Cooperative effects in photon statistics of molecular dimers with spectral diffusion

The two-point fluorescence intensity correlation function g(2)t and the Mandel parameter Mt are calculated for a strongly pumped dimer of two-level molecules undergoing Gaussian-Markovian frequency fluctuations. The effects of detuning and saturation are examined. All fluctuation time scale regimes are explored using a continued fraction solution of the stochastic Liouville equation for the generating function. Bunching and antibunching are observed for slow and fast fluctuations, respectively. The short-time antibunching dip in g(2) and its variation with intermolecular coupling, the exciton annihilation rate, and laser detuning are studied.     

Absorption and emission spectroscopy of molecular trimers: Cyclic versus linear geometries

The spectroscopic properties of molecular trimers are studied within a model where three degenerate electronically excited states are coupled via dipole–dipole interactions. Taking a single vibrational degree of freedom for each monomer into account, this results in a non-adiabatic nuclear dynamic which determines features of the spectra. The cases of a cyclic and a linear coupling scheme are regarded and it is investigated how these different geometries influence the absorption and emission spectra.     

Absorption spectroscopy of molecular trimers

Absorption properties of molecular trimers are studied within a model including a single monomer internal vibrational degree of freedom. Upon photoabsorption, three excited electronic states which are coupled excitonically are accessed. Band shapes resulting from different electronic coupling strengths and geometries are analyzed. It is shown that geometric information can be extracted from the band intensities. Taking data recorded for perylene bisimide aggregates as an example, the spectra for monomer, dimer, and trimer systems are compared.     

Photon emission from a driven single-molecule source: a renormalization group approach

The photon emission from a single molecule driven simultaneously by a laser and a slow electric radio frequency (rf) field is studied. We use a non-Hermitian Hamiltonian approach which accounts for the radiative decay of a two-level system modeling the single-molecule source. We apply the renormalization group method for differential equations to obtain long time solution of the corresponding Schrodinger equation, which allows us to calculate the average waiting time for the first photon emission. Then, we analyze the conditions for suppression and enhancement of photon emission in this dissipative two-level system. In particular we derive a transcendental equation, which yields the nontrivial rf field control parameters, for which enhancement and suppression of photon emission occurs. For finite values of radiative decay rate an abrupt transition to the state when both situations are indistinguishable is found for certain values of the rf field parameters. Our results are shown to be in agreement with the available experiments [Ch. Brunel et al., Phys. Rev. Lett. 81, 2679 (1998)].     

Two-dimensional optical spectroscopy: two-color photon echoes of electronically coupled phthalocyanine dimers

Two-color photon echo peak shift spectroscopy was used to study electronic coupling in a phthalocyanine homodimer. Two optical parametric amplifiers were used to produce pulses to excite the split lower states of LuPc2-. The existence of a two-color peak shift indicates the existence of correlation between these two dipole-allowed states. The nature of this correlation is discussed based on theoretical predictions of the interactions between exciton and charge resonance states.     

Super- and sub-Poissonian photon statistics for single molecule spectroscopy

We investigate the distribution of the number of photons emitted by a single molecule undergoing a spectral diffusion process and interacting with a continuous wave laser field. The spectral diffusion is modeled based on a stochastic approach, in the spirit of the Anderson-Kubo line shape theory. Using a generating function formalism we solve the generalized optical Bloch equations and obtain an exact analytical formula for the line shape and Mandel's Q parameter. The line shape exhibits well-known behaviors, including motional narrowing when the stochastic modulation is fast and power broadening. The Mandel parameter, describing the line shape fluctuations, exhibits a transition from a quantum sub-Poissonian behavior in the fast modulation limit to a classical super-Poissonian behavior found in the slow modulation limit. Our result is applicable for weak and strong laser fields, namely, for arbitrary Rabi frequency. We show how to choose the Rabi frequency in such a way so that the quantum sub-Poissonian nature of the emission process becomes strongest. A lower bound on Q is found and simple limiting behaviors are investigated. A nontrivial behavior is obtained in the intermediate modulation limit, when the time scales for spectral diffusion and the lifetime of the excited state become similar. A comparison is made between our results and previous ones derived, based on the semiclassical generalized Wiener-Khintchine formula.     

Single molecule photon emission statistics of driven three-level systems

We study the statistics of photon emission from three-level single molecule systems. The generating function method [Y. Zheng and F. L. H. Brown, Phys. Rev. Lett. 90, 238305 (2003)] is used to calculate steady state absorption line shapes and Mandel's Q parameter as a function of excitation frequency, as well as the time dependence associated with approach to the steady state. The line shape calculations confirm known results derived via other methods, while the Q parameter results display complex frequency dependences not amenable to simple interpretation. This study confirms the applicability of the generating function formalism to multilevel quantum systems, including the proper modeling of quantum coherence effects.     

Vibrational spectroscopy of solid state molecular dimers

The IR and Raman spectra of α- and β-perylene crystal vibrations are investigated, β-perylene is monomeric and α-perylene has face-to-face dimers. Frequencies and forms of the lattice vibrations as well as vibron relaxation and localization are discussed. Polarization ratios in α crystals are perturbed by coupling to dimer vibrations.     

Ultrafast dynamics in excited ammonia dimers and trimers

Ammonia dimers and trimers are studied in a femtosecond pump probe experiment. The pump laser (6.2 eV) excites the cluster into the à state which is ionized either by 4.6 eV or by 3.1 eV probe photons. Characteristic differences are explained in terms of a kinetic model involving an internal protonated neutral excited state as an intermediate.     

Optical dephasing of molecular dimers in mixed crystals: Picosecond photon echo experiments

Picosecond photon echo experiments are used to examine optical dephasing of substitutional dimers and monomers of tetracene and pentacene in p-terphenyl host crystals. A comparison of experiments on tetracene and pentacene dimers permits the mechanism responsible for temperature-dependent optical dephasing to be determined. It is shown that excitation of librations rather than scattering between delocalized dimer states is the principal mechanism.     

Single molecule photon emission statistics in the slow modulation limit

A framework for calculating photon emission statistics for single chromophores perturbed by slow environmental fluctuations is introduced. When internal chromophore dynamics are significantly faster than time scales for environmental modulation it becomes possible to invoke a type of adiabatic approximation, allowing for straightforward calculation of photon counting moments including explicitly quantum effects. Unlike previous exact treatments, the present methodology involves calculation of dynamics reflecting only the modulation characteristics of the environment and quantum dynamics of an isolated chromophore separately, i.e., the complicated intermingling of chromophore quantum dynamics and the environmental modulation are suppressed via the adiabatic approximation. This leads to significant conceptual and computational simplifications. Within its regime of applicability, the present approximation reproduces exact calculations quantitatively. We demonstrate this accuracy explicitly for the case of a two-level chromophore modulated by a number of different stochastic models.     

A correlation study of boron dimers and trimers

We have carried out ab initio molecular orbital studies of neutral and charged boron dimers and trimers, using a large basis set. Electron correlation effects are included through the techniques of fourth order many body perturbation theory. Results for total energies, geometries, binding energies, and binary fragmentation energies are presented, and where possible compared with published results. Stabilities of the geometries considered are further studied through a vibrational-mode analysis. The ground state of B₂ is predicted to be a triplet; of B ₂ ^? , a quartet, and of B ₂ ⁺ a doublet. The ground state of B₃ is a triangular doublet, of B ₃ ^? a linear singlet and of B ₃ ⁺ a triangular singlet.     

Synthesis of covalently linked porphyrin dimers and trimers

The synthesis of covalently linked porphyrin dimers and trimers is described. Mono- and dihydroxyporphyrins were synthesized by transeslerifying 5,10,15,20-tetra(4-carbomethoxy-phenyl)porphyrin with ethylene glycol. The mixture of transesterified porphyrins were separated by preparative thin layer chromatography. Metal derivatives were made of the mono- and dihydroxyporphyrins and these were reacted with the acid chloride of a monocarboxyporphyrin to yield hybrid dimers and trimers containing one melalloporphyrin and either one or two free base porphyrins. The structures and purity of the dimers and trimers were established by measuring the absorbance spectra, nmr spectra, and molecular weight by gel permeation chromatography.     

Cationic oligomerization of anethole: Selective synthesis of dimers and trimers

A linear unsaturated dimer of anethole [II, (E)-1,3-bis(p-methoxyphenyl)-2-methylpentene-1], was prepared in 98% yield with an acetyl perchlorate (AcClO₄) catalyst in a nonpolar solvent (C₆H₆) at a high temperature (70°C). At 0°C a linear unsaturated trimer was formed in high yield with dimer II. The geometric structure of the linear unsaturated dimers was determined by analysis of the nuclear Overhauser effect (NOE) on their ¹H-NMR spectra. NOE analysis showed that at 0°C with AcClO₄, trans-anethole gives the (E)-form (II), whereas cis-anethole yields the (Z)-form. On the other hand, with a metal-halide catalyst (BF₃OEt₂) a cyclic dimer and a cyclic trimer were produced in high yields in a polar solvent [(CH₂Cl₂)] at 70°C; higher oligomers (≥ tetramer) were scarcely formed. The effect of catalysts on the structure of oligomers was explained in terms of the interaction between a growing carbocation and a counterion.     

Soliton model of electron transfer in mixed-valence dimers and trimers

The soliton approximation is examined for mixed-valence dimers and trimers with one migrating electron. The calculations use Hamilton's canonical equations and a time-dependent wave function of the soliton type. In the two limiting cases (strong and weak vibronic coupling), the soliton approximation correlates well with the exact analytical solution. As in the adiabatic approximation at g²/v=1, the delocalized limit (quasifree electron) is transformed to the localized one (electron locked on the center). For molecular trimers, the soliton approximation allows us to reveal the cases where the transfer of an electron from the first to the third center is accompanied by electron density concentration on the intermediate center. Institute of Chemistry, Academy of Sciences, Moldova Republic. Translated fromZhurnal Strukturnoi Khimii, Vol. 35, No. 6, pp. 46–53, November–December, 1994. Translated by L. Smolina     

Syntheses of hematoporphyrin dimers and trimers with ether linkages

In order to aid in elucidation of the structure of the active components in hematoporphyrin derivative (Hpd), the first syntheses of an ether-linked hematoporphyrin dimer (6) and trimer (12) are described. After ester hydrolysis, these compounds were positively identified, by comparative HPLC, as components in Photofrin®-II.     

Intersystem crossing from singlet states of molecular dimers and monomers in mixed molecular crystals: picosecond stimulated photon echo experiments

An experimental study of the excited-state dynamics of pentacene dimers and monomers in p-terphenyl host crystals is presented. Picosecond stimulated photon echoes, picosecond photon echoes, and fluorescence lifetime measurements are used to study intersystem crossing and homogeneous dephasing of delocalized dimers and monomers at 1.8 K. It is found that the dimer states can have intersystem crossing rate constants which are orders of magnitude greater than the corresponding monomers. Three mechanisms are considered to explain the differences between dimer and monomer intersystem crossing. Fluorescence lifetime measurements and photon echo measurements demonstrate that the only source of homogeneous line broadening at 1.8 K is population relaxation. These measurements combined with the stimulated echo measurements show that differences in lifetimes exhibited by the various dimer and various monomer sites are due solely to differences in intersystem crossing rate constants.     

Configurational probabilities for monomers, dimers and trimers in fluids

A new analytical approach is proposed to model aggregation of molecules with isotropic, nearest-neighbor, attractive interactions. By treating the clustering process as a chain reaction, equations with the exact high temperature limit are derived by evaluating the occupation probabilities of nearest neighbors based on the Ono-Kondo approach for a hexagonal lattice to calculate the configurational probabilities of i-mers (i = 1, 2, 3). Equilibrium constants for dimers and trimers are calculated based on the configurational probability data. The proposed model agrees well with Monte Carlo simulations at medium and high temperatures. At low temperatures, the model can be improved by considering the full set of site densities in the first shell of a central trimer. Approximate analytical solutions derived from exact calculations of the grand partition function for monomer adsorption on a 4 x N hexagonal lattice with cylindrical boundary conditions also are presented.     

Subphthalocyanine-fused dimers and trimers: synthetic, electrochemical, and theoretical studies

Subphthalocyanine (SubPc)-fused dimers and trimers bearing fluorine, iodine, and thioether peripheral substituents were synthesized and characterized. Absorption spectroscopy and electrochemical studies revealed (i) that the substituents have a strong effect on the electronic properties of the macrocycles and (ii) that there is good communication between the subphthalocyaninic moieties within the oligomeric structures. Theoretical calculations at DFT/6-31G(d,p) computational level and electron density studies support the experimental findings. The frontier orbitals in the dimers and trimers were also shown to be significantly altered with respect to those of SubPcs as a consequence of the extension of the conjugation associated with symmetry breaking. Time-dependent density functional theory calculations reproduced the differences observed in the UV-vis spectra of the fused dimers and the monomeric SubPcs.