Kohn-Sham Molecular Orbitals Research Articles

GW with hybrid functionals for large molecular systems

A low-cost approach for stochastically sampling static exchange during time-dependent Hartree–Fock-type propagation is presented. This enables the use of an excellent hybrid density functional theory (DFT) starting point for stochastic GW quasiparticle energy calculations. Generalized Kohn–Sham molecular orbitals and energies, rather than those of a local-DFT calculation, are used for building the Green function and effective Coulomb interaction. The use of an optimally tuned hybrid diminishes the starting point dependency in one-shot stochastic GW, effectively avoiding the need for self-consistent GW iterations.

Kohn-Sham fragment energy decomposition analysis.

We introduce the concept of Kohn-Sham fragment localized molecular orbitals (KS-FLMOs), which are Kohn-Sham molecular orbitals (MOs) localized in specific fragments constituting a generic molecular system. In detail, we minimize the local electronic energies of various fragments, while maximizing the repulsion between them, resulting in the effective localization of the MOs. We use the developed KS-FLMOs to propose a novel energy decomposition analysis, which we name Kohn-Sham fragment energy decomposition analysis, which allows for rationalizing the main non-covalent interactions occurring in interacting systems both in vacuo and in solution, providing physical insights into non-covalent interactions. The method is validated against state-of-the-art energy decomposition analysis techniques and with high-level calculations.

"Hydridic Hydrogen-Bond Donors" Are Not Hydrogen-Bond Donors.

Herein, we dismiss a recent proposal by Civiš, Hobza, and co-workers to modify the IUPAC definition of hydrogen bonds in order to expand the scope from protonic Y-Hδ+ to hydridic Y-Hδ- hydrogen-bond donor fragments [J. Am. Chem. Soc. 2023, 145, 8550]. Based on accurate Kohn-Sham molecular orbital (KS-MO) analyses, we falsify the conclusion that interactions involving protonic and hydridic hydrogens are both hydrogen bonds; they are not. Instead, our quantitative KS-MO, energy decomposition, and Voronoi deformation density analyses reveal two fundamentally different bonding mechanisms for protonic Y-Hδ+ and hydridic Y-Hδ- fragments which go with charge transfer in opposite directions. On one hand, we confirm the IUPAC definition for regular hydrogen bonds in the case of protonic Y-Hδ+ fragments. On the other hand, complexes involving Y-Hδ- fragments are, in fact, acceptors in other well-known families of Lewis-acid/base interactions, such as halogen bonds, chalcogen bonds, and pnictogen bonds. These mechanisms lead to the same spectroscopic phenomenon in both the Y-Hδ+ and Y-Hδ- fragments, that is, the redshift in the Y-H stretching frequency, which is, thus, not an exclusive indicator for hydrogen bonding.

Kohn-Sham Density in a Slater Orbital Basis Set.

Finite, atom-centered Slater basis sets are used to determine approximate Kohn-Sham molecular orbitals. This is achieved by minimizing the kinetic energy plus the sum-squared difference between the Kohn-Sham density and the full configuration interaction density. As a result of the finite basis, a weight factor is introduced to balance the two minimization components. Results herein show that this can be done systematically, without sensitive dependence on the choice of scaling factor. In addition, the algorithm is applied to the LiH diatomic for fractional electron counts, where stretching the bond introduces significant reorganization of the electron density. The analysis will show the correct KS orbital structure and reveal the effects of correlation and electron locality on the KS solutions.

Computational study of the interactions of tetravalent actinides (An = Th-Pu) with the α-Fe13 Keggin cluster.

In recent years, evidence has emerged that actinide (An) uptake at the enhanced actinide removal plant (EARP) at the UK's Sellafield nuclear site occurs via An interactions with an α-Fe13 Keggin molecular cluster during ferrihydrite formation. We here study theoretically the substitution of aquo complexes of the actinides Th-Pu onto a Na-decorated α-Fe13 Keggin cluster using DFT at the PBE0 level. The optimised Pu-O and Pu-Fe distances are in good agreement with experiment and Na/An substitutions are significantly favourable energetically, becoming more so across the early 5f series, with the smallest and largest ΔrG° being for Th and Pu at -335.7 kJ mol-1 and -396.0 kJ mol-1 respectively. There is strong correlation between the substitution reaction energy and the ionic radii of the actinides (Δrε0R2 = 0.97 and ΔrG° R2 = 0.91), suggesting that the principal An-Keggin binding mode is ionic. Notwithstanding this result, Mulliken and natural population analyses reveal that covalency increases from Th-Pu in these systems, supported by analysis of the occupied Kohn-Sham molecular orbitals where enhanced An(5f)-O(2p) overlap is observed in the Np and Pu systems. By contrast, quantum theory of atoms in molecules analysis shows that U-Keggin binding is the most covalent among the five actinides, in keeping with previous studies.

Activation of dihydrogen by group‐14 substituted germylenes

AbstractWe have investigated the structural and thermodynamic parameters of group‐14 substituted germylenes and their reactivity toward the H2 molecule using density functional theory (DFT). We conducted the detailed Kohn–Sham molecular orbital (KS‐MO) analysis to quantify the effective factors behind the increased reactivity of germylenes in going from C to Sn as substituents. The quantum theory of atoms in molecules (QTAIM), non‐covalent interaction (NCI), and natural bond orbital (NBO) analyses revealed the nature of bonds and interactions and demonstrated the reactivity trend of germylenes in the presence of H2. The results showed that in going from C to Sn, the reactivity increased due to an improvement in ‐donation interaction between the filled lone‐pair orbital of the germylene (LPGe) and the *‐orbital of H2, which decreased the reaction barrier ( E‡). As the germylene substitution was varied from C to Sn, a significant reactivity was observed for the germylene toward the H2. This observation was caused by a reduction in steric repulsion between the germylene and the H2 and less activation energy due to the higher ‐donation and lower back‐donation. We have presented the reactivity of new and rationally designed germylenes toward H2 using various analyses that will serve as a guide for the activation of small molecules such as H2, which is employed in many subsequent reactions.

High-order harmonic generation from aligned HCN molecules under orthogonally and linearly polarized two-color laser fields

Molecular high-order harmonic generation and molecular orbital ionization probabilities are calculated under orthogonally and linearly polarized two-color laser fields. When a second-harmonic field is applied, the high-order harmonics generated under the linearly polarized two-color laser fields in the antiparallel case are stronger than those generated in the orthogonal polarization case and even stronger than those of the parallel polarization case. The results show that ionization probabilities of various orbitals and harmonic orders are dependent on spatial symmetry of molecular orbitals. It is found that the ionization of low-lying Kohn-Sham molecular orbitals contributes significantly to the ionization and molecular high-order harmonic generation processes. The ionization probability maximum occurs when molecular orbital densities are maximum in the direction of laser field polarization. Furthermore, we show that the degeneracy of π orbitals is broken when the laser-molecule alignment angle deviates from the field axis. Accordingly, we indicated one component of the π orbital is effectively contributed to the ionization and high-order harmonic generation processes. Finally, to confirm the recollision model in the high-order harmonic generation, the quantum time-frequency analysis is used to extract electron paths information on subcycle time scales.

S-Shaped Fused Azacorannulene Dimer: Structural and Redox Properties

S-Shaped Fused Azacorannulene Dimer: Structural and Redox Properties

Dimeric aza-BODIPY and Dichloro-aza-BODIPY: A DFT Study

Density functional theory (DFT) computations were performed to unveil the electronic structures and the Kohn-Sham Molecular Orbitals (MOs) of the dimeric aza-BODIPY molecule and its chlorinated form. The optimized conformation of dimers is well in alignment with the one provided in the literature. The HOMO LUMO gap of dichloro-derivative is smaller than that of the dimeric aza-BODIPY molecule by 35.0 meV. The predicted HOMO energies of -6.40 and -6.60 eV point out the good stabilities of both compounds. They were reported to demonstrate bathochromic shifts of 40 and 57 nm compared to their monomers substituted by H and Cl, respectively. The intriguing photophysical behaviors of these molecules were investigated by conducting the Tamm-Dancoff density functional theory (TDA-DFT) calculations. The max values emerge from the HOMO-1 -> LUMO+1 (83-86%) transitions, whereas the low energy transitions arise from HOMO -> LUMO (89%). Therefrom predicted ELUMO->HOMO of the dimeric aza-BODIPY and dichloro-derivative are 1.89 and 1.87 eV, respectively, which are matching well with the reported literature values.

Quantum chemical studies on chelation in nano-bio conjugate between ZnO nanoparticles and cellular energy carrier molecules

Nano-bio complexes, made up of nanoparticle and biomolecules, have wide applications in biomedical nanotechnologies. This makes microscopic understanding of such materials important. Here, we carry out quantum chemical calculations based on DFT on nano-bio conjugate between Zn12O12 cluster (ZnONP) and energy carrier biomolecules in cellular environment, like, ATP, ADP and AMP. We focus on microscopic details of chelation by individual groups, namely, phosphate, ribose and adenine of these molecules with ZnONP. Electronic structures and bonding interactions in ground states of all the complexes are presented through the molecular orbital (MO) theory and the natural bond orbital (NBO) analyses as well as the Raman Spectra. DFT-optimized geometries and bond indices suggest presence of Zn–N(adenine) bond and multiple Zn–O(phosphate) bonds. Phosphate groups form additional O–H⋯O non-classical bonds with ZnONP. Kohn-Sham MOs and natural population analyses suggest that the adenine moiety forms a coordinate covalent bond (Zn–N) with ZnONP through adenine → ZnONP charge transfer (CT), while phosphate groups from coordinate covalent bonds (Zn–O) through ZnONP → phosphate CT in all nano-bio complexes, leading to better stability of bio-molecules-ZnONP complex with increasing of number of phosphate groups in the bio-molecules.

Covalency in actinide(iv) hexachlorides in relation to the chlorine K-edge X-ray absorption structure.

Chlorine K-edge X-ray absorption near edge structure (XANES) in actinideIV hexachlorides, [AnCl6]2− (An = Th–Pu), is calculated with relativistic multiconfiguration wavefunction theory (WFT). Of particular focus is a 3-peak feature emerging from U toward Pu, and its assignment in terms of donation bonding to the An 5f vs. 6d shells. With or without spin–orbit coupling, the calculated and previously measured XANES spectra are in excellent agreement with respect to relative peak positions, relative peak intensities, and peak assignments. Metal–ligand bonding analyses from WFT and Kohn–Sham theory (KST) predict comparable An 5f and 6d covalency from U to Np and Pu. Although some frontier molecular orbitals in the KST calculations display increasing An 5f–Cl 3p mixing from Th to Pu, because of energetic stabilization of 5f relative to the Cl 3p combinations of the matching symmetry, increasing hybridization is neither seen in the WFT natural orbitals, nor is it reflected in the calculated bond orders. The appearance of the pre-edge peaks from U to Pu and their relative intensities are rationalized simply by the energetic separation of transitions to 6d t2gversus transitions to weakly-bonded and strongly stabilized a2u, t2u and t1u orbitals with 5f character. The study highlights potential pitfalls when interpreting XANES spectra based on ground state Kohn–Sham molecular orbitals.

Predicting and Understanding Non-Covalent Interactions Using Novel Forms of Symmetry-Adapted Perturbation Theory.

Although sometimes derided as "weak" interactions, non-covalent forces play a critical role in ligand binding and crystal packing and in determining the conformational landscape of flexible molecules. Symmetry-adapted perturbation theory (SAPT) provides a framework for accurate ab initio calculation of intermolecular interactions and furnishes a natural decomposition of the interaction energy into physically meaningful components: semiclassical electrostatics (rigorously obtained from monomer charge densities), Pauli or steric repulsion, induction (including both polarization and charge transfer), and dispersion. This decomposition helps to foster deeper understanding of non-covalent interactions and can be used to construct transferable, physics-based force fields. Separability of the SAPT interaction energy also provides the flexibility to construct composite methods, a feature that we exploit to improve the description of dispersion interactions. These are challenging to describe accurately because they arise from nonlocal electron correlation effects that appear for the first time at second order in perturbation theory but are not quantitatively described at that level.As with all quantum-chemical methods, a major limitation of SAPT is nonlinear scaling of the computational cost with respect to system size. This cost can be significantly mitigated using "SAPT0(KS)", which incorporates monomer electron correlation by means of Kohn-Sham (KS) molecular orbitals from density functional theory (DFT), as well as by an "extended" theory called XSAPT, developed by the authors. XSAPT generalizes traditional dimer SAPT to many-body systems, so that a ligand-protein interaction (for example) can be separated into contributions from individual amino acids, reducing the cost of the calculation below that of even supramolecular DFT while retaining the accuracy of high-level ab initio quantum chemistry.This Account provides an overview of the SAPT0(KS) approach and the XSAPT family of methods. Several low-cost variants are described that provide accuracy approaching that of the best ab initio benchmarks yet are affordable enough to tackle ligand-protein binding and sizable host-guest complexes. These variants include SAPT+aiD, which uses ab initio atom-atom dispersion potentials ("+aiD") in place of second-order SAPT dispersion, and also SAPT+MBD, which incorporates many-body dispersion (MBD) effects that are important in the description of nanoscale materials. Applications to drug binding highlight the size-extensive nature of dispersion, which is not a weak interaction in large systems. Other applications highlight how a physics-based analysis can sometimes upend conventional wisdom regarding intermolecular forces. In particular, careful reconsideration of π-π interactions makes clear that the quadrupolar electrostatics (or "Hunter-Sanders") model of π-π stacking should be replaced by a "van der Waals model" in which conformational preferences arise from a competition between dispersion and Pauli repulsion. Our analysis also suggests that molecular shape, rather than aromaticity per se, is the key factor driving strong stacking interactions. Looking forward, we anticipate that XSAPT-based methods can play a role in screening of drug candidates and in materials design.

The Gauche Effect in XCH2 CH2 X 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.

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.

The pnictogen bond: a quantitative molecular orbital picture.

We have analyzed the structure and stability of archetypal pnictogen-bonded model complexes D3Pn⋯A− (Pn = N, P, As, Sb; D, A = F, Cl, Br) using state-of-the-art relativistic density functional calculations at the ZORA-M06/QZ4P level. We have accomplished two tasks: (i) to compute accurate trends in pnictogen-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) and Voronoi deformation density (VDD) analyses of the charge distribution. We have found that pnictogen bonds have a significant covalent character stemming from strong HOMO–LUMO interactions between the lone pair of A− and σ* of D3Pn. As such, the underlying mechanism of the pnictogen bond is similar to that of hydrogen, halogen, and chalcogen bonds.

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.

Distortion-Controlled Redshift of Organic Dye Molecules.

It is shown, quantum chemically, how structural distortion of an aromatic dye molecule can be leveraged to rationally tune its optoelectronic properties. By using a quantitative Kohn–Sham molecular orbital (KS‐MO) approach, in combination with time‐dependent DFT (TD‐DFT), the influence of various structural and electronic tuning parameters on the HOMO–LUMO gap of a benzenoid model dye have been investigated. These parameters include 1) out‐of‐plane bending of the aromatic core, 2) bending of the bridge with respect to the core, 3) the nature of the bridge itself, and 4) π–π stacking. The study reveals the coupling of multiple structural distortions as a function of bridge length and number of bridges in benzene to be chiefly responsible for a decreased HOMO–LUMO gap, and consequently, red‐shifting of the absorption wavelength associated with the lowest singlet excitation (λ≈560 nm) in the model cyclophane systems. These physical insights together with a rational approach for tuning the oscillator strength were leveraged for the proof‐of‐concept design of an intense near‐infrared (NIR) absorbing cyclophane dye at λ=785 nm. This design may contribute to a new class of distortion‐controlled NIR absorbing organic dye molecules.

Theoretical analyses of chemical bonding in terminal EThF2 (E = O, S, Se, Te)

Analyses of chemical bonding and geometric structures in species with chalcogen elements EThF2 (E = O, S, Se, Te) are performed by the density functional theory. Kohn–Sham molecular orbitals and Th–E bond lengths of these species both indicate multiple bond character for the terminal chalcogen complexes. This is also confirmed by natural bond orbital analyses using the one-electron density matrix generated by relativistic density functional calculations. Theoretical analyses indicate that electron donation from E to Th increases down the chalcogen group (O < S < Se < Te). These molecules can serve as examples of multiple bonding between actinide elements and selenium or tellurium.

New light on an old debate: does the RCN-PtCl2 bond include any back-donation? RCN←PtCl2 backbonding vs. the IR νC[triple bond, length as m-dash]N blue-shift dichotomy in organonitriles-platinum(ii) complexes. A thorough density functional theory - energy decomposition analysis study.

For a series of organonitrile [RCN (R = Me, CF3, Ph, CH3Ph, CF3Ph)] ligands, the nature of the N-Pt bond in the related cis-/trans-(RCN)2PtCl2 complexes has been computationally investigated by Density Functional Theory. A fragment based bond analysis has been performed in the canonical Kohn-Sham molecular orbitals framework, and it has been ultimately assessed that this bond is characterized both by N→Pt σ and by N←Pt π contributions. Voronoi Deformation Density charges further confirms the occurrence of N←Pt π interactions. Moreover, the Energy Decomposition Analysis-Natural Orbital for Chemical Valence (EDA-NOCV) method shows that the strength of the N←Pt π interaction is not negligible by contributing to about 30-40% of the total orbital interaction. Finally, the well-known νC[triple bond, length as m-dash]N blue-shift occurring upon coordination to PtII, has been thoroughly investigated by exploiting the EDA-NOCV and by evaluating νC[triple bond, length as m-dash]N and force constants. The origin of the νC[triple bond, length as m-dash]N blue-shift in these systems has been discussed on the basis of the CN bond polarization. N←Pt π backbonding causes only a systematic decrease of the observed νC[triple bond, length as m-dash]N blue-shift when compared to the one calculated for RCN-X (X = H+, alkaline, Lewis acids) herein reported (X = purely σ acceptors).

Isocorroles as Homoaromatic NIR-Absorbing Chromophores: A First Quantum Chemical Study

Density functional theory calculations of magnetically induced current densities have revealed high diatropic ring currents in unsubstituted isocorrole consistent with homoaromatic character. An examination of the Kohn-Sham molecular orbitals showed clear evidence of homoconjugative interactions in four occupied π-type molecular orbitals as well as in the LUMO. Remarkably, substituents at the saturated meso position were found to exert a dramatic influence on the overall current density pattern. Thus, whereas bis(trimethylsilyl)-substitution strongly enhanced the peripheral diatropic current (consistent with enhanced homoaromaticity), difluoro-substitution engendered a strong, net paratropic current (consistent with antihomoaromaticity). In this respect, isocorroles stand in sharp contrast to benzenoid aromatics, for which substituents typically exert a small influence on the current density distribution.