EXACT CONSTRAINT METHODS FOR MOLECULAR DYNAMICS

COMPUTATIONALLY EFFICIENT MOLECULAR DYNAMICS ALGORITHMS ARE AN ENABLING TECHNOLOGY TO DEAL WITH PRACTICAL PROBLEMS IN RATIONAL DRUG DESIGN, IN THE DESIGN OF ADVANCED POLYMER COMPOSITES, AND IN THE CHOICE OF PROPER ZEOLITE MOLECULAR FILTERS FOR FUEL OPTIMIZATION FROM PETROLEUM PRODUCTION. SIMPLE UNCONSTRAINED MOLECULAR DYNAMICS SIMULATIONS NEED TO USE SMALL STEPS TO TRACK THE HIGH FREQUENCY DYNAMICS THAT RESULT FROM STIFF SPRINGS REPRESENTING BONDS AND ANGLES. TO INCREASE THE STEP SIZE, CONSTRAINTS ARE INTRODUCED IN THE PARTICLE EQUATIONS BY INCLUDING A TERM REPRESENTING THE CONSTRAINT GRADIENT MULTIPLIED BY A LAGRANGE MULTIPLIER. WHILE STILL RIGOROUS, ITINTRODUCES NEW COMPUTATIONAL OVERHEADS, AND THIS HAS LED, IN TURN, TO THE APPROXIMATE AND NOT ENTIRELY SATISFACTORY SHAKE ALGORITHM. SHAKE WORKS WELL WITH BONDS AND ANGLES, BUT FAILS TO GENERALIZE ARBITRARY CONSTRAINTS. AN ALGORITHM ORIGINATING IN THE SPACECRAFT WORLD IS PROPOSED THAT RECURSIVELY FINDS AN EXACT SOLUTION TO THE LAGRANGE MULTIPLIERS. THE ALGORITHM, CALLED EXACT, REPRESENTS AN EXACT CONSTRAINT TECHNIQUE, CAN HANDLE OPEN AND CLOSED LOOPS, IS HIGHLY EFFICIENT, CAN GENERALIZE TO ARBITRARY CONSTRAINTS, AND IS WELL-SUITED FOR PARALLEL IMPLEMENTATION. EARLY TEST INDICATIONS SHOW GREAT COMPUTATIONAL EFFICIENCY THROUGH LARGE STEP SIZES, IMPROVED ACCURACY, AND GREAT VERSATILITY IN THE CHOICE OF CONSTRAINTS.