9.3 Constrained Optimization

9.3.3 Zeroed out Hessians for Frozen Atoms Constraints

(May 16, 2021)

Frequency calculations for a system with frozen atom constraints are invalid as they introduce imaginary frequencies. These arise because the Hessian computed for the frequency calculation has different physics compared to the gradient computed during the fixed-atom optimization.

One possible workaround is to zero out the elements of the Hessian associated with the frozen atoms. This removes the contribution of the frozen atoms to the normal modes and reduces the number of frequencies computed. For a system with N atoms, where n atoms are frozen, there will be 3(N-n)-6 normal modes, or 3(N-n)-5 if the system is linear.

FRZN_OPT
       Controls whether the job uses zeroed Hessian technique in the frequency calculations
TYPE:
       LOGICAL
DEFAULT:
       False
OPTIONS:
       False Do not use the zeroed out Hessian True Use the zeroed out Hessian
RECOMMENDATION:
       False

FRZ_ATOMS
       Controls the number of frozen atoms
TYPE:
       INTEGER
DEFAULT:
       No default
OPTIONS:
       User defined
RECOMMENDATION:
       None

Example 9.7  Frequency calculations using zeroed out Hessian technique. Note the frozen atom indices are specified in the $frozen_opt section.

$molecule
   0 1
   C        -0.0014570824    1.4001468208    0.0000000000
   H        -0.0030029737    2.4867609686    0.0000000000
   C        -1.2093554750    0.6986986619    0.0000000000
   H        -2.1525287416    1.2392252926    0.0000000000
   C        -1.2094237515   -0.6985901650    0.0000000000
   H        -2.1508487680   -1.2427180000    0.0000000000
   C        -0.0003285453   -1.3965954363    0.0000000000
   H        -0.0006460438   -2.4839940415    0.0000000000
   C         1.2098250013   -0.6978846084    0.0000000000
   H         2.1493830451   -1.2446769146    0.0000000000
   C         1.2133329176    0.6987868208    0.0000000000
   H         2.1550504173    1.2408406009    0.0000000000
$end

$rem
   JOBTYPE      freq
   METHOD       b3lyp
   BASIS        6-31G*
   FRZN_OPT     1  ! Turns on the freq calculation with frozen Hessians
   FRZ_ATOMS    2  ! No. of frozen atoms
   SYM_IGNORE   true
   SYMMETRY     false
$end

$frozen_opt
1 11
$end

View output