Tuning aryl, hydrazine radical cation electronic interactions using substituent effects

Absorption spectra for 2,3-diaryl-2,3-diazabicyclo[2.2.2]octane radical cations (2(X)(*+)) and for their monoaryl analogues 2-tert-butyl-3-aryl-2,3-diazabicyclo[2.2.2]octane radical cations (1(X)(*+)) having para chloro, bromo, iodo, cyano, phenyl, and nitro substituents are reported and compared with those for the previously reported 1- and 2(H)(*+) and 1- and 2(OMe)(*+). The calculated geometries and optical absorption spectra for 2(Cl)(*+) demonstrate that p-C6H4Cl lies between p-C6H4OMe and C6H5 in its ability to stabilize the lowest energy optical transition of the radical cation, which involves electron donation from the aryl groups toward the pi*(NN)(+)-centered singly occupied molecular orbital of 2(X)(*+). Resonance Raman spectral determination of the reorganization energy for their lowest energy transitions (lambda(v)(sym)) increase in the same order, having values of 1420, 5300, and 6000 cm(-1) for X = H, Cl, and OMe, respectively. A neighboring orbital analysis using Koopmans-based calculations of relative orbital energies indicates that the diabatic aryl pi-centered molecular orbital that interacts with the dinitrogen pi system lies closest in energy to the bonding pi(NN)-centered orbital and has an electronic coupling with it of about 9200 +/- 600 cm(-1), which does not vary regularly with electron donating power of the X substituent.     

Ionization energies of Ni(II) and Cu(II) bis-chelates with sulphur-containing ligands

Quantum-chemical calculations on Ni(II) and Cu(II) dithiophosphates and dimethyldithiocarbaminates, Cu(II)difluorodithiophosphate and their cations have been done using the MOLCAO method with semiempirical approximation CNDO/2. Ionization potentials calculated in accordance with Koopmans' theorem and as differences between total energies of neutral molecules and cations are discussed. It was found that MO rescaling observed under ionization is more essential for Ni(II) than for Cu(II) compounds. In Ni(II) chelates the orbital energies of neutral molecules correlate linearly with the experimental ionization potentials.     

The nature of transitions in electronic absorption spectra of radical cations of dipyrroles with phenylene bridging groups

The electronic absorption spectra of radical cations of dipyrroles with a phenylene bridge were studied by laser flash photolysis and quantum chemical methods. Intense absorption bands of the radical cations in the visible region (λ_max ≈ 500 nm, ε_max > 2 · 10⁴ L mol⁻¹ cm⁻¹) are caused by excitation of electrons from single occupied MOs to the LUMO. In the near IR region, calculations predict additional, relatively intense (f≈ 0.27–0.29) electronic transitions associated with excitation of electrons from low-lying MOs to the single occupied MO.     

Structure,bonding, and spectra of cyclic dithia radical cations: a theoretical study

Ab initio molecular orbital and hybrid density functional theory methods are employed to characterize the structure, bonding and properties of several cyclic dithia radical cation systems, particularly in the context of intra molecular two-center three-electron (2c-3e) bonding between two sulfur atoms. The calculated results are able to interpret the time-resolved transient optical spectra obtained from pulse radiolysis technique for these positively charged dithia systems in aqueous solution. Visualization of the appropriate molecular orbital (MO) in the systems is able to depict the presence of a 2c-3e bond between two sulfur atoms and its sigma character. Geometry optimizations of these doublet systems are carried out at restricted open shell Becke's half-and-half (BHH) nonlocal exchange and Lee-Yang-Parr (LYP) nonlocal correlation functionals (BHHLYP) with 6-311+G(d,p) basis set including solvent effects adopting Onsager's reaction field model. Hessian calculations are done at the same level to check the nature of the equilibrium geometry. Energy data are further improved by performing MP2/6-311+G(d,p) calculations on these radical cation systems. Excited-state calculations are done following configuration interaction with single-electron excitation (CIS) method and the optical transition wavelength from the highest doubly occupied molecular orbital (HDOMO) to the lowest singly occupied molecular orbital (LSOMO) is seen to correspond and match to the position of the absorption maxima (lambda(max)) obtained from the experimental spectra for all these radical cation systems in aqueous solution. These calculations are able to resolve a long-standing ambiguity in the assignment of intra molecular 2c-3e bonding in the case of the 3-methyl-2,4-dithiapentane radical cation system and to provide new insights into bonding features of this odd electron system as well as of other cyclic dithia systems studied.     

Substituent effects on the energies of the electronic transitions of geminally diphenyl-substituted trimethylenemethane (TMM) radical cations. Experimental and theoretical evidence for a twisted molecular and localized electronic structure

Substituent effects on the energies (Eob) of electronic transitions of geminally diphenyl-substituted trimethylenemethane (TMM) radical cations 5a-k*+ and those of structurally related 1,1-diarylethyl cations 7a-k+ were determined experimentally by using electronic transition spectroscopy. In addition, transition energies of these radical cations were determined by using density functional theory (DFT) and time-dependent (TD)-DFT calculations. The electronic transition bands of 5a-k*+ and 7a-k+ have maxima (lambdaob) that appear at 500-432 and 472-422 nm, respectively. A Hammett treatment made by plotting the Eob values relative to that of the diphenyl-TMM radical cation 5d*+ (DeltaEob) vs the cationic substituent parameter sigma+ give a favorable correlation with a boundary point at sigma+ = 0.00 and a positive rho for sigma+ < 0 and a negative rho for sigma+ > 0. A comparison of the lambdaob and rho values for 5a-k*+ and 7a-k+ suggests that the chromophore of 5*+ is substantially the same as that of 7+. The results of TD-DFT calculations, which reproduce the experimental electronic transition spectra and relationships between DeltaEob and sigma+, and suggest that the absorption band of 5*+ is associated with the SOMO-X --> SOMO transition, while that of 7+ is due to the HOMO --> LUMO transition. Another interesting observation is that Cl and Br substituents in the diphenyl-substituted TMM radical cations and 1,1-diarylethyl cations 7a-k+ act as electron-donating groups in terms of their effect on the corresponding electronic transitions. The results show that the molecular structure of 5*+ is a considerably twisted and that 5*+ has a substantially localized electronic state in which the positive charge and odd electron are localized in the respective diarylmethyl and the allyl moieties.     

Koopmans' theorem in the ROHF method: canonical form for the Hartree-Fock Hamiltonian

Since the classic work of Roothaan [Rev. Mod. Phys. 32, 179 (1960)], the one-electron energies of a ROHF method are known as ambiguous quantities having no physical meaning. Together with this, it is often assumed in present-day computational studies that Koopmans' theorem is valid in a ROHF method. In this work we analyze the specific dependence of orbital energies on the choice of the basic equations in a ROHF method which are the Euler equations and different forms of the generalized Hartree-Fock equation. We first prove that the one-electron open-shell energies epsilon(m) derived by the Euler equations can be related to the respective ionization potentials I(m) via the modified Koopmans' formula I(m)= -epsilon(m)f(m) where f(m) is an occupation number. As compared to this, neither the closed-shell orbital energies nor the virtual ones derived by the Euler equations can be related to the respective ionization potentials and electron affinities via Koopmans' theorem. Based on this analysis, we derive the new (canonical) form for the Hamiltonian of the Hartree-Fock equation, the eigenvalues of which obey Koopmans' theorem for the whole energy spectrum. A discussion of new orbital energies is presented on the examples of a free N atom and an endohedral N@C(60) (I(h)). The vertical ionization potentials and electron affinities estimated via Koopmans' theorem are compared with the respective observed data and, for completeness, with the respective estimates derived via a DeltaSCF method. The agreement between observed data and their estimates via Koopmans' theorem is qualitative and, in general, appears to possess the same accuracy level as in the closed-shell SCF.     

Ab initio calculations on CICN and ONCI

Ab initio calculations are presented for the molecules CICN and ONCI with optimization of all geometric parameters. Calculated equilibrium geometries for CICN are in good agreement with microwave data; however, the calculated N-Cl distance in ONCI is about 0.1 Å shorter than obtained by electron diffraction. Orbital energies are calculated by means of Koopmans' theorem and also by ΔSCF calculations. The importance of relaxation energy is shown by comparing the calculated orbital energies with experimental data from photoelectron spectra of the valence levels.     

Koopmans-based analysis of the optical spectra of p-phenylene-bridged intervalence radical ions

[Figure: see text]. The optical spectra of 10 p-phenylene-bridged delocalized intervalence compounds MC6H4M*- or *+ are analyzed using the Koopmans-based method, which considers only transitions from filled orbitals to the singly occupied orbital (SOMO), called Hoijtink type A transitions, and from the SOMO to unoccupied orbitals, Hoijtink type B transitions, and ignores configuration interaction. The radical ions with quinonoid structures, those that form ring-M double bonds with M = C(CN)2, NMe2, 3-oxo-9-azabicyclo[3.3.1], NPPh3, and O when the odd electron of the intervalence oxidation level is removed, are calculated to have the lowest-allowed type B transition lying mostly above the lowest-allowed A transition, with B(i)- A(j) decreasing in the order shown from +14 370 to -1390 cm(-1), and the more intense second-lowest-allowed type B transition B(i) - A(j) from +14 940 to +7070 cm(-1). The five radical anions with benzenoid structures, which form ring-M single bonds with X = CN, CO2Me, CHO, C3HMeBF2O2, and NO2 when the odd electron of the intervalence oxidation level is removed, have a B(i)- A(j) value of the opposite sign that increases in magnitude from -2880 to -17 050 cm(-)(1) in the order shown. Configuration interaction is of course present in the observed spectra, and the predictions ignoring it mostly overestimate transition energies by 1900-2600 cm(-1) for the quinonoid compounds (but by 450 cm(-1) for the M = C(CN)2 radical anion), and by 1000-1400 cm(-1) for the benzenoid compounds (2500 cm(-1) for the M = CN radical anion). The very simple Koopmans-based model is useful for considering the optical spectra of these radical ions.     

Excitation energies expressed as orbital energies of Kohn–Sham density functional theory with long-range corrected functionals

A new simple and conceptual theoretical scheme is proposed for estimating one-electron excitation energies using Kohn–Sham (KS) solutions. One-electron transitions that are dominated by the promotion from one initially occupied orbital to one unoccupied orbital of a molecular system can be expressed in a two-step process, ionization, and electron attachment. KS with long-range corrected (LC) functionals satisfies Janak's theorem and LC total energy varies almost linearly as a function of its fractional occupation number between the integer electron points. Thus, LC reproduces ionization energies (IPs) and electron affinities (EAs) with high accuracy and one-electron excitation energies are expressed as the difference between the occupied orbital energy of a neutral molecule and the corresponding unoccupied orbital energy of its cation. Two such expressions can be used, with one employing the orbital energies for the neutral and cationic systems, while the other utilizes orbital energies of just the cation. Because the EA of a molecule is the IP of its anion, if we utilize this identity, the two expressions coincide and give the same excitation energies. Reasonable results are obtained for valence and core excitations using only orbital energies.     

Spin-orbit relativistic long-range corrected time-dependent density functional theory for investigating spin-forbidden transitions in photochemical reactions

A long-range corrected (LC) time-dependent density functional theory (TDDFT) incorporating relativistic effects with spin-orbit couplings is presented. The relativistic effects are based on the two-component zeroth-order regular approximation Hamiltonian. Before calculating the electronic excitations, we calculated the ionization potentials (IPs) of alkaline metal, alkaline-earth metal, group 12 transition metal, and rare gas atoms as the minus orbital (spinor) energies on the basis of Koopmans' theorem. We found that both long-range exchange and spin-orbit coupling effects are required to obtain Koopmans' IPs, i.e., the orbital (spinor) energies, quantitatively in DFT calculations even for first-row transition metals and systems containing large short-range exchange effects. We then calculated the valence excitations of group 12 transition metal atoms and the Rydberg excitations of rare gas atoms using spin-orbit relativistic LC-TDDFT. We found that the long-range exchange and spin-orbit coupling effects significantly contribute to the electronic spectra of even light atoms if the atoms have low-lying excitations between orbital spinors of quite different electron distributions.     

The methyl isocyanide isomerization: A CNDO/2 study with partitioning of energy

Ab initio LCAO MO SCF calculations have been carried out to predict core electron binding energies and shifts in fluoro- and chloro-methanes. The quality of the calculations ranges from a better than double zeta basis set to minimal STO (3 G) basis set. Predictions of binding energies and shifts are made using Koopmans' theorem, hole state calculations and equivalent cores calculations. Using a flexible basis set there is very little difference in the prediction of shifts by these three methods but for minimal basis set calculations the equivalent cores calculations give the best results.     

Temperature change of OD ESR and freon matrix ESR of the radical cations of 9,10-octalin and cyclohexene

The optical detection (OD) ESR and Freon matrix ESR spectra were observed for the radical cations of 9,10-octalin and cyclohexene from 77 to 300 K. The observed spectral change was attributed to ring inversion in both radical cations based on MO calculations and an analysis by the modified Bloch equation. The activation energy for the inversion of the radical cation of octalin was calculated as 18.8 kJ mol⁻¹.     

Structures and reactions of radical cations of some bicycloalkanes and their related alkenes as studied by 4 k matrix esr

The σ radical cations of most typical bicycloalkanes such as norbornane and bicyclo[2,2,2]octane are radiolytically produced at 4 K in halogenocarbon matrices and are studied by ESR spectroscopy. Their electronic and geometrical structures as well as their dynamical behaviors have been elucidated from the hyperfine structures and their temperature changes. The semi occupied molecular orbital (SOMO) of the former cation is 4a₂, in which the unpaired electron delocalizes over the four exo C-H bonds giving large hyperfine coupling. The latter is a Jahn-Teller active species and exhibits static distortion from D_3h to C_2v at 4 K in CFCl₃, and the SOMO is likely to be 6b₂, in which the unpaired electron delocalizes over the four endo C-H bonds giving large proton coupling, although a dynamically averaged structure with 12 equivalent methylene protons is observed in C-C₆F₁₂ as well as in CFCl₂CF₂Cl matrices at 77 K. The unpaired electron distribution in bicycloalkane radical cations is similar to that in cycloalkane radical cations previously studied. Upon warming both the cations undergo deprotonation to give 2-yl alkyl radicals from the exo or endo C-H bond, at which the higher unpaired electron density is populated. In addition to these radical cations, the structures and reactions of the radical cations of the related bicycloalkenes such as norbornadiene, quadricyclane, and bicyclo[2,2,2]octene have also been studied. The hydride ion transfer to an olefinic radical cation to form an alkyl radical is observed for the bicyclo[2,2,2]octene radical cation as the first example observed by ESR.     

Empty level structure and dissociative electron attachment cross section in (bromoalkyl)benzenes

The gas-phase electron transmission (ET) and dissociative electron attachment (DEA) spectra are reported for the series of (bromoalkyl)benzenes C6H5(CH2)nBr (n = 0-3), where the bromine atom is directly bonded to a benzene ring or separated from it by 1-3 CH2 groups, and the dihalo derivative 1-Br-4-Cl-benzene. The relative DEA cross sections (essentially due to the Br- fragment) are reported, and the absolute cross sections are also evaluated. HF/6-31G and B3LYP/6-31G* calculations are employed to evaluate the virtual orbital energies (VOEs) for the optimized geometries of the neutral state molecules. The pi* VOEs, scaled with empirical equations, satisfactorily reproduce the corresponding experimental vertical electron attachment energies (VAEs). According to the calculated localization properties, the LUMO (as well as the singly occupied MO of the lowest lying anion state) of C6H5(CH2)3Br is largely localized on both the benzene ring and the C-Br bond, despite only a small pi*/sigma*C-Br interaction and in contrast to the chlorine analogue where the LUMO is predicted to possess essentially ring pi character. This would imply a less important role of intramolecular electron transfer in the bromo derivative for production of the halogen negative fragment through dissociation of the first resonant state. The VAEs calculated as the anion/neutral energy difference with the 6-31+G* basis set which includes diffuse functions are relatively close to the experimental values but do not parallel their sequence. In addition the SOMO of some compounds is not described as a valence MO with large pi* character but as a diffuse sigma* MO.     

Orbital correlation diagrams based on multiconfigurational variation of moments II. Application

A formalism was developed in the multiconfigurational variation of moments (MCM ) framework, which yields physically meaningful orbital energies for occupied and virtual orbitals starting from self-consistent field (SCF ) calculations. This is possible through a skillful distribution of the correlation energy on the orbital energies. The application of this method is demonstrated by SINDO 1 calculations on the dissociation of H₂ and the following symmetry-forbidden reactions: (1) torsion of ethylene; (2) ring opening of (a) cyclobutene, and (b) cyclopropyl cation; (3) cycloreversion of 1, 1-dicyano-2-methoxycyclobutane. The allowed reactions corresponding to 2a and 2b are investigated in the SCF scheme. The energy hypersurfaces are calculated for all reactions and the MO correlation diagrams are presented and discussed.     

Temporary anion states of pyrimidine and halopyrimidines

The empty-level electronic structures of pyrimidine and its 2-chloro, 2-bromo, and 5-bromo derivatives have been studied with electron transmission spectroscopy (ETS) and dissociative electron attachment spectroscopy (DEAS) in the 0-5 eV energy range. The spectral features were assigned to the corresponding anion states with the support of theoretical calculations at the ab initio and density functional theory levels. The empty orbital energies obtained by simple Koopmans' theorem calculations, scaled with empirical equations, quantitatively reproduced the energies of vertical electron attachment to π* and σ* empty orbitals measured in the ET spectra and predicted vertical electron affinities close to zero for the three halo derivatives. The total anion currents of the halo derivatives, measured at the walls of the collision chamber as a function of the impact electron energy, presented intense maxima below 0.5 eV. The mass-selected spectra showed that, in this energy, range the total anion current is essentially due to halide fragment anions. The DEA cross sections of the bromo derivatives were found to be about six times larger than that of the chloro derivative. The absolute cross sections at incident electron energies close to zero were evaluated to be 10(-16)-10(-15) cm(2).     

An analysis of the zero differential overlap approximation. Towards an improved semiempirical MO method beyond it

Summary Some systematic errors of the zero differential overlap (ZDO) approximation in semiempirical molecular orbital (MO) methods are discussed. In electron methods, a power series expansion of the inverse square rootS ^–1/2 of the overlap matrix and application of the Mulliken approximation to the two-electron integrals show that the ZDO Hamiltonian coincides with the Hamiltonian obtained by explicit performance of the Löwdin transformation up to first-order terms of diatomic overlap densities. Higher than first-order terms lead to a systematic up-shift of the canonical MO energies. Although a power series expansion ofS ^–1/2 is no longer possible in all-valence-electron methods, the MO levels resulting from the ZDO approximation are also systematically placed at too low energies, especially the low-lying occupied and the virtual MOs. A method based on explicit performance of the Löwdin transformation and retaining the simplicity of the ZDO approach for the calculation of Fock matrix elements is developed. The parameters of this method are obtained by very simple manipulations of the original ZDO parameters. Numerical calculations show that a considerable improvement of the MO energy spectrum in the inner valence region can be obtained in this way