The nature of the chemical bond revisited: an energy-partitioning analysis of nonpolar bonds

The nature of the chemical bond in nonpolar molecules has been investigated by energy-partitioning analysis (EPA) of the ADF program using DFT calculations. The EPA divides the bonding interactions into three major components, that is, the repulsive Pauli term, quasiclassical electrostatic interactions, and orbital interactions. The electrostatic and orbital terms are used to define the nature of the chemical bond. It is shown that nonpolar bonds between main-group elements of the first and higher octal rows of the periodic system, which are prototypical covalent bonds, have large attractive contributions from classical electrostatic interactions, which may even be stronger than the attractive orbital interactions. Fragments of molecules with totally symmetrical electron-density distributions, like the nitrogen atoms in N(2), may strongly attract each other through classical electrostatic forces, which constitute 30.0 % of the total attractive interactions. The electrostatic attraction can be enhanced by anisotropic charge distribution of the valence electrons of the atoms that have local areas of (negative) charge concentration. It is shown that the use of atomic partial charges in the analysis of the nature of the interatomic interactions may be misleading because they do not reveal the topography of the electronic charge distribution. Besides dinitrogen, four groups of molecules have been studied. The attractive binding interactions in H(n)E-EH(n) (E=Li to F; n=0-3) have between 20.7 (E=F) and 58.4 % (E=Be) electrostatic character. The substitution of hydrogen by fluorine does not lead to significant changes in the nature of the binding interactions in F(n)E-EF(n) (E=Be to O). The electrostatic contributions to the attractive interactions in F(n)E-EF(n) are between 29.8 (E=O) and 55.3 % (E=Be). The fluorine substituents have a significant effect on the Pauli repulsion in the nitrogen and oxygen compounds. This explains why F(2)N-NF(2) has a much weaker bond than H(2)N-NH(2), whereas the interaction energy in FO-OF is much stronger than in HO-OH. The orbital interactions make larger contributions to the double bonds in HB=BH, H(2)C=CH(2), and HN=NH (between 59.9 % in B(2)H(2) and 65.4 % in N(2)H(2)) than to the corresponding single bonds in H(n)E-EH(n). The orbital term Delta E(orb) (72.4 %) makes an even greater contribution to the HC triple bond CH triple bond. The contribution of Delta E(orb) to the H(n)E=EH(n) bond increases and the relative contribution of the pi bonding decreases as E becomes more electronegative. The pi-bonding interactions in HC triple bond CH amount to 44.4 % of the total orbital interactions. The interaction energy in H(3)E-EH(3) (E=C to Pb) decreases monotonically as the element E becomes heavier. The electrostatic contributions to the E-E bond increases from E=C (41.4 %) to E=Sn (55.1 %) but then decreases when E=Pb (51.7 %). A true understanding of the strength and trends of the chemical bonds can only be achieved when the Pauli repulsion is considered. In an absolute sense the repulsive Delta E(Pauli) term is in most cases the largest term in the EPA.     

On the paucity of molecular actinide complexes with unsupported metal-metal bonds: a comparative investigation of the electronic structure and metal-metal bonding in U2X6 (X = Cl, F, OH, NH2, CH3) complexes and d-block analogues

Density functional calculations have been performed on M2X6 complexes (where M = U, W, and Mo and X = Cl, F, OH, NH2, and CH3) to investigate general aspects of their electronic structures and explore the similarities and differences in metal-metal bonding between f-block and d-block elements. A detailed analysis of the metal-metal interactions has been conducted using molecular orbital theory and energy decomposition methods. Multiple (sigma and pi) bonding is predicted for all species investigated, with predominant f-f and d-d metal orbital character, respectively, for U and W or Mo complexes. The energy decomposition analysis involves contributions from orbital interactions (mixing of occupied and unoccupied orbitals), electrostatic effects (Coulombic attraction and repulsion), and Pauli repulsion (associated with four-electron two-orbital interactions). The general results suggest that the overall metal-metal interaction is stronger in the Mo and W species, relative to the U analogues, as a consequence of a significantly less destabilizing contribution from the combined Pauli and electrostatic ("pre-relaxation") effects. Although the orbital-mixing ("post-relaxation") contribution to the total bonding energy is predicted to have a larger magnitude in the U complexes, this is not sufficiently strong to compensate for the comparatively greater destabilization that originates from the Pauli-plus-electrostatic effects. Of the pre-relaxation terms, the Pauli repulsion is comparable in analogous U and d-block compounds, contrary to the electrostatic term, which is (much) less favorable in the U systems than in the W and Mo systems. This generally weak electrostatic stabilization accounts for the large pre-relaxation destabilization in the U complexes and, ultimately, for the relative weakness of the U-U bonds. The origin of the small electrostatic term in the U compounds is traced primarily to MX(3) fragment overlap effects.     

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).     

Pauli repulsion in the open shell species BeH and Co+

Using the natural bond orbital method, one may associate the valence bond configuration and Lewis structure concepts to wave functions consisting of molecular orbitals and thus gain intuitive insight into the molecular potential energy curves. Natural bond orbital analysis of the restricted open shell Hartree–Fock and unrestricted Hartree–Fock wave functions for the BeH ground state provides an intuitive model to help understand the nature of the bonding in this open shell species. The contrasting behavior of the bonding orbitals for different spins can be attributed to differences in the Pauli repulsive interactions with the lonepair orbitals. Such behavior occurs in BeH(²Σ) but does not in CO⁺(²Π) because the Pauli repulsion depends on the orbital overlap.     

Pancake Bonding: An Unusual Pi-Stacking Interaction

A category of parallel π-stacking interaction, termed pancake bonding, is surveyed. The main characteristics are: the interaction occurs among radicals with highly delocalized π-electrons in their singly occupied molecular orbitals (SOMOs), the contact distances in the π-stacking direction are shorter than the typical van der Waals distances, and the stabilization obtained by the bonding combination of the SOMO orbitals leads to direct atom-to-atom overlap with strong orientational preferences. These atypical intermolecular interactions contain a component of electron sharing between the radicals that can be viewed as covalent-like. Pancake bonded dimers characteristically have low-lying singlet and triplet states and show characteristic interlayer vibrational modes. Pancake bonded aggregates serve as molecular components in many conducting and other functional organic materials. The role of van der Waals (vdW) interactions in pancake bonded dimers, chains, and other aggregates is different from closed shell vdW aggregates: here the Pauli repulsions reduce the attractive dispersion interaction significantly. Fluxionality between π- and σ-bonded aggregates often occur in the context of pancake bonding. Both experimental and computational aspects are reviewed.     

Chemical bonding in phosphane and amine complexes of main group elements and transition metals

The geometries and bond dissociation energies of the main group complexes X3B-NX3, X3B-PX3, X3Al-NX3, and X3Al-PX3 (X = H, Me, Cl) and the transition metal complexes (CO)5M-NX3 and (CO)5M-PX3 (M = Cr, Mo, W) have been calculated using gradient-corrected density functional theory at the BP86/TZ2P level. The nature of the donor-acceptor bonds was investigated with an energy decomposition analysis. It is found that the bond dissociation energy is not a good measure for the intrinsic strength of Lewis acidity and basicity because the preparation energies of the fragments may significantly change the trend of the bond strength. The interaction energies between the frozen fragments of the borane complexes are in most cases larger than the interaction energies of the alane complexes. The bond dissociation energy of the alane complexes is sometimes higher than that of the borane analogues because the energy for distorting the planar equilibrium geometry of BX3 to the pyramidal from in the complexes is higher than for AlX3. Inspection of the three energy terms, DeltaE(Pauli), DeltaE(orb), and DeltaE(elstat), shows that all three of them must be considered to understand the trends of the Lewis acid and base strength. The orbital term of the donor-acceptor bonds with the Lewis bases NCl3 and PCl3 have a higher pi character than the bonds of EH3 and EMe3, but NCl3 and PCl3 are weaker Lewis bases because the lone-pair orbital at the donor atoms N and P has a high percent s character. The calculated DeltaE(int) values suggest that the trends of the intrinsic Lewis bases' strengths in the main-group complexes with BX3 and AlX3 are NMe3 > NH3 > NCl3 and PMe3 > PH3 > PCl3. The transition metal complexes exhibit a somewhat different order with NH3 > NMe3 > NCl3 and PMe3 > PH3 > PCl3. The slightly weaker bonding of NMe3 than that of NH3 comes from stronger Pauli repulsion. The bond length does not always correlate with the bond dissociation energy, nor does it always correlate with the intrinsic interaction energy.     

The Gauche Effect in XCH2CH2X Revisited

We have quantum chemically investigated the rotational isomerism of 1,2-dihaloethanes XCH₂CH₂X (X = F, Cl, Br, I) at ZORA-BP86-D3(BJ)/QZ4P. Our Kohn-Sham molecular orbital (KS-MO) analyses reveal that hyperconjugative orbital interactions favor the gauche conformation in all cases (X = F−I), not only for X = F as in the current model of this so-called gauche effect. We show that, instead, it is the interplay of hyperconjugation with Pauli repulsion between lone-pair-type orbitals on the halogen substituents that constitutes the causal mechanism for the gauche effect. Thus, only in the case of the relatively small fluorine atoms, steric Pauli repulsion is too weak to overrule the gauche preference of the hyperconjugative orbital interactions. For the larger halogens, X⋅⋅⋅X steric Pauli repulsion becomes sufficiently destabilizing to shift the energetic preference from gauche to anti, despite the opposite preference of hyperconjugation.     

Structure and bonding analysis of dimethylgallyl complexes of iron, ruthenium, and osmium [(η5-C5H5)(CO)2M(GaMe2)] and [(η5-C5H5)(Me3P)2M(GaMe2)

Density functional theory calculations have been performed for the dimethylgallyl complexes of iron, ruthenium, and osmium [(η(5)-C(5)H(5))(L)(2)M(GaMe(2)] (M = Fe, Ru, Os; L = CO, PMe(3)) at the DFT/BP86/TZ2P/ZORA level of theory. The calculated geometry of the iron complex [(η(5)-C(5)H(5))(CO)(2)Fe(GaMe(2))] is in excellent agreement with structurally characterized complex [(η(5)-C(5)H(5))(CO)(2)Fe(Ga(t)Bu(2))]. The Pauling bond order of the optimized structures shows that the M-Ga bonds in these complexes are nearly M-Ga single bond. Upon going from M = Fe to M = Os, the calculated M-Ga bond distance increases, while on substitution of the CO ligand by PMe(3), the calculated M-Ga bond distances decrease. The π-bonding component of the total orbital contribution is significantly smaller than that of σ-bonding. Thus, in these complexes the GaX(2) ligand behaves predominantly as a σ-donor. The contributions of the electrostatic interaction terms ΔE(elstat) are significantly smaller in all gallyl complexes than the covalent bonding ΔE(orb) term. The absolute values of the ΔE(Pauli), ΔE(int), and ΔE(elstat) contributions to the M-Ga bonds increases in both sets of complexes via the order Fe < Ru < Os. The Ga-C(CO) and Ga-P bond distances are smaller than the sum of van der Waal radii and, thus, suggest the presence of weak intermolecular Ga-C(CO) and Ga-P interactions.     

Phthalocyanoiron complex with bridged ligands. Electronic structure of monomers and polymers

Electronic structure aspects related to the semiconducting properties of monomers and polymers of phthalocyanoiron with bidentate bridging ligands, PcFe–L₂ and ? [PcFe(L)]_n, have been investigated from density functional calculations [L = pyrazine, triazine, tetrazine, pyridine, 4,4′‐bipyridine, bipyridyacetylene, and bis(4‐pyridyl)bencene]. The following relevant results have been obtained: (a) an energy analysis in terms of electrostatic interaction, Pauli repulsion, and occupied/virtual orbital interactions show that the Pauli repulsion is the origin that the axial ligands (L) prefer be located toward the aza positions of the macrocycle, and (b) the intrinsic semiconducting properties depend of the frontier band. The valence band is composed largely by the transition metal d_xy orbital. The conduction band is composed of a mixture between the metallomacrocycle and bridged ligand orbitals for systems formed by pyrazine, bipyridine, and bipyridyacetylene. However, this composition is different when the ligands are triazine and tetrazine, which show a band composed of π* orbitals. These systems are predicted to show the higher conductivity within the series, in agreement with experimental results. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 82: 170–181, 2001     

A challenge to chemical intuition: donor-acceptor interactions in H3B-L and H2B+-L (L=CO; EC5H5, E=N-Bi)

The equilibrium geometries and bond energies of the complexes H(3)B-L and H(2)B(+)-L (L=CO; EC(5)H(5): E=N, P, As, Sb, Bi) have been calculated at the BP86/TZ2P level of theory. The nature of the donor-acceptor bonds was investigated by energy decomposition analysis (EDA). The bond strengths of H(3)B-L have the order CO>N>P>As>Sb>Bi. The calculated values are between D(e)=37.1 kcal mol(-1) for H(3)B-CO and D(e)=6.9 kcal mol(-1) for H(3)B-BiC(5)H(5). The bond dissociation energies of the cations H(2)B(+)-CO and H(2)B(+)-EC(5)H(5) are larger than for H(3)B--L, particularly for complexes of the heterobenzene ligands. The calculated values are between D(e)=51.9 kcal mol(-1) for H(2)B(+)-CO and D(e)=122.1 kcal mol(-1) for H(2)B(+)-NC(5)H(5). The trend of the BDE of H(2)B(+)-CO and H(2)B(+)-EC(5)H(5) is N>P>As>Sb>Bi>CO. A surprising result is found for H(2)B(+)-CO, which has a significantly stronger and yet substantially longer bond than H(3)B-CO. The reason for the longer but stronger bond in H(2)B(+)-CO compared with that in H(3)B-CO comes mainly from the change in electrostatic attraction and pi bonding at shorter distances, which increases more in the neutral system than in the cation, and to a lesser extent from the deformation energy of the fragments. The H(2)B(+)<--NC(5)H(5) pi( perpendicular) donation plays an important role for the stronger interactions at shorter distances compared with those in H(3)B-NC(5)H(5). The attractive interaction in H(2)B(+)--CO further increases at bond lengths that are shorter than the equilibrium value, but this is compensated by the energy which is necessary to deform BH(2) (+) from its linear equilibrium geometry to the bent form in the complex. The EDA shows that the contributions of the orbital interactions to the donor-acceptor bonds are always larger than the classical electrostatic contributions, but the latter term plays an important role for the trend in bond strength. The largest contributions to the orbital interactions come from the sigma orbitals. The EDA calculations suggest that heterobenzene ligands may become moderately strong pi donors in complexes with strong Lewis acids, while CO is only a weak pi donor. The much stronger interaction energies in H(2)B(+)-EC(5)H(5) compared with those in H(3)B-EC(5)H(5) are caused by the significantly larger contribution of the pi(perpendicular) orbitals in H(2)B(+)-EC(5)H(5) and by the increase of the binding interactions of the sigma+pi( parallel) orbitals.     

Role of the Fermi surface in adsorbate-metal interactions: an energy decomposition analysis

We present the result of a fragment-based energy decomposition analysis on some molecule-surface interactions. The analysis allows us to quantify the Pauli repulsion, its relief, and the attractive orbital interaction energy. In a metal, the existence of incompletely occupied energy bands causes significant relief of the Pauli repulsion due to escape of antibonding electrons to unoccupied states at the Fermi energy. This is the key electronic structure feature of metals that causes metal-molecule bond energies to be stronger and dissociation barriers of chemisorbed molecules to be much lower than those in comparable systems with no or one metal atom. As examples, we discuss the energy decomposition for the activated dissociation of hydrogen on the Cu surface and its unactivated dissociation on Pd, and for the (activated) chemisorption of N2 on W. We show that in all cases the relief of Pauli repulsion is of crucial importance for the chemisorption energy and for the low (or nonexistent) dissociation barriers. The barrier to the chemisorption well for nitrogen on tungsten is clearly related to a late relief of the Pauli repulsion. The relief of Pauli repulsion is important in lowering the barrier to dissociation of H2 on both Cu and Pd, but the difference in barrier heights for Cu and Pd appears to not be due to stronger relief of Pauli repulsion on Pd but primarily to the Pauli repulsion itself being stronger on Cu than on Pd, the relief energy being quite comparable on the two metals.     

Nature of M-Ga bonds in dihalogallyl complexes (η5-C5H5)(Me3P)2M(GaX2) (M = Fe, Ru, Os) and (η5-C5H5)(OC)2Fe(GaX2) (X = Cl, Br, I): a DFT study

Density functional theory (DFT) calculations have been performed on the terminal dihalogallyl complexes of iron, ruthenium, and osmium (η(5)-C(5)H(5))(Me(3)P)(2)M(GaX(2)) (M = Fe, Ru, Os; X = Cl, Br, I) and (η(5)-C(5)H(5))(OC)(2)Fe(GaX(2)) (X = Cl, Br, I) at the BP86/TZ2P/ZORA level of theory. On the basis of analyses suggested by Pauling, the M-Ga bonds in all of the dihalogallyl complexes are shorter than M-Ga single bonds; moreover, on going from X = Cl to X = I, the optimized M-Ga bond distances are found to increase. From the perspective of covalent bonding, however, π-symmetry contributions are, in all complexes, significantly smaller than the corresponding σ-bonding contribution, representing only 4-10% of the total orbital interaction. Thus, in these GaX(2) complexes, the gallyl ligand behaves predominantly as a σ donor, and the short M-Ga bond lengths can be attributed to high gallium s-orbital character in the M-Ga σ-bonding orbitals. The natural population analysis (NPA) charge distributions indicate that the group 8 metal atom carries a negative charge (from -1.38 to -1.62) and the gallium atom carries a significant positive charge in all cases (from +0.76 to +1.18). Moreover, the contributions of the electrostatic interaction terms (ΔE(elstat)) are significantly larger in all gallyl complexes than the covalent bonding term (ΔE(orb)); thus, the M-Ga bonds have predominantly ionic character (60-72%). The magnitude of the charge separation is greatest for dichlorogallyl complexes (compared to the corresponding GaBr(2) and GaI(2) systems), leading to a larger attractive ΔE(elstat) term and to M-Ga bonds that are stronger and marginally shorter than in the dibromo and diiodo analogues.     

The Nature of Chemical Bonds from PNOF5 Calculations

Natural orbital functional theory (NOFT) is used for the first time in the analysis of different types of chemical bonds. Concretely, the Piris natural orbital functional PNOF5 is used. It provides a localization scheme that yields an orbital picture which agrees very well with the empirical valence shell electron pair repulsion theory (VSEPR) and Bent’s rule, as well as with other theoretical pictures provided by valence bond (VB) or linear combination of atomic orbitals–molecular orbital (LCAO‐MO) methods. In this context, PNOF5 provides a novel tool for chemical bond analysis. In this work, PNOF5 is applied to selected molecules that have ionic, polar covalent, covalent, multiple (σ and π), 3c–2e, and 3c–4e bonds.     

The strength and selectivity of perfluorinated nano-hoops and buckybowls for anion binding and the nature of anion-π interactions

Perfluorinated cycloparaphenylenes (F-[n]CPP, n = 5–8), boron nitride nanohoop (F-[5]BNNH), and buckybowls (F-BBs) were proposed as anion receptors via anion-π interactions with halide anions (Cl⁻, Br⁻ and I⁻), and remarkable binding strengths up to −294.8 kJ/mol were computationally verified. The energy decomposition approach based on the block-localized wavefunction method, which combines the computational efficiency of molecular orbital theory and the chemical intuition of ab initio valence bond theory, was applied to the above anion-π complexes, in order to elucidate the nature and selectivity of these interactions. The overall attraction is mainly governed by the frozen energy component, in which the electrostatic interaction is included. Remarkable binding strengths with F-[n]CPPs can be attributed to the accumulated anion-π interactions between the anion and each conjugated ring on the hoop, while for F-BBs, additional stability results from the curved frameworks, which distribute electron densities unequally on π-faces. Interestingly, the strongest host was proved to be the F-[5]BNNH, which exhibits the most significant anisotropy of the electrostatic potential surface due to the difference in the electronegativities of nitrogen and boron. The selectivity of each host for anions was explored and the importance of the often-overlooked Pauli exchange repulsion was illustrated. Chloride anion turns out to be the most favorable anion for all receptors, due to the smallest ionic radius and the weakest destabilizing Pauli exchange repulsion.     

On the Electride Nature of Na-hP4

Early quantum mechanical models suggested that pressure drives solids towards free-electron metal behavior where the ions are locked into simple close-packed structures. The prediction and subsequent discovery of high-pressure electrides (HPEs), compounds assuming open structures where the valence electrons are localized in interstitial voids, required a paradigm shift. Our quantum chemical calculations on the iconic insulating Na-hP4 HPE show that increasing density causes a 3s→3pd electronic transition due to Pauli repulsion between the 1s2s and 3s states, and orthogonality of the 3pd states to the core. The large lobes of the resulting Na-pd hybrid orbitals point towards the center of an 11-membered penta-capped trigonal prism and overlap constructively, forming multicentered bonds, which are responsible for the emergence of the interstitial charge localization in Na-hP4. These multicentered bonds facilitate the increased density of this phase, which is key for its stabilization under pressure.     

The bonding in the ozone molecule: From a different perspective

A new qualitative treatment of the bonding in ozone is presented. It is based upon a combination of several simple concepts: the nonparticipation of the pairs of electrons tightly held in the atomic 2s orbitals; simple overlap of the 2p orbitals to form sigma bonds; interaction of three 2p orbitals to yield bonding and nonbonding pi molecular orbitals that are populated by electron pairs; and van der Waals repulsion between the two terminal oxygen atoms forcing these atoms apart to yield the bond angle of 117° as a compromise. Both the assumptions and the resulting bonding picture are in accord with the photoelectron spectroscopic data, the results from sophisticated molecular orbital calculations, and the common physical properties of ozone.     

Energy decomposition analysis of metal-metal bonding in [M2X8]2- (X=Cl, br) complexes of 5f (U, Np, Pu), 5d (W, Re, Os), and 4d (Mo, Tc, Ru) elements

The electronic structures of a series of [M2X8]2- (X=Cl, Br) complexes involving 5f (U, Np, Pu), 5d (W, Re, Os), and 4d (Mo, Tc, Ru) elements have been calculated using density functional theory, and an energy decomposition approach has been used to carry out a detailed analysis of the metal-metal interactions. The energy decomposition analysis involves contributions from orbital interactions (mixing of occupied and unoccupied orbitals), electrostatic effects (Coulombic attraction and repulsion), and Pauli repulsion (associated with four-electron two-orbital interactions). As previously observed for Mo, W, and U M2X6 species, the general results suggest that the overall metal-metal interaction is considerably weaker or unfavorable in the actinide systems relative to the d-block analogues, as a consequence of a significantly more destabilizing contribution from the combined Pauli and electrostatic (prerelaxation) effects. Although the orbital-mixing (postrelaxation) contribution to the total bonding energy is predicted to be larger in the actinide complexes, this is not sufficiently strong to compensate for the comparatively greater destabilization originating from the Pauli-plus-electrostatic effects. A generally weak electrostatic contribution accounts for the large prerelaxation destabilization in the f-block systems, and ultimately for the weak or unfavorable nature of metal-metal bonding between the actinide elements. There is a greater variation in the energy decomposition results across the [M2Cl8]2- series for the actinide than for the d-block elements, both in the general behavior and in some particular properties.     

Understanding glycine conformation through molecular orbitals

The four most stable C(s) conformers of glycine have been investigated using a variety of quantum-mechanical methods based on Hartree-Fock theory, density-functional theory (B3LYP and statistical average of orbital potential), and electron propagation (OVGF) treatments. Information obtained from these models were analyzed in coordinate and momentum spaces using dual space analysis to provide insight based on orbitals into the bonding mechanisms of glycine conformers, which are generated by rotation of C-O(H) (II), C-C (III), and C-N (IV) bonds from the global minimum structure (I). Wave functions generated from the B3LYP/TZVP model revealed that each rotation produced a unique set of fingerprint orbitals that correspond to a specific group of outer valence orbitals, generally of a' symmetry. Orbitals 14a', 13a', 12a', and 11a' are identified as the fingerprint orbitals for the C-O(H) (II) rotation, whereas fingerprint orbitals for the C-C (III) bond rotation are located as 16a' [highest occupied molecular orbital (HOMO)], 15a' [next highest molecular occupied molecular orbital (NHOMO)], 14a', and 12a' orbitals. Fingerprint orbitals for IV generated by the combined rotations around the C-C, C-O(H), and C-N bonds are found as 16a', 15a', 14a', 13a', and 11a', as well as in orbitals 2a" and 1a". Orbital 14a' is identified as the fingerprint orbital for all three conformational processes, as it is the only orbital in the outer valence region which is significantly affected by the conformational processes regardless rotation of which bond. Binding energies, molecular geometries, and other molecular properties such as dipole moments calculated based on the specified treatments agree well with available experimental measurements and with previous theoretical calculation.     

Theory of electron localization and its application to blue-shifting hydrogen bonds

We propose a theory of electron localization or stabilization by electron localization through the interactions between occupied (i) and vacant (j*) orbitals under certain conditions, which have been believed so far to cause only electron delocalization. Electrons localize when the electrons redistributed by the interaction are more stable in the i-th occupied orbital than in the overlap region: h(ij*) > s(ij*)h(ii) for s(ij*) > 0. Electron delocalization occurs when h(ij*) < s(ij*)h(ii) for s(ij*) > 0. The h(ij*) and s(ij*)h(ii) terms represent the energy of the electrons in the overlap region and the energy of the redistributed electrons in the occupied orbital, respectively. The theory of electron localization is substantiated by the correlation of the C-H bond lengths of fluorinated methanes H(4-n)CF(n) (n = 1, 2, 3) to the electron population of the σ(CH) bonding orbital, and successfully applied to understanding blue-shifting hydrogen bonds in F(3)CH···X (X = CO, N(2), OC, Ne, OC(CH(3))(2)) and designing some proton donors, HCO(2)CH(3) and hypervalent molecules HPF(4) and HSF(5), for blue-shifting hydrogen bonds.     

Atomic orbital deformation in bond formation: energy effects

Changes in the radial dependence of atomic orbitals which accompany electronegativity equalization during molecule formation may be monitored by the parallel use of flexible and constrained basis sets in molecular orbital calculations. The stabilization associated with orbital deformation in molecules like BH₃ or CH₄, which contain many bonding MOs in the valence shell, is due to an increase in the attractive, one-electron term in the molecular energy expression relative to the electron repulsion term. The stabilization which occurs in molecules with an excess of non-bonding electrons in the valence shell is due to reduced interelectronic repulsion.