36.2.5 Approximating hessian matrix elements (HESSIAN)

By default, the MOLPRO geometry optimization utilizes a force field approximation to the hessian (``Model Hessian'', see R. Lindh, A. Bernhardsson, G. Karlström and P. Malmqvist Chem. Phys. Lett. 241, 423 (1995).) which speeds up convergence significantly. The Model Hessian is parameterized for the elements up to the third row and is used by default unless the molecule contains atoms from higher rows. Alternatively, the model Hessian of Schlegel can be used.

HESSIAN[,key], value, param1, param2;

where key can be

MODEL

Use Lindh's Model Hessian in optimization (default).

MODEL,SCHLEGEL

Use Schlegel Model Hessian.

MODEL,VDW

Add vdW terms to Lindh's Model Hessian.

SCHLEGEL

Same as MODEL,SCHLEGEL]

VDW

Same as MODEL,VDW

NOMODEL

Don't use Model Hessian approximation to the hessian.

For minimizations, the Model Hessian provides very good approximations the Hessian matrix, improving convergence rapidly, so it was chosen as default. At present it is implemented for the first three row elements.

You may also put in individual matrix elements of the hessian: value sets starting value for hessian matrix element between parameters param1, param2. If param2 is omitted it defaults to param1 (diagonal element). If the Model Hessian is disabled, the initial hessian is diagonal, with values 1hartree*bohr**(-2) for all lengths, 1 hartree*radian**(-2) for all angles. This is usually quite reasonable except for cases such as dihedral angles. A reasonable strategy for complicated cases is to perform an optimization with a small basis set at the SCF level with PRINT,HESSIAN in order to obtain an approximate starting hessian. These values are set before processing the START record (see above). This option is obsolete if the Model Hessian is used (default unless heavy elements are present).

In transition state searches the hessian matrix is evaluated numerically (see NUMHES section 32.2.15). Alternatively, the cartesian hessian matrix evaluated in a previous frequency calculation (see FREQUENCIES section 33) can be used with the HSTART command (see section 32.2.16). It is also possible to use the numerical hessian or the hessian from a frequency calculation in minimizations. Note that numerical hessians cannot be computed when dummy atoms holding basis functions are present.