SBM CDT 2019 Computational Module - Day 2 Dr Fernanda Duarte - duarte Research Group
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SBM CDT 2019
Computational Module
Day 2
Dr Fernanda Duarte
Department of Chemistry, University of Oxford
http://fduartegroup.org 1
Workplan
Tuesday Wednesday Friday
9:00-10:00
Lecture 2 Lecture 3*
10:30-12:00 Lecture 1 Project Work Project Work
14:00- 17:00 Lab session Project Work Presentations
Lab session Project Work Presentations
2
Outline (Lecture 2)
• Day 1
• The good side: Applications of DFT in Chemistry
• The other side …. Challenges in DFT modelling
• A bit more on Functionals and Basis sets
3
3
Computational Chemistry
Why should you care?
Hˆ = Hˆ N + Hˆ e
Ĥ Y = E Y Born-Oppenheimer Approximation
Y = y ey N
Theory
Electronic Schrödinger Equation
Modelling
Hˆ ey e = Eey e
-! 2 electrons electrons nuclei
ZA electrons
1
Hˆ e =
2m
å i
Ñi2 - å å
i A ri - R A
+ å
i< j ri - r j
Kinetic energy Coulomb attraction Electronic repulsion
(nuclei-electrons)
Experiments
Synthesis
Kinetics
spectroscopy
“Artificial Intelligence will not replace chemists. But chemists who doesn’t use (AI)
will be replace by those who do” Willem Van Hoorn 4
Computational Chemistry
What is - and why is it relevant?
Which System Do I Have?
What Do You Want to Compute (and Why)?
Which Model /Method Should I Choose?
Verify Approach (vs. Experiment)
Interpret/Analyse 5
Computational Chemistry
Which System Do I Have?
10 atoms – organic molecule – singlet
6
Computational Chemistry
What Do I Want to Compute (and Why)?
Asymmetric Induction via 1,2-Addition to Carbonyl Compounds
Conformations for the starting material and TS
Which product is preferred?
What is the molecular origin of such preference?
7
Computational Chemistry
Which Model /Method Should I Choose?
Chemical Accuracy
{φi} double hybrid:
ωB97X-2, XYG3, B2PLYP
HF/3-21G
εx hybrid-GGA: hyper-meta-GGA:
NOT recommended
Simplicity
B3LYP, mPW1K M06-2X, M11,TPSSh
Accuracy
Many known deficiencies
τ or meta-GGA: …
∇2ρ(r) τHCTH,TPSS, M06-L But fast…
∇ρ(r) GGA: Wong and Paddon-Row
PBE, BLYP, OLYP, B97 Theoretical evidence in support of the Anh – Eisenstein
electronic model in controlling π-facial stereoselectivity in
nucleophilic additions to carbonyl compounds
ρ(r) LDA: VWN, GPW92
J. Chem. Soc. Chem. Commun. 1990, 456
Hartree Fock theory
8
Computational Chemistry
Which System Do I Have?
What Do You Want to Compute (and Why)?
Often the most
Which Model /Method Should I Choose? interesting result is
when the “calculation
gets it wrong”
Verify Approach (vs. Experiment/Previous studies)
Interpret/Analyse
9
Computational Chemistry
Conformational Analysis: 2 minima
ΔG = -RTlnK
K = exp[-(ΔΔG)/RT]/RT
K = e-3.6 kcal/mol /(0.001987)(298) = [A]/[B]
Thus % min1 = (0.0023/1.0023) x 100% = 99.8%
T(K) = 298 R(kcal mol-1) = 0.001987
R(kJ K-1 mol-1) = 8.3144598 ×10−3
h(J*s) = 6.6262 x 10-34 kb(J/K) = 1.3807 x 10-23
10Computational Chemistry
Conformational Analysis: 2 minima
k BT - DG
k= e / RT
h
T(K) = 298 R(kcal mol-1) = 0.001987
R(kJ K-1 mol-1) = 8.3144598 ×10−3
h(J*s) = 6.6262 x 10-34 kb(J/K) = 1.3807 x 10-23 11Computational Chemistry
Asymmetric Induction via 1,2-Addition to Carbonyl Compounds
Cornforth model J. Am. Chem. Soc. 1959
polar Felkin−Anh (PFA) model Tetrahedron Lett. 1968
Computational Organic Chemistry
Steven M. Bachrach
Paddon-Row, Rondan & Houk J. Am. Chem. Soc. 1982, 104, 7162.
Houk, Paddon-Row, Rondan, Wu, Brown, Spellmeyer, Metz, Li & Longarich Science 1986, 231, 1108
Cee, Cramer & Evans J. Am. Chem. Soc. 2006, 128, 2920
12Computational Chemistry
Physical Organic Chemistry
transforms slowly at room temperature
O
benzene benzene
endo + O exo
diastereomer RT Δ diastereomer
O
Kinetic Thermodynamic
Product Product
13
https://pubs.rsc.org/en/Content/ArticleLanding/2016/CS/C6CS00573JComputational Chemistry
transforms slowly at room temperature
O
benzene benzene
endo + O exo
diastereomer RT Δ diastereomer
O
Kinetic Thermodynamic
Product Product
20.4
19.6 +
+ ΔΔG
O
O
O
O O
O 0.0
+
-6.7
+ ΔΔGrxn -7.6
+ 14
https://pubs.rsc.org/en/Content/ArticleLanding/2016/CS/C6CS00573JComputational Chemistry
15
https://pubs.rsc.org/en/Content/ArticleLanding/2016/CS/C6CS00573JComputational Chemistry
Conformations
ΔG
n = exp[-(ΔG2-ΔG1)/RT] ni/∑n (%)
(kcal mol-1)
0.0 1.00 83.4
1.0 0.18 15.4
2.5 0.01 1.2
5.0 0.00 0.0
1.20 100.0
T(K) = 298 R(kcal mol-1) = 0.001987
R(kJ K-1 mol-1) = 8.3144598 ×10−3
16
http://www.metadynamics.cz/eyring/eyring.htmlComputational Chemistry
Kinetics k BT - DG
k= e / RT
h
T(K) = 298 R(kcal mol-1) = 0.00831
R(kJ K-1 mol-1) = 8.3144598 ×10−3
h(J*s) = 6.6262 x 10-34 kb(J/K) = 1.3807 x 10-23
ΔG‡ k t1/2
t1/2
(kcal mol-1) (s-1) (s-1)
12 9.8 x 103 7.1 x 10-5 70.5μs
17 2.11 3.3 x 10-1 327 ms
22 4.5 x 10-4 1.5 x 103 25min
27 9.8 x 10-8 7.1 x 106 81.1 days
30 6.2 x 10-10 2.4 x 10-6 35.5 years
17
http://www.metadynamics.cz/eyring/eyring.htmlComputational Chemistry
When there are competing pathways leading from interconverting intermediates, the product
ratio is determined by the relative heights of the highest energy barriers leading to the products"
18
http://www.metadynamics.cz/eyring/eyring.htmlComputational Chemistry
Experimental Determinations of Activation Parameters
ΔG‡ = ΔH‡ – TΔS
entropy: energy associated with conformation, bond strength, vibrational states and how changes
in these properties affect the overall energy of the system.
enthalpy: can be related to the height of the surface while entropy is related to the width of the
channels leading from one energy well to another
19
http://www.metadynamics.cz/eyring/eyring.htmlComputational Chemistry
Experimental Determinations of Activation Parameters
ions of Activation and Arrhenius Parameters
ΔG‡ = ΔH‡ – TΔS
tically manipulated to give the equation of a line with a
Eyring plot
kh slope H
ln
kBT
y-intercept S
1 / T (K-1)
equation allows one to experimentally determine values
Arrhenius plot
20
slope Ea
ln k
http://www.metadynamics.cz/eyring/eyring.html
y-intercept AWhat is DFT useful for?
Phosphate/sulfate hydrolysis
Dissociative
Associative
2.34 2.45
n g
2.27 1.75
m i
For
Bond
P-r e a k i ng
B o n d B
Olg
21
Neese et al. J. Chem. Phys. 2013, 138, 034106
Kumar et al. Chem. Sci. 2018, 9, 2655What is DFT useful for?
Phosphate/sulfate hydrolysis
associative dissociative
Linear Free energy Relationship (LFER)
-4
a. 3,5-NO2 -1.42±0.03
NO2 O O NO2
b.
O O 4-NO 2 O-6 O O O X
2 O O c. 3-NO2-4-Cl
S P CH3 P P
X O d. O O O O -8 O O O
3-NO2
log k/ s-1
P
O O e. 3,4-Cl -10
f. 3-Cl -12
g. 4-Cl
h. H -14
-16
-18
6 8 10 12 14
pKa
22
Duarte et al. J. Am. Chem. Soc. 2015, 137, 1081 (Cover article and Spotlight)
Duarte et al. J. Am. Chem. Soc. 2016, 138, 10664he aromatic ring.41 This complexes (A), (C), (E), and (G) CCSD(T) calculations were also
What is DFT useful for?
otein inter-residue inter- carried out using a dielectric constant of 4.2 (diethyl ether) and
plexes can adopt at least 78.4 (water). 30
haped) or parallel. While In relation to the D6h symmetry of benzene, two vectors in the
in gas-phase, parallel- plane of the ring represent extreme scenarios of displacement –
nd have been observed Magnitudes and origins of nonbonded interactions
one towards a C–H bond (angle displacement) and the other
3
We studied the parallel towards a C–C bond (side displacement). These vectors are
relevance.7,44 For [C6H6] related by a rotation of m ¼ 30# about the C6 axis (Fig. 3). By 35
r and parallel arrange- plotting a potential energy curve (PEC) with vertical distance
ns.45 We included
Cation–πboth interactions [C6H6][NH4]+ [C6H6][Gdm]+
y (Eint) of each model
termolecular separation 40 ]
el to the aromatic plane.
e center of mass of both
x,y) displacements are
ng as shown (Fig. 3).
45
generated at the domain-
[C6H6][ImiP]+ [C6H6][ImiT]+
d cluster with perturba-
T),46 level of theory. An
is set, aug-cc-pVTZ, was
TZ, and QZ quality basis 50
Na]+ complex (Fig. S1†).
on closely matches that
asis, with an interaction Fig. 3 (Left) Parameters describing the relative geometry for PEC
CCSD(T) energies achieve calculations between the cation and benzene using the distance (R),
compared to CCSD(T),47 vertical offset (Rz, along the normal) and horizontal offsets (Rx and Ry, 55
y considered benchmark parallel to the plane of benzene). (Right) The side and angle 23
displacements of the cation relative to benzene corresponding to
on energies.48 DLPNO- vectors pointing to a C–C/C–H bond by adjusting X and Y coordinates,
Neese
ganic et al. J. is
molecules Chem.
accu-Phys. 2013, 138, 034106
used to describe the difference in geometry between pairs of
Kumar et al. Chem. 49 Sci. 2018, 9, 2655We computed DLPNO-CCSD(T)/aug-cc-pVTZ interaction energies f
24
along an intermolecular axis perpendicular to the aromatic plane, as show
–7.4 kcal mol–1
A C E F
[C6H6][Gdm]+
Magnitudes and origins of nonbonded interactions
D
–7.5 kcal mol–1
B D F G
C
-3 3 kcal/mol
Figure 4. Top: DLPNO-CCSD(T)/aug-cc-pVTZ interaction energies (kcal mol–1) as a function of intermolecular
separation of cation–π complexes. Minimum energies (Emin) and equilibrium separations (Rz) shown. Bottom: NCI
isosurfaces at the minimum energy separations.
12
–18.7 kcal mol–1
A C E
What is DFT useful for?
[C6H6][NH4]+
B
–19.2 kcal mol–1
DLPNO-CCSD(T)/aug-cc-pVTZ
B D F
CPCM-MP2/cc-pVTZ
A
-3 3 kcal/mol
Figure 4. Top: DLPNO-CCSD(T)/aug-cc-pVTZ interaction energies (kcal mol–1) asWhat is DFT useful for?
Kinetic Catalytic Model Angewandte
Chemie
elimination to form a weakly
bonded complex 17 between the
product and [HCo(CO)3]. Finally,
to complete the formal catalytic
cycle, this species can release the
product and add carbon monoxide.
DFT optimisation and frequency
While the above cycle is de-
scribed as starting from monomeric
B3LYP/6-311G(d)
1, this species is known to be in
(fairly rapid) equilibrium with
[Co2(CO)8] 23 under catalytic con-
ditions. For this species CCSD(T)
Single-point energies
calculations are not possible
CCSD(T)-F12 (explicit treatment of
(because of computational expense
and multireference behavior) so
electron correlation).
our computed energy is based on
DFT. The calculated free energy
change of 30.6 kJ mol!1 for forming
two equivalents of 1 from 23 and
hydrogen is in good agreement
with the experimental value mea-
sured in heptane (22.6 kJ mol!1).[17]
Alkene hydrogenation is
a wasteful side reaction in some
applications of hydroformylation,
but has not been considered in
previous studies of the cobalt-cata-
lyzed reaction.[10] We propose that
it occurs from intermediate 6, by
addition of H2 instead of CO, to
yield the dihydrogen complex 20,
over a low barrier TS19. In contrast
to the case of the related complex
13, which yields product 18 through
25
Scheme 1. Modeled catalytic cycle for alkene hydroformylation and hydrogenation. oxidative addition/reductive elimi-
nation, release of propane 22 is
Harvey et al Angew. Chem. Int. Ed. 2014, 53, 8672 found to occur through a one-step
s-bond metathesis over TS21. ThisWhich Softwares Do I Use?
!Turbomole 6.2 $$
http://www.turbomole.com
Gaussian 09/16 $$$$$$
!Q-Chem 3.2 $$$$
http://www.gaussian.com
http://www.q-chem.com
General purpose, easy interface
!Molpro7 $$$$
http://www.molpro.net
!ADF 2010 $$$$$$$$$$$$$$$$$$$$$$$$$
Accurate correlated ab initio methods
http://www.scm.com
General purpose, DFT-oriented
!Molcas 7$?
http://www.teokem.lu.se/molcas
!Jaguar 2010 $$$$$$$$$$$$$$$$$$$$$$$$$
Excited states (CASSCF, RASSCF, CASPT2)
http://www.schrodinger.com/products/14/7
General purpose, fast DFT
!Crystal 09 $
!Spartan’10 $$
http://www.crystal.unito.it
http://www.wavefun.com/products/spartan.html
General purpose, fast DFT and post-HF
General purpose, GUI included
Solid state and physics, periodic conditions
26Which Softwares Do I Use?
!Abinit 6.6
!GAMESS Oct1, 2010 http://www.abinit.org
http://www.msg.ameslab.gov/gamess Light and portable DFT code
General purpose and highly scalable !Dirac 6.6
!NWChem 6.0 http://wiki.chem.vu.nl/dirac/index.php/Dirac_Program
http://www.nwchem-sw.org Properties using relativistic calculations
General purpose and intensively parallelized !Siesta 3.0
!Orca 2.8 http://www.icmab.es/siesta
http://www.thch.uni-bonn.de/tc/orca Simulations of materials
General purpose, extra-fast RI-DFT and RI-CC !CPMD 3.13
!Dalton 2.0 http://www.cpmd.org
http://www.kjemi.uio.no/software/dalton Carr-Parrinello Molecular Dynamics
General purpose, multi-reference calculations !CP2K
!Mopac 2009 http://cp2k.berlios.de
http://openmopac.net/MOPAC2009.html Solid state, liquids and biological simulations
Semiempirical methods (PM3, PM6) !Octopus 3.2
!SAPT 2008 http://www.tddft.org/programs/octopus/wiki
http://www.physics.udel.edu/~szalewic/SAPT Symmetry-Adapted Perturbation Theory
TDDFT 27Break
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