Computational Needs and Resources in Crystallography Proceedings of a Symposium, Albuquerque, New Mexico, April 8, 1972. (1973) / Chapter Skim
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What New Developments are in the Wind?
What New Developments are in the Wind?
Pages 47-76
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From page 47... ...
Session II What New Developments Are in the Wind? Session Chairman: William R
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From page 48... ...
The following remarks will be restricted to the least-squares approach; however, significant developments are also occurring in the Fourier field, the Fast Fourier Transform algorithm being used to decrease computing time substantially. An important preliminary for any crystal structure refinement is the selection of an appropriate mathematical model for the structure under study.
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From page 49... ...
crystallographers is spent in the structure-refinement step. Furthermore, the greater part of this computer time is used in forming the matrix of the least-squares normal equations; consequently, it is often worthwhile and sometimes essential to approximate the matrix by an alternate matrix requiring less computer time and less computer memory.
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From page 50... ...
Recalculate only the matrix elements influenced by parameters which undergo appreciable shifts 3. Analytical matrix approximations An untried but seemingly logical extension from the one-atom blockdiagonal matrix is the "cross-word puzzle" matrix where all interaction terms between close-neighbor atom are added to the block-diagonal matrix.
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From page 51... ...
The first factor in Table 2 contains the calculated squared structure factor divided by the variance of the observed squared structure factor. This factor can be eliminated from the list by making the following approximation: Approximation 1 - The magnitude of the calculated squared structure is assumed to be proportional to the variance of the observed squared factor.
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From page 52... ...
Sums of 3 to 5 Gaussian functions currently are used successfully to replace scattering- factor table- look-up procedures in crystallographic programs. The same tabulated Gaussian coefficients could be used in a double summation; however, a more efficient procedure is to fit new Gaussian coefficients directly to the scattering factor product, taking care to make the fit acceptable for the entire range of The third factor in Table 2, the product of anisotropic Gaussian temperature factors for atoms m and n, presents no difficulty.
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From page 53... ...
An exact solution for this general case with anisotropic temperature factors and spherical truncation is quite difficult, but some success has been achieved with empirical correction factors applied to Eq.
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From page 54... ...
We use the inverted analytical matrix to calculate the complete variance-covariance matrix for a published structure without computing structure factors or their derivatives. The only data needed to generate the analytical matrix are the structural parameters, a matrix scale factor, and a truncation parameter.
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From page 55... ...
in the asymmetric unit. If we write out the equation for the 171 supposedly unique elements in the symmetric 18 by 18 matrix, ^, for positional and anisotropic thermal parameters, we quickly discover that considerable redundancy is present, only 103 elements actually being unique.
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From page 56... ...
If you have a published structure, and use this to calculate structure factors, this is a data set more or less like the experimental data set, more to the structure's right and less to the structure's wrong. From that data set you select, depending on your knowledge, which reflections have been left out.
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From page 57... ...
Additional parameters may also improve the time advantage because the sum over the Patterson vectors converges rapidly as a function of interatomic separation; consequently the long vectors can safely be omitted from the summation.
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In this paper we consider whether such changes are likely to arise out of developments in direct methods. Structures of Moderate Size In the direct methods, the problem of structure determination is converted into the mathematical problem of solving a system -- usually a large system -- of equations or relations involving the structure factors as principal variables.
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From page 59... ...
have recently been concerned with improving the accuracy of the type of formula that permits approximate values, if not of the phases at least of the cosines of the structure invariants, to be computed from the structure factor magnitudes alone; these values are therefore available at every step i. Indeed the most interesting thing about this latter type of relation may be the fact that the possession from the outset of the full set of cosine invariants, even in approximation, allows one to think in terms of pure direct methods that are not step-by-step in nature; these may possibly have no greater overall chances of success than the step-by-step technique, but would at least be free to some extent of the extreme branching in which the latter can so easily get caught.
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From page 60... ...
Barrett and Zwick (1971) attempted phase extension beyond the limit of multiple isomorphous replacement on myoglobin by a different method, which is not really a direct method, but without success.
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The authors have found a means of expressing this requirement in terms of conditions among the structure factors, and have devised a discrete search method for selecting sets of phases by computer that approximately satisfy the requirement. The method is apparently in regular use at their laboratory, where it facilitates considerably the structure determination for this type of system.
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From page 62... ...
the actual time to solution in any given case may prove to be much smaller, or much larger , than the predicted mean time. As larger structures are attempted by purely direct methods, this unpredictability of machine time will increasingly have to be allowed for in the budgeting of resources.
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I personally have thought that the most interesting comparison would be with Jensen's final 1.5 A set. Dewar: If direct methods start to involve large amounts of computer time, we should be wary of using criteria like computer costs per 63
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So far this has been unsuccessful but it may be of interest to note the computer times involved in the calculation of cosine averages for this particular complex. There are approximately one thousand E's above 1.4, ten thousand reflections altogether.
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From page 65... ...
It appears, again using artificial structures, that the structure factor magnitudes can be perturbed with random errors up to a standard deviation of 30% without as a rule preventing the refinement from locating the correct minimum. Similarly the procedure appears normally to tolerate the introduction of random errors up to a standard deviation of 30° in the starting set of phases (to 3 A)
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From page 66... ...
. For subsequent processing of the collected data a magnetic tape drive is desirable.
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In every other respect the CDC 6600 is a much more powerful computer. Because of the large core memory, all structure factor data and the normal equations of a least-squares program can be resident.
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From page 68... ...
Diffractometer programs would also be written in FORTRAN IV but using machine-language subroutines for driving the goniometer axes, reading the encoders and sealer, opening and closing the shutter, etc. Table 1 Comparison of Nova 1200 and GDC 6600 Nova 1200 with Structure Minimal Nova 1200 Determination Package CDC 6600 Magnetic Tape Drive many 1 1 Core Speed i.Ons 1.2 MS 1.2jis Word Size 60 bits 16 bits 16 bits Core Size 131 000 words 4000 words 16 000 words 131 000-word disk Table 1 continued 68
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Data collection must have the magnetic tape drive available for output of the intensity data. Therefore, production of a Fourier map could not be done simultaneously with data collection.
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After this, several operations could be performed without using the magnetic-tape drive and could be effectively overlapped with data collection. The proposed system in the crystallographer's laboratory is clearly more convenient than a centralized computing facility.
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Calculated from Nova 800 performance. Typically, we at Syntex use about one hour of CDC 6600 computer time for a structure with 40-50 non-hydrogen atoms in the asymmetric unit.
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From page 72... ...
Because of the above arguments, Syntex has decided to make available to customers a Structure Determination Package which would consist of a 131 000-word fixed head disc, 12 000-word core, and floating point hardware for those who already have a Pl Autodiffractometer or AD-l Autodonsitometer, and a stand-alone unit consisting of a NOVA 1200, a 131 000word fixed head disc, 16 000-word core, floating point hardware, and a magnetic tape drive for those who do not have the Syntex instruments. Software will consist of a FORTRAN IV compiler modified to make efficient use of the floating point hardware, a Disc Operating System modified to allow time-sharing of data collection with data processing, machine language subroutines for the diffractometer, FORTRAN versions of the current diffractometer programs, and FORTRAN programs properly broken up into overlays for the basic crystallographic programs.
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From page 73... ...
In conclusion, whether crystallographers would be inclined to buy the Syntex package or whether they would wish to buy directly from the computer manufacturers and provide their own software, I believe that serious consideration should be given to the small dedicated computer. Not only does it provide the desirable features of FORTRAN data-collection programs and the convenience of having one's own computer, but it also provides, in many cases, a substantial cost saving compared to the centralized computer approach used by most crystallographers today.
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From page 74... ...
He is able to search his electron diffraction data and his radial distributions and look at very fine portions. With respect to Fourier maps, instead of having to print them out you can set up a graphic interaction display for picking out the things you want.
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From page 75... ...
Corfield: I think this system is not totally unreasonable, but what makes it reasonable is the availability of inexpensive hardware floatingpoint arithmetic units. We've had at Ohio State University for the past two or three years a system rather more sophisticated than this but that does not have hardware floating-point arithmetic.
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