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# 9.4.3 Frozen Atoms

(July 14, 2022)

Absolute atom positions can be frozen with the FIXED section. The section starts with the FIXED keyword as the first line and ends with the ENDFIXED keyword on the last. The format to fix a coordinate or coordinates of an atom is:

atom    coordinate_reference

coordinate_reference can be any combination of up to three characters $X$, $Y$ and $Z$ to specify the coordinate(s) to be fixed: $X$, $Y$, $Z$, XY, XZ, YZ, XYZ. The fixing characters must be next to each other. e.g.,

FIXED
2 XY
ENDFIXED


means the $x$-coordinate and $y$-coordinate of atom 2 are fixed, whereas

FIXED
2 X Y
ENDFIXED


will yield erroneous results.

Note:  When the FIXED section is specified within $opt, the optimization will proceed in Cartesian coordinates. Note that frequency calculations for a system with frozen atom constraints will generally produce 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 simply 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. This “zeroing out” approach can be requested with a pair of$rem variables, FRZN_OPT and FRZ_ATOMS, as described below. A more elegant approach is to replace the strictly fixed atomic positions with soft harmonic confining potentials, which achieves effectively the same result but allows for relaxation (i.e., optimization) of all atomic coordinates, so that a proper vibrational frequency calculation can be performed. The use of harmonic confining potentials as a replacement for fixed atom constraints is described in Section 9.4.7.

FRZN_OPT

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

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

Example 9.10  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