Hardness and excitation energy

The concept of the ensemble Kohn-Sham hardness is introduced. It is shown that the first excitation energy can be given by the Kohn-Sham hardness (i.e. the energy difference of the ground-state lowest unoccupied and highest occupied levels) plus an extra term coming from the partial derivative of the ensemble exchange-correlation energy with respect to the weighting factorw in the limitw → 0. It is proposed that the first excitation energy can be used as a reactivity index instead of the hardness.     

Higher order alchemical derivatives from coupled perturbed self-consistent field theory

We present an analytical approach to treat higher order derivatives of Hartree-Fock (HF) and Kohn-Sham (KS) density functional theory energy in the Born-Oppenheimer approximation with respect to the nuclear charge distribution (so-called alchemical derivatives). Modified coupled perturbed self-consistent field theory is used to calculate molecular systems response to the applied perturbation. Working equations for the second and the third derivatives of HF/KS energy are derived. Similarly, analytical forms of the first and second derivatives of orbital energies are reported. The second derivative of Kohn-Sham energy and up to the third derivative of Hartree-Fock energy with respect to the nuclear charge distribution were calculated. Some issues of practical calculations, in particular the dependence of the basis set and Becke weighting functions on the perturbation, are considered. For selected series of isoelectronic molecules values of available alchemical derivatives were computed and Taylor series expansion was used to predict energies of the "surrounding" molecules. Predicted values of energies are in unexpectedly good agreement with the ones computed using HF/KS methods. Presented method allows one to predict orbital energies with the error less than 1% or even smaller for valence orbitals.     

A comparative analysis of Hartree-Fock and Kohn-Sham orbital energies

Hartree-Fock and Kohn-Sham orbital energies, the latter computed with several different exchange/correlation functionals, are compared and analyzed for 12 molecules. The Kohn-Sham energies differ significantly from experimental ionization energies, but by amounts that are, for a given molecule and exchange/correlation functional, roughly the same for all of the valence orbitals. With the exchange/correlation functionals used, the energy of the highest occupied Kohn-Sham orbital does not approximate the corresponding ionization potential any better than do the other orbital energies. Received: 24 October 1997 / Accepted 31 October 1997     

Koopmans-like approximation in the Kohn-Sham method and the impact of the frozen core approximation on the computation of the reactivity parameters of the density functional theory

A Koopmans-like approximation is introduced in the spin-polarized version of the Kohn-Sham (KS) density functional theory to obtain a relation between KS orbital energies and vertical ionization potential and electron affinity. Expressions for reactivity indexes (like electronegativity, hardness, electrophilicity, and excitation energies) include KS frontier orbital energies and additional contributions associated with the self-interaction correction. Those reactivity parameters were computed with different exchange-correlation functionals to test the approach for a set of small molecules. The results show that the present approximation provides a better way to estimate hardness, electronegativity, and electrophilicity than just the use of frontier orbital energy values. However KS HOMO and LUMO energy gap gives a better agreement with excitation energies.     

Examining the impact of ancillary ligand basicity on copper(I)–ethylene binding interactions: a DFT study

A theoretical investigation at the density functional theory level (B3LYP) has been conducted to elucidate the impact of ligand basicity on the binding interactions between ethylene and copper(I) ions in [Cu(η ²-C₂H₄)]⁺ and a series of [Cu(L)(η ²-C₂H₄)]⁺ complexes, where L = substituted 1,10-phenanthroline ligands. Molecular orbital analysis shows that binding in [Cu(η ²-C₂H₄)]⁺ primarily involves interaction between the filled ethylene π-bonding orbital and the empty Cu(4s) and Cu(4p) orbitals, with less interaction observed between the low energy Cu(3d) orbitals and the empty ethylene π*-orbital. The presence of electron-donating ligands in the [Cu(L)(η ²-C₂H₄)]⁺ complexes destabilizes the predominantly Cu(3d)-character filled frontier orbital of the [Cu(L)]⁺ fragment, promoting better overlap with the vacant ethylene π*-orbital and increasing Cu → ethylene π-backbonding. Moreover, the energy of the filled [Cu(L)]⁺ frontier orbital and mixing with the ethylene π*-orbital increase with increasing pK _a of the 1,10-phenanthroline ligand. Natural bond orbital analysis reveals an increase in Cu → ethylene electron donation with addition of ligands to [Cu(η ²-C₂H₄)]⁺ and an increase in backbonding with increasing ligand pK _a in the [Cu(L)(η ²-C₂H₄)]⁺ complexes. Energy decomposition analysis (ALMO-EDA) calculations show that, while Cu → ethylene charge transfer (CT) increases with more basic ligands, ethylene → Cu CT and non-CT frozen density and polarization effects become less favorable, yielding little change in copper(I)–ethylene binding energy with ligand pK _a. ALMO-EDA calculations on related [Cu(L)(NCCH₃)]⁺ complexes and calculated free energy changes for the displacement of acetonitrile by ethylene reveal a direct correlation between increasing ligand pK _a and the favorability of ethylene binding, consistent with experimental observations.     

Sandwich complexes of Si, Ge, Sn, and Pb with cyclopentadienyl type derivatives of corannulene and fullerene C60: stability estimates and molecular and electronic structure prediction by the MNDO/PM3 method

The ability of cyclopentadienyl type derivatives of corannulene C₂₀H₁₀ and fullereneI _h -C₆₀ to form η⁵-π-complexes and the problem of their existence is discussed. MNDO/PM3 calculations of half-sandwich complexes η⁵-π-MC₂₀H₁₅, η⁵-π-MC₂₀H ₁₅ ⁺ , η⁵-π-MC₆₀H₅, η⁵-π-MC₆₀H₅ and sandwich complexes 2η⁵-π-M(C₂₀H₁₅)₂, 2η⁵-π-M(C₂₀H₁₅)₂, 2η⁵-π-M(C₆₀H₅)₂ (M=Si, Ge, Sn, Pb) were performed. For all systems studied, local minima were found on corresponding potential energy surfaces and the heats of formation, geometric parameters, and distributions of effective atomic charges were calculated. Sandwich complexes are most likely to exist with M=Si and Ge. The energy and geometric characteristics of η⁵-π-complexes of corannulene were compared with those of η⁵-π-complexes of fullereneI _h -C₆₀. It was concluded that the results of quantum-chemical calculations of sandwich type corannulene derivatives can be used for simulation of the geometry and electronic structure of analogous complexes of fullereneI _h -C₆₀. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 9, pp. 1649–1656, September, 1999.     

Synthesis and structure of (boratabenzene)rhodacarborane (η-7,8-C2B9H11)Rh(η-C5H5BMe)

The bromide complex [(η-C₅H₅BMe)RhBr₂]₂ (1) was synthesized by the reaction of the cyclooctadiene derivative (η-C₅H₅BMe)Rh(1,5-C₈H₁₂) with Br₂. The reaction of compound 1 with Tl[Tl(η-7,8-C₂B₉H₁₁)] gave (boratabenzene)rhodacarborane (η-7,8-C₂B₉H₁₁)Rh-(η-C₅H₅BMe) (2). The structure of compound 2 was determined by X-ray diffraction     

Density functional study on zerovalent lanthanide bis(arene)-sandwich complexes

Several zerovalent lanthanide bis(arene)-sandwich complexes, Ln(η⁶-C₆H₆)₂, Ln = La, Ce, Eu, Gd and Lu, have been studied by means of density functional theory. The calculated geometries are in good agreement with experiment. The calculated dissociation energies of the bond Ln-(η⁶-C₆H₆) may be considerably underestimated, but they correctly reveal the variation regularity. The bonding in these molecules can be described in terms of a relatively weak π-electron donation from benzene to Ln and a stronger electron back-donation from Ln 5d to the benzene π* orbitals. During bond formation, there is electron promotion from Ln 6s to 5d instead of from 4f to 5d, in opposition to the proposal of Anderson et al. The relativistic effect only slightly influences the molecular geometry, but decreases the bonding energy considerably through lowering the Ln 6s level and raising the 5d level. It enhances the trend of the bonding energy to decrease along the lanthanide series. Received: 22 June 1998 / Accepted: 9 September 1998 / Published online: 17 December 1998     

An electrochemical investigation on the reduction path of the arene complexes [CpM(arene)]2+ and [(η-9-SMe2-7,8-C2B9H10)M(arene)]2+ (M=Rh, Ir)

The reduction behavior of the isoelectronic complexes [CpM^III(η⁶-C₆R₆)]²⁺ (M=Rh, Ir; R=H, Me) and [(η-9-SMe₂-7,8-C₂B₉H₁₀)M^III(η⁶-C₆R₆)]²⁺ (M=Rh, Ir; C₆R₆ = C₆H₆, C₆H₅OMe, C₆H₃Me₃) has been studied by cyclic voltammetry and controlled potential coulometry in acetonitrile and propylene carbonate at 253 and 298 K, respectively. The extent of chemical reversibility of the pertinent sequences Rh(III)/Rh(II)/Rh(I) and Ir(III)/Ir(I) is highly dependent on both the nature of the solvent and the intrinsic electronic properties of the arene substituents. The arene η⁶ coordination makes the derivatives in their lower oxidation states notably short lived, even if, in some cases, the use of propylene carbonate improves their stability or causes the increase in their lifetimes before changing the arene coordination from η⁶ to η⁴. Cations [(η-9-SMe₂-7,8-C₂B₉H₁₀)M(η⁶-C₆R₆)]²⁺ were obtained by the bromide abstraction from [(η-9-SMe₂-7,8-C₂B₉H₁₀)MBr₂]₂ with Ag⁺ in the presence of benzene and its derivatives. The structure of [(η-9-SMe₂-7,8-C₂B₉H₁₀)Ir(η⁶-C₆H₅OMe)](BF₄)₂ was determined by X-ray diffraction.     

30-Electron cationic iron- and cobalt-containing triple-decker complexes with a central cyclopentadienyl ligand. The first synthesis of the parent triple-decker iron complex with cyclopentadienyl ligands, [(η-C5H5)Fe(μ-η:η-C5H5)Fe(η-C5H5)]PF6

The parent 30-electron triple-decker iron complex with cyclopentadienyl ligands, [(η-C₅H₅)Fe(μ-η:η-C₅H₅)Fe(η-C₅H₅)]PF₆ (1), was prepared for the first time by visible-light irradiation of ferrocene and [(η-C₅H₅)Fe(η-C₆H₆)]PF₆ in CH₂Cl₂ at 0 °C. An analogous reaction performed with the use of (η-C₅H₅)Co(η-C₄Me₄) (2) instead of ferrocene afforded the thermally labile 30-electron cationic iron-cobalt triple-decker complex [(η-C₅H₅)Fe(μ-η:η-C₅H₅)Co(η-C₄Me₄)]PF₆. The latter reacted with compound 2 at 20 °C to form the symmetrical 30-electron cationic dicobalt triple-decker complex [(η-C₄Me₄)Co(μ-η:η-C₅H₅)Co(η-C₄Me₄)] PF₆. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya. No. 7, pp. 1364–1367, July, 1999.     

Syntheses, structures, and magnetic properties of new rare earth coordination polymers constructed by 1,3,5-benzenetriacetic acid

Three new coordination polymers with formula [Gd(bta)(H₂O)·1.39H₂O] _n (1), [Dy(bta)(H₂O)·1.35H₂O] _n (2) and [Y(bta)(H₂O)₂·0.5H₂O] _n (3) were synthesized by using corresponding rare earth nitrates and 1,3,5-benzenetriacetic acid (H₃bta) under hydrothermal/solvothermal reaction conditions, and characterized by single-crystal X-ray diffraction. In these complexes, the carboxylate groups of bta³⁻ adopt different coordination modes, namely one carboxylate group adopts μ₂-η¹:η¹-bridging and each of the other two carboxylate groups adopts μ₂-η²:η¹-bridging coordination modes in 1 and 2, and one carboxylate group adopts a μ₂-η²:η¹-bridging coordination mode and each of the other two carboxylate groups adopts a μ₂-η¹:η¹-bridging mode for the major component and one carboxylate group adopts a μ₂-η²:η¹-bridging coordination mode, one has a μ₂-η¹:η¹-bridging mode and the third has a monodentate mode for the minor component in 3. The magnetic properties of the complexes 1 and 2 were investigated in the temperature range of 1.8–300 K.     

Simulation of molecular and electronic structure of η5-π-complexes of fullereneI h -C 60 with half-sandwich XCp species (X=Si, Ge, Sn)

The molecular and electronic structure of hypothetical complexes of unsubstituted fullerene C₆₀ withI _h symmetry and its cyclopentadienyl type derivatives were simulated by the MNDO/PM3 method taking the C₆₀(XC[) _n molecules (n=1, 2, 10, 12; X=Si, Ge, Sn) and η⁵-C₆₀H₅XCp (X=Ge, Sn), respectively, as example. The complexes 12η⁵-πC₆₀(XCp)₁₂ and η⁵-πC₆₀XCp withI _h andC _5v symmetry, respectively, were found to be the most stable compounds. The energies of the X−C₆₀ bonds in these complexes are close to those of X−Cp bonds in bis(cyclopentadienyl) complexes XCp₂ and are substantially higher than the energies of similar bonds in complexes of unsubstituted fullerene η¹-πC₆₀(XCp)⁻ and η⁵-πC₆₀(XCp)⁺. Geometric parameters and spin densities in radicals C₆₀XCp and biradicals C₆₀(XCp)₂ and C₆₀H₁₀ were calculated. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 11, pp. 2155–2165, November, 1998.     

Synthesis of the first metallacarborane triple-decker complexes with a central cyclopentadienyl ligand

The previously unknown metallacarboranes (η-C₅R₅)Ru(η-9-Me₂S-7,8-C₂B₉H₁₀) (R=H or Me) and (η-C₅H₅)Ni(η-9-Me₂S-7,8-C₂B₉H₁₀) were prepared and used in the synthesis of the first metallacarborane triple-decker complexes with a central cyclopentadienyl ligand, viz., [(η-C₅R₅)Ru(μ-η:η-C₅Me₅)Ru(η-9-Me₂S-7,8-C₂B₉H₁₀)]PF₆ (R=H or Me), [(η-9-Me₂S-7,8-C₂B₉H₁₀)Ni(μ-η:η-C₅H₅)Ni(η-9-Me₂S-7,8-C₂B₉H₁₀)]PF₆, and [(η-C₅H₅)Ni(μ-η:η-C₅H₅)Ni(η-9-Me₂S-7,8-C₂B₉H₁₀)]BF₄. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 7, pp. 1368–1373, July, 1999.     

Electrophilic substitution reactions of ferracarborane 3-(η5-Cp)-4-SMe2-3,1,2-FeC2B9H10

Mercuration and bromination reactions of ferracarborane 3-(η⁵-Cp)-4-SMe₂-3,1,2-FeC₂B₉H₁₀ (1) were investigated. Mercuration of 1 under mild conditions (mercury trifluoroacetate in dichloromethane) results in 8-monosubstituted mercury derivative as the only reaction product. Depending on the reaction conditions, bromination of 1 results in 8-mono- or 7,8-disubstituted bromo derivatives. The structures of the monomercury and dibromo derivatives of 1 were established by X-ray analysis. Published inIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 9, pp. 1609–1615, September, 2000.     

Synthesis of functionalized aminopyrazole and pyrazolopyrimidine derivatives: Molecular modeling and docking as anticancer agents

Three new functionalized 4-aminopyrazole derivatives were synthesized and cyclized with phenyl isothiocyanate to yield the corresponding three pyrazolo[4,3-d]pyrimidine analogues. The DFT quantum chemical calculations were utilized in the determination of the frontier molecular orbital energies and Fukui’s indices. The data showed that they have a low HOMO-LUMO energy gap, ranging from 1.16 to 2.35 eV for 5 and 6, respectively. The newly created analogues' cytotoxic qualities were evaluated in comparison to the reference 5-florouracil (5-Fu) using an in vitro MTT cytotoxicity screening investigation toward four different cell lines, including HCT-116, HepG2, MCF-7, and WI38. The results showed variable potency against human cell lines, with MCF-7 and HepG-2 showing cytotoxic selectivity. The most potent agent against MCF-7 and HCT-116 human cancer cells were found to be aminopyrazole and pyrazolopyrimidine derivatives 4–9. The structure–activity relationships (SAR) for the synthesized compounds were discussed. The examined compounds had superior cytotoxic properties; the most potent derivative 7, had an IC₅₀ ranged from 11.51 ± 0.35 to 21.25 ± 0.37 µM. Meanwhile, quantum chemical computation used independent variables E_H, E_L, ΔE_H-L, χ and η were applied to determine the best way to describe activity. As a result, an increase in the HOMO-LUMO gap and hardness will result in an increase in the anticancer activity. While the E_H, E_L, and showed negative coefficients, increasing them will decrease the anticancer activity. Furthermore, 5IVE protein's crystal structure for KDM5A was docked with the newly created aminopyrazole and pyrazolopyrimidine derivatives to afford the theoretical prediction on the KDM5A enzyme.     

Derivative discontinuity, bandgap and lowest unoccupied molecular orbital in density functional theory

The conventional analysis of Perdew and Levy, and Sham and Schlu?ter shows that the functional derivative discontinuity of the exchange-correlation density functional plays a critical role in the correct prediction of bandgaps, or the chemical hardness. In a recent work by the present authors, explicit expressions for bandgap prediction with all common types of exchange-correlation functionals have been derived without invoking the concept of exchange-correlation energy functional derivative discontinuity at all. We here analyze the two approaches and establish their connection and difference. The present analysis further leads to several important results: (1) The lowest unoccupied molecular orbital (LUMO) in DFT has as much meaning in describing electron addition as the highest occupied molecular orbital (HOMO) in describing electron removal. (2) Every term in the total energy functional contributes to the energy gap because of the discontinuity of the derivative of the density (or density matrix) with respect to the number of electrons, ((?ρ(s)(r('),r))/?N)(v(s) ), at integers. (3) Consistent with the Perdew-Levy-Sham-Schlu?ter conclusion that the exact Kohn-Sham energy gap differs from the fundamental bandgap by a finite correction due to the functional derivative discontinuity of the exchange-correlation energy, we show that the exchange-correlation functional cannot be an explicit and differentiable functional of the electron density, either local or nonlocal. The last result is further strengthened when we consider Mott insulators. There, the exact exchange-correlation functional needs to have an explicitly discontinuous (nondifferentiable) dependence on the density or the density matrix. (4) We obtain exact conditions on the derivatives of total energy with respect to the spin-up and spin-down number of electrons.     

Quantum chemical studies of propene,ethylene, acetylene and dihydrogen reactivity in the insertion reaction into the titanium-alkyl bond

Using the ab initio method of SCF MO LCAO

1 SCF MO LCAO: Self-consistent field molecular orbital linear combination of atomic orbitals.

in a valency-splitted basis of the Gaussian functions we have studied the addition of various monomers (C₃H₈, C₂H₄, C₂H₂) and dihydrogen to the titanium-alkyl bond in the complex H₂TiCH₃. The structure of transition states in the insertion reaction, heats of π-complex formation and activation energies for the insertion of the coordinated monomers have been calculated. The calculation results show that the reactivity decreases in the order C₂H₂ > C₂H₄ > C₃H₈ > H₂. According to the results obtained, the energy of the π^*-antibonding orbital of monomers can serve as an index of relative reactivity in the insertion reaction into the metal-alkyl bond.     

Synthesis of the cyclooctadiene and cyclooctenediyl cobalt complexes. Structures of [(η2,η2-cyclooctadiene)Co(η-1,2,4,5-C6H2Me4)]BF4 and [(η1,η3-cyclooctenediyl)Co(η-9-SMe2-7,8-C2B9H10)

Cobaltacarboranes (η¹, η³-cyclooctenediyl)Co(Carb) (Carb = η-9-SMe₂-7,8-C₂B₉H₁₀, η-1-tBuHN-1,7,9-C₃B₈H₁₀) were synthesized by the reaction of the carborane anions [Carb]⁻ with the acetonitrile complex [(η¹, η³-cyclooctenediyl)Co(MeCN)₃]⁺ generated in situ upon the dissolution of [(η¹, η³-cyclooctenediyl)Co(η-1,4-C₆H₄Me₂)]⁺ in MeCN. The structures of (η¹,η³-cyclooctenediyl)Co(η-9-SMe₂-7,8-C₂B₉H₁₀ and [(η²,η²-cyclooctadiene)Co((η-1,2,4,5-C₆H₂Me₄)]BF₄ were determined by X-ray diffraction analysis.     

Reaction of a naphthalene complex C10H8Yb(THF)2 with cyclopentadienyl-substituted alcohols and amines as a convenient synthetic route to the half-sandwich complexes of divalent ytterbium

The reactions of ytterbium naphthalene complex C₁₀H₈Yb(THF)₂ with 2-cyclopentadienylethanol, 1-cyclopentadienylpropan-2-ol, 3-cyclopentadienyl-1-butoxypropan-2-ol, and cyclopentadienyldimethylsilyl-tert-butylamine were studied. The bivalent ytterbium complexes with chelate bifunctional cyclopentadienyl ligands [(η⁵−C₅H₅)CH₂CH₂(η¹−O)]Yb(THF), [(η⁵−C₅H₅)CH₂CH₂(η¹−O)]Yb(DME). [(η⁵−C₅H₅)CH₂CH(Me)(η¹−O)]Yb(THF), [(η⁵−C₅H₅)CH₂CH(CH₂OC₄H₉)(η¹−O)]Yb(THF), and [(η⁵−C₅H₅)SiMe₂(η¹−N(Bu¹))]Yb(THF) were obtained and characterized. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 4, pp. 742–745, April, 2000.     

Binding of ansa- and non-ansa-titanocene anticancer drugs to DNA: a DFT study

The complexes [Ti(η⁵-C₂H₄{CMe₂CH₂CH₂CH=CH₂})₂Cl₂] (1) and [Ti{Me₂Si(η⁵-C₅Me₄)(η5-C₅H₃{CMe₂CH₂CH₂CH=CH₂})}Cl₂] (2) exhibited significant antitumor activity, but the detailed mechanism of antitumor effect remains unknown. In current research, we studied the hydrated 1 and 2 bindings to potential biological targets, purine bases, and phosphate group, using density functional theory and IEF-PCM solvation models. Our calculations reveal that the monoaquated complex binding to guanine shows the lowest activation free-energy with 15.3 and 21.5 kcal/mol for the complexes 1 and 2, respectively. In the diaquaed 1, the lowest activation-free energy is 16.7 kcal/mol for the guanine and closely followed by the phosphate group is 18.3 kcal/mol, while the lowest activation-free energy is 16.9 kcal/mol for the complex 2 binding to the phosphate group. In addition, natural orbital population analysis (NPA) method was performed for the investigation of major electronic characteristics.