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 H 2 –  based picture H H  H2 Deformation density (Differential density) (1) qualitative data by inspection of the sign of  : negative (outflow), positive (inflow) of density due to bond formation H H 1. Start from promolecular state (atom/fragments)  H =1s 2 ADF webinar, Kraków-restoftheworld, 28th Feb., 2014

The Natural Orbitals for Chemical Valence (NOCV) NOCV’s also decompose the deformation density  : useful qualitative data by inspection of the sign of  : negative (outflow), positive (inflow) of density 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: /qua , Mitoraj, M.; Michalak, A. J. Mol. Model. 2008, 14, 681. NOCV’s ( ) diagonalize the deformation density matrix : where  P=P-P 0, density matrix of the combined molecule, P 0 - density matrix of the considered molecular fragments. NOCV’s are in pairs: Radoń, M. Theor Chem Account 2008, 120,337.

back donation back donation The contours of the deformation density (  ) and the contributions from the pairs of complementary orbitals for the heme/CO system  q  = 0.74  q  = 1.04

-D e =  E total =  E dist +  E elstat +  E Pauli +  E orb ETS: Energetic estimation of  k A combination of ETS and NOCV - (ETS-NOCV) NOCV: ETS-NOCV: Mariusz P. Mitoraj, Artur Michalak and Tom Ziegler „A combined charge and energy decom- Position scheme for bond analysis” J. Chem. Theory Comput., 2009, 5 (4), pp 962–975. electronic factor

Dative bonds – systems with symmetry (CO) 5 Cr=CH 2 donation back donation  :CN - > PH 3 > NH 3 > C 2 H 4 > CS > CO > N 2 > NO +  :NO + > CS > CO > N 2 > C 2 H 4 > PH 3 > CN - > NH 3 for Ni(NH 3 ) 3 X complexes: Donor/acceptor properties of ligands Mitoraj Mariusz, Michalak A (2007) „ Donor-Acceptor Properties of Ligands from the Natural Orbitals for Chemical Valence” Organometallics, 26,

Dative Bond NH 3  BH 3 - Calculations Define closed shell fragments, NH 3 and BH 3 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 NH 3  BH 3 - Calculations M.Mitoraj J. Phys. Chem. A, 2011, 115 (51), pp 14708–14716

Crystal of Ammonia Borane, NH 3 BH 3 M.Mitoraj J. Phys. Chem. A, 2011, 115 (51), pp 14708–14716

Inter-Molecular-Hydrogen Bonds Adenine-Thymine kcal/mol, (BP86/TZ2P) A-T  E int  E orb  E Pauli 38.7  E prep 2.1  E elstat  E total - experiment  E total – other theoretical results  E orb =-22.0 Rafał Kurczab, Mariusz P. Mitoraj, Artur Michalak and Tom Ziegler J. Phys. Chem. A,2010, 114, N   *(H-N) H-N covalency! O-H O   *(H-N)

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 CH 3 -CH 3 CH 2 =CH 2 GeH 2 =GeH 2 H 3 CC  CCH 3

Quadruple bond; Re 2 Cl 8 2-  [-1.3 kcal/mol]  1[-65.5 kcal/mol]  2[-65.5 kcal/mol]  [-84.3 kcal/mol]

 E total =-31.3kcal/mol  E orb =  E steric =211.4 Cr 2, formally sixtuple bond, b Cr2-Nal = 6.01  E orb = kcal/mol Typical-Multiple bonds-TM J. Chem. Theory Comput., 2009, 5 (4), pp 962–975.

Ethane Built from two methyl radicals 1. Define CH 3 regions (uneven number of electrons); 2. Run SP RESTRICTED ! Calculations for CH 3 fragments to get the fragment MO’s; (1/2  + 1/2  electrons for SOMO of CH 3 ) 3. Use fragoccupations keyword in order to keep the right occupations for each CH 3 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

 E total =-31.3kcal/mol  E orb =  E steric =211.4 Cr 2, sextuple bond, b Cr2-Nal = 6.01  E orb = kcal/mol Typical-Multiple bonds-TM J. Chem. Theory Comput., 2009, 5 (4), pp 962–975.

Cr 2 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 ); Should be like Cr  but it is Cr 6* 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 4. Run SP ETS-NOCV calculations for whole molecule in the basis of previously calculated fragment MO’s Cr   Cr

Better Fragment MO’s from unrestriced run: advanced ’manual’ usage advanced ’manual’ usage 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); ADF uses in principle only ‚rectricted’ fragments, however, one might cheat him 5. Rerun final ETSNOCV calculations (do not recalculate the fragments!)

Agostic intramolecular RH---Metal interaction Ni-diimine cationic Brookhart model catalyst 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 Ni-C  C  -H polarization C  -C 

ETSNOCV (red-outflow,blue-inflow) -8.3 kcal/mol Halogen Bonding CF 3 I---NH 3 from ETS-NOCV perspective N-I covalency N   *(C-F) charge accumulation, increase s-character (pointed out by prof. Grabowski) Charge outflow, increase positive charge Grabowski S. Chem. Rev., 2011, 111 (4), pp 2597–2625

Domination of the electrostatic factor is due to the presense of σ-hole on iodine atom: F F F I Halogen Bonding CF 3 I---NH 3 from ETS-NOCV perspective (Politzer P, Lane P, Concha MC, Ma Y, Murray J (2007) JMolModel, 13, 305, „An Overview of Halogen Bonding”

Halogen Bonding CF 3 I---NH 3 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 F I Electrostatic potential picture ETS-NOCV picture  (C-F) bond  -hole Charge Anisotropy

Can ETS-NOCV discriminate between halogen and hydrogen bonding within the same molecule? 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? bonding within the same molecule? 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