10.4 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 10.217 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 10.218 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 10.219 One-dimensional frozen PES scan of methanol

 
$molecule
0 1
 C
 O  C RCO
 H1 C RCH1 O H1CO
 X  C 1.0a 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
 correlatoin  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

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

(10.1)

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 10.220 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