Mariusz P. Mitoraj

A Combined Charge and Energy Decomposition Scheme for Bond Analysis

UNLABELLED In the present study we have introduced a new scheme for chemical bond analysis by combining the Extended Transition State (ETS) method [ Theor. Chim. Acta 1977, 46, 1 ] with the Natural Orbitals for Chemical Valence (NOCV) theory [ J. Phys. Chem. A 2008, 112, 1933 ; J. Mol. MODEL 2007, 13, 347 ]. The ETS-NOCV charge and energy decomposition scheme based on the Kohn-Sham approach makes it not only possible to decompose the deformation density, Δρ, into the different components (such as σ, π, δ, etc.) of the chemical bond, but it also provides the corresponding energy contributions to the total bond energy. Thus, the ETS-NOCV scheme offers a compact, qualitative, and quantitative picture of the chemical bond formation within one common theoretical framework. Although, the ETS-NOCV approach contains a certain arbitrariness in the definition of the molecular subsystems that constitute the whole molecule, it can be widely used for the description of different types of chemical bonds. The applicability of the ETS-NOCV scheme is demonstrated for single (H3X-XH3, for X = C, Si, Ge, Sn) and multiple (H2X═XH2, H3CX≡XCH3, for X = C, Ge) covalent bonds between main group elements, for sextuple and quadruple bonds between metal centers (Cr2, Mo2, W2, [Cl4CrCrCl4](4-)), and for double bonds between a metal and a main group element ((CO)5Cr═XH2, for X = C, Si, Ge, Sn). We include finally two applications involving hydrogen bonding. The first covers the adenine-thymine base pair and the second the interaction between C-H bonds and the metal center in the alkyl complex.

Bond Orbitals from Chemical Valence Theory

Two sets of orbitals are derived, directly connected to the Nalewajski-Mrozek valence and bond-multiplicity indices: Localized Orbitals from the Bond-Multiplicity Operator (LOBO) and the Natural Orbitals for Chemical Valence (NOCV). LOBO are defined as the eigenvectors of the bond-multiplicity operator. The expectation value of this operator is the corresponding bond index. Thus, the approach presented here allows for a discussion of localized orbitals and bond multiplicity within one common framework of chemical valence theory. Another set of orbitals discussed in the present work, NOCV, are defined as eigenvectors of the overall chemical valence operator. This set of orbitals can be especially useful for a description of bonding in transition metal complexes, as it allows for separation of the deformation density contributions originating from the ligand --> metal donation and metal --> ligand back-donation.

Palladium Catalysts for Dehydrogenation of Ammonia Borane with Preferential B−H Activation

Cationic Pd(II) complexes catalyzed the dehydrogenation of ammonia borane in the most efficient manner with the release of 2.0 equiv of H(2) in less than 60 s at 25 degrees C. Most of the hydrogen atoms were obtained from the boron atom of the ammonia borane. The first step of the dehydrogenation reaction was elaborated using density functional theory calculations.

Applications of natural orbitals for chemical valence in a description of bonding in conjugated molecules

AbstractNatural orbitals for chemical valence (NOCV) were used to describe bonding in conjugated π-electron molecules. The ‘single’ C–C bond in trans-1,3-butadiene, 1,3-butadiene-1,1,4,4-tetra-carboxilic acid, 1,3,5,7-octatetraene, and 11-cis-retinal was characterized. In the NOCV framework, the formation of the σ-bond appears as the sum of two complementary charge transfer processes from each vinyl fragment to the bond region, and partially to the other fragment. The formation of the π-component of the bond is described by two pairs of NOCV representing the transfer of charge density from the neighboring ‘double’ C–C bonds. The NOCV eigenvalues and the related fragment-fragment bond multiplicities were used as quantitative measures of the σ- and π- contributions. The σ-component of the ‘single’ C-C bonds appears to be practically constant in the systems analyzed, whereas the π-contributions increase from butadiene (ca. 7.5%) to retinal (ca. 14%). FigureNatural orbitals for chemical valence (NOCV) contributions to the deformation density describing the π-component of the ‘single’ C–C bonds in butadiene and retinal

Multiple boron-boron bonds in neutral molecules: an insight from the extended transition state method and the natural orbitals for chemical valence scheme.

We have analyzed the character of B═B and B≡B bonds in the neutral molecules of general form: LHB═BHL (2-L) and LB≡BL (3-L), for various ancillary ligands L attached to the boron center, based on a recently developed method that combines the extended transition state scheme with the theory of natural orbitals for chemical valence (ETS-NOCV). In the case of molecules with the B═B bond, 2-L, we have included L = PMe(3), PF(3), PCl(3), PH(3), C(3)H(4)N(2)═C(NHCH)(2), whereas for molecules containing the B≡B connection, 3-L, the following ligands were considered L = CO, PMe(3), PCl(3), (Me(2)NCH(2)CH(2)O)(2)Ge. The results led us to conclude that use of phosphorus ligands leads to strengthening of the B═B bond by 6.4 kcal/mol (for 2-PMe(3)), by 4.4 (for 2-PF(3)) and by 9.2 (for 2-PH(3)), when compared to a molecule developed on the experimental basis, 2-C(3)H(4)N(2) (ΔE(total) = -118.3 kcal/mol). The ETS scheme has shown that all contributions, that is, (i) orbital interaction ΔE(orb), (ii) Pauli repulsion ΔE(Pauli), and (iii) electrostatic stabilization ΔE(elstat), are important in determining the trend in the B═B bond energies, ΔE(total). ETS-NOCV results revealed that both σ(B═B) and π(B═B) contributions are responsible for the changes in ΔE(orb) values. All considered molecules of the type LB≡BL, 3-L, exhibit a stronger B≡B bond when compared to a double B═B connection in 2-L (|ΔE(total)| is lower by 11.8-42.5 kcal/mol, depending on the molecule). The main reason is a lower Pauli repulsion contribution noted for 3-CO, 3-PMe(3), and 3-PCl(3) molecules. In addition, in the case of 3-PMe(3) and 3-PCl(3), the orbital interaction term is more stabilizing; however, the effect is less pronounced compared to the drop in the Pauli repulsion term. In all of the systems with double and triple boron-boron bonds, the electronic factor (ΔE(orb)) dominates over the electrostatic contribution (ΔE(elstat)). Finally, the strongest B≡B connection was found for 3-Ge [L = (Me(2)NCH(2)CH(2)O)(2)Ge], predominantly as a result of the strongest σ- and π-contributions, despite the highest destabilization originating from the sizable bulkiness of the germanium-containing ligand. The data on energetic stability of multiple boron-boron bonds (relatively high values of bond dissociation energies |ΔE(total)|), suggest that it should be possible to isolate experimentally the novel proposed systems with double B═B bonds, 2-PMe(3), 2-PF(3), 2-PCl(3), and 2-PH(3), and those with triple B≡B connections, 3-PMe(3), 3-Ge, and 3-PCl(3).

Bonding in ammonia borane: an analysis based on the natural orbitals for chemical valence and the extended transition state method (ETS-NOCV).

In the present study the natural orbitals for chemical valence (NOCVs) combined with the energy decomposition scheme (ETS) were used to characterize bonding in various clusters of ammonia borane (borazane): dimer D, trimer TR, tetramer TE, and the crystal based models: nonamer N and tetrakaidecamer TD. ETS-NOCV results have shown that shortening of the B-N bond (by ~0.1 Å) in ammonia borane crystal (as compared to isolated borazane molecule) is related to the enhancement of donation (by 6.5 kcal/mol) and electrostatic (by 11.3 kcal/mol) contributions. This, in turn, is caused solely by the electrostatic dipole-dipole interaction between ammonia borane units; dihydrogen bonding, BH···HN, formed between borazane units exhibits no direct impact on B-N bond contraction. On the other hand, formation of dihydrogen bonding appeared to be very important in the total stabilization of single borazane unit, namely, ETS-based data indicated that it leads to significant electronic stabilization ΔE(orb) = -17.5 kcal/mol, which is only slightly less important than the electrostatic term, ΔE(elstat) = -19.4 kcal/mol. Thus, both factors contribute to relatively high melting point of the borazane crystal. Deformation density contributions (Δρ(i)) obtained from NOCVs allowed to conclude that dihydrogen bonding is primarily based on outflow of electron density from B-H bonding orbitals to the empty σ*(N-H) (charge transfer component). Equally important is the covalent contribution resulting from the shift of the electron density from hydrogen atoms of both NH and BH groups to the interatomic regions of NH···HB. Quantitatively, averaged electronic strength of dihydrogen bond per one BH···HN link varies from 1.95 kcal/mol (for the crystal structure model, N), 2.47 kcal/mol (for trimer TR), through 2.65 kcal/mol (for tetramer TE), up to 3.95 kcal/mol (for dimer D).

Applications of the ETS-NOCV method in descriptions of chemical reactions

AbstractThe present study characterizes changes in the electronic structure of reactants during chemical reactions based on the combined charge and energy decomposition scheme, ETS-NOCV (extended transition state–natural orbitals for chemical valence). Decomposition of the activation barrier, ΔE#, into stabilizing (orbital interaction, ΔEorb, and electrostatic, ΔEelstat) and destabilizing (Pauli repulsion, ΔEPauli, and geometry distortion energy, ΔEdist) factors is discussed in detail for the following reactions: (I) hydrogen cyanide to hydrogen isocyanide, HCN → CNH isomerization; (II) Diels-Alder cycloaddition of ethene to 1,3-butadiene; and two catalytic processes, i.e., (III) insertion of ethylene into the metal-alkyl bond using half-titanocene with phenyl-phenoxy ligand catalyst; and (IV) B–H bond activation catalyzed by an Ir-containing catalyst. Various reference states for fragments were applied in ETS-NOCV analysis. We found that NOCV-based deformation densities (Δρi) and the corresponding energies ΔEorb(i) obtained from the ETS-NOCV scheme provide a very useful picture, both qualitatively and quantitatively, of electronic density reorganization along the considered reaction pathways. Decomposition of the barrier ΔE# into stabilizing and destabilizing contributions allowed us to conclude that the main factor responsible for the existence of positive values of ΔE# for all processes (I, II, III and IV) is Pauli interaction, which is the origin of steric repulsion. In addition, in the case of reactions II, III and IV, a significant degree of structural deformation of the reactants, as measured by the geometry distortion energy, plays an important role. Depending on the reaction type, stabilization of the transition state (relatively to the reactants) originating either from the orbital interaction term or from electrostatic attraction can be of vital importance. Finally, use of the ETS-NOCV method to describe catalytic reactions allows extraction of information on the role of catalysts in determination of ΔE#. FigureContours of dominant deformation density contributions, Δρ1, together with the corresponding energies ΔEorb(1) obtained from the ETS-NOCV method for the transition state (TS) and the product (cyclohexene) of Diels-Alder cycloaddition of ethene to 1,3-butadiene. Black and white colors used in the representation of Δρ1 indicate carbon and hydrogen atoms, respectively. The blue/red colors in the contours corresponds to accumulation/depletion of electron density upon bond formation

Physical nature of interactions in ZnII complexes with 2,2′-bipyridyl : quantum theory of atoms in molecules (QTAIM), interacting quantum atoms (IQA), noncovalent interactions (NCI), and extended transition state coupled with natural orbitals for chemical valence (ETS-NOCV) comparative studies

In the present account factors determining the stability of ZnL, ZnL2, and ZnL3 complexes (L = bpy, 2,2′-bipyridyl) were characterized on the basis of various techniques: the quantum theory of atoms in molecules (QTAIM), energy decomposition schemes based on interacting quantum atoms (IQA), and extended transition state coupled with natural orbitals for chemical valence (ETS-NOCV). Finally, the noncovalent interactions (NCI) index was also applied. All methods consistently indicated that the strength of the coordination bonds, Zn–O and Zn–N, decreases from ZnL to ZnL3. Importantly, it has been identified that the strength of secondary intramolecular heteropolar hydrogen bonding interactions, CH···O and CH···N, increases when going from ZnL to ZnL3. A similar trend appeared to be valid for the π-bonding as well as electrostatic stabilization. In addition to the above leading bonding contributions, all techniques suggested the existence of very subtle, but non-negligible additional stabilization from the CH···HC electronic exchange channel; these interactions are the weakest among all considered here. From IQA it was found that the local diatomic interaction energy, Eint(H,H), amounts at HF to −2.5, −2.7, and −2.9 kcal mol(–1) for ZnL, ZnL2, and ZnL3, respectively (−2.1 kcal mol(–1) for ZnL at MP2). NOCV-based deformation density channels showed that formation of CH--HC contacts in Zn complexes causes significant polarization of σ(C–H) bonds, which accordingly leads to charge accumulation in the CH···HC bay region. Charge depletion from σ(C–H) bonds was also reflected in the calculated spin–spin (1)J(C–H) coupling constants, which decrease from 177.06 Hz (ZnL) to 173.87 Hz (ZnL3). This last result supports our findings of an increase in the local electronic CH···HC stabilization from ZnL to ZnL3 found from QTAIM, IQA, and ETS-NOCV. Finally, this work unites for the first time the results from four methods that are widely used for description of chemical bonding.

QTAIM and ETS-NOCV analyses of intramolecular CH···HC interactions in metal complexes.

The topological analysis, based on the quantum theory of atoms in molecules (QTAIM) of Bader and the ETS-NOCV charge and energy decomposition method have been used to characterize coordination bonds, chelating rings, and additional intramolecular interactions in the ZnNTA and ZnNTPA complexes in solvent. The QTAIM and ETS-NOCV studies have conclusively demonstrated that the H-clashes (they are observed only in the ZnNTPA complex and classically are interpreted as steric hindrance destabilizing a complex) are characterized by (i) the electron flow channel between the H-atoms involved, as discovered by the ETS-NOCV analysis (on average, ΔE(orb) = -1.35 kcal mol(-1)) and (ii) QTAIM-defined a bond path that indicates the presence of a preferred quantum-mechanical exchange channel, hence, they should be seen as H-H intramolecular bonding interactions. The main reason for the formation of a weaker ZnNTPA complex was attributed to the strain energy (from both QTAIM and ETS-NOCV techniques) and the larger Pauli repulsion contribution found from the ETS-NOCV analysis. An excellent agreement between physical properties controlling the stability of the two complexes was found from the two techniques, QTAIM and ETS-NOCV.

σ-Donor and π-Acceptor Properties of Phosphorus Ligands: An Insight from the Natural Orbitals for Chemical Valence

The bonding between phosphorus ligands X = PCl(3), PF(3), P(OCH(3))(3), PH(3), PH(2)CH(3), PH(CH(3))(2), P(CH(3))(3) and the metal-containing fragments [Ni(CO)(3)], [Mo(CO)(5)], and [Fe(CO)(4)] have been studied by Natural Orbitals for Chemical Valence (NOCV). The main attention was paid to estimation of donor (Deltaq(d)) /acceptor (Deltaq(bd)) properties of X on the basis of NOCVs charge criterion. All ligands X are found to be both sigma-donors and pi-acceptors. The best sigma-donor and pi-acceptor ligands are P(CH(3))(3) and PY(3) (Y horizontal line F,Cl), respectively, in both the nickel and molybdenum complexes. The NOCV contributions to deformation density show that the sigma-component corresponds to the donation from the lone electron pair of phosphorus, enhanced further by a transfer from ancillary halogen atoms (in the case of PCl(3) and PF(3)) to a bonding region and to oxygen atoms of carbonyls. The pi-bonding is due to the electron transfer from the metal into the empty orbital of X, mostly exhibiting phosphorus 3p character. It was shown that within the molecular orbital framework, the trend for the donor/acceptor strength of X can be explained by the difference in the orbital energies of the orbitals involved in the donation/back-donation. Regarding the influence of the metal fragment on the donor/acceptor properties of X, it was demonstrated that the relative order of the phosphorus ligands remains in general intact. The only exception is the P(OCH(3))(3) ligand changing its position in molybdenum series compared to the nickel complexes. However, a change in the metal-containing fragment can influence the magnitude of electron transfer. For the set of phosphorus ligands studied here the effect is much less pronounced than for other ligands studied previously.