Introduction

The program `Queen of Spades' (QS from now on), is an attempt to write a multi-dimensional, multi-model, space-group general, molecular (re)placement program. The classical approach to the problem of placing n copies of m different search models in the asymmetric unit of a target structure, is to divide this 6n-dimensional problem into a succession of 3-dimensional searches (rotational search followed by translational search for the first model, followed by a rotational search and a translational search for the second model etc). QS will attempt to solve this problem by a direct minimisation of a suitably chosen statistic (like the R-factor, or the correlation coefficient) in the 6n-dimensional space defined by the rotational and translational parameters of the n molecules. ¹ The minimisation algorithm is based on a modified reverse Monte Carlo procedure^2,3,4,5which is made (possibly) practical through (i) the calculation and in-core storage of the molecular transforms of the search models, and (ii) by keeping a table containing the contribution of each molecule to each reflection (thus making the CPU time per step independent of the number of molecules).

Footnotes

... molecules.¹

I should add here, that treating the molecular replacement problems as 6n-dimensional, is like shooting a sparrow with a cannon. In reality (and for n molecules per asymmetric unit), the molecular replacement problems can be divided into two 3n-dimensional problems : a 3n dimensional cross rotation function (which will simultaneously determine the orientations of all molecules present in the asymmetric unit), and a 3n-dimensional translation function (which will determine their positions). The 6n-dimensional approach would only be valid if the self and cross vectors were not topologically segregated in the Patterson function.

... procedure²

Metropolis, N., Rosenbluth, A.W., Rosenbluth, M.N., Teller, A.H. & Teller, E. (1953), ``Equation of State Calculations by Fast Computing Machines'', J. Chem. Phys., 21, 1087-1092.

...^,3

Kirkpatrick, S., Gelatt, C.D. Jr. & Vecchi, M.P. (1983), ``Optimization by Simulated Annealing'', Science, 220, 671-680.

...^,4

McGreevy, R.L. & Pusztai, L. (1988), ``Reverse Monte Carlo Simulation: a new technique for the determination of disordered structures'', Mol. Simulation, 1, 359-367.

...^,5

Keen, D.A. & McGreevy, R.L. (1990), ``Structural modelling of glasses using reverse Monte Carlo simulation'', Nature, 344, 423-425