Minicomputers and Large Scale Computations - ACS Publications

13 Theoretical Chemistry via Minicomputer

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PETER K. PEARSON, ROBERT R. LUCCHESE, WILLIAM H. MILLER, and HENRY F. SCHAEFER III

Downloaded by CALIFORNIA INST OF TECHNOLOGY on December 1, 2017 | http://pubs.acs.org Publication Date: June 1, 1977 | doi: 10.1021/bk-1977-0057.ch013

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Department of Chemistry, University of California, Berkeley, CA 94720

C e r t a i n l y one of the most important and f a r - r e a c h i n g developments i n chemistry over the past decade has been the emergence of theory as a p r e d i c t i v e t o o l of s e m i - q u a n t i t a t i v e reliability. T h i s statement i s no way meant to detract from the pre-1960 t h e o r e t i c a l chemistry that p r o v i d e d , through the work of men such as Linus P a u l i n g , Robert M u l l i k e n , and Henry E y r i n g , the modern foundations of valence theory and chemical kinetics. Contemporary t h e o r e t i c a l research i s o b v i o u s l y b u i l t upon the achievements of these p i o n e e r s . However the d i s t i n g u i s h ing feature of modern t h e o r e t i c a l chemistry i s the ability not only to c o r r e l a t e e x i s t i n g experimental data (and make rough q u a l i t a t i v e p r e d i c t i o n s ) , but a l s o to provide an a priori d e s c r i p t i o n of chemical phenomena that allows p r e c i s e p r e d i c t i o n s to be tested by experiment. The most s t r i k i n g example of t h i s new age of theory i s the understanding that the s i n g l e - c o n f i g u r a t i o n s e l f - c o n s i s t e n t - f i e l d (SCF) approximation for e l e c t r o n i c wave functions provides e q u i l i b r i u m geometries i n very c l o s e agreement with a v a i l a b l e experimental data ( 1 ) . I f one defines chemistry as the union of s t r u c t u r e , e n e r g e t i c s , and dynamics on the molecular level, then it seems f a i r to say that theory has a f i r m grasp on at l e a s t one t h i r d of t h i s branch of s c i e n c e . Furthermore, s i n c e SCF theory may now be a p p l i e d fairly r o u t i n e l y (2) to systems as l a r g e as TCNQ-TTF (Figure 1) the range of applicability i s c l e a r l y rather broad. A second major i n s i g h t gleaned over the past decade i s the r e a l i z a t i o n that the d e t a i l e d dynamics of chemical r e a c t i o n s are w e l l described by ordinary c l a s s i c a l mechanics, i . e . , by c l a s s i c a l t r a j e c t o r y s t u d i e s (3). Although most t h e o r e t i c a l s t u d i e s to date have d e a l t with the c a n o n i c a l A + BC -> AB + C r e a c t i o n (for which the most d e t a i l e d experimental data i s a v a i l a b l e ) (4), systems as l a r g e as the methyl isocyanide r e a c t i o n CH NC + CH CN 3

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171 Lykos; Minicomputers and Large Scale Computations ACS Symposium Series; American Chemical Society: Washington, DC, 1977.

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are r e a d i l y a c c e s s i b l e (5). In f a c t i t i s reasonable to assume that much of the future research i n t h i s area w i l l be d i r e c t e d toward a t h e o r e t i c a l understanding of model organic r e a c t i o n s . The l i n k between the above two branches of theory i s c l e a r : e l e c t r o n i c s t r u c t u r e theory has as a p r i n c i p l e aim the e l u c i d a t i o n of the p o t e n t i a l energy s u r f a c e ( s ) ; while the theory of dynamics or c o l l i s i o n processes begins with the same p o t e n t i a l energy s u r f a c e ( s ) . The present research p r o j e c t had i t s genesis i n c o l l a b o r a t i v e s t u d i e s between WHM (dynamics) and HFS ( e l e c t r o n i c structure). Here we have assembled a " f i n a l " (only i n the sense of a r a p i d l y approaching deadline) report on our use of a minicomputer for research i n modern t h e o r e t i c a l chemistry. At the outset we should s t a t e that we have already w r i t t e n many words on t h i s s u b j e c t , and r e p e t i t i o n of these would not appear to serve a purpose. A modified v e r s i o n of the o r i g i n a l proposal has been published i n Computers and Chemistry. That proposal goes i n t o the j u s t i f i c a t i o n and economic m o t i v a t i o n for t h i s p i l o t p r o j e c t . Secondly, Appendix I contains four i n t e r i m reports d e s c r i b i n g i n d e t a i l our experiences with the new machine. We s t r o n g l y encourage the reader to go over these documents c a r e f u l l y . F i n a l l y we note that the proposal for a N a t i o n a l Resource for Computation i n Chemistry (NRCC) has brought squarely to the a t t e n t i o n of the chemical community the need for improved computational f a c i l i t i e s . We therefore a l s o urge the reader to give s e r i o u s c o n s i d e r a t i o n to the r e p o r t s of Wiberg (6) and B i g e l e i s e n (_7) committees. The Economic Argument The minicomputer chosen was the Datacraft 6024/4, which was f u l l y assembled at Berkeley on March 13, 1974. Thus our e x p e r i ence spans a p e r i o d of roughly three y e a r s . Although the same

Lykos; Minicomputers and Large Scale Computations ACS Symposium Series; American Chemical Society: Washington, DC, 1977.


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machine i s s t i l l i n production (ours i s machine #3 of about 200 produced to d a t e ) , s e v e r a l company changes have occurred and our minicomputer i s now c a l l e d the H a r r i s Corporation Slash Four. The cost of the machine was e s s e n t i a l l y $130,000, i n c l u d i n g C a l i f o r n i a s t a t e s a l e s tax. No overhead on the purchase p r i c e was r e q u i r e d . Assuming a m o r t i z a t i o n over a four year p e r i o d , t h i s amounts to $2708 per month. The other l a r g e cost i s that of maintaining the s e r v i c e c o n t r a c t , c u r r e n t l y $1715/month ($1280 to the H a r r i s Corporation and $435 to the UC Berkeley overhead). On t h i s b a s i s the t o t a l cost i s $4423/month or $7.30 per hour i f we assume 20 hours of usage per day, as shown to be r e a l i s t i c i n Appendix I . As noted by one of the reviewers, t h i s cost might be further reduced i n a chemistry department where there i s already a t e c h n i c a l s t a f f member with extensive d i g i t a l hardware e x p e r t i s e . Of course the insurance aspects o f the maintenance contract would be l o s t i n t h i s case. Extensive timing comparisons (Appendix I) have shown the minicomputer to be 25-30 times slower than the C o n t r o l Data Corporation (CDC) 7600. Thus the minicomputer generates the equivalent o f 1 hour o f 7600 c e n t r a l processor (cpu) time per $200. For comparison, we c i t e the charge s t r u c t u r e of the Lawrence Berkeley Laboratory (LBL) CDC 7600. This machine i s g e n e r a l l y a v a i l a b l e to NSF grantees and o f f e r s 7600 machine time at p r i c e s roughly f i v e times l e s s expensive than commercial r a t e s . Nevertheless the LBL r a t e s range from roughly $350 to $900 per hour of cpu time. The former f i g u r e r e f e r s to weekend deferred p r i o r i t y time. On t h i s b a s i s , then, one concludes that the m i n i computer i s *\> 2-4 times more economical than the 7600. However, as we d i s c u s s i n d e t a i l i n the o r i g i n a l proposal and i n Appendix I , the above f i g u r e s i n c l u d e input-output charges ( e s p e c i a l l y d i s k accesses) f o r the H a r r i s machine, but these are a d d i t i o n a l charges (often r a t h e r severe) on the CDC 7600. Thus as i s seen i n Appendix I , the cost e f f e c t i v e n e s s of the m i n i computer sometimes exceeds that o f the 7600 by a f a c t o r of s i x or seven. In a l l f a i r n e s s , the minicomputer does not provide the q u a l i t y of s e r v i c e of the LBL CDC 7600, a smoothly f u n c t i o n i n g p r o f e s s i o n a l l y operated computer c e n t e r . Much of the savings made i s simply a consequence o f the f a c t that our o p e r a t i o n involves no paid employees other than graduate students and postdoctorals. Research Accomplishments The u l t i m a t e t e s t of the present proposal i s undoubtedly whether the chemistry research completed j u s t i f i e s the NSF funds expended. Since t h i s document i s intended f o r p e r u s a l by academic and i n d u s t r i a l research chemists, we leave t h i s judgment to you. A v a i l a b l e upon request i s a l i s t of seventy p u b l i c a t i o n s based on



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research c a r r i e d out using the H a r r i s Slash Four minicomputer. In s e v e r a l cases the research was c a r r i e d out i n c o l l a b o r a t i o n with t h e o r i s t s from other i n s t i t u t i o n s . When such studies made use of machines i n a d d i t i o n to the minicomputer, an a s t e r i s k i s indicated. Papers i n the course of p u b l i c a t i o n w i l l be provided on request. Not wishing to be e n t i r e l y i m p a r t i a l , we add the o p i n i o n that the minicomputer has allowed us to make a number of important c o n t r i b u t i o n s both to theory and to chemistry. With t h i s machine, our choice of problems has been p r i m a r i l y based on chemical i n t u i t i o n and s c i e n t i f i c i n c l i n a t i o n , r a t h e r than the p r e s s i n g economic circumstances many t h e o r e t i c a l chemists r e g r e t t a b l y face. Developmental Work i n Progress As mentioned i n the i n t r o d u c t i o n , we are j u s t now beginning to take f u l l advantage of the H a r r i s machine. Bruce G a r r e t t , a student of Professor M i l l e r ' s i s continuing work on the development of a quantum mechanical t r a n s i t i o n s t a t e theory. Cliff Dykstra has developed (8) and i s c o n t i n u i n g to work on a Theory of S e l f Consistent E l e c t r o n P a i r s (TSCEP), a fundamentally new approach to the c o r r e l a t i o n problem (9). Also i n Professor Schaefer's group, Robert Lucchese, Jim Meadows, B i l l Swope, and Bernie Brooks are working together to develop a new system of programs for l a r g e s c a l e c o n f i g u r a t i o n i n t e r a c t i o n (CI) s t u d i e s of e l e c t r o n c o r r e l a t i o n i n molecules. The l a t t e r programs are described i n some d e t a i l elsewhere (10). Thus, although t h i s report i s o f f i c i a l l y l a b e l e d " f i n a l " , there i s much work yet to be done i n the development of new t h e o r e t i c a l methods and comput a t i o n a l techniques. It i s i n such cases, where o r i g i n a l programs have been w r i t t e n s p e c i f i c a l l y for the minicomputer, that i t s advantages become most c l e a r l y apparent. In t h i s regard i t i s noteworthy that most students who have taken the time (perhaps one month) to f a m i l i a r i z e themselves with the mini a c t u a l l y prefer i t to the CDC 7600. Qualms A balanced view r e q u i r e s us to admit that a l l i s not sweetness and l i g h t . We have already noted that there i s no convenient computer center s t a f f to operate the machine. When problems occur we not only must c a l l the customer engineer, but a l s o p o i n t him r a t h e r c a r e f u l l y i n the d i r e c t i o n of the problem. As one of the reviewers has pointed out, t h i s i s at l e a s t i n part a r e s u l t of the f a c t that the support s e r v i c e s of the H a r r i s Corporation are s u b s t a n t i a l l y l e s s than those of IBM or CDC. An absolute n e c e s s i t y i s the presence of one very b r i g h t , knowledgeable, and r e s p o n s i b l e computer expert i n the group. The Lord has blessed us with two such i n d i v i d u a l s , Dr. Peter Pearson (who went on to



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greater things i n September of 1974) and more r e c e n t l y Mr. Robert Lucchese. This s o r t of i n d i v i d u a l i s r e q u i r e d to make system changes and updates, determine whether the machine i s r e a l l y s i c k or j u s t out of shape, and show the customer engineer e x a c t l y which machine i n s t r u c t i o n i s f a i l i n g when a d e f i n i t e problem i s located. A l s o , debugging a l a r g e program i s much more d i f f i c u l t than on the CDC 7600. Programmers always blame most of t h e i r mistakes on the computer and t h i s can be e s p e c i a l l y true when a m i n i i s involved. O c c a s i o n a l l y one finds a student who i s simply u n w i l l ing to go through the exhaustive checking that i s necessary to debug a l a r g e s c a l e program on a machine such as the H a r r i s Slash Four. Successful u t i l i z a t i o n of the machine r e q u i r e s the p h y s i c a l presence of one student at any given time. For some i n d i v i d u a l s the idea of spending the n i g h t with a computer i s not a pleasant one. We have found that the only s a t i s f a c t o r y s o l u t i o n to t h i s problem i s to have a s u f f i c i e n t number of students (at l e a s t 10) using the machine that they simply cannot a f f o r d to r i s k the p o s s i b i l i t y of being absent i n the event of a machine h a l t . Two a d d i t i o n a l weaknesses of the m i n i r e l a t i v e to a l a r g e machine such as the 7600 are (a) the smaller memory and (b) the l a r g e amounts of elapsed time required to complete a given j o b . The former l i m i t a t i o n r e s t r i c t s u s , f o r example, to using about 80 contracted gaussian functions i n e l e c t r o n i c s t r u c t u r e c a l c u l a tions. Although C l i f f Dykstra has developed a method of i n c r e a s ing t h i s l i m i t to 120 contracted f u n c t i o n s , such a computation might run i n t o trouble on the second p o i n t . That i s , about 24 hours i s the p r a c t i c a l l i m i t for a s i n g l e j o b . In g e n e r a l , the other users become q u i t e h o s t i l e i f a job r e q u i r e s even t h i s long. In a d d i t i o n , 24 hours i s about the mean time i n t e r v a l between machine f a i l u r e s i f the machine i s running a s i n g l e j o b . I t should be noted that t h i s time r e s t r i c t i o n (to about 1 hour of 7600 time per job) would be a s e r i o u s b a r r i e r i n accomplishing some of the goals set out for the NRCC (6, 7 ) · I n t e r f a c i n g with Experiments A question we are frequently asked i s "Could you handle three or four o n - l i n e experiments at the same time?" The answer to t h i s q u e s t i o n , at l e a s t for the H a r r i s Slash Four, i s an unequivocal no. The cost e f f e c t i v e n e s s of machines such as ours i s i n part a r e s u l t of i t s somewhat r e s t r i c t e d c a p a b i l i t i e s . If one wants the f l e x i b i l i t y of an IBM 370 system, t i e d i n to 43 t e l e t y p e s , one should probably be w i l l i n g to pay ten times more to c a r r y out a p a r t i c u l a r task i n computational chemistry. Our system i s i d e a l l y s u i t e d to batch o p e r a t i o n s , where only one job runs at a time. In fact i f a p a r t i c u l a r job i s long and not r e s t a r t a b l e (many of our programs are now r e s t a r t a b l e ) i t i s b e t t e r not even to read i n another job during execution. Thus the p o s s i b i l i t y of o n - l i n e experiments i s d e f i n i t e l y s l i m .


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However, there are a l l kinds of experimental chemists who r e l y on computers f o r number crunching jobs designed to a i d i n the a n a l y s i s of t h e i r data. Such jobs are w e l l s u i t e d to a machine such as the Slash Four and could very w e l l provide a major p a r t of the j u s t i f i c a t i o n for a proposal to the NSF. In l i g h t of s e v e r a l reviewers comments, we f e e l compelled to note that the newer H a r r i s machines ( e s p e c i a l l y the Slash Seven) now have v i r t u a l memory, which allows genuine t i m e - s h a r i n g . Having observed the Slash Seven at the I n t e r n a t i o n a l Engineering Company i n San F r a n c i s c o we must conclude that the simultaneous p r o c e s s i n g of three or four users i s now a r e a l i t y on the Slash Seven. Although v i r t u a l memory i s an a d d i t i o n a l expense (perhaps $20,000) i t would c e r t a i n l y be worthwhile i n s i t u a t i o n s where o n - l i n e data a c q u i s i t i o n i s a primary task. Environmental Impact U n t i l q u i t e r e c e n t l y , the primary medium f o r the disseminat i o n of the r e s u l t s of t h i s minicomputer experiment has been personal c o n t a c t . A f t e r the o r i g i n a l proposal was submitted, copies were mailed to ^ 25 prominent t h e o r e t i c a l chemists. The i n t e r i m reports have been d i s t r i b u t e d on request, of which we have had *\> 50 from research chemists. Another ^ 50 v i s i t o r s , i n c l u d i n g an NSF review team, have toured the Berkeley f a c i l i t y . A s l i g h t l y modified v e r s i o n of the o r i g i n a l proposal was published (Volume 1, pages 85-90) i n the new j o u r n a l Computers and Chemistry. Professor Schaefer presented an i n v i t e d paper "Are Minicomputers S u i t a b l e for Large Scale S c i e n t i f i c Computation" i n September 1975 a t the Eleventh Annual IEEE Computer Society Conference i n Washington, D . C . The same l e c t u r e was given e a r l i e r at the IBM Research Laboratory, San Jose. The trade j o u r n a l Computerworld published a popular d e s c r i p t i o n of the experiment i n i t s March 8, 1976 i s s u e . A number o f recent papers have mentioned the Berkeley m i n i experiments. Most recent and perhaps the most i n t e r e s t i n g i s that of I s a i a h S h a v i t t , (11) e n t i t l e d "Computers and Quantum Chemistry." F i n a l l y , the American Chemical S o c i e t y ' s D i v i s i o n of Computers i n Chemistry, under the d i r e c t i o n of Professor Peter Lykos, has organized the present symposium (June, 1977 i n Montreal) on "Minicomputers and Large Scale Computations". Several research groups (perhaps 20) have expressed serious i n t e r e s t i n a c q u i r i n g t h e i r own minicomputer for purposes comparable to our own. However, to our knowledge the only group to a c t u a l l y do so i s that of the l a t e Professor Don L . Bunker of the U n i v e r s i t y of C a l i f o r n i a at I r v i n e . Although the Hewlett-Packard machine purchased by Professor Bunker with NSF support was much l e s s expensive (and p r o p o r t i o n a l l y slower) than the H a r r i s Slash Four, he found i t to be adequate f o r h i s research i n dynamics and a v a s t improvement over h i s former dependence on an incompetent campus computer c e n t e r .


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Since the d r a f t v e r s i o n of t h i s f i n a l r e p o r t was prepared, two groups of t h e o r e t i c a l chemists have ordered H a r r i s Slash Sevens. These are the groups headed by Professor P h i l l i p C e r t a i n at the U n i v e r s i t y of Wisconsin and by D r s . John T u l l y and Frank S t i l l i n g e r at B e l l Telephone L a b o r a t o r i e s . These and other i m p l i c a t i o n s of our research have been noted i n recent semi-popular reviews i n Science (12) and Nature (13).


The Future The controversy concerning the r e l a t i v e merits of m i n i computers and l a r g e machines i s l i k e l y to continue f o r some time. At present both the Slash Four and CDC 7600 appear to be r e l a t i v e l y economical a l t e r n a t i v e s . The r e a l l o s e r s i n such comparisons are the machines between these two extremes (11). For example, s e v e r a l u n i v e r s i t i e s and research i n s t i t u t e s ( e . g . the U n i v e r s i t y of C a l i f o r n i a , the U n i v e r s i t y of Washington, Colorado State U n i v e r s i t y , and B a t t e l l e , Columbus) are c u r r e n t l y using the CDC 6400. Although the 6400 i s only about 1.5 times f a s t e r than the H a r r i s Slash Four, the cost of using t h i s machine can be as high (at Berkeley) as $420/hour. This i s c l e a r l y an absurd s t a t e of a f f a i r s , and we would encourage the abused supporters of such machines to consider t h e i r a l t e r n a t i v e s . Since our o r i g i n a l p r o p o s a l , s e v e r a l developments have occurred i n the minicomputer a r e a . At that time the H a r r i s Slash Four was by f a r the f a s t e s t machine a v a i l a b l e i n our p r i c e range. Since then at l e a s t four machines of n e a r l y comparable speed have appeared: the Data General E c l i p s e , the V a r i a n V75, the System Engineering L a b o r a t o r i e s (SEL) 32/55, and the Interdata 8/32. We have been e s p e c i a l l y i n t e r e s t e d i n the SEL 32 s i n c e i t i s a true 32 b i t machine and might be s i g n i f i c a n t l y f a s t e r than the H a r r i s Slash Four i f a powerful 64 b i t f l o a t i n g p o i n t processor were available. In f a c t , such a f a s t f l o a t i n g p o i n t processor appears to be a r e a l p o s s i b i l i t y for SEL i n the near f u t u r e . In a d d i t i o n the new H a r r i s Slash Seven i s about 30% f a s t e r than our Slash Four machine. Another encouraging development i s the f a c t that memory p r i c e s have now come down by n e a r l y a f a c t o r of two r e l a t i v e to our purchase p r i c e for the 64K of Datacraft 24 b i t core memory. Thus i t seems q u i t e reasonable that future m i n i purchasers w i l l not be r e q u i r e d to r e s t r i c t themselves to small memory machines. C e r t a i n l y the most s p e c t a c u l a r t e c h n o l o g i c a l achievement of the l a s t three years i s the i n t r o d u c t i o n by F l o a t i n g Point Systems ( P o r t l a n d , Oregon) of t h e i r high speed array processor. At a cost of °o $40,000, t h i s device i s able to c a r r y out 38 b i t f l o a t i n g point operations at e s s e n t i a l l y the speed of the 7600. Professor Kent Wilson of UC San Diego has already purchased the FPS array processor for use i n s i m u l a t i n g the c l a s s i c a l dynamics of b i o l o g i c a l systems (14). We have studied t h i s device c a r e f u l l y and while very e n t h u s i a s t i c about i t , have some r e s e r v a t i o n s . F i r s t the 38 b i t



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word, corresponding to 8 plus s i g n i f i c a n t f i g u r e s , i s not q u i t e adequate f o r our type of t h e o r e t i c a l computations. As we have emphasized on many o c c a s i o n s , the 48 b i t word of the H a r r i s machine i s i d e a l for our purposes. Secondly, i n t e r f a c i n g the FPS device to a standard mini i s going to be q u i t e a c h a l l e n g e , and hand coding must be done whenever the array processor i s to be used. Since the a r r a y processor i s so much f a s t e r than the host m i n i , the FPS must be used very j u d i c i o u s l y to avoid i t s degradation. In short we do not f e e l that the FPS array processor i s s u i t able at present for general l a r g e s c a l e computations. The use of such a s p e c i a l i z e d device would tend to "freeze" one i n t o a p a r t i c u l a r t h e o r e t i c a l approach, with future options s e v e r e l y limited. However, the mere f a c t that FPS can manufacture a device of t h i s speed for only $40,000 i s c e r t a i n l y a remarkable a c h i e v e ment. We look forward to the further development of t h i s concept. F i n a l l y i t must be noted that a very important development has a l s o occurred i n the l a r g e s c a l e machine area. This i s the i n t r o d u c t i o n of the CRAY machine, which i s at l e a s t a f a c t o r of f i v e f a s t e r than the 7600 and w i l l be s o l d at e s s e n t i a l l y the same p r i c e (y $10 m i l l i o n ) . At present CDC has l e g a l l y succeeded i n s t a l l i n g the o f f i c i a l d e l i v e r y of the f i r s t CRAY, but t h i s should not be allowed to continue i n d e f i n i t e l y . Our personal o p i n i o n i s that by the time the CRAY machine becomes commercially a v a i l a b l e , both H a r r i s and SEL w i l l have introduced machines about f i v e times the speed of the H a r r i s Slash Four. Thus i t seems l i k e l y that the present r e l a t i v e economic comparisons w i l l be v a l i d for perhaps another f i v e y e a r s . A f t e r completion of our d r a f t r e p o r t , we learned of the i n t r o d u c t i o n of the PDP 11T55 machine by the D i g i t a l Equipment Corporation. Although timing and p r i c i n g information i s s t i l l incomplete, t h i s new DEC m i n i claims to exceed the speed of the H a r r i s Slash Four. We are s k e p t i c a l that a c o r p o r a t i o n as l a r g e and "respectable" as DEC w i l l be competitive with H a r r i s or SEL, but t h i s announcement i s c e r t a i n l y welcome. At the very l e a s t i t w i l l force H a r r i s and SEL to a c c e l e r a t e the development and r e l e a s e o f t h e i r new f a s t e r machines. Recommendat ions The greatest challenge p r e s e n t l y before the NSF (and ERDA) with respect to computation i n chemistry i s the above mentioned NRCC. We s t r o n g l y recommend that these bodies agree as q u i c k l y as p o s s i b l e on a procedure for implementing the NRCC (hopefully for F i s c a l 1978). One c o n c l u s i o n drawn from our i n v e s t i g a t i o n s i s that the u l t i m a t e goal o f the NRCC should not be the a c q u i s i t i o n o f i t s own 7600, but rather of the much more powerful and economical CRAY machine. Although i n i t i a l implementation w i l l probably involve some f r a c t i o n of a 7600, the CRAY a l t e r n a t i v e should be kept i n the forefront of c o n s i d e r a t i o n .



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At the same time the NSF should continue to c a r e f u l l y monitor new developments i n the minicomputer a r e a . A reasonable procedure would i n v o l v e the funding of two such minis per year for the next f i v e y e a r s . Our H a r r i s Slash Four has remained f o r t u i t i o u s l y current during the four p l u s years s i n c e the submission of our p r o p o s a l . However, as discussed i n the previous s e c t i o n , the winds of change are now beginning to blow. P e r s o n a l l y we intend to submit a new proposal to NSF as soon as a r e l i a b l e manufacturer meets the f o l l o w i n g s p e c i f i c a t i o n : for l e s s than $200,000 complete ( i n c l u d i n g C a l i f o r n i a s a l e s tax) a machine four times the speed of the Slash Four. Our current o p i n i o n i s that innovations of a l e s s comprehensive nature are not worth the t r i b u l a t i o n s (see Appendix) inherent i n breaking i n a new machine. Since the H a r r i s Slash Four w i l l s t i l l be a very d e s i r a b l e machine ( e s p e c i a l l y with i t s r e s i d e n t programs, i n c l u d ing POLYATOM, GAUSSIAN 70, SCEP, and BERKELEY), we would leave i t to the d i s c r e t i o n of the NSF to f i n d a s u i t a b l e new owner. Appendix I Interim Reports on the Berkeley Minicomputer P r o j e c t . Q u a r t e r l y Report No. 1, December 14,

1973

Notice was r e c e i v e d on June 15, 1973 that the proposal "Large Scale S c i e n t i f i c Computation v i a Minicomputer" had been funded to the extent of $129,600 by the N a t i o n a l Science Foundation. At t h i s p o i n t f i n a l n e g o t i a t i o n s with the Datacraft Corporation was entered i n t o . The U n i v e r s i t y of C a l i f o r n i a was represented by Mr. R. J . B r i l l i a n t of the Purchasing O f f i c e , while Datacraft was represented by Mr. Don F a l t i n g s , of t h e i r Walnut Creek o f f i c e . A f i n a l agreement was reached on October 5, 1973. The primary change r e l a t i v e to the proposed system was the s u b s t i t u t i o n of a 56,000,000 byte d i s k for the o r i g i n a l 28,000,000 byte d i s k . In a p a r a l l e l development, we r e c e i v e d a l e t t e r on June 28, 1973 from Professor D. R. W i l l i s , A s s i s t a n t to the C h a n c e l l o r Computing. On behalf of the Campus Advisory Committee on Computing, Professor W i l l i s requested that we advise him on how progress reports could best be made, on a r e g u l a r and c o n t i n u i n g basis. On August 30, 1973, we agreed to f i l e q u a r t e r l y r e p o r t s , one or two typewritten pages l o n g , to the Berkeley Campus Computing Committee. These q u a r t e r l y reports w i l l a l s o be sent to D r . W. H . Cramer, Program D i r e c t o r f o r Quantum Chemistry, N a t i o n a l Science Foundation. The m a j o r i t y o f the 6024/4 system was d e l i v e r e d at Berkeley on November 14, 1973. As discussed with D a t a c r a f t , the s c i e n t i f i c a r i t h m e t i c u n i t ( f l o a t i n g p o i n t hardware) and 56 megabyte d i s k did not appear. These items are scheduled at be d e l i v e r e d i n e a r l y January, 1974. In the meantine, a temporary 11 megabyte d i s k was s u p p l i e d by D a t a c r a f t .


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The Datacraft engineer, Mr. Mike Crumbliss, a r r i v e d i n Berkeley on November 19 and proceeded to connect the system. Several e a r l y problems were c l e a r e d up during the f i r s t week. For example, an i n a b i l i t y to plug i n the f i n a l 8,000 words of memory was traced to a misadjustment i n the power supply. With i n the f i r s t week the machine was able to d i a g o n a l i z e a 50 χ 50 matrix i n s i n g l e p r e c i s i o n ( s i x s i g n i f i c a n t f i g u r e s ) . This c a l c u l a t i o n was done using the benchmark program HDIAG discussed i n our NSF p r o p o s a l . However, the machine was unable to properly d i a g o n a l i z e the same 50 χ 50 matrix i n double p r e c i s i o n . This e r r o r , which as of today s t i l l o c c u r s , was traced back to trouble i n the square root r o u t i n e , which i n turn f a i l s due to an e r r o r i n the f l o a t i n g p o i n t d i v i d e o p e r a t i o n . The s p e c i f i c problem i s that the quantity (1.0 - 2"^ )/1.0 i s computed to give 1.0 2_3 8 _ 2~ . The Datacraft engineers are working on t h i s problem now and i n d i c a t e that i t should be resolved s h o r t l y . Despite the p e c u l i a r d i v i d e problem o u t l i n e d above, Professor M i l l e r ' s c l a s s i c a l t r a j e c t o r y programs appear to execute properly i n both s i n g l e and double p r e c i s i o n . The complex-valued t r a j e c t o r i e s run only i n s i n g l e p r e c i s i o n , since the f l o a t i n g point hardware i s r e q u i r e d f o r double p r e c i s i o n complex o p e r a t i o n s . The f i r s t e l e c t r o n i c s t r u c t u r e program we are attempting to set up i s HETINT, Professor Schaefer's diatomic molecular i n t e g r a l s program. The program has been rearranged to f i t i n memory w i t h out o v e r l a y i n g , but does not yet execute properly due to the d i v i d e e r r o r discussed above. In general we have found the double p r e c i s i o n software to execute 150-200 times slower than the CDC 7600. This i s about as expected, and a f a c t o r of 3-4 from the f l o a t i n g p o i n t hardware w i l l put us i n the speed range discussed i n the p r o p o s a l . In our research groups, the i n d i v i d u a l most knowledgeable about computers and computing i s Mr. Peter K. Pearson, and he has taken over r e s p o n s i b i l i t y f o r the care o f the system and dissemination o f necessary information to the other research students. At l e a s t four other students have a good grasp o f the system. In that most of us know a great deal more about computers than we d i d one month ago, i t appears that our m i n i computer experiment has had considerable e d u c a t i o n a l value already. On March 29, 1974 our i n s t a l l a t i o n w i l l be v i s i t e d by a s p e c i a l N a t i o n a l Science Foundation committee, t e n t a t i v e l y composed of D r s . W. H . Cramer (NSF), 0. W. Adams (NSF), J . C . Browne ( U n i v e r s i t y o f Texas), and P . G. Lykos ( I l l i n o i s I n s t i t u t e of Technology). 8

η

Q u a r t e r l y Report No. 2, March 27, 1974 Our f i r s t q u a r t e r l y r e p o r t documented the a r r i v a l of most of the Datacraft 6024/4 system, described i n our NSF p r o p o s a l . This proposal has now been modified s l i g h l y so as to be s u i t a b l e f o r



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p u b l i c a t i o n , and w i l l appear i n the new j o u r n a l "Computers and Chemistry". At the time of our f i r s t r e p o r t , the 6024/4 had been unable to s u c c e s s f u l l y complete our 50 χ 50 matrix d i a g o n a l i z a t i o n bench mark i n double p r e c i s i o n , due to an e r r o r i n the f l o a t i n g p o i n t d i v i d e subroutine. Shortly t h e r e a f t e r t h i s e r r o r was further traced by Peter Pearson to a machine i n s t r u c t i o n , the AMD i n s t r u c t i o n , Add Memory Double. We should point out here that the Datacraft engineers (or those of any other data p r o c e s s i n g manufacturer) can u s u a l l y solve a problem only a f t e r i t has been traced to a s p e c i f i c machine i n s t r u c t i o n f a i l u r e . In the present case, the AMD i n s t r u c t i o n d i d f u n c t i o n p r o p e r l y when one of the c e n t r a l processor byte s l i c e boards was put on an extender board. This being the case, the e r r o r was e l i m i n a t e d by p o s i t i o n i n g a piece o f copper f o i l between the two offending cpu byte s l i c e boards. The matrix d i a g o n a l i z a t i o n then executed properly at a speed 166 times slower than the CDC 7600. With the f l o a t i n g point hardware, however, we expect (see o r i g i n a l proposal) the benchmark to execute at a speed 49 times slower than the 7600. With the AMD i n s t r u c t i o n c o r r e c t e d , we r e t u r n to the problem of implementing HETINT, Professor Schaefer's diatomic molecular i n t e g r a l s program. Although the program d i d execute, i n c o r r e c t answers were obtained. Peter Pearson e v e n t u a l l y traced t h i s d i f f i c u l t y to improper treatment of exponents by the system's a r i t h m e t i c r o u t i n e s i n underflow cases. In f a c t , he had to modify the f l o a t i n g p o i n t subroutines for double p r e c i s i o n add, subtract, and m u l t i p l y . This was a p a r t i c u l a r l y d i f f i c u l t j o b , s i n c e at that time we d i d not have the source program l i s t i n g s for the software f l o a t i n g point subroutines. With these c o r r e c t i o n s made, HETINT executed p r o p e r l y on December 19, 1973. This program executes at a speed roughly 105 times slower than the CDC 7600. The next major program to be implemented was the Ohio S t a t e Cal Tech-Berkeley v e r s i o n of POLYATOM, a general molecular program for the computation of m u l t i c o n f i g u r a t i o n SCF wave functions (the o r i g i n a l v e r s i o n of POLYATOM was developed by J u l e s Moskowitz and co-workers at NYU). To t h i s end, Dean Liskow began an i n t e n s i v e e f f o r t on the f i r s t of the year. One of the most serious d i f f i c u l t i e s was the setup of the overlay s t r u c t u r e , c o n s i s t i n g of three l e v e l s with seven segments. Success was achieved on January 11 when a proper s e l f - c o n s i s t e n t - f i e l d wave f u n c t i o n f o r the water molecule was obtained. Comparison with the 7600 r e s u l t s showed an accuracy of between 9 and 10 s i g n i f i cant figures f o r the t o t a l energy. Toward the end of January, we began to run POLYATOM on a production b a s i s . One of the f i r s t problems t a c k l e d was the p o s s i b l e existence o f two isomers of the NOâ i o n . A (9s 5p/5s 3$ gaussian b a s i s was centered on each atom, and the three geometric a l parameters optimized for the nonsymmetric form. A complete c a l c u l a t i o n at a s i n g l e geometry r e q u i r e d between four and s i x hours of elapsed time. This i s about a f a c t o r of 85


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times slower than the CDC 7600. During the same p e r i o d Gretchen Schwenzer used the 6024/4 f o r a thorough p r e l i m i n a r y study of H S and the two h y p o t h e t i c a l hypervalent molecules SHi+ and SH6. S i m i l a r 7600 timing comparison were obtained. Due to the f l o a t i n g p o i n t software's i n a b i l i t y to perform complex operations i n double p r e c i s i o n (11 s i g n i f i c a n t f i g u r e s ) , we have thus f a r been unable to implement Professor M i l l e r ' s s e m i c l a s s i c a l programs i n v o l v i n g complex-valued t r a j e c t o r i e s ( i . e . , generalized tunneling). Several r e a l - v a l u e d t r a j e c t o r y programs ( r o t a t i o n a l e x c i t a t i o n of He + H and t r a j e c t o r y φ "surface-hopping" c a l c u l a t i o n s for 0( D) + N2 -*-0(^P) + N2 ) i n i t i a l l y ran s u c c e s s f u l l y but numerical ^ r e p r o d u c i b i l i t i e s began occuring. This was a source of much f r u s t r a t i o n , and was perhaps due to c r o s s t a l k between s e v e r a l a d d i t i o n a l byte s l i c e boards. To c o r r e c t t h i s problem s e v e r a l a d d i t i o n a l sheets of copper f o i l were p o s i t i o n e d i n the c e n t r a l processor one week ago. The l a r g e d i s k (56 megabyte) and s c i e n t i f i c a r i t h m e t i c u n i t (SAU) a r r i v e d at Berkeley on March 13, 1974. This was two months a f t e r the promised d e l i v e r y date and a source of c o n s i d e r able f r u s t r a t i o n . I t i s important to note here that none of the time comparisons made heretofore u t i l i z e d the SAU ( f l o a t i n g p o i n t hardware). The i n d i v i d u a l hardware f l o a t i n g point add, s u b t r a c t , m u l t i p l y , and d i v i d e i n s t r u c t i o n s execute at speeds 6-14 times f a s t e r than the software subroutines. R e a l i s t i c a l l y , however, we expect the SAU to r e s u l t i n an o v e r a l l i n c r e a s e i n speed of a f a c t o r of 2 to 3. This would put us w i t h i n our o r i g i n a l estimate of being a f a c t o r o f 64 slower than the 7600. As of the time of w r i t i n g of t h i s r e p o r t , n e i t h e r the l a r g e d i s k nor SAU are yet f u l l y o p e r a t i o n a l . The Datacraft engineers are h o p e f u l , however, that the complete system w i l l be f u n c t i o n a l w i t h i n a week. 2


2

X

Q u a r t e r l y Report No. 3, June 17,

1974

A w e l l - r e s p e c t e d book d e s c r i b i n g the f i r s t twelve months of infancy makes a statement to the e f f e c t that the t h i r d month of your c h i l d ' s l i f e makes the f i r s t two seem bearable i n retrospect. In a remarkably analogous manner, the f r u s t r a t i o n s of the f i r s t two quarters with our Datacraft 6024/4 minicomputer were more than compensated by the successes of the t h i r d q u a r t e r , j u s t completed. Our second q u a r t e r l y report l e f t o f f with the machine i n o p e r a t i v e due to the recent a r r i v a l of the 56 megabyte d i s k and f l o a t i n g p o i n t processor [referred to by Datacraft as the s c i e n t i f i c a r i t h m e t i c u n i t (SAU)]. Since the NSF v i s i t a t i o n committee (Drs. W. H . Cramer, 0. W. Adams, J . C. Browne and P . G. Lykos) was to a r r i v e on March 29, one might d e s c r i b e the s i t u a t i o n on March 27 as being on the verge of p a n i c . From F o r t Lauderdale Datacraft flew out Mr. R u s s e l l P a t t o n , d i r e c t o r of f i e l d service. Working through the n i g h t , he and Mr. Ron P l a t z



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i n s t a l l e d a separate power supply for the SAU and l o c a t e d and corrected a problem with the d i s k automatic block c o n t r o l l e r . With these m o d i f i c a t i o n s implemented, Peter Pearson was able to execute the 50 χ 50 matrix d i a g o n a l i z a t i o n benchmark program. In the l a s t q u a r t e r l y r e p o r t , we noted t h a t , without the f l o a t i n g p o i n t hardware, (SAU), t h i s program executes at a speed 166 times slower than the CDC 7600. With the SAU and the standard Datacraft 6024 compiler a r a t i o of 59 was found. Using the "optimizing" compiler ( a c t u a l l y s t i l l a r a t h e r crude c o m p i l e r ) , the d i a g o n a l i z a t i o n executed at a speed 43 times slower than the 7600. T h i s r e s u l t i s c o n s i s t e n t with the f a c t o r of 49 p r e d i c t e d i n the o r i g i n a l p r o p o s a l , a modified v e r s i o n of which has now been accepted for p u b l i c a t i o n i n the new j o u r n a l Computers and Chemistry. The NSF v i s i t a t i o n provided the framework for a thorough d i s c u s s i o n of the machine's progress through March 29. Bill Cramer and B i l l Adams s t r e s s e d the importance of keeping an accurate record of machine u t i l i z a t i o n , a key f a c t o r i n the economic a n a l y s i s c e n t r a l to t h i s experiment. Peter Lykos suggest ed we c a l i b r a t e the 6024/4 using the MFLOPS (measure of f l o a t i n g point operations per second) benchmark. A copy of MFLOPS has been obtained and an a n a l y s i s w i l l be presented i n the next quarterly report. Jim Brown gave us many u s e f u l i n s i g h t s from h i s experience at the U n i v e r s i t y of Texas as both chemist and computer s c i e n t i s t . Don F a l t i n g s of Datacraft was on hand to answer a number of questions from the committee and b r i e f l y d i s c u s s some new features ( i n c l u d i n g v i r t u a l memory) of the Datacraft l i n e . F i n a l l y , i t was agreed that a second v i s i t a t i o n would be a d v i s a b l e , a f t e r the machine i s f u l l y o p e r a t i o n a l and i t s c h a r a c t e r i s t i c s thoroughly documented. Steady progress was made during the f i r s t 10 days of A p r i l . That i s , a number of programs were modified to run on the complete system, i n c l u d i n g SAU and l a r g e d i s k . However, s e v e r a l nagging problems p e r s i s t e d , one being that 5.4 v o l t s , 0.4 above the recommended l e v e l , were required to s u s t a i n the c e n t r a l processor. When t h i s minimum f u n c t i o n i n g voltage increased to 5.5 v o l t s , Datacraft advised us to turn the machine o f f . After a week of i n v e s t i g a t i o n , t h i s s u r p r i s i n g l y s u b t l e problem was l o c a t ed and q u i c k l y e l i m i n a t e d on A p r i l 22 by replacement of an i n t e grated c i r c u i t on the memory timing and c o n t r o l board. As i t turned o u t , t h i s small machine defect had been r e s p o n s i b l e f o r many of the problems encountered during the f i r s t f i v e months of operation. Not only d i d the machine run properly at 5.0 v o l t s , but i t was a l s o p o s s i b l e to remove the pieces of copper f o i l p r e v i o u s l y necessary (see Q u a r t e r l y Reports 1 and 2) to s h i e l d the d i f f e r e n t boards from each o t h e r . Since A p r i l 22, the 6024/4 has been running q u i t e smoothly. Some o c c a s i o n a l p a r i t y e r r o r s were put to r e s t by replacement of a memory board chip on May 16. A current problem with the add memory to double (AMD) i n s t r u c t i o n has been temporarily r e l i e v e d



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by a sheet of copper f o i l between byte s l i c e boards 2 and 3. However, these are minor problems, and o v e r a l l we have been very pleased with the o p e r a t i o n of the machine during t h i s q u a r t e r . With t e c h n i c a l problems pushed i n t o the background, we were able to turn to the c e n t r a l goal of the experiment, the e v a l u a t i o n of the performance of the 6024/4 r e l a t i v e to the CDC 7600 . For t h i s purpose we report the r e s u l t s of two d i r e c t comparisons, one i n v o l v i n g e l e c t r o n i c s t r u c t u r e theory and the other molecular c o l l i s i o n theory. I t i s to be emphasized that the programs used are by no means o p t i m a l l y e f f i c i e n t . However, of primary i n t e r e s t here are the r e l a t i v e speeds of the two machines, and for t h i s purpose our comparisons should be v a l i d . The f i r s t t e s t case arose i n Dean Liskow's study of the chemisorption of hydrogen by c l u s t e r s of b e r y l l i u m atoms. For the BesH system, a double zeta b a s i s set was adopted: Be(4s 2p), H(2s l p ) . The modified POLYATOM program was used to compute s e l f c o n s i s t e n t - f i e l d wave functions for t h i s open s h e l l doublet. The r e s u l t s are summarized below: Times f 6024/4

(seconds) 7600

^

Ratio

Generate l i s t of unique nonzero i n t e g r a l s Compute unique

3091

174

17.8

2506

119

21.5

integrals

( t o t a l of 476,000)

SCF (time per i t e r a t i o n ) 1548 36 43.5 T h i s comparison i n d i c a t e s that the SCF i t e r a t i o n s show the 6024/4 i n the worst l i g h t . We intend to c o r r e c t t h i s weakness by r e c o d ing t h i s s e c t i o n of POLYATOM i n machine language. However, a l l our d i r e c t comparisons with the 7600 must of n e c e s s i t y employ the same FORTRAM programs. The complete c a l c u l a t i o n , i n c l u d i n g 17 SCF i t e r a t i o n s , r e q u i r e d 0.25 cpu hours on the 7600 and cost $243. The i d e n t i c a l c a l c u l a t i o n r e q u i r e d a t o t a l of 8.86 hours of 6024/4 time, or an o v e r a l l f a c t o r of 35 longer than the 7600. The second t e s t case arose from George Z a h r ' s study of the quenching of 0 ( * ϋ ) by N 2 . Assuming a simple a n a l y t i c a l p o t e n t i a l energy s u r f a c e , c l a s s i c a l t r a j e c t o r i e s were performed w i t h i n the surface-hopping model of Preston and T u l l y . 330 such t r a j e c t o r i e s r e q u i r e d 480 minutes on the 6024/4 and 18.2 minutes on the 7600. The 7600 cost was $193. The Datacraft machine i s seen to be a f a c t o r o f 26 slower. Note that t h i s computation i n v o l v e s v i r t u a l l y no input/output o p e r a t i o n s . Both of the above comparisons show the Datacraft minicomputer to be s i g n i f i c a n t l y f a s t e r than the f a c t o r of 64 p r e d i c t e d i n our o r i g i n a l proposal. There we concluded that the t o t a l monthly cost ( i n c l u d i n g a m o r t i z a t i o n over four years) of the 6024/4 would be $4156. Experience has shown t h i s f i g u r e , which we now round to


13.

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185

$4200, to be r e a l i s t i c . Yet to be f i r m l y e s t a b l i s h e d i s the average number of hours of computing a t t a i n e d per day at our installation. We w i l l d i s c u s s t h i s point i n d e t a i l i n our next quarterly report. However, i f we take the p e s s i m i s t i c view that only 12 hours of computing per day are achieved, 360 hours per month t r a n s l a t e s i n t o a cost of $11.67/hour. Thus the BesH job c i t e d above costs $103, as opposed to $243 for the 7600. The 0( D) + N2 job by the same c r i t e r i o n cost $93, as opposed to $193 for the 7600. Again i t i s only f a i r to remark that the c i t e d 7600 costs at the Lawrence Berkeley Laboratory i n c l u d e only o p e r a t i o n a l expenses and completely n e g l e c t the i n i t i a l purchase p r i c e of the machine. Added i n proof: A s u r p r i s i n g l y simple r e o r d e r i n g of the POLYATOM f i l e s t r u c t u r e (no changes i n the FORTRAN program) by Peter Pearson has r e s u l t e d i n n e a r l y a f a c t o r of two increase i n the SCF speed c i t e d above.


1

Report No. 4, March 30,

1975

By the time of w r i t i n g of our l a s t r e p o r t , i t had become clear that the Datacraft 6024/4 minicomputer was meeting or exceeding the goals that had been set for i t . The past nine months have served to s u b s t a n t i a l l y strengthen that c o n c l u s i o n . A p a r t i c u l a r l y c r u c i a l t e s t has been passed i n that i t i s now apparent that r e l a t i v e l y l i t t l e maintenance of the machine i s required. T y p i c a l l y , i t i s necessary to c a l l the computer engineer once or twice per month, and r e p a i r "down time" for a t y p i c a l month i s roughly one day. In f a c t , the s e r v i c e c o n t r a c t i s necessary p r i m a r i l y as an insurance p o l i c y , s i n c e we would otherwise be unprotected against d i s a s t e r s , e . g . , i f for some mysterious reason the e n t i r e memory were burned out. In t h i s regard i t should be noted that the Datacraft Corporation was swallowed up by the H a r r i s Corporating during t h i s p e r i o d . Thus our minicomputer i s now marketed as the H a r r i s Slash Four. The only e f f e c t (on us) of t h i s takeover was the increased cost of the s e r v i c e c o n t r a c t , for which H a r r i s proposed a p r i c e of $1500/month T h i s suggestion was p a r t i c u l a r l y d i s t r e s s i n g to us s i n c e (a) i t represented a l a r g e increase over the $1155/month we had budgeted for and (b) the U n i v e r s i t y of C a l i f o r n i a has during the past year changed i t s p o l i c y and we now pay 34% overhead on the s e r v i c e contract. A f t e r some d e l i c a t e n e g o t i a t i o n s H a r r i s lowered the s e r v i c e contract p r i c e to $1280/month and we accepted i t . Before l e a v i n g the subject of maintenance, i t should be mentioned that most of our problems r e q u i r i n g s e r v i c e i n v o l v e the t e l e t y p e and l i n e p r i n t e r . I t turns out that n e i t h e r of these devices was intended for the s o r t of f u l l time usage they are receiving. I n c i d e n t a l l y , the t e l e t y p e i s not covered under the new s e r v i c e c o n t r a c t , but i s i n s t e a d s e r v i c e d by U n i v e r s i t y of C a l i f o r n i a personnel.



186

MINICOMPUTERS

A N DLARGE

SCALE

COMPUTATIONS

In one r e s p e c t , the minicomputer has proved l e s s expensive to operate than we had p r e d i c t e d . In the o r i g i n a l p r o p o s a l , $300/ month was a l l o c a t e d for " e l e c t r i c i t y , c a r d s , paper, e t c . " As i t turns out, although we do pay the above-mentioned overhead of $437/month on the s e r v i c e c o n t r a c t , the U n i v e r s i t y pays our e l e c t r i c a l b i l l , and the cost of c a r d s , paper, e t c . , i s l e s s than $50/month. Thus t h i s savings of $250/month p a r t i a l l y cancels the high cost of the s e r v i c e c o n t r a c t . During t h i s p e r i o d we have from time to time run programs to gather s t a t i s t i c s on the u t i l i z a t i o n of the minicomputer. These data suggest that the machine i s busy for about 90% of the time i t i s not being s e r v i c e d . Thus the o v e r a l l ( i n c l u d i n g r e p a i r down time) u t i l i z a t i o n i s i n excess of 85%, a f i g u r e considered q u i t e acceptable for l a r g e s c a l e machines. T h i s u t i l i z a t i o n r a t e i s a l s o remarkably c l o s e to the 20 hours/day estimated i n our o r i g i n a l proposal. I t i s necessary, however, to point out that such a r a t e could not be achieved (without a paid operator) w i t h out an aggressive and hard working group of eleven a c t i v e users (students and p o s t d o c t o r a l s ) . Since each user z e a l o u s l y guards h i s ^ 13 hours/week, he/she i s quite l i k e l y to be on hand should any temporary machine problem i n t e r r u p t his/her j o b . Due to machine demand, i t should be noted that jobs r a r e l y run longer than 13 hours; and the thought ( r a i s e d i n our o r i g i n a l proposal) of jobs running c o n s e c u t i v e l y for one month has been long s i n c e abandoned. A t y p i c a l job now runs for about two hours. Scheduling the computer turned out to be more of a problem than we i n i t i a l l y a n t i c i p a t e d . I t was c l e a r i n J u l y , 1974 that the machine had become s u f f i c i e n t l y popular that "good w i l l " would not be a s u f f i c i e n t deterrent to squabbles. The system that has now been s e t t l e d upon i n v o l v e s g i v i n g each a c t i v e user 13 hours of machine time per week. In a d d i t i o n four hours (10 AM - 2 PM) per weekday are a v a i l a b l e on a f i r s t c o m e - f i r s t serve b a s i s for debug j o b s , with a time l i m i t of ten minutes. The time i s signed up for on Thursday afternoons for the week beginning Saturday. The order of sign-up i s a r e g u l a r one, with the user having f i r s t choice one week being demoted to l a s t choice the f o l l o w i n g week. A final r e s t r i c t i o n i s that the b l o c k to time between 2 AM and 8 AM cannot be s u b d i v i d e d . That i s , a s i n g l e user takes the e n t i r e b l o c k . Although t h i s scheduling system w i l l probably be s l i g h t l y r e v i s e d on o c c a s i o n , i t seems to be working reasonably w e l l at present. Two major program conversion e f f o r t s were undertaken s i n c e the t h i r d r e p o r t . The f i r s t , i n v o l v i n g the Gaussian 70 programs of Hehre, Lathan, D i t c h f i e l d , Newton, and Pople, i s now completed. The second, i n v o l v i n g the polyatomic c o n f i g u r a t i o n i n t e r a c t i o n (CI) program of Charles F . Bender, began very r e c e n t l y and has been implemented thus f a r only i n a r e s t r i c t e d v e r s i o n . The Gaussian 70 conversion was deemed e s p e c i a l l y important s i n c e i t now appears that t h i s program w i l l become s i g n i f i c a n t l y more widely d i s t r i b u t ed than any previous ab i n i t i o progarm for s i n g l e determinant SCF studies. Thus the times we report with t h i s program may serve as


13.

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187

a b a s i s for comparison w i t h many other types of computers. The major d i f f i c u l t y i n the implementation of Gaussian 70 was the r e l a t i v e l y complicated (for the 6024/4) overlay s t r u c t u r e . One o f the e a r l i e s t s t u d i e s undertaken u s i n g Gaussian 70 i n v o l v e d the C H - C £ 2 molecular complex. Using the standard ST0-3G b a s i s set (162 p r i m i t i v e gaussians, 54 contracted f u n c t i o n s ) , a complete c a l c u l a t i o n at one geometry, i n c l u d i n g 8 SCF i t e r a t i o n s , r e q u i r e d 64 minutes of 6024/4 elapsed time. Thus i t i s c l e a r that the study o f reasonably complicated organic systems u s i n g minimum b a s i s sets i s q u i t e f e a s i b l e with the minicomputer. Using analogous minimum b a s i s s e t s , computations have been c a r r i e d out on (CH30)2P0 Ca Cl (67 c o n t r a c t e d f u n c t i o n s ; 59 minutes f o r i n t e g r a l s plus 86 minutes f o r 13 SCF i t e r a t i o n s ) and the Bei3 c l u s t e r (65 contracted f u n c t i o n s ; 80 minutes f o r i n t e g r a l s , 250 minutes f o r 20 SCF i t e r a t i o n s ) . We continue to i n v e s t i g a t e a l a r g e number of systems u s i n g the B e r k e l e y - C a l Tech-Ohio State v e r s i o n of POLYATOM. Advantages o f t h i s program are that i t y i e l d s exact s p i n eigenfunctions f o r opens h e l l systems and can perform l i m i t e d MCSCF computations. One of the l a r g e r systems studied was the NH3-C&F charge t r a n s f e r complex. A b a s i s set of s i z e Cil(12s 9p ld/6s 4p I d ) , N,F(9s 5p ld/4s 2p I d ) , H(4s/2s) was used, t o t a l i n g 62 contracted f u n c t i o n s . A l i s t of non zero-unique i n t e g r a l s i s generated i n 40 minutes ( t h i s process need be done only once f o r the e n t i r e p o t e n t i a l c u r v e ) , i n t e g r a l computation r e q u i r e d 130 minutes, and 11 SCF i t e r a t i o n s consumed 50 minutes. A study of trimethylene methane which we had e a r l i e r found exceedingly d i f f i c u l t to f i n i s h on the 7600 (due to cost c o n s i d e r a t i o n s ) has now been completed on the 6024/4. Using a double zeta b a s i s set (120 p r i m i t i v e functions contracted to 52), 74 minutes were r e q u i r e d f o r i n t e g r a l g e n e r a t i o n . Twenty SCF i t e r a t i o n s on the A 2 ground s t a t e (two SCF hamiltonians) devoured 220 minutes o f elapsed time. During the past nine months, a s e r i e s of production runs was made on the g l y o x a l molecule (HC0)2 u s i n g a standard double zeta basis set. S i n c e , a number of runs were a l s o made on the 7600, a comparison of the costs f o r the e n t i r e p r o j e c t i s p o s s i b l e . The POLYATOM timing comparisons are seen i n Table I . 6



E T AL.

6

2

3

The r a t i o of elapsed 6024/4 time to 7600 CPU time i s 25.0, a very encouraging f i g u r e . Since the cost of machine time on the m i n i i s about $8/hour ( i n c l u d i n g a m o r t i z a t i o n of the purchase p r i c e over four y e a r s ) , the t o t a l minicomputer cost of the p r o j e c t was l e s s than $3500. An i n t e r e s t i n g development has been the i n c r e a s i n g use of the m i n i i n an i n t e r a c t i v e mode. This i s e s p e c i a l l y h e l p f u l i n SCF calculations. The t o t a l energy i s p r i n t e d on the t e l e t y p e a f t e r each SCF i n t e r a c t i o n and the user has four o p t i o n s : a) c o n t i n u e ; b) go to a weighted averaging of o r b i t a l s ; c) go to an e x t r a p o l a t i o n scheme; d) stop. Use of t h i s i n t e r a c t i v e feature can remarkably improve the r a t e of convergence f o r c e r t a i n types of molecular systems.


188

MINICOMPUTERS

Table I .

A N DLARGE

COMPUTATIONS

POLYATOM timing comparisons f o r g l y o x a l . 7600 Job


SCALE

Cost

6024/4 Minutes Elapsed Time

35

8

9

215

34

46

240

61

86

CPU-Seconds

Lister Integrals (cis/trans) Integrals (gauche) SCF - ground s t a t e per i t e r a t i o n SCF - e x c i t e d s t a t e s per i t e r a t i o n

6

2.75

2.5

17

7.70

7

Glyoxal P r o j e c t : 3 70 60 130 40

listers 105 cis/trans integrals 8050 gauche i n t e g r a l s 14400 SCF ground s t a t e 7020 SCF - e x c i t e d s t a t e s vertical 13600 60 SCF - e x i c t e d s t a t e s geometry search _ 7140 a

24 2380 3660 3250

27 3220 5160 3510

6160

5800

b

c

50,315 $18,719 14.0 hours a) b) c) d)

3240

3245 c

20,957 349.3 hours

Based on nine SCF i t e r a t i o n s for convergence. Based on twenty SCF i t e r a t i o n s for convergence. Based on seven SCF i t e r a t i o n s for convergence. I f run e x c l u s i v e l y on weekends and h o l i d a y s , cost reduced to $9360. I f i n a d d i t i o n run at deferred p r i o r i t y , cost f a l l s to $7488.

Much of WHM's current research i n v o l v e s n u m e r i c a l l y computed classical trajectories. In " c l a s s i c a l S-matrix" c a l c u l a t i o n s , for example, c l a s s i c a l t r a j e c t o r i e s , and the a c t i o n i n t e g r a l along them, are used to construct quantum mechanical S-matrix elements for s p e c i f i c c o l l i s i o n processes. A l s o , a newly formulated quantum mechanical v e r s i o n of t r a n s i t i o n s t a t e theory, which c o r r e c t l y incorporates n o n - s e p a r a b i l i t y of the t r a n s i t i o n s t a t e , uses t r a j e c t o r i e s — p e r i o d i c t r a j e c t o r i e s i n imaginary time—to determine the net r a t e constant f o r r e a c t i o n . Although the c a l c u l a t i o n of c l a s s i c a l t r a j e c t o r i e s themselves i s f a i r l y standard nowadays, these novel kinds of theory u s u a l l y i n v o l v e search



13.

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189

procedures, i . e . , they require particular classical trajectories rather than a Monte Carlo average over them a l l . The ability to operate the minicomputer "hands on" has greatly facilitated the application of these new kinds of theoretical models. Also, this type of work requires a great deal of new program debugging, and the 6024/4 has proved quite adequate in this regard, even though the diagnostics are not as comprehensive as those produced by the LBL 7600. Our final fairly typical timing comparison concerns a threedimensional phase space integral calculation. To obtain the rate constant for D + H2 at 200°K, 237 classical trajectories ,(both real and imaginary) were computed. The minicomputer required 60 minutes for this job, while the 7600 used 2.42 minutes of CPU time. Thus the 7600 was a factor of 25 quicker than the 6024/4. The cost of the 7600 job was $20.57. This comparison puts the large machine in a relatively favorable light since there are essentially no 7600 input/output charges associated with trajectory-oriented jobs of this type. In closing we note that this factor of 25 is characteristic of trajectory studies, which involve the numerical integration of ordinary differential equations. Ac knowledgment s We wish to sincerely thank Drs. W. H. Cramer and 0. W. Adams of NSF for their support of this project, especially during its early and more controversial stages. We also thank Professors Jim Brown, Edward Hayes, Maurice Schwartz, Don Secrest, Stanley Hagstrom, and Peter Lykos for their thoughtful comments on the draft version of this report. * Supported by the National Science Foundation, Grant GP-39317. ** Present address: Lawrence Livermore Laboratory, University of California, Livermore, California 94550. *** Address after September 15, 1977: Arthur Amos Noyes Laboratory of Chemical Physics, California Institute of Technology, Pasadena, California 91125 Literature Cited 1. 2. 3. 4.

Pople, J . Α., "Modern Theoretical Chemistry", Vol. IV, ed., H. F. Schaefer, Plenum, New York, 1977. Cavallone, F . , and Clementi, Ε . , J . Chem. Phys. (1975), 63, 4304. Miller, W. H., Advances in Chemical Physics (1974), 25, 69. Herschbach, D. R., Faraday Discussion Chem. Soc. (1973), 55, 233.


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5. 6.

Bunker, D. L . , Accounts of Chemical Research (1974), 7, 195. Wiberg, Κ. B., "A Study of a National Center for Computation in Chemistry", National Academy of Sciences, Washington, D.C., March, 1974. 7. Bigeleisen, J . , "The Proposed National Resource for Computa tion in Chemistry: A User-Oriented Facility", National Academy of Sciences, Washington, D.C., June, 1975. 8. Dykstra, C. E., Schaefer, H. F., and Meyer, W., J. Chem. Phys. (1976), 65, 2740, 5141. 9. Schaefer, H. F., "The Electronic Structure of Atoms and Molecules: A Survey of Quantum Mechanical Results", AddisonWesley, Reading, Massachusetts, 1972. 10. Lucchese, R. R., Brooks, B. R., Meadows, J. H., Swope, W. C., and Schaefer, H. F., J. Computational Phys., in press. 11. Shavitt, I., paper presented at the Third ICASE Conference on Scientific Computing, Williamsburg, Virginia, April 1-2, 1976. 12. Robinson, A. L . , Science (1976), 193, 470. 13. Richards, G., Nature (1977), 266, 5597, 18. 14. Wilson, K. R., "Multiprocessor Molecular Mechanics", in Computer Networking and Chemistry, Peter Lykos, editor (American Chemical Society, Washington, D.C., August, 1975.


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