to move the work on to the CRAY at the appropriate stages within 3 to 6 months of the start date. In the event, the removal of the Y-MP and installation of the Cray J90 overtook this plan. We had several difficulties with the J90: in the first place, code which previously ran on the Y-MP was rejected by the new compilers, and caused us some hassle to overcome the problems; the second was that turnaround was not good, and the system seemed difficult to use. As a result, we continued with the local facilities, and more or less abandoned the use of the RAL machines when we discovered that the code ran faster on our local, slightly elderly, DEC Alpha workstation. Our subsequent use of the RAL allocation was therefore minimal.

From the scientific point of view, the project has been extremely
successful. We have more than achieved all the targets that we set
ourselves in the Spring of 1995. In particular, we discovered how to
design very fast algorithms for the key relativistic molecular
integrals late that year, completely overturning all our earlier ideas
on how to do this. As a result, calculations for which we had
expected to use supercomputers could be transferred to desktop
workstations. A further major breakthrough came when we realized in
the Spring of 1997 that it was possible to set up the relativistic
molecular structure problem in a manner compatible with QED (Quiney,
Skaane and Grant, 1997, *J. Phys. B: At. Mol. Opt. Phys. * ** 30** L829-834)). These
major breakthroughs have enabled us to run polyatomic calculations on
the DEC Alphastation 500/400 purchased with the aid of an EPSRC grant
GR/L55155 as well as calculations on diatomics as originally
envisaged. We have also adapted other modern ideas for studying
molecules with a large number of atoms to run Dirac-Hartree-Fock
calculations for such molecules as Germanocene (Ge(cp)_{2}), with 21
atomic centres, and for atomic clusters with up to about 20 atoms.

Something of the range of our work is indicated in the list of
publications attached. Two things should be noted: the first is that
we have still to write up the details of our new BERTHA code (the last
two items), and that the articles with Dr. Scott do not reflect our
current thinking, but rather what we were doing early in 1995.
Nevertheless, Dr. Scott was highly influential in using the algebraic
computer system, MAPLE, to explore a range of algorithms that might be
used for relativistic molecular integral generation and we are certain
that we shuld not have got as far as we have done without using
MAPLE.

**PUBLICATIONS and ARTICLES IN PREPARATION**

H. M. Quiney, H. Skaane and I. P. Grant, *Ab initio*
relativistic quantum chemistry: four components good, two-components
bad! *Adv. Quant Chem.* **32**, 1-49 (1998). (Thematic volume:
*Quantum Systems in Chemistry and Physics* Guest Editors: S. Wilson, P. J.
Grout, R. McWeeny, J. Maruani and Y. G. Smeyers).

T. C. Scott, M. B. Monagan, I. P. Grant and V. R. Saunders, Numerical computation of molecular integrals via optimized
(vectorized) FORTRAN code. *Nucl. Instr. and Methods in Physics
Research* **A 389** 117-120 (1997)

H. M. Quiney, H. Skaane and I. P. Grant, Relativistic
calculation of electromagnetic interactions in molecules, * J. Phys. B: At. Mol. Opt. Phys. * **30** L829-834
(1997).

H. M. Quiney, H. Skaane and I. P. Grant, Hyperfine and
PT-odd effects in YbF .
*J. Phys. B:
At. Mol. Opt. Phys. * **31** L85-95 (1998).

T. C. Scott, I. P. Grant, M. B. Monagan and V. R. Saunders, Generation of Optimized FORTRAN Code for Molecular Integrals
of Gaussian-Type Functions, *MapleTech* Vol. 4, No. 2,
pp. 15-24 (Boston, Birkhäuser, 1997).

H. M. Quiney, H. Skaane and I. P. Grant, Relativistic,
quantum electrodynamic and many-body effects in the water molecule,
*Chem. Phys. Letts.*, **290**, 473-480, (1998).

**In preparation**

I. P. Grant, H. M. Quiney and H. Skaane,
BERTHA: an *ab initio* relativistic molecular electronic structure
program

H. M. Quiney, H. Skaane and I. P. Grant, Relativistic molecular
integrals with Dirac spinors

August 1998