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Subsections


Geometry Optimization

DivCon includes various optimization techniques[] to locate both minima and first-order saddle points (transition structures). On the one hand, the algorithms for locating minima are specially adapted to treat large optimization problems. On the other hand, the methods for optimizing transition structures in DivCon work reasonably well for small and medium size systems.

General Minimization Parameters


MAXOPT=int / OPTMAX=int

Do a maximum of int cycles of optimization. Default: 10 x Number of Geometrical Parameters. (Note: MAXOPT and OPTMAX are interchangeable)


RESTART

Read in restart file from previous run. To create the restart file, please see DUMP (page [*]).


ETEST=float

User-defined geometry optimization energy change criterion. Default : 0.002 kcal/mol.


GTEST=float

User-defined maximum gradient component criterion. Default : 0.500 kcal/ (mol Å).


XTEST=float

User-defined geometry optimization coordinate change criterion. Default : 0.001 Å / 0.001 degrees.


Minimum Optimization

For the semiempirical minimization of large biomolecules, it is advisable to take the starting point from a previously Force-Field minimized structure. The current default optimization method when using OPT alone is LBFGS. The default is subject to change in future DivCon versions.


OPT=STEEP (-opt steep)

Geometry optimization proceeds by means of function evaluations along the search direction defined as the minus gradient vector. The steepest descent algorithm is very simple and requires only storage of the gradient. It is well known that this method can oscillate around the minimum path towards the critical point and its rate of convergence slows down as the minimum is approached. STEEP should be used mainly to partially relax a poor starting point during a given number of optimization cycles.


OPT=CONJGRAD (-opt conjgrad)

The conjugate gradient method performs quite robust energy minimization along a line that is constructed so that it is "conjugate" to the previous search directions. This avoids the partial "undoing" on every optimization step observed in the steepest descent method. The conjugate gradient method avoids handling of the Hessian and requires only storage for two gradient vectors. Usually, this has been the method of choice for treating very large systems (hundreds and thousand of atoms) by means of classical Force Field or Quantum Mechanical Semiempirical methods.


OPT=BFGS (-opt bfgs)

A fast pseudo Newton-Raphson algorithm, which expands the Energy function to second order around the current point using an approximate Hessian, is also implemented in DivCon. The BFGS (Broyden-Fletcher-Goldfarb-Shanno) formula is the most popular Hessian updating scheme to minimize molecular geometries and ensures the positive definite character of the updated Hessian matrix. However, the method requires the storage, inversion and updating of the full Hessian matrix. This algorithm is practical for only medium size systems.


OPT=LBFGS (-opt lbfgs / -opt)

The Limited memory BFGS minimizer can be used to minimize large systems efficiently[]. The LBFGS method stores only diagonal Hessian and small number m of previous steps and gradient vectors. This pseudo Newton-Raphson algorithm performs quite well for highly non-linear functions, requiring about 2 times less function and gradient evaluations than the Conjugate Gradient method implemented in DivCon. This method should be used routinely when optimizing large systems.


LSEARCH=float / NOLNSR

LSEARCH is a variable with default value of 1.0, which controls the accuracy of the line search routine in the LBFGS minimizer. Lower values result in a more accurate linear search at the cost of requiring more energy and gradient evaluations. If the linear search fails during a LBFGS minimization run, changing the value of LSEARCH may be a remedy of the problem. When the NOLNSR keyword is used, there is no linear search during a LBFGS minimization. Pure LBFGS steps are taken by the minimizer.


DIAGTERM=float

DIAGTERM is a variable with default value of 0.0001, which scales the initial diagonal form of the inverse Hessian in the LBFGS minimizer. Low values are recommended when optimizing large systems.


DIIS / NODIIS

The DIIS method attempts to find an optimum linear combination of previous geometries[]. The corresponding linear coefficients are determined by minimizing the norm of an interpolated error vector built as a combination of error vectors. Among the different approaches used to define the DIIS error vectors, DivCon uses the quasi Newton-Step error vector and the energy error vector for OPT=LBFGS and OPT=BFGS, respectively. For the LBFGS method, NODIIS is the default option (see below) whereas DIIS is the default for the standard BFGS algorithm. Note that the DIIS technique needs to store coordinates and gradients of the last mdiis optimization steps.

The usual implementation of the DIIS technique for the OPT=BFGS method has been included in DivCon while the DIIS module for the LBFGS method has been especially adapted for treating large systems. In order to increase the efficiency of the LBFGS-DIIS method, the computation of the error vector takes advantage of the LBFGS updating scheme of the inverse Hessian matrix and is only activated at the latter stages of a minimization run. For some systems, the DIIS technique consistently reduces the number of optimization cycles maintaining a favorable CPU rate with respect to the NODIIS LBFGS method. However, the DIIS-LBFGS method is more unstable given that sudden increases of the gradient norm may occur, halting thus the optimization run.


FORCE-IT

Geometry optimization will halt if the energy increases on three successive cycles unless the user overrides it with the keyword FORCE-IT.


ADDMM / NOMM

Add MM correction to peptide torsional barrier (keyword is on by default). The NOMM keyword will turn off the molecular mechanics correction for peptide torsions.


ROTATE=float

Used to set the rotation angle for energy barrier


Transition Structure Optimization

Transition structure (TS) optimizations can be carried out with the Partitioned Rational Function Optimization, the Newton Raphson or the Quasi Newton Algorithm. All of these are common methods which are based on some form of augmented Hessian Newton-Raphson approach and use the Powell update formula. Since these methods require the full Hessian matrix, the memory requirements can be large. Location of a TS demands a quite accurate Hessian which can be obtained from an updating scheme (Powell formula is used by DivCon) and/or the numerical calculation of the second derivative matrix.


OPT=TS

Use the Partitioned Rational Function optimized (see below, page 14).


OPT=TSNR

The standard Newton Raphson (NR) formula is used to calculate the optimization step within a trust radius of 0.10 Å. Provided that the initial geometry is close to the TS and the Hessian has exactly one negative eigenvalue, this method should converge to the correct solution.


OPT=TSPRFO

With respect the NR formula, the augmented Hessian methods are designed to generate a search towards a saddle point, even when started in a region where the Hessian has not the correct structure. The P-RFO algorithm employs two shift parameters of the Hessian eigenvalues in order to ensure a proper maximization along the TS mode and minimization along the rest of modes. The norm of P-RFO step is scaled down when its value is greater than 0.10 Å. Identical to OPT=TS.


OPT=TSQNA

The QNA method (also known as the Trust Radius Image Minimization) uses only one shift parameter and restricts the total step length to the trust radius whose optimum value is changed along the optimization.


HESS=CALCFC

Hessian is calculated numerically at the initial point and subsequently updated using the Powell formula (Default option).


HESS=CALCDUMP

Hessian is calculated numerically at the initial point and every DUMP cycles of optimization (see page [*]).


HESS=CALCALL

Hessian is calculated numerically every optimization step.


HESS=READ

The initial Hessian is read from the HESS parameter in the input file with format READ(INPT,'(5E16.8)') ((HESS(I,J),J=1,I),I=1,3*NATOMS). Default units of the Hessian elements are kcal/(mol Å2).


NOMODEFOLLOW

Disable the use of the mode following technique. To ensure that the TS mode is being followed smoothly from one iteration to the next, the P-RFO and QNA algorithms follow the mode which has the greatest overlap with mode followed on the previous cycle.


Restrained Atoms


BELLY

A subset of the atoms in the system, the belly group, will be allowed to relax their position during optimization while the rest of the atoms will be kept at fixed positions by zeroing the corresponding forces. Currently, the BELLY option requires optimization of both minimum or transition structures using Cartesian coordinates (a FREQ calculation can be also subjected to the BELLY option).

The BELLY parameter must be included in the input file in order to specify the BELLY parameter block. Two formats are possible:

BELLY

  ATOMS 144-178 310-332

END_BELLY
This means that the BELLY group of moving atoms will be constituted from atom 144 to atom 178, and from atom 310 to atom 332. Alternatively, the BELLY parameter block can be selected using residue numbering:

BELLY

  RESIDUES 10-13 20

END_BELLY
Only residues from 10 to 13 and residue 20 will be allowed to move during minimization.


Frequency Calculations


FREQ (-freq)

Computes force constants and the resulting vibrational frequencies using double numerical differentiation with a step size of 0.01 Å. This value of the step size represents a good compromise between accuracy and numerical problems. The resultant Hessian matrix in Cartesian coordinates is written in the divcon.hss output file with units of kcal/(mol Å2). Vibrational frequencies are computed by determining the second derivatives of the energy with respect to nuclear coordinates followed by transformation into mass-weighted coordinates. Of course, this is only valid at a critical point. By specifying both FREQ and OPT keywords, the frequencies will be computed after successful completion of the optimization task.


THRMO

Report thermodynamic quantities from a frequency calculation.

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