Initial Hessian

In a Geometry Optimization (or Transition State search) the Hessian matrix - second derivatives of the energy with respect to changes in coordinates - is updated while the program steps around in an attempt to find the (local) energy minimum. The quality of the initial Hessian may have a considerable impact on the required number of steps to reach geometric convergence.

By default the initial Hessian is read from a restart file - see the key restart - or constructed from a force field [11] that is implemented in the program. In the latter case the user can modify the so-generated initial Hessian in four ways:

1. By setting all diagonal elements to some constant.
2. By defining three constants, one for distances (or Cartesian displacements, as the case may be),
   one for bond angles, and one for dihedral angles.
   All diagonal elements of the Hessian are adapted accordingly.
3. By supplying a list of diagonal values.
4. By giving diagonal-Hessian values for one or more specific coordinates.

For each element i for which a diagonal Hessian value Hii is supplied the off-diagonal elements Hij, (all j i­j) are set to zero.

A combination of the above options is possible. The rules of how combinations are interpreted by the program are:

• The program first initializes the Hessian using the force field (or restart data).
• If a single constant (1) or three constants (2) are supplied, all diagonal elements are adjusted
  (and all off diagonal elements are set to zero).
• If a list of diagonal values is supplied (3), this overrides the first so many values of the diagonal.
  Such a list is not required to cover all diagonal elements.
  If the list is shorter than the dimension of the Hessian, i.e. the number of atomic coordinates,
  only the first so many elements will be adjusted.
• If any individual elements are supplied specifically (4),
  their values are replaced in the diagonal defined thus far.

All input values of the Hessian are in units of Hartree/bohr2 for Cartesian coordinates and bond lengths. Hartree/radian2 for bond angles and dihedral angles.

The first 3 options are controlled by the key HESSDIAG:

HESSDIAG {General}
{ List
end }

HESSDIAG

A general key: it has either an argument (General), or a data block (List). It is also possible to supply the argument and the data block, but this requires that the continuation symbol (&) is given after the argument, separated from the argument by at least one blank.

General

Must be either a single numerical value, or one or more named specifications of options, in the format optionname=value.

If a single numerical value is given, this value is assigned to all the options that are available. If the named-option format is applied, any named options that are not found get the value 1.0.
The options are: rad=radvalue to assign a value to all Hessian diagonal elements that refer to distance coordinates (bond length in case of z-matrix coordinates, Cartesian coordinates otherwise),

ang=angvalue to assign a value to all elements that refer to bond angles, and finally dih=dihvalue for dihedral angles.
ang and dih are not significant in Cartesian optimizations.

List

A list of numerical values, which may expand over any number of lines. If n numbers are supplied, they are assigned to the first n diagonal elements of the Hessian. The remaining diagonal elements, if any, are not effected. The maximum number of Hessian diagonal elements equals the number of atomic coordinates.

The force field derived initial Hessian can be printed for inspection. Type in input:

HESSTEST

ADF will construct and print the initial Hessian and then abort.