# 9.8.4 Vibrational Spectra

The inherent nuclear motion of molecules is experimentally observed by the molecules’ response to impinging radiation. This response is typically calculated within the mechanical and electrical harmonic approximations (second derivative calculations) at critical-point structures. Spectra, including anharmonic effects, can also be obtained from dynamics simulations. These spectra are generated from dynamical response functions, which involve the Fourier transform of auto-correlation functions. Q-Chem can provide both the vibrational spectral density from the velocity auto-correlation function

 $D(\omega)\propto\int_{-\infty}^{\infty}dt\ e^{-i\omega t}\langle\vec{v}(0)\bm{% \cdot}\vec{v}(t)\rangle$ (9.18)

and infrared absorption intensity from the dipole auto-correlation function

 $I(\omega)\propto\frac{\omega}{2\pi}\int_{-\infty}^{\infty}dt\ e^{-i\omega t}% \langle\vec{\mu}(0)\bm{\cdot}\vec{\mu}(t)\rangle$ (9.19)

These two features are activated by the AIMD_NUCL_VACF_POINTS and AIMD_NUCL_DACF_POINTS keywords, respectively, where values indicate the number of data points to include in the correlation function. Furthermore, the AIMD_NUCL_SAMPLE_RATE keyword controls the frequency at which these properties are sampled (entered as number of time steps). These spectra—generated at constant energy—should be averaged over a suitable distribution of initial conditions. The averaging indicated in the expressions above, for example, should be performed over a Boltzmann distribution of initial conditions.

Note that dipole auto-correlation functions can exhibit contaminating information if the molecule is allowed to rotate/translate. While the initial conditions in Q-Chem remove translation and rotation, numerical noise in the forces and propagation can lead to translation and rotation over time. The trans/rot correction in Q-Chem is activated by the PROJ_TRANSROT keyword.

AIMD_NUCL_VACF_POINTS
Number of time points to use in the velocity auto-correlation function for an AIMD trajectory
TYPE:
INTEGER
DEFAULT:
0
OPTIONS:
0 Do not compute velocity auto-correlation function. $1\leq n\leq\mbox{{\small AIMD\_STEPS}}$ Compute velocity auto-correlation function for last $n$ time steps of the trajectory.
RECOMMENDATION:
If the VACF is desired, set equal to AIMD_STEPS.

AIMD_NUCL_DACF_POINTS
Number of time points to use in the dipole auto-correlation function for an AIMD trajectory
TYPE:
INTEGER
DEFAULT:
0
OPTIONS:
0 Do not compute dipole auto-correlation function. $1\leq n\leq\mbox{{\small AIMD\_STEPS}}$ Compute dipole auto-correlation function for last $n$ timesteps of the trajectory.
RECOMMENDATION:
If the DACF is desired, set equal to AIMD_STEPS.

AIMD_NUCL_SAMPLE_RATE
The rate at which sampling is performed for the velocity and/or dipole auto-correlation function(s). Specified as a multiple of steps; i.e., sampling every step is 1.
TYPE:
INTEGER
DEFAULT:
None.
OPTIONS:
$1\leq n\leq\mbox{{\small AIMD\_STEPS}}$ Update the velocity/dipole auto-correlation function every $n$ steps.
RECOMMENDATION:
Since the velocity and dipole moment are routinely calculated for ab initio methods, this variable should almost always be set to 1 when the VACF/DACF are desired.

PROJ_TRANSROT
Removes translational and rotational drift during AIMD trajectories.
TYPE:
LOGICAL
DEFAULT:
FALSE
OPTIONS:
FALSE Do not apply translation/rotation corrections. TRUE Apply translation/rotation corrections.
RECOMMENDATION:
When computing spectra (see AIMD_NUCL_DACF_POINTS, for example), this option can be used to remove artificial, contaminating peaks stemming from translational and/or rotational motion. Recommend setting to TRUE for all dynamics-based spectral simulations.