Low Energy Path OPTmization This method optimizes a low energy path between a series of molecular structures. Energy minimization is done with constraints on center of mass translation, rotation and orthogonality of step to path vector. Reference : Choi, C. and Elber, R., J. Chem. Phys. 94:751 (1991) Source Code : rxncor/lupopt.src Krzysztof Kuczera, 12-Mar-1997, Lawrence, KS. * Menu: * Syntax:: Syntax of the LUPOpt command * Description:: Description of the keywords and options for setting up the low energy path calculation. * Memory:: Memory Requirements

Syntax for the LUPOpt Command LUPOpt [NPATh integer] [UOUT integer] [INIT integer] - [EPSEner real] [MAXCycle integer] [STEP real] [IPVOpt integer] - [LPrint integer] [for 'INIT 2' this line should be followed directly by NPATH lines containing names of formatted CHARMM COOR files, no blank lines] Variable Default Meaning NPATH MXPATH Number of path points UOUT 21 Unit number for output trajectory with optimized path INIT 1 Initialization mode: =1 - straight line in Cartesian space from MAIN to COMP coordinates =2 - read path from set of files, file names supplied below, 1 per line, no blank lines EPSE 0.001 Structure will be classified as converged if energy change is lower than EPSE in one step MAXC 100 Number of path optimization cycles. Each cycle involves making one SD step for each of the structures 2,3,...,NPATH-1 STEP 0.01 Length of optimization step in CHARMM units IPVO 1 Path vector option =1 - standard option, path vector is I -> I+1 =2 - symmetric option, path vector is I-1 -> I+1 LPRINT 1 Frequency of printing out path energies

Algorithm description: ---------------------- Work is in Caretsian space, path optimized by constrained steepest descent. See C.Choi & R.Elber, J.Chem.Phys. 94:751-760 (1991). 1. An initial conformational path is read in a) linear interpolation between MAIN and COMP coordinates b) series of structures in CHARMM COOR files (see LUPINI) structures I=1,2,...,NPATH 2. For each structure inside path I=2,3,...,NPATH-1 a. Path vector is computed b. A steepest descent step is taken, subject to rigid-body and path constraints (see LUPCNS) c. Step is accepted if energy decreases d. Convergence is checked by monitoring energy change 3. If procedure has converged along whole path, stop; otherwise return to step 2, possibly decreasing step. Path initialization: -------------------- Option 1 is simplest, but may lead to very poor initial guess, even for buatne t->g! Option 2 is more involved, but allows for more flexibility. E.g. model structires along a straight line in dihedral space may be generated from CHARMM or QUANTA, or a TRAVEL path may be input. Path optimization: ------------------ For each structure gradient components along 7 LUP constraints are removed (see LUPCNS) and a steepest descent (SD) step is performed. The step length is formally STEP, due to CHARMM conventions it is actually STEP*SQRT(NATOM), i.e. Xi -> Xi - (STEP/GNORM)*Gi where Xi -coordinate, Gi - gradient component, GNORM = SQRT[(Sum_i Gi**2)/Natom] If the energy of the new structure is lower than before, the step is accepted and new coords are stored on HEAP; if the energy is higher, the step is rejected and coordinates are reset. If steps are rejected for more than half of the structures in a cycle, STEP is divided by 2. Progress in path optimization is monitored by printing out energies of all current structures every LPRI cycles. Path constraints: ----------------- The 7 constraints involve : 1-6 : rigid body translations and rotations and 7: the path vector. See LUPCNS As described by Ron Elber, the constraints are linear in Cartesian coordinates, i.e. their Cartesian gradinets are 3*Natom dimensional constant vectors. To simplify procedure the vectors are orthonormalized. Gradient projections along these vectors are then eliminated.

Memory Usage The INTEGER*4 arrays of heap pointers IBX,IBY,IBZ are given a fixed dimension in LUPOPT: MXPATH=200. This can be changed by hand. Memory could be a problem for large systems. The path structures are stored on the HEAP : NPATH*3*NATOM REAL*8 Constraint vectors, also on heap 7*3*NATOM REAL*8 One working coordinate set 3*NATOM REAL*8 Altogether: (NPATH+8)*3*NATOM REAL*8 + neglible extras for pointers and coorio

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