Low-frequency vibrational modes usually emerge due to hindered or near-free rotations around a single bond within a molecule. The harmonic approximation is problematic for such internal rotations and yields an infinite vibrational entropy in the limit of vanishing frequencies.
To fix this issue, Grimme
460
Chem. Eur. J
(2012),
18,
pp. 9955.
Link
proposed to enforce a finite vibrational entropy by interpolating between the entropy of the free rotor and the harmonic vibrational entropy as
| (10.42) |
where
| (10.43) |
is the damping function of Chai and Head-Gordon,
207
Phys. Chem. Chem. Phys.
(2008),
10,
pp. 6615.
Link
with and as fixed parameters.
It is used as a weighting function and allows for a smooth transition from the free rotor entropy at small frequencies
to the harmonic vibrational entropy for frequencies above the cutoff .
This was later extended to interpolate the vibrational enthalpy contributions between a free rotor
and a harmonic oscillator with zero-point vibrational energy
, as
776
J. Phys. Chem. C
(2015),
119,
pp. 1840.
Link
| (10.44) |
This again reduces the error associated with treating translational and rotational degrees of freedom as low-frequency vibrations, which is especially important for the adsorption or association of larger molecules. This procedure is known as the quasi-rigid-rotor-harmonic-oscillator (qRRHO) approach.
The qRRHO scheme is the default in Q-Chem, and all thermodynamic quantities are printed for the RRHO (without interpolations) and qRRHO schemes at standard temperature and pressure (298.15 K and 1.00 atm). To change the latter, the user can specify an $isotopes section (see examples and Section 10.7.2 for details). and for both interpolator functions can be modified through QRRHO_ALPHA and QRRHO_OMEGA_CUTOFF respectively.
QRRHO_ALPHA
QRRHO_ALPHA
Specifies the exponent in the damping function of Chai and Head-Gordon,
used for interpolating the vibrational enthalpy and entropy in the qRRHO scheme.
Specify MRRHO_ALPHA to change the exponent for the entropy interpolation separately.
TYPE:
INTEGER
DEFAULT:
4
OPTIONS:
Dimensionless interpolator exponent used in the qRRHO scheme.
RECOMMENDATION:
Use the default.
QRRHO_OMEGA_CUTOFF
QRRHO_OMEGA_CUTOFF
Sets the frequency cutoff in the Chai-Head-Gordon damping function for interpolating the vibrational enthalpy
and entropy in the qRRHO scheme. Specify MRRHO_OMEGA_CUTOFF to change the frequency cutoff
for the entropy interpolation separately.
TYPE:
INTEGER
DEFAULT:
100
OPTIONS:
Interpolator cutoff frequency used in the qRRHO scheme in cm.
RECOMMENDATION:
Use the default.
Example 10.31 Harmonic vibrational analysis at the HF/3-21G level of theory, where the thermodynamic properties for RRHO and qRRHO are printed at 298.15 K and 1.00 atm.
$molecule 0 1 C 1.682185104800 0.240320237000 0.000000000000 O 0.894276382600 1.089998584000 0.000000000000 O 2.480949717100 -0.590833069200 0.000000000000 C -1.682185094800 -0.240320333400 0.000000000000 O -0.894276273900 -1.089998812500 0.000000000000 O -2.480949835800 0.590833394100 0.000000000000 $end $rem JOBTYPE opt METHOD hf BASIS 3-21G INTEGRAL_SYMMETRY false POINT_GROUP_SYMMETRY false $end @@@ $molecule read $end $rem JOBTYPE freq METHOD hf BASIS 3-21G INTEGRAL_SYMMETRY false POINT_GROUP_SYMMETRY false $end
Example 10.32 Harmonic vibrational analysis at the HF/3-21G level of theory, where the thermodynamic properties for RRHO and qRRHO are printed at standard temperature and pressure as well as two additional temperatures (273.15 K and 313.15 K). Please see Section 10.7.2 for further details on the $isotopes section.
$molecule 0 1 C 1.682185104800 0.240320237000 0.000000000000 O 0.894276382600 1.089998584000 0.000000000000 O 2.480949717100 -0.590833069200 0.000000000000 C -1.682185094800 -0.240320333400 0.000000000000 O -0.894276273900 -1.089998812500 0.000000000000 O -2.480949835800 0.590833394100 0.000000000000 $end $rem JOBTYPE opt METHOD hf BASIS 3-21G INTEGRAL_SYMMETRY false POINT_GROUP_SYMMETRY false $end @@@ $molecule read $end $rem JOBTYPE freq METHOD hf BASIS 3-21G ISOTOPES true INTEGRAL_SYMMETRY false POINT_GROUP_SYMMETRY false $end $isotopes 2 1 0 273.15 1.0 0 313.15 1.0 $end