Example: Mobile Block Hessian: CH4¶
A frequency calculation is performed using the mobile block Hessian (MBH)method. The coordinates in the ATOMS section should be the partially optimized coordinates (or the fully optimized coordinates would work too).
Example input how to do a block constraint:
ATOMS C 0.000000 0.000000 0.000000 b=b1 H 0.634671 0.634671 0.634671 b=b1 H -0.634671 -0.634671 0.634671 b=b1 H -0.634671 0.634671 -0.634671 b=b1 H 0.634671 -0.634671 -0.634671 END CONSTRAINTS block b1 END
Such geometry optimization will not be discussed here any further. The next input for ADF shows how to perform a frequency calculation with MBH.
$ADFBIN/adf <<eor TITLE Methane BASIS Type DZ Core None END ATOMS C 0.000000 0.000000 0.000000 b=b1 H 0.634671 0.634671 0.634671 b=b1 H -0.634671 -0.634671 0.634671 b=b1 H -0.634671 0.634671 -0.634671 b=b1 H 0.634671 -0.634671 -0.634671 b=b2 END NumericalQuality verygood SYMMETRY nosym GEOMETRY frequencies disrad=0.001 mbh b1 branch new END End input eor
The flag b=b1 in the ATOMS section adds the label ‘b1’ to some of the atoms. The four atoms labeled ‘b1’ will be considered as a block with fixed internal geometry.
In the GEOMETRY section, a Mobile Block Hessian calculation is requested by using the FREQUENCIES and MBH keywords. Here the atoms with label ‘b1’ are selected to be in the same mobile block. The position/orientation of the block are supposed to be optimized in a preceding partial optimization run. In the vibrational analys, the block ‘b1’ is only allowed to vibrate as a whole. The number of resulting modes/frequencies is 3 for the fifth atom plus 6 for the block ‘b1’ (3 position/3 orientation), resulting in 9 frequencies in total. Since 6 of those frequencies are zero due to translational and rotational invariance of the system, one will find 3 non-zero characteristic frequencies in the output. In practice with ADF not exactly 6 zero’s are found, but they are close to zero.
The quality of the frequencies/modes depends largely on the block choice. Best results are obtained when grouping atoms in a block if those atoms are known to form rather rigid structures. For instance, grouping the 11 atoms of benzene side group into a block, will usually result in representative frequencies. In this example the block choice is only illustrative for the methodology.