geometry optimisation modelling oh + c 2 h 4 *ch 2 -ch 2 -oh ch 3 -ch 2 -o* 3d pes
TRANSCRIPT
![Page 1: Geometry Optimisation Modelling OH + C 2 H 4 *CH 2 -CH 2 -OH CH 3 -CH 2 -O* 3D PES](https://reader036.vdocuments.site/reader036/viewer/2022062308/56649e175503460f94b02fcc/html5/thumbnails/1.jpg)
Geometry OptimisationModelling
![Page 2: Geometry Optimisation Modelling OH + C 2 H 4 *CH 2 -CH 2 -OH CH 3 -CH 2 -O* 3D PES](https://reader036.vdocuments.site/reader036/viewer/2022062308/56649e175503460f94b02fcc/html5/thumbnails/2.jpg)
1,2
1,4
1,6
1,8
2,0
2,21,0
1,5
2,0
2,5
3,0
-100
0
100
200
300
400
500
C--
--O
dis
tanc
e in
A
O---H distance in A
Energy in kJ / m
ol
OH + C2H4
*CH2-CH2-OH
CH3-CH2-O*
3D PES
![Page 3: Geometry Optimisation Modelling OH + C 2 H 4 *CH 2 -CH 2 -OH CH 3 -CH 2 -O* 3D PES](https://reader036.vdocuments.site/reader036/viewer/2022062308/56649e175503460f94b02fcc/html5/thumbnails/3.jpg)
What computational chemistry can do for you:
- structural properties (bond lengths, bond angles and dihedral)
-energetic properties (which isomer is more stable,
how fast a reaction should go: reactant and TS energies
- chemical reactivity (from electron distribution nucleophilic and electrophilic sites)
C O
Nuc
- spectral properties (IR, UV and NMR spectra)
- interaction properties (molecular fitting)
Lewars
![Page 4: Geometry Optimisation Modelling OH + C 2 H 4 *CH 2 -CH 2 -OH CH 3 -CH 2 -O* 3D PES](https://reader036.vdocuments.site/reader036/viewer/2022062308/56649e175503460f94b02fcc/html5/thumbnails/4.jpg)
Introduction
G-R
Structure1
ReagentStructure2
R - G1
ReagentR - G2
R - ClOH-
R - OH + Cl-
H3C
CH
H3C
CH2 Br
1-Bromo-2-methylpropane
1-bróm-2-metilpropán
izobutil-bromid
carbon skeletonfunctional group
the ultimate goal: interconversion of one structure to another one
architecture of the moleculestereochemistry
![Page 5: Geometry Optimisation Modelling OH + C 2 H 4 *CH 2 -CH 2 -OH CH 3 -CH 2 -O* 3D PES](https://reader036.vdocuments.site/reader036/viewer/2022062308/56649e175503460f94b02fcc/html5/thumbnails/5.jpg)
property=f(structure)
Physical properties
Chemical reactivities
Biological activities molecular structure
activity=f(structure)
reactivity=f(structure)
property=f(structure)
Optimization
Geometry
![Page 6: Geometry Optimisation Modelling OH + C 2 H 4 *CH 2 -CH 2 -OH CH 3 -CH 2 -O* 3D PES](https://reader036.vdocuments.site/reader036/viewer/2022062308/56649e175503460f94b02fcc/html5/thumbnails/6.jpg)
Geometrical distortion
Internalenergy
Stable structure
Geometrical distortion
Internalenergy
Multiple stable structures
the energy differences (DE) is a measure of relative stability.
stable structure 1 stable structure 2K
Stable structures and transition statesStable structures
and transition states TS
![Page 7: Geometry Optimisation Modelling OH + C 2 H 4 *CH 2 -CH 2 -OH CH 3 -CH 2 -O* 3D PES](https://reader036.vdocuments.site/reader036/viewer/2022062308/56649e175503460f94b02fcc/html5/thumbnails/7.jpg)
Typical reaction mech.
VARIABLES: 3 translational coordinates and 3 rotational coordinates of a general n-atomic molecule leave (3n – 6) internal coordinates.
Potential Energy Surface (PES) representation of chemical reaction
![Page 8: Geometry Optimisation Modelling OH + C 2 H 4 *CH 2 -CH 2 -OH CH 3 -CH 2 -O* 3D PES](https://reader036.vdocuments.site/reader036/viewer/2022062308/56649e175503460f94b02fcc/html5/thumbnails/8.jpg)
Nomenclature• PES equivalent to Born-Oppenheimer surface• Point on surface corresponds to position of nuclei • Minimum and Maximum
• Local• Global • Saddle point (min and max)
![Page 9: Geometry Optimisation Modelling OH + C 2 H 4 *CH 2 -CH 2 -OH CH 3 -CH 2 -O* 3D PES](https://reader036.vdocuments.site/reader036/viewer/2022062308/56649e175503460f94b02fcc/html5/thumbnails/9.jpg)
Terminology
![Page 10: Geometry Optimisation Modelling OH + C 2 H 4 *CH 2 -CH 2 -OH CH 3 -CH 2 -O* 3D PES](https://reader036.vdocuments.site/reader036/viewer/2022062308/56649e175503460f94b02fcc/html5/thumbnails/10.jpg)
Geometry Optimization
• Basic Scheme • Find first derivative (gradient) of potential energy• Set equal to zero• Find value of coordinate(s) which satisfy equation
![Page 11: Geometry Optimisation Modelling OH + C 2 H 4 *CH 2 -CH 2 -OH CH 3 -CH 2 -O* 3D PES](https://reader036.vdocuments.site/reader036/viewer/2022062308/56649e175503460f94b02fcc/html5/thumbnails/11.jpg)
Modeling Potential energy (1-d)
U(r) U(req ) dUdr rreq
(r req ) 12
d2Udr2
rreq
(r req )2
neq
rr
n
n
eq
rr
rrdr
Ud
nrr
dr
Ud
eqeq
)(!
1....)(
3
1 33
3
![Page 12: Geometry Optimisation Modelling OH + C 2 H 4 *CH 2 -CH 2 -OH CH 3 -CH 2 -O* 3D PES](https://reader036.vdocuments.site/reader036/viewer/2022062308/56649e175503460f94b02fcc/html5/thumbnails/12.jpg)
Modeling Potential energy (>1-d)
U(r a r ) U(ra ) dU
dr rra
ri
i
1
2ri
d2U
dridrj rreq
rj .....i, jij
c -b r +
1
2r T A
r
Hessian
![Page 13: Geometry Optimisation Modelling OH + C 2 H 4 *CH 2 -CH 2 -OH CH 3 -CH 2 -O* 3D PES](https://reader036.vdocuments.site/reader036/viewer/2022062308/56649e175503460f94b02fcc/html5/thumbnails/13.jpg)
Find Equilibrium Geometry for the Morse Oscillator
)()(0
)()(0
)()(0
2)(0
00
00
00
0
)1(2
) )1(2
))(0( )1(2
)1(
RRaRRa
RRaRRa
RRaRRa
RRaHH
eeaD
aeeD
eaeDdRdV
eDV
![Page 14: Geometry Optimisation Modelling OH + C 2 H 4 *CH 2 -CH 2 -OH CH 3 -CH 2 -O* 3D PES](https://reader036.vdocuments.site/reader036/viewer/2022062308/56649e175503460f94b02fcc/html5/thumbnails/14.jpg)
Find Equilibrium Geometry for the Morse Oscillator
Re
RRe
aDiff
eeaDdR
dV
eDV
RRa
RRa
RRaRRa
RRaHH
,0 c)
,0)1( b)
02 a)
0 )1(2
)1(
)(
0)(
0
)()(0
2)(0
0
0
00
0
![Page 15: Geometry Optimisation Modelling OH + C 2 H 4 *CH 2 -CH 2 -OH CH 3 -CH 2 -O* 3D PES](https://reader036.vdocuments.site/reader036/viewer/2022062308/56649e175503460f94b02fcc/html5/thumbnails/15.jpg)
Bottlenecks
• No Functional Form• More than one variable• Coupling between variables
![Page 16: Geometry Optimisation Modelling OH + C 2 H 4 *CH 2 -CH 2 -OH CH 3 -CH 2 -O* 3D PES](https://reader036.vdocuments.site/reader036/viewer/2022062308/56649e175503460f94b02fcc/html5/thumbnails/16.jpg)
Geometry Optimization(No Functional Form)
• Bracketing (w/parabolic fitting)• Find energy (E1) for given value of coordinate xi
• Change coordinate (xi+1=xi- x) to give E2
• Change coordinate (xi+2=xi + x) to give E3
• If (E2>E1 and E3>E1) then xi+1> xmin >xi+2
• Fit to parabola and find parabolic minimum• Use value of coordinate at minimum as starting point for
next iteration• Repeat to satisfaction (Minimum Energy error tolerance)
![Page 17: Geometry Optimisation Modelling OH + C 2 H 4 *CH 2 -CH 2 -OH CH 3 -CH 2 -O* 3D PES](https://reader036.vdocuments.site/reader036/viewer/2022062308/56649e175503460f94b02fcc/html5/thumbnails/17.jpg)
Terminology
![Page 18: Geometry Optimisation Modelling OH + C 2 H 4 *CH 2 -CH 2 -OH CH 3 -CH 2 -O* 3D PES](https://reader036.vdocuments.site/reader036/viewer/2022062308/56649e175503460f94b02fcc/html5/thumbnails/18.jpg)
Potential Energy Surface (PES)
A force field defines for each molecule a unique PES.Each point on the PES represents a molecular conformation characterized by its structure and energy.Energy is a function of the coordinates.(Next) Coordinates are function of the energy.
ener
gy
coordinates
CH3
CH3
CH3
![Page 19: Geometry Optimisation Modelling OH + C 2 H 4 *CH 2 -CH 2 -OH CH 3 -CH 2 -O* 3D PES](https://reader036.vdocuments.site/reader036/viewer/2022062308/56649e175503460f94b02fcc/html5/thumbnails/19.jpg)
Goal of Energy Minimization
A system of N atoms is defined by 3N Cartesian coordinates or 3N-6 internal coordinates. These define a multi-dimensional potential energy surface (PES).
A PES is characterized by stationary points:
• Minima (stable conformations)• Maxima• Saddle points (transition states)
Goal of Energy Minimization• Finding the stable conformations
ener
gy
coordinates
![Page 20: Geometry Optimisation Modelling OH + C 2 H 4 *CH 2 -CH 2 -OH CH 3 -CH 2 -O* 3D PES](https://reader036.vdocuments.site/reader036/viewer/2022062308/56649e175503460f94b02fcc/html5/thumbnails/20.jpg)
Classification of Stationary Points
0.0
4.0
8.0
12.0
16.0
20.0
0 90 180 270 360
transition state
local minimum
global minimum
ener
gy
coordinate
TypeMinimum MaximumSaddle point
1st Derivative000
2nd Derivative*positivenegativenegative
* Refers to the eigenvalues of the second derivatives (Hessian) matrix
![Page 21: Geometry Optimisation Modelling OH + C 2 H 4 *CH 2 -CH 2 -OH CH 3 -CH 2 -O* 3D PES](https://reader036.vdocuments.site/reader036/viewer/2022062308/56649e175503460f94b02fcc/html5/thumbnails/21.jpg)
Minimization Definitions
0
ix
f0
2
2
ix
f
Given a function:
Find values for the variables for which f is a minimum:
),,( 3321 Nxxxxff
Functions• Quantum mechanics energy• Molecular mechanics energy
Variables• Cartesian (molecular mechanics)• Internal (quantum mechanics)
Minimization algorithms• Derivatives-based• Non derivatives-based
![Page 22: Geometry Optimisation Modelling OH + C 2 H 4 *CH 2 -CH 2 -OH CH 3 -CH 2 -O* 3D PES](https://reader036.vdocuments.site/reader036/viewer/2022062308/56649e175503460f94b02fcc/html5/thumbnails/22.jpg)
A Schematic Representation
Starting geometry
Ý Easy to implement; useful for well defined structuresß Depends strongly on starting geometry
![Page 23: Geometry Optimisation Modelling OH + C 2 H 4 *CH 2 -CH 2 -OH CH 3 -CH 2 -O* 3D PES](https://reader036.vdocuments.site/reader036/viewer/2022062308/56649e175503460f94b02fcc/html5/thumbnails/23.jpg)
Population of Minima
Most minimization method can only go downhill and so locate the closest (downhill sense) minimum.No minimization method can guarantee the location of the global energy minimum.No method has proven the best for all problems.
Global minimum
Most populated minimum
Active Structure
![Page 24: Geometry Optimisation Modelling OH + C 2 H 4 *CH 2 -CH 2 -OH CH 3 -CH 2 -O* 3D PES](https://reader036.vdocuments.site/reader036/viewer/2022062308/56649e175503460f94b02fcc/html5/thumbnails/24.jpg)
A General Minimization Scheme
Starting point x0
Minimum?
Calculatexk+1 = f(xk)
Stopyes
No
![Page 25: Geometry Optimisation Modelling OH + C 2 H 4 *CH 2 -CH 2 -OH CH 3 -CH 2 -O* 3D PES](https://reader036.vdocuments.site/reader036/viewer/2022062308/56649e175503460f94b02fcc/html5/thumbnails/25.jpg)
Two Questions
f(x,y)
Where to go (direction)?
How far to go (magnitude)?
This is where we want to go
![Page 26: Geometry Optimisation Modelling OH + C 2 H 4 *CH 2 -CH 2 -OH CH 3 -CH 2 -O* 3D PES](https://reader036.vdocuments.site/reader036/viewer/2022062308/56649e175503460f94b02fcc/html5/thumbnails/26.jpg)
How Far To Go? Until the Minimum
Real function
Cycle 1: 1, 2, 3
Cycle 2: 1, 2, 4
Line search in one dimension• Find 3 points that bracket the minimum
(e.g., by moving along the lines and recording function values).
• Fit a quadratic function to the points.• Find the function’s minimum through
differentiation.• Improved iteratively.
Arbitrary Step• xk+1 = xk + lksk, lk = step size.• Increasel as long as energy reduces.• Decrease l when energy increases. 4
3
21
5
![Page 27: Geometry Optimisation Modelling OH + C 2 H 4 *CH 2 -CH 2 -OH CH 3 -CH 2 -O* 3D PES](https://reader036.vdocuments.site/reader036/viewer/2022062308/56649e175503460f94b02fcc/html5/thumbnails/27.jpg)
Where to go?• Parallel to the force (straight downhill): Sk = -gk
How far to go?• Line search• Arbitrary Step
Steepest Descent
![Page 28: Geometry Optimisation Modelling OH + C 2 H 4 *CH 2 -CH 2 -OH CH 3 -CH 2 -O* 3D PES](https://reader036.vdocuments.site/reader036/viewer/2022062308/56649e175503460f94b02fcc/html5/thumbnails/28.jpg)
Steepest Descent: Example
-15 -10 -5 0 5 10 15
-15
-10
-5
0
5
10
15441
361289
169225
12181
4925
91
Starting point: (9, 9)
Cycle 1:Step direction: (-18, -36)Line search equation:Minimum: (4, -1)
Cycle 2:Step direction: (-8, 4)Line search equation:
Minimum: (2/3, 2/3)
92 xy
15.0 xy
22 2),( yxyxf
y
xg
4
2kk gS
![Page 29: Geometry Optimisation Modelling OH + C 2 H 4 *CH 2 -CH 2 -OH CH 3 -CH 2 -O* 3D PES](https://reader036.vdocuments.site/reader036/viewer/2022062308/56649e175503460f94b02fcc/html5/thumbnails/29.jpg)
Steepest Descent:Overshooting
SD is forced to make 90º turns between subsequent steps (the scalar product between the (-18,-36) and the (-8,4) vector is 0 indicating orthogonality) and so is slow to converge.
![Page 30: Geometry Optimisation Modelling OH + C 2 H 4 *CH 2 -CH 2 -OH CH 3 -CH 2 -O* 3D PES](https://reader036.vdocuments.site/reader036/viewer/2022062308/56649e175503460f94b02fcc/html5/thumbnails/30.jpg)
Ligand geometry
scoring: -11.2 kcal/mol scoring: -5.7 kcal/mol
![Page 31: Geometry Optimisation Modelling OH + C 2 H 4 *CH 2 -CH 2 -OH CH 3 -CH 2 -O* 3D PES](https://reader036.vdocuments.site/reader036/viewer/2022062308/56649e175503460f94b02fcc/html5/thumbnails/31.jpg)
Orientation - interactions
scoring: -11.2 kcal/mol scoring: -5.7 kcal/mol
![Page 32: Geometry Optimisation Modelling OH + C 2 H 4 *CH 2 -CH 2 -OH CH 3 -CH 2 -O* 3D PES](https://reader036.vdocuments.site/reader036/viewer/2022062308/56649e175503460f94b02fcc/html5/thumbnails/32.jpg)
KON
FORM
ÁCIÓ
S TÉ
R
.
Prot
ein
fold
ing
és
konf
orm
áció
s té
r
SZER
KEZE
TI
ÉS
Polim
er m
olek
ulák
sz
erke
zete
i és
reak
ciói
Kis
mol
ekul
ák
és re
akci
óik
Configuration and conformational space
C2H4O2
![Page 33: Geometry Optimisation Modelling OH + C 2 H 4 *CH 2 -CH 2 -OH CH 3 -CH 2 -O* 3D PES](https://reader036.vdocuments.site/reader036/viewer/2022062308/56649e175503460f94b02fcc/html5/thumbnails/33.jpg)
Energy landscape
![Page 34: Geometry Optimisation Modelling OH + C 2 H 4 *CH 2 -CH 2 -OH CH 3 -CH 2 -O* 3D PES](https://reader036.vdocuments.site/reader036/viewer/2022062308/56649e175503460f94b02fcc/html5/thumbnails/34.jpg)
R
RCT
TC
TS
3.ábra
●OH + + H2OC6H13N2O3
![Page 35: Geometry Optimisation Modelling OH + C 2 H 4 *CH 2 -CH 2 -OH CH 3 -CH 2 -O* 3D PES](https://reader036.vdocuments.site/reader036/viewer/2022062308/56649e175503460f94b02fcc/html5/thumbnails/35.jpg)
Summery I.
![Page 36: Geometry Optimisation Modelling OH + C 2 H 4 *CH 2 -CH 2 -OH CH 3 -CH 2 -O* 3D PES](https://reader036.vdocuments.site/reader036/viewer/2022062308/56649e175503460f94b02fcc/html5/thumbnails/36.jpg)
Summery II.