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# 10.9.3 Partial Hessian Vibrational Analysis

(July 14, 2022)

The computation of harmonic frequencies for systems with a very large number of atoms can become computationally expensive. However, in many cases only a few specific vibrational modes or vibrational modes localized in a region of the system are of interest. A typical example is the calculation of the vibrational modes of a molecule adsorbed on a surface. In such a case, only the vibrational modes of the adsorbate are useful, and the vibrational modes associated with the surface atoms are of less interest. If the vibrational modes of interest are only weakly coupled to the vibrational modes associated with the rest of the system, it can be appropriate to adopt a partial Hessian approach. In this approach, 103 Besley N. A., Metcalf K. A.
J. Chem. Phys.
(2007), 126, pp. 035101.
, 100 Besley N. A., Bryan J. A.
J. Phys. Chem. C
(2008), 112, pp. 4308.
only the part of the Hessian matrix comprising the second derivatives of a subset of the atoms defined by the user is computed. These atoms are defined in the $alist block. This results in a significant decrease in the cost of the calculation. Physically, this approximation corresponds to assigning an infinite mass to all the atoms excluded from the Hessian and will only yield sensible results if these atoms are not involved in the vibrational modes of interest. VPT2 and TOSH anharmonic frequencies can be computed following a partial Hessian calculation. 443 Hanson-Heine M. W. D., George M. W., Besley N. A. J. Chem. Phys. (2012), 136, pp. 224102. It is also possible to include a subset of the harmonic vibrational modes with an anharmonic frequency calculation by setting ANHAR_SEL = TRUE in the$rem section. This can be useful to reduce the computational cost of an anharmonic frequency calculation or to explore the coupling between specific vibrational modes.

Alternatively, vibrationally averaged interactions with the rest of the system can be folded into a partial Hessian calculation using vibrational subsystem analysis. 1360 Zheng W. J., Brooks B. R.
Biophys. J.
(2005), 88, pp. 3109.
, 1301 Woodcock H. L. et al.
J. Chem. Phys.
(2008), 129, pp. 214109.
Based on an adiabatic approximation, this procedure reduces the cost of diagonalizing the full Hessian, while providing a local probe of fragments vibrations, and providing better than partial Hessian accuracy for the low frequency modes of large molecules. 378 Ghysels A. et al.
J. Comput. Chem.
(2010), 31, pp. 994.
Mass-effects from the rest of the system can be vibrationally averaged or excluded within this scheme.

PHESS

PHESS
Controls whether partial Hessian calculations are performed.
TYPE:
INTEGER
DEFAULT:
0 Full Hessian calculation
OPTIONS:
1 Partial Hessian calculation. 2 Vibrational subsystem analysis (massless). 3 Vibrational subsystem analysis (weighted).
RECOMMENDATION:
None

N_SOL

N_SOL
Specifies number of atoms included in the Hessian.
TYPE:
INTEGER
DEFAULT:
No default
OPTIONS:
User defined
RECOMMENDATION:
None

PH_FAST

PH_FAST
Lowers integral cutoff in partial Hessian calculation is performed.
TYPE:
LOGICAL
DEFAULT:
FALSE Use default cutoffs
OPTIONS:
TRUE Lower integral cutoffs
RECOMMENDATION:
None

Example 10.25  This example shows a partial Hessian frequency calculation of the vibrational frequencies of acetylene on a model of the C(100) surface

$comment acetylene - C(100) partial Hessian calculation$end

$molecule 0 1 C 0.000 0.659 -2.173 C 0.000 -0.659 -2.173 H 0.000 1.406 -2.956 H 0.000 -1.406 -2.956 C 0.000 0.786 -0.647 C 0.000 -0.786 -0.647 C 1.253 1.192 0.164 C -1.253 1.192 0.164 C 1.253 -1.192 0.164 C 1.297 0.000 1.155 C -1.253 -1.192 0.164 C 0.000 0.000 2.023 C -1.297 0.000 1.155 H -2.179 0.000 1.795 H -1.148 -2.156 0.654 H 0.000 -0.876 2.669 H 2.179 0.000 1.795 H -1.148 2.156 0.654 H -2.153 -1.211 -0.446 H 2.153 -1.211 -0.446 H 1.148 -2.156 0.654 H 1.148 2.156 0.654 H 2.153 1.211 -0.446 H -2.153 1.211 -0.446 H 0.000 0.876 2.669$end

$rem JOBTYPE freq METHOD hf BASIS sto-3g PHESS TRUE N_SOL 4$end

$alist 1 2 3 4$end