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, 165, 150, , 165, 180.
Example 9.18 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 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 9.19 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 Å to 2.0 Å for methanol.
Example 9.20 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
Q-Chem supports one-dimensional restrained PES scans including bond-length, bond-angle, torsional, atom to center of mass of two atoms, and atom to a set of atoms. Note that the set of atoms is defined as the atoms with indices from atom2 to atom3, where the atoms indexed at atom2 and atom3 are included in the set. These restrained scans apply a harmonic potential to bias geometry optimization. Q-Chem also supports restrained PES scans for transition state search of typical S2 reactions where the geometry restraints have the form
| (9.46) |
Here, and are two bond lengths in the reaction coordinate and is a force constant for restraining in the range of . To perform a restrained PES scan, the following format should be specified.
$scan r12 atom1 atom2 Rmax Rmin incr force_constant ... rbend atom1 atom2 atom3 Rmax Rmin incr force_constant ... rtors atom1 atom2 atom3 atom4 Rmax Rmin incr force_constant ... r1to23 atom1 atom2 atom3 Rmax Rmin incr force_constant ... r1toset atom1 atom2 atom3 Rmax Rmin incr force_constant ... r12mr34 atom1 atom2 atom3 atom4 Rmin Rmax incr force_constant ... r12pr34 atom1 atom2 atom3 atom4 Rmin Rmax incr force_constant ... $end
Example 9.21 One-dimensional restrained PES scan of chloromethane S2 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
Example 9.22 One-dimensional restrained torsional PES 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 rtors 1 2 3 4 -180 180 15 1000.0 $end
Example 9.23 One-dimensional restrained PES scan pulling Na+ to benzene
$molecule 1 1 Na 0.0000000000 0.0000000000 -1.8358304117 C 1.4040705495 0.0000000000 0.5608720717 C 0.7020352748 -1.2159607646 0.5608720717 C -0.7020352748 -1.2159607646 0.5608720717 C -1.4040705495 0.0000000000 0.5608720717 C -0.7020352748 1.2159607646 0.5608720717 C 0.7020352748 1.2159607646 0.5608720717 H 2.4900504384 0.0000000000 0.5941562674 H 1.2450252192 -2.1564469363 0.5941562674 H -1.2450252192 -2.1564469363 0.5941562674 H -2.4900504384 0.0000000000 0.5941562674 H -1.2450252192 2.1564469363 0.5941562674 H 1.2450252192 2.1564469363 0.5941562674 $end $rem JOBTYPE PES_SCAN BASIS STO-3G METHOD B3LYP DFT_D D3_BJ $end $scan R1toSet 1 2 13 2.3 1.8 -0.1 1000.0 $end