Transcript Kein Folientitel

COSMO Polarization Charge Densities
as Key Information for
Solubility and Partitioning
Property Prediction
and 3D-QSAR
Andreas Klamt
COSMOlogic GmbH&Co.KG
Leverkusen, Germany
& Inst. of Physical and Theor. Chemistry,
Univ. of Regensburg
The molecular electrostatic potential MEP / ESP
Polarity, i.e. electrostatics, is generally accepted as most important for the
interactions of molecules, and thus for the understanding and prediction
of the behaviour drug molecules.
Hydrogen bonding is considered as a special flavor of polarity.
Molecular electrostatic potentials are the most widely used concept to
quantify and visualize molecular polarity.
But it has a few nasty aspects:
1) It diverges at the positions of the atomic nuclei,
2) It decays only slowly with the distance from the molecule.
3) There is no clear recipe, at which place
or on which surface the MEP should be considered.
4) On the same surface, MEPs of ions on a different scale
than those of neutral compounds. They are hardly comparable.
Let us look for an alternative representation
of molecular polarity.
The conductor polarization charge density
electron
density
The conductor can be taken
into account during the
quantum chemical calculation
using the
Conductor-like Screening Model
(COSMO, Klamt, Schüürmann, 1993)
polarization charge density
s = polarization charge / area
 energy, geometry, polarization charge
density and conformations in conductor
The COSMO embedding already gives an approximate representation of a polar solvent.
For less polar solvents it can be scaled by a simple function f(e) = (e-1)/(e+0.5).
 COSMO has become one of the most popular continuum solvation models
But all dielectric continuum models are fundamentally wrong,
and COSMO-RS follows a different concept !
Interactions of molecules swimming in a conductor
There are no
long-range interactions
of molecules
in conductor!!!
We only
get idea
an energy
change DE,Quantify
if the twointeraction
cavities contact
each
Basic
of COSMO-RS:
energies
as other.
local interactions of COSMO polarization charge densities s and s‘
s s‘
DEcontact = E(s,s‘)
Emisfit (s , s ' )  aeff
'
2
(s  s ' ) 2
Ehb (s , s ' )  aeff chb (T ) min{ 0, ss 's hb }
2
Ehb (s , s ' )  aeff chb (T ) min{ 0, ss 's hb }
2
Linear dependence of EHB on s ESP as HB-descriptor
HB-energies calculated from BP-TZVP clusters with
COSMO
(HF as donor)
DFT-HB-cluster calculations for a week and a strong
donor
0
DFT/COSMO hydrogen bond energies
5.00
-2
0
0.5
1
1.5
N_acc
s (e/nm²)
-6
1
1.2
1.4
1.6
1.8
2
2.2
-8
-10
2.4
2.6
C_acc
S_acc
2.8
donor=HCN)
-12
-5.00
2.5
O_acc
-4
0.00
2
C_acc_s
N_acc_s
-14
O_acc_s
-16
S_acc_s
C_acc_w
-18
-10.00
N_acc_w
O_acc_w
-20
S_acc_w
-15.00
-20.00
donor=HF)
s is the better local interaction descriptor!
Polarization charge densities provide a predictive quantification of hydrogen bond energies
Klamt, Reinisch, Eckert, Hellweg, Diedenhofen, Phys. Chem. Chem. Phys., 2012,14, 955ff
Ehb (s , s ' )  aeff chb (T ) min{ 0, ss 's hb }
exp. hydrogen bond enthalpies
2
Phys. Chem. Chem. Phys.,
2013,15, 7147-7154
Interpretation of experimental
hydrogen-bond enthalpies and
entropies from COSMO
polarisation charge densities
Klamt, Reinisch, Eckert, Graton,
Le Questel
s s‘
Interaction energy of individual contacts:
Emisfit (s , s ' )  aeff
'
2
(s  s ' ) 2
Ehb (s , s ' )  aeff chb (T ) min{ 0, ss 's hb }
2
In a dense liquid all surface pieces are bound in
surface pairs, and the total interaction energy can be
expressed as a sum of surface interactions Eint(s,s‘).
But for liquid phase properties we need free energies,
i.e. contact probabilities of all possible contacts!
For an efficient statistical thermodynamics we reduce the ensemble of
molecules to an ensemble of pair-wise interacting surface segments.
For handling this we need histograms of surface polarity.
Water

5
pwater(s) (amount of surface)
4.5
4
3.5
3
2.5
2
1.5
1
0.5
0
-0.020
-0.015
-0.010
-0.005
0.000
s
0.005
0.010
0.015
[e/A2]
Screening charge distribution on molecular surface
reduces to "s-profile"
0.020
X
p (s )
25
20
Water
Methanol
Acetone
Benzene
15
Chloroform
Hexane
10
5
0
-0.020
-0.015
-0.010
-0.005
0.000
0.005
0.010
0.015
s [e/A ]
2
Screening charge distribution on molecular surface
reduces to "s-profile"
0.020
Next we need the solve the statistical thermodynamics
of an ensemble of surface pieces with a composition:
 x p (s )
(s ) 
 x area
i
pS
i
i
i
i
I.e. we need to calculate chemical potentials and contact probabilities of the pairwise
interacting surface pieces. “Three weeks of sleepless nights“ led to the exact equation:
interaction energy
of s and s‘
solvent s-profile,
i.e. compostion of
solvent S wrt s
 Eint (s , s ' )   S (s ' ) 
 S (s )  kT ln  ds ' pS (s ' exp 

kT


s-potential, i.e.
“pseudo“- chemical
potential of a segment of
polarity s in solvent S
free energy costs
of getting partner
s‘ available
requires iterative solution: µS(s‘)=0
i
5
s-profiles
and
s-potentials of
representative liquids
X
p (s )
0
W ater
Methanol
Acetone
5
Benzene
Chloroform
0
0.70
Hexane
5
hydrophobicity
-0.005
0.000
s [e/A2]
0.005
2
-0.010
0.010
0.015
0.020
0.10
Water
X
-0.015
0.30
 (s ) [kJ/mol A ]
0
0.020
0.50
-0.10
Methanol
affinity for
HB-donors
affinity for
HB-acceptors
Acetone
Benzene
-0.30
Chloroform
Hexane
-0.50
-0.020
-0.015
-0.010
-0.005
0.000
s [e/A2]
0.005
0.010
0.015
0.0
For getting the chemical of a soluteX in a solvent we project the
solvent s-potential back to the solute surface:
   a 
kT ln 
a S(s
S (s
X
S
X
S
 X
X
S ,comb
 X
  dsp d(s p ((ss S kT
ln 
(

s

X
0.30
0.20
spotential
0.10
0.00
-0.10
-0.20
-0.30
Methanol
-0.40
-0.50
-0.020
-0.015
-0.010
-0.005
0.000
s [e/A2]
0.005
0.010
0.015
X
S
X
S ,comb
This is the central equation of COSMO-RS,
since knowing the chemical potential as a function
of composition and temperature
we do have
„size correction“
or almost
the entire liquid phase thermodynamics
in our hands.
combinatorial contribution
(“lended from chem. eng.“):
depends on solute and solvent
volumes and areas
(e.g. from COSMO cavity)
0.020
2fold
For flexible molecules there
are multiple local minima
(conformations)
COSMO-RS knows the
internal energy (from DFT)
and the individual free energy
from central COSMO-RS eq.
At every temperature and
composition COSMO-RS
can calculate the total
free energy of the compound
(from the partition function)
and the exp. values of the all
properties.
Property Calculation
chemical potential of solute X in S:
 SX   ds p X (s  S (s    kT ln AS
chemical potential of solute X in the gasphase:  vapor pressures
X
X
X
X
 Gas
 Evac
 ECOSMO
 AX  el ( )  nring
 0


partition coefficients

K SX,S '  exp ( SX   SX' ) / kT

activity coefficients  arbitrary liquid-liquid equilibria
 SX  exp ( SX   XX ) / kT 
vapor pressure

X
PXX  exp ( gas
  XX ) / kT

Chemical Structure
Phase Diagrams
Flow Chart of
1.0
COSMO-RS
B ina ry M ixt ure o f
B ut a no l a nd Wa t e r
at 60° C
0.8
0.6
y
Calculated
Experiment
0.4
Equilibrium data:
activity coefficients
vapor pressure,
solubility,
partition coefficients
Quantum Chemical
Calculation with COSMO
(full optimization)
0.2
miscibility gap
0.0
0.0
0.2
0.4
x 0.6
0.8
1.0
s-potential of mixture
sigma-potential
0.1
0.05
0
-0.02
-0.01
0
0.01
-0.05
-0.1
s-profiles
of compounds
sigma-profiles
-0.15
-0.2
14
ideally screened molecule
energy + screening charge
distribution on surface
12
10
vanillin
w ater
Fast Statistical
Thermodynamics
acetone
8
6
Database of
COSMO-files
(incl. all common
solvents)
4
other compounds
DFT/COSMO
2
-0.02
0
-0.01
0
0.01
screening charge density [e/A²]
0.02
s-profile
of mixture
COSMOtherm
0.02
2
1
0
-1
a) DGhydr (in kcal/mol)
-2
-11
2
-10
1
COSMOtherm currently is the most
accurate tool for DGsolv prediction:
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
0
-1
-2
-4
2
1
Residuals
0
-1
-2
2
1
0
-1
-2
-5
1
0
-1
-2
-4
2
-3
-2
-1
0
1
2
c) log KV.
Octanol/Water
A. Klamt, B. Mennucci, J. Tomasi,
Barone, C.
-1
0
1
2
3
4
5
Curutchet, M. Orozco and F. Javier Luque,
"On 6the
Performance of Continuum Solvation Methods. A
Comment on “Universal Approaches to Solvation
Modeling”" Acc. Chem. Res., 2009, 42 (4), pp 489
d) log KHexane/Water
------
-2
2
Accuracy (kcal/mol) on 2343 data
b) log Pvapor (in bar)
COSMOtherm 0.48
SM8
0.52 (fitted on this data set!)
PCM
~ 0.9 (only 3 solvents)
-4
SAMPL 2009 blind test for prediction of
DGsolv of very demanding compounds
45 entries from molecular dynamics,
e) logSolvation
KBenzene/Water
Monte Carlo, Continuum
Models, and other methods:
-3
-3
-2
-2
-1
-1
0
1
0
2
1
3
2
4
5
3
6
4
5
COSMO-RS error is about 0.5 kcal/mol smaller than
the that of the second best entry.
-1
f) log KEther/Water
-2
-3
-2
-1
0
1
2
Results of parametrization based on DFT
(DMol3: BP91, DNP-basis
650 data
17 parameters
rms = 0.41 kcal/mol
7
1
0
alkanes
alkenes
alkines
alcohols
ethers
carbonyls
esters
aryls
diverse
amines
amides
N-aryls
nitriles
nitro
chloro
water
3
A. Klamt, V. Jonas, J. Lohrenz, T. Bürger,
J. Phys. Chem. A, 102, 5074 (1998)
meanwhile:
COSMOtherm2.1_0110 with Turbomole
BP91/TZVP
Limited by
rms = 0.29 kcal/mol
accuracy of
DFT!
Applications to Phase Diagrams
1.0
Winner of the
and Azeotropes
1st,5th,6th IFPSC
(AICHE/NIST)
0.9
Binary Mixture of
1-butanol (1) and water
at 60° C
0.8
0.7
y
0.6
Calculated
Experiment
0.5
0.4
0.3
0.2
miscibility gap
0.1
0.0
0.0
1.0
0.1
0.2
0.3
0.4
0.5
x
0.6
0.7
0.8
0.9
1.0
1.0
Binary mixture of
Butanol(1) and Heptane (2)
at 50° C
0.8
Binary mixture of
ethanol (1) and benzene (2)
at 25° C
0.8
0.6
0.6
Calculated
Experiment
y
y
Calculated
Experiment
0.4
0.4
0.2
0.2
0.0
0.0
0.0
0.2
0.4
x
0.6
0.8
1.0
0.0
0.2
0.4
x
0.6
0.8
1.0
COSMOtherm prediction of drug solubility in diverse solvents
(blind test performed with Merck&Co., Inc., Rahway, NJ, USA)
all predictions are
relative to ethanol
solvents:
triethylamine
heptane
Water
1-Propanol
2-Propanol
DMF
Ethyl Acetate
Methanol
Heptane
Toluene
Chlorobenzene
Acetone
Ethanol
Acetonitrile
(Triethylamine)
Butanol
Example
Absolute solvent screening with estimated DGfus
Absolute Solubility of Artemisinin
Gfus=11.39 kJ/mol
0
-1
-2
-3
log(x)
-4
Experiment
Experiment 2
COSMO-RS
-5
-6
-7
Methanol
Ethanol
EtOH/H2O x_EtOH=0.77
EtOH/H2O x_EtOH=0.47
EtOH/H2O x_EtOH=0.27
EtOH/H2O x_EtOH=0.14
Water pH7.2
Acetonitrile
DMI
DMF
Ethylacetate
Acetone
Dimethylcarbonate
Propylene carbonate
Toluene
Chloroform
Hexane
Cyclohexane
All data are simulated / measured at 20°C
Yellow points indicate alternative experimental measurements, the experimental range is additionally visualized by black lines.
Data and DGfus are extracted from Lapkin A., Peters M., Greiner L., Chemat S., Leonhard K., Liauw M., Leitner M., Screening of new
solvents for artemisinin extraction process using abinitio methodology, Green Chem., 2010, DOI: 10.1039/b922001a
Artemisinin:
„Conformational analysis of cyclic acidic -amino acids
in aqueous solution - an evaluation of
different continuum hydration models."
by Peter Aadal Nielsen, Per-Ola Norrby, Jerzy W. Jaroszewski, and Tommy Liljefors, for JACS
Method
Solvent
rms
Model
(kJ/mol)
AM1
SM5.4A
4.6
PM3
SM5.4P
13.6
AM1
SM2.1
7.4
HF/6-31+G* C-PCM
3.1
HF/6-31+G* PB-SCRF
4.7
AMBER*
GB/SA
13.2
MMFF
GB/SA
18.5
rms (4 points)
(kJ/mol)
5.6
16.2
9.0
3.8
5.8
16.2
19.9
Max Dev
(kJ/mol)
9.2
20.5
16.7
5.9
8.8
24.3
31.4
BP-DFT/TZVP COSMO-RS 2.2
2.6
4.8
COSMO-RS was evaluated as a blind test !!!
COSMOtherm first principle pKa prediction
( A. Klamt, et. al. J. Phys. Chem. A 2003, 107, 9380-9386)
18.00
16.00
pKa = 0.58(0.01)DGdiss /(RTln10) +1.66
2
N=64 R =0.982, rms=0.50
pKa_exp
14.00
12.00
10.00
all
8.00
6.00
alcohols
4.00
carboxylic acids
2.00
inorganic acids
0.00
0
10
latest results for bases (pKb):
similar rms
20
DGdiss
subst. phenols
30
40
N-acids (uracils,
imines)
formicacid
aceticacid
chloroaceticacid
dichloroaceticacid0
trichloroaceticacid
n-pentanoicacid
2,2-dimethylpropanoicacid
benzoicacid
oxalicacid0
maleicacid3
fumaricacid
carbonicacid0
phenol
pentachlorophenol
ethanol
2,2,2-trichloroethanol
hypochlorousacid
hypobromousacid
hypoiodousacid
nitrousacid
sulfurousacid
phosphoricacid2
boricacid
5-fluorouracil
5-nitrouracil
cis-5-formyluracil
thymine
trans-5-formyluracil
Uracil
and others
1
Water Solubility log(xH2O)
calculated with COSMOtherm
0
-1
BOSS-Dataset of Jorgensen and Duffy
-2
-3
R2= 0.90
rms=0.66
n = 150
Experiment
-4
-5
-6
-7
DGfus < 0
-8
DGfus > 0
-9
McFarland Test Set
questionable
-10
-11
X
logS
-12
DG
X
S
X
fus
X
= (µ X-µ S+ min(0,DGfus))/1.365
= 0.54 µ
X
X
water
- 0.18*N
ringatom
+0.0029*volume
-13
-13
-12
-11
-10
-9
-8
-7
-6
-5
-4
-3
Calculated
COSMO-RSol has rmse of 0.6 on pesticide test set,
Competing method shows 1.3 on that dataset.
-2
-1
0
1
s-moment regressions enable a range of other ADME predictions
s-moment logBB regression
logBB = 0.0046 area -0.017 sig2 -0.0029 sig3 +0.19
n = 103, r² = 0.71, rms = 0.40
data from: "Modeling Blood-Brain Barrier Partitioning Using Topological Structure
Descriptors", Rose, Hall, Hall, and Kier, MDL-Whitepaper, 2003
1.5
minimum_COSMO_conf.
1.0
CORINA_optimized
exp.
0.5
0.0
-2.0
-1.5
-1.0
-0.5
0.0
-0.5
-1.0
-1.5
-2.0
calc.
0.5
1.0
1.5
logBB
logK_IA
logK_HSA
logK_OC
…
COSMOflat: Simulation of molecules at a flat interface
Concept:
- Just a flat interface between two
arbitrariry user-defined liquids,
(typically one his hydrophobic and other is water)
-construct a total partition sum
- get the probability to find the
solute in a certain depth and orientation.
- get the total free energy change of the solute at this
interface
(conformations can be taken into account, e.g.
stretched vs. collapsed

- surface activity
- surface and interfacial tension
COSMOmic: Simulation of molecules in micelles and membranes (2)
o
o
COSMOmic: A Mechanistic Approach to the Calculation of Membrane-Water Partition
Coefficients and Internal Distributions within Membranes and Micelles, J. Phys. Chem. B, 2008
Andreas Klamt, Uwe Huniar, Simon Spycher, and Jörg Keldenich|
Micelle and Interface Properties: COSMOmic
Example: Free energy profiles through DMP (dimethylphthalate) membrane
MD-simulations*,**
COSMOmic (5 minutes calc. time)
acetamide
25
aceticacid
benzene
20
ethane
methylacetate
15
methylamine
methanol
10
h2o
5
0
0
5
-5
-10
-15
-20
-25
* Simulation results of Daniele Bemporad and Jonathan W. Essex University of Southampton, UK and
** see also Claude Luttmann, J. Phys. Chem. B 2004, 108, 4875ff
10
15
20
25
30
35
Cocrystal-Screening with COSMOtherm
excess heat of mixing!
 Initial tests gave better results than current state-of-the-art method
[1] (6 false positive results versus only 2 with COSMOtherm!)
 Fast screening against large
databases with harmless food
ingredients (EAFUS, GRAS) within
minutes with COSMOfrag
technology.
[1] Hunter et al., Chem. Sci. 2011, 2, 883–
890.
Probability of cocrystallization
So far all COSMO-RS application examples were relevant for
drug-development. Now to drug-design:
Retinal
- the interactions of ligands with receptors are exactly of the same
type as those of solutes and solvents (electrostatics, hydrogen
bonding, vdW – and all in the liquid state) !
-but position plays a far more important role than in liquids: The
right polarity must be at the right place!
- nevertheless, it is a necessary criterium that the molecules have
the right polarities, i.e. a suitable s-profile is a necessary, but not
sufficient condition for strong binding.
COSMOsim
bio-isoster search based on s-profiles
If physiological distribution and drug-receptor binding are to a large
degree determined by s-surfaces and s-profiles, it makes sense to
screen for drug-candidates s-profile-similarity:
- search is based on surface polarity (s) and not on structure => scaffold hopping
- either search over full COSMO-files of COSMOfrag-DB (60000 compounds)
- screen millions of candidate compounds using the COSMOfrag method
- see also: Thormann M, Klamt A, Hornig M, Almstetter M
COSMOsim: bioisosteric similarity based on COSMO-RS sigma profiles.
[J Chem Inf Model. 2006, 46:1040-53]
CCC(=O)O
ZFQCMUCKI
0
1
OC(=O)C=C
ITPZMBCLI
1
0.8169
CCCC(=O)O
IAVMXKDKI
2
0.7996
CC=CC(=O)O
RGQGEAHMI
3
0.791
CC(=C)C(=O)O
WCMTTAFLI
4
0.765
CC=CC(=O)O
VGZSDPDLI
5
0.7584
CC(C)C(=O)O
DGWQYNDKI
6
0.7487
OCC1CO1
SDLNNSMIA
7
0.7269
CC(O)C#N
HTYYARCJZ
8
0.7233
Oc1nnns1
NBAKLRQLI
9
0.7171
CC(O)C(=O)O
WOJBMNDKV
10
0.7109
CC(=O)O
CZWYICCKI
11
0.7052
Clc1nnn[nH]1
JMAKWZALI
12
0.7041
CC(=NO)C
EZHYEWAJI
13
0.6983
OCCC(=O)O
FFBMJKDKI
14
0.6978
CC(=O)C=NO
HOMSZUGLI
15
0.6919
Oc1csnn1
UMBRJEKLI
16
0.6885
OC(=O)C1CCC1
CUOCJIGKI
17
0.6817
OCCS
HLKLSJLHI
18
0.6804
CC1CC1C(=O)O
GXSEIQGKP
19
0.6767
propionic acid similars
12
10
p7
8
p8
6
p9
p12
4
p13
p0
2
p15
0
-0.03 -0.02 -0.02 -0.01 -0.01 0
-2
p7
p12
0.01 0.01 0.02 0.02 0.03
p9
p8
p13
p15
COSMOsim3D
bio-isoster search based on s-surfaces
idea and initial implementation by Dr. M. Thormann, Origenis AG
presented as CUBEsim on COSMO-RS symposium 2009
- places s-surfaces of target and probe on a grid
- alignes probe on target
- 10 -100 different start orientations ( first 21 systematic), ~ 5s – 30s
- gives 3D simlarity measure (CS3D)
- search for molecules with maximum similarity of 3D-s-surfaces
M.Thormann, Origenis
Separation of true and random
bioisosteric pairs
Enrichment of active drugs
in MDDR activity classes
PharmBench performance
PharmBench: reproducing X-ray alignments (performed by Paolo
Tosco, Univ. Turino)
COSMOsar3D:
COSMOsim3D based Molecular Field Analysis:
PLS
Comparison of 3D QSAR models for GPB data set using LSM
and LSP descriptors
8
LSP, training set
7
LSP, test set
LSM, training set
experimental pKi
6
LSM, test set
5
4
3
2
1
0
0
1
2
3
4
5
6
7
8
predicted pKi
The most predictive and robust MFA method presented ever!
COSMOsim3D: 3D-Similarity and Alignment Based on COSMO
Polarization Charge Densities J. Chem. Inf. Model., 2012, 52,2149
COSMOsar3D: Molecular Field Analysis Based on Local COSMO σ-Profiles,
J. Chem. Inf. Model., 2012, 52 ,2157
COSMOsar3D: COSMOsim3D based Molecular Field Analysis:
- do alignment with COSMOsim3D
- use the grid of local s-profiles as descriptor array
by the local s-profiles you have high quality local information about
- electrostatics
- hydrogen bonding
- hydrophobic interactions
- shape
- the ~2Å grid spacing represents some local flexibility and fuzzyness, i.e. it mimics that the
ligand and receptor can slightly adjust to each other.
- If we just assume that the virtual receptor provides a local s-potential at each grid point, then
the binding free energy (including desolvation) should be a linear functional of the local sprofiles! Hence a multi-dimensional regression analysis (as PLS) should have a very good
chance to generate a predictive model for binding constants.
COSMOsim3D based Molecular Field Analysis should be favorable compared
to standard MFA methods! (patent application submitted)
out off the box
COSMOsar3D outperforms
all 7 standard methods
Robustness of COSMOsar3D
compared to standard MFA
and no cutoff-values are required!
COSMOfrag: A fast shortcut of COSMOtherm
suited for HTS-ADME prediction
1) large database of precalculated drug-like compounds (about 130000, incl. ions)
2) for new compound find most similar fragments in database
3) compose approximate COSMO surface from surface fragments
4) write a meta-cosmo-file or a full 3D fcos-file for 3D-QSAR
COSMOfrag requires less than 0.5 sec/compound  HTS
CF-COSMO files (.fcos):
- COSMOsim3D usually would require one quantum-chemical calculation for each
conformation of a ligand which shall be tested. That is doable, but quite time-consuming for
screening ~ 5 min. on AM1/SVP level
- COSMOfrag was able to generate s-profiles for new compounds in less than a second based
on finding the most similar atoms in a big database of ~60000 pre-calculated drug-like
compounds.
-NEW: COSMOfrag now can generate in a second an approximate 3D-COSMO file
(*_cf.cosmo) by searching for the most similar atoms, transforming the respective COSMO
segments into the new local atomic
coordinate system.
CF-cosmo files do not provide a nice
closed COSMO surface, but have the
polarity roughly in the right spatial
reagion.
But they are sufficient for
COSMOsim3D screening.
Summary:
1) The Conductor polarization charge density s provides rich information about molecular
interactions!
2) The COSMO-RS statistical thermodynamics converts s into free energies in liquid
phases and thus yields activity coefficients, solubility … This enables many useful
applications in drug development and formulation: solvent screening, co-crystal
screening, reaction media selection and optimization, ADME predictions, …
3 s-profiles and local 3D- s-profiles are very useful for the description of ligand-receptor
binding.
Information content of s-surfaces
The electrostatic
potential ESP
calculated by DFT with
(or without) COSMO
is dominated by dipole
moment. Almost no
local features (lone pair
directions, structure on
halogen atoms) can be
seen.
The conductor
polarization charge
density s, calculated
from DFT/COSMO,
shows lone pair
directions and many
polarity details (e.g. on
halogen atoms).
It is a very good local
measure of polarity.
If s is calculated from
ESP-fitted point
charges, the picture
looks similar on the
first glance, but all
details get lost, because
a point charge
representation is unable
to reflect sub-atomar
orbital features!