Many-Atom Molecular Dynamics with an Array Processor - ACS

12 Many-Atom Molecular Dynamics with an Array Processor

Downloaded by UNIV OF MASSACHUSETTS AMHERST on May 19, 2018 | https://pubs.acs.org Publication Date: June 1, 1977 | doi: 10.1021/bk-1977-0057.ch012

KENT R. WILSON Department of Chemistry, University of California—San Diego, La Jolla, CA 92093

"The change of motion is proportional to the motive force impressed; and is made in the direction of the right line in which the force is impressed." Sir Isaac Newton, Philosophiae Naturalis Principia Mathematica, 1687. I.

Introduction and History

A. Theoretical Instruments. We chemists traditionally have built specialized instrumentation for experimental studies. We are now beginning also to build specialized instrumentation for theory (1). While we are accustomed to designing and building, for example, special spectrometers or molecular beam machines to efficiently probe the experimental side of a particular class of chemical questions, it is now becoming clear that with comparable effort we can also design and build specialized computational systems which will efficiently probe particular classes of theoretical problems. The reasons for building specialized instrumentation in either case are similar; that we want to explore chemical questions beyond the range of what we can learn using general purpose commercial instrumentation which must sacrifice specific efficiency to generalized applicability. B. Plastic Hardware. We are accustomed to thinking of computer software as plastic, malleable; employed to adapt a general purpose computer to our specific needs. The advance of computer science and technology has now softened hardware as well, making it also plastic, moldable to effectively fit the task at hand. But while hardware is plastic, it still has restraints. It flows more easily in some directions than in others. Thus, the initial task is to find those chemical problems which are best suited to this natural direction of hardware flow. For example, it is now cheaper to replicate many identical hardware units than to produce even a few different units. Therefore, one direction of hardware flow is toward structures composed of many identical units, working in parallel (2-4). The American Chemical SocietyandLibrary Lykos; Minicomputers Large Scale Computations 1155 16th st. N . w. ACS Symposium Series; American Chemical Washington. D. C. Society: 2O036Washington, DC, 1977.

MINICOMPUTERS

148

AND LARGE

SCALE

COMPUTATIONS


congruent chemistry involves those t h e o r e t i c a l problems which can be cast i n t o forms i n v o l v i n g many simultaneous p a r a l l e l streams o f computation. C. Mechanical Molecules. One such chemical area i s the c l a s s i c a l mechanical treatment o f how n u c l e i , or roughly speaking atoms, i n t e r a c t on a Born-Oppenheimer p o t e n t i a l s u r f a c e . The i d e a t h a t the forces among a c o l l e c t i o n o f p a r t i c l e s determine both t h e i r s t a t i c c o n f i g u r a t i o n (molecular s t r u c t u r e ) and t h e i r motions (molecular dynamics) i s an o l d one. Newton, i n the 17th century, already understood the fundamental concepts o f c l a s s i c a l l y i n t e r a c t i n g p a r t i c l e s and considered t h a t macroscopic p r o p e r t i e s might r e s u l t from m i c r o s c o p i c i n t e r a c t i o n s . By the 19th century, with the acceptance o f the atomic theory, the view that chemistry should u l t i m a t e l y be an e x e r c i s e i n mechanics be came a popular one. The nature o f the underlying mechanics became apparent f i f t y years ago with the development o f quantum mechanics; i t i s now c l e a r that what the e l e c t r o n s are doing i s i n h e r e n t l y a quantum problem, but given a p o t e n t i a l surface derived e i t h e r from a t h e o r e t i c a l quantum computation o f e l e c t r o n i c energy or from a f i t to experimental measurements, that what the n u c l e i are doing both i n terms o f molecular s t r u c t u r e and molecular dynamics can be handled i n most cases reasonably w e l l by t h a t approximate form o f quantum mechanics c a l l e d c l a s s i c a l mechanics. (In a sense t h i s i s unfortunate, for chemistry would be an even more subtle and i n t e r e s t i n g p u z z l e i f P l a n c k s constant were l a r g e r . ) We w i l l thus concentrate here on the advantages which com p u t e r hardware p l a s t i c i t y can b r i n g to c l a s s i c a l molecular dy namics. (Molecular s t a t i c s o r molecular s t r u c t u r e w i l l be viewed i n t h i s context as that subset o f molecular dynamics for which the energy has been reduced to a g l o b a l minimum.) The s t r u c t u r e o f the computation i s exceedingly s i m p l e , a d e s i r a b l e s i t u a t i o n f o r a f i r s t essay i n t o a d i f f e r e n t mode o f s o l u t i o n . Given Ν atoms, we have, from Newton's Second Law, 1

F. = m. "

1

m

Q

£j ;

dt

Z± £±(£v

i = 1,

..., Ν

(1)

2

•••>iT )"-V V(r , N

i

...,r )

1

(2)

N

i n which j ; . , the force on the i t h atom, l o c a t e d at _r. , i s a func t i o n o f the p o s i t i o n s , · · · > JTN> °^ °^ ° whose masses are n ^ , n^, and V i s the Bom-Oppenheimer p o t e n t i a l t

n

e

s

e

t

a

t

m

s

surface seen by the n u c l e i .

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

12.

Molecular Dynamics

WILSON

149

D. Two Molecular Dynamics. S t r a n g e l y , the a p p l i c a t i o n o f t h i s viewpoint, that chemistry may be understood as the d e t a i l e d mechanics o f atomic motions, has l e d to two q u i t e d i s t i n c t f i e l d s , each c a l l e d by the same name, molecular dynamics, which have r e mained q u i t e separate f o r twenty y e a r s . Both f i e l d s , which are compared i n Table I , grew up i n the l a t e 1950 s , one (5) out o f s t a t i s t i c a l mechanics (SM), l a r g e l y (but not e x c l u s i v e l y ) concerned with e q u i l i b r i u m and steady s t a t e p r o p e r t i e s , u s u a l l y o f f l u i d s composed o f many simple p a r t i c l e s : hard spheres, atoms or s i m p l i f i e d molecules. The breakthrough which t r i g g e r e d the development o f the f i e l d was computational, the a b i l i t y provided by the e l e c t r o n i c computer to a c t u a l l y c a l c u l a t e the t r a j e c t o r i e s of many i n t e r a c t i n g p a r t i c l e s .


f

TABLE I .

Comparison of two f i e l d s

c a l l e d molecular dynamics

Category

Molecular Dynamics (SM)

Molecular Dynamics (CK)

historical antecedents

statistical

chemical k i n e t i c s

initiating breakthrough

computational

experimental

major application

e q u i l i b r i u m and steady s t a t e

chemical

number o f atoms

many

few

major state

liquid

vacuum ( i s o l a t e d molecules)

mechanics

reactions

The other molecular dynamics (6^, 7) grew out o f chemical k i n e t i c s (CK) and has been concerned with understanding the d e t a i l e d mechanics of the mechanisms o f chemical r e a c t i o n s , usua l l y i n v o l v i n g r e l a t i v e l y few atoms, s m a l l e r molecules c o l l i d i n g and r e a c t i n g i n i s o l a t i o n , the "vacuum" phase. The development of the f i e l d was i n i t i a t e d by experimental advances, the a b i l i t y p r o v i d e d by molecular beam and i n f r a r e d chemiluminescence t e c h niques to measure the r e s u l t s o f i n d i v i d u a l chemical r e a c t i o n events. What we are now attempting i s a synthesis drawing from both f i e l d s o f molecular dynamics, a computational advance which w i l l allow through mechanics the study o f the d e t a i l e d mechanisms o f chemical r e a c t i o n s i n v o l v i n g many atoms, often o c c u r r i n g i n solution.


150

MINICOMPUTERS AND LARGE

SCALE

COMPUTATIONS


E. D i f f i c u l t i e s and D i r e c t i o n s . Given that the s t r u c t u r e of E q s . (1) and (2) i s so s i m p l e , why i s n ' t the d e t a i l e d mech anism o f many-atom chemical r e a c t i o n s r o u t i n e l y s t u d i e d by com puting the t r a j e c t o r i e s o f the atoms? Three major d i f f i c u l t i e s are as f o l l o w s . 1. Potential surface. In r e a l i t y , we know q u a n t i t a t i v e l y r e l a t i v e l y l i t t l e about the b a s i c determinant o f molecular s t r u c t u r e and dynamics, the forces among atoms. I f we would have to compute from f i r s t p r i n c i p l e s the p o t e n t i a l surface to chemical accuracy s e p a r a t e l y f o r each large molecule o f i n t e r e s t along with a l l the i n t e r a c t i o n s with surrounding solvent mole c u l e s , the problem would seem insurmountable. Our chemical experience, c o n c e p t u a l i z a t i o n , nomenclature and system o f c a t a l o g i n g o f molecules, however, i s based on the f a i t h t h a t mole cules can be analyzed i n t o f u n c t i o n a l groups which r e t a i n t h e i r approximate i d e n t i t y and nature from molecule to molecule. Thus the force f u n c t i o n s , £^(£η> · · · > £ ) > to a f i r s t approximation should be decomposable i n t o i ) l o c a l force functions which describe chemical f u n c t i o n a l groups and which are approximately t r a n s f e r a b l e from molecule to molecule and i i ) terms which des c r i b e the i n t e r a c t i o n among f u n c t i o n a l groups. This t r a n s f e r a b l e force function approach has been e x t e n s i v e l y developed i n v i b r a t i o n a l spectroscopy ( 8 ) , organic chemistry (9-12) and biochemis t r y (13, 14) and the wide extent o f i t s a p p l i c a b i l i t y i s s t r e s s e d i n a recent review by Warshel (15), who describes both the usual type of f u l l y e m p i r i c a l p o t e n t i a l surface treatment and a v e r s i o n i n which π e l e c t r o n s are t r e a t e d i n a formulation de r i v e d from semiempirical quantum mechanics. Thus a reasonable approach to p o t e n t i a l surfaces i s the p a t i e n t c o l l e c t i o n and refinement with respect to t h e o r e t i c a l c a l c u l a t i o n s and comparison o f computed to measured parameters of a l i b r a r y o f force functions which should be at l e a s t approx imately t r a n s f e r a b l e from molecule to molecule. N

2. Computational speed. I f one wishes to study the de t a i l e d molecular dynamics o f r e a c t i o n s o f even simple molecules i n s o l u t i o n , one must consider at l e a s t a s i n g l e s o l v a t i o n s h e l l around each molecule, and thus at l e a s t the order o f 100 atoms. Given x, y and ζ components for E q s . (1) and (2), one must solve the order o f 300 coupled d i f f e r e n t i a l equations, i n t e g r a t i n g forward for thousands or perhaps m i l l i o n s of time steps. The number o f a r i t h m e t i c operations i n v o l v e d i s therefore i n e v i t a b l y large. I f one wishes to i n t e r a c t with the on-going c a l c u l a t i o n s , viewing the t r a j e c t o r i e s o f the atoms and seeing the r e s u l t s o f m o d i f i c a t i o n s o f parameters w i t h i n a reasonable waiting time, the p r o c e s s i n g system must be a r a p i d one even by today's l a r g e computer standards. T h i s d i f f i c u l t y , however, i s overshadowed by an even more demanding and s u b t l e one.



12.

WILSON

Molecular Dynamics

151

3. I n i t i a l c o n d i t i o n s . U n f o r t u n a t e l y , we u s u a l l y do not know i n advance where to s t a r t , which set o f i n i t i a l p o s i t i o n s and v e l o c i t i e s for the atoms w i l l l e a d , as time proceeds, to the chemical process o f i n t e r e s t . For most chemical r e a c t i o n s we can't j u s t assemble our molecules and allow them to r a t t l e around toward e q u i l i b r i u m , f o r on the time s c a l e o f i n t e r n a l molecular motion most chemical r e a c t i o n s o f i n t e r e s t w i l l a l most never occur i n an e q u i l i b r i u m system. Thus a random ap proach doesn't solve the problem. A quick c a l c u l a t i o n shows that a brute force systematic approach won't solve i t e i t h e r . Consider a systematic search through j u s t 10 d i f f e r e n t i n i t i a l p o s i t i o n vectors and 10 d i f ferent i n i t i a l v e l o c i t y vectors f o r each o f 100 atoms. This would give ΙΟΟίΟΟ = 1 0 (a number greater than the estimated number o f atoms i n the u n i v e r s e ) , d i f f e r e n t i n i t i a l phase space p o i n t s , each o f which would have to be i n t e g r a t e d forward i n time t o decide i f i t d i d indeed l e a d to the r e a c t i o n o f i n t e r e s t . Such a brute force approach i s now and w i l l always remain i n feasible. I f n e i t h e r random nor brute force systematic approaches are g e n e r a l l y f e a s i b l e , what can be done? One p o s s i b l e ap proach i s the development o f techniques to automatically i d e n t i fy c r i t i c a l configurations or saddle p o i n t s (or more p r e c i s e l y surfaces or regions i n phase space (16) through which r e a c t i o n t r a j e c t o r i e s must p a s s ) . I f one can i d e n t i f y such a phase space r e g i o n , one can then i n t e g r a t e both forward and backward i n time to t r a c e out the e n t i r e t r a j e c t o r y , and one can explore neighboring t r a j e c t o r i e s as w e l l . T h i s approach can be s t r a i g h t forward for systems with s u f f i c i e n t symmetry, such as defect jumps i n c r y s t a l s (17), and i t s extension to more complex mole c u l a r systems can a l s o be expected t o be pursued. Another a l t e r n a t i v e , perhaps complementary to the above, i s t o t r y to use the human chemist's accumulated understanding of the mechanisms o f chemical r e a c t i o n s to guide the machine's calculations. We chemists at l e a s t think we have some know ledge o f the way to r e l a t i v e l y o r i e n t two molecules and how to shove them at one another to get them to r e a c t . We t h i n k we have some f e e l i n g f o r the r e a c t i o n pathway from reactants to p r o d u c t s , for the bonds which must change and f o r the c r i t i c a l c o n f i g u r a t i o n s ( t r a n s i t i o n s t a t e s , a c t i v a t e d complexes) which must be t r a v e r s e d . U n f o r t u n a t e l y , t h i s chemists's understanding i s l a r g e l y p i c t o r i a l and i n t u i t i v e , but our computers need n u m e r i c a l guidance as to p o s i t i o n s and v e l o c i t i e s i n order to p r o ceed. T h i s need to b r i n g together the chemist's non-numerical mechanistic understanding o f the r e a c t i o n pathway with the machine's a b i l i t y t o c a l c u l a t e forward and backward along the r e a c t i o n t r a j e c t o r y once given the p o t e n t i a l surface and the atomic p o s i t i o n s and v e l o c i t i e s at any given p o i n t on the t r a j e c t o r y has l e d us to work on techniques of c l o s e r man-machine interaction. 2 0 0



152

MINICOMPUTERS

AND LARGE

SCALE

COMPUTATIONS

The f i r s t need i s v i s i o n . In order t o comprehend the molec u l a r dynamics o f r e a c t i o n s i n v o l v i n g a hundred or more atoms, i t i s imperative to be able to watch the motions, the t h r e e dimensional (3D) t r a j e c t o r i e s o f the atoms i n v o l v e d . Fortun a t e l y t h i s i s a w e l l - s o l v e d problem, with s e v e r a l s p e c i a l i z e d d i s p l a y systems now being commercially a v a i l a b l e which make f e a s i b l e the v i s u a l i z a t i o n o f the 3D motions o f hundreds o r even thousands o f atoms i n r e a l time (human, not molecular) and even i n c o l o r and/or s t e r e o , i f d e s i r e d . In a d d i t i o n , films can e a s i l y be made u s i n g even r e l a t i v e l y simple d i s p l a y t e r m i n als which can allow the o f f - l i n e v i s u a l i z a t i o n o f molecular dynamics. We q u i c k l y d i s c o v e r e d , however, that v i s i o n alone i s i n s u f ficient. We want to manipulate atoms, fragments w i t h i n molecules or e n t i r e molecules which are c l o s e l y surrounded by other atoms, fragments and molecules, i n order to a r r i v e at some p o i n t on a r e a c t i o n - p a t h phase-space t r a j e c t o r y . To do t h i s we must remain w i t h i n the energy range which i s thermally allowed. However i n a dense system, as i s w e l l known i n Monte Carlo c a l c u l a t i o n s (18), almost a l l randomly chosen new configurations are e n e r g e t i c a l l y i n a c c e s s i b l e , because the atoms are almost a l l already up against hard r e p u l s i v e w a l l s (19) and a random displacement w i l l almost always send the energy too h i g h . Thus, j u s t as p o t e n t i a l surface referenced importance sampling (18) i s used to guide the choice o f new configurations i n Monte C a r l o c a l c u l a t i o n s , some feedback from the p o t e n t i a l energy surface i s needed t o guide the human chemist i n manipulating atoms, fragments and molecules to reach a p o i n t on the r e a c t i o n p a t h . We have found that v i s i o n i s a poor feedback t o o l for maneuvering on a multidimensional p o t e n t i a l surface and we b e l i e v e that t h i s i s at l e a s t i n p a r t because touch r a t h e r than v i s i o n i s the n a t u r a l human sense when forces and torques are to be p e r ceived. This has l e d us to the development of man-machine touch i n t e r f a c e s (1_, 20) more c l o s e l y l i n k man and machine beyond what i s p o s s i b l e with v i s i o n alone. t

0

F. Goal. Our goal thus i s to develop and use an " i n s t r u ment f o r theory" which we c a l l NEWTON, a c l o s e r man-machine symbiosis focused on the understanding of the molecular dynamics o f many-atom chemical r e a c t i o n s , a machine which opens a window to the m i c r o s c o p i c world o f the 3D t r a j e c t o r i e s o f moving atoms, v i s u a l i z e d as we w i s h , elements l a b e l e d , bonds shown. We wish to be able to b u i l d up the system o f i n t e r e s t from atoms, fragments and molecules, adjusting the p o s i t i o n s and v e l o c i t i e s to correspond to our understanding o f mechanism, r e a c t i o n path and c r i t i c a l c o n f i g u r a t i o n i n order to i n i t i a t e the d e s i r e d chemical r e a c t i o n . We want to c o n t r o l energy, temperature and pressure by the turn o f knobs and t o d i s p l a y the c a l c u l a t e d values as the process proceeds. Our viewpoint (angle and zoom) should be v a r i a b l e , as w e l l as which atoms are to be



12.

WILSON

Molecular Dynamics

153

displayed. One should be able to c o n t r o l the speed of passage of computed time; i n c r e a s i n g (up to the computational l i m i t ) , decreasing, freeze framing, or backing up and then r e a d j u s t i n g parameters and r e s t u d y i n g . One would l i k e to c a l c u l a t e and d i s p l a y derived parameters such as bond lengths and angles, p r o gress along a defined r e a c t i o n coordinate or computed s p e c t r a to compare with measured s p e c t r a . In a d d i t i o n , a r e c o r d of the run, i n c l u d i n g a l l input parameters and atomic t r a j e c t o r i e s , should be stored for future a d d i t i o n a l a n a l y s i s . As we w i l l see i n the f o l l o w i n g s e c t i o n , most o f these instrumental goals have been achieved, at l e a s t , i n a p r e l i m i n a r y fashion. II.

Instrumentation

Two versions o f NEWTON have now been b u i l t and t e s t e d , the e a r l i e r v e r s i o n able to handle a few atoms and the present one a hundred or more atoms. A. I n i t i a l V e r s i o n . The f i r s t implementation of the NEWTON concept i s shown s c h e m a t i c a l l y i n Figure 1. As i t i s described elsewhere (1), i t w i l l only b r i e f l y be mentioned here. The equations o f motion are i n t e g r a t e d i n a minicomputer, the moving atoms are d i s p l a y e d on an Evans and Sutherland (E $ S) P i c t u r e System and the user can c o n t r o l the p o s i t i o n and v e l o c i t y of any s e l e c t e d atom by using the "Touchy-Feely" touch i n t e r f a c e , feeling the forces imparted by neighboring atoms. T h i s system served to show that such an instrument could be b u i l t , but was only adequate to handle a few i n t e r a c t i n g atoms and manipulate them atom by atom. B. Present V e r s i o n . The current system, which can handle a hundred i n t e r a c t i n g atoms f a s t enough for i n t e r a c t i v e use (at approximately 10 i n t e g r a t i o n time steps per second) i s shown as a block diagram i n Figure 2 and as a photograph i n Figure 3. Several hundred atoms can be handled at reduced speed. The equations o f motion are i n t e g r a t e d i n a F l o a t i n g Point Systems (FPS) AP120B Array Processor which runs f o r our a p p l i c a t i o n at a through-put o f s e v e r a l f l o a t i n g p o i n t operations per microsecond and which forms, with the help o f i t s h o s t , essentially a general-purpose processor capable of s e v e r a l simultaneous o p e r a t i o n s , with p a r a l l e l and p i p e l i n e d f l o a t i n g p o i n t adder and multiplier. At p r e s e n t , i t lacks d i r e c t higher l e v e l language capability. I t s approximate r e l a t i v e power may be judged by comparisons i n d i c a t i n g a speed 3 to 4 times slower (21) than a C o n t r o l Data Corporation (CDC) 7600 and 10 to 50 times f a s t e r (22) than a Data General (DG) E c l i p s e under Fortran V . It should be r e a l i z e d that a l l such comparisons are a f u n c t i o n o f program mix and e f f i c i e n c y of coding. V i s u a l i n t e r a c t i o n with the user i s through a dynamic 3D



MINICOMPUTERS

AND LARGE

χ

IBM

1800

CAMAC CRATE

CAMAC CRATE

SCALE

COMPUTATIONS

META 4

VISUAL PROCESSOR CAMAC CRATE

TTY

VISUAL INTERFACE

TOUCH INTERFACE

Figure 1. Block diagram of system used to test crudely the con cept of NEWTON. The touchstone of the touch interface drives the central carbon atom of a methane molecule, allowing it to be moved and the forces on it from the other atoms to be felt by the user. The molecule is displayed on the Evans à- Sutherland (Eb-S) Picture System, and the differential equations are integrated in real (human) time by the Digital Scientific Meta-4 computer to give the trajectories displayed on the Picture System. The Meta-4 is linked through three CAMAC crates and an IBM 1800 to the California Data Processors (CDP) 135 emulating a Digital Equipment Corporation (DEC) Ρ DP 11/40 which in turn runs symbiotically with the Picture System processor.



WILSON

Molecular Dynamics

155

UNIX COP

Figure 2. Block diagram of present NEWTON instrument designed for interactive study of the molecular dynamics of chemical reactions involving a hundred or more atoms. The user interacts with NEWTON by setting parameters such as temperature, pressure, and time step through knobs and teletype, by watching the motion of the atoms and the values of calculated parameters on the screen of the Eb-S Picture System and by adjusting the positions and velocities of atoms with the touch interface. The coupled differential equations (Newtons Second Law) are integrated in the Floating Point Systems (FPS) Array Processor to calculate the atomic trajectories. Other parts of the Chemistry Department Computer Facility (into which NEWTON is integrated) which are used as part of NEWTON include a CDF 135 emulating a DEC PDP 11/40 which serves as host for the Array Processor and the Picture System and a Varian 72 which handles disk management.



MINICOMPUTERS

AND LARGE

SCALE

COMPUTATIONS

Figure 3. Photograph of NEWTON showing Eù-S Picture System screen on the left, control knobs and FPS Array Processor in the background X TRANSLATION MOTOR

Figure 4. Schematic of "Touchy-Twisty' designed for force-torque—position—orientation man—machine communication, a touch interface to assemble and manipulate three-dimensional objects. A handball containing force-torque vector sensors is driven to position and orientation by three nester computerdriven rotational stages carried by three nested computer-driven transitional stages.



12.

WILSON

Molecular Dynamics

157

d i s p l a y u s i n g an Evans and Sutherland P i c t u r e System which allows the motions o f the a p p r o p r i a t e l y l a b e l e d atoms to be seen as they are c a l c u l a t e d . A C a l i f o r n i a Data Processors (CDP) 135 emulating a D i g i t a l Equipment Corporation (DEC) PDP 11/40 serves as host for both the Array Processor and the P i c t u r e System. B i n o c u l a r stereo and c o l o r presentations are a v a i l a b l e by v i s u a l f u s i o n of s p i n n i n g - d i s k c o n t r o l l e d s e q u e n t i a l images, but i n p r a c t i c e are only r a r e l y used. R o t a t i o n o f the system o f molec u l e s i s a b e t t e r depth cue and l a b e l i n g o f atoms i s a s u f f i c i e n t identifier. O r i e n t a t i o n of view, angular v e l o c i t y of r o t a t i o n and zoom are a l l c o n t r o l l a b l e by knobs and buttons. Temperature i s v a r i e d by k n o b - c o n t r o l l e d , mass-weighted v i s c o s i t y which removes energy as v i s c o s i t y i s increased or adds energy i f v i s c o s i t y i s formally made n e g a t i v e . E x t e r n a l pressure i s c o n t r o l l e d by changing the s i z e of an e l a s t i c - w a l l e d boundary cube. Other boundary c o n d i t i o n s , for example, p e r i o d i c r e p e t i t i o n or a f r e e f l o a t i n g drop are a l s o p o s s i b l e . Temperature and pressure are c a l c u l a t e d from atomic v e l o c i t i e s , forces and p o s i t i o n s and are d i s p l a y e d on the P i c t u r e System screen. NEWTON i s i n t e g r a t e d i n t o the Chemistry Department Computer F a c i l i t y , which i n c l u d e s a dozen processors interconnected through a system based on the CAMAC convention. Others of these processors which are used i n conjunction with NEWTON i n c l u d e a V a r i a n 72 which handles d i s k management, an IBM 1800 which cont r o l s p e r i p h e r a l s and a second CDP 135 emulating a DEC PDP 11/40 which runs a UNIX time-shared operating system used for program e d i t i n g and f i l e manipulation. C. Touch I n t e r f a c e . We wish to b u i l d up our chemical systems of i n t e r e s t not j u s t atom by atom, but from fragments and whole molecules and we wish a l s o to be able to reach i n t o the simulated volume and guide fragments and molecules i n t o the d e s i r e d coordinates and v e l o c i t i e s to a r r i v e at a p o i n t along the r e a c t i v e t r a j e c t o r y for the chemical process of i n t e r e s t . The atom by atom touch i n t e r f a c e d e s c r i b e d above, i n v o l v i n g force and p o s i t i o n (1^20), i s no longer s u f f i c i e n t i f we wish to assemble and manipulate three dimensional objects such as f r a g ments and molecules i n v o l v i n g f o r c e , torque, p o s i t i o n and o r i e n t a tion. Therefore we are b u i l d i n g (20) what we c a l l a "TouchyTwisty" which i s shown i n Figures 4-6. A b a l l for the u s e r ' s hand (the handball) i s d r i v e n by three nested computer-controlled t r a n s l a t i o n a l stages c a r r y i n g three nested computer-controlled r o t a t i o n a l stages to follow the x , y , z p o s i t i o n of the center of mass as w e l l as the o r i e n t a t i o n o f three defined axes w i t h i n a designated fragment or molecule. The force and torque v e c t o r s exerted by the user on the handball w i l l be sensed by i n t e r n a l f l e x i n g members with s t r a i n gauge pickups (see Figure 6) and w i l l be added a p p r o p r i a t e l y to the forces already exerted by surrounding atoms on each atom o f the designated molecule, and w i l l t h e r e f o r e a f f e c t the on-going




SCALE

COMPUTATIONS

Figure 5. Photograph of "Touchy-Twisty" partially constructed

Figure 6. Photograph of force-torque resolver inside handball, under construction. Strain gauges will be mounted on the flexing members to pick up components of force and torque.


12.

WILSON

Molecular Dynamics

159

c a l c u l a t i o n of that m o l e c u l e s t r a j e c t o r y . Thus, as the user t r i e s to t r a n s l a t e or r o t a t e the handball-molecule i n a way which matches chemical p o s s i b i l i t y as described by the p o t e n t i a l s u r f a c e , i t w i l l move r e l a t i v e l y f r e e l y , being unhindered by opposing forces from surrounding atoms. Conversely, i f one t r i e s to t r a n s l a t e or r o t a t e the handball-molecule so that r e p u l s i v e walls o f surrounding atoms are impinged upon, i t w i l l move only with d i f f i c u l t y , as these atoms must be shoved out o f the way to proceed. T h i s type o f touch i n t e r f a c e i s designed s p e c i f i c a l l y to i n t e r a c t with a dynamic system, as i t s communication with the user i s i n t i m a t e l y l i n k e d to the computer's a b i l i t y to s i m u l t a neously i n t e g r a t e the equations o f motion of the objects involved i n the dynamic s i m u l a t i o n .


f

III.

Chemical A p p l i c a t i o n s

While the mechanical molecule approach to the molecular dynamics o f many-atom chemical r e a c t i o n s i s i n p r i n c i p l e a p p l i c a b l e to almost any chemical r e a c t i o n , our lack o f s u f f i c i e n t general q u a n t i t a t i v e knowledge of interatomic forces makes i t wise to concentrate, at l e a s t i n i t i a l l y , on cases i n which the many-atom complexity a r i s e s l a r g e l y from the r e p e t i t i o n of simple u n i t s , for example polymers i n which the monomer i s the repeated u n i t and r e a c t i o n s of smaller molecules i n s o l u t i o n i n which the solvent molecule i s repeated, so that the number o f force parameters to be determined remains manageable. Two o f our current i n t e r e s t s are t h e r e f o r e dynamic approaches to v i b r a t i o n a l spectra i n s o l u t i o n and to the microscopic understanding o f solvation. A. Dynamic Approach to V i b r a t i o n a l S p e c t r a . I f we observe a small molecule, the v i b r a t i o n a l spectrum ( i n f r a r e d or Raman) i s a s e r i e s of w e l l - d e f i n e d l i n e s , and we know how to i n v e r t such s p e c t r a to gain information on the p o t e n t i a l surface near the e q u i l i b r i u m geometry (8, 23). I f we go to many-atom systems, i . e . large molecules or c o l l e c t i o n s o f c l o s e l y i n t e r a c t i n g molecules as i n a l i q u i d , instead o f w e l l - d e f i n e d l i n e s we f i n d broad continuous bands and we can no longer i n v e r t to the p o t e n t i a l surface i n the same d i r e c t way. However, we can s t i l l proceed i n the opposite d i r e c t i o n , c a l c u l a t i n g the v i b r a t i o n a l spectrum from the p o t e n t i a l energy s u r f a c e . (Such an approach was perhaps b e t t e r known before the day o f modern computers when a c t u a l mechanical models o f molecules were constructed from springs and masses and d r i v e n by an e c c e n t r i c disk on a motor whose speed was v a r i e d to f i n d the resonances corresponding to the normal f r e quencies (24, 25).) For example, we can use l i n e a r response theory (26-31) to r e l a t e the spectrum o f the n a t u r a l f l u c t u a t i o n s o f a parameter i n a system at e q u i l i b r i u m to the response spectrum we would f i n d i f we drove that parameter with a weak e x t e r n a l


160


SCALE

COMPUTATIONS

perturbation. Thus we can s t a r t with a p o t e n t i a l surface V(r . . . , r ) , c a l c u l a t e the t r a j e c t o r i e s r - ( t ) , £ (t) of atoms upon i t at e q u i l i b r i u m at a chosen temperature, c a l culate (for example, i n the f i r s t approximation by a s s i g n i n g p a r t i a l atomic charges) the time v a r y i n g d i p o l e moment y(t) from the t r a j e c t o r i e s , and then c a l c u l a t e the i n f r a r e d spectrum from the power spectrum or from the F o u r i e r transform o f the time c o r r e l a t i o n of the d i p o l e moment (29, 30). 1 5

N

V( , Downloaded by UNIV OF MASSACHUSETTS AMHERST on May 19, 2018 | https://pubs.acs.org Publication Date: June 1, 1977 | doi: 10.1021/bk-1977-0057.ch012

E l

N

r ) N

X l

(t),

r (t) N

- > }i(t) — • Α ( ω )

(3)

S i m i l a r l y , by assigning an approximate r e l a t i o n s h i p b e tween p o l a r i z a b i l i t y and atomic c o o r d i n a t e s , one should be able to compute Raman s p e c t r a . For example, we have used the L e m b e r g - S t i l l i n g e r p o t e n t i a l (32) f o r water to c a l c u l a t e i n f r a r e d s p e c t r a at approximately room temperature f o r e q u i l i b r a t e d i s o l a t e d water molecules and then for l a r g e r and l a r g e r c l u s t e r s . The spectrum s h i f t s smoothly from the gas-phase l i n e spectrum toward the broad bands c h a r a c t e r i s t i c o f the l i q u i d phase, the bending ( s c i s s o r s ) v i b r a t i o n moving up i n energy and broadening as expected and the asymmetric and symmetric s t r e t c h e s moving down i n energy and melding together to form what i n the l i q u i d i s a s i n g l e broad peak. The L e m b e r g - S t i l l i n g e r p o t e n t i a l was designed f o r somewhat d i f f e r e n t ends, and by i t s nature as a c e n t r a l force approximation, a sum o f two body terms, V ^ , V and V Q H

Q 0

i t cannot accurately reproduce the i s o l a t e d molecule spectrum. Nonetheless, i t i s i n s t r u c t i v e to see that the expected gas to l i q u i d s h i f t s are t a k i n g p l a c e as the c l u s t e r s i z e grows. S i m i l a r c a l c u l a t i o n s with more r e a l i s t i c p o t e n t i a l s are i n preparation for several l i q u i d s . There are two purposes to such c a l c u l a t i o n s . The f i r s t i s to improve our knowledge o f i n t e r a t o m i c f o r c e s , i n p a r t i c u l a r non-bonded and i n t e r m o l e c u l a r f o r c e s , which we need f o r f u r t h e r molecular dynamics s t u d i e s . For example, we can set up a parameterized p o t e n t i a l function which i s constrained i n regards to that which we know such as e q u i l i b r i u m bond lengths and angles and d i s s o c i a t i o n e n e r g i e s , but which contains a d j u s t able parameters such as those d e s c r i b i n g non-bonded i n t e r a c t i o n s . Then we can i t e r a t i v e l y change the adjustable parameters to t r y to gain b e t t e r agreement between c a l c u l a t e d and measured s p e c t r a , h o p e f u l l y converging on an improved p o t e n t i a l s u r f a c e . The second purpose i s to t r y to change our present under standing o f l i q u i d s t a t e v i b r a t i o n a l s p e c t r a , which i s mainly q u a l i t a t i v e , i n t o q u a n t i t a t i v e understanding based on p o t e n t i a l surfaces and molecular dynamics. For example, i f we b e l i e v e we have a reasonable p o t e n t i a l s u r f a c e , we should be able to assign



12.

WILSON

Molecular Dynamics

161

s p e c t r a l features by d r i v i n g the simulated system o f molecules with a simulated e l e c t r i c f i e l d o s c i l l a t i n g at the frequency o f the s p e c t r a l feature and then watching and analyzing the a c t u a l computed t r a j e c t o r i e s which the atoms follow i n response to t h i s perturbation. Such an approach i s not r e a l l y a new one, as i t resembles the technique (33) used f o r t y years ago to analyze s t r o b o s c o p i c a l l y the normal motions o f molecules modelled mechanically by masses and springs and d r i v e n by an external mechanical o s c i l l a t o r y p e r t u r b a t i o n . The advent of systematic procedures for the a n a l y s i s o f v i b r a t i o n a l l i n e spectra (8, 23) has made such mechanical molecule approaches unnecessary f o r few atom systems, but has not solved the problem for many-atom systems. With the present a v a i l a b i l i t y o f very f a s t computing systems such as our array processor and our a b i l i t y to v i s u a l l y recognize complex motions with the a i d o f dynamic computer g r a p h i c s , we can now apply t h i s mechanical molecule approach i n a new form to many-atom s p e c t r a , i n p a r t i c u l a r s p e c t r a i n s o l u t i o n . B. Dynamics o f S o l v a t i o n . A second area o f a p p l i c a t i o n i s the understanding o f s o l v a t i o n i n terms o f the t r a j e c t o r i e s o f the atoms. Most r e a c t i o n s o f i n t e r e s t to chemists and most o f the chemistry i n l i v i n g systems occur i n s o l u t i o n , yet we understand very l i t t l e o f s o l v a t i o n , and even l e s s o f chemical r e a c t i o n s i n s o l u t i o n , i n terms o f a q u a n t i t a t i v e microscopic p i c t u r e i n v o l v i n g atomic motions. The modelling of the molecular dynamics of s o l v a t i o n i n i s o l a t e d d r o p l e t s o f up to hundreds o f solvent molecules i s r e l a t i v e l y s t r a i g h t f o r w a r d ; the large d i f f i c u l t y comes i n t r y i n g to match the p r o p e r t i e s of bulk s o l u t i o n s with c a l c u l a t i o n s i n v o l v i n g f i n i t e numbers o f molecules. The key to the l a t t e r appears to be i n the boundary c o n d i t i o n s : whether to choose, f o r example, p e r i o d i c boundary c o n d i t i o n s , a d i e l e c t r i c - s u r r o u n d e d c a v i t y or a surface l a y e r which i s f i x e d i n the c o n f i g u r a t i o n o f bulk solvent (34). In the i l l u s t r a t i o n s shown i n Figures 7-9 we have chosen the easy way out, by modelling i s o l a t e d d r o p l e t s . These stereo p a i r s , which may be seen by most people i n depth by a s l i g h t c r o s s i n g o f the eyes, represent i n d i v i d u a l frames from the c a l c u l a t e d time h i s t o r y o f a water c l u s t e r , the s o l v a t i o n o f a c h l o r i d e ion i n water and the process o f d i s s o l u t i o n and s o l v a t i o n o f an u l t r a c r y s t a l l i t e o f NaCl i n water. The water p o t e n t i a l i s again L e m b e r g - S t i l l i n g e r (32) with e l e c t r o s t a t i c i n t e r a c t i o n s and approximate r e p u l s i v e cores for the i n t e r a c t i o n s with and among the i o n s . IV.

Some Thoughts on the Future

A. Future A p p l i c a t i o n s . The author suspects that i n the long r u n , the most i n t e r e s t i n g many-atom molecular dynamics i s l i k e l y to be found i n biomolecular r e a c t i o n s . While up to the p r e s e n t , biochemistry and molecular b i o l o g y have concentrated on



162

MINICOMPUTERS

Figure 7.

AND

LARGE

SCALE

COMPUTATIONS

A time-step in the evolution of a cluster of 31 water molecules

Figure 8.

A time-step in the history of a chloride ion solvated in an isolated water droplet

Figure 9.

and ion solvation of a crystallite of NaCl A time-step in the dissolution



12.

WILSON

Molecular Dynamics

163

s t a t i c s , i . e . the r e l a t i o n s h i p o f s t r u c t u r e and f u n c t i o n , i t seems c l e a r that the f u n c t i o n i n g o f at l e a s t many o f the most i n t e r e s t i n g biomolecules must be understood i n terms o f dynamics, t h e i r time e v o l u t i o n . A very long p e r i o d o f s e l e c t i o n has undoubtedly moulded many biomolecules i n t o very e f f i c i e n t machines whose dynamics as yet i s l a r g e l y s p e c u l a t i v e . Examples of such biomachinery are to be found i n enzymic a c t i o n (35) and a l l o s t e r i c e f f e c t s , muscle c o n t r a c t i o n , membrane transport ( p a r t i c u l a r l y a c t i v e t r a n s p o r t ) , aspects o f drug-receptor i n t e r a c t i o n , and biomolecular self-assembly. Perhaps as the past twenty years have seen such great progress i n the understanding of biomolecular s t r u c t u r e - f u n c t i o n r e l a t i o n s h i p s , the next twenty years may see s i m i l a r progress i n understanding the more complete p i c t u r e of biomolecular s t r u c t u r e - d y n a m i c s - f u n c t i o n . While some molecular dynamic c a l c u l a t i o n s on biomolecules are already i n progress i n batch mode, for example r e t i n a l photoi s o m e r i z a t i o n (36), water around a d i p e p t i d e to study the d i f f e r e n c e i n dynamics near h y d r o p h i l i c and hydrophobic s i t e s (37) and motions o f a s i m p l i f i e d small p r o t e i n , p a n c r e a t i c t r y p s i n i n h i b i t o r (38), such c a l c u l a t i o n s are s e v e r e l y hindered by l i m i t s to a v a i l a b l e computational speed. How can such l i m i t s be transcended? B. F a s t e r Computation. With a few more orders o f magnitude i n computer speed, the mechanism o f most r e a c t i o n s of i n t e r e s t to chemists would be a c c e s s i b l e to study by many-atom molecular dynamics. How can such speed increases be achieved? Two d i r e c t i o n s are apparent: more powerful elements ( i n t e g r a t e d c i r c u i t s ) and the i n t e r c o n n e c t i o n o f these elements i n a r c h i t e c t u r e s which more e f f i c i e n t l y match the problem to be s o l v e d . I t i s thought that there i s another f a c t o r o f 30 s t i l l to be r e a l i z e d i n l i n e a r shrinkage i n metal oxide semiconductor (MOS) technology before fundamental p h y s i c a l l i m i t s are reached (39). T h i s t r a n s l a t e s i n t o a 30 increase i n packing d e n s i t y on a chip and another f a c t o r o f 30 i n speed, f o r a t o t a l gain o f perhaps four orders of magnitude. Thus we can look forward to continuing s u b s t a n t i a l gains i n computational power per element by t h i s and probably by other routes as w e l l . A complementary approach i s the a r c h i t e c t u r e o f interconnecting the elements. The c l a s s i c a l mechanics of a set of i n t e r a c t i n g p a r t i c l e s i s a problem p a r t i c u l a r l y amenable to s p e c i a l i z e d computer a r c h i t e c t u r e because i ) the algorithms are r e l a t i v e l y 2

* Such increases i n s p e c i a l i z e d computer power are i n progress i n other areas as w e l l (1_) . Examples i n c l u d e the P a r a l l e l E l e ment Processing Ensemble (PEPE) f o r m i s s i l e t r a c k i n g b e i n g cons t r u c t e d f o r the Army Advanced B a l l i s t i c M i s s i l e Defense Agency which i s designed (4) to run many times f a s t e r than any e x i s t i n g general purpose processor as w e l l as the s p e c i a l aerodynamic computer (40) being considered by NASA which would be two orders o f magnitude f a s t e r than e x i s t i n g general purpose machines.


MINICOMPUTERS


164

AND LARGE

SCALE

COMPUTATIONS

simple and h i g h l y r e p e t i t i v e and i i ) the computation can be s p l i t i n t o p a r a l l e l streams which need communicate only once (or p e r haps a few times with more complex i n t e g r a t i o n schemes) f o r each i n t e g r a t i o n time s t e p . Thus, i n s t e a d o f an array processor we can consider arrays o f processors or even arrays o f array p r o cessors (1). When one considers such computational systems composed o f so many a c t i v e elements, s e v e r a l s i m i l a r i t i e s between computer a r c h i t e c t u r e and molecular a r c h i t e c t u r e become evident (39). The b a s i c determinant o f s t r u c t u r e becomes not the l o g i c a l e l e ments (atoms) themselves, but r a t h e r t h e i r interconnections (bonds) and these now become the focus o f design (39) as shown i n Table I I . Table I I .

E v o l u t i o n o f emphasis o f computer a r c h i t e c t u r e l o g i c a l elements to interconnections (39).

from

Characteristics

Past

Future

large,

slow,

expensive

logical elements

interconnections

small,

fast,

cheap

interconnections

logical

elements

Because computer a r c h i t e c t u r e can now be constructed cont a i n i n g so many elements and i n t e r c o n n e c t i o n s , the same problems in human c o n c e p t u a l i z a t i o n a r i s e as i n systems composed o f many atoms and bonds, that no one person can p o s s i b l y understand a l l the r e l a t i o n s h i p s among the i n d i v i d u a l d e t a i l e d p a r t s o f the system. In response, the same approach o f emphasizing the symmetry o f the s i t u a t i o n becomes u s e f u l . For example, one obvious way o f i n t e r c o n n e c t i n g processors i n p a r a l l e l i s a s i n g l e bus, as shown i n Figure 10. To a chemi s t t h i s i s a l i n e a r polymer and shares i t s symmetry. I f one branches the b u s , i t ' s a branched polymer, o r one can make c y c l i c systems, e t c . A very appealing s o l u t i o n f o r a problem such as molecular dynamics which i s to be solved i n terms o f C a r t e s i a n space i s to map the 3D problem space onto a 3D space o f an array o f p r o c e s sors (39) , an example o f which i s shown i n Figure 11. Two ways of c a r r y i n g out such a mapping f o r our case are as f o l l o w s . F i r s t , one could map each atom onto a processor and then "dyn a m i c a l l y r e a l l o c a t e processors" so as to maintain near n e i g h bor r e l a t i o n s h i p s as atoms move about on t h e i r t r a j e c t o r i e s . A key question to i n v e s t i g a t e i s whether there i s a l o c a l r e a l l o c a t i o n algorithm which w i l l e f f i c i e n t l y maintain a s a t i s f a c t o r y mapping by querying only other processors i n the v i c i n i t y , and then exchanging assignments o f processors to atoms. A second



12.

WILSON

Molecular Dynamics

165

PROCESSORS

oooooooo BUS Figure 10. The symmetry of an array of processors connected by a bus, or equivalently the symmetry of a linear polymer

Figure 11. The symmetry of a simple cubic 3D array of processors, or equivalently of a 3D simple cubic crystal lattice



166

MINICOMPUTERS

AND LARGE SCALE

COMPUTATIONS

approach i s t o map regions o f 3D coordinate space onto s p e c i f i c p r o c e s s o r s ; i n other words, to d i v i d e a l l the space i n which the atoms move i n t o volumes such that each processor takes care o f a l l atoms which happen to be i n that volume. When an atom crosses the boundary o f t h a t volume, i t would be reassigned to the processor h a n d l i n g the adjacent volume. In c o n s i d e r i n g such a scheme, i t i s important to note t h a t the force on any given r e a l atom i s only a function o f the p o s i t i o n s o f other atoms w i t h i n some f i n i t e volume about that atom (1) and thus that each processor only need communicate with a l o c a l i z e d set o f other p r o c e s s o r s . Thus i n the l i m i t o f a very large number Ν o f atoms, the number o f a r i t h m e t i c operations r e q u i r e d , i f done p r o p e r l y , to solve the molecular dynamics i n creases only p r o p o r t i o n a l l y to N , i n contrast to widely h e l d opinion (shared u n t i l r e c e n t l y by the author) t h a t i t must r i s e f a s t e r than N . T h i s i s t r u e both i n force c a l c u l a t i o n from a r e a l i s t i c p o t e n t i a l surface i n c l a s s i c a l mechanics, i n that i n r e a l i t y a l l i n t e r a t o m i c forces i n dense systems are damped out at some d i s t a n c e by i n t e r v e n i n g movable and p o l a r i z a b l e atoms as w e l l as i n quantum mechanics i n that i n t e g r a l s among o r b i t a l s s u f f i c i e n t l y separated can be ignored. I f we consider 3D arrays o f p r o c e s s o r s , we chemists already know a l l the p o s s i b l e d i f f e r e n t symmetries o f how to b u i l d the processor array (39), the " c r y s t a l computer" (41) . The p o s s i b l e symmetries w i t h i n each u n i t composing the array are j u s t the symmetries o f c r y s t a l u n i t c e l l s and the symmetries with which the u n i t s can be stacked o r interconnected i n t o 3D arrays are j u s t the l a t t i c e symmetries, the 14 Bravais l a t t i c e s , the grand t o t a l o f a l l combined u n i t c e l l and l a t t i c e symmetry p o s s i b i l i t i e s b e i n g the 230 space groups (42). I f we r e s t r i c t ourselves to b u i l d i n g from symmetric, i d e n t i c a l u n i t s which stack i n t o a s p a c e - f i l l i n g 3D a r r a y , the p o s s i b i l i t i e s are even more l i m i t e d and i n fact we can r e f e r back to the Greeks for the s o l i d t e s s e l lations. Out o f the r e g u l a r and Archimedean polyhedra there are only 5 which are space f i l l i n g : the cube, t r i a n g u l a r p r i s m , hex agonal p r i s m , rhombic dodecahedron and t r u n c a t e d octahedron (43). C. Other Instruments for Theory. One can imagine other instruments f o r other t h e o r i e s . Instead o f a NEWTON f o r c l a s s i cal mechanics, one could consider b u i l d i n g a machine for quantum c a l c u l a t i o n s , a SCHRODINGER o r a HEISENBERG. One can again map 3D c o n f i g u r a t i o n space onto a 3D array o f p r o c e s s o r s , e i t h e r o r b i t a l (s) or atom(s) to p r o c e s s o r or volume o f space to p r o c e s s o r . And a g a i n , as the number Ν o f atoms grows large enough, one r e gion o f space w i l l no longer d i r e c t l y a f f e c t another and the a r i t h m e t i c operations i n v o l v e d i n the c a l c u l a t i o n w i l l s c a l e , i n the l i m i t o f q u i t e large N , p r o p o r t i o n a l l y as N . L a s t l y , one might want to b u i l d a SEMI, a s e m i c l a s s i c a l i n strument f o r s o l v i n g quantum mechanically ( e i t h e r ab i n i t i o or semi empiric a l l y ) for the e l e c t r o n i c wavefunction and using t h i s


12.

Molecular Dynamics

167

wavefunction to a n a l y t i c a l l y derive (44-46, 8_, 15) on the f l y a force function for the n u c l e i whose t r a j e c t o r i e s are being i n t e grated c l a s s i c a l l y . For a system o f very large Ν i t i s no longer f e a s i b l e to c a l c u l a t e and s t o r e a p o t e n t i a l function Cl , £ j j i n advance on a 3N - 6 dimensional mesh. For s e m i c l a s s i c a l dynamics, a l l one needs anyway are the forces at those r e l a t i v e l y few p o i n t s a c t u a l l y sampled by the sequence o f n u c l e a r coordinate sets generated by the c l a s s i c a l numerical i n t e g r a t i o n o f the n u c l e a r t r a j e c t o r i e s . It should be noted that a l l o f the instruments for theory described above could be implemented as the same 3D array o f stored-program p r o c e s s o r s . v


WILSON

V.

1

Summary

While we chemists have long b u i l t s p e c i a l i z e d instruments f o r experimental s t u d i e s , we are now d i s c o v e r i n g that we can also b u i l d s p e c i a l i z e d instruments f o r theory, computational apparatus designed to e f f i c i e n t l y solve p a r t i c u l a r classes o f chemical problems. An example i s NEWTON, an instrument we have constructed to study the d e t a i l e d mechanism, i . e . the molecular dynamics, of many-atom chemical r e a c t i o n s , p a r t i c u l a r l y i n s o l u tion. NEWTON allows the chemist to c o n t r o l the s t a t e o f a simulated system o f i n t e r a c t i n g molecules: s e l e c t i o n o f the p a r t i c u l a r molecules, i n i t i a l conditions o f p o s i t i o n and v e l o c i t y , parameters o f the p o t e n t i a l surface, temperature and p r e s s u r e . In response, atomic t r a j e c t o r i e s are c l a s s i c a l l y i n t e g r a t e d on the i n t e r a t o m i c p o t e n t i a l surface i n a very fast p r o c e s s o r . The chemist can watch the e v o l v i n g molecular dynamics on a 3D d i s p l a y and i n t e r a c t with the molecules through knobs, keyboard and touch i n t e r f a c e . A p p l i c a t i o n s i n progress i n c l u d e dynamic s t u d i e s o f v i b r a t i o n a l s p e c t r a i n s o l u t i o n and the dynamics o f the s o l v a t i o n process. With i n c r e a s e d computer speed, much o f biochemistry might become a c c e s s i b l e ; the r e l a t i o n among s t r u c t u r e , dynamics and function for example i n enzymic a c t i o n , a c t i v e t r a n s p o r t and biomolecular s e l f - a s s e m b l y . Hope f o r such speed increases l i e s i n two d i r e c t i o n s : more power per computational u n i t and the adaptation o f o v e r - a l l computer a r c h i t e c t u r e to match the s t r u c ture o f the problem to be s o l v e d . A p a r t i c u l a r l y appealing route i s the mapping o f c a l c u l a t i o n s i n three dimensional con f i g u r a t i o n space onto a three dimensional array o f p a r a l l e l p r o c e s s o r s , a route which can be a p p l i e d e q u a l l y to c l a s s i c a l , s e m i - c l a s s i c a l and quantum c a l c u l a t i o n s , a l l o f which can be shown to s c a l e only p r o p o r t i o n a l l y to the number Ν o f atoms i n the l i m i t o f very large N . Acknowledgement The v i b r a t i o n a l s p e c t r a and dynamics o f s o l v a t i o n are by


168

MINICOMPUTERS AND LARGE SCALE COMPUTATIONS

Peter Berens. Thanks to John Cornelius and the staff of the Chemistry Department Computer Facility for their help, to Sylvia Francl for aid on vibrational spectra, and to the Division of Computer Research of the National Science Foundation and to the Division of Research Resources, National Institutes of Health (RR-00757) whose support has made this work possible. Literature Cited Downloaded by UNIV OF MASSACHUSETTS AMHERST on May 19, 2018 | https://pubs.acs.org Publication Date: June 1, 1977 | doi: 10.1021/bk-1977-0057.ch012

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.

16. 17.

Wilson, K. R. in "Computer Networking and Chemistry," Lykos, P., ed., American Chemical Society, Washington, D. C . , 1975, p. 17. Murtha, J . C . , Adv. Computers (1966) 7, 1. Lorin, H . , "Parallelism in Hardware and Software," PrenticeHall, Inc., Englewood Cliffs, New Jersey, 1972. Comptre Corporation, Enslow, Philip H . , Jr., ed., "Multi processors and Parallel Processing," John Wiley & Sons, New York, 1974. Berne, B. J., ed., "Statistical Mechanics, Part B: TimeDependent Processes," Vol. 6 of "Modern Theoretical Chemistry," Plenum Publishing, New York, 1977. Levine, R. D., and Bernstein, R. B., "Molecular Reaction Dynamics," Oxford University Press, New York, 1974. Miller, W. Η., ed., "Dynamics of Molecular Collisions, Parts A & Β," Vols. 1 & 2 of "Modern Theoretical Chemistry," Plenum Publishing, New York, 1976. Califano, S., "Vibrational States," John Wiley, London, 1976. Williams, J . D., Stand, P. J., and Schleyer, P.v.R., Ann. Rev. Phys. Chem. (1968) 19, 531. Kitaigorodsky, A. I., "Molecular Crystals and Molecules," Academic Press, New York, 1973. Hopfinger, A. J., "Conformational Properties of Macromolecules," Academic Press, New York, 1973. Shipman, L. L., Burgess, W., and Sheraga, Η. Α., Proc. Nat. Acad. Sci. USA (1975) 72, 543. Blout, E. R., Bovey, F. Α., Goodman, Μ., and Lotan, Ν., eds., "Peptides, Polypeptides and Proteins," John Wiley & Sons, New York, 1974. Momany, F. Α., McGuire, R. F . , Burgess, A. W., and Sheraga, Η. Α., J . Phys. Chem. (1975) 79, 2361. Warshel, A. in "Semiempirical Methods of Electronic Struc ture Calculation, Part A: Techniques," Segal, G. A., ed., Vol. 7 of "Modern Theoretical Chemistry," Plenum Pub lishing, New York, 1977. Bunker, D. L., "Theory of Elementary Gas Reaction Rates," Pergamon Press, Oxford, 1966, Sections 2.2 and 3.2. Bennett, C. H . , in "Diffusion in Solids: Recent Develop ments," Burton, J . J., and Nowich, A. S., eds., Academic Press, New York, 1975.


12. WILSON 18.

19. 20.


21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41.

Molecular Dynamics

169

Valleau, J . P., and Whittington, S. G., in "Statistical Mechanics, Part A: Equilibrium Techniques," Berne, B. J., ed., Vol. 5 of "Modern Theoretical Chemistry," Plenum Pub lishing, New York, 1977. Weeks, J. D., Chandler, D., and Andersen, H. C., J . Chem. Phys. (1971) 54, 5237. Atkinson, W. D., Bond, Κ. E . , Tribale, G. L. III, and Wilson, K. R., Comput. $ Graphics (1977) 2, 97. Sutherland, G., Lawrence Livermore Laboratories, Livermore, California, private communication. Park, T. C., Loma Linda University, Loma Linda, California, private communication. Wilson, Ε. B. J r . , Decius, J . C., and Cross, P. C., "Mole cular Vibrations," McGraw-Hill, New York, 1955. Kettering, C. F., Shutts, L. W., and Andrews, D. H., Phys. Rev. (1930) 36, 531. Herzberg, G. Η., "Molecular Spectra and Molecular Structure II. Infrared and Raman Spectra of Polyatomic Molecules," D. Van Nostrand, Princeton, New Jersey, 1945. Kubo, R. in "Lectures in Theoretical Physics Vol. 1," Brittin, W. F., and Dunham, L. G., eds., Interscience Publishers, New York, 1959. Kadanoff, L. P., and Martin, P. C., Ann. Phys. (1963) 24, 419. Felderhof, B. U., and Oppenheim, I., Physica (1965) 31, 1441. Gordon, R. G., Advan. Magn. Resonance (1968) 3, 1. Berne, B. J., in "Physical Chemistry, An Advanced Treatise, Vol. VIIIB, Liquid State," Henderson, D., ed., Academic Press, New York, 1971. Kampen, N. G. van, Physica Norvegica (1971) 5, 10. Lemberg, H. L . , and Stillinger, F. H., J. Chem. Phys. (1975) 62, 1677. Andrews, D. H., and Murray, J. W., J . Chem. Phys. (1934) 2, 634. Warshel, Α., University of Southern California, Los Angeles, California, private communication. Warshel, Α., and Levitt, Μ., J . Mol. Biol. (1976) 103, 227. Warshel, Α., Nature (1976) 260, 679. Karplus, Μ., and Rossky, P. J., "Abstracts of Papers," Chemical Institute of Canada and American Chemical Society, Montreal, 1977, phys. 66. Levitt, Μ., MRC Laboratory of Molecular Biology, Cambridge, U. Κ., private communication. Sutherland, I. E . , California Institute of Technology, Pasadena, California, private communication. Datamation (March, 1977) 23, 150. O'Leary, G., Floating Point Systems, Portland, Oregon, private communication.


170 42. 43. 44.

Henry, N. F. Μ., and Lonsdale, Κ., eds., "International Tables for X-Ray Crystallography Vol. 1," Kynoch Press, Birmingham, England, 1952. Cundy, Η. Μ., and Rollett, A. P., "Mathematical Models," Oxford University Press, London, 1961. Gerratt, J., and Mills, I. M., J. Chem. Phys. (1968) 49, 1719. Pulay, P., Molec. Phys. (1969) 17, 197. Pulay, P., and Török, F., Molec. Phys. (1973) 25, 1153.


45. 46.

MINICOMPUTERS AND LARGE SCALE COMPUTATIONS


Many-Atom Molecular Dynamics with an Array Processor - ACS

Recommend Documents