Ultrafast solvent-induced spin-flip and nonadiabatic coupling: ClF in argon solids

Femtosecond pump-probe spectra show direct evidence for ultrafast solvent-induced spin flip in photodissociation-recombination events of ClF, a light diatomic molecule, for which the spin-orbit coupling is weak. The bound triplet states ((3)Pi) of ClF are probed and the dynamics for excitation to the singlet state ((1)Pi(1)) is compared with excitation to the triplet state B((3)Pi(0)). The population initially excited to the singlet state (1)Pi(1) is transferred to the bound triplet states (3)Pi within tau(f)=0.5 ps. Oscillations in the spectra indicate wave packet dynamics with the triplet state period of 300 to 400 fs in both cases. According to simulations of F(2)/Ar, most of the initially excited singlet state population is converted to repulsive and weakly bound triplet states within approximately 60 fs. In the first ps, 40% of the triplet population accumulates in the weakly bound (3)Pi states, in good accord with the experiment.     

Excitation of lowest electronic states of thymine by slow electrons

Excitation of lowest electronic states of the thymine molecules in the gas phase is studied by elec- tron energy loss spectroscopy. In addition to dipole-allowed transitions to singlet states, transitions to the lowest triplet states were observed. The low-energy features of the spectrum at 3.66 and 4.61 eV are identified with the excitation of the first triplet states 1₃ A′ (π → π*) and 1₃ A″ (n → π*). The higher-lying features at 4.96, 5.75, 6.17, and 7.35 eV are assigned mainly to the excitation of the π → π* transitions to the singlet states of the molecule. The excitation dynamics of the lowest states is studied. It is found that the first triplet state 1³ A′(π → π*) is most efficiently excited at a residual energy close to zero, while the singlet 2₁ A′(π → π*) state is excited with almost identical efficiency at different residual energies.     

Excitation of lowest electronic states of the uracil molecule by slow electrons

The excitation of lowest electronic states of the uracil molecule in the gas phase has been studied by electron energy loss spectroscopy. Along with excitation of lowest singlet states, excitation of two lowest triplet states at 3.75 and 4.76 eV (±0.05 eV) and vibrational excitation of the molecule in two resonant ranges (1?C2 and 3?C4 eV) have been observed for the first time. The peak of the excitation band related to the lowest singlet state (5.50 eV) is found to be blueshifted by 0.4 eV in comparison with the optical absorption spectroscopy data. The threshold excitation spectra have been measured for the first time, with detection of electrons inelastically scattered by an angle of 180°. These spectra exhibit clear separation of the 5.50-eV-wide band into two bands, which are due to the excitation of the triplet 1³ A?? and singlet 1¹ A?? states.     

Singlet and triplet bipolarons on the triangular lattice

We study the Coulomb-Fröhlich model on a triangular lattice, looking in particular at states with angular momentum. We examine a simplified model of crab bipolarons with angular momentum by projecting onto the low energy subspace of the Coulomb-Fröhlich model with large phonon frequency. Such a projection is consistent with large long-range electron-phonon coupling and large repulsive Hubbard U. Significant differences are found between the band structure of singlet and triplet states: The triplet state (which has a flat band) is found to be significantly heavier than the singlet state (which has mass similar to the polaron). We test whether the heavier triplet states persist to lower electron-phonon coupling using continuous time quantum Monte Carlo (QMC) simulation. The triplet state is both heavier and larger, demonstrating that the heavier mass is due to quantum interference effects on the motion. We also find that retardation effects reduce the differences between singlet and triplet states, since they reintroduce second order terms in the hopping into the inverse effective mass.     

“W = 0” pairing in Cu-O clusters and in the plane

The Cu-O plane and the clusters that possess the same C_4v symmetry around a Cu ion have 2-hole eigenstates of the kinetic energy with vanishing on-site repulsion (W=0 pairs). Cluster calculations by exact diagonalisation show that these are the quasiparticles that lead to a paired ground state, and have superconducting flux-quantisation properties. Here, we extend the theory to the full plane, and show that the W=0 quasiparticles are again the natural explanation of superconducting flux-quantisation. Moreover, by a new approach which is exact in principle, we calculate the effective interaction between two holes added to the ground state of the repulsive three-band Hubbard model. To explain how a noninteracting electron gas becomes a superconductor when switching the local Coulomb interaction, we obtain a closed-form analytic expression including the effects of all virtual transitions to 4-body intermediate states (exchange of an electron-hole pair). Our scheme is ready to include other interactions which are not considered in the Hubbard model but may be important. In the plane, the W=0 pairs have ¹ B ₂ and ¹ A ₂ symmetry. The effective interaction in these channels is attractive and leads to a Cooper-like instability of the Fermi liquid, while it is repulsive for triplet pairs. From , we derive an integral equation for the pair eigenfunction; the binding energy of the pairs is in the range of tens of meV. However, our symmetry-based method is far more general than the model. Received 18 December 1998     

1,3(n-π*) excited states of benzaldehyde

Geometries of the first triplet and first singletn-π* excited states of benzaldehyde have been optimized using thesindo 1 molecular orbital wave-function (with CI) and the Newton-Raphson method. The triplet excited state geometry of the molecule is found to be appreciably non-planar whereas that of the singlet excited state is planar. A crossing of molecular orbitals occurs in going from the ground state equilibrium geometry to the triplet and singletn-π* excited state equilibrium geometries. Existence of the para-directing effect of the singletn-π* transition for electronic charges found in an earlier work is confirmed by the present work. The tripletn-π* excitation rearranges electronic charges mainly on the CHO group. It is found that the dipole moment of the molecule would appreciably increase following the singletn-π* excitation whereas the same would appreciably decrease following the tripletn-π* excitation.     

Intersystem crossing in oligothiophenes studied by fs time-resolved spectroscopy

High triplet quantum yields of more than 90% for bithiophene and terthiophene have to be connected with very fast and effective formation of triplets after excitation. We studied these processes with fs pump–probe spectroscopy. The time behaviour of transient optical spectra within the singlet and triplet manifold was examined for bi- and terthiophene (2T and 3T) in solution. For 2T we used two-photon absorption for excitation. We found transient spectra of the excited singlet state, the triplet state and that of radical cations. The kinetics of the excited-state absorption was described by a bi-exponential function. Additionally we observed formation and recombination of radical cations. The recombination is connected with triplet formation. Both processes could be described by a time constant of 62 ps±9 ps. For 3T we found a dependence of the processes on excitation energy using one-photon absorption. The triplet quantum yield increased with higher excitation energy. The kinetics becomes bi-exponential with increasing amplitude of the short time constant of 2 ps at increasing excitation energy. The main reasons for the effective intersystem crossing (ISC) in both oligothiophenes are – besides the high spin-orbit coupling factor introduced by the sulphur atom – the almost isoenergetic positions of the S ₁ and T ₂ states, detected by PD-PES [1]. At higher photon excitation energy for 3T above the band gap an additional channel for ISC was detected. We believe that during the geometric change from the non-relaxed non-planar to the relaxed planar excited state S ₁, ultrafast intersystem crossing takes place. Received: 6 December 1999 / Published online: 2 August 2000     

Pairing mechanism in the doped Hubbard antiferromagnet: the 4×4 model as a test case

We introduce a local formalism, in terms of eigenstates of number operators, having well defined point symmetry, to solve the Hubbard model at weak coupling on a N × N square lattice (for even N). The key concept is that of W = 0 states, that are the many-body eigenstates of the kinetic energy with vanishing Hubbard repulsion. At half filling, the wave function demonstrates an antiferromagnetic order, a lattice step translation being equivalent to a spin flip. Further, we state a general theorem which allows to find all the W = 0 pairs (two-body W = 0 singlet states). We show that, in special cases, this assigns the ground state symmetries at least in the weak coupling regime. The N = 4 case is discussed in detail. To study the doped half filled system, we enhance the group theory analysis of the 4×4 Hubbard model introducing an Optimal Group which explains all the degeneracies in the one-body and many-body spectra. We use the Optimal Group to predict the possible ground state symmetries of the 4×4 doped antiferromagnet by means of our general theorem and the results are in agreement with exact diagonalization data. Then we create W = 0 electron pairs over the antiferromagnetic state. We show analitycally that the effective interaction between the electrons of the pairs is attractive and forms bound states. Computing the corresponding binding energy we are able to definitely predict the exact ground state symmetry. Received 24 October 2000     

Antiferromagnetism and superconductivity in a model with extended pairing interactions

The competition between antiferromagnetism and the d + id superconducting state is studied in a model with near and next near neighbour interactions in the absence of any on-site repulsion. A mean field study shows that it is possible to have simultaneous occurrence of an antiferromagnetic and a singlet d + id superconducting state in this model. In addition, such a coexistence generates a triplet d + id superconducting order parameter with centre of mass momentum Q = (π,π) dynamically having the same orbital symmetry as the singlet superconductor. Inclusion of next nearest neighbour hopping in the band stabilises the d_xy superconducting state away from half filling, the topology of the phase diagram, though, remains similar to the near neighbour model. In view of the very recent observation of a broad region of coexistence of antiferromagnetic and unconventional superconducting states in organic superconductors, the possibility of observation of the triplet state has been outlined. Received 30 November 2000 and Received in final form 27 March 2001     

Magnetic field effect on the pairing state competition in quasi-one-dimensional organic superconductors (TMTSF)2X

We study the effect of the magnetic field on the pairing state competition in organic conductors (TMTSF)₂X by applying random phase approximation to a quasi-one-dimensional extended Hubbard model. We show that the singlet pairing, triplet pairing and the Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) superconducting states may compete when charge fluctuations coexist with spin fluctuations. This rises a possibility of a consecutive transition from singlet pairing to FFLO state and further to S_z = 1 triplet pairing upon increasing the magnetic field. We also show that the singlet and S_z = 0 triplet components of the gap function in the FFLO state have “d-wave” and “f-wave” forms, respectively, which are strongly mixed.     

Algebraic solution of the Hubbard model on the infinite interval

We develop the quantum inverse scattering method for the one-dimensional Hubbard model on the infinite line at zero density. This enables us to diagonalize the Hamiltonian algebraically. The eigenstates can be classified as scattering states of particles, bound pairs of particles and bound states of pairs. We obtain the corresponding creation and annihilation operators and calculate the S-matrix. The Hamiltonian on the infinite line is invariant under the Yangian quantum group Y(su(2)). We show that the n-particle scattering states transform like n-fold tensor products of fundamental representations of Y(su(2) ) and that the bound states are Yangian singlet.     

EPR of photo-excited triplet states: A personal account

A sketch is presented of the path that has led from Zavoisky’s pioneering experiments to modern investigations by electron paramagnetic resonance (EPR) of the phosphorescent (S = 1) triplet state of polyatomic molecules or ions. The group-theoretical method first introduced by Wigner in his analysis of the multiplets of atomic spectroscopy, likewise provides a key for understanding the zero-field splitting and selection rules for radiative decay of the phosphorescent triplet state. Examples to illustrate the progress made through EPR experiments are selected from three fields. (i) Conformational instability on excitation. Both the zero-field splitting and the electron spin density distribution provide unique fingerprints of a triplet state’s geometry — structural information of a kind that is nonexistent for singlet states! Illustrations are provided by benzene C₆H₆ and fullerene C₆₀. (ii) The optical pumping cycle. The spin selectivity of singlet-to-triplet intersystem crossing and radiative decay of the individual spin components of the triplet state is discussed. In practice this selectivity is put to advantage by performing EPR on triplet states in zero-field by means of optical detection. In turn, such experiments have led to a detailed insight into the spin-orbit coupling mechanisms responsible for the spin selectivity of the above processes. The high sensitivity attainable with optical detection has recently culminated in EPR experiments on single molecules. (iii) Quantum interference. In a triplet state of low symmetry two of the spin sublevels may decay to the ground state by the emission of photons of a common polarization (i.e., out of plane for an aromatic hydrocarbon). In such a situation quantum interference between the two decay channels can be induced by an appropriate preparation of the excited state. An example is shown where flash-excitation in the singlet manifold followed by rapid intersystem crossing causes theS = 1 spin angular momentum to be created in a spin state which is not an eigenstate of the zero-field splitting tensor. This nonstationary character of the initial triplet state, which reflects the spin-orbit coupling pathway, is observed through the detection of a spontaneous microwave signal following the 25 ps laser flash.     

Effects of α‐cyclopropyl on heterocyclic carbenes stability at DFT

α‐Cyclopropyl stability impacts on singlet and triplet heterocyclic carbenes with acyclic, cyclic, and cyclic‐unsaturated structures are compared and contrasted to di‐t‐butyl as well as t‐butylcyclopropylcarbenes through appropriate isodesmic reactions at B3LYP/AUG‐cc‐pVTZ level. Substitution of one of the t‐butyl groups of di‐t‐butylcarbene with a cyclopropyl alters the ground state multiplicity from triplet to singlet with a singlet–triplet energy separation (ΔE_s–t) of 7.2 kcal/mol. Additional heteroatom substitution increases ΔE_s–t values for the resulting α‐heteroatom cyclopropylcarbenes in the following order: amino > oxy > thio > phophino. α‐Cyclopropyl group stabilizes singlet states of all our carbenes two to three times more than their corresponding triplet states. The ΔE_s–t values of all the carbenes are increased through cyclization, while the introduction of unsaturation in the rings causes small and rather random changes. To probe the kinetic stability of the species, we calculated the transition states for the opening of cyclopropyl through 1,2‐C shift. Interestingly, the 4.1 kcal/mol energy barrier in cyclopropylcarbene is significantly increased in the presence of heteroatoms to 31.2 kcal/mol for aminocyclopropylcarbene. The reactivity of the species is discussed in terms of nucleophilicity and electrophilicity issues showing our carbenes, especially acyclic ones, more nucleophilic than the common N‐heterocyclic carbenes. Copyright © 2010 John Wiley & Sons, Ltd.     

Small bipolarons in the 2-dimensional Holstein-Hubbard model. I. The adiabatic limit

The spatially localized bound states of two electrons in the adiabatic two-dimensional Holstein-Hubbard model on a square lattice are investigated both numerically and analytically. The interplay between the electron-phonon coupling g, which tends to form bipolarons and the repulsive Hubbard interaction , which tends to break them, generates many different ground-states. There are four domains in the phase diagram delimited by first order transition lines. Except for the domain at weak electron-phonon coupling (small g) where the electrons remain free, the electrons form bipolarons which can 1) be mostly located on a single site (small , large g); 2) be an anisotropic pair of polarons lying on two neighboring sites in the magnetic singlet state (large , large g); or 3) be a “quadrisinglet state” which is the superposition of 4 electronic singlets with a common central site. This quadrisinglet bipolaron is the most stable in a small central domain in between the three other phases. The pinning modes and the Peierls-Nabarro barrier of each of these bipolarons are calculated and the barrier is found to be strongly depressed in the region of stability of the quadrisinglet bipolaron. Received 10 December 1998     

A theoretical analysis of the excited states in 2-benzoylthiophene

The lower excited states of 2-benzoylthiophene have been studied using ab initio quantum chemical methods based on multiconfigurational wave functions. Six singlet and six triplet excited states have been characterized. The geometry has been optimized for the two lowest triplet states, which are responsible for the photoreactivity of the chromophore in the photosensitizing drug tiaprofenic acid. The T¹(π → π?) and T₂(n → π?) states have been found to be close in energy with the π → π? state slightly lower. The excited states have been characterized using density difference and spin density plots. The different photochemical behaviour of the two triplet states can be rationalized from the theoretical data.     

Phonon-free mechanism of superconductivity in compounds containing quasi-two-dimensional NiB complexes

A study is made of some characteristics of phonon-free pairing of hybridized p and d electrons in planar NiB complexes in the presence of strong short-range Hubbard repulsion. A generalized Hubbard model is used to calculate the superconductivity phase diagram as a function of the degree of underfilling of the 2p ⁶ and 3d ¹⁰ shells in NiB complexes. The phase region of states having the highest superconducting transition temperatures is established. Fiz. Tverd. Tela (St. Petersburg) 40, 198–201 (February 1998)     

Singlet–triplet oscillations and far-infrared spectrum of four-minima quantum-dot molecule

We study ground states and far-infrared spectra (FIR) of two electrons in four-minima quantum-dot molecule in magnetic field by exact diagonalization. Ground states consist of altering singlet and triplet states, whose frequency, as a function of magnetic field, increases with increasing dot–dot separation. When the Zeeman energy is included, only the two first singlet states remain as ground states. In the FIR spectra, we observe discontinuities due to crossing ground states. Non-circular symmetry induces anticrossings, and also an additional mode above ω₊ in the spin-triplet spectrum. In particular, we conclude that electron–electron interactions cause only minor changes to the FIR spectra and deviations from the Kohn modes result from the low-symmetry confinement potential.     

Energy transfer in a thin film of TPD fluorescent molecules doped with PtOEP and Ir(ppy)3 phosphorescent molecules

A thin film of triphenylamine dimer, N,N′-bis(3-methylphenyl)-N,N′-bis(phenyl)-benzidine (TPD), doped with fac tris(2-phenylpyridine) iridium (Ir(ppy)₃) and platinum octaethyl porphine (PtOEP) is characterized by photoluminescence emission measurements at several excitation wavelengths and photoluminescence excitation measurements at relevant emission wavelengths in the temperature range from 10 K to room temperature. The investigated film is a phosphorescent OLED material with singlet absorbing host (TPD) and triplet emitting guests [Ir(ppy)₃ and PtOEP]. At short wavelength excitation simultaneous triple band emission from singlet TPD, triplet Ir(ppy)₃ and TPD, and from triplet PtOEP is observed. Förster-type singlet-singlet state energy transfer from TPD to Ir(ppy)₃ and PtOEP, intra-component intersystem crossing, and Dexter-type triplet-triplet energy transfer between the substituents are studied.     

Properties of oligothiophene polycations

The different electronic states of trications and tetracations have been studied for oligomers made of n 3,4‐ethylenedioxythiophene units, where n ranges from 2 to 30. Results have been compared with those obtained for neutral, monodications and dications of the same n‐oligomers. For the longer oligomer (n ≥ 24) trications, the doublet and quartet states are isoenergetic, while the triplet and quintet states are isoenergetic for tetracations of the same length. Analysis of the geometry reveals three separated polarons for the doublet and quartet states of tricationic n‐oligomers, even though that of the former state has been attributed to a heavy spin contamination. In contrast, the structure of tetracations shows double bipolaron character for the singlet state and two polaron pairs for both the triplet and quintet states. Analyses of both charge and spin density distributions support the polaronic or bipolaronic behavior predicted by molecular geometry for the different electronic states. Results have been also used to evaluate the ionization potentials and the π‐π^* lowest transition energy of infinite polymer chains. Copyright © 2014 John Wiley & Sons, Ltd.