9 Exploring Potential Energy Surfaces: Critical Points and Molecular Dynamics

9.6 Potential Energy Scans

(June 30, 2021)

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, -165, -150, , 165, 180.

Example 9.14  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

View output

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 to 180 degree in 30 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 9.15  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

View output

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 9.16  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
   EXCHANGE       s
   CORRELATION    vwn
   BASIS          3-21g
   FROZEN_SCAN    true
$end

$scan
   stre 1 2 1.0 2.0 0.5
$end

View output

Q-Chem also supports one-dimensional restrained PES scan for transition state search of typical SN2 reactions. The geometry restrains are

k(R12±R34-R)2, (9.4)

which is a harmonic potential applied to bias geometry optimization. R12 and R34 are two bond lengths in the reaction coordinate. R constrains the range of R12±R34, 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 9.17  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
   METHOD    b3lyp
   BASIS     6-31G*
$end

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

View output