9.7.1 Overview

It is often useful to scan the potential energy surface (PES), optimizing all other degrees of freedom for each particular value of the scanned variable(s). Such a “relaxed” scan may provide a rough estimate of a pathway between reactant and product—assuming the coordinate(s) for the scan has been chosen wisely—and is often used in development of classical force fields to optimize dihedral angle parameters. Ramachandran plots, for example, are key tools for studying conformational changes of peptides and proteins, and are essentially two-dimensional torsional scans.

In certain cases, relaxed scans might encounter some difficulties on optimizations. A “frozen” scan can be easier to perform because of no geometry optimizations although it provides less information of real dynamics.

Q-Chem supports one- and two-dimensional PES scans, by setting JOBTYPE = PES_SCAN in the $rem section. In addition, a $scan input section with the following format should be specified, in the format below but with no more than two bond-length, bond-angle, or torsional variables specified.

$scan
   stre  atom1  atom2  value1 value2 incr
   ...
   bend  atom1  atom2  atom3  value1 value2 incr
   ...
   tors  atom1  atom2  atom3  atom4  value1 value2 incr
   ...
$end

Note:  Potential scans with JOBTYPE = PES_SCAN are available for ground-state potential energy surfaces only, although one may compute excitation energies along the scanned coordinate(s) by including appropriate keywords for vertical excitation in the $rem section, e.g., CIS_N_ROOTS for CIS/TDDFT excited states.

The first example below demonstrates how to scan the torsional potential of butane, which is a sequence of constrained optimizations with the C1–C2–C3–C4 dihedral angle fixed at $-$180${}^{\circ }$, $-$165${}^{\circ }$, $-$150${}^{\circ }$, $\mathrm{\dots }$, 165${}^{\circ }$, 180${}^{\circ }$.

The next example is a two-dimension potential scan. The first dimension is a scan of the C1–C2–C3–C4 dihedral angle from $-$180${}^{\circ }$ to 180${}^{\circ }$ degree in 30${}^{\circ }$ intervals; the second dimension is a scan of the C2–C3 bond length from 1.5 Å to 1.6 Å in 0.05 Å increments.

To perform a frozen PES scan, set FROZEN_SCAN to be TRUE and use input geometry in Z-matrix format. The example demonstrates a frozen PES of the C1–C2 bond stretching from 1.0 Å to 2.0 Å for methanol.

Q-Chem also supports one-dimensional restrained PES scan for transition state search of typical S${}_{\mathrm{N}}$2 reactions. The geometry restraints have the form

which is a harmonic potential applied to bias geometry optimization. Here, $R_{12}$ and $R_{34}$ are two bond lengths in the reaction coordinate and $k$ is a force constant for restraining $R$ in the range of $R_{12}\pm R_{34}$. To perform a restrained PES scan, the following format should be specified.

$scan
 r12mr34  atom1  atom2  atom3  atom4  Rmin  Rmax  incr  force_constant
 r12pr34  atom1  atom2  atom3  atom4  Rmin  Rmax  incr  force_constant
$end