Introduction to Computational Quantum Chemistry
Lesson 07: Reaction Coordinates and Transition State
Calculations
(Prepared by Radek Marek Research Group)
Lesson 07 - Reaction Coordinates and Transition State Calculations 1
REVIEW: Potential Energy Surface
the PES of a molecule is obtained by the total interactions of:
nuclear-nuclear repulsion
electron-electron interaction
electron-nuclear attraction
important Points on the PES
stationary points:
∂E
∂qi
= 0 (1)
local minimum:
∂2
E
∂q2
i
> 0 for all degrees of freedom (2)
nth
order saddle point:
∂2
E
∂q2
i
< 0 for n degrees of freedom (3)
(Prepared by Radek Marek Research Group)
Lesson 07 - Reaction Coordinates and Transition State Calculations 2
REVIEW: Potential Energy Surface (Cont.)
a two-dimensional cut from a multidimensional PES illustrates one
direction view of the reaction coordinates
the energy differences of TS − R is the activation energy while the
P − R is the reaction energy
however, these are only stationary points on a much larger potential
energy surface (PES). The actual landscape of this surface can also be
explored to see how the various stationary points connect.
(Prepared by Radek Marek Research Group)
Lesson 07 - Reaction Coordinates and Transition State Calculations 3
Potential Energy Scan
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).
possible to adjust distances as well as atomic and dihedral angles
(Prepared by Radek Marek Research Group)
Lesson 07 - Reaction Coordinates and Transition State Calculations 4
Potential Energy Scan, Cont.
PES scan may provide a rough estimate of a pathway
between reactants, TS, and products, assuming the
coordinate(s) for the scan has been chosen wisely
PES scan is often used in development of classical force
fields
(Prepared by Radek Marek Research Group)
Lesson 07 - Reaction Coordinates and Transition State Calculations 5
Intrinsic Reaction Coordinate (IRC)
TS (transition state), the Hessian needs to display the required number
of negative eigenvalues
it is also necessary to confirm the TS connections to both sides
(reactants and products).
(Prepared by Radek Marek Research Group)
Lesson 07 - Reaction Coordinates and Transition State Calculations 6
Intrinsic Reaction Coordinate (IRC), Cont.
the Intrinsic Reaction Coordinate (IRC) is the minimum
energy reaction pathway (MERP) in mass-weighted
cartesian coordinates between the TS to its reactants R
and products P.
the molecule takes moving down the product and reactant
valleys with zero kinetic energy.
the Gonzalez-Schlegel method for following the coordinate
can be used in Gaussian using the IRC keyword, latest
version using (HPC algorithm).
(Prepared by Radek Marek Research Group)
Lesson 07 - Reaction Coordinates and Transition State Calculations 7
Transition State Methods
mapping reaction coordinates and search of transition
state (TS)
manual optimizations search for REACTANTS, TS,
PRODUCTS (with aid from PES Scan)
advance methods such as QST2,QST3, etc
(Prepared by Radek Marek Research Group)
Lesson 07 - Reaction Coordinates and Transition State Calculations 8
ACTIVITY 1: PES SCAN
rotational transition state in hydrogen peroxide (H-O-O-H) using
Gaussian
(MANUAL) frozen optimization per angle:
the last line of the Z-Matrix describes a value of 0.0 degree for the
H/O/O/H dihedral angle d4, the tailing character F indicating that
this variable is frozen and not to be varied during the geometry
optimization, then change it from 0.0 to 180
(Prepared by Radek Marek Research Group)
Lesson 07 - Reaction Coordinates and Transition State Calculations 9
ACTIVITY 1: PES SCAN, Cont.
(FULL SCAN) can be achieved in a single job:
initial value of 0.0 degree for the H/O/O/H dihedral angle d4 but
also specifies a scan of 18 steps, is varied by +10.0 degrees.
in order to avoid problems caused through changes in the point
group along the pathway, the nosymm keyword is added.
(Prepared by Radek Marek Research Group)
Lesson 07 - Reaction Coordinates and Transition State Calculations 10
ACTIVITY 1: PES SCAN, Cont.
examine the output file and look for the keyword "Summary of
Optimized Potential Surface Scan", you can see the energy eigenvalues
as d4 changes
add module gaussview
open the file using gv {filename}
go to menu bar Results > scan, Energy and RMS values are presented
you can visualize the molecular movements by clicking the animate play
button
(Prepared by Radek Marek Research Group)
Lesson 07 - Reaction Coordinates and Transition State Calculations 11
ACTIVITY 2: Reaction Coordinate and TS Search
we will study a classic SN2 reactions (known to have double well
potentials), using Gaussian.
SN2 reaction: Br−
+ CH3Cl → Cl−
+ CH3Br
use B3LYP functional, the 6-31+G(d) basis set for all atom
first perform a geometry Optimization and Freq for all Reactants
and Products
for an initial guess of transition state structure (TS), obtain it from
PES scan by varying the both distances of Br and Cl, refer to this
manual: https : //gaussian.com/scan/
NOTE: to save time, use the coordinates provided in the next
page, this structure is a good starting point for a PES SCAN
refer to this manual: https : //gaussian.com/scan/
(Prepared by Radek Marek Research Group)
Lesson 07 - Reaction Coordinates and Transition State Calculations 12
ACTIVITY 2: Reaction Coordinate and TS Search
perform your SCAN from this structure (fucos on B1 and B2) bond lengths
C
Cl 1 B1
Br 1 B2 2 A2
H 1 B3 2 A3 3 D3
H 1 B4 2 A4 3 D4
H 1 B5 2 A5 3 D5
variables:
B1 2.0 9 0.1
B2 2.0 9 0.1
A2 179.13318
B3 1.06210
A3 89.25624
D3 135.20467
B4 1.06224
A4 90.30745
D4 352.54852
B5 1.08241
A5 91.90132
D5 243.91238
(Prepared by Radek Marek Research Group)
Lesson 07 - Reaction Coordinates and Transition State Calculations 13
ACTIVITY 2: Reaction Coordinate and TS Search,
Cont.
once you found a good TS candidate, be sure it has
strongest imaginary frequency among others that refers to
the bond breaking/forming of the Br · · · C · · · Cl, that’s why
it’s necessary to perform a preliminary FREQ calculation
if it’s viable, proceed to Transition State Optimization
for Transition State (TS) minimization use
#P B3LYP/6-31G(d) opt(TS,ModRedundant,noeigentest)
nosymm freq
the option above only calculate freq once on the initial
structure (calcfc), freq calculation for every step is also
available (CalcAll) but is not typically necessary for this
simple system
(Prepared by Radek Marek Research Group)
Lesson 07 - Reaction Coordinates and Transition State Calculations 14
ACTIVITY 2: Reaction Coordinate and TS Search,
Cont.
after a successful TS Optimization, open the structure and
examine the frequencies using Gabedit or Avogadro, if the
frequencies are okay, you now got a Transition State
Structure
use the optimize TS structure and proceed with IRC
calculation for the confirmation
#P B3LYP/6-31G(d) scf=(tight,direct) int=finegrid
IRC(calcfc,maxpoints=500,maxcyc=500,stepsize=10)
by default IRC run examines every direction, you can also
chose specific directions as Forward and Reverse options
refer to this manual: https : //gaussian.com/irc/
(Prepared by Radek Marek Research Group)
Lesson 07 - Reaction Coordinates and Transition State Calculations 15
ACTIVITY 2: Reaction Coordinate and TS Search,
Cont.
once you have successful IRC calculation, open
Gaussview for visualization
open the file using gv {filename}
go to menu bar Results > IRC, it allows you to view Total
Energy and RMS Gradient along IRC values are presented
you can visualize the molecular movements by clicking the
animate play button
(Prepared by Radek Marek Research Group)
Lesson 07 - Reaction Coordinates and Transition State Calculations 16
ASSIGNMENT
This process concerns the proton transfer in
malonaldehyde, find the transition state geometry:
use DFT methods PBE, B3LYP, and then try MP2. Be sure
to use cc-pVDZ basis set. Verify your obtained transition
state geometry.
(Prepared by Radek Marek Research Group)
Lesson 07 - Reaction Coordinates and Transition State Calculations 17
END
(Prepared by Radek Marek Research Group)
Lesson 07 - Reaction Coordinates and Transition State Calculations 18