Variational treatment on the energy of the He‐sequence ground state with weakest bound electron potential model theory

The concept of spin–orbital of the weakest bound electron is described used to construct the antisymmetric wave function of atomic or ionic systems within weakest bound electron potential model theory (WBEPM theory). The total energies of He‐sequence (Z = 2–9) in the ground states is calculated with a variational method. The effect of fixed orbital approximation is discussed quantitatively. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Ab initio quasirelativistic calculations on electronic transitions in ICl by the multireference many‐body perturbation theory

A quasirelativistic perturbative method of ab initio calculations on ground and excited molecular electronic states and transition properties within the relativistic effective core potential approximation is presented and discussed. The method is based on the construction of a state‐selective many‐electron effective Hamiltonian in the model space spanned by an appropriate set of Slater determinants by means of the second‐order many‐body multireference perturbation theory. The neglect of effective spin–orbit interactions outside of the model space allows the exploitation of relatively high nonrelativistic symmetry during the evaluation of perturbative corrections and therefore dramatic reduction of the cost of computations without any contraction of the model‐space functions. One‐electron transition properties are evaluated via the perturbative construction of spin‐free transition density matrices. Illustrative calculations on the X0⁺ ? A1, B0⁺, and (ii)1 transitions in the ICl molecule are reported. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

Calculations of D‐wave bound states and resonance states of the screened helium atom using correlated exponential wave functions

We have investigated the effects of screened Coulomb (Yukawa) potentials on the bound ^1,3D states and the doubly excited ^1,3 D^e resonance states of helium atom using highly correlated exponential basis functions. The Density of resonance states are calculated using stabilization method. Highly correlated exponential basis functions are used to consider the correlation effect between the charged particles. A total of 18 resonances (nine each for ¹ D^e and ³ D^e states) below the n = 2 He ⁺ threshold has been calculated. For each spin states, this includes four members in the 2pnp series, three members in the 2snd series, and two members in 2pnf series. The resonance energies and widths for various screening parameters ranging from infinity to a small value for these ^1,3 D^e resonance states are reported along with the bound‐excited 1s3d ^1,3 D state energies. Overall behavior of the spectral profile of 1s3d ¹D state of helium atom due to electron‐electron and electron‐nucleus screening are also presented. Accurate resonance energies and widths are also reported for He in vacuum. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Hellmann–Feynman theorem near the threshold

The features of the spectrum structure are considered for situations where some parameter λ of the N‐electron Hamiltonian reaches the threshold value η under which the discrete energy level falls into the continuous spectrum. The electron density properties are also studied. It is proved that for a sequence of the wave functions converging in energy to the lower bound of the continuous spectrum as λ approaches η the corresponding sequence of the electron densities converges to the density of the (N ? 1)‐electron ground state. The results generalize the Hellmann–Feynman theorem for the cases where only the one‐side energy derivatives exist or there is no limiting wave function. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

High‐spin silicon fullerene Si60 and its oligomers

High‐spin states of the Si₆₀ fullerene and its oligomers are considered semiempirically by using sequential and parallel implementations of the AM1 codes. The states are energetically favorable and nearly degenerated over triplet, quintet, and septet spins. All atoms of the Si₆₀ fullerene are in sp³‐configuration, which is supported by atomic spin density in addition to electron density, the latter to be responsible for the formation of chemical bonds. Spotted distribution of spin density over atoms provides molecular magnetism of the molecule. A similar picture is disclosed for oligomers {Si₆₀}_n with n up to 8, which according to computational results should be magnetic with a fractal‐like distribution of spin density over atoms. Opposite the latter, composites Si₆₀C₆₀ and Si₆₀H₆₀ behave conventionally and are nonmagnetic. A way of the Si₆₀ fullerene synthesizing is suggested via the above composite product as intermediates. The considered oligomers are proposed as a model of silicon nanofibers observed recently. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

Theoretical study on regularity of changes in quantum defects in Rydberg state series of many‐valence electron atoms within WBEPM theory

Within the scheme of the weakest bound electron potential model theory, the regularity of changes in quantum defects in 40 “spectrum‐level‐like series” of several many‐valence electron atoms of the third period was studied. The n–δ curves of the 40 spectrum‐level‐like series could be classified into three types; for all such series the quantum defects δ could be expanded as a polynomial of the principal quantum number n in a spectrum‐level‐like series. With regularity, the level energies of high Rydberg states in a series can be predicted accurately. By carefully studying and explaining the three types of 40 n–δ curves, the conclusion was reached: the type of the n–δ curve, i.e., the regularity of changes in quantum defects in a spectrum‐level‐like series, was determined by both the energy level and the azimuthal quantum number l of the weakest bound electron. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 81: 232–237, 2001     

GRECP/5e‐MRD‐CI calculation of the electronic structure of PbH

The correlation calculation of the electronic structure of PbH is carried out with the generalized relativistic effective core potential (GRECP) and multireference single‐ and double‐excitation configuration interaction (MRD‐CI) methods. The 22‐electron GRECP for Pb is used and the outer core 5s, 5p, and 5d pseudospinors are frozen using the level‐shift technique, so only five external electrons of PbH are correlated. A new configuration selection scheme with respect to the relativistic multireference states is employed in the framework of the MRD‐CI method. The [6, 4, 3, 2] correlation spin–orbit basis set is optimized in the coupled cluster calculations on the Pb atom using a recently proposed procedure, in which functions in the spin–orbital basis set are generated from calculations of different ionic states of the Pb atom and those functions are considered optimal that provide the stationary point for some energy functional. Spectroscopic constants for the two lowest‐lying electronic states of PbH (²Π_1/2, ²Π_3/2) are found to be in good agreement with the experimental data. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

Long‐Lived Charge Separation in Novel Axial Donor–Porphyrin–Acceptor Triads Based on Tetrathiafulvalene,Aluminum(III) Porphyrin and Naphthalenediimide

Two self‐assembled supramolecular donor–acceptor triads consisting of Al^III porphyrin (AlPor) with axially bound naphthalenediimide (NDI) as an acceptor and tetrathiafulvalene (TTF) as a secondary donor are reported. In the triads, the NDI and TTF units are attached to Al^III on opposite faces of the porphyrin, through covalent and coordination bonds, respectively. Fluorescence studies show that the lowest excited singlet state of the porphyrin is quenched through electron transfer to NDI and hole transfer to TTF. In dichloromethane hole transfer to TTF dominates, whereas in benzonitrile (BN) electron transfer to NDI is the main quenching pathway. In the nematic phase of the liquid crystalline solvent 4‐(n‐pentyl)‐4′‐cyanobiphenyl (5CB), a spin‐polarized transient EPR spectrum that is readily assigned to the weakly coupled radical pair TTF^.+NDI^.? is obtained. The initial polarization pattern indicates that the charge separation occurs through the singlet channel and that singlet–triplet mixing occurs in the primary radical pair. At later time the polarization pattern inverts as a result of depopulation of the states with singlet character by recombination to the ground state. The singlet lifetime of TTF^.+NDI^.? is estimated to be 200–300 ns, whereas the triplet lifetime in the approximately 350 mT magnetic field of the X‐band EPR spectrometer is about 10 μs. In contrast, in dichloromethane and BN the lifetime of the charge separation is <10 ns.     

Studies of a Large Odd‐Numbered Odd‐Electron Metal Ring: Inelastic Neutron Scattering and Muon Spin Relaxation Spectroscopy of Cr8Mn

The spin dynamics of Cr₈Mn, a nine‐membered antiferromagnetic (AF) molecular nanomagnet, are investigated. Cr₈Mn is a rare example of a large odd‐membered AF ring, and has an odd‐number of 3d‐electrons present. Odd‐membered AF rings are unusual and of interest due to the presence of competing exchange interactions that result in frustrated‐spin ground states. The chemical synthesis and structures of two Cr₈Mn variants that differ only in their crystal packing are reported. Evidence of spin frustration is investigated by inelastic neutron scattering (INS) and muon spin relaxation spectroscopy (μSR). From INS studies we accurately determine an appropriate microscopic spin Hamiltonian and we show that μSR is sensitive to the ground‐spin‐state crossing from S=1/2 to S=3/2 in Cr₈Mn. The estimated width of the muon asymmetry resonance is consistent with the presence of an avoided crossing. The investigation of the internal spin structure of the ground state, through the analysis of spin‐pair correlations and scalar‐spin chirality, shows a non‐collinear spin structure that fluctuates between non‐planar states of opposite chiralities.     

Photochemical Reactions and Photoinduced Electron‐Transfer Processes in Liquids,Frozen Solutions,and Proteins as Studied by Multifrequency Time‐Resolved EPR Spectroscopy

In this overview, modern multifrequency EPR spectroscopy, in particular at high magnetic fields, is shown to provide detailed information about structure, motional dynamics, and spin chemistry of transient radicals and radical pairs occurring in photochemical reactions. Examples discussed comprise photochemical reactions in liquid solution and light‐initiated electron transfer processes both in biomimetic donor–acceptor model systems in frozen solution or liquid crystals and in natural photosynthetic‐reaction‐center protein complexes. The transient paramagnetic states exhibit characteristic electron polarization (CIDEP) effects. They contain valuable information about structure and dynamics of the transient reaction intermediates. Moreover, they are exploited for signal enhancement. Continuous‐wave (cw) and pulsed versions of time‐resolved high‐field EPR spectroscopy, such as cw‐transient‐EPR (TREPR) and pulsed‐electron‐spin‐echo (ESE) experiments, are compared with respect to their advantages and limitations for the specific system under study. For example, W‐band (95‐GHz) TREPR spectroscopy in conjunction with a continuous‐flow system for light‐generated short‐lived transient spin‐polarized radicals of organic photoinitiators in solution was performed with a time resolution of 10 ns. The increased Boltzmann polarization at high fields even allows detection of transient radicals without CIDEP effects. This enables one to determine initial radical polarization contributions as well as radical‐addition reaction constants. Another example of the power of combined X‐band and W‐band TREPR spectroscopy is given for the complex electron‐transfer and spin dynamics of covalently linked porphyrin–quinone as well as Watson–Crick base‐paired porphyrin–dinitrobenzene donor–acceptor biomimetic model systems. Furthermore, W‐band ESE experiments on the spin‐correlated coupled radical pair in reaction centers of the purple photosynthetic bacterium Rb. sphaeroides reveal details of distance and orientation of the pair partners in their charge‐separated transient state. The results are compared with those of the ground‐state P₈₆₅Q_A. The high orientation selectivity of high‐field EPR provides single‐crystal‐like information even from disordered frozen‐solution samples. The examples given demonstrate that high‐field EPR adds substantially to the capability of ‘classical’ spectroscopic and diffraction techniques for determining structure–dynamics–function relations of biochemical systems, since transient intermediates can be observed in real time in their working states on biologically relevant time scales.     

Excited states of OsO4: A comprehensive time‐dependent relativistic density functional theory study

A large number of scalar as well as spinor excited states of OsO₄, in the experimentally accessible energy range of 3–11 eV, have been captured by time‐dependent relativistic density functional linear response theory based on an exact two‐component Hamiltonian resulting from the symmetrized elimination of the small component. The results are grossly in good agreement with those by the singles and doubles coupled‐cluster linear response theory in conjunction with relativistic effective core potentials. The simulated‐excitation spectrum is also in line with the available experiment. Furthermore, combined with detailed analysis of the excited states, the nature of the observed optical transitions is clearly elucidated. It is found that a few scalar states of ³T₁ and ³T₂ symmetries are split significantly by the spin‐orbit coupling. The possible source for the substantial spin‐orbit splittings of ligand molecular orbitals is carefully examined, leading to a new interpretation on the primary valence photoelectron ionization spectrum of OsO₄. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Superconductivity in cuprates: Details of electron phonon coupling

The Bardeen‐Cooper‐Schrieffer (BCS) model explains superconductivity (SC) as due to correlation between electronic momentum and nuclear momentum (phonons) in a free electron gas. The BCS model lacks chemical specificity, however, since the coupling mechanism is left unspecified. After the discovery of high T_C superconductivity in 1986 it was concluded that electron–phonon interactions are insufficient to explain electron pairing. A large part of theoretical research has since been aiming at finding another mechanism that would allow us to consider the superconducting system as a gas of charged free bosons. However, there appears to be no reason to assume free electrons in oxides. In this article the free‐electron criterion is therefore replaced by the criterion that a pair of electrons can move freely between sites without resistance, i.e., without activation energy. Electron pair transfer is treated in a many‐electron real space approach using standard mixed‐valence theories. Mott‐Hubbard‐U is strictly defined, its dependence on breathing mode coordinates analyzed, and the connection between U and the energy gap for superconductivity clarified. d‐wave gap anisotropy is found to be consistent with the general atomic level model presented here. Softening of phonon half‐breathing modes in inelastic neutron scattering (INS) is connected to mixed‐valency. The fundamental vibronic interaction between spin density wave (SDW) and charge density wave (CDW) states leads to a new phase with energy gap and electron pair carriers that can only be the superconducting phase. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Intramolecular Spin Alignment within Mono‐Oxidized and Photoexcited Anthracene‐Based π Radicals as Prototypical Photomagnetic Molecular Devices: Relationships Between Electrochemical,Photophysical, and Photochemical Control Pathways

AnOV is a π‐conjugated radical built from an anthracene (An) unit linked by a p‐phenylene to an oxoverdazyl (OV) moiety. The mono‐oxidized (cationic) form of AnOV was generated both electrochemically and photochemically (in the presence of an electron acceptor). The triplet nature (S=1) of the electronic ground state of AnOV ⁺ was demonstrated by combining spectroelectrochemistry, electron‐spin resonance (ESR) experiments, and ab initio molecular orbital (MO) calculations. The intramolecular spin alignment (ISA) within AnOV ⁺ results from the ferromagnetic coupling (J_electrochem>0) of the two unpaired electrons located on the oxidized electron donor (An⁺) and on the pendant OV radical. The spin‐density distribution pattern of AnOV ⁺ is akin to that of AnOV when photopromoted ( AnOV *) to its high‐spin (HS) lowest excited quartet (S=3/2) state. This high‐spin state results from the ferromagnetic coupling (J_photophys>0) of the triplet locally excited state of An (³An*) with the doublet ground state of OV. As a shared salient feature, AnOV ⁺ and AnOV * (HS) show a spin delocalization within the domain of activated An in either An⁺ or ³An* (nexus states) forms. The present study essentially contributes to establish and clarify relationships between electrochemical, photophysical, and photochemical pathways to achieve ISA processes within AnOV . In particular, we discuss the impact of the spin polarization of the unpaired electron of OV on electronic features of the An electron‐donating subunit. Close analysis of this polarizing interplay allows one to derive a novel functional paradigm to manipulate electron spins at the intramolecular level with light and under an external magnetic field. Indeed, two original functional elements are identified: light‐triggered donors of spin‐polarized electrons and spin‐selective electron acceptors, which are of potential interest for molecular spintronics.     

Electron Spin Exchange in Linked Phenothiazine–Viologen Charge Transfer Complexes Incorporated in “Through‐Ring” (Rotaxane) α‐Cyclodextrins

A series of covalently bound phenothiazine (PHZ) donor and methylviologen (V) acceptor compounds with polymethylene chain spacers (C₈, C₁₀, C₁₂) were incorporated in a “through‐ring” (rotaxane) fashion to α‐cyclodextrin (α‐CD) hosts such that the alkyl chains were fully extended, with the donor and acceptor on opposite sides of the α‐CD cylinder. Photoexcitation of the PHZ unit induces electron transfer from the PHZ first excited triplet state to the V moiety, forming a biradicaloid charge‐separated state. Time‐resolved electron paramagnetic resonance (TREPR) spectroscopy at the X‐band and Q‐band microwave frequencies was used to investigate the spin exchange interaction, J, in these biradicaloids. Simulation of the spectra using a “static” model for spin‐correlated radical pairs allows extraction of the J values, which are negative in sign and have absolute values range from 2 to 1000 Gauss. Comparison of the PHZ_nV (n = 8, 10, 12) spectra to those obtained using phenyl ether spacers indicates that π‐bonds may assist the electronic coupling. The results are discussed in terms of through‐bond vs through‐space electronic coupling mechanisms.     

Co‐Conformational Distribution of Nanosized [2]Catenanes Determined by Pulse EPR Measurements

The co‐conformational ensembles of three differently sized [2]catenanes were studied by measuring pair correlation functions corresponding to the separation of nitroxide spin labels—one attached to each of the two macrocycles—with the double electron–electron resonance (DEER) experiment. A geometric model for the [2]catenanes was derived that approximates the macrocycles by circles and takes into account the topological constraint. Comparison of the experimental to the theoretically predicted pair correlation functions gives insight into the co‐conformational distribution and the size of the macrocycles. It was found that the macrocycles of the medium‐ and large‐sized catenanes in chloroform are close to fully expanded, while they are partially collapsed in glassy o‐terphenyl. For the small‐sized catenane, moderate interaction between the unsaturated sections of the macrocycles in chloroform is indicated by a slight overrepresentation of short label‐to‐label separations in the pair correlation function.     

Singlet Fission for Photovoltaics with 130 % Injection Efficiency

A novel pentacene dimer ( P2 ) and a structurally analogous monomer ( P1 ) were synthesized for use in n‐type dye‐sensitized solar cells. In P2 , the triplet excited states formed by the rapid, spin‐allowed process singlet fission were expected to enable carrier multiplication in comparison to the slow, spin‐forbidden intersystem crossing seen in P1 . A meta‐positioning of the two pentacenes and the carboxylate anchor were chosen in P2 to balance the intramolecular dynamics of singlet fission and electron injection. Electron injection from energetically low‐lying triplet excited states of pentacene units necessitated the intrinsic and extrinsic lowering of the Fermi level of the semiconductor. Indium‐zinc oxide in the presence of Li⁺ was found to be the optimum choice for the photoelectrodes. Efficient electron injection from the triplet excited states of P1 and P2 was found, with a carrier multiplication of nearly 130 %.     

Application of the unitary group approach to evaluate spin density for configuration interaction calculations in a basis of S2 eigenfunctions

We present an implementation of the spin‐dependent unitary group approach to calculate spin densities for configuration interaction calculations in a basis of spin symmetry‐adapted functions. Using S² eigenfunctions helps to reduce the size of configuration space and is beneficial in studies of the systems where selection of states of specific spin symmetry is crucial. To achieve this, we combine the method to calculate U(n) generator matrix elements developed by Downward and Robb (Theor. Chim. Acta 1977, 46, 129) with the approach of Battle and Gould to calculate U(2n) generator matrix elements (Chem. Phys. Lett. 1993, 201, 284). We also compare and contrast the spin density formulated in terms of the spin‐independent unitary generators arising from the group theory formalism and equivalent formulation of the spin density representation in terms of the one‐ and two‐electron charge densities.     

Charge‐transfer transitions and optic spectra of chromites: A model computation

In the cluster approach, we consider the peculiarities of charge‐transfer (CT) states and CT O 2p → Cr 3d transitions in the octahedral (CrO₆)^9? complex. We have computed the reduced matrix elements of electric‐dipole transition operator on many‐electron wave functions — the initial and final states of CT transitions. We have parameterized the obtained results and computed the relative intensities of various allowed CT transitions in the absence of the mixing of CT configurations having the same symmetry. Using the Tanabe‐Sugano technique, we have taken into account this mixing and obtained the energies of many‐electron CT transitions and their actual intensities as well. We have also allowed for the Coulomb interaction between the 2p‐electrons of the O^2? ligands and the 3d‐electrons of the central Cr³⁺ ion in the (CrO₆)^9? cluster. This interaction proved insignificant for the optic spectra. Modeling the optic spectrum of chromium‐based oxides has yielded a complicated CT band consisting of 33 lines with the main maximum at about 7 eV and satellites in the range of 4–5 and 8–9 eV. The total extent of the CT band is about 8 eV. The model spectrum is in satisfactory agreement with experimental data, which shows the limited validity of the generally accepted notion of a simple structure of CT spectra. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Resonance states of atomic anions

We study destabilization of an atom in its ground state with decrease of its nuclear charge. By analytic continuation from bound to resonance states, we obtain complex energies of unstable atomic anions with nuclear charge that is less than the minimum “critical” charge necessary to bind N electrons. We use an extrapolating scheme with a simple model potential for the electron, which is loosely bound outside the atomic core. Results for O^2? and S^2? are in good agreement with earlier estimates. Alternatively, we use the Hylleraas basis variational technique with three complex nonlinear parameters to find accurately the energy of two‐electron atoms as the nuclear charge decreases. Results are used to check the less accurate one‐electron model. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 82: 255–261, 2001