Applications of ETS-NOCV method in description of various
types of chemical bonds
Mariusz P. Mitoraj
Jagiellonian University
Cracow, Poland
Department of Theoretical Chemistry
ADF webinar, Kraków-rest-of-the-world, 28th Feb., 2014
Examples of theoretical quantities for visualization of chemical bond
ADF webinar, Kraków-restoftheworld, 28th Feb., 2014
Formation of chemical bond in H2 –  based picture
1. Start from promolecular state (atom/fragments)
H
H
H2
H=1s2
H
   H
2
 2H
H=1s2
H
Deformation density (Differential density)
(1) qualitative data
by inspection of the sign
of : negative (outflow),
positive (inflow) of density
due to bond formation
ADF webinar, Kraków-restoftheworld, 28th Feb., 2014
The Natural Orbitals for Chemical Valence (NOCV)
NOCV’s ( ψ i   C ij * λ i) diagonalize the deformation density matrix:
i
 PC i  v i C i
;
i = 1, M
where P=P-P0 , density matrix of the combined molecule,
P0- density matrix of the considered molecular fragments.
NOCV’s
also decompose the deformation density :

useful qualitative data
by inspection of the sign
of : negative (outflow),
positive (inflow) of density
M
ρ(r) 

2
vkψk
(r)
k 1
NOCV’s are in pairs:
M /2
  (r ) 
 v k [  k (r )   k ( r)] 
2
k1
2
M /2
 
k
( r)
k1
Radoń, M. Theor Chem Account 2008, 120,337.
Mitoraj, M.; Michalak, A. Organometallics 2007, 26(26); 6576., Michalak, A.; Mitoraj, M.; Ziegler, T. J.
Phys. Chem. A. 2008, 112 (9), 1933, Mitoraj, M.; Michalak, A. J. Mol. Model., 2008, 14, 681, Mitoraj,
M.; Zhu, H.; Michalak, A.; Ziegler, T. 2008, International Journal of Quantum Chemistry, DOI:
10.1002/qua.21910., Mitoraj, M.; Michalak, A. J. Mol. Model. 2008, 14, 681.
The contours of the deformation density () and the contributions
from the pairs of complementary orbitals for the heme/CO system
n
 (r ) 
  i i r 
2
i 1
q = 0.74
q = 1.04
donation
back
donation
back
donation
A combination of ETS and NOCV - (ETS-NOCV)
ETS: -De=Etotal= Edist + Eelstat + EPauli + Eorb
λμ
 E orb 
electronic
factor
 Pλμ Fλμ
orb
TS
N/2
NOCV:
ρ
orb

(r) 
N/2
2
2
v k [  ψ  k ( r )  ψ k ( r )] 
k 1
 ρ k (r)
k 1
ETS-NOCV:
 E orb  Tr(  P
orb
F
TS

)  Tr ( C  P
orb
CC

N/2
F
TS
C) 

k 1
M /2
 E orb 

k 1
N/2
TS
TS
v k [  F k ,  k  Fk , k ] 
M /2
TS
v k [  F k

TS
F k ]


k
k
 E orb
 E k
orb
k 1
Energetic estimation
of k
Mariusz P. Mitoraj, Artur Michalak and Tom Ziegler „A combined charge and energy decomPosition scheme for bond analysis” J. Chem. Theory Comput., 2009, 5 (4), pp 962–975.
Dative bonds – systems with symmetry
(CO)5Cr=CH2
donation
back
donation
Donor/acceptor properties of ligands for Ni(NH3)3 X complexes:
:CN- > PH3 > NH3 > C2H4 > CS > CO > N2 > NO+
:NO+ > CS > CO > N2 > C2H4 > PH3 > CN- > NH3
Mitoraj Mariusz, Michalak A (2007) „ Donor-Acceptor Properties of Ligands from the Natural Orbitals for
Chemical Valence” Organometallics, 26, 6576-6580
Dative Bond NH3BH3 - Calculations
• Define closed shell fragments, NH3 and BH3
• Run SP calculations to get the fragment MO’s
• Run SP ETS-NOCV calculations for whole molecule in the basis
of previously calculated fragment MO’s
Dative Bond NH3BH3 - Calculations
M.Mitoraj J. Phys. Chem. A, 2011, 115 (51), pp 14708–14716
Crystal of Ammonia Borane, NH3BH3
M.Mitoraj J. Phys. Chem. A, 2011, 115 (51), pp 14708–14716
Inter-Molecular-Hydrogen Bonds
Adenine-Thymine
kcal/mol,
(BP86/TZ2P)
A-T
Eint
-13.0
Eorb
-22.0
EPauli
38.7
Eprep
2.1
Eelstat
-31.9
Etotalexperiment99
-12.1
Etotal – other
theoretical
results
Eorb=-22.0
-13.2
O*(H-N)
N*(H-N)
O-H
H-N covalency!
Rafał Kurczab, Mariusz P. Mitoraj, Artur Michalak and Tom Ziegler
J. Phys. Chem. A,2010, 114, 8581.
Hydrogen Bond A-T Calculations
• Define closed shell fragments, Adenine and Thymine
• Run SP calculations to get the fragment MO’s
• Run SP ETS-NOCV calculations for whole molecule in the basis
of previously calculated fragment MO’s
ADF webinar, Kraków-restoftheworld, 28th Feb., 2014
Covalent bonds
CH3-CH3
CH2=CH2
GeH2=GeH2
H3CCCCH3
Quadruple bond; Re2Cl82[-84.3 kcal/mol]
2[-65.5 kcal/mol]
1[-65.5 kcal/mol]
[-1.3 kcal/mol]
Typical-Multiple bonds-TM
Cr2, formally sixtuple bond, bCr2-Nal = 6.01
Etotal=-31.3kcal/mol
Eorb=-242.7
Esteric=211.4
Eorb=-242.7 kcal/mol
J. Chem. Theory Comput., 2009, 5 (4), pp 962–975.
Ethane Built from two methyl radicals
1. Define CH3 regions (uneven number of electrons);
2. Run SP RESTRICTED ! Calculations for CH3 fragments
to get the fragment MO’s; (1/2 + 1/2 electrons for SOMO of CH3)
3. Use fragoccupations keyword in order to keep the right occupations
for each CH3
fragoccupations
f1 A 5 // 4
subend
f2 A 4 // 5
subend
End
4. Run SP ETS-NOCV calculations for whole molecule in the basis
of previously calculated fragment MO’s -alpha-and beta-NOCV’s
Typical-Multiple bonds-TM
Cr2, sextuple bond, bCr2-Nal = 6.01
Etotal=-31.3kcal/mol
Eorb=-242.7
Esteric=211.4
Eorb=-242.7 kcal/mol
J. Chem. Theory Comput., 2009, 5 (4), pp 962–975.
Cr2 Built from two Cr+Cr
1. Define Cr regions (uneven number of electrons);
2. Run SP RESTRICTED ! Calculations for Cr fragments
using OCCUPATION keyword (A 18 1 1 1 1 1 1);
Should be like Cr but it is Cr 6* (1/2 + 1/2) so we must:
3. Use fragoccupations keyword in order to keep the right occupations
for each Cr.
fragoccupations
Region_1
A 15//9
subend
Region_2
A 9//15
subend
End
Cr
Cr
4. Run SP ETS-NOCV calculations for whole molecule in the basis
of previously calculated fragment MO’s
Better Fragment MO’s from unrestriced run:
advanced ’manual’ usage
ADF uses in principle only ‚rectricted’ fragments, however,
one might cheat him
1. Run open shell calculations for a given fragment;
2. Save tape21  ascii (dmpkf) copy the final MO’s
(from the section Eig-CoreSFO_A, MO’s expressed in SFO);
3. Run fragment calculations by setting SCF=0 wrong MO’s
save tape21asciifind Eig-CoreSFO_A section, then:
4. Take MO’s and occupations, energies, from step 2 and paste them to
Tape21 from step 3…..it gives you right fragment MO’s
Transform asciibinary(udmpkf);
5. Rerun final ETSNOCV calculations (do not recalculate the fragments!)
Agostic intramolecular RH---Metal interaction
Ni-diimine cationic Brookhart model catalyst
C-H
polarization
Ni-C
C-C
Mariusz P. Mitoraj, Artur Michalak and Tom Ziegler „On the Nature of the Agostic Bond between
Metal Centers and -Hydrogen Atoms in Alkyl Complexes. An Analysis Based on the Extended
Transition State Method and the Natural Orbitals for Chemical Valence Scheme (ETS-NOCV)”
Organometallics, 2009, 28 (13), pp 3727
Halogen Bonding CF3I---NH3 from ETS-NOCV perspective
H
H
F
N
H
I
C
F
F
Charge outflow, increase positive charge
ETSNOCV(red-outflow,blue-inflow)
-8.3 kcal/mol
N-I covalency
N*(C-F)
charge accumulation, increase s-character
(pointed out by prof. Grabowski)
Grabowski S. Chem. Rev., 2011, 111 (4), pp 2597–2625
Halogen Bonding CF3I---NH3 from ETS-NOCV perspective
Domination of the electrostatic factor is due to the presense of σ-hole
on iodine atom:
F
F
I
F
(Politzer P, Lane P, Concha MC, Ma Y, Murray J (2007) JMolModel,
13, 305, „An Overview of Halogen Bonding”
Halogen Bonding CF3I---NH3 from ETS-NOCV perspective
Prof. Politzer, „Program & Book of Abstracts”, MIB 2011,
„….The weakness of this interpretation (electrostatic) is that it is
simple and straightforward, and therefore is viewed by some with
suspicion.
F
F
C
F
F
I
-hole
I
(C-F) bond
F
F
Electrostatic potential
picture
Charge
Anisotropy
ETS-NOCV picture
Can ETS-NOCV discriminate between halogen and hydrogen
bonding within the same molecule?
Anion receptor based on urea, which involve hydrogen and halogen
Bonding at the same time|:
Chudzinski, et all, JACS, 2011, 133, 10559
Can ETS-NOCV discriminate between halogen and hydrogen
bonding within the same molecule?
-22.3 kcal/mol
-6.3 kcal/mol
Yes: ETS-NOCV can separate halogen and hydrogen connections
Cl- / rest
• Define closed shell fragments, Cl minus + rest of the complex
• Run SP calculations to get the fragment MO’s
• Run SP ETS-NOCV calculations for whole molecule in the basis
of previously calculated fragment MO’s
ADF webinar, Kraków-restoftheworld, 28th Feb., 2014
Thank You very much for
Your Attention!
ADF webinar, Kraków-restoftheworld, 28th Feb., 2014
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