Population inversion,temperature, and photon distributions of the generalized fermionic Ising ferromagnetic model: Path‐integral representation of the spin system

The quantum partition function and the emerging energy of a fermionic Ising ferromagnetic model involving all possible interactions (generalized Ising model) are obtained from an appropriate tracing of the analytic propagator path integral over Grassmann variable coherent nonorthogonal states in the imaginary time domain. The dynamics derived from the interaction of this system with a single‐mode cavity field in the rotating wave approximation is investigated for nonresonant states within the framework of the Jaynes–Cummings two‐level model consisting of the vacuum state and a thermally averaged manifold of excited states. Time evolution of the population inversion is computed in the nanosecond time scale, assuming that the initial coherent state of the field is given by a Poisson distribution. The limit of high temperatures characterizing the manifold of excited states becomes chaotic with rapid oscillations, whereas the ground state is described correctly in the thermodynamic limit by the vacuum state. A breakup is seen in the photon distribution into a series of peaks because of the detuning between the spin system and the field. However, this structure is smeared out, and the general shape is preserved in the computation emerging from the Laplace transform of the photon distribution. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Ultrafast Exciton Self‐Trapping and Delocalization in Cycloparaphenylenes: The Role of Excited‐State Symmetry in Electron‐Vibrational Coupling

Upon photon absorption, π‐conjugated organics are apt to undergo ultrafast structural reorganization via electron‐vibrational coupling during non‐adiabatic transitions. Ultrafast nuclear motions modulate local planarity and quinoid/benzenoid characters within conjugated backbones, which control primary events in the excited states, such as localization, energy transfer, and so on. Femtosecond broadband fluorescence upconversion measurements were conducted to investigate exciton self‐trapping and delocalization in cycloparaphenylenes as ultrafast structural reorganizations are achieved via excited‐state symmetry‐dependent electron‐vibrational coupling. By accessing two high‐lying excited states, one‐photon and two‐photon allowed states, a clear discrepancy in the initial time‐resolved fluorescence spectra and the temporal dynamics/spectral evolution of fluorescence spectra were monitored. Combined with quantum chemical calculations, a novel insight into the effect of the excited‐state symmetry on ultrafast structural reorganization and exciton self‐trapping in the emerging class of π‐conjugated materials is provided.     

Synthesis,Structural Characterization,Photophysics, and Broadband Nonlinear Absorption of a Platinum(II) Complex with the 6‐(7‐Benzothiazol‐2′‐yl‐9,9‐diethyl‐9 H‐fluoren‐2‐yl)‐2,2′‐bipyridinyl Ligand

A platinum complex with the 6‐(7‐benzothiazol‐2′‐yl‐9,9‐diethyl‐9H‐fluoren‐2‐yl)‐2,2′‐bipyridinyl ligand ( 1 ) was synthesized and the crystal structure was determined. UV/Vis absorption, emission, and transient difference absorption of 1 were systematically investigated. DFT calculations were carried out on 1 to characterize the electronic ground state and aid in the understanding of the nature of low‐lying excited electronic states. Complex 1 exhibits intense structured ¹π–π* absorption at λ_abs<440 nm, and a broad, moderate ¹M LCT/¹LLCT transition at 440–520 nm in CH₂Cl₂ solution. A structured ³π–π*/³M LCT emission at about 590 nm was observed at room temperature and at 77 K. Complex 1 exhibits both singlet and triplet excited‐state absorption from 450 nm to 750 nm, which are tentatively attributed to the ¹π–π* and ³π–π* excited states of the 6‐(7‐benzothiazol‐2′‐yl‐9,9‐diethyl‐9H‐fluoren‐2‐yl)‐2,2′‐bipyridine ligand, respectively. Z‐scan experiments were conducted by using ns and ps pulses at 532 nm, and ps pulses at a variety of visible and near‐IR wavelengths. The experimental data were fitted by a five‐level model by using the excited‐state parameters obtained from the photophysical study to deduce the effective singlet and triplet excited‐state absorption cross sections in the visible spectral region and the effective two‐photon absorption cross sections in the near‐IR region. Our results demonstrate that 1 possesses large ratios of excited‐state absorption cross sections relative to that of the ground‐state in the visible spectral region; this results in a remarkable degree of reverse saturable absorption from 1 in CH₂Cl₂ solution illuminated by ns laser pulses at 532 nm. The two‐photon absorption cross sections in the near‐IR region for 1 are among the largest values reported for platinum complexes. Therefore, 1 is an excellent, broadband, nonlinear absorbing material that exhibits strong reverse saturable absorption in the visible spectral region and large two‐photon‐assisted excited‐state absorption in the near‐IR region.     

Two‐Photon Voltmeter for Measuring a Molecular Electric Field

We present a new approach for determining the strength of the dipolar solute‐induced reaction field, along with the ground‐ and excited‐state electrostatic dipole moments and polarizability of a solvated chromophore, using exclusively one‐photon and two‐photon absorption measurements. We verify the approach on two benchmark chromophores N,N‐dimethyl‐6‐propionyl‐2‐naphthylamine (prodan) and coumarin 153 (C153) in a series of toluene/dimethyl sulfoxide (DMSO) mixtures and find that the experimental values show good quantitative agreement with literature and our quantum‐chemical calculations. Our results indicate that the reaction field varies in a surprisingly broad range, 0–10⁷ V cm^?1, and that at close proximity, on the order of the chromophore radius, the effective dielectric constant of the solute–solvent system displays a unique functional dependence on the bulk dielectric constant, offering new insight into the close‐range molecular interaction.     

The Role of Ligand‐Field States in the Ultrafast Photophysical Cycle of the Prototypical Iron(II) Spin‐Crossover Compound [Fe(ptz)6](BF4)2

Light‐induced excited spin‐state trapping (LIESST) in iron(II) spin‐crossover compounds, that is, the light‐induced population of the high‐spin (S=2) state below the thermal transition temperature, was discovered thirty years ago. For irradiation into metal–ligand charge transfer (MLCT) bands of the low‐spin (S=0) species the acknowledged sequence takes the system from the initially excited ¹MLCT to the high‐spin state via the ³MLCT state within ca. 150 fs, thereby bypassing low‐lying ligand‐field (LF) states. Nevertheless, these play a role, as borne out by the observation of LIESST and reverse‐LIESST on irradiation directly into the LF bands for systems with only high‐energy MLCT states. Herein we elucidate the ultrafast reverse‐LIESST pathway by identifying the lowest energy S=1 LF state as an intermediate state with a lifetime of 39 ps for the light‐induced high‐spin to low‐spin conversion on irradiation into the spin‐allowed LF transition of the high‐spin species in the NIR.     

Synthesis,One‐ and Two‐Photon Photophysical and Excited‐State Properties,and Sensing Application of a New Phosphorescent Dinuclear Cationic Iridium(III) Complex

A new phosphorescent dinuclear cationic iridium(III) complex ( Ir1 ) with a donor–acceptor–π‐bridge–acceptor–donor (D? A? π? A? D)‐conjugated oligomer ( L1 ) as a N^N ligand and a triarylboron compound as a C^N ligand has been synthesized. The photophysical and excited‐state properties of Ir1 and L1 were investigated by UV/Vis absorption spectroscopy, photoluminescence spectroscopy, and molecular‐orbital calculations, and they were compared with those of the mononuclear iridium(III) complex [Ir(Bpq)₂(bpy)]⁺PF₆^? ( Ir0 ). Compared with Ir0 , complex Ir1 shows a more‐intense optical‐absorption capability, especially in the visible‐light region. For example, complex Ir1 shows an intense absorption band that is centered at λ=448 nm with a molar extinction coefficient (ε) of about 10⁴, which is rarely observed for iridium(III) complexes. Complex Ir1 displays highly efficient orange–red phosphorescent emission with an emission wavelength of 606 nm and a quantum efficiency of 0.13 at room temperature. We also investigated the two‐photon‐absorption properties of complexes Ir0 , Ir1 , and L1 . The free ligand ( L1 ) has a relatively small two‐photon absorption cross‐section (δ_max=195 GM), but, when complexed with iridium(III) to afford dinuclear complex Ir1 , it exhibits a higher two‐photon‐absorption cross‐section than ligand L1 in the near‐infrared region and an intense two‐photon‐excited phosphorescent emission. The maximum two‐photon‐absorption cross‐section of Ir1 is 481 GM, which is also significantly larger than that of Ir0 . In addition, because the strong B? F interaction between the dimesitylboryl groups and F^? ions interrupts the extended π‐conjugation, complex Ir1 can be used as an excellent one‐ and two‐photon‐excited “ON–OFF” phosphorescent probe for F^? ions.     

Synthesis and two‐photon absorption properties of conjugated polymers with N‐arylpyrrole as conjugated bridge and isolation moieties

Three novel conjugated polymers with N‐arylpyrrole as the conjugated bridge were designed and synthesized, which emitted strong one‐ or two‐photon excitation fluorescence in dilute tetrahydrofuran (THF) solution with high quantum yields. The maximal two‐photon absorption (TPA) cross‐sections of the polymers, measured by the two‐photon‐induced fluorescence method using femtosecond laser pulses in THF, were 752, 1114, and 1869 GM, respectively, indicating that the insertion of electron‐donating or electron‐withdrawing moieties into the polymer backbone could benefit to the increase of the TPA cross‐section. Their large TPA cross‐sections, coupled with the relatively high emission quantum yields, made these conjugated polymers attractive for practical applications, especially two‐photon excited fluorescence. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011     

Excited‐State Dynamics of the Metal String Complex Co3(dpa)4(NCS)2 from Femtosecond Transient Absorption Spectra

Transient absorption spectroscopy is used to study the excited‐state dynamics of Co₃(dpa)₄(NCS)₂, where dpa is the ligand di(2‐pyridyl)amido. The ππ*, charge‐transfer, and d–d transition states are excited upon irradiation at wavelengths of 330, 400 and 600 nm, respectively. Similar transient spectra are observed under the experimental temporal resolution and the transient species show weak absorption. We thus propose that a low‐lying metal‐centered d–d state is accessed immediately after excitation. Analyses of the experimental kinetic traces reveal rapid conversion from the ligand‐centered ππ* and the charge‐transfer states to this metal‐centered d‐d state within 100 fs. The excited molecule then crosses to a second d–d state within the ligand‐field manifold, with a time coefficient of 0.6–1.4 ps. Because the ground‐state bleaching band recovers with a time coefficient of 10–23 ps, we propose that an excited molecule crosses from the low‐lying d–d state either directly within the same spin system or with spin crossing via the state ²B to the ground state ²A₂ (symmetry group C₄). In this trimetal string complex, relaxation to the ground electronic surface after excitation is thus rapid.     

Poly(1,4‐diketo‐3,6‐diphenylpyrrolo[3,4‐c]pyrrole‐alt−3,6‐carbazole/2,7‐fluorene) as high‐performance two‐photon dyes

This article reports the synthesis, one‐ and two‐photon absorption, and excited fluorescence properties of poly(1,4‐diketo‐3,6‐diphenylpyrrolo[3,4‐c]pyrrole‐alt‐N‐octyl‐3,6‐carbazole/2,7‐fluorene) ( PDCZ / PDFL ). PDCZ and PDFL are synthesized by the Suzuki cross‐coupling of 2,5‐dioctyl‐1,4‐diketo‐3,6‐bis(p‐bromophenylpyrrolo[3,4‐c]pyrrole and N‐octyl‐3,6‐bis(3,3‐dimethyl‐1,3,2‐dioxaborolan‐2‐yl)carbazole or 2,7‐bis(3,3‐dimethyl‐1,3,2‐dioxaborolan‐2‐yl)fluorene and have number‐average molecular weights of 8.5 × 10³ and 1.14 × 10⁴ g/mol and polydispersities of 2.06 and 1.83, respectively. They are highly soluble in common organic solvents and emit strong orange one‐ and two‐photon excited fluorescence (2PEF) in THF solution and exhibit high light and heat stability. The maximal two‐photon absorption cross‐sections (δ) measured in THF solution by the 2PEF method using femtosecond laser pulses are 970 and 900 GM per repeating unit for PDCZ and PDFL , respectively. These 1,4‐diketo‐pyrrolo[3,4‐c]pyrrole‐containing polymers with full aromatic structure and large δ will be promising high‐performance 2PA dyes applicable in two‐photon science and technology. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2014 , 52, 944–951     

Interstate Crossing‐Induced Chemiexcitation as the Reason for the Chemiluminescence of Dioxetanones

The decomposition reaction of dimethyl‐1,2‐dioxetanone in dichloromethane was studied by using a DFT approach. The low efficiency of triplet and singlet excited‐state formation was rationalised. A charge‐transfer process was demonstrated to be involved in the chemiluminescence process. Present and previous results allow us to define an interstate crossing‐induced chemiexcitation (ICIC) mechanism for the chemiluminescence of dioxetanones. Charge transfer is needed to reach a transition state, in the vicinity of which direct population of excited states is possible. The chemiexcitation process is then governed by singlet/triplet intersystem crossings. Structural modifications then modify the rate of these crossings and the singlet ground and excited‐state interaction, thereby modulating the efficiency of this process and the spin of the resulting products.     

Toward assessment of density functionals for vibronic coupling in two‐photon absorption: A case study of 4‐nitroaniline

In this study, we predict vibronic two‐photon absorption (TPA) spectra for 4‐nitroaniline in vacuo. The simulations are performed using density functional theory and the approximate second‐order coupled‐cluster singles and doubles model CC2. Thereby we also demonstrate the possibility of simulations of vibronic TPA spectra with ab initio wavefunction methods that include electron correlation for medium‐sized systems. A special focus is put on the geometric derivatives of the second‐order transition moment and the dipole moment difference between the charge‐transfer excited state and the ground state. The results of CC2 calculations bring new insight into the vibronic coupling mechanism in TPA spectra of 4‐nitroniline and demonstrate that the mixed term is quite large and that it also exhibits a negative interference with the Franck‐Condon contribution. © 2015 Wiley Periodicals, Inc.     

Photomagnetism of a sym‐cis‐Dithiocyanato Iron(II) Complex with a Tetradentate N,N′‐Bis(2‐pyridylmethyl)1,2‐ethanediamine Ligand

A comprehensive study of the magnetic and photomagnetic behaviors of cis‐[Fe(picen)(NCS)₂] (picen=N,N′‐bis(2‐pyridylmethyl)1,2‐ethanediamine) was carried out. The spin‐equilibration was extremely slow in the vicinity of the thermal spin‐transition. When the cooling speed was slower than 0.1 K min^?1, this complex was characterized by an abrupt thermal spin‐transition at about 70 K. Measurement of the kinetics in the range 60–70 K was performed to approach the quasi‐static hysteresis loop. At low temperatures, the metastable HS state was quenched by a rapid freezing process and the critical T(TIESST) temperature, which was associated with the thermally induced excited spin‐state‐trapping (TIESST) effect, was measured. At 10 K, this complex also exhibited the well‐known light‐induced excited spin‐state‐trapping (LIESST) effect and the T(LIESST) temperature was determined. The kinetics of the metastable HS states, which were generated from the freezing effect and from the light‐induced excitation, was studied. Single‐crystal X‐ray diffraction as a function of speed‐cooling and light conditions at 30 K revealed the mechanism of the spin‐crossover in this complex as well as some direct relationships between its structural properties and its spin state. This spin‐crossover (SCO) material represents a fascinating example in which the metastability of the HS state is in close vicinity to the thermal spin‐transition region. Moreover, it is a beautiful example of a complex in which the metastable HS states can be generated, and then compared, either by the freezing effect or by the LIESST effect.     

Concise Synthesis and Two‐Photon‐Excited Deep‐Blue Emission of 1,8‐Diazapyrenes

Efficient violet–blue‐emitting molecules are especially useful for applications in full‐color displays, solid‐state lighting, as well as in two‐photon absorption (TPA) excited frequency‐upconverted violet–blue lasing. However, the reported violet–blue‐emitting molecules generally possess small TPA cross sections. In this work, new 1,8‐diazapyrenes derivatives 3 with blue two‐photon‐excited fluorescence emission were concisely synthesized by the coupling reaction of readily available 1,4‐naphthoquinone O,O‐diacetyl dioxime ( 1 ) with internal alkynes 2 under the [{RhCl₂Cp*}₂]–Cu(OAc)₂ (Cp*=pentamethylcyclopentadienyl ligand) bimetallic catalytic system. Elongation of the π‐conjugated length of 1,8‐diazapyrenes 3 led to the increase of TPA cross sections without the expense of a redshift of the emission wavelength, probably due to the rigid planar structure of chromophores. It is especially noteworthy that 2,3,6,7‐tetra(4‐bromophenyl)‐1,8‐diazapyrene ( 3c ) has a larger TPA cross section than those of other molecules reported so far. These experimental results are explained in terms of the effects of extension of the π‐conjugated system, intramolecular charge transfer, and reduced detuning energy.     

Excited State Intramolecular Proton Transfer and Photophysics of a New Fluorenyl Two‐Photon Fluorescent Probe

The steady‐state photophysical, NMR, and two‐photon absorption (2PA) properties of a new fluorene derivative ( 1 ) containing the 2‐(2′‐hydroxyphenyl)benzothiazole (HBT) terminal construct is investigated for use as a fluorescence probe in bioimaging. A comprehensive analysis of the linear spectral properties reveals inter‐ and intramolecular hydrogen bonding and excited state intramolecular proton transfer (ESIPT) processes in the HBT substituent. A specific electronic model with a double minimum potential energy surface is consistent with the observed spectral properties. The 2PA spectra are obtained using a standard two‐photon induced fluorescence method with a femtosecond kHz laser system, affording a maximum 2PA cross section of ～600 GM, a sufficiently high value for two‐photon fluorescence imaging. No dependence of two‐photon absorption efficiency on solvent properties and hydrogen bonding in the HBT substituent is observed. The potential use of this fluorenyl probe in bioimaging is demonstrated via one‐ and two‐photon fluorescence imaging of COS‐7 cells.     

Intramolecular photoexcitation dynamics and magnetic field effects in an intermediate-case molecule

Molecular vibration and rotation play a significant role in the intramolecular photoexcitation dynamics of the so-called intermediate-case molecule, and the fluorescence intensity, decay and polarization of s-triazine vapor are shown to depend on the excited rovibronic level of the S₁ state. Fluorescence characteristics are interpreted by assuming three zero-order states: (1) a zero-order singlet state that carries the absorption intensity and emits fluorescence with sharp structure; (2) zero-order singlet states that do not carry the absorption intensity but emit broad fluorescence; and (3) zero-order triplet states. The interaction among these states depends not only on the vibrational level but also on the rotational level excited. It is suggested that the number of triplet states coupled to the singlet state increases with increasing excess vibrational energy. It is also suggested that K-scrambling occurs both in the triplet manifold following intersystem crossing (ISC) and in the singlet manifold following intramolecular vibrational energy redistribution (IVR). The fluorescence intensity and decay of s-triazine vapor are significantly influenced by a magnetic field, and the field effects are interpreted in terms of the spin decoupling in the triplet manifold following ISC; the role of external magnetic fields is to mix the spin sublevels of different rovibronic levels coupled to the excited singlet state. Magnetic depolarization of fluorescence also occurs because of the efficient interaction between the excited singlet state and the triplet state.     

Slow relaxation of longitudinal multispin orders in weakly and strongly coupled two‐spin systems

Longitudinal multispin order (LOMO) corresponds to a nonequilibrium population distribution in spin systems that exhibit scalar (J), dipolar, or quadrupolar coupling. We investigated the relaxation of longitudinal two‐spin order (2‐LOMO) in systems that had either weakly or strongly J‐coupled spins. Our results indicated longer relaxation times for the 2‐LOMO state compared with the corresponding longitudinal single‐spin state (1‐LOMO). Accessing nuclear spin states that have relaxation times longer than T₁, without the use of external contrast agents, is potentially useful for in vivo imaging and also for studying systems using dynamically hyperpolarized nuclear spins where longer life times are sought to increase the time available to study (bio)chemical events. Copyright © 2012 John Wiley & Sons, Ltd.     

Synthesis and structure‐activity relationship of several aromatic ketone‐based two‐photon initiators

Several novel aromatic ketone‐based two‐photon initiators containing triple bonds and dialkylamino groups were synthesized and the structure‐activity relationships were evaluated. Branched alkyl chains were used at the terminal donor groups to improve the solubility in the multifunctional monomers. Because of the long conjugation length and good coplanarity, the evaluated initiators showed large two‐photon cross section values, while their fluorescence lifetimes and quantum yields strongly depend on the solvent polarity. All novel initiators exhibited high activity in terms of two‐photon‐induced microfabrication. This is especially true for fluorenone‐based derivatives, which displayed much broader processing windows than well‐known highly active initiators from the literature and commercially available initiators. While the new photoinitiators gave high reactivity in two‐photon‐induced photopolymerization at concentration as low as 0.1% wt, these compounds are surprisingly stable under one photon condition and nearly no photo initiation activity was found in classical photo DSC experiment. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011     

One‐ and two‐photon activity of cross‐conjugated photoinitiators with bathochromic shift

Intrigued by the good performance of 1,5‐diphenylpenta‐1,4‐diyn‐3‐one ( DPD ) as photoinitiator for radical polymerization we prepared and investigated several donor substituted derivatives. UV‐Vis spectroscopy revealed a gradual red‐shift of λ_max and higher extinction in the order of the donor capability. A methoxy‐substituted derivative ( O‐DPD ) exhibited significant photoinitiation activity in photo‐DSC experiments. Steady state photolysis experiments showed decreased decomposition rates with increasing donor capability. A dimethylamino derivative N‐DPD was even photostable under these conditions. Because of to the D‐π‐A‐π‐D system of these compounds two‐photon induced 3D photopolymerization experiments were performed and N‐DPD showed outstanding performance compared to often applied single photon initiators. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 3280–3291, 2007     

Refractive index‐modulated grating in two‐mode planar polymeric waveguide produced by two‐photon polymerization

A polymeric waveguide film was manufactured by spinning the materials on quartz substrate. Two‐photon‐initiated photopolymerization was carried out by tight‐focusing femtosecond laser pulses in the two‐mode planar waveguide. A typical index‐modulated grating of 2.5 × 2 mm areas without morphology was fabricated. The results show that peak‐to‐peak modulation depth of the surface profile of grating region was only about 7 nm. The diffraction efficiency (DE) of the grating with a spacing period 2 µm was 0.17% and the corresponding index modulation reached 5.7 × 10^?3. Copyright © 2007 John Wiley & Sons, Ltd.     

A theoretical study of the excited‐state decay of acylhydrazones

Acylhydrazones is a novel yet underexploited class of molecular switches. In the present paper, we investigated the excited‐state decay of three model systems of acylhydrazones in the gas phase by a combination of electronic structure calculations and Tully's surface hopping dynamic simulations. Our computational results demonstrated that the S₂(n_Nπ*) state decay of the three model systems leads to both the imine‐like photo‐isomerization through the S₁(n_Nπ*)/S₀ intersection and population of the S₁(n_Oπ*) state that will cross to the triplet manifold. The position of phenyl substituent was found to have an effect on the ratio of the two S₁ states. The present theoretical work provides some understandings of the intramolecular mechanism for de‐population of the excited electronic states of acylhydrazones.