# 9.5 Potential Energy Scans

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 equal to 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


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}$, $\ldots$, 165${}^{\circ}$, 180${}^{\circ}$.

Example 9.10  One-dimensional torsional scan of butane

$molecule 0 1 C 1.934574 -0.128781 -0.000151 C 0.556601 0.526657 0.000200 C -0.556627 -0.526735 0.000173 C -1.934557 0.128837 -0.000138 H 2.720125 0.655980 -0.000236 H 2.061880 -0.759501 -0.905731 H 2.062283 -0.759765 0.905211 H 0.464285 1.168064 -0.903444 H 0.464481 1.167909 0.903924 H -0.464539 -1.167976 0.903964 H -0.464346 -1.168166 -0.903402 H -2.062154 0.759848 0.905185 H -2.720189 -0.655832 -0.000229 H -2.061778 0.759577 -0.905748$end

$rem JOBTYPE pes_scan METHOD hf BASIS sto-3g$end

$scan tors 1 2 3 4 -180 180 15$end


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.

Example 9.11  Two-dimensional torsional scan of butane

$molecule 0 1 C 1.934574 -0.128781 -0.000151 C 0.556601 0.526657 0.000200 C -0.556627 -0.526735 0.000173 C -1.934557 0.128837 -0.000138 H 2.720125 0.655980 -0.000236 H 2.061880 -0.759501 -0.905731 H 2.062283 -0.759765 0.905211 H 0.464285 1.168064 -0.903444 H 0.464481 1.167909 0.903924 H -0.464539 -1.167976 0.903964 H -0.464346 -1.168166 -0.903402 H -2.062154 0.759848 0.905185 H -2.720189 -0.655832 -0.000229 H -2.061778 0.759577 -0.905748$end

$rem JOBTYPE pes_scan METHOD hf BASIS sto-3g$end

$scan tors 1 2 3 4 -180 180 30 stre 2 3 1.5 1.6 0.05$end


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 Åto 2.0 Åfor methanol.

Example 9.12  One-dimensional frozen PES scan of methanol

$molecule 0 1 C O C RCO H1 C RCH1 O H1CO X C 1.00 O XCO H1 180.0 H2 C RCH2 X H2CX H1 90.0 H3 C RCH2 X H2CX H1 -90.0 H4 O ROH C HOC H1 180.0 RCO = 1.421 RCH1 = 1.094 RCH2 = 1.094 ROH = 0.963 H1CO = 107.2 XCO = 129.9 H2CX = 54.25 HOC = 108.0$end

$rem JOBTYPE pes_scan FROZEN_SCAN true EXCHANGE s CORRELATION vwn BASIS 3-21g$end

$scan stre 1 2 1.0 2.0 0.5$end


Q-Chem also supports one-dimensional restrained PES scan for transition state search of typical S${}_{\rm N}$2 reactions. The geometry restrains are

 $k\left(R_{12}\pm R_{34}-R\right)^{2},$ (9.2)

which is a harmonic potential applied to bias geometry optimization. $R_{12}$ and $R_{34}$ are two bond lengths in the reaction coordinate. $R$ constrains the range of $R_{12}\pm R_{34}$, and $k$ is a force constant. 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


Example 9.13  One-dimensional restrained PES scan of chloromethane SN2 reaction

$molecule -1 1 C 0.418808 -1.240869 0.249048 Cl -0.775224 -1.495584 1.586668 H 1.408172 -1.490565 0.631227 H 0.147593 -1.907736 -0.568952 H 0.413296 -0.199000 -0.092071 Cl 1.947359 1.619163 -1.747832$end

$rem JOBTYPE pes_scan EXCHANGE b3lyp BASIS 6-31G*$end

$scan r12mr34 1 2 1 6 -2.0 2.0 0.2 1000.0$end