Kohn-Sham Molecular Orbital Theory Research Articles

Chemical Bonding in Silicon Carbonyl Complexes.

Although silylene‐carbonyl complexes are known for decades, only recently isolable examples have been accomplished. In this work, the bonding situation is re‐evaluated to explain the origins of their remarkable stability within the Kohn‐Sham molecular orbital theory framework. It is shown that the chemical bond can be understood as CO interaction with the silylene via a donor‐acceptor interaction: a σ‐donation from the σ CO into the empty p‐orbital of silicon, and a π‐back donation from the sp 2 lone pair of silicon into the π*CO antibonding orbitals. Notably, it was established that the driving force behind the surprisingly stable Si−CO compounds, however, is another π‐back donation from a perpendicular bonding R−Si σ‐orbital into the π*CO antibonding orbitals. Consequently, the pyramidalization of the central silicon atom cannot be associated with the strength of the π‐back donation, in sharp contrast to the established chemical bonding model. Considering this additional bonding interaction not only shed light on the bonding situation, but is also an indispensable key for broadening the scope of silylene‐carbonyl chemistry.

Not Carbon s-p Hybridization, but Coordination Number Determines C-H and C-C Bond Length.

A fundamental and ubiquitous phenomenon in chemistry is the contraction of both C−H and C−C bonds as the carbon atoms involved vary, in s–p hybridization, along sp3 to sp2 to sp. Our quantum chemical bonding analyses based on Kohn–Sham molecular orbital theory show that the generally accepted rationale behind this trend is incorrect. Inspection of the molecular orbitals and their corresponding orbital overlaps reveals that the above‐mentioned shortening in C−H and C−C bonds is not determined by an increasing amount of s‐character at the carbon atom in these bonds. Instead, we establish that this structural trend is caused by a diminishing steric (Pauli) repulsion between substituents around the pertinent carbon atom, as the coordination number decreases along sp3 to sp2 to sp.

A Quantitative Molecular Orbital Perspective of the Chalcogen Bond.

We have quantum chemically analyzed the structure and stability of archetypal chalcogen‐bonded model complexes D2Ch⋅⋅⋅A− (Ch = O, S, Se, Te; D, A = F, Cl, Br) using relativistic density functional theory at ZORA‐M06/QZ4P. Our purpose is twofold: (i) to compute accurate trends in chalcogen‐bond strength based on a set of consistent data; and (ii) to rationalize these trends in terms of detailed analyses of the bonding mechanism based on quantitative Kohn‐Sham molecular orbital (KS‐MO) theory in combination with a canonical energy decomposition analysis (EDA). At odds with the commonly accepted view of chalcogen bonding as a predominantly electrostatic phenomenon, we find that chalcogen bonds, just as hydrogen and halogen bonds, have a significant covalent character stemming from strong HOMO−LUMO interactions. Besides providing significantly to the bond strength, these orbital interactions are also manifested by the structural distortions they induce as well as the associated charge transfer from A− to D2Ch.

How Oriented External Electric Fields Modulate Reactivity.

A judiciously oriented external electric field (OEEF) can catalyze a wide range of reactions and can even induce endo/exo stereoselectivity of cycloaddition reactions. The Diels–Alder reaction between cyclopentadiene and maleic anhydride is studied by using quantitative activation strain and Kohn–Sham molecular orbital theory to pinpoint the origin of these catalytic and stereoselective effects. Our quantitative model reveals that an OEEF along the reaction axis induces an enhanced electrostatic and orbital interaction between the reactants, which in turn lowers the reaction barrier. The stronger electrostatic interaction originates from an increased electron density difference between the reactants at the reactive center, and the enhanced orbital interaction arises from the promoted normal electron demand donor–acceptor interaction driven by the OEEF. An OEEF perpendicular to the plane of the reaction axis solely stabilizes the exo pathway of this reaction, whereas the endo pathway remains unaltered and efficiently steers the endo/exo stereoselectivity. The influence of the OEEF on the inverse electron demand Diels–Alder reaction is also investigated; unexpectedly, it inhibits the reaction, as the electric field now suppresses the critical inverse electron demand donor–acceptor interaction.

Origin of asynchronicity in Diels-Alder reactions.

Asynchronicity in Diels–Alder reactions plays a crucial role in determining the height of the reaction barrier. Currently, the origin of asynchronicity is ascribed to the stronger orbital interaction between the diene and the terminal carbon of an asymmetric dienophile, which shortens the corresponding newly formed C–C bond and hence induces asynchronicity in the reaction. Here, we show, using the activation strain model and Kohn–Sham molecular orbital theory at ZORA-BP86/TZ2P, that this rationale behind asynchronicity is incorrect. We, in fact, found that following a more asynchronous reaction mode costs favorable HOMO–LUMO orbital overlap and, therefore, weakens (not strengthens) these orbital interactions. Instead, it is the Pauli repulsion that induces asynchronicity in Diels–Alder reactions. An asynchronous reaction pathway also lowers repulsive occupied–occupied orbital overlap which, therefore, reduces the unfavorable Pauli repulsion. As soon as this mechanism of reducing Pauli repulsion dominates, the reaction begins to deviate from synchronicity and adopts an asynchronous mode. The eventual degree of asynchronicity, as observed in the transition state of a Diels–Alder reaction, is ultimately achieved when the gain in stability, as a response to the reduced Pauli repulsion, balances with the loss of favorable orbital interactions.

The Nature of Nonclassical Carbonyl Ligands Explained by Kohn-Sham Molecular Orbital Theory.

When carbonyl ligands coordinate to transition metals, their bond distance either increases (classical) or decreases (nonclassical) with respect to the bond length in the isolated CO molecule. C−O expansion can easily be understood by π‐back‐donation, which results in a population of the CO's π*‐antibonding orbital and hence a weakening of its bond. Nonclassical carbonyl ligands are less straightforward to explain, and their nature is still subject of an ongoing debate. In this work, we studied five isoelectronic octahedral complexes, namely Fe(CO)6 2+, Mn(CO)6 +, Cr(CO)6, V(CO)6 − and Ti(CO)6 2−, at the ZORA‐BLYP/TZ2P level of theory to explain this nonclassical behavior in the framework of Kohn–Sham molecular orbital theory. We show that there are two competing forces that affect the C−O bond length, namely electrostatic interactions (favoring C−O contraction) and π‐back‐donation (favoring C−O expansion). It is a balance between those two terms that determines whether the carbonyl is classical or nonclassical. By further decomposing the electrostatic interaction ΔV elstat into four fundamental terms, we are able to rationalize why ΔV elstat gives rise to the nonclassical behavior, leading to new insights into the driving forces behind C−O contraction.

SN2 versus E2 Competition of F- and PH2- Revisited.

We have quantum chemically analyzed the competition between the bimolecular nucleophilic substitution (SN2) and base-induced elimination (E2) pathways for F– + CH3CH2Cl and PH2– + CH3CH2Cl using the activation strain model and Kohn–Sham molecular orbital theory at ZORA-OLYP/QZ4P. Herein, we correct an earlier study that intuitively attributed the mechanistic preferences of F– and PH2–, i.e., E2 and SN2, respectively, to a supposedly unfavorable shift in the polarity of the abstracted β-proton along the PH2–-induced E2 pathway while claiming that ″...no correlation between the thermodynamic basicity and E2 rate should be expected.″ Our analyses, however, unequivocally show that it is simply the 6 kcal mol–1 higher proton affinity of F– that enables this base to engage in a more stabilizing orbital interaction with CH3CH2Cl and hence to preferentially react via the E2 pathway, despite the higher characteristic distortivity (more destabilizing activation strain) associated with this pathway. On the other hand, the less basic PH2– has a weaker stabilizing interaction with CH3CH2Cl and is, therefore, unable to overcome the characteristic distortivity of the E2 pathway. Therefore, the mechanistic preference of PH2– is steered to the SN2 reaction channel (less-destabilizing activation strain).

Halogen Bonds in Ligand-Protein Systems: Molecular Orbital Theory for Drug Design.

Halogen bonds are highly important in medicinal chemistry as halogenation of drugs, generally, improves both selectivity and efficacy toward protein active sites. However, accurate modeling of halogen bond interactions remains a challenge, since a thorough theoretical investigation of the bonding mechanism, focusing on the realistic complexity of drug–receptor systems, is lacking. Our systematic quantum-chemical study on ligand/peptide-like systems reveals that halogen bonding is driven by the same bonding interactions as hydrogen bonding. Besides the electrostatic and the dispersion interactions, our bonding analyses, based on quantitative Kohn–Sham molecular orbital theory together with energy decomposition analysis, reveal that donor–acceptor interactions and steric repulsion between the occupied orbitals of the halogenated ligand and the protein need to be considered more carefully within the drug design process.

Alkali Metal Cation Affinities of Neutral Maingroup-Element Hydrides across the Periodic Table.

We have carried out an extensive quantum chemical exploration of gas-phase alkali metal cation affinities (AMCAs) of archetypal neutral bases across the periodic system using relativistic density functional theory. One objective of this work is to provide an intrinsically consistent set of values of the 298 K AMCAs of all neutral maingroup-element hydrides XHn of groups 15–18 along the periods 1–6. Our main purpose is to understand these trends in terms of the underlying bonding mechanism using Kohn–Sham molecular orbital theory together with a canonical energy decomposition analysis (EDA). We compare the trends in XHn AMCAs with the trends in XHn proton affinities (PAs). We also examine the differences between the trends in AMCAs of the neutral XHn bases with those in the corresponding anionic XHn–1– bases. Furthermore, we analyze how the cation affinity of our neutral Lewis bases changes along the group-1 cations H+, Li+, Na+, K+, Rb+, and Cs+.

Hydride affinities of cationic maingroup-element hydrides across the periodic table

We have quantum chemically explored the gas-phase hydride affinities (HA) of archetypical cationic Lewis acids across the periodic table, using relativistic density functional theory (DFT) at ZORA-BP86/QZ4P. One purpose of this work is to establish an intrinsically consistent set of values of the 298 K HAs of all cationic maingroup-element hydrides (XHn–1+) in which we have varied the central atom X along groups 14–17 and periods 2–6. Our main purpose is to understand the emerging trends in HA values in terms of the underlying bonding mechanism using Kohn-Sham molecular orbital (MO) theory together with a quantitative bond energy decomposition analysis (EDA).

Tuning Heterocalixarenes to Improve Their Anion Recognition: A Computational Approach.

We have explored and analyzed the physical factors through which noncovalent interactions in anion sensing based on calixarene-type hosts can be tuned, using dispersion-corrected DFT and Kohn-Sham molecular orbital (KS-MO) theory in conjunction with a canonical energy decomposition analysis (EDA). We find that the host-guest interaction can be enhanced through the introduction of strongly electron-withdrawing groups at particular positions of the arene and triazine units in the host molecule as well as by coordination of a metal complex to the arene and triazine rings. Our analyses reveal that the enhanced anion affinity is caused by increasing the electrostatic potential in the heterocalixarene cavities. This insight can be employed to further tune and improve their selectivity for chloride ions.

Nature and strength of chalcogen-π bonds.

Chalcogen-π interactions occur between a covalently bound chalcogen atom that enters into a non-covalent interaction with an unsaturated moiety, a bonding motif found in various structures, such as, proteins. In this work, we have systematically explored and analyzed chalcogen-π interactions in model systems X2DA (with D = O, S, Se, Te; X = halogen; A = acetylene, ethylene and 2-butyne), using relativistic density functional theory (DFT). The nature and trends in stability of the chalcogen-π bonds are analyzed and interpreted in terms of quantitative MO theory in combination with a matching canonical energy decomposition analysis (EDA) scheme. We find that chalcogen-π bonds increase in strength as the X-D electronegativity difference becomes greater. Moreover, 2-butyne was found to participate in the strongest non-covalent interaction due to enhanced orbital interactions.

Alkali Metal Cation Affinities of Anionic Main Group-Element Hydrides Across the Periodic Table.

We have carried out an extensive exploration of gas-phase alkali metal cation affinities (AMCA) of archetypal anionic bases across the periodic system using relativistic density functional theory at ZORA-BP86/QZ4P//ZORA-BP86/TZ2P. AMCA values of all bases were computed for the lithium, sodium, potassium, rubidium and cesium cations and compared with the corresponding proton affinities (PA). One purpose of this work is to provide an intrinsically consistent set of values of the 298 K AMCAs of all anionic (XHn-1- ) constituted by main group-element hydrides of groups 14-17 along the periods 2-6. In particular, we wish to establish the trend in affinity for a cation as the latter varies from proton to, and along, the alkali cations. Our main purpose is to understand these trends in terms of the underlying bonding mechanism using Kohn-Sham molecular orbital theory together with a quantitative bond energy decomposition analyses (EDA).

Nature of the Ru-NO Coordination Bond: Kohn-Sham Molecular Orbital and Energy Decomposition Analysis.

We have analyzed structure, stability, and Ru−NO bonding of the trans‐[RuCl(NO)(NH3)4]2+ complex by using relativistic density functional theory. First, we focus on the bond dissociation energies associated with the three canonical dissociation modes leading to [RuCl(NH3)4]++NO+, [RuCl(NH3)4]2++NO, and [RuCl(NH3)4]3++NO−. The main objective is to understand the Ru−NO+ bonding mechanism in the conceptual framework of Kohn–Sham molecular orbital theory in combination with a quantitative energy decomposition analysis. In our analyses, we have addressed the importance of the synergism between Ru−NO+ σ‐donation and π‐backdonation as well as the so‐called negative trans influence of the Cl− ligand on the Ru−NO bond. For completeness, the Ru−NO+ bonding mechanism is compared with that of the corresponding Ru−CO bond.

Cooperativity in the Self-Assembly of the Guanine Nucleobase into Quartet and Ribbon Structures on Surfaces.

The guanine nucleobase can self-assemble into tetrameric or ribbon structures on surfaces or in solution. The origin for the occurrence of different aggregation patterns has not yet been investigated. Herein, a quantum chemical study on the different self-assembled structures of guanine and xanthine by using dispersion-corrected DFT is presented. Theoretical investigations can be used to explain, from an electronic point of view, the differences between the experimental findings. With quantitative Kohn-Sham molecular orbital theory and the accompanying energy decomposition analysis, the hydrogen-bonding mechanism within the guanine ribbons can be disclosed and the preferred self-assembled structures under different experimental conditions can be explained. An important role of the σ-electronic system in the guanine self-assembled structures is revealed as the main factor for the switch between different arrangements on surfaces and in crystals.

Alkali Metal Cation versus Proton and Methyl Cation Affinities: Structure and Bonding Mechanism.

We have analyzed the structure and bonding of gas‐phase Cl−X and [HCl−X]+ complexes for X+= H+, CH3 +, Li+, and Na+, using relativistic density functional theory (DFT). We wish to establish a quantitative trend in affinities of the anionic and neutral Lewis bases Cl− and HCl for the various cations. The Cl−X bond becomes longer and weaker along X+ = H+, CH3 +, Li+, and Na+. Our main purpose is to understand the heterolytic bonding mechanism behind the intrinsic (i.e., in the absence of solvent) alkali metal cation affinities (AMCA) and how this compares with and differs from those of the proton affinity (PA) and methyl cation affinity (MCA). Our analyses are based on Kohn–Sham molecular orbital (KS‐MO) theory in combination with a quantitative energy decomposition analysis (EDA) that pinpoints the importance of the different features in the bonding mechanism. Orbital overlap appears to play an important role in determining the trend in cation affinities.

How amino and nitro substituents direct electrophilic aromatic substitution in benzene: an explanation with Kohn-Sham molecular orbital theory and Voronoi deformation density analysis.

The substituent effect of the amino and nitro groups on the electronic system of benzene has been investigated quantum chemically using quantitative Kohn-Sham molecular orbital theory and a corresponding energy decomposition analysis (EDA). The directionality of electrophilic substitution in aniline can accurately be explained with the amount of contribution of the 2pz orbitals on the unsubstituted carbon atoms to the highest occupied π orbital. For nitrobenzene, the molecular π orbitals cannot explain the regioselectivity of electrophilic substitution as there are two almost degenerate π orbitals with nearly the same 2pz contributions on the unsubstituted carbon atoms. The Voronoi deformation density analysis has been applied to aniline and nitrobenzene to obtain an insight into the charge rearrangements due to the substituent. This analysis method identified the orbitals involved in the C-N bond formation of the π system as the cause for the π charge accumulation at the ortho and para positions in the case of the NH2 group and the largest charge depletion at these same positions for the NO2 substituent. Furthermore, we showed that it is the repulsive interaction between the πHOMO of the phenyl radical and the πHOMO of the NH2 radical that is responsible for pushing up the πHOMO of aniline and therefore activating this π orbital of the phenyl ring towards electrophilic substitution.

The Role of Aromaticity, Hybridization, Electrostatics, and Covalency in Resonance-Assisted Hydrogen Bonds of Adenine-Thymine (AT) Base Pairs and Their Mimics.

Hydrogen bonds play a crucial role in many biochemical processes and in supramolecular chemistry. In this study, we show quantum chemically that neither aromaticity nor other forms of π assistance are responsible for the enhanced stability of the hydrogen bonds in adenine–thymine (AT) DNA base pairs. This follows from extensive bonding analyses of AT and smaller analogs thereof, based on dispersion-corrected density functional theory (DFT). Removing the aromatic rings of either A or T has no effect on the Watson–Crick bond strength. Only when the smaller mimics become saturated, that is, when the hydrogen-bond acceptor and donor groups go from sp2 to sp3, does the stability of the resulting model complexes suddenly drop. Bonding analyses based on quantitative Kohn–Sham molecular orbital theory and corresponding energy decomposition analyses (EDA) show that the stronger hydrogen bonds in the unsaturated model complexes and in AT stem from stronger electrostatic interactions as well as enhanced donor–acceptor interactions in the σ-electron system, with the covalency being responsible for shortening the hydrogen bonds in these dimers.

Why 1,2-quinone derivatives are more stable than their 2,3-analogues?

In this work, we have studied the relative sta- bility of 1,2- and 2,3-quinones. While 1,2-quinones have a closed-shell singlet ground state, the ground state for the studied 2,3-isomers is open-shell singlet, except for 2,3-naphthaquinone that has a closed-shell singlet ground state. In all cases, 1,2-quinones are more stable than their 2,3-counterparts. We analyzed the reasons for the higher stability of the 1,2-isomers through energy decomposition analysis in the framework of Kohn-Sham molecular orbital theory. The results showed that we have to trace the ori- gin of 1,2-quinones' enhanced stability to the more efficient bonding in the π-electron system due to more favorable overlap between the SOMO π of the ·C 4n−2 H 2n -CH·· and ··CH-CO-CO· fragments in the 1,2-arrangement. Further- more, whereas 1,2-quinones present a constant trend with

All-metal aromatic clusters M42− (M = B, Al, and Ga). Are π-electrons distortive or not?

The π-electrons in benzene, the quintessential aromatic molecule, were previously shown to be distortive, i.e., they prefer localized double bonds alternating with single bonds. It is the σ-electrons that force the double bonds to delocalize, leading to a regular, D(6h) geometry. Herein, we computationally investigate the double-bond localizing or delocalizing propensities of σ- and π-electrons in the archetypal all-metal aromatic cluster Al(4)(2-) and its second- and fourth-period analogs B(4)(2-) and Ga(4)(2-), using Kohn-Sham molecular orbital (MO) theory at BP86/TZ2P in combination with quantitative bond energy decomposition analyses (EDA). We compare the three all-metal aromatic clusters with the structurally related organic species C(4)H(4)(2+), C(4)H(4), and C(4)H(4)(2-). Our analyses reveal that the π-electrons in the group-13 M(4)(2-) molecules have a weak preference for localizing the double bonds. Instead, the σ-electrons enforce the regular D(4h) equilibrium geometry with delocalized double bonds.